ML110070272

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Mhi'S Outputs Related to US-APWR DCD RAI No. 636-4732
ML110070272
Person / Time
Site: 05200021
Issue date: 12/28/2010
From: Ogata Y
Mitsubishi Heavy Industries, Ltd
To: Ciocco J
Document Control Desk, Office of New Reactors
References
UAP-HF-10356
Download: ML110070272 (151)


Text

Ar MITSUBISHI HEAVY INDUSTRIES, LTD.

16-5, KONAN 2-CHOME, MINATO-KU TOKYO, JAPAN December 28, 2010 Document Control Desk U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 Attention: Mr. Jeffery A. Ciocco Docket No.52-021 MHI Ref: UAP-HF-10356

Subject:

MHI's Outputs related to US-APWR DCD RAI No. 636-4732

Reference:

1) "Request for Additional Information No. 636-4732 Revision 0, SRP Section:

03.06.02 - Determination of Rupture Locations and Dynamic Effects Associated with the Postulated Rupture of Piping, Application Section:

3.6.2," dated 9/23/2010.

2) "MHI's Responses to US-APWR DCD RAI No. 636-4732," UAP-HF-10335, dated 12/15/2010.

With this letter, Mitsubishi Heavy Industries, Ltd. ("MHI") transmits to the U.S. Nuclear Regulatory Commission ("NRC") Outputs related to US-APWR DCD RAI No. 636-4732.

Enclosed are revised presentation material, UAP-HF-10320, entitled "Response to RAI 636-4732 for Pipe Break Hazard Analysis Revision 1 (Proprietary)", 10 out of 17 references cited in Reference 2, entitled "MHI's Responses to US-APWR DCD RAI No. 636-4732,"

UAP-HF-10335, dated 12/15/2010, technical report, MUAP-10017-P Revision 1, entitled "Methodology of Pipe Break Hazard Analysis (Proprietary)", and MUAP-1 0017-NP Revision 1, entitled "Methodology of Pipe Break Hazard Analysis (Non-Proprietary)". The Technical Reports is being submitted electronically in compact discs (CDs). These materials were prepared to reflect the discussion results at the conference call with NRC held on December 1.

Additionally, Remained 7 references cited in Reference 2 will be submitted to NRC later.

The enclosed presentation material and technical report contains information that MHI considers proprietary, and therefore the material and report should be withheld from disclosure pursuant to 10 C.F.R. § 2.390 (a)(4) as trade secrets and commercial or financial information which is privileged or confidential. Accordingly, the Report is being submitted in two versions, in separate compact discs. One version (in CD 1) contains the complete proprietary version of the Report. The non-proprietary version of the Report is enclosed in CD 2. In the non-proprietary version, the proprietary information, bracketed in the proprietary version, is replaced by the designation "[ ]". In accordance with the NRC submittal procedures, this letter includes an Affidavit that identifies the reasons why the proprietary version of the Report should be withheld from disclosure pursuant to 10 C.F.R. § 2.390 (a)(4).

Please contact Dr. C. Keith Paulson, Senior Technical Manager, Mitsubishi Nuclear Energy Systems, Inc. if the NRC has questions concerning any aspect of this submittal. His contact information is provided below.

Sincerely, Yoshiki Ogata, General Manager- APWR Promoting Department Mitsubishi Heavy Industries, LTD.

Enclosures:

1. Affidavit of Atsushi Kumaki
2. Revised Presentation Material, UAP-HF-10320, "Response to RAI 636-4732 for Pipe Break Hazard Analysis Revision 1 (Proprietary)"
3. References cited in Response to RAI 636-4732 for Pipe Break Hazard Analysis Revision 1
4. CD 1: Technical Report, MUAP-1 0017-P Revision 1, "Methodology of Pipe Break Hazard Analysis (Proprietary)"
5. CD 2: Technical Report, MUAP-1 0017-NP Revision 1 "Methodology of Pipe Break Hazard Analysis (Non-Proprietary)"

The file contained in each CD is listed in Attachments 1 hereto.

CC: J. A. Ciocco C. K. Paulson Contact Information C. Keith Paulson, Senior Technical Manager Mitsubishi Nuclear Energy Systems, Inc.

300 Oxford Drive, Suite 301 Monroeville, PA 15146 E-mail: ckpaulson@mnes-us.com Telephone: (412) 373-6466

Enclosure 1 Docket No.52-021 MHI Ref: UAP-HF-10356 MITSUBISHI HEAVY INDUSTRIES, LTD.

AFFIDAVIT I, Atsushi Kumaki, state as follows:

1. I am Groupl Manager, Licensing Promoting Group in Promoting Department, of Mitsubishi Heavy Industries, LTD (MHI"), and have been delegated the function of reviewing MHI's US-APWR documentation to determine whether it contains information that should be withheld from public disclosure pursuant to 10 C.F.R. § 2.390 (a)(4) as trade secrets and commercial or financial information which is privileged or confidential.
2. In accordance with my responsibilities, I have reviewed the enclosed documents, UAP-HF-10320 and MUAP-10017 Revision 1 and have determined that portions of the document contain proprietary information that should be withheld from public disclosure.

All pages contain proprietary information as identified with the label "Proprietary" on the top of the page, and the proprietary information has been bracketed with an open and closed bracket as shown here "[ ]". The first page of the document indicates that all information identified as "Proprietary" should be withheld from public disclosure pursuant to 10 C.F.R. § 2.390 (a)(4).

3. The information identified as proprietary in the enclosed documents has in the past been, and will continue to be, held in confidence by MHI and its disclosure outside the company is limited to regulatory bodies, customers and potential customers, and their agents, suppliers, and licensees, and others with a legitimate need for the information, and is always subject to suitable measures to protect it from unauthorized use or disclosure.
4. The basis for holding the referenced information confidential is that it describes the unique design and methodology developed by MHI for performing the plant design of protection against postulated piping failures.
5. The referenced information is being furnished to the Nuclear Regulatory Commission

("NRC") in confidence and solely for the purpose of information to the NRC staff.

6. The referenced information is not available in public sources and could not be gathered readily from other publicly available information. Other than through the provisions in paragraph 3 above, MHI knows of no way the information could be lawfully acquired by organizations or individuals outside of MHI.
7. Public disclosure of the referenced information would assist competitors of MHI in their design of new nuclear power plants without incurring the costs or risks associated with the design of the subject systems. Therefore, disclosure of the information contained in the referenced document would have the following negative impacts on the competitive position of MHI in the U.S. nuclear plant market:

A. Loss of competitive advantage due to the costs associated with the development of the methodology related to the analysis.

B. Loss of competitive advantage of the US-APWR created by the benefits of the approach to jet expansion modeling that maintains the desired level of conservatism.

I declare under penalty of perjury that the foregoing affidavit and the matters stated therein are true and correct to the best of my knowledge, information and belief.

Executed on this 2 8 th day of December, 2010.

Atsushi Kumaki, General Manager-APWR Promoting Department Mitsubishi Heavy Industries, LTD.

Docket No.52-021 MHI Ref: UAP-HF-10356 Enclosure 3 UAP-HF-10356 Docket No.52-021 References cited in Response to RAI 636-4732 for Pipe Break Hazard Analysis Revision 1 December, 2010

44 Blast waves and blast loading Blast waves and blest boading 45 "able 3A T

Z (m/kg*') b OA 8.50 0.6 8.60 0.8 10.00 1.0 9.00 1.5 3.50 2.0 1.90 5.0 0.65 10.0 0.20 20.0 0.12 50.0 024 100.0 0.50 Pi P.

Ts FIpgre 3.15 Blast wave profls: real, consevtve, impulse equality angle of incidence. in this case the incident blast wavefront, travelling at velocity U, into air at ambient pressure, undergoes reflection when the forward moving air molecules comprising the blast wave are brought to rest and further compressed inducing a reflected overpressure on the wall 7 which is of higher magnitude than the incident overpressure. The situation is Figure 3.14 Blast wave parameters vs distance orT )kg TNT hemisphericalsurace burst DISTANgE illustrated in-Figure 3.16.. .. . ..-

-.-.-.....- (after Ref 10) .

As mentioned above shock front parameters were first calculated by Rankine and Hugoniot derived from considerations of conservation of momentum and energy. From these equations, and assuming that air 3.9 Blast wave Interactions behaves as a real gas with specific heat ratio Cp/C, = ell a, significant blast front parameters are obtainable.

When blast waves encounter a solid surface or an object made of a medium For zero incidence, reflected peak pressure pr is given by more dense than that transmitting the wave, they will reflect from it and, depending on its geometry and size, diffract around it. The simplest case is p,-- 2p.+ (y+Z1)q. (3.36) that of an infinitely large rigid wall on which the blast wave impinges at zero

46 Blast waves and blast loading Blast waves and blast loading 47 P., P. PO UP UP= P, P, P. P + P.

U",

T. T. U, .O U.o-0 P U,

T U

INCIDENT WAVE I REFLECTED WAVE A Figure 3.16 Face-on reflection where the dynamic pressure qj is (3.37)

Here p, is the density of the air and u, is the particle velocity behind the wavefront. It can be shown that U.= -- V [lI F-I -1l (3.38)

IYP LY-1jpEOj where a. is the speed of sound at ambient conditions. Substitution of Equations 3.37 and 3.38 into Equation 3.36 and rearrangement gives 4

Pr = 2P. [-7p+ p' (3.39) when, for air, y is set equal to 1.4.

Inspection of this equation indicates that an upper and lower limit to Pr z.

can be set. When the incident overpressure ps is a lot less than ambient pressure (e.g. at long range from a small charge) the equation reduces to Figure 3.17 Face-on reflection: blast wove parameters vs scaled distance for spherical (3.40) charges of TNT (after Ref. 6)

Pr = 2p.

When ps is a lot greater than ambient pressure (e.g. at short range from a Reflected overpressure and impulse data are also given in the graphs of large charge) Equation 3.39 reduces to Figures 3.10 and 3.14 for 1 kilogramme spherical and hemispherical charges Pr = 8p, (3.41) of TNT respectively.

If a reflection coefficient CR is defined as the ratio of p, to p. then the 3.9.1 Regular and Mach reflection Rankine-Hugoniot relationships predict that CR will lie between 2 and 8.

However, because of gas dissociation effects at very close range, measure- In the discussion above, the angle of incidence a, of the blast wave on the ments of CR of up to 20 have been made. Figure 3.17 shows reflected surface of the target structure was zero. When a, is 90* there is no reflection overpressure and impulse tr for normally reflected blast wave parameters and the target surface is loaded by the peak overpressure which is some-plotted against scaled distance Z. It is worth noting that the lowest possible times referred to as 'side-on' pressure. For oq between these limits either value of Z corresponds to the surface3of the (spherical) TNT charge. If TNT is regular reflection or Mach reflection occurs.

taken as being of density 1600 kg/m , the limiting Z value is 0.053. Consider firstly regular reflection which is illustrated in Figure 3.18.

Blast and Ballistic Loading of Structures To Elizabeth, Caroline and Rachel and Janice, Alexander, Iona, Douglas, Amy and Alastair P. D. Smith Senior Lecturer, Civil Engineering Group, Cranfield University, Royal Military College of Science J. G. Hetherington Head, Design Group, Cranfield University, Royal Military College of Science i- -

[ N E M A N N NUTTERWORTH OXFORD AMSTERDAM BOSTON SAN DIEGO SAN FRANCISCO LONDON NEWYORK PARIS SINGAPORE SYDNEY TOKYO

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ýEXPERIMENTAL' STUDY .ON AN, IMPINGEMENT HIGH-PRESSURZE STEAM JET ,!;::

F7MASU DAnd -T.-AKATOGAWA

!:*!~i;:*:iKAWANISHI and M. ISONO *?i::!i**ii:.:

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Nuclear Engineering and Design 67 (1981) 273-286 273 North-Holland Publishing Company it., EXPERIMENTAL STUDY ON AN IMPINGEMENT HIGH-PRESSURE STEAM JET F. MASUDA and T. NAKATOGAWA MAPI Engineering Center. Mitsubishi Atomic Power Industries. Ina, 1-2-1. Taito, Taito-ku, Tokyo, Japan and K. KAWANISHI and M. ISONO Takasago Technical Institute, Mitsubishi Heavy Industries, Ltd., Takasago, Hyogo. Japan

  • .
  • j Received 29 September 1981 An experimental study on impingement high-pressure steam jet was performed as one of the efforts to establish evaluation methods for effects caused by a jet under the postulated pipe rupture accident in a nuclear power plant.

An ejected steam jet from a nozzle into the atmosphere is impinged vertically on the flat plate. Nozzle reaction, jet impingement force and impingement pressure distribution were measured over a wide range of impingement distances.

Employed nozzles are circles and ellipses. The steam is supplied under steady state and dry saturated, and the pressure is approximately 4.56 MPa.

From the data of nozzle reaction and impingement force, these are mutually equal and are proportional to the.stagnant pressure upstream of the nozzle; and from this data, the thrust coefficient for each nozzle was calculated. Based on the data of impingement pressure distribution, the jet is roughly divided into three regions on the axis according to the characteristics of distribution in both circular an elliptical nozzles. In addition, in the case of a circular nozzle, locations where the characteristics of distribution distinctly change depend on the location of Mach disk. In the case of an elliptical nozzle, expansion on the minor axis is remarkably higher than on the major axis, particularly near the nozzle exit.

1. Introduction been carried out to clarify the characteristics Of im-pingement jet and incidental effects. In a previous study, In the design of a nuclear power plant, it is required the fundamental experimental study on subcooled water to secure the safety of the plant against effects caused and steam jet was carried out and the 'results were by jet flow under the postulated pipe rupture accident. reported in Paper F6/2 of 5th SMiRT [1]. At present,
  • -J These effects include thrust forces, impingement loads, the experimental study of an impingement steam jet was environmental changes and so on. They have a serious carried out to obtain more detailed data and to further effect on the structural design of the building, equip- clarify the characteristics over a wide axial range, in-ment and the other components. For thrust forces and cluding the effects of nozzle geometry.

environmental changes, sufficient information or under- In this paper, representative results of the experi-standing seems'to have been obtained. On the other ment are described and the characteristics of pressure hand, for the characteristics of a high-energy jet, the distribution of a jet are discussed in relation to the work up to now has not been enough to establish internal structure of the jet.

applicable evaluation methods in the design. Particu-larly, there are many unknown characteristics of a jet in the case of high-energy fluid conditions such as high- 2. Experimental apparatus and procedure pressure steam present under the highly under-expanded condition or subcooled water behaving as a two-phase A scheme of the experimental apparatus is shown in

'jet including moreover, the effects of nozzle geometry fig. I. A steam jet is ejected downward into the atmo-supposed in the design. spheric environment and impinged vertically on the flat With these considerations, an experimental study has plate. The nozzle reaction force is measured by the load 0029-5493/81/0000-0000/$02.75 © 1981 North-Holland

Y .  :

274 F. Masuda et al. / Experimental stud)"on impingenzentjet Steam flow

'1. Steam supply pipe

2. Nozzle
3. Loadcell (for nozzle reaction)
4. Impingement plate
5. Loadcell (for impingement force)
6. Pressure trin'smitter Fig. I. Sketch of experimental apparatus.

i

l edge (R=5)

(a) Circular nozzle

  • 19 Sharp edge Round edge (R=3.2) 44.8 (b) Elliptical nozzle Fig. 2. Nozzle geometry.

r

.:4 F. Masuda et al. / Experimentalstud), on impingementjet 275 cell in contact with the nozzle. Impingement force and 500 impingement pressure distribution are measured by the load cells and pressure gauge attached to the impinge-ment plate. The impingment plate is devised to be 400 movable horizontally and vertically to permit the mea-surements of axial variation of impingement forces and pressure distributions. 300 As shown in fig. 2, two types of nozzles are em- 1 ployed. One is circular (short pipe) and the other ellipti- 0 cal opened in the longitudinal side of the pipe simulat-ing the break geometry of which the aspects ratio is 4, Z 20o postulated in the design. For surveying the effect of flow contraction, two types of edge entrances, round S' and sharp, are provided with each nozzle type. -a 100 .,

The steam is supplied under steady state and dry saturated, and the pressure is approximately 4,56 MPa.

Furthermore, for surveying an internal structure of the jet, pressure distributions of the free jet were also mea- 0 sured using the Pitot tube.

gJet on pressure Po-P. IMPal Fig. 4. Impingement jet forces for the elliptical nozzle.

3. Experimental results and discussion 3.1. Nozzle reaction and impingement force force data. From the relation shown in the figures, these Measured nozzle reaction forces are plotted in fig. 3 forces are approximated as for the circular nozzles and in fig. 4 for the elliptical nozzles. Practically no differences were observed be-FR = j = K(P - P.P)A., (1) tween the impingement force data and nozzle reaction where FR is nozzle reaction, Fj impingement force, K thrust coefficient, Po stagnation pressure upstream of 500 nozzle, P. environmental pressure (= 101.3 kP.a) and A, discharge area. Using experimental data the thrust coef-ficient K for each nozzle is obtained from eq. (1) as 4W / follows:

K= 1.21, circular nozzle with round edge;.

K= 1.12, circular nozzle with sharp edge; K= 1.14, elliptical nozzle with round edge; K= 1.08, elliptical nozzle with sharp edge.

z These values are smaller than K= 1.24 which is ob-tained from Moody's critical flow model for the ideal nozzle [2], though the value for the circular nozzle with 200 round edge is practically equal. The value for the sharp edge is relatively smaller than for the round edge; it shows that the flow contraction causes a reduction of Etoo reaction and impingement forces. The value for the ellipse is relatively smaller than for the circle with the same edge type; it may show that an upstream pressure drop to the exit and a contraction effect at the exit cause the reduction of forces.

0 Variation of impingement forces and central pres-'

Ejection pressure Po-P* (MPa) sures on the plate at impingement distances H/D=

Fig. 3. Impingement jet forces for the circular nozzle. 0.01-0.5 were measured for the circular nozzle. As

276 F. Masuda et al. / Experimental study on impingement jet 5

i - ) Fj 400 0 0 aL.

4

-1 z

LL 300 CL Ps " 18 0

200 2 (

CD a,

E E Fi E.

100F 0

0 0.1 0.2 0.3 0.4 0.5 Normalized impingement distance H/D Fig. 5. Impingement jet forces and central pressures at short distances (circular nozzle R = 5. Pt- P = 3.92 MPa).

shown in fig. 5, impingement forces and pressures in- 3.2.1. Characteristics of an impingement jet from the crease with decreasing the distance. Such a tendency is circular nozzle attributed to the fact that the sonic plane moves from Typical structures of highly under-expanded free and the nozzle exit to the gap between the nozzle lip and the impingement jet from the circular nozzle are shown in

-/ plate surface, namely, the flow is choked in the gap and fig. 6. The Schlieren photographs in Kukita's study [3]

hence the central flow becomes nearly stagnant and the were referred to when drawing the figure.

high-pressure region acting on the plate surface in- First, for a free jet near the nozzle exist, as flow is creases. choked at the exit, the exit pressure is higher than the ambient pressure. Hence a discharged flow rapidly ex-3.2. Characteristicsof impingement pressuredistribution pands and is present with the structure formed by some shock waves as shown in fig. 6. As for the impingement From application to the design evaluation point of jet, three typical flow patterns occur with increasing view, it is required to seize various characteristics of impingement distance. In the region near the nozzle impingement jets, taking into consideration the initial exit, flow is supersonic and when intercepted by the fluid condition, nozzle geometry, impingement distance, plate, a detached shock wave is formed in front of the target geometry or inclination, ambient pressure and so plate. In the region downstream to the Mach disk, the on. occurrence of a recirculation stream in front of the plate Here, the basic experiments were carried out in order has been verified by some other studies [3,4]. In the 9

to determine the characteristics of impingement high- further region, characteristics are transformed into those pressure steam jet in relation to the effects of ejection of a turbulent jet, which are well known.

pressure, impingement distance and nozzle geometry. Some of the measured pressure distributions on an The pressure distributions were measured at the im- impingement jet are shown in fig. 7 and the measured pingement distances HID = 0.5-62.5 for the circulax Pitot pressure distributions on a free jet are shown in nozzle and H=5-373 mm for the elliptical nozzle fig. 8 for Po = 4.02 MPa. For P8 = 2.06, 3.04, 4.02 MPa (major diameter = 20 mm, minor diameter = 5 mm). variations of central pressure are shown in fig. 9. In

F. Masuda et at. / Experimental study on impingenentjet 277 1 Intercepting shock 2 Jet boundary 3 Mach disk 4 Triple point 5 Reflecting shock 6 Slip line 7 Mixing region (a) Free jet Patterns of impingement pressure E

CL E

CM Ci C

K (b) Impingement let Fig. 6. Structure of highly under-expanded jet.

fig. 9, Donaldson's data [4] on an air jet (Po = 0.6 MPa) location where the flat pattern is formed is approxi-are reproduced, the measured data on a free jet (P. = mately equal to that of the Mach disk given by Love et 4.02 MPa) and Mach disk locations given by Love et al. al. [5], and the end of the first region may be defined by

[5] are also shown. An impingement jet is roughly this location. (Though the location of the Mach disk in divided into three regions on the jet axis according to Love's study is for an air jet, the differences of char-the characteristics of distributions shown in fig. 7: acteristics between steam and air are expected to be (1) First region. In the region near the nozzle exit, a small. As for the measured data on a free jet, the rapid expansion accompanied by a reduction of im- verified location of the Mach disk practically agrees pingement pressure occurs and the pressure profile with that of Love's study as shown in fig. 9 as the changes from convex (like the hanging bell) type to the beginning of the flat portion.)

type which has shoulders. Increasing the distance fur- Considering that the detached shock wave is formed ther, the central peak falls and a flat pattern occurs. The in front of the plate in this first region, the variation of

279 F. Masuda et at / Experimental study on impingementjet H/D (see right axis) D-o 0.5 0- --- o 3.'3 0 - v 6.3 (see left axis) /6.3 t

Pi - PoW Po- P-40.8 0.031 0.6 0.02j I C,4 0.0

-4 -3 -2 0 23 4 0

D H/D f A- -- A 13 PJ -Pa, 0---- 30 P"-Po*

0.0; 0 -3 -2 -1 0 2 3 r

D H/D 9j X--X 52-5 0.1 0.05--0 62.5

.0 P - P

-Q - -ý 0.010 -

0- 1 " f t t I I tI I I II I * ,

-8 -7 -6 -5 -4 -3 -2. -I 0 1 2 3 4 5 6 7 8 D

Fig. 7. Impingement pressure profiles (Po =4.02"MPa, circular nozzle with sharp edge entrance).

F. Masuda et al. / Experimentalstu4y on impingement jet 279 0.05-0.50 0 . 23.3 0=

, .r....

0.25

.- 2/

0,6 (See right axis) 0

-8 -6 -4 -2 2 4 6 g 8D Fig. 8. Pitot pressure profiles on a tree jet (Po =4.02 MPa, circular nozzle with round edge entrance).

central pressure is approximately expreksed by the nor- where P0 : total pressure upstream of shock, P.: total mal shock wave relation for stagnation' pressure ratio pressure downstream of shock, k: ratio of specific beats, across the shock wave as follows: M,: Mach number upstream of shock. The result calcu-lated using eq. (2) is shown in fig. 9 as a broken line. (In Po (k+l)M?÷2 [k k--( k- I the calculations, the Mach number distribution in Owen et al.'s study [6] for an ideal gas (k= 1.4) equivalent to P0o (k- I)M12+2 j 2kM1'-(.k- 1)J air was referred to.)

Compared with the data on a free jet, the calculated

//

290 F. Masuda el al. / Experimentalstudy on impingement jet PO (Total pressure) 0 X Donaldson's data [ 4 1 Air, Po = 0.6 MPa 1.0 X

0.5 X X X

X X

X 0' X 0.

0.1 oa C

E IM C

Mach disk cO0s

.E

'0 E .,\

0 Z Entrance edge Pa IMPa) R =5 0.O.1 4.02 S 3.04 U Pitot pressure (Pa = 4.02 MPa) 2.06 A shock relation, Eq(3} for k=-Normal 1.4 T ..... i...

i5 I . . .w I r 0i

'*" 0.5 1 5 10 50 100U H

Normalized impingement distance Fig. 9. Variation of central impingement pressure for the circular nozzle.

result approximately agrees, but is slightly higher. This from eq. (2) (or the data on a free jet), the former is slight shift may show the difference of 'characteristics slightly higher near the nozzle exit and gradually sep-between steam and ideal gas: Besides, comparing the arates on nearing the Mach disk location. These tenden-data of an impingement jet with the calculated results cies may be attributed to the reason that the detached

F. Masuda et al / Experimentalstudyv on impingement jet 281 shock is formed away from the plate and the distance a free jet becomes conspicuous on nearing the Mach between the detached shock and the plate increases on disk location such as given in fig. 8, this condition may nearing the Mach disk location. Here, noticing that the cause a smooth delivery of flow from the central portion peripheral peak (corresponding to the jet boundary) on to be intercepted and central pressure to be increased Pi -P, PO-PWo o.81 0.6 (along the major axis) 0.4 H (mm) 0 5 0.2 10 15 20 t5 30 X (rm Mi) f H (mm)

P o- Pýo

-- 33 53 0.04 0.02

('.

-- 50 -40 20 10 20 30 40 5t 60 X (n raml f H (mm)

P1-P0 0 6--- s80 PO-P 00 -X- 375 0.02 0.01 0o I11 2 -- ,

-120 -100 -80 40 - 20 0 20 40 60 80 100 120 X (mini --

Fig. 10a. Impingement pressure profiles for the elliptical nozzle (R=0, P0 =4.56 MPa, X direction).

282 F Masuda et al. / Experirnentalstudy on impingernentjet when impinged on the plate, and that is why the dis- occur in this region. However, as the central pressure tance between the detached shock and the plate in- reduces on increasing the impingement distance, the creases. pressure profile changes from the flat type to the con-(2) Second region. Marked radial expoansion does not cave (like the saddle-back) type. Then the recovery of

)

Y (Mm)n t HMmm)

Pi - p, 0 33 Po - Po

- &---- 53 0.08 o.06J

(

0 70 -60 ' -50 -40 -30 -20I -10 0 10 20 30 40 50 60 70 80 Y 1mm,-

P1 -e H (mm) ),

PC - P_

2130

--- 250 0 I I . -. I I I I " 1 I

-160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 Y (Mm) --

Fig. 10b. Impingement pressure profiles for the elliptical nozzle (R=0, Po =4.56 MPa, Y direction).

-..-.-.- ~-.-...

F Masuda el al. / Ex-perimental study on impingementjet 283 pressure occurs in the center on increasing the impinge- maximum recovery pressure occurs. As shown in fig. 9, ment distance and a re-transition of the pattern from the location at which the bottom pressure occurs corre-the flat type to the smooth type is seen. The end of the sponds to about 2.5 times the distance to the Mach disk, second region may be defined as the point where the and the location at which the maximum recovery pres-P0 (Total pressure)

  • J X Pi along the major axis Y .alongtheminor axits...

Pj - P** -...

D [(major dia.) x (minor dia.)]

Po - P= Pe 0.01 H/D = 37.5 0

32 0.05

/- F 0

0.10 0.05 0

0.25

.. 0

  • 0.25 XD orY/D Fig. II. Pitot pressurc profiles on a free jet (Po =4.02 MPa. elliptical nozzle with round edge entrance).

i~iliiiii!! 77 7:

284 F. Masuda ei al. / Experimentalstudy on impingement jet sure occurs corresponds to about 5 times that distance. bottom pressure is approximately equal to that calcu-The bottom pressure and the maximum recovery pres- lated with the normal shock wave relation at the Mach sure increase slightly on decreasing the-stagnation pres- disk location.

sure P0. In addition to the above, it is seen that the (3) Third region. In this region, the jet expands grad-Po0 (Total pressure)

I0 D S [(major dia.) x (minor dia.)]% Z (0 r,

T11L 1 1-' cal 0.5

'I R 0.1 "L

ea

0. 0.05 C1 E

7.

Po (MPa) Po" (MPa) Entrance.

edge R=0 z 4.56 4.07 0 Pitot pressure on free jet (Po" = 4.02MF a) 6j 2.33 2.08 001 PO Corrected value with pressure drop fr-100 H _

Normalized impingement distance D Fig. 12. Variation of central impingement pressure for the elliptical nozzle. "

0-i

2iil F. Masuda et al. / Experimental study on impingement jet 285 ually and the central pressure decays monotonically as than on the minor axis, this condition is liable to further the mixing region grows. As is well known, the char- promote the growth of a mixing region on the major acteristics of the impingement pressure distribution is axis and to cause the transition to the turbulent jet at a given by the half-width expression once the mixing shorter distance.

region is fully developed. Referring to fig. 9, transitional points to linear decay reflecting the characteristics of turbulent jet are equivalent to about 10 times the dis- .4. Conclusion tance to the Mach disk location.

Principal results in this study are as follows.

3.2.2. Characteristics of an impingement jet from the (1) The values of the thrust coefficient, K, for each ellipticalnozzle nozzle type were obtained from measurements of nozzle Up to now, sufficient theoretical or experimental reaction forces and impingement forces. Comparing information on the highly under-expanded jet dis- these values with the value 1.24, obtained theoretically charged from the nonaxisymmetric nozzle, such as the by applying Moody's critical flow model, the value for ellipse in this study, has not been found. the circular mozzle with around edge entrance is practi-Some of the measured pressure distributions on an cally equal, and for other nozzle types substantial reduc-impingement jet for P0 = 4.56 MPa are shown in fig. tion exists.

10a along the major axis and in fig. 10b'along the minor (2) Impingement forces in the region near the nozzle axis, while Pitot pressure distributions on a free jet for exit (HID = 0.01-0.5) for the circular nozzle were also P 0 = 4.02 MPa are shown in fig. 11. For Po = 2.33 MPa measured. It was found that impingement forces in this (Po* = 2.08 MPa) and Po = 4.56 MPa (P0* = 4.07 MPa), region were greater than those in a further region on the the variations of central pressure are shown in fig. 12. jet axis.

Here, Po* denotes the stagnant pressure proportionally (3) For both circular and elliptical nozzles, the pat-corrected with the reduction rate of thrust coefficient of tern of impingement pressure distribution of a jet re-the circular nozzle with a round edge entrance. markably changes with increasing impingement dis-As shown in figs. IOa and lOb, Ithe variations of tances and a jet is roughly divided into three regions on patterns with increasing impingementdistance are simi- the jet axis according to the characteristics of distri-lar to the case of the circular nozzle. Therefore, im- bution.

pingement jet from the elliptical nozzle may be roughly (4) For a circular jet, locations where the pattern of divided into three regions on the jet axis, similar to the impingement pressure distribution distinctly changes case of the circular nozzle. depend on the location of the Mach disk which is In addition to the above similaritywith the circular determined by the stagnant pressure at the nozzle exit.

A . nozzle, the following particular characteristics are seen: These locations are approximately expressed by multi-(I) The expansion along the minor axis is greater plying constants, which are common for any value of than that along the major axis in the measured region. the stagnant pressure, by the distance to the Mach disk.

This tendency is remarkable in the region near the (5) For an elliptical jet, the expansion on the minor nozzle exit. 1 axis is greater than that on the major axis, particularly (2) Concerning the transition of the type of pressure near the nozzle exit. The locations where the pattern of profile, the results of measurements show that the tran- impingement pressure distribution distinctly changes sition on the major axis occurs at a shorter impingement depend on the stagnant pressure at the nozzle exit, distance than that on the minor axis. similar to the case of the circular jet. Concerning the Here, considering the behavior of expansion near the transition of the type of pressure profile, however, the nozzle exit, expansion near both the ends of the major transition on the major axis occurs at a shorter impinge-axis is three-dimensional, and near the center nearly ment distance than that on the minor axis.

two-dimensional. In such a condition, a reduction of pressure near both ends of the major axis is more rapid than that near the center, and hence expansion on the References major axis may be suppressed. This behavior can be verified by the variations of location of a peripheral

[I] K. Kitade et al., Experimental study of pipe reaction force peak (corresponding to the jet boundary) on the jet axis and jet impingement load at the break. Paper F6/2 of 5th in fig. 1I. In addition, for transition to the turbulent jet, SMiRT, Berlin (August 1979).

since the expansion width on the major axis is narrower [2] F.J. Moody, Maximum flow rate of a single component

286 F. Masuda et al / Experimental study on impingenientjet two-phase mixturc, J. Heat Transfer. ASME, Series C. Vol. [5] ES. Love et al.. Experimental and theoretical studies of 87 (1965). axisymmetric free jets. NASA Technical Report R-6 (1959).

[3] Y. Kukita. Study on unstable phenomena of supersonic [6] P.L. Owen et al., The flow in an axially-symmetric super-impinging jets. Ph. D. Thesis, University of Tokyo (Decem- sonic jet from a neary sonic orifices into a vacuum. Brit.

bcr 1974). A.R.C. Technical Report, R&M 2616 (1952).

[4] C.D. Donaldson et al.. A study of free'jet impingement.

Part I: Mean properties of free and impinging jets. J. Fluid Mech. 45. Part 2 (1971).

-I

AIAA JOURNAL Vol. 40, No. 4, April 2002 Experimental and Computational Investigation of Supersonic Impinging Jets F. S. Alvi*

FloridaA&M University and FloridaState University, Tallahassee,Florida32310 and J. A. Laddl and W. W. Bower4 The Boeing Company, St. Louis, Missouri 63166 The results of an experimental and computational study of a moderately underexpanded axisymmetric super-sonicjet issuing from a converging nozzle and impinging on a ground plane are presented. The goal ofthis work is to develop a better understanding of the impingingjet flowfield, which is of significant practical interest because of its presence in short takeoff and vertical landing (STOVL) aircraft during hover as well as in other aerospace-related and industrial applications. The experimental measurements include flow visualization, surface-pressure distribu-tions, and velocity field data obtained using particle image velocimetry (PIV). The experimental data, especially the velocity field measurements, were used to verify the accuracy of computational predictions. Computational results obtained using two different turbulence models produced almost identical results. Comparisons with experimental results reveal that both models capture the significant features of this complex flow and were in remarkably good agreement with the experimental data for the primary test case. The experiments and computations both revealed the presence of the impingement zone stagnation bubble, which contains low velocity recirculating flow. Other features, including the complex shock structure and the high-speed radial wall jet, were also found to be very similar. The ability to measure and predict accurately the impinging jet behavior, especially near the ground plane, is critical because these are regions with very high mean shear, thermal loads, and unsteady pressure forces, which contribute directly to the problem of ground erosion in STOVL applications.

Introduction to significant erosion caused by the extremely high shear stresses H IGH-SPEED impinging jets can occur in a variety of and wall heat-transferrates created in this flow. Finally, the outwasfi aerospace-relatedapplications.Thesejet flows are particularly from the hot impinging jets can be drawn into the engine inlets, troublesome to short takeoff and vertical landing (STOVL) aircraft, a phenomenon known as hot gas ingestion, thus degrading engine such the Harrier/AV-8 family, during hover mode. In these instances performance and potentially risking engine failure.

the flowfield producedby the impingementof the high-speedliftjets Some of the problems just outlined are known to occur for the produces adverse local flow conditions, which can potentially lead subsonic Harrier family of aircraft. They are expected to become to the degradation of aircraft performance in a number of areas dur- more acute for the future generation of the supersonic STOVL air-ing hover. These adverse effects, collectively referred to as ground craft, where the environment is expected to be more severe because effects, are the result of the highly unsteady nature of the flow gen- of the impingement of supersonic jets operating at higher temper-erated by the impingement of the high-speed jet(s) on the ground atures. Consequently, the study of supersonic impinging jet flows plane and the pressure field caused by the natural entrainment by is of great interest from a practical perspective. Furthermore, the these jets. They include lift loss caused by flow entrainment asso- complex nature of the impinging jet flowfield, which often includes ciated with the lifting jets, which induces low surface pressures on multiple shock and shock/shear layer interactions, subsonic, su-the airframe resultingin a "suckdown" force opposite to lift. The lift personic and separated flows, makes this flow interesting from a loss typically increases in magnitude as the aircraft approaches the fundamental fluid dynamics standpoint.

ground and can be greater than 60% of the total lift jet thrust when Impinging jet flows have been the focus of research for over the jets are very close to the ground plane.' Increased noise or over- three decades, where their fluid dynamic and acoustic properties all sound-pressure levels associated with high-speed impingingjets have been carefully examined by a number of capable investiga-and the sonic fatigue of structural elements in the vicinity of the tors. Notable among the acoustic studies are those by Neuwerth,2 nozzle exhaust caused by unsteady loading is also an area of con- Powell, 3 Tam and Ahuja,4 Henderson and Powell,5 and most re-cern. In addition to higher levels, the noise spectrum is dominatedby cently Krothapalli et al. 1 One of the primary outcomes of these discrete tones, which, if close to the aircraft panel frequencies, can aeroacoustic studies is that the highly unsteady, oscillatory nature further aggravate the sonic fatigue problem. Furthermore, the im- of impingingjet, which is accompaniedby discrete, high-amplitude pingementof hot, high-speedliftjets on the landing surface can lead acoustic tones, referred to as impingement tones, is caused by a feedback loop. The globally oscillatory behavior of the jet and the resulting impingement tones have been explained well by a feed-Presented as Paper 2000-2224 at Fluids 2000, Denver, CO, 19-22 June back mechanism derived from earlier work by Powell. 6 Recently, 2000; received 7 August 2000; revision received 24 July 2001; accepted for Krothapalli et al.' demonstrated that the feedback phenomenon publication 20 September 2001. Copyright © 2001 by the authors. Pub-lished by the American Institute of Aeronautics and Astronautics, Inc., with might also be responsiblefor the lift loss, described earlier, through permission. Copies of this paper may be made for personal or internal use, the generation of large-scale structures in the jet shear layer. Be-on condition that the copier pay the $10.00 per-copy fee to the Copyright cause the focus of the present work is the mean behavior of the Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include impinging jet, a more detailed discussion of the unsteady properties the code 0001-1452,02 $10.00 in correspondence with the CCC. is outside the scope of this article. The interested reader is directed

  • Associate Professor, Fluid Mechanics Research Laboratory, Department to the references just cited. Suffice it to say that the fluid dynamic of Mechanical Engineering. Senior Member AIAA. and acoustic properties of this flow appear to be intimately related.

lEngineer/Scientist, Mailcode 1067126, P.O. Box 516. Member AIAA. The structure and fluid dynamic properties of this flow have t

Boeing Technical Fellow, Mailcode 1067126, P.O. Box 516. Associate also been investigated in a number of studies. In a classic study Fellow AIAA. Donaldson and Snedeker7 ' examined the flowfield using schlieren 599

600 ALVI, LADD, AND BOWER these data are the first of their kind to provide detailed velocity and vorticity field information over the entire flow. The PIV measure-ments combined with acoustic data, flow visualization, and mean and unsteady pressure fields have provided significant insight into the overall behavior of this flow. In addition to the experimental study, a collaborative computational effort was also initiated with The Boeing Company. Boeing is performing computational fluid dynamics (CFD) for selected test cases where the experimental data have been used to benchmark the computational code in order to establish its accuracy. Previous studies of free and impinging com-pressible jets have been made at Boeing by Wlezien et al., 5 who computed acoustic fields from a direct Navier-Stokes simulation and the acoustic analogy equation. An assessment of several one-and two-equation turbulence models for twin impinging jets was a) nnaaowgrapn made by Ladd and Korakianitis,"6 who obtained good predictions of impingement region velocity data and fair predictions of upwash fountain properties when compared to water-tunnel laser doppler velocimetry data. Detailed results of some of these experimental studies addressing the aeroacoustic properties of the single imping-ing jet flows have been published by Krothapalli et al.' and Alvi and Iyer.14 In the present paper we present a review and comparison of significant experimental and computational results for selected relevant cases. By combining experimental and computational re-sults, one might gain further insight into physics governing this Wall Jet complex flow, thus revealing the value of such collaborative com-putational and experimental studies. A discussion of the strengths and weaknesses of the computational code and suggestions for fu-ture improvement is also presented.

b) Flowfield schematic Experimental Methods

-Annular Peak Cp Test Models and Facilities The relatively simple configuration used for the experimentaland computational study is shown in Fig. 2. It consists of an axisym-metric nozzle, which produces the high-speed jet impinging on a ground plane. For some cases a circular disk, referred to as a "lift" plate, is placed at the nozzle exit plane. The disk has an annular hole from which the jet issues and is meant to represent a generic outer moldline from which the jet exhausts. The relevant geomet-c) Pressure distribution ric parameters, also indicated in Fig. 2, included, the nozzle exit Fig. 1 Stagnation bubble flowfield. diameter; D, the lift plate diameter; and h, the distance between the ground plane and the nozzle exit. Two axisymmetric nozzles, a Mach 1.5 C-D and a converging or sonic nozzle both with identi-photography, surface flow visualization, mean surface-pressure cal throat diameters of 25.4 mm, are used to generate the primary flow. The diameterof the lift plate is approximately 10d or 25.4 cm.

measurements, and, to a limited extent, surface heat-transfer rates.

The experimental studies were conducted using both nozzles over Carling and Hunt9 and Lamont and Hunt'" have further studied this a wide range of nozzle pressures and ground plane distances, with flow, concentratingon the impingement zone, which lies at the cen-and without the lift plate 4 ; however, in the present paper discus-ter of the flowfield, and the wall jet region (see Fig. 1). In addition, sion will be limited to the sonic nozzle operating at a fixed pressure Gubanovaet al.," Ginzberg et al.,"2 and Gummer and Hunt13 have ratio without the lift plate. The test conditions for the primary case also examined the flow structure in detail, particularly in the im-used for comparison in this study are as follows: nozzle pressure pingementzone. The impingement zone is perhaps the most impor-ratio (NPR) = 5, where NPR is defined as the ratio of the jet stag-tant and certainly the most complex part of this flow, and although nation pressure P0 to ambient pressure P. at the nozzle exit. The previous studies have provided some insight into this flow region ambient pressure was assumed to be constant at 14.7 psia, hence the some issues such as the conditions for the formation of a stagnation jet was operatedat P0 = 73.5 +/- 0.5 psia. The nominal jet stagnation bubble in the impingement zone 1.3 are still not well understood.

temperature for the experimental study was 20'C. The ground plane Further discussion of this issue is delayed until the beginning of was a distance of three diameters from the nozzle exit (h /d = 3) for the Results and Discussion section; a more detailed review of this the primary test case; results for other ground plane heights are also issue can be found in Alvi and Iyer.14 In summary, although ear-briefly discussed to examine the influence of nozzle height on the lier studies provided valuable insight into the flowfield behavior, flow behavior.

they mainly relied on measurements of mean surface-pressuredis-tributions and surface flow visualization. Until recently, very little quantitative data have been available in the flowfield above the sur- Primary

  • ,K_.*.._ [*Nozzle face, especially in the critical near-surface flow in the impingement and wall-jet regions.

To address some of these issues and to gain a better understand- ý.4,-t Instrumented

<- Lift Plate ing of supersonic impinging jet flows, especially their behavior in the context of STOVL aircraft, a comprehensive experimental in-h D

vestigation of the impinging jet flowfield was initiated at the Fluid Mechanics Research Laboratory (FMRL), Florida A&M University (variable) Instrumented and Florida State University, Tallahassee, Florida, a few years ago. Ground Plate One of the most notable contributions of this ongoing experimen-Fig. 2 Seo i j t c/o- .

tal effort has been the velocity field data obtained using the parti-cle image velocimetry (PIV) technique. To the authors' knowledge Fig. 2 Supersonic impinging jet test configuration.

ALVI, LADD, AND BOWER 601 The experimentswere conductedin the STOVL facility of FMRL. which translates to an uncertainty in the pressure coefficient Cp A high-pressureblowdown compressed air facility was used to sup- (defined later) of +/-0.005. In addition to the mean pressure ports, ply air to the nozzles. The air is stored in a bank of large-capacity the ground plane was also equipped with high-frequency pressure storage tanks, which are supplied by a high-displacement recipro- transducers to allow for unsteady surface pressures to be measured; cating air compressor. To simulate different aircraft heights above however, the unsteady properties will not be discussed in this paper, the ground, the ground plane is mounted on a hydraulic lift and can and the readeris referred to Refs. I and 14. Mean and instantaneous be moved relative to the model. In the experiments described here, flow visualization images were obtained using a shadowgraph sys-the ground plane consisted of an instrumented 1 x I m aluminum tem with a field of view of approximately 30 cm in diameter. The plate, which was centered underneath the model. More details of shadowgraph system employed a conventional single pass arrange-the STOVL hover rig can be found in Wardwell et al.' 7 ment with a collimated beam; a variable frequency, white light stro-boscopic flash unit was used as the light source.

Measurement Techniques Computational Methods To obtain whole-field velocity data in this flow using PIV, the primary jet was seeded with small (- I fzm) oil droplets generated The computations were conducted using the WIND computer using a modified Laskin nozzle, and the ambient air was seeded with program. This flow solver is based on a time-marching solution to smoke particles approximately 5 Am in diameter using a Rosco fog the Reynolds-averaged Navier-Stokes equations. The code is ap-generator.The flow was illuminated with a thin light sheetgenerated plicable for flow speeds ranging from approximately Mach 0.05 to by a dual-head Spectra Physics Nd-Yag laser with a repetition rate hypersonic and supports a variety of flow types includingfinite rate, of 15 Hz. Each PIV image pair was acquired using a Kodak ES 1.0 chemically frozen, and perfect gas. The full form of the stress tensor digital video camera capable of recording 8-bit digital image pairs is used (no thin-layer approximations). The equations are solved via in separate frames at a rate of 15 image pairs/s. Further details of an approximately factored upwind schemethat has been shown to be this PIV techniquecan be found in Refs. l and 14. One of the main second-order accurate in physical space. A more detailed descrip-advantages of this P1V techniqueis a novel processingscheme with tion of the numerical procedurecan be found in Bush2' or Cain and high spatial resolution that uses image matching to extractthe parti- Bush. 21 Ideal gas is assumed in the present work, and Sutherland's cle displacements, hence the velocities, from particle image pairs."8 law is used to vary the laminar viscosity as a function of temperature.

This image-processing technique allows for measurements to be The molecular and turbulentPrandtl numbers are assumed constant made in regions of high velocity gradients. at values of 0.72 and 0.9, respectively. To minimize computation Despite the use of the advanced processing scheme, particle lag is times, all solutions presentedin this paper were obtained assuming inherent in any particle-trackingscheme, and some lag will always axisymmetric flow.

occur. This is especially true in regions with very high velocity In the WIND program flow turbulence can be represented using gradients, such as in the vicinity of shock waves. Consequently, algebraic, one-equation, or two-equation modeling. For the present it is expected that the location of strong shocks will be partially study three different types of turbulence models were employed.

"smeared" because of particle lag. Similarly, although to a lesser These included the one-equation Spalart-Allmaras model, 22 the extent, particle lag will also occur in otherregions with high velocity two-equation shear stress transport(SST) model, 2' and the Spalart-gradients such as the wall jet or in the large-scale vortical structures Allmaras model with a correction for streamline curvature and sys-with highly rotational flow. In addition, in areas very close to the tem rotation (SARC). 24 As the results will show, both the two-surface, such as the impingement zone and the wall jet, reflections equation SST model and the one-equation SARC model provide of the laser sheet by the surface can also lead to larger errors in very similar results, which are both in very good agreement with the velocity field and/or yield regions where velocity data cannot the experimental data.

be obtained. Ross et al."9 conducted a detailed investigation of the effect of particle size and shock strength on the accuracy of PIV Spalart One-Equation Model with Rotation and Curvature Correction measurements using an earlierand less accurate processingscheme. Various corrections have been introduced in the past by other Their measurements show that for -1 A m seed particles, particle researchers, such as Launder et al. 25 and Park and Chung,2" to ac-deceleration caused by a strong oblique shock begins within 1 mm countfor streamline curvature and rotation. These corrections,how-of the actual shock location, where the deceleration rate increases ever, are applicable only to the specific flows for which they were with increasing shock strength. Hence, we expect that the initial designed. To account for these phenomena for general flow appli-location of the normal shock, the strongest possible shock, should cations, more complex turbulence models such as Reynolds-stress be accurately represented within 1-2 mm in the PIV data. A more formulation have been employed. These sophisticated models re-detailed investigation of the particle lag is outside the scope of this quire fewer assumptions than one- or two-equation models but are paper, and the reader is referred to Ross et al.' 9 and Alvi and Iyer"4 too computationally intensive to be practical for routine engineer-for a more comprehensive discussion. The conclusions regarding ing applications. Recently, the curvature correction modification of the flowfield behavior that are reached in light of the PIV velocity Spalart and Shur2'4 has been added to the baseline Spalart model and field data will not be materially affected. This is particularly true applied to several three-dimensionalconfigurations2 7 The baseline for the present paper where the PIV data are used only to examine Spalart model has been shown to produce results similar to the two-the mean flow features and behavior. It is impossible to determine equation SST model for many flows but does not perform as well the absolute uncertainty of the PIV measurements because detailed for problems such as the supersonic impinging jet where the shear-velocity field data are not available in literature for this flowfield--a layer growth rates and strong rotation effects are significant. Dif-motivation for the present study. However, in the absence of shock ferences between predictions from the baseline Spalart and SARC waves the mean velocity field data obtained using PIV show that one-equation models are presented for some 27 cases in this paper and the velocity data are in very good agreement, in general within 3%, are studied more in depth in Mani et al.

with the exit velocity calculatedu sing isentropicrelations.The mean PIV results presented in this paper were obtained by averaging 80 Shear-Stress Transport Two-Equation Model image pairs. Although a larger numberof images were recorded for The SST two-equation turbulence model from Menter23 is now most cases, using more than 80 image pairs did not change the mean used routinely in many aerospace CFD applications at The Boeing velocity field. Company, St. Louis, Missouri. It is a blended model that exploits The mean surface-pressure distributions were obtained by se- the advantagesof both the k-e model and the k-w of Wilcox.2" The quentially scanning a series of surface-pressure taps along a ra- k-E models, such as those from Jones and Launder, 29 have numer-dial line on the ground plane. The pressures were scanned using a ical difficulties when attempting to integrate to the wall. There are Scanivalve'T unit connected to a Validyne strain-gaugetransducer. assumptions about the boundary values of 8, which give rise to a Several seconds of data were digitized and recorded at each port to high degree of numerical stiffness in this region. Conversely, the obtain an accurate measurement of the mean surface pressures. The k-E model does quite well for free shear-layer problems, particu-surface pressures were measured with an accuracy of +/-0.3 psia, larly in two dimensions. The main advantage of the k-to model is

602 ALVI, LADD, AND BOWER that it behaves well for wall-boundedproblems because of the phys- lack thereof) of a stagnation bubble. The interested reader is re-ically sound boundary conditions on both k and o. The Menter SST ferred to these references, especially the study by Kalghatgi and model employs the Wilcox k-w model near the wall but transitions Hunt, 3 1which specifically addresses this issue. Very briefly, as the to the k-e model via a switching function.This model is sometimes supersonic flow in the primary jet approaches the ground plane, referred to as the SST model because it has the ability to account it decelerates through the formation of a plate shock. If the jet is for the transport of the principal turbulent shear stress in adverse not ideally expanded, oblique shocks in the jet plume (indicated pressure gradient boundary layers. This modeling feature is based as "jet shocks" in Fig. Ib) interact with the plate shock resulting on Bradshaw's*o assumption that the principal shear stress is pro- in the well-known triple-shock structure, where the third shock is portional to the turbulent kinetic energy and is expressed through a generally referred to as the tail shock. It is the nature of this inter-modification of the eddy viscosity. The interested reader is referred action that appears to determine the flowfield in the impingement to the original paper by Menter 23 for details of this two-equation zone. When present, the stagnation bubble was hypothesizedto en-turbulence model formulation. close a region of recirculating fluid with relatively low velocities.

However, until the present study very little direct and detailed evi-Results and Discussion dence of the flow in this stagnation bubble has been available, and Before a detailed discussion and comparison of the experimental the nature of the flow in the stagnation bubble had primarily been and computationalresults, we provide an overview of the global im- understood through interpretation of surface-pressuredistribution s, pingingjet flowfield noting some of its principal features. Figure Ia surface streakline patterns,7' 9 and schlieren or shadowgraph flow shows an instantaneous shadowgraph of the principal test case, visualization.

NPR = 5, hId = 3; shown directly below the shadowgraph image is a schematic of the impinging jet flowfield model (Fig. Ib) and a Experimental Velocity Field corresponding pressure distribution sketch (Fig. Ic). The imping- As already mentioned, detailed, whole flowfield velocity mea-ing jet flowfield can be divided into three main regions! The first surements were obtained using PIV for a range of NPRs and ground region is the main jet column, where the flow is primarily inviscid plate distances using both sonic and converging- diverging nozzles, and contains expansion and compression/shock waves for nonide- with and without the lift plate. However, in this paperthe discussion ally expandedjets. The impingement zone is the second region and will be limited to the sonic nozzle without the lift plate, operating at is an area in the vicinity of the jet impingement point character- NPR = 5 with the groundplane at h/d = 3. This was selected as our ized by strong gradients leading to significant changes in local flow feature case because, as the shadowgraph image and the flowfield properties. This area is also referred to as the shock layer. Finally, sketch in Fig. 1 reveal, the flow is very complex with shock/shock the radial wall jet, the third distinct region, is the area outside the and shock/shear-layer interactions and areas of flow acceleration impingement zone, which contains the jet flow redirected radially and deceleration into locally supersonic and subsonic regions. All outward after impingement. All three zones have been indicated in PIV measurements are obtained in the central plane of the jet. The Fig. lb. The flow schematic depicts the impingement region with a mean velocity field for the primary test case is shown in Fig. 3, where stagnation bubble, and the sketch of the surface-pressure distribu- the vector plot has been overlaidon the out-of-planevorticity color tion beneath shows the distinctive pressure profile correspondingto contour plot on the left half of the figure. The right half displays the presence of a stagnation bubble. Surface-pressuredistributions the streamline pattern superposed on the vorticity contours, where with such annularpeaks are commonly used as distinct indicatorsof the units of vorticity for this and other similar vorticity contours are the presence of a stagnation or separation bubble; for cases where s-'. In the velocity vector plots shown in this paper, the length of a stagnation bubble is not formed, the surface-pressuredistribution the vector is proportional to the velocity magnitude. The streamline shows a central peak. The details of the impinging jet flow features patterns were created from the measured velocity vector field using (e.g., shape of the plate and tail shocks) are strongly dependent on the software package TecPlotTM.

the jet Mach number and the ground plane distance and will vary Several features are clearly revealed in Fig. 3. First, the shear layer from the sketch in Fig. lb. at the jet boundary is readily apparent as a region of high vorticity The presence, and the reasons for the formation, of a stagna- in the vorticity contourplots. As the jet shear layer approaches the tion bubble have been and remain the subject of some debate. 3 surface, it turns outward around r/d ý I and forms the outer bound-3 Gubanovaet al.," Gummer and Hunt,1 and Kalghatgi and Hunt ' ary of the wall jet. Also clearly evident in this figure is the presence have conducted detailed investigations of the impinging jet flow of the strong Mach disk shock revealed by the dramatic decrease in structure, particularly in the impingement zone, for a range of con- the flow velocity, apparent from the change in vector lengths. The ditions. These investigators discuss reasons for the formation (or velocity field data show that the Mach disk occurs around y/d tý1.8, K1 Fig. 3 Experimental vorticity contour plot with vdocity vectors and streamlines: sonic nozzle, NPR=5, hd=3.

ALVI, LADD, AND BOWER 603 which roughly corresponds to the Mach disk location observed in impingement locations in the PIV data and the annular peaks in the the instantaneousand mean shadowgraphsshown in Figs. la and 4, mean surface-pressuredistributions were found to be in agreement respectively. One of the most striking features observed in Fig. 3 is for most of the cases examined."4 This lends some credence to the the region of recirculating flow, the stagnation bubble, in the center hypothesis proposed by earlier investigators," who suggested that of the impingement zone. The presence and extent of the recirculat- the impingement of the slip-line flow leads to the formation of the ing flow in the stagnation bubble is best revealed in the streamline separation bubble.

plot in the right half of Fig. 3. The streamline plot also shows that the impinging flow is divided into two streams, where the outer one flows into the wall jet while the inner stream is wrapped into Comparison of Computational Results the stagnation bubble. In addition to the outer shear layer at the from Different Turbulence Models jet periphery, the inner shear layer or slip line is also visible in Initially we will compare computational results for the primary the vorticity plots as a region of high shear. Because the slip line test case using the SARC and SST turbulence models to determine emanates from the triple-shock intersection, the beginning of the the relative accuracy of each model. This will be followed by a inner shear layer should in principle correspond to the triple-point comparison between the experimental and computational results location on the shadowgraphs. Although the precise location of the with each of the two models. As mentioned before, the NPR = 5, h/d = 3 case was selected because of the complexity of the flow triple point is difficult to determine from the shadowgraphs, its rel-revealed by the measurements where a strong shock appears in the ative location on the PIV plots and shadowgraphs is approximately the same. The region where the inner shear layer impinges on the jet plume followed by a recirculation bubble near the ground plane.

ground plane approximatelycoincideswith the location of the annu- An axisymmetric grid plane containingfive zones and nearly 30,000 lar pressure peak on the measured surface pressure distribution for points was employed for the simulation. Almost two-thirds of this this case (shown in Fig. 5). Although not shown here, the slip-line number were concentrated in the nozzle plume and wall-jet forma-tion region.

Initial attemptsat using local time steppingto obtain a steady-state solutionfor this case yielded large oscillationsin the shear-layerand wall-jet formationregions.Thi s unsteady behavior, supported by ex-perimentaldata,"4 32 then required the computation to be made using the time-accurate mode of the program. The solution from the relax-ation method was then usedonly to providean initial solutionfor the unsteady computation. In the time-accurate calculation integration of the dependent variables is obtained using a constant time interval at all spacings. This time interval must be chosen to be sufficiently small so that the numerical scheme remains stable at the smallest grid points having the largest flow gradients. This same time interval must then be used at all grid points to preserve the time accuracy.

This approach, although requiring many more iterations, allows an estimate of the time-averagedflowfield to be obtained. The temporal Experiment: snaaowgrapn scheme used for the current simulations is first order, but, as shown in the following sections, it still yields fairly accurate estimates of the mean flowfield. The mean flow data are obtained by averaging the data over several hundred time intervals, each interval being around 1.5 its. These intervals are approximately five times larger than the required 0.3-As time interval used as the integration step in the numerical scheme. Several time averages of different numbers of samples were found to produce the same mean flowfield as long as at least 50 1.5-As intervals were averaged. This number of sam-ples represents a good compromise between resolving the higher-frequency content of the flow and keeping the required amount of data storage to a manageable level. The computation time for a typical two-dimensional unsteady problem is then roughly 20CPU Spalart Twbdmee sSTq Turmadm hours on a single-processorSG-0 2 workstation.

CFD computed: density contours A comparison of the computed Mach-number contours from the SARC and the two-equation SST model is shown in Fig. 6. There Fig. 4 Comparison of mean shadowgraph image and density contours is a strong shock present for this configuration, which occurs after from two turbulence models: sonic nozzle, NPR = 5, h/d = 3.

the flow expands to nearly M = 2.8. The shock location is seen to be approximately the same for both models. It has been determined that an accurate prediction of the location and strength of this shock is vital in obtaining a good prediction of the recirculation bubble shown in Fig. 6 and the streamline patterns in Fig. 7.

The Mach contours in Fig. 6 indicate that the computed growth of the radial wall-jet thickness is slightly higher from the SARC model. The mean streamline traces are seen to be nearly identical from both methods and are consistent with the experimental obser-vations. The excellent agreement in the computationalresults using the two models is clearly evident in these and subsequent plots.

Both models appear to capture the essential features of this flow; a more detailed comparison between experimental and computa-tional results is presented in the following section. In a numeri-cal study for a limited number of cases, Kitamura and Iwamoto 3" computed the presence of such a stagnation bubble. However, their CLO 04 Q 1.2 "1 0 14 U 2U 32 3U 4.0 published results were of limited resolution, and the comparison to experimental results was nominal. To the authors' knowledge, the Fig. 5 Computed and measured ground plane pressures for sonic noz- present work provides the first detailed comparison of experimental zle, NPR = 5, h/d= 3. and computational results for this flowfield, especially in the

604 ALVI, LADD, AND BOWER Spalart One-Equation Model with SST Two-Equation Model Rotation and Curvature Correction Fig. 6 Comparison of computed Mach-number contours using two turbulence models: sonic nozzle, NPR = 5, hd = 3.

density contours from both turbulence models are almost identical, and there is a striking similarity between the computed flow struc-tures with features observed in the shadowgraph. The triple-shock structure, which includes the jet shock, tail shock, and the Mach disk, is captured by the computations, and their locations approxi-mately coincide with the experimental observations. The computed density contours also reveal the presence of the inner shear layer and the outer boundaries of the stagnation bubble.

To further assess the accuracy of the CFD predictions, compar-isons are presented in Fig. 8 of the line contours plots of the mean velocity field obtained from the PIV data and the computation using the SST turbulence model. The computed data have been interpo-lated to the same locations represented by the PIV data for a direct comparison. Only the velocity contours from the SST model are presented in this figure, although results from the SARC model SST Two-Equation Model (not shown) are nearly identical. Once again, the computationspre-I*Oi, IIIlDI1 Ilgla I*LIfVlglUg* t.,O1T*gCUOD*

dict the measured velocity field very well with some discrepan-Fig. 7 Computed streamline paths using two turbulence models: sonic cies. Both computational models predict the location of the Mach nozzle, NPR = 5, h/d =3. disk slightly closer to the ground plane than does the measurement.

Consequently, the vertical extent of the separation bubble is also marginally underpredicted. The magnitude and extent of the high impingement and wall-jet regions, at a level of resolution not ob- velocity region in the jet core, upstream of the Mach disk, is some-tained before. what higher in the PIV measurements than in the CFD predictions, Although the computed data presented in the current work were and there is a discrepancy in the velocity magnitudes in the wall obtainedusingthefull 30,000-pointcomputationalgrid, simulations jet, very close to the wall. However, it is clearly evident that overall using half the number of points in the vertical and lateral direction the computations yield very good predictions for the entire flow-yielded nearly identical results. This is a good indication of grid field, including the jet core velocities, the recirculation region, and independence and that adding additional points in the domain will in the wall jet. These characteristics are of critical importance from not improve the accuracy. The mesh was constructed so that the a practical perspective because of their influence on ground erosion.

height of the first point above the wall is near y+ = 3 at the location The comparison between CFD and PIV results continuesin Fig. 9, of maximum wall-jet velocity near r/d = 1.25. Unfortunately, the which shows the mean vorticity contours and the velocity vectors tight clustering at this location limits the maximum stable time-step from experimental and computationaldata. (The numbers in paren-size that can be used for the entire simulation. theses above the contours indicate the grid size used for the in-terpolated data.) The similarity of the CFD and PIV data in the Comparison of Experimental and Computational recirculation region and the overall flow structure can be easily Results: Primary Test Case seen. There appears to be a greater expansion angle at the nozzle An example of a time-averaged shadowgraph revealing the flow exit in the experiment than what is predicted in the CFD results.

structure can be seen in Fig. 4. This figure also shows mean den- Also, as in Fig. 8, the Mach disk appears closer to the ground in sity contours from the CFD simulation using both models. A direct the computations than the PIV data, resulting in a smaller sepa-comparison among the details observed in the shadowgraphs and ration bubble above the surface. However, the radial extent of the density contours is not strictly valid because a shadowgraph is an stagnation bubble, defined by the impingement location of the in-integrated image, sensitive to the second spatial derivative of den- ner shear layer/slip line on the surface, is in very close agreement sity in the flowfield. However, a comparison in the overall flow with the experimental results within r/d - 0.1. This agreement in structure and primary flow features can still be made. Computed the radial extent of the stagnation bubble is also supported by the

ALVI, LADD, AND BOWER 605 CFD Average Experiment 13 600.0 12 408 3 11 416 7 0 ----- 1. 375A 42 ---- 9 333.3

  • 291.7 125 -- 7 250.0 167 6 208.3 S 18,.7 209 4 125.0 3 632 334- 2 41.7 1 0,0 375 -

417 -

459 Fig. 8 Comparison of velocity contours from CFD and experimental PIV data: sonic nozzle, NPR=5, hid =3.

ODAvftp- (12Q0) E -(20x0)

SSTmetimcemhiei Fig. 9 Measured (PIV) and computed velocity vectors and vorticity contours: sonic nozzle, NPR = 5, h/d = 3.

comparison of the surface pressure distributions, presented earlier impingement point is well below the jet total pressure that is nor-in Fig. 5. A comparisonofthe vorticitycontours revealsthe remark- mally recoveredfor an ideally expanded nozzle without a separation able similarity in the shape and magnitude of the diffusing vorticity bubble. The recirculating bubble divides the jet core and deflects it values between the computational and experimental results. It is radially outward so that the peak pressure is lower than the stag-clear that the vorticity field is well predicted by the computations nation pressure and occurs away from center of the interaction. In indicating an accurate simulation of the strength and location of the principle, the pressure peak should correspond to the location of primary jet shear layer, which is redirected into the wall-jet shear the stagnation streamline in the inner shear layer, which divides the layer. As noted earlier, the inner shear layer that emanates from the jet flow that is redirected into the wall jet from the fluid that is en-triple point (Fig. Ib) is also extremely well predicted in terms of trained into the recirculation bubble. This is the behavior observed shape and vorticity levels. in the present case where the pressure peak occurs roughly around A comparison of the predicted and measured ground plane r/d = 1, a location that correspondsto the impingementof the inner surface-pressure distributions is shown in Fig. 5. Results from nu- shear layer as seen in Fig. 9. The baseline Spalart model is seen to merical solutions employing several turbulence models are included significantly overpredict the pressure throughout the impingement and compared to the experimental data. The dependent variable in region, whereas the inclusion of the curvature formulation (SARC) this figure Cp represents the nondimensional surface-pressure co- produces a distribution in agreement with the SST model prediction efficient, where Cp = (P, - P-)/(Po - P.) and P, is the surface and in much betteragreement with the experimentalresults. A closer pressure. The x axis represents the radial location, nondimension- comparison of the SST or SARC results with the experimentaldata alized by the nozzle throat diameter, in this case same as the exit reveals that the greatest discrepancy between computational and the diameter d. experimental data occurs in the central portion of the impingement The overall pressure distribution with a low-pressure plateau and zone. In this region (r/d roughly less than 0.4) both models overpre-an annular peak is typical of an impingement flow with a recircu- dict the plateau pressure by as much as 30%. The overpredictionof lation bubble (Fig. 1) as discussed earlier. The pressure near the the pressure in this region is expected if one realizes that r/d < 0.4

606 ALVI, LADD, AND BOWER roughly defines the radial extent of the Mach disk formed above the r., is the wall shear stress and (Po - P.) is the difference between impingement zone (see Fig. 3). As noted earlier, the computations the jet stagnation and the freestream ambient pressure.

underpredictthe strengthof the Mach disk (see Fig. 8), which in turn Several points are of interest in this distribution. First, we see that would overpredict the pressures recovered downstream of the Mach the skin friction is very low, almost zero, in the central portion of disk on the impingement surface. Notwithstandingsome differences the flowfield. A look at the velocity contour plot (Fig. 8) and the in pressures in certain regions, the overall agreement between the vorticity contour plots (Fig. 9) confirms that this area of the surface predicted and measured distributions is very good. lies under the separation bubble and is a region of very low veloci-In addition to the primary experimental data, surface pressures ties and negligiblevorticities, hence minimal shearstresses. Moving obtained for a similar configuration at British Aerospace34 are also radially outward, there is a rapid increase in the skin friction start-shown in Fig. 5. The BAe axisymmetric nozzle had an exit diameter ing at r/d -0.3 and ending at rid -0.7, where a (negative) peak of 120 mm and a jet total temperature of T, = 1800F and operated in the wall shear stress is present. The negative values of the shear at the same NPR as the cold jet in the present study. The plot shows stress are caused by the fact that fluid in the stagnation bubble is that the normalized pressure distributions from this experiment are moving radially inward in this region, as illustrated in the vortic-in good agreement with the present (FAMU-FSU) cold jet data and ity/vector plots in Fig. 3 and Fig. 9. Figure 3 also shows that the the computations. The agreement of these three data sets provides negative peak at r/d - 0.7 roughly corresponds to the inner extent further confidence in the ability of the CFD code to capture the of the slip line impingement on the surface, an area where high features of interest in this complex flowfield. shear stresses are expected. A more dramatic rise in the skin friction The grounderosion problemis a resultof the unusuallyhigh mean occurs between r/d ýý 0.7 and 1.2 with a skin friction peak at the and unsteady loads imparted on the impingement surface by the hot, latter location. Figure 3 clearly shows that this region corresponds high-speedimpingingjet(s). An examination of the velocity contour to the slip-line impingement and the inception of a new boundary plot shown in Fig. 8 illustratesthat the radial wall-jetregion contains layer in the wall jet, which is bounded by a high-speed outer flow, fluid with very high velocities, in close proximity to the wall. As hence the significantly higher shear stresses. The skin friction goes an example, Fig. 8 shows that wall-jet velocities in the range of through a sign changein this area with a zero occurringat rid - 0.9, 250- 350 m/s are found within a few millimeters from the surface, which by definition is the location of the attachment line in the com-resulting in very high velocity gradients and wall shear stresses. The puted flow. The agreement between the zero skin-friction location radial distribution of the computed nondimensionalizedwall shear and slip-line impingement point in the experimental results indi-stress, shown in Fig. 10, provides the magnitudes of the computed cates that rid

  • 0.9 is close to the actual location of the attachment shear stresses for the primary test case. In this plot the ordinate line. This attachment line divides the stagnation bubble flow from depicts the skin friction Cf, defined as Cf = r,,/(Po - P-), where the wall-jet flow, an observation supported by the surface-pressure distribution of Fig. 9, where the pressure peak occurs at the same radial location. In summary, it is clear that the jet impingement and wall-jet regions are areas of not only very high shear stresses but also large gradients in shear stresses where the flow goes through 0.003 rapid changes in direction. Given the analogy between skin-friction and heat-transfercoefficients, it is reasonableto expectthat this high skin friction be accompaniedby high wall heating.35 This behavior, 0.002 combined with the fact that4 this region is dominated by very high 34 fluctuating pressure loads,' can result in severe ground erosion.

Ly30.001 __ ____ __

Comparison of Secondary Cases Finally, we briefly compare experimental and computational re-sults for two other cases at the same pressure, NPR = 5, and two

-0.001 heights, hid = 2 and 1.6. Similar to Fig. 9, experimental and com-putationalvelocity vector/velocity contourplots for these two cases

-0.002 are shown in Figs. 11 and 12. This is followed by a comparison of 0 0.5 1 1.5 rid 2 2.5 3 3.5 4 the experimental and computational surface-pressure distributions for both heights shown in Fig. 13.

Fig. 10 Computed skin-friction distribution: sonic nozzle, NPR = 5, The comparison between CFD and PIV results for hid = 2 in hid = 3. Fig. II shows an overall agreement in the computed and measured Experiment - (IOOx8O)

Fig. 11 Comparison of velocity vectors and vorticity contours from CFD and PIV*:sonic nozzle, NPR = 5, hMd= 2.

ALVI, LADD, AND BOWER 607 CFD Average - (100x80) Experiment - (100x80)

SST Turbulence Model Fig. 12 Comparison of velodty vectors and vorticity contours from CFD and PIV: sonic nozzle, NPR = 5, h/d = 1.6.

0.48 0.44 0.40 0.36 0.32 0.28 0.24 i 0.20 0.16 0.12 0.08 0.04 0.00

-0.04

-0.08 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 rid Fig. 13 Comparison of measured and computed surface-pressure distributions: sonic nozzle, NPR = 5, h/d = 1.6 and 2.

flow structure and the velocity field. As in the primary test case reasons similar to those outlined in our discussion of Figs. 5, 8, and (hid= 3), the Mach disk, triple point, and the inner shear layer are 9 for the primary test case.

all captured by the computations. However, a closer look reveals The comparison between CFD and PIV results for h/d= 1.6 that there is less diffusion of vorticity in the primary jet and wall-jet shown in Fig. 12 follows the same trend as Fig. 11. Although overall shear layer in the computed flow, where these shear layers appear there is good agreement between the computed and measured re-more compact with higher vorticity values relative to the measured sults, there are differences especially in the impingement region in flowfield. Additionally, the triple point and the origin of the slip line the vicinity of the Mach disk. The triple point is much more diffused (marked for clarity in Fig. 13) in the computed flowfield appears relative to the measured flow, even more so than that observed in diffused, almost bifurcated, and the impingement location of the Fig. 11. Similarly, there is a more significant difference between the slip line is closer to the centerline than indicated by the PIV data. experimental and computed pressure distributions (Fig. 13) in the As expected, these differences in the computed and measured impingementregion.The computed flow for this case fails to capture velocity field translate into a discrepancy in the pressure distribu- the annular peak clearly present in the measured distribution.

tion in Fig. 13. Although the computations reveal the presence of In general, there is very good agreement between the compu-the stagnation bubble, indicated by the annular pressure peaks, the tational results and the measured data, where the computations magnitude of the pressure in the impingement region downstream captured the essential features of the flow. However, it appears of the Mach disk is significantly overpredicted. This is presumably that, as the interaction strength increases, that is, as the nozzle to caused by an underprediction of the strength of the Mach disk for ground plane distance decreases, the differences between the two

608 ALVI, LADD, AND BOWER data increase systematically.This discrepancy is generally confined fers from deficiencies, which cannot be addressed until computer to the impingement zone, a region close to the interaction center- speeds enable large scale, cost-effective solutions to the Reynolds-line. It appears that the disparity might be caused by the inability stress equations or direct-numerical-simulaion methods to be of the computational scheme to accurately predict the behavior of utilized.

the flow in the vicinity of the Mach disk. Differences between the The ability to measure and predict accurately the impinging jet experimental and computational data become more pronounced as behavior, especially near the ground plane, is critical because these the strength of the Mach disk increases. One reason for this behavior are regions with very high mean shear, thermal loads, and unsteady could be attributed to lack of adequate axial grid resolution in the pressure forces. An understanding of these flow characteristics is region of the Mach disk. Adapting the grid distribution to the flow essential because they contribute directly to the study of ground gradients, either manually or with true grid adaptation, would most erosion. We believe that this collaborative experimental and com-likely increase the accuracy of the resulting numerical data. An- putational effort has been very fruitful and has provided unique data other important consideration is the time accuracy of the numerical and insight into this complex flow behavior.

scheme. It is possible that the first-order scheme used in the current work suppresses some of the unsteadiness of the jet and wall shear Acknowledgments layers, which in general become more unsteady for lower heights. We gratefully acknowledgethe continued supportof NASA Ames This behavior would then lead to the apparent "underdiffusion" of Research Center and NASA Headquartersfor sponsoringthe exper-the time-averaged vorticity contours already discussed. imental portion for this work. We appreciate the advice and help of A. Krothapalli and L. Lourenco during this study. The assistance Conclusions of R. Elavarasan and K. Iyer in conducting some of the tests is also appreciated. Finally, we thank Charney Davy for her help in In this paper experimental and computational results for a mod- processing some of the data.

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4 Tam, C. K. W., and Ahuja, K. K., 'Theoretical Model of Discrete Tone icant features of this complex flow and were in remarkably good Generation by Impinging Jets," Journalof FluidMechanics, Vol. 214, May agreement with the experimental data obtained for the present test 1990, pp. 67-87.

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Donaldson, C. DuP., and Snedeker, R. S., "A Study of Free Jet Impinge-The complex shock structureand the high-speed radial wall jet were found to be similar in the experimental and computational data. ment. Part 1. Mean Properties of Free and Impinging Jets," Journalof Fluid 28 1 319 Mechanics, Vol. 45, Pt. 2, Jan. 1971, pp. - .

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RAREFIED GAS DYNAMICS PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS, HELD AT THE INSTITUTE FOR AEROSPACE STUDIES, UNIVERSITY OF TORONTO, 1964 Edited by J. H. de Leeuw INSTTrUTE FOR AEROSPACE STUDIES, UNIVERSITY OF TORONTO, TORONTO, CANADA Volume II 1966 NEW YORK LONDON ACAD EMIC PRESS

StI Section 7 EXPERIMENTAL METHODS l.l.r ci a, IN RAREFIED GAS DYNAMICS hII Ian I ... i t I ip ')rc! u-.. [I;[, I tile". p~i.:,",ill': I; The Structure and Utilization of Supersonic Free Jets iI .Ikt.lc.

' 11d in Low Density Wind Tunnels' , 22lcIt c*li ,,p~

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.. jild~ it~rD HARRY ASHKENAS pl'l il ll~llcit' ,,I' Jet Propulsion Laboratory, Pasadena, California tdr~w. ill Ihc- Ile and FREDERICK S. SHERMAN University of California, Berkeley, California II. ResL W I f,;III. Ii 'l The aim of this paper is to give a concise and easily employed guide to the , i t'litl, 1:, i%,oll results of the theory of inviscid and slightly viscous flow in the central core of a supersonic free jet; to give a risumr and confirmation of experimental t ,,'.

'i~ tII

  • l  ; ll. .

results concerning the location of shock waves at high Reynolds number; to apply this information to the prediction of jet sizes and the Mach and hi'.ed (i. tilt:

Reynolds number ranges corresponding to various pumping systems; and to give a preliminary experimental description of the manner in which the I', Ci'. j,,rlli ;1!1 jet flow itself undergoes transition from an inviscid-continuum flow to a hv :tplnlicd. Ni, I W\Cl:111 an "

free-molecular flow as the orifice Reynolds number decreases.

,Indt I1.ý IllaIll\

i".1 kt i,,.,iiiiullcl hat'.c becicl Ill '.

I. Introduction .lpplicd lo lilt I ( -,C- .'11/. I At the Rarefied Gas Dynamics Symposium of 1962, considerable attention )?.2 bw W. S was drawn to the process of unconfined expansion from a sonic orifice into a low-pressure chamber as an effective means of obtaining high Mach number flows of very low-density gases. These "free jet" flows were discussed in the context of aerodynamically-intensified molecular beam sources (Bier and . .nI ll.f.l k.

Hagena, 1963; Scott and Drewry, 1963; Fenn and Deckers, 1963), and were suggested as a useful supplement to conventional nozzle-confined expansions i'.. Ceiat,.'rli n,."

I This paper presents the results of one phase of research carried out at the Jet Pro- 1. Th,: F-igl pulsion Laboratory, California Institute of Technology, under Contract No. NAS7-100, sponsored by the National Aeronautics and Space Administration and at the University It- I. Itcr1 of California under Contract Nonr-222(45), sponsored by the Office of Naval Research and the Office of Scientific Research.

84

85 SUPERSONIC FREE JETS-STRUCrURE AND UTLIZATION 1963a). They had also been for some classes of wind tunnel tests (Sherman, with aerodynamic schemes of isotope extensively studied in connection separation (Zigan, 1962).

and considerable In the last two years interest in these flows has intensified, their accurate description, as a function of progress has been made toward orifice, the specific-heats-ratio of the gas, and the the pressure ratio across the of California at orifice Reynolds number. Groups at both the University Laboratory in Pasadena have been working Berkeley and the Jet Propulsion of the a complementary fashion on this. problem, and because actively and in results was deemed feasible.

proximity of the two groups, a joint report of our will report a success-Another paper at the symposium (Maslach et al., 1964) of the free jet flow in a determination of cylinder and strip ful application drag in the near-free-molecule regime.

II. Results of Inviscid Flow Theory a thin wall or through The transonic inviscid flow through a circular hole in presents an unsolved problem in a rapidly converging axisymmetric nozzle However, the details of flow in the transonic region potential flow theory.

more than a nozzle diameter evidently have little influence in the region treatments of the supersonic region have been downstream, and successful assumption that flow in the plane of the orifice or nozzle exit based on the of characteristics may then is uniform and slightly supersonic. The method data at a number of discrete mesh points.

be applied, yielding accurate flow (1948) were the first to carry out such a computation, Owen and Thornhill of comparison and for many years their solution has been the only standard for the task Computer programs more than adequate for experimentalists.

years, but have been have been in existence in many organizations for several problems, exemplified by the work of applied to much more complicated The computations used in this paper were performed in Love et al. (1959).

and Space Company in Palo tention 1962 by W. S. Wolff of the Lockheed Missiles is capable of finding the jet boundary and the into a Alto, using a program which almost up to the point of Mach intersection. They number barrel shock location, 1.67, 1.40, or 1.2857),

d in the assumed a perfect gas with constant specific heats (y tier and and uniform exit flow at a Mach number of 1.10.

.nd were panSlOfS Ii A.Centerline Property Distributions jet flows exhibit a le Jet Pro- , . The High Supersonic Region. The computed free inertia-dominated simple and self-similar development in the NAS7.1. relatively barrel shock (see niVeeocb tFeion of high Mach number isentropic flow, inside the " at a distance

'9g.1). There the streamlines appear to radiate from a "source SReS*': Fi

86 HARRY ASHKENAS AND FREDERICK S. SHERMAN S( 1'!

xo downstream of the orifice, the flow speed has very nearly attained its adiabatic-flow limit, and density decreases along each streamline in proportion to the inverse square of distance from this source. The variation of density ' I 1l.

II,, M .l~'ll; from streamline to streamline (i.e., with polar angle 0, at constant distance. R, from the "source") is approximately independent of R. These facts are

,I 1 1iIc, AhI:

II*d'~ lI11131 , 'i

, /,)

I I FIG. I. Inviscid flow geometry:

11 2 R = [r2 + (x - XX)- = tan-Ir/(X - Xo).

commented on in a preliminary way in an earlier unpublished report (Sherman, 1..!:11H11I lit. 1:tlldtHl 1963b).

"* !hlwd tlm, il

a. Mach Number. The analogy to a "simple" (purely radial) source 1low is strong and suggested the following extremely accurate fitting formula for 11CIh', l,tM h'rIC II.,r h~1 rlhl, *I' the centerline Mach number of a free jet.

ii1:1 111 till 11111 v M =Aix Xo)' - (-I- t-xo)---- (1) rI' lt IIP The constants A and xo depend upon y. A preliminary value of x was 0

found by projecting streamlines back to the axis. The final values were found r,'

as follows. /,..

For a chosen value of x 0 , Eq. (1) is solved for \\ l tc il III

,':I jillipir '..C I i 2+/- + 1,+112 M+ I , I call i A=7 I" , ulc l

2. 'rh,-2 Trarirno Values of M and xID are inserted from the characteristics solution, and if the value of xo is good, the same value of A (except only for a small random Ihcrkelcy. T11L co scatter due to mesh-size errors in the characteristics computation) results for all values ofM > 5.5, a value which indicates the threshold of the inertia- inl the +ll lgttl dominated region. If this does not happen at first, xo is adjusted until it does.

UTILIZATION 87 SUPERSONIC FREE JETS-STRUCTURE AND the computer data in The final values in Table I cause Eq. (1) to reproduce maximum deviations being about this region within this random scatter, the

%of M. of the form It is tempting to continue Eq. (1) with a third term D~X0 ) 3 (l data fit, extending and indeed values of C can be found which give an accurate These values are included in upstream to surprisingly small values of x[D.

that the scatter in the computer data Table I, but with the explicit warning TABLE I Y xo/D xo'/D A C ,, 2 XMIn Xmin 3r "

3.26 0.31 2.5D LOD 1.365 1.67 0.075 0.04 0.13 3.65 0.20 6D LOD 1.662 1.40 0.40 3.96 b 4D 1.888 1,2857 0.85 -

fitting formulas give accuracy a For values of x >x,,n, the two-term or three-term within the random scatter of the computer data.

3 b No third term of form C (x -xoID)- (Y-V) seems to fit.

form of precludes any definite conclusion as to the correctness of the analytic we have not even been able to extend our 2-term this last term. In fact, formula in this way, for the case of y = 9/7.

b. Impact Pressure.Since impact pressure is the easiest quantity to obtain experimentally, we give explicit fitting formulas for it in the form 2 (2)

- +o + 1*-(* A xo')

id While in principle the constant xo' should be the same as xo of Eq. (1), we can improve the impact pressure prediction at small x (without harming it at large x) by readjusting xo' as shown in Table I. The resulting formula gives

- % or better prediction of the characteristics data for x/D Z 2.5 for all y.

2, The Transonic Region. Effects of Entry Shape. The assertion made

'h 0 .* above about the weak reliance of the flow in the high supersonic region upon the details of the transonic exit conditions was verified experimentally at lo1i0t, Brkeley. The centerline static pressure was measured with a 0.300-in.-diam

ultb te on the axis of a 3.00-in.-diam nozzle. The nose of the tube was always rtdi - in the stagnation chamber and the static pressure taps were 13 in. aft of the I

FREDERICK S. SHERMAN SI.AP 88 HARRY ASHKENAS AND flow through point s s 'lcictcd support. The tests compared the nose and 14 in. upstream of the a gradually converging lw% c.\ihilNjcd c with that through a thin-plate (-il-a in. thick) orifice throat section. They covered nozzle with a 0.9-ino-long constant-diameter nozzle Reynolds numbers of 7960; M _<4, for the region in which 0.05 _< assumption at deduced with an isentropic flow 2660; and 690. Mach numbers within 1  % for a given geometry, internally :t:

these Reynolds numbers agreed X%iIll ;fillr higher Mach number with trend toward heails- r'alio ;v. ,,

there being a very slight systematic Tlhis 411*11111:i decreasing Reynolds number.

I 6

I

.30 i 0.30 5

dr I lt,, hiCl" r 30/4 t,/2 A (Il...Ic,l*ct :111.11 NOZZLE GEOMETRY 3

x. .Ill itf'lIl.II it !!I THE THIN PLATE ORIFICE EXPERIMENTAL DATA(FROM WAS A SQUARE- EDGED i STATICPRESSURE PROBE) 2 HOLE IN A SHEET OF 690 < Re *-p-u-D/p.L<B2BO THICKNESS t/0O0.021 Io o
  • NOZZLE C . { ,,i .:'tt t 0 THIN PLATE ORIFICE 0-t 0 Q__-00 94 .tII ( id )I iWt 0 _a _ n

-4 X/f

'-.: 1(ii;IrIII centerline Mach number.

FIG. 2. Effect of entry geometry on I~?,lhI lllt II come t gether are compared in Fig. 2. They Results for the two geometries difference for x: D about 1. The small residual very quickly as x/D exceeds and the theoretical result for the two entry shapes

  • I'Ih l'.11.1 I'~l

> 1/2, between the results for assigning to can be effectively removed by t *7lt'~

.i Ii uniform exit flow at M = 1.10, which is slightly snialler diameter," D*, . if" i l

  • the nozzle or orifice an "effective
I ,l and by the uniform flow section assumed for the theory, than the diameter of D*ID = 0.975

slightly upstream. For the nozzle moving the effective source will be discussed later, and xo/D = 0.6. As for the orifice D*/D = 0.943 number, but the values decreasing Reynolds D* may decrease further with of essentially inviscid flow.

are thought to be characteristic cited here III. Sho Region Properties in the Inertia-Dominated B. Angular Variation of Flow and hCnIc behavior of the density field, The approximately self-similar region consists in Pfl' the inertia-dominated the impact pressure field, in 2 for a large number of a function of 0. When pR was computed being only

89 SUPERSONIC FREE JETS-STRUCTURE AND UTILIZATION points selected from the data of the method-of-characteristics calculation, simple formula they exhibited considerable scatter, but could be fitted by the p(R, 0) 2/

(7to3) p(R, 0) = cos*

on specific with an accuracy of about 3 % of p(R, 0). The constant 0 depends heats ratio as shown in Table I.

This formula, and its counterpart p(r, x) = cos2 0 cos2 (4) p(0,x) of aerodynamic are sufficiently accurate for such purposes as the correction 1964; Ko, 1964) drag data for radial variation of dynamic pressure (Tang, region) but the (the speed u is essentially constant in the inertia dominated form is almost certainly not theoretically significant. In suggested analytic 2 is inconsistent with the particular, it gives a value of O2pD0O at 0 = 0 which centerline Mach number distribution given by Eq. (1).

C. Experimental Verification of the Inviscid Theory Some of the earliest quantitative data on free jet structure were obtained by interferometric techniques by Ladenburg et al. (1949). Owen and Thornhill (1948) cited a successful comparison of their theory with impact pressure data of Hartmann and Lazarus (1941). A recent extensive study using impact r pressure and mass flow probes was made by Reis (1962) and a considerable body of data has been accumulated by the present authors and their co-workers.

r Samples or impact pressure data on the jet centerline and in various cross sections normal to the axis are shown in Figs. 3 and 4.

In general, there seems to be no difficulty in obtaining impact pressure data

)r 5 which are in excellent accord with theory if due care is taken to have the 5; 'Probe not too large (thereby incurring probe "displacement" effects) nor 5; too small (necessitating a probe calibration for probe viscous effects), nor too ier, highly yawed.

  • l Shck av

. Shock Wave Configurations in Nearly Inviscid Flow Il.

0or a given specific heats ratio the shape and size of the barrel shock and 7,R; Mach disk are determined by the pressure ratio across the orifice or nozzle.

r of *. Comprehensive photographic study was made by Bier and Schmidt (1961)

e 0 _DIn Po, mm H Q- TUNNEL x 67 0.375 0.35 JPL 0.I 0 104 0.750 04,5 A 400 0.750 1.04 0.5375 5.20 1* 1000 1200 0-750 '3.12

+ 8500 2.035 8.10 1.00 2-7.3 UCB

'* o 14000 LJ U) 0.01 4 40000 v 49000 o 68000 0.50 0.125 0.25 132 760 527

-2.07 I

-i = .

-=0-0.640 )

(n u3 0.001

<)

4 a-I . .. . - I ý - -, i 0.0001 100 10 0/

DIA. xiD AXIAL, DISTANCE FROM ORIFICE/ORIFICE FIG 4Radil M I I - 1 LUUIUII, /= Ili.

Ft<~. 3. Axi~~ irnouct ~ressurc dtnributi~,n y..~~5.

................................... w....

4

SUPERSONIC FREE JETS-STRUCTURE AND UTILIZATION 91 covering a wide range of pressure ratios and a variety of monatomic, diatomic, and triatomic gases. We have checked their results for axial distance to the Mach disk by impact pressure and free-molecule wire techniques and find that xMID = 0. 6 7(po/pl)"12 , (5) independent of the value of y, for 15 < Po/Pi < 17,000. Our data are shown in Fig. 5. The scatter which is evident arises in determinations of the "location" of rather .thick shocks. For these shocks xm represents the point of minimum impact pressure as sketched in Fig. 5.

o000 AIR IMPACT PRESS. UCB ;900 ReD < 47600 O ARGON IMPACT PRESS.

x AIR WIRE TEMP x NITROGEN IMPACT PRESS. JPL 134 Re 0 < 5350 I0 PLENUM CHAMBER I00 PRESSURE/TEST I000 CHAMBER I0000 PRESSURE pR/PI S

FIG. 5. Mach disk location.

A relation of the form of Eq. (4) was predicted by Adamson and Nicholls (1959), who argued that the static pressure behind the Mach disk would be about equal to the test chamber pressure. A similar argument might be advanced for the impact pressure behind the shock, and we indeed find PItlPI to be very nearly independent of po/lp, a fact which is useful in the Planning of experiments in the free jet, and in estimating conditions just upstream of the Mach disk. Our data are shown in Fig. 6.

Bier and Schmidt (1961) also measured the maximum diameter of the barrel shock and the Mach disk diameter as a function of po/Pl. They found, for air, Dm-*,", =0.42 and 0.48 at Po/Pi = 20 and 1000.

Corres g gratios are about 25 % larger for CO 2 (y 917) and about

'2.0% smaller for argon (y z 5/3).

SUPERSOý S. SHERMAN 92 HARRY ASHKENAS AND FREDERICK A. Dissipation Effecta ORIFICE D GAS y

.2.03 2 AiR 7/5 xx 1.8 x 2.03 ARGON 5/3 Thiswere class of, last investigat Xx o 0.250 AIR 7/5 disk, I

AIR 7/5 1.7 A 0.125 model. A result was on sonic flow properl 1.6 use of inviscid theor) 0 A certain small error. Ii bation is due almost it 6- I 1.X 0 depletes the directed 1.4 - energy significantly-The analysis made asymptotic series in i i

p.2ijI AIO t !I-initial condition whi, o0.o000 Mo1000 0 100 1000 ft/Pg radius, slightly largei PESRRATOACR= ORIFICE, With the perfect g.

Fia. 6. Impact pressure behind Mach disk.

tgre, IV. Viscous Effects in Free Jets jet are of four types: can be combined wit Viscous effects in the free produce a the converging nozzle, which can (a) boundary-layer growth on of the flow pattern near the and a distortion change in effective orifice size coefficient with to show that the variation of nozzle discharge orifice. This effect is seen in flow downstream, and is of the scale of the Reynolds number and in a shrinking is more than a few hundred.

Reynolds number generally very smallif the nozzle effect on the the firstsubscript where zero viscous perti growth at the free jet boundary. This has no Reynolds (b) mixing-layer of low With a viscosity-te until, under circumstances flow inside the shock barrel layer begins to overlap with$ the asymptotic result ratio, the mixing number and high pressure the shock barrel and the downstream portions of and eventually to eradicate the Mach disk. bottom of tl I Waves that form the sides and

-2y/(y-(c) thickening of the shock layer, is the MO..

with the growth of the mixing M, ý -

barrel. This, in combination from the tyIP

'of the observed transition prominent qualitative feature effusion, but it presurnabl to free-molecular wbeteA and A are th nearly-inviscid flow pattern of these shocks, as long as any su' the flow upstream does not influence flow exists. fronm in the "core" of the flow, arising (d) viscous dissipation, etc., temperature gradients in that regio i asymptotic r, velocity and S-5/3, at which slight but nonvanishing at points on or near the t4sr Conditic the effects may be of experimental significance These so large the orifice, at Reynolds numbers axis and far downstream from insignificant.

the first three classes of effects are

93 SUPERSONIC FREE JETS-STRUCTURE AND UrmIZATON A. Dissipation Effects In the Core of the Mach This last class of viscous effects, along with the thickening by Sherman (1964) by use of a simple source-flow disk, were investigated number (based model. A result was a prediction of the minimum Reynolds permit the on sonic flow properties and the sonic sphere radius) which would theory to specify the Mach number at a given radius within a use of inviscid that the Mach number pertur-certain small error. In particular, it was found to a small amount of viscous dissipation, which bation is due almost entirely directed kinetic energy only negligibly, but raises the internal depletes the energy significantly-a characteristic hypersonic effect.

in The analysis made use of an "outer" expansion of all flow properties series in inverse integral powers of the Reynolds number, and an asymptotic initial condition which assigned an inviscid value to the velocity at a fixed radius, slightly larger than the sonic radius.

With the perfect gas assumption, the expansion for velocity and tempera-ture, u =Uo + (1/Re)ul + ,

T =To + (l/Re)T, + .. (6) can be combined with one for the Mach number e M =M0[1 + (ml/Re) + .- ,(7) b to show that is (8)

M = (ul/uo) - 1/2(T1 ]To),

le where subscript zero denotes the inviscid approximation and subscript one the first viscous perturbation.

h, With a viscosity-temperature law, z oc T7 with constant 0o,there followed the asymptotic result for large radius,

- 1)/2y* t* 1,*

+-* 1+( )(

het hl P Q; ) (9) aly m, 1 + 2 (y - 1)(1 - (o) r.

Ich where p and A are the viscosity coefficients in the Navier-Stokes relation

.on. U(Ou,1x0 + Oujl/x) + Atdiv u 6,j jet This asymptotic result is accurate for Mo _ 7 for y = 7/5 and MO 10 is quite negligible.

that

  • for Y= these U**nder 5/3, at which values conditions we can contribution the readily show that -m, toism, of uiluo simply proportional

S. SHERMAN HARRY ASHKENAS AND FREDRCICK relation, where (D is the viscous (

This follows from the perfect gas .! expand this in inverse po to the entropy increase of the gas.

dp (00) axis can be represented I dT dS such results, on the axis, T Cl P source flow, and the continuity equation for the simple and pur 2 = const.

at which the integrating to r from a radius r, Combining these equations and entropy is called zero, we get Treating the Prandtl r to a final form, S

In T = (- 1) In u - 2(y - 1) In r + const.

definition of Re, and combining with the CSS, =f 14 V Expanding this in inverse powers of mi, we find (12) mI IS Y-IU ____~lu right is negligible for large r. In this w = d(In p)/d(In in which the second term on the of the involving T can be expr(

over to the free jet itself, by use This same approach can be carried 2 constant. Then we can combine We have integrated E of pur general continuity equation in place and employing the curv (9) and (10) into given by the Ames Resea D(n T) D(S/CI) _ ( _) div u, in Fig. 7a are for stagn.

Dt Dt the centerline Mach nun plenum chamber, It turns out that the the jet axis from a point in the which may be integrated along is expanded in inverse powers ofI near the plane of the ori When the result to the point of observation. grand in Eq. (16). For I:

I Re, we find and the dominant term Y- Ildivuoui cix, (13 the same as the domin, M

ml= S I 2Co ~

j-.idx \uo0 v-divu (u\ 2U2 1 U0 u 0o term represents viscous assume that for tb the lateral stretching o) along the axis, We shall now aymptotic result for m, where u is the scalar speed the contribution of tb Mach numbers) of interest, large values of x (and high is negligible, and thus w on the right, which will be of order u 1/uo, integral 270 -. OU(l use only (v* I + 2 (y MI1 -- I Ot/l-v-,

calculated along the jet axis, if wet The entropy perturbation s$, is readilyall that is needed is the distributiOn In fact, given the inviscid flow field.

MO versus x. reduces to Eq. (15) flow. Here w(

'tarve The basic equation employed is di c 00. For the Sutherh S- SO (~ div'q) -v

SUPERSONIC FREE JETS-STRUCTURE AND UrILIZATION 95 flux vector. We where (D is the viscous dissipation function and q the heat expand this in inverse powers of Re and assume that the inviscid flow near the gives axis can be represented by power series in distance from the axis. This such results, on the axis, as div u, = Mo2 ulao/x, and avo/Or = (Mo" - 1) Duo/Ox (v and r are velocity and position components normal to the axis).

reduce Eq. (15)

Treating the Prandtl number, Pr pcl/k, as constant, we to a final form, 4 2

_____ 1)[((A/- + l)M - M + ] M2 2 (dx) so - 2 + (y- l)M I]

+ _[V 2T jdT\ d (16)

In this to d(ln p)]d(ln T) may be treated as a function of T. The terms involving T can be expressed in terms of M.

3/4, We have integrated Eq. (16) for air, assuming A = 0, y = 7/5, Pr =

and employing the curves for unit Reynolds number versus Mach number, given by the Ames Research Staff (1953), to determine pu/p. The cases shown in Fig. 7a are for stagnation temperatures of 500,. 500' and 1400'F, and use the centerline Mach number distribution for the thin-plate orifice.

It turns out that the heat condition terms are relatively most important near the plane of the orifice, where they actually produce a negative net inte-grand in Eq. (16). For large x, these terms become negligible rather rapidly, and the dominant term in the integrand is the very first one, which is just the same as the dominant term in the simple source flow. Physically, this term represents viscous dissipation arising from the "hoop stresses" due to the lateral stretching of the expanding fluid particles. The corresponding asymptotic result for m, is

+ 1]Al2V/J(y-)]-2.I /y+l ,-tC(+ 1)/2(- 1)1 2y(y - 1)[(A/p)

1) ml + 2(y - 1)(1 - co)

~~1 \ 1 1o+ 2(7-)(l-w)

['*Ix of, x (x D)( (17)

.whichreduces to Eq. (15) when A = (y + 1)/(y - 1)](l+ 1)/4, the value for a sim-iPle source flow. Here we have assumed that co approaches a constant limit as iS) i

  • 0. For the Sutherland viscosity law, which is used in NACA TR 1135,

SUPERSON:

the limiting value of (x - xo/D)2 - ". In prE expanded to very lay

  • this region, and they

_ from the origin to tY 10,/ Sutherland law (i.e., a

/ ,.-to an eventual linear g

/ /very different at large 3

T.283 K T.284 'K SUTHERLAND 4

duction of model tes T.-5 To=

K* 34 "//*/* T.-1032 *K T.-53 K T cII 'K well-based method o To0 32°K // r0-1needed.'

T.-1032 /' The curve for mn(x 100 (a) of the minimum o

/ for given accuracy in

i. given orifice Re. The 19* tion theory, but is inch Mo when m,/Re is only Fig. 7b.

B. Boundary Layer Efi

  • SUTHERLAND FOR TZTC FThe variation of e m 1._2 T J_\*)(7 IX 2(-()Y A investigated experime

. 7v/S, A-3.7 3 (ORIFICE), ,.o, "-4 'K (a) < 2500, with a squar,

_1.0 10oothat the experimental 0o0 probe viscous effects

-6 flow, and for shock with the predictions dependent upon Re.

100 "effects of larger mag seen in the flows fror authors, this constitu V. formation, since this Ki. nRe nl/Re*sOOI effeCts to the lowest p C. Thickening of Sho(

- LAW *K~UNEAR FOR O"K<u4< Little can be said I 02'-1 j LAWO*r' ........ ,oRT ' to . Idng-layer thickeni Re*=, = -IlItou'llI reporled in t Pe-W for low tempq Fo. 7.(a) mach number perturbation in air. 'b) Mach numberReynotds l relations in air, po.P'.

7u

SUPERSONIC FREE JETS-STRUCTURE AND UTILIZATION 97 the limiting value of a) is 3/2, and m1 eventually grows in proportion to (x - xo/D)2l. In practice, wind tunnel workers having to deal with flows expanded to very low temperatures often disregard the Sutherland law in this region, and they extrapolate viscosity data along a line p oc T (w= 1),

from the origin to the point of tangency with a linear p - T plot of the Sutherland law (i.e., at about T = 114'K for air). This procedure would lead to an eventual linear growth ofm, with x, and results which are quantitatively V, very different at large x, as seen in Fig. 7a. In this calculation, as in the re-duction of model test data obtained in high Mach number free jets, some well-based method of viscosity prediction for low temperatures is sorely needed. 2 The curve for ml(x) can be employed for two types of useful predictions, (a) of the minimum orifice Re required if the inviscid theory is to be trusted for given accuracy in M, and (b) the maximum M which can be obtained at a given orifice Re. The latter prediction strains one's faith in a small perturba-tion theory, but is included because the calculations show that M,,is attained when m1 /Re is only about 0.2 to 0.3. Some results are shown for air in Fig. 7b.

B. Boundary Layer Effects in the Entry Section The variation of effective orifice diameter with Reynolds number was investigated experimentally at the Jet Propulsion Laboratory for 13 < Re

< 2500, with a square-edged orifice of thickness t = 0.0266D. It was found that the experimental axial impact-pressure distribution, when corrected for probe viscous effects by calibration factors determined in a uniform nozzle flow, and for shock displacement effect, could be brought into agreement with the predictions of inviscid flow theory by the assumption of a D*ID dependent upon Re. The results are presented graphically in Fig. 8. Similar effects of larger magnitude and qualitatively different Re-dependence are seen in the flows from gradually converging nozzles. In the opinion of the authors, this constitutes an advantage of the thin-plate orifice for free jet formation, since this geometry postpones the onset of one class of viscous effects to the lowest possible Reynolds number.

C. Thickening of Shock Waves and Mixing Layer Little can be said theoretically about the dramatic process of shock and mixing-layer thickening, and the interaction between them as Reynolds 2Results reported in this volume by Anderson, Andres, Fenn, and Maise indicate a value . =i for low temperature argon.

SUPERSONIC I FREDERICK S. SHERMAN 98 HARRY ASHKENAS AND 0,epral&,o?.d?

0 0

a 0.9ý 0 C3 0 8

D=0.446" LONG-NOZZLE; ARC LENGTHW2.2,"

0.1 0

P/D=O.O3, D0'.749' A SOUARE-EOGE. ORiFICE; SOUARE-EDGEDORMFICE; t/O'.027,ODO.375" z 0

I ý . . I . .

I . , , . ' .

ý I I ., II I 1000 10,000 a.T . I 00 10 0 0 ReOD H

0 "

diameter.

FiG. 8. Effective orifice to impact pressure decreases. Experimental evidence to date is limited 00 number studies. 61 surveys and flow visualization "dip" which we exhibit a broadening of the 0"

pressure surveys Axial impact entry into this dip is very disk. Since the upstream -J associate with the Mach of the Mach disk detect the upstream beginnings smooth it is very hard to impact pressure data. for air at x/D = 6 and fromRadial impact pressure surveys taken at JPL The ordinate is direct.

shown for a wide range of Re in Fig. 9.

Polp, = 100 are viscous, or yaw effects.)

output, uncorrected for probe, pressure transducer flow outside the.

associated with the recompressed The peak impact pressure as Re decreases, and the' to.the centerline pressure shock barrel falls relative as they are consumed by the peaks move slightly toward the axis vapo.

residual sodium of this. process, using the mixing layer. Visual observations gas flows by Vali anl suggested for rarefied resonant-scattering technique been made at Berkeley.

Thomas (1962), have also dimensionl by Bier and Hagena (1963), an appropriate ba As suggested and its neighboring of the Mach disk criterion for the disappearance the approach toward unity of a Knud entities is shock as recognizable path behind the Ma..

on Mach disk diameter and mean free number based to that of the gas in path is very nearly equal disk. The latter mean free To. When we take the invi p, and temperature test chamber, with pressure to the measured P01l ()H suo.

disk diameter corresponding flow value for Mach "test chamber mean a KM, with it and the and form a Knudsen number,

S,* , 0 .

cb = ~ C 0 0 ~

G..-.

RADIAL PITOT PRESSURE DISTRIBUTIONS x/1 =6.0 p./p, =1OO 150 4

-Re0 =1170

  • Z 125 C

E Z 100 0

w w 75-I--

0

  • - 50 N, a-N U.Z 10.5 RADIAL DISTANCE FROM JET AXIS, in.

FiG. 9. Radial pitot pressure distributions.

'.0

FREDERICK S. SHERMAN SJPERSONI(

100 HARRY ASHKENAS AND survey just ahead pressure peaks of the radial path," we find that the impact by the Mach

= 0.1, and the last recompression of the Mach disk vanish at KM technique,, vanishes at KM = 0.3.

disk, visible by the sodium-scattering V. Application of Free Jets A. Attainable Jet Size The distance xM turns out, under measure of the volumetric capacity the pumps will handle a mass as Wind Tunnel Streams reasonable assumptions, to of the wind tunnel pumping flow rate ?h at a suction is pressure To. Then be a simple plant.

equal Suppose to the I

stagnation temperature Fic test chamber pressure Pl. The XM 0.75 -- i- Berkeley No. 4 wind tv xm turns out to atmosphere, T. = 3000) at the University of California, Propulsion Laboratory For the No. 4 Wind Tunnel of the (m vs. Pl) being due to the nonlinearity Actually, this view oi be 11 to 14 in., the variation tunnel Laboratory low density wind of if rh/ll, is small. An pump curve. For the Jet Propulsion accurate if po/p>i >15 and above is quite desire to have negligibhi xM is about 6 in. The relationship nozzle throat is only a small fraction The viscous flow an; in the if the boundary layer thickness Fig. 10 curves for m,/I of the nozzle radius.

is used, a curve results Number Ranges nearly inviscid flow atf B. Available Mach and Reynolds The criterion K*, = (

is Mach and Reynolds number range picture in the vicinity ol The roughest outline of available J corresponding by fixing To and then determining the boundaries (b) to a maximum plenumj of the relation of jet d (a) to a minimum test chamber pressure, pi,,,,. and obtained to a fixed value of P, just upstream we fix attention on conditions 15.3 in., p. - 0.0038 t, chamber pressure, Po,..*.Then Simple argumenatsi desirable test region. able with the steam eje, of the Mach disk, which is the most to core, lead Within the available ran assuming isentropic flow in the

-) The high pressure limi 1.35p,(

ReM because of the possibili M(T Currently investigating t (a) L 2 RTo) 112 (T _*- ) A*To) any condensation effects

'h2e STP conditions to a M(T)Ili(To) = (TITo 0) In this volume makes a for which we have assumed C. Effect of Stagnation f M

(b)

It may be desirable t Static temperature!

of Califol in Fig. 10 for the University These boundaries are sketched

SUPERSONIC FREE JETS-STRUCTURE AND UTILIZATION 101 IOO FREE JET OPERATIONSr0=t55 , ROA AT

./at" OPERATING RANGE SUC.p1 .6Omnicro DESIGNPOINTSOF CONVENTIONAL NOZZLES (UCB)

RelL, (in00 Fio. 10. Free jet operations; To =535°R.

Berkeley No. 4 wind tunnel, for which we take p,_ = 0.060 torr, Po,... = I atmosphere, To = 300'K, and consider air to have co =3/4, and for the Jet Propulsion Laboratory Leg 1 tunnel, p,_,. = 0.002 torr.

Actually, this view of things may be quite oversimplified if P, is very low, of if th/p1 is small. Another low-pressure boundary criterion is set by the desire to have negligible viscous effects in the core of the jet.

The viscous flow analysis of Section III has been applied to draw into Fig. 10 curves for m,/Re. = 0.05, again with co = 1. If the Sutherland law is used, a curve results for this boundary, which improves the prospects for nearly inviscid flow at high M.

The criterion KM = 0.1, indicating the total collapse of the inviscid flow picture in the vicinity of the Mach disk, is also indicated in Fig. 10. By virtue of the relation of jet dimensions to pumping speed, this criterion reduces to a fixed value of p, for a given pumping plant. For Berkeley, with Dm 5.3 in., p, = 0.0038 torr, an order of magnitude lower than the p, attain-able with the steam ejectors. For JPL, DM = 2.9 in., p, = 0.0069 torr, well within the available range.

The high pressure limit (po_. = 1 atmosphere) may also be too approximate, because of the possibility of condensation of the air components. We are Currently investigating this experimentally, and have been unable to isolate any condensation effects on impact pressure data, even when expanding from the STP conditions to a Mach number of 22! (The paper of Bier and Hagena in this volume makes a major contribution on this point.)

C. Effect of Stagnation Heating It may be desirable to increase To to avoid condensation, and to bring loCal static temperatures up to values at which the viscosity may be reliably

S. SHERMAN SUPERM 102 HARRY ASHKENAS AND FREDERICK which may be of collateral consequences, estimated. This has a number of To, and take co = 4.

rihp 1 is independent estimated if we assume that to a considerable oversimplification.

The latter assumption leads 14 fixed Po/,l or Mm.

(a) D increases as T, for To(y - 1)/4 for fixed D.

(b) MM increases as as To 114 for fixed MM, RemIL.

(c) M/Re. decreases a 1 2

)- for fixed P, and MM.

(d) ReM/L decreases as ToO a j

T;01/2)-o for fixed p, and M,. 4 (e) Rem!L decreases as I - U C

4 Evaluation in Viscous and 2

a VI. Techniques of Experimental w I-. *(~

C'~

More Rarefied Regimes

~(

w -

jet structure in the C, 0 experimental picture of free At the present date even the N 2 effects are at first 00 U.

clear, because the viscous -o highly viscous regime is not such as static temperature those flow properties, rather subtle, influencing only to measure.

and pressure, which are hardest A. Impact Pressure Measurements hypersonic flow in use of the impact tube in The key point to recognize and T. Hence a viscous 2 independent of M is that p ;e pu quite accurately affects p or u will not be easily T but hardly effect which greatly increases of M and T on the except through the influence seen in impact pressure data, on probe readings.

viscous or molecular flow effects Re made of the latter effects in ihe extended range of M and The evaluation been extensively major task in itself, which has available by the free jet is a Laboratory. Measurements were made undertaken at the Jet Propulsion an unbonded-in conjunction with pitot tubes using externally chamfered the tubes used pressure transducer. The geometry of strain-gage-diaphragm was similar, viz.

(a) 100 external chamfer 1.25 (b) Ratio of O.D. to I.D. =

of length to outside radius = 100.

(c) Ratio number fiol to the low density, high Mach Pitot tube corrections applicable in the jet were deduced as follows: 10.

(1962) (obtained in a conventional The pitot tube data of Ashkenas starting point for a boot-stra.

were used as a density nozzle flow at M = 4) regiO.

three geometrically similar pitot tubes; the small procedure using covered with these t

< 4.5 was systematically the free jet between 3.5 <M (0v301) 3anss from 0.1 to 7.0 mm 149g.

ranging pitot tubes at stagnation pressures

-J 4

0 w

U, U,

4 0

a-I-

0 I-0.

0

4 U,

4

4
4 U,

U,

4 a-I-

0 a.

N i0-1 4 6 too 2 4 6 10' 2 a REYNOLDS NUMBER BEHIND NORMAL SHOCK (BASED ON PITOT-TUBE DIAMETER), Re 2 ,,

0-Fio. 11. Pitot tube corrections. L.J

SUPERSONIC S. SHERMAN 104 HARRY ASHKENAS AND FREDERICK

.nearly inviscid flow conc was found to the corrected pitot tube data impact pressure determined from over the entire pressure effects arises with pum Thornhill values, be within 2% of the Owen and for the axial impact pressure lower operating pressure solution range, and thus the characteristics The pitot tube but it appears likely thi the flow conditions studied.

distribution is assumed valid for Mach numbers available understood.

the entire range of may then be calibrated over are shown in The inviscid theory o tube correction curves obtained in this manner expressed by simple for in the jet. Pitot Mach numbers; were obtained for integer Fig. 11. Note that these curves data for noninteger slightly viscous flow sees was used in reducing linear interpolation between curves by For implementation (

It will be noted in Fig. 11 that the pressures sensed experimental data at vet Mach numbers. calculated from as 300% of the ideal value the pitot tube can range as high viscosity at very low terr the Rayleigh pitot tube formula. Conclusive experimenl involve direct measuren B. Molecular Beam Methods quantities as static pre involves methods look promising to the free-jet diagnostic problem A powerful, but subtle, approach flow and the determination of the perfection of the bea from the jet the skimming of molecular beams Bier and Hagena beam, as has been done by the velocity distribution of the be perfect, however, that the "skimming" process (1963). It is imperative, of the distribution function, and it is in the sense of causing no perturbation of known has been obtained exceptin a flow Adamson. T. C., and Nichol(

hard to prove that a perfect skim iterative improvements Ames Rescarch, Staff (1953), 1 procedure, involving properties. A careful boot-strap seems Ashkenas, IF. (1962), JPL Cal of the flow properties and the skimmer operation, Bier, K., and Hagena, 0. (19 in knowledge pp. 478-496. Academic Prec indicated.' Bier, K., and Schmidt, B. (19e Fenn, J. B., and Deckers, j.

C. Electron Beam Methods Vol, 1, pp. 497-515. Acadeg by Hartmann, J., and Lazarus, F to obtain the local static temperature Another attractive possibility, beam (Muntz, Ko, D. (1964), Univ. Calif. Ai spectra of N, by an electron Ladenburg. R., Van Voorhis, the excitation of rotational band results at Berkeley by F. Robben. His preliminary Love, E. S.. Grigsby, C. E., L 1961) is being explored theory for the. Maslach, G. j., Willis, D. R.,

of an elaboration of Muntz's seem to indicate the necessity can be successfully Muntz, E. P. (1961). UTIA Rt Whether this excitation and de-excitation processes. Owen, P. L., and Thornhill C achieved remains to be seen. Res, V. H. (1962). Princeton I SecOt, J. E., Jr., and Drewry, ed.), Vol. 1, pp. 516-538. Ac Slherman,. F. S. (1963a). I, "

VII. Conclusions 228-260. Acadcmic Press, N jets be seriot *ltenma 1 , F. S. (19636). Lockh study, the proposal that free 6m"an, After two years of further wind tunnel stream seeMfl F. S. (1964) Arc.

it of low density considered as an alternative type of the Mach and ReYn0

!.4, S. (1964). Univ Calif. At a,.W., and Thomas G. M.

extensions be substantiated. Truly impressive Berkeley can be obtained, wl '3fn, F. (1962). Z. Na.'prforjc such as that at number ranges of a tunnel volume, by And is reported elsewhere in this Significant progress in this direction Andres, Fenn, and Maise.

SUPERSONIC FREE JETS-STRUCTURE AND UTILIZATION 105 nearly inviscid flow conditions are maintained. A greater concern with viscous effects arises with pumping systems with lower mass flow capacities and lower operating pressure levels, such as that at the Jet Propulsion Laboratory, but it appears likely that the resulting flows will be very useful when fully understood.

The inviscid theory of free jets is in good shape and can be conveniently expressed by simple formulas in the region where M Z 5.5. The theory of slightly viscous flow seems reasonable, but is experimentally unconfirmed.

For implementation of the viscous flow theory and for the reduction of experimental data at very high Mach numbers, better means for estimating viscosity at very low temperatures are urgently required.

Conclusive experimental evidence concerning viscous effects in the jet must involve direct measurement of the Mach number or of such inaccessible quantities as static pressure or temperature. Molecular beam sampling methods look promising, but must be accompanied by conclusive proof of the perfection of the beam-skimming process.

REFERENCES Adanmson, T. C., and Nicholls, J. A. (1959). J. Aerospace Sci. 26, 16.

Ames Research Staff (1953). NACA Tech. Rept. 1135.

Ashkenas, H. (1962). JPL CalTech Space Programs Summary 37-15, Vol. 4.

Bier, K., and Hagena, 0. (1963). In "Rarefied Gas Dynamics" (J. Laurmann, ed.), Vol. 1, pp. 478-496. Academic Press, New York.

Bier, K., and Schmidt, B. (1961). Z. Angew. Phys. 13, 493.

Fenn, J. B., and Deckers, J. (1963). In "Rarefied Gas Dynamics" (J. Laurmann, ed.),

Vol. I, pp. 497-515. Academic Press, New York.

Hartmann, J., and Lazarus, F. (1941). Phil. Mag. 31, 35.

Ku, D. (1964). Univ. Calif. Aero. Sci. Proj. Rept. AS-64-4.

Ladenburg, R., Van Voorhis, C. C., and Winckler, J. (1949). Phys. Rev. 76, 662.

Love, E. S., Grigsby, C. E., Lee, L. P., and Woodling, M.J. (1959). NASA TR-R-6.

Mmslach, G. J., Willis, D. R., Tang, S., and Ko, D. (1964). These Proceedings.

Muntz, E. P. (1961). UTIA Rept. 71.

Owen. P. L., and Thornhill, C. K. (1948). Aero. Res. Council R & M 2616, Great Britain.

Reis, V. H. (1962). Princeton Univ. Mech. Eng. Dept. Rept. FLD-7.

Scott, J. E., Jr., and Drewry, J. E. (1963). In "Rarefied Gas Dynamics" (J. Laurmann, I]

cd.). Vol. 1, pp. 516-538. Academic Press, New York.

Sherman, F. S. (1963a). In "Rarefied Gas Dynamics" (Q. Laurmann, ed.), Vol. 2, pp.

228-260. Academic Press, New York.

y Sherman, F. S. (1963b). Lockheed Missiles and Space Co. Rept. 6-90-63-61.

Sherman, F. S. (1964). Arch. MVech. Stos. 16, 471.

Tang, S. (1964). Univ Calif. Aero Sci. Proj. Rept. AS-64-3.

Vali, W., and Thomas, G. M. (1962). ARS (Am. Rocket Soc.) J. 32, 1114.

Zigan, F. (1962). Z. Naturforsch. 17a, 772.

Shock Waves (2005) 14(4): 259-272 DOI 10.1007/s00193-005-0270-9 I A S. I. Kim

  • S. 0. Park Oscillatory behavior of supersonic impinging jet flows Received: 20 July 2004 / Accepted: 17 June 2005 / Published online: 18 October 2005

© Springer-Verlag 2005 Abstract Oscillatory flows of a choked underexpanded su- it contains both supersonic and subsonic flow regions, and personic impinging jet issuing from a convergent noz- involves interaction of shock and expansion waves with jet zle have been computed using the axisymmetric unsteady shear layers. An important problem in a supersonic imping-Navier-Stokes system. This paper focuses on the oscillatory ing jet flowfield is that the jet of very high temperature and flow features associated with the variation of the nozzle-to- speed leads to a severe thermal and mechanical loading on plate distance and nozzle pressure ratio. Frequencies of the the impinging plate. The supersonic impinging jet becomes surface pressure oscillation and flow structural changes from oscillatory under certain operating conditions after the ini-computational results have been analyzed. Staging behavior tial transient impinging behavior. The unsteady oscillation of the oscillation frequency has been observed for both cases can make thermal and mechanical loading more severe. An of nozzle-to-plate distance variation and pressure ratio vari- oscillatory supersonic impinging jet produces severe noise ation. However, the staging behavior for each case exhibits at discrete frequencies, which may cause sonic fatigue of different features. These two distinct staging behaviors of the structures and also may damage various instruments and the oscillation frequency are found to correlate well if the equipment in the vehicle.

frequency and the distance are normalized by the length of Earlier researchers [1-5] have investigated the flow the shock cell. It is further found that the staging behavior structure and the mean flow characteristics of the super-is strongly correlated with the change of the pressure wave sonic impinging jet flow by using Schilieren photography pattern in the jet shear layer, but not with the shock cell and mean surface pressure and temperature measurements.

structure. These earlier studies disclosed many significant features of the flow including surface pressure and temperature distri-Keywords Self-sustained oscillation

  • Supersonic butions. However, the data available in the earlier reports impinging jet
  • Staging behavior
  • Underexpanded jet.

are mostly limited to mean flow properties. A more detailed Plate shock review of these studies can be found in Alvi and Iyer [6].

PACS 02.60.Cb; 47.40.-x; 47.40.Nm; 47.35.+1; 4 7.15.-x Subsequent works have focused on unsteady flow oscillations and acoustic properties. One of the primary outcomes of these studies is that the highly unsteady oscillatory nature of impinging jet, which is accompanied 1 Introduction by discrete, high-amplitude acoustic tones referred to as im-pingement tones, is caused by a feedback loop. Krothapalli A supersonic jet impinging onto a flat plate is a fundamen- [7], Powell [8], and Tam and Ahuja [9] identified a feedback tal flow often encountered in space or missile launch vehicle mechanism for self-sustained oscillations of the impinging systems and supersonic STOVL aircraft. The flow is of prac- jet flows. The energy of the feedback loop is provided by the tical significance, since it may undermine safe operations. In instability waves in the shear layer of the jet. Flow visual-spite of the simple geometry, the flowfield is rather complex; ization studies show that the shear layer contains large-scale vortical structures. Upon interacting with the impinging Communicated by K. Takayama surface, the downstream traveling coherent structures of the jet generate strong pressure fluctuations near the impinge-S. I. Kim -S. 0. Park (lE ment region that lead to acoustic waves (intense acoustic Department of Aerospace Engineering Korea Advanced Institute of Science and Technology disturbances) in the near sound field. These acoustic waves 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea propagate upstream through the ambient medium and, upon E-mail: sopark@kaist.ac.kr reaching the nozzle exit, excite the flow instability waves

260 S. I. Kim, S. 0. Park (or periodic structures) of the shear layer of the jet. This instability usually generates large-scale vortical structures in the shear layer. These coherent structures grow as they propagate downstream. The downstream traveling vortical structures and the upstream propagating acoustic waves form the feedback loop.

It has been reported that the frequency of the imping- F 0 ing tone exhibits staging behavior as the nozzle-to-plate 'rxr -- 2r ReM-£ 1,-L distance varies [7, 8]. Krothapalli [7] obtained the near 3_

3x, Ox 2r)

Gv sound field microphone signal and surface pressure signal " r r60 o -Re-, 3 (14r) 3* , r (A r

at several moderate pressure ratios for a choked underex-panded impinging jet issuing from a rectangular nozzle. Utxr + V'rr - qr --

It was found that the frequencies of the dominant peak in both the sound and pressure signals coincide. Sakakibara The variables are normalized by the nozzle exit prop-and Iwamoto [10] carried out laminar Navier-Stokes erties. Length is normalized by the nozzle exit diameter, computations of convergent nozzle impinging jet flows D, density by Pe, velocity by the speed of sound, Ce, for various nozzle-to-plate distances. They found that temperature by Te, pressure by peCý2, time by D/Ce, and the flow oscillates when the nozzle-to-plate distance was viscosity by ge. We assume that the gas is perfect so that greater than 2.3 times the exit diameter of the convergent p = pT/y. (2) nozzle, and also showed that the frequency of the surface pressure oscillation exhibited staging behavior. Discrepan-The stress terms are cies between the frequencies of the impinging tone from measurement and of the surface pressure from their com-putation were identified, these being attributed to the grid

  • = Mo. 2-e /"12ox- -uav 57, Re. 3' Ox Or/

problem.

The present study is concerned with the surface pressure Moo2 aOu Orv oscillation and the oscillatory flow structural changes of tr,-R A-Il +21, Re,,, 3 Ox Or]

axisymmetric supersonic jets from a converging choked nozzle at moderate nozzle pressure ratios. More specifically, M ,2 ( au aO *)

we will focus on the staging behavior of pressure oscilla- 3Re,, Ox Or r tions for various conditions. For a given pressure ratio, we M~o fOu Ovr\

change the nozzle-to-plate distance and the pressure ratio T:xr =Trx = R"'-olZ Ir 4-+-X for a given nozzle-to-plate distance. We then show how Re,, Or ax) the staging behavior for these two different cases can be 2 correlated. 2 Mm v 2 Mm0 a' v2 T --- .+ -r-- u -

3 Reow r 3 Re air- r 2 Mo 0 /UV\

2 Numerical approaches (3) 3 Re,,, x r 2.1 Numerical scheme and the heat flux terms are We consider a laminar compressible flowfield governed by Mo ,I 07A the following equations written in a cylindrical coordinate Re~o Pr(y - 1) Ox (x, r) system: MW AL OT

=-Reoo Pr(y - 1) Or" (4)

OQ OE OF OE, OF, Ot + Ox + Or + G Ox + Or + G, (1) The molecular viscosity is calculated using Sutherland's law:

pu E= pu2 4- p Q E 3 TT /

2 l + 110.4/Te,' (5)

T + 110.4/Te "

pet (pet + p)u The Modified Low-Diffusion Flux-Splitting Scheme pv pv (MLDFSS), adopted in Lee and Park [11], is used to F [ pv G= pvI evaluate the inviscid fluxes on the cell surfaces. Central dif-ference is used to calculate viscous terms. For time accurate calculations, we adopt the subiteration time advance scheme L(pet + p)v._ L(pet + p)v- of Pulliam [12], which is formulated as

Oscillatory behavior of supersonic impinging jet flows 261 Free boundary N N

N N

Nozzle N 0.9 Region A N

N N 0.7 Nozzle N exit -IDI2=Renter line N N 0, Flow H

Fig. 1 Computational flow model and boundary conditions 7-t1

[i +tý

_a (aR(QP))] (Q+1 _QP) 1+p I

Fig. 2 Surface pressure time histories at the center of the plate for various grids, H/D = 2.8 and PO/Pa 3.0 x (l -Qnl 1+ Q`l] (6) are run under the operating condition of Po/Pa = 3.0 (Po is where QP and QP+l are the solutions of subiteration level, the stagnation chamber pressure) and HID = 2.8. Surface and Q" and Qf-l are the solutions of previous time levels.

pressure oscillations at several radial locations, the ampli-The solution at time level n + I is given by the converged tude of the pressure oscillation, and the shock cell structures solution QP+l. In this study, we take 6 = 1 and ýo = 1/2, are compared for the four different grid systems. The four which gives the three point backward implicit scheme grids are (1) 101(x) x 51(r); AXmin = Armin = 0.01D, to result in the second-order accuracy in time. For the (2) 181(x) x 61(r); AXmin = Armin = 0.001D, (3) 301(x) calculation of Jacobian matrices, R/BaQ, in the implicit part (left-hand side) of (6), we use Steger-Warming's flux x 65(r); Axmin = Armin = 0.001D, (4) 351(x) x 65(r);

AXmin = Ar in = 0.0001D in the jet plume and impinge-vector splitting scheme for inviscid fluxes, and retain only ment region (Region A of H(x) x R(r) in Fig. I). The non-mixed derivative terms for viscous fluxes. To solve pressure histories are recorded at r/D = 0.0, 0.5 and 1.0 the discretized equations, we adopt the point symmetric Gauss-Seidel (point SGS) scheme. for all the test cases. The computation is carried out until about 200D/ Ve (Ve is the nozzle exit velocity, Ve = Ce ). A self-sustained oscillatory state is found to be reached after t , t00D/ Ve. Beyond this time, the frequency of oscilla-2.2 Grid and time step refinement tions becomes a constant value. Figure 2 shows an example of the predicted surface pressure history at r/D = 0.0 for We consider axisymmetric supersonic impinging jet flows various grids. For these four grids, the maximum surface driven by the sonic flow of a convergent nozzle as sketched pressures at r/D = 0.0 are 0.981 P0 , 1.161P 0 , 1.277P 0 , and in Fig. 1. The nozzle exit diameter D is 10 mm. The ambient 1.292 P0 . The surface pressure variation for grid 1 converged air temperature Ta and the static pressure Pa are 288.15 K to a steady value eventually, while the results of the other and I atm, respectively. In the present computation, we grids exhibit a self-sustained oscillation. The pressure assume that the choked sonic flow condition is achieved at amplitudes of oscillation for grids 2, 3, and 4 are 0.240P 0 ,

the nozzle. Thus, the inlet boundary of this computation 0.191P 0 , and 0.199Po, respectively. It is seen that the is the nozzle exit where the pressure, the velocity and the discrepancy between these values is reduced as the grid is temperature are fixed from the isentropic relations. No slip refined. Further, the pressure histories of the grids 3 and 4 are and adiabatic wall boundary conditions have been used for almost the same. We thus conclude that the grid 3 system is the nozzle wall and the impinging plate. The first-order ex- capable of capturing the oscillatory features of the flow and trapolation is applied on the far field free boundary, which is the resolution must be sufficient, and hence is used through-located at 20 times the nozzle exit diameter from the jet axis. out the present calculations. We recall here that Sakakibara A multi-block system of structured grids is used. Grid and Iwamoto [101 used the grid of Axmin 2 0.01D and points are clustered near the wall and the jet plume region. Armin

  • 0.0ID. Hence, the present grid system is far denser Tests are conducted to select a suitable grid, which can cap- than theirs. Choice of the time step is an important factor in ture the salient features of flow oscillation. Grid test cases unsteady flow analysis. We have tested two different time

262 S. I. Kim, S. 0. Park A G

/A

/

/

/

/

/

/ E B C D

E F t (as) a Fig. 3 The computational domain of circular pulse jets steps: Atl = O.003D/Ve and At 2 = O.O005D/Ve. These two time steps correspond approximately to 0.0017 and 0.0003 times the pressure oscillation period. By scrutinizing the pressure oscillation patterns including the amplitude and the time period of the oscillation, we have found that Atl is sufficient for unsteady analysis. E 2.3 Validation 2-A Exp. (Ishil el al.)

The use of the present code in predicting unsteady flowfield -- Num. (Ishil et al.)

is validated against the unsteady circular pulse jet of Ishii 1 Present et al. [1.3]. In this circular pulse jet, air is accelerated by a shock in a shock tube with a constant circular cross-section C I I r I I I I I and exhausted from the open end into a test chamber. The 0 100 200 300 jet strength was controlled by one parameter P4 /PI, where t (Vis)

P1 and P4 were initial gas pressures in the low-pressure b and high-pressure chambers, respectively. The computa- Fig. 4 Comparison with experimental data. (a) The diameter, DM and tional domain is shown in Fig. 3. We employ a 600 x 400 (b) the axial distance, XM of the unsteady Mach disk grid system in axial and radial directions with the uniform mesh size of Ax = Ay = 0.025. On the outer boundary AG and the downstream boundary FG, the ambient gas condi-tion is applied: (P, p, u, v) = (PI, Pl, 0, 0), where the sub- supersonic impinging jet flow with those of the impinging script 1 denotes the ambient value. On the solid walls AB, tone from the measurement. For the purpose of comparison, BC, CD, we apply no slip condition and on the jet axis EF, the present calculation is done using the same operating con-the symmetric condition. On the upstream boundary DE, the dition of Sakakibara and Iwamoto, where the diameter of the shock condition (P, p, u, v) = (PE, PE, uE, 0) is applied, convergent nozzle is 10 mm, and the nozzle pressure ratio is where the quantities denoted by the subscript E are obtained Po/ Pa = 3.0. The first task of the present analysis is to make through the Rankine-Hugoniot relations for a specified sure that a self-sustained oscillation is indeed achieved. This shock Mach number. In accordance with the experiment, the is done by extending the computation time to over 300D/ Ve.

length BC and CD were set to be equal to the duct radius DE Figure 5a gives a time history of pressure variation on the

(=I cm). In the present validation experiment, we calculate surface of the impinging plate. The flow is seen to have two cases: P4 /P1 = 25 (PE/PI = 3.61) and P4 /P1 = 50 reached a self-sustained oscillatory state after a transient (PE/PI = 5.00). We compare the time change of the diam- period of about IOOD/ Ve. The frequencies of the surface eter DM and the axial distance XM of the Mach disks from pressure oscillations from the present computation are the duct exit as shown in Fig. 4a and b. The present results shown in Fig. 6. Figure 6 shows that the frequencies of the are found to be in good agreement with those of Ishii et al. surface pressure oscillation of the present computation are Sakakibara and Iwamoto [10] compared the frequencies in good accord with the impinging tones of the experimental of the surface pressure from their computation of the measurements.

Oscillatory behavior of supersonic impinging jet flows 263 Oscillatory behavior of supersonic impinging jet flows 263 1.4 40 1 1I 1 1 35 P Present (P./P,=3.0) 1.2 Sakaklbara &Iwamoto (1998, PWP,=3.0)

Powell (1988, PJP,=2.70) 30 USF- 0 Powell (1988, PP,=3.04)

S.8 N25-3o "--*i* _________ _

r=O.> teStage V Vl 0- 0.6 o20 *_Stage

0. a) Stage IV 4 )~

LL 0 0 15 0.2 r= I.OD 0 25 50 75 100 125 150 Time, t V /D a10 . . . . . .. .. . . . . .

2 25 3 3.5 4 103 ... H /D 1O' Fig. 6 Frequencies of the pressure oscillation and the impinging tones versus distance (USF stands for upper secondary frequency) 10 (HID 2.0-4.0) with the nozzle pressure ratio fixed at E P0/Pa = 3.0. In this case, the nozzle chamber pressure Mio" I and the nozzle exit pressure are 3.0 and 1.585 times larger than the ambient pressure, respectively. Thus, the jet is in an underexpanded condition. The jet issuing from the o 10-1 nozzle exit undergoes expansion and compression cycles repeatedly. The shock cell structures of the expansion fan 10' and compression shock are disturbed by the impingement and hence exhibit periodic structural changes accompanying 10 pressure oscillation.

To characterize the oscillatory behavior of the flow, 10 20000 40000 60000 80000 1OOOOQ power spectra of the surface pressures have been calculated Frequency, Hz (Fig. 5b). The frequency of the pressure oscillation was b

Fig. 5 (a) Surface pressure histories at riD = 0.0 and 1.0; (b) power 0.6 0.9 spectrum of pressure signal at rID = 0.0, HID = 2.5, and Io/Po =

3.0 0.5 0 AP/Po 0.8 3 Results and discussion 0.4 0.7 0.3 - 0.

For impinging supersonic jet flows, important operating II parameters that affect the flow characteristic are the nozzle a?, 0.2 -- -A-

  • 0.5 0 pressure ratio (NPR = Po/P5 ) and the distance from the - Stge A nozzle exit to the impinging plate (H). Therefore, the os- "1 0.1 - sttage V1--0.4 cillatory features of surface pressure and the flow structural Stae IV Ao changes of the impinging jet flows are investigated by Ao.1 varying these two operating conditions. -0.A*
  • 0.2

-0.21 *0.2 3.1 Impinging jet flow oscillation: A effect of nozzle-to-plate distance -03 2 2.5 3 3.5 .... 4 First, we examine the oscillatory behavior of the flow HID byFvarying the dane fthe nscillatozzlbeha tofr thepla Fig. 7 The amplitudes of the surface pressure and the plate shock os-by varying the distance from the nozzle to the plate (H) cillations, Po/P. = 3.0 (AP is the amplitude of the pressure oscilla-for a given pressure ratio. The nozzle-to-plate distance tion at r/D = 0.0, AX, is the amplitude of the plate shock oscillation is varied from 2.0 to 4.0 times the nozzle exit diameter along the jet axis)

264 S. I. Kim, S. 0. Park a.*

a.

a a- a.

c d Fig. 8 Variation of pressure distribution along thejet axis, Po/P. = 3.0. (a) HID = 2.5 in Stage IV; (b) HID = 2.8 in Stage V; (c) HID = 3.6 in Stage V; (d) HID = 4.0 in Stage VI (T is the pressure oscillation period) obtained through the FFT analysis of the time series of the the nozzle-to-plate distance. Thus, within a specific range surface pressure (using 4096 data, the sampling rate is about of each stage the frequency of oscillation decreases as the 0.03D/Ve 2 0.84kts). The frequencies of the pressure distance increases. In the present computation, three stages oscillations at the center (r/D = 0.0) of the plate for various labeled IV-VI and the upper secondary frequencies (the nozzle-to-plate distance ratios (HID) are shown in Fig. 6. cases of HID = 2.0 and 2.1) have been observed.

Powell [8] found that the impinging tones, referred to as Figure 7 depicts how the amplitudes of the surface the principal tones, formed a sawtooth pattern with at least, pressure and the plate shock excursions vary with HID.

and probably more than, seven possible stages (labeled The amplitude, A P in Fig. 7, denotes the difference II through VIII) for the range of HID = 0.5-7.0. Some between the maximum and the minimum pressure during separate tones were found to occur; these had the same the oscillation cycle. When a supersonic jet flow impinges general slope as the principal tones. These were called upper perpendicularly on a flat plate, a strong normal shock, secondary tones in that they are not an integral part of the known as 'plate shock' or 'standoff shock', appears over dominant sawtooth pattern. We see that Powell's findings the plate. In the oscillatory case, the plate shock moves up are essentially demonstrated in Fig. 6. Figure 6 indicates and down along the jet axis like a plane wave oscillation.

that the frequency changes with a jump at a certain HID at The frequencies of the plate shock oscillations are identical which the oscillation enters into a different stage. It is not with those of the surface pressure oscillations. The plate yet clearly understood why this staging behavior occurs. shock position, Xs, is measured from the impinging plate This will be touched upon later in the present discussion. to the plate shock. The extent of plate shock position, AXs, As shown in Fig. 6, the pressure oscillation frequency is also contained in Fig. 7. When HID = 2.5, the flow decreases smoothly as the distance from the nozzle to oscillation is in Stage IV with relatively large amplitude and the plate increases within a specific range of HID. The lower frequency. When HID = 2.6, the oscillation jumps traveling time of a disturbance increases as the geometrical to Stage V. The frequency of oscillation increases abruptly length of the feedback loop lengthens due to the increase of to a much higher frequency while the amplitude of pressure

Oscillatory behavior of supersonic impinging jet flows 265

./D xJD b

x/D x/D c d Fig. 9 Instantaneous flowfields for various HID, Po/P 5 = 3.0. (a) corresponds to instant 4 of Fig. 8a; (b) to instant I of Fig. 8b; (c) to instant 4 of Fig. 8c; (d) to instant 3 of Fig. 8d oscillation suddenly drops to about half of the amplitude tions given in Fig. 8. When HID is small, the plate shock of the case of HID = 2.5. The amplitude of oscillation, is located behind the second expansion region. During the however, increases again together with the frequency oscillation, a 'double shock' structure is seen to appear as decrease as HID increases. Beyond HID = 3.6, the flow exemplified in the pressure distribution 4 of Figs. 8a and 9a.

goes into Stage VI accompanying again the abrupt increase As HID increases up to about 2.8, the second compression of frequency and the decrease of amplitude. We further find region following the second expansion region starts to ap-from Fig. 7 that the amplitude of pressure oscillation is in pear during the oscillation (instant 1 of Figs. 8b and 9b). No direct proportion of the plate shock motion, AX,. 'double shock' structure is found in this case. When HID Not only does the plate shock oscillate, but also the increases further, the third and sometimes fourth expansion jet flow structure changes periodically. We present instan- regions appear. The compression in this case may involve taneous static pressure variations along the jet centerline two normal shocks as seen in Fig. 9c. When HID increases in Fig. 8 for various cases. From Fig. 8, we find that the further beyond 3.6, a curved plate shock following the third pressure distribution of the expansion region in the first cell or fourth expansion region is seen to appear (Fig. 9d). A from the nozzle, characterized by a monotonic decrease, scrutinization of Figs. 8 and 9 reveals that the 'staging' does not vary with time for all the cases. However, the behavior is not precisely differentiated by the shock cell pressure distribution over the compression region in the first structure. In two consecutive stages (i.e., Stages IV and cell and the region beyond are seen to undergo significant V, and Stages V and VI), we can always find very similar changes with time. In Fig. 8, t = 0.UT (marked by '1') flow structures as viewed from the pressure distributions of refers to the instant when the pressure behind the first com- Fig. 8. Further, we may find distinctly different structural pression shock (near x/D = 1.0) becomes the largest, and patterns in the same stage as demonstrated in Fig. 8b and c.

the pressure distribution marked by '3' is the distribution at It is reported by Powell [8] that the frequency ratio for the instant when the pressure behind the first compression each successive stage bears the ratio of successive pairs region becomes the smallest. Pressure distributions exhib- of integers; herein lies the rationale for the assignment of ited in all the figures suggest that the shock cell structures the stage number IV, V, VI, etc. In the present results, the are continuously changing during the cycle of oscillation. frequency of HID = 2.5 (18.2kHz) in Stage IV almost As can be anticipated, we see that more cell structures are bears the ratio 4:5 with that of HID = 2.6 (22.2kHz) in added as HID increases. Figure 9 illustrates instantaneous Stage V, and the frequencies of the cases of HID = 3.6 in flowfields corresponding to some of the pressure distribu- Stage V and 3.7 in Stage VI (16.6 and 19.8 kHz) give the

266 S. 1.Kim, S. 0. Park 266 S. I. Kim, S. 0. Park HID-= 2.

0.5 S 0

/ iHID/2.

ft ft 0.5 -=

0, HID 3. ' -

7 S .. . 1 ..

0.25 0.5 0.'75 1 xlD x/H a b HID= 2.5 0.5 L ft ft

'5i 6 ..

0.5>

0 H-1o3.7 *....."' '.t'

~0. 0.25 0.5 0.75 x/D xlH c d Fig. 10 Instantaneous pressure distributions for various HID, Po/Pa = 3.0. (ac) along the jet center line; (b,d) along the r = 0.75D line; (a),

(b) correspond to instant I of Fig. 8; (c,d) to instant 4 of Fig. 8 ratio of integers 5:6. This reminds us of the behavior of the the corresponding pressure distributions along the jet axis standing wave in an open-ended pipe. We thus examine the are entirely different each other as HID values are widely pressure distribution around the jet edge region where the jet apart. These observations lead us to conclude that the 'stag-interacts strongly with the ambient air. Figure 10 displays ing behavior' for HID variation is directly correlated with the pressure distribution along the r = 0.75D line (0.25D the interaction of the jet with the ambient air occurring in apart from the nozzle lip line) in juxtaposition with the the shear layer rather than with the jet shock cell structure.

pressure distributions along the jet centerline. Note that the pressure along r = 0.75D line is normalized by the mean 3.2 Impinging jet flow oscillation:

pressure of the corresponding pressure distribution. We find effect of nozzle pressure ratio that the pressure distribution along r = 0.75D line exhibits a similar pattern with a standing wave in an open-ended The nozzle pressure ratio, which is another important oper-pipe. From Fig. 6, we have seen that the 'staging' occurs ating parameter, affects the flow characteristics: the shock at around HID = 2.5 and 3.6: HID = 2.5 belongs to cell structure in an underexpanded jet is also altered with Stage IV and HID = 2.6 to Stage V; HID = 3.6 to Stage the variation of the nozzle pressure ratio. Therefore, it is V and HID = 3.7 to Stage VI. Figure 10 indicates that expected that the oscillatory features of the impinging jet are the pressure distribution along r = 0.75D line changes its also affected by the nozzle pressure ratio at a given nozzle-pattern as HID changes from 2.5 to 2.6, and 3.6 to 3.7, to-plate distance. As the nozzle pressure ratio increases, the while the pressure distribution along the centerline shows length of the first shock cell increases. Prandtl [14] derived no significant variations as HID crosses these demarcation the following formula for the length, A, of the first cell in points. Further, the pressure distributions along r = 0.75D an underexpanded jet issuing from a convergent nozzle.

line for HID = 2.6 and 3.6 are of the same pattern signi-fying that these two cases belong to the same stage, while AID = 1.2, (Po/Pa- 1.9) (7)

Oscillatory behavior of supersonic impinging jet flows 267 Oscillatory behavior of supersonic impinging jet flows 267

  • U OP/P 0 0.3 A 0)5/0 D.4
  • U I I
  • E~ I N 0.2 I I I U".3 I I I
0. S I I 0 0.1 I A A Cr 0.

do -0 I IG I LL

- 0.2I

... . A A Al A 'A I I I Ad Group I lGroupn15 roup 011 Group IV

-0.2 , . . i. , , .... - i ,- . . . 0.,

Z.s 3 J.b 4 4.0 b Nozzle Pressure Ratio, P. / P. Nozzle Pressure Ratio, P0 / P.

a Fig. 12 Amplitudes of the surface pressure and the plate shock osci la-tions for HID= 2.0 (A P is the amplitude of the pressure oscillation at r/D = 0.0, A X, is the amplitude of the plate shock oscillation along the jet axis) cillations for HID = 2.0. In contrast to the corresponding patterns for the case of nozzle-to-plate distance variation (Fig. 7), AP and AXs are found to be very irregular.

We have also examined these variations for the case of HID = 3.0 to find that they are likewise very irregular. This suggests that the flow structure may vary in a disorderly manner as the chamber pressure increases for a given HID than that for the case of HID variation for a given pressure ratio. To illustrate this point, we present typical flow struc-tures for various pressure ratios in Fig. 13. At the pressure ratio of 2.5 the jet has two cells as seen in Fig. 13a. For the cases of Group U, only one cell appears and the plate shock Nozzle Pressure Ratio, P. / P. is located at the end of the first cell (Fig. 13b). As the pres-b sure ratio increases further, a strong normal shock (Mach disk) develops in the first cell. All of the cases in Groups III Fig. 11 Frequencies of the pressure oscillation with the nozzle pres-sure ratio variation. (a) HID = 2.0; (b) HID = 3.0 and IV have the Mach disk appearing in the first cell, as seen in Fig. 13c and d. The flow downstream of the Mach disk becomes subsonic, and therefore, no further shock (plate To investigate the effect of pressure ratio, we carry out shock) appears. In these flows, the Mach disk oscillates and computations for various nozzle pressure ratios. The nozzle a large separation bubble is found to be present in the im-pressure ratio (NPR = Po/Pa) is varied from 2.0 to 5.0 pinging region (Fig. 13c and d). Although Groups III and IV with the nozzle-to-plate distance fixed either at HID = 2.0 flows have quite different oscillation frequencies (Fig. I Ia),

or 3.0. Frequency variation of the pressure oscillations in they have rather similar flow structures. This rather drastic these cases is shown in Fig. 11. We see that the oscillation variation of flow structures including a large separation bub-frequencies do not change with pressure ratio within a ble explains why the amplitudes of pressure and shock os-specific range of Po/Pa in contrast to the case of the nozzle- cillations (AP and AX,) are so irregular as given in Fig. 12.

to-plate distance variation shown in Fig. 6. However, the When HID = 3.0, the flow structures become more frequency goes through a step change at a certain pressure versatile as there is more space available for adjustment ratio exhibiting again 'staging' behavior. Krothapalli [7] when compared to the case of HID = 2.0. For the pressure investigated a choked underexpanded impinging jet issuing range of PO/Pa = 3.7-4.2 (Group II in Fig. 1lb), flow struc-from a rectangular nozzle. The impinging tone frequency tures seen in Fig. 14 alternate during the oscillation cycle.

variation corresponding to the pressure ratio (Po/Pu) from Figure 14a illustrates an oblique shock with Mach disk at the 2 to 5.8 at several fixed distances HIW = 14, 21, 28 (W is center, and in Fig. 14b, we see no strong oblique shock and the width of the rectangular nozzle) also exhibited staging no Mach disk in the first cell. In this range, the plate shock behavior similar to the one shown in Fig. 11. is always present as demonstrated in Fig. 14. When the Figure 12 displays the amplitudes of the surface pressure pressure ratio is increased further to Po/Pa = 4.4-4.6, the and the plate shock (or the shock closest to the plate) os- change of the jet flow structure becomes even more drastic

268 S. L.Kim, S. 0. Park 268 S. I. Kim, S. 0. Park x/D x/D a b x/D x/D c d Fig. 13 Typical instantaneous flow structures and streamlines of the supersonic impinging jet for various nozzle pressure ratio, HID = 2.0. (a)

Po/P. = 2.5 in Group 1; (b) Po/Pa = 3.5 in Group II; (c) Po/Pa 4.0 in Group m; (d) Po/Pa = 5.0 in Group TV 1PRESSURE CONTOURS PRESSURE CONTOURS 0.5 0.

-1 -

R STREAMLINES 0 12 3 0 12 xJD xtD a b Fig. 14 Typical two instantaneous jet flow structures, Po/P. = 4.0, and HID = 3.0

Oscillatory behavior of supersonic impinging jet flows 269 Oscillatory behavior of supersonic impinging jet flows 269 0

a b c d Fig. 15 Various instantaneous jet flow structures at various instants, Po/Pa = 4.5, and HID = 3.0 as seen in Fig. 15. In this case, no discernible oscillation and 11. At a given pressure ratio, the number of shock frequency could be found (see Fig. I lb). A typical surface cells may increase if the nozzle-to-plate distance increases.

pressure oscillation and its power spectrum are given in At a given nozzle-to-plate distance, if the pressure ratio Fig. 16c and d where no distinct characteristic frequency decreases then the length of the first shock cell will decrease can be identified. It is interesting to note that characteristic as given by (7). Accordingly, the number of shock cells may oscillation frequencies were identified for these pressure increase. This qualitative argument suggests that the length ratios when H/D = 2.0 (see Fig. I la). When the pressure of the first shock cell may serve well as the characteristic ratio is increased to Po/Pa = 5.0, a characteristic oscillation length. Henderson [15] also used the first shock cell length, frequency reappeared as plotted in Fig. I lb. In this case, the A, as the reference length in her study of acoustics of the compression shock with Mach disk was very strong so that supersonic impinging jet. Figure 17 displays mean pressure no plate shock was observed. distributions for various cases with the axial distance normalized by the length of the first shock cell, A, defined by (7). We see that the mean pressure distributions for 3.3 Connection between the two staging behaviors pressure variation and those for distance variation exhibit of 3.1 and 3.2 somewhat similar features. The frequency of the surface pressure oscillation is re-plotted in Fig. 18. The frequency is We now seek for a relation between the staging behaviors non-dimensionalized by A/Ca, Ca being the speed of sound for the case of distance variation at a fixed pressure ratio at the ambient condition. The circle and triangle symbols and for the case of pressure variation at a fixed distance. represent the data for the case of pressure variations at a These two distinct staging behaviors are presented in Figs. 6 fixed distance, and the rectangle symbols correspond to the

270 S. 1. Kim, S. 0. Park 0.8 15i' E

0.6 2 10' a.

0.4 0

C-10 0.2 0 0 nl . . . . . . .

U 10 20 00 40 50 20000 40000 60000 80000 100000 Frequency, Hz Time, t V. / D a b

,t V. D Frequency, Hz c d Fig. 16 (a,c) Surface pressure histories and (b,d) power spectrum of the pressure signal at r/D = 0.0 and H/D = 3.0. (a,b) PO/Pa = 4.2 in Group IT; (c,d) Po/P. = 4.5 a-*

a.

x/A a b Fig. 17 Mean pressure distributions along the jet axis. (a) case of distance variation and fixed pressure, Po/Pa = 3.0; (b) case of pressure variation and fixed distance, HID = 3.0

Oscillatory behavior of supersonic impinging jet flows 271 Oscillatory behavior of supersonic impinging jet flows 271 0.5 . . . . i . .

H/D=2.5 & PP.=3.0 04 ... ................

HID-2.0 & PoIP.=3.5 o"

-K -mtagetVg 0.6 -

H/D=3.0 & P/P*=4.0 ./' --- \\

0.41 1!5 2 2.5 3 3.5 0.25 0.5 0.75 1 H/A x/H Flig. 18 Normalized frequency-distance characteristics (square, dis- a tance variation; triangle and circle, pressure variation) 0.5 ' . .. . . . . . . .

H/D=2.6 &P 0/P,=3.0 case of distance variation at a fixed pressure ratio. We find from Fig. 18 that the frequency characteristics for the two cases match very well each other. In Sect. 3.1, we have 0.

=- 0.2 discussed the staging behavior in terms of the pressure wave pattern in the jet shear layer. To confirm this further, we plot H/D=2.0 & P/P,=2.3 01 ........ ..... .% .. .

the pressure distributions along the r = 0.75D line for the Z .........

cases of the pressure variation and the distance variation in Fig. 19. Note that the dotted-line pressure curves have a different scale to effectively present the pressure wave HID0=3.0 & Po/P --3.5 pattern. Figure 19 evidently elucidates that the pressure -0.5 wave pattern in the jet shear layer characterizes the staging behavior for both cases. This leads us to confirm again that the staging behavior is not due to the jet shock cell 0 0.25 0.5 0.75 1 structure. x/H b

Fig. 19 Patterns of the instantaneous pressure distribution along the r = 0.75D line. (a) pattern of Stage IV; (b) pattern of Stage V (square, 4 Conclusion the case of distance variation; triangle and circle, the case of pressure variation)

By using the axisymmetric unsteady Navier-Stokes system, the oscillatory features of the surface pressure and the flow structural change of supersonic impinging jet are be caused by the interaction of the jet shear layer with the investigated by varying the nozzle-to-plate distance ratio ambient air as evidenced by the pressure wave pattern in the (HID) and the nozzle pressure ratio (Po/Pa). For both jet edge region but not by the jet shock cell structure.

cases, the frequency of the surface pressure oscillation is found to exhibit 'staging' behavior; the frequency does not Acknowledgements This work was financially supported in part by vary smoothly with either the distance or the pressure ratio. the Agency for Defense Development and by the Brain Korea 21 The frequency jumps discontinuously at a specific value project from the Ministry of Education, Korea. Constructive criticism and suggestions from the reviewers are also acknowledged.

of HID or Po/P.. The staging behavior with the distance variation is in good agreement with the previous studies.

The staging behavior with the pressure variation in which Nomenclature the oscillation frequency undergoes a step change when the pressure ratio crosses a specific value is different from that C speed of sound of the distance variation in the sense that the frequency of D nozzle exit diameter (= 2R) the surface pressure oscillation remains constant in a given et total energy stage. These two seemingly very different staging behaviors f frequency of the frequency can be correlated well if the frequency and H distance from nozzle exit to impinging plate the nozzle-to-plate distance are normalized by the length of P pressure the first shock cell and the speed of sound at the ambient r radial coordinate condition. The staging behavior for both cases are found to t time

272 S. 1. Kim, S. 0. Park 272 S. I. Kim, S. 0. Park T temperature, oscillation period 4. Kalghatgi, G.T., Hunt, B.L.: The occurrence of stagnation bubbles U velocity in x direction in supersonic jet impingement flows. Aero. Quart. 27, 169-185 V velocity in r direction (1976) 2 2 5. Lamnont, P.1, Hunt, B.L.: The impingement of underexpanded V velocity, ,u + V axisymmetric jets on perpendicular and inclined flat plates. J.

x X* axial coordinate Fluid Mech. 100, 471-511 (1980) distance from the plate to the plate shock 6. Alvi. F.S., tyer, K.G.: Mean and unsteady flowfield properties of supersonic impinging jets with lift plates. AIAA Paper 99-1829 viscosity (1999)

Y specific heat coefficient 7. Krothapalli, A.: Discrete tones generated by an impinging A length of the first shock cell underexpanded rectangular jet. AIAA J. 23, 1910-1915 (1985)

8. Powell, A.: The sound-producing oscillations of round underex-panded jets impinging on normal plates. J. Acoust. Soc. Am. 83, Subscripts 515-533 (1988) 0 chamber condition, total properties 9. Tam, C.K.W., Ahuja, K.K.: Theoretical model of discrete a ambient condition tone generation by impinging jets. J. Fluid Mech. 214, 67-87 (1990) e properties at the nozzle exit 10. Sakakibara, -Y., Iwamoto, J.: Numerical study of oscillation v viscous term mechanism in underexpanded jet impinging on plate. J. Fluids Eng. 120,477-481 (1998)
11. Lee, C.H., Park, S.O.: Computations of hypersonic flows over blunt body using a modified low-diffusion flux-splitting scheme.

References CFD J. 10, 490-500 (2002)

12. Pulliam, T.H.: Time accuracy and the use of implicit methods.

I. Donaldson, C.D., Snedeker, R.S.: A study of free jet impinge- AIAA Paper 93-3360 (1993) ment. Part 1. Mean properties of free and impinging jets. J.Fluid 13. Ishii, R., Fujimoto, H., Hatta, N., Umeda, Y.: Experimental and Mech. 45, 281-319 (1971) numerical analysis of circular pulse jets. J. Fluid Mech. 392,

2. Ginzberg, I.P., Semilentenko, B.G., Terpigorev, V.S., Uskov, V.N.: 129-153 (1999)

Some singularities of supersonic underexpanded jet interaction 14. Prandtl, L.: Uber die stationdrem Welten in Einem Gasstrahle.

with a plane obstacle. J. Eng. Phys. 19, 1081-1084 (1973) Phys. Z. 5,599-601 (1904)

3. Carling, IC., Hunt, B.L.: The near wall jet of a normally imping- 15. Henderson, B.: The connection between sound production and ing, uniform, axisymmetric, supersonic jet. J. Fluid Mech. 66, jet structure of the supersonic impinging jet. J. Acoust. Soc. Am.

159-176 (1974) 111,735-747 (2002)

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Computation of Tone Noise From Supersonic Jet Impinging on Flat Plates Ching Y. Loh Taitech, Inc., Beavercreek, Ohio March 2005

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Computation of Tone Noise From Supersonic Jet Impinging on Flat Plates Ching Y. Loh Taitech, Inc., Beavercreek, Ohio Prepared for the 43rd Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and Astronautics Reno, Nevada, January 10-13, 2005 Prepared under Contract NAS3-03072 National Aeronautics and Space Administration Glenn Research Center March 2005

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COMPUTATION OF TONE NOISE FROM SUPERSONIC JET IMPINGING ON FLAT PLATES Ching Y. Loh Taitech, Inc.

Beavercreek, Ohio 45430 Abstract theoretical model for the acoustic feedback loop. In the A supersonic jet impinging normally on a flat meantime, experimentalists are conducting various phys-plate has both practical importance and theo- ical experiments in search for the feedback mechanism retical interests. The physical phenomenon is in different impinging jet situations. Alvi and lyer [9]

not fully understood yet. Research concen- studied the impinging jet with lift plate, Krothapalli et al trates either on the hydrodynamics (e.g. lift [8] investigate both the jets with convergent nozzle and loss for STOVL) or on the aeroacoustic load- convergent-divergent (C-D) nozzles. Henderson et al[4 -

ing. 7] performed experiments of sound producingimpinging In this paper, a finite volume scheme-the jets on small and large plates.

space-time conservation element and solution Numerical simulations of unsteady impinging jets element (CE/SE) method-is employed to nu- have also been carried out. Kim and Park [10] used the merically study the near-field noise of an un- popular TVD upwind scheme. Sakakibara and Iwamoto derexpanded supersonic jet from a converg- [11] also used TVD scheme to study oscillations in im-ing nozzle impinging normally on a flat plate. pinging jets and the generation of acoustic waves.

The numerical approach is of the MILES type In the present paper, a MILES (monotonically inte-(monotonically integrated large eddy simula- grated large eddy simulation) type scheme is used to in-tion). The computed results compare favorably vestigate the problem of a jet impinging on a flat plate.

with the experimental findings. The MILES approach appears somewhat similar to LES, but there is no explicit filtering since the cell-averaging process is already equivalent to spatial filtering. Due to 1 Introduction certain built-in numerical dissipation in a MILES finite High speed impinging jets are important to aircraft in-volume scheme, the SGS (subgrid scale) model is not dustry. For vertical landing and short take-off (STOVL) needed. The recent space-time conservation element and airbomed vehicles propelled by jet engines, there are un-solution element method (CE/SE) [12-13] is a MILES desirable and adverse effects from the impinging jets.

type finite volume method with generally less numeri-These include up to 60% lift loss and the acoustic load-cal dissipation and is adopted for the computation. As ing and noises generated by a feedback loop between the demonstrated in previous papers, the CE/SE scheme is jet and the ground.

well suited for aeroacoustics computation [15,16]. Be-Research on jet impinging normally on a flat plate has cause of the CE/SE non-reflecting boundary conditions unfolded in a broad way. Some researchers concentrate (NRBC), which are based on the physics of plane wave on the hydrodynamics and investigate the lift loss, other propagation [14], a smaller near field computational do-researchers focus on the sound produced and the aeroa-main can be used in the present numerical simulation and coustic loading of the impinging jets. There are a vast helps to save both memory and CPU time.

number of papers published on these topics. For exam-The governing equations and the 2-D axisymmetric ple, after careful observations over the experimental data, Powell [1] pointed out that the small instability waves unstructured Navier-Stokes (N-S) CE/SE scheme used here is briefly reviewed in Section 2. Section 3 illustrates (vortices) around the jet shear layers and the consequent radial wall jet are responsible for the noise as they inter- the noise problems of an impinging jet on normal flat act with the flat plate and produce sound waves. Ho and plates, both large and small, with the initial and bound-Nosseir [2] explained the feedback loop in the imping- ary conditions. The numerical results are presented and ing jets; while Tam and Ahuja [3] put forward another NASA/CR-2005-213426 1

compared to available experimental findings [4 - 7] in Q3 = -U2/Uiy, Q4 = -G 4/y.

Section 4. Concluding remarks are drawn in Section 5. By considering (x,y,t) as coordinates of a three-dimensional Euclidean space, E 3 , and using Gauss' di-2 The Governing Equations and the vergence theorem, it follows that Eq. (1) is equivalent to Unstructured Axisymmetric CE/SE the following integral conservation law:

Navier-Stokes Solver As our main concern lies in the aeroacoustical behav-iors of the impinging jets which remain axisymmetric in m = 1,2,3,4, (2)

JS(v) H, *dS = JQmdV, the problems under investigation according to the exper-imental results [4 - 7], it is appropriate to adopt and solve where S(V) denotes the surface around a volume V in the axisymmetric Navier-Stokes equation system. E 3 and Hm = (Fm, Gm, Urn).

2.1 Conservation Form of the Unsteady 2.2 Treatment of the Source Term Axisymmetric Navier-Stokes Equations The treatment is identical to the one used in [17] and is Consider a dimensionless conservation form of the un- briefly reiterated here. Since the source term Q itself is a steady axisymmetric Navier-Stokes equations of a per- function of the unknown U, a local iterative procedure is fect gas. Let p, u, v, p, and y be the density, streamwise needed to determine U. The discretized integral equation velocity component, radial velocity component, static (2) reduces to the form pressure, and constant specific heat ratio, respectively.

The axisymmetric Navier-Stokes equations then can be U- Q(U)At = UH, (3) written in the following vector form:

where UH is the local homogeneous solution (Q = 0 Ut + F,, +G =Q,(1) locally). Note that UH only depends on the solution at the previous time step, i.e., UH is obtained using explicit where x, y > 0, and t are the streamwise and radial co- formulas. A Newton iterative procedure to determine U ordinates and time, respectively. The conservative flow is then variable vector U and the flux vectors in the streamwise U(i+l) = U( -I O* I'(U**-U]

and radial directions, F and G, are given by: 1

)- [P(U(i)) - UH],

U= U2 F = (') G3 where i is the iteration number and U3 ' F3 '

U(U4) F4 G4 P(U) = U - Q(U)At.

Normally, U at the previous time step is a good initial with guess U(°) and the procedure takes about 2-3 iterations UI=p, U2 =pu, U 3 =pv, to converge. The Jacobian matrix is given by U4 = p/(y - 1) + p(u + v 2 )/2.

2 1 0 At Y 0 The flux vectors are further split into inviscid and viscous 1+ UUly 3 At Uuly 2 At 0 fluxes: 2 U At F = Fi - Fv, G = Gi - G, 0 1+U 3U Aty 0

1 where the subscripts i and v denote 'inviscid' and 'vis- SA, A2 A3 1+/- uy_

3A 2Uly cous' respectively. Details of these terms can be found in where e.g. [17, 16].

The right hand source term Q is the same as in the U At - 1)(+/- U3) axisymmetric Euler equations [ 17, 16]: A 1 =- U31ly [-yU 4 U1 Q

(Qx Q2 (Q4)

A2 =-(7-Y -; 1l)U 2U3 At '

At yy-1U2 +3U2 + _yU 4

A3 y 2 U? U, where The inverse of the Jacobian, i e, (--*)- can easily be Q1 = -U derived analytically for this particuiar case, thus, leading 3 /y, Q2 = -U 2 U3 /Uly, to a savings in CPU time.

NASA/CR-2005-213426 2

2.3 Review of the CE/SE Numerical Scheme flat plate The space-time conservation element and solution ele-ment(CE/SE) method is a recently developed finite vol-ume method, with second order accuracy in both space and time. Here, CE (conservation element) stands for a control volume or cell, while SE (solution element) stands for the cell interfaces. Despite its nominal sec-ond order accuray, the scheme may offer high resolution, lower dissipation and dispersion errors [12, 13]. As a re-sult of the following advantageous features, the CE/SE scheme is chosen as the numerical tool for computation:

1. conservation in both space and time, the integral Figure 1: A sketch of the impinging jet problem.

equations of conservation laws are literally solved;

2. only a compact cell stencil is needed, (hence both the conservative variables U and their gradients Ux, UY are unknowns);
3. careful and accurate surface flux calculation;
4. truly multi-dimensional, simple but effective non-reflecting boundary conditions (NRBC);
5. effortless implementation of computation, no nu-merical fix or parameter choice is needed;
6. the scheme is of MILES type (monotonically in-tegrated large eddy simulation), the finite volume Figure 2: Typical computational domain for impinging cell-averaging plays a role of filter, while the van jet nozzle exit.

Albada limiter plays a role similar to a SGS model.

ambient density Po, the ambient speed of sound and the

7. naturally adapted to unstructured grid, robust diameter of the nozzle exit are chosen as the scales for enough to cover a wide spectrum of compressible density, velocity and length. The computational domain flow: from weak linear acoustic waves to strong, includes a near field of the flow. Figure 2 and 3 show discontinuous waves (shocks), appropriate for both typical computational domains for the current impinging CFD ( computational fluid dynamics) and CAA jet problems. As the flow is considered as axisymmetric, (computational aeroacoustics). the two-dimensional computational domains are half of With an unstructured grid, the CE/SE scheme is easily the axial section of the corresponding 3-D domains. In adapted to complicated geometries. More details about the case of a small plate with diameter d, equal to D, the the unstructured CE/SE method can be found in [13]. domain ranges from x = -3 to x = 7 (sponge/buffer The weighted a - E CE/SE scheme is used here. zone not included) in the stream direction; while in the case of a large plate, the domain ranges from x = -2 3 The Impinging Jet Problem to x = 3.4 or x = 4.5 with the nozzle exit always lo-When a supersonic underexpanded jet impinges nor- cated at x = 2. The axial location of the end flat plate mally on a flat plate, some shock cell structure is formed, depends on the ratio of h/D. Here h/D=1.4 and 2.5. Typ-and near the flat plate a stand-off or plate shock appears. ically, there about 35,000 to 40,000 triangulated cells in As the jet flow approaches the plate, it is turned into a the domain. They are formed by dividing a rectangle cell radial wall jet(Fig. 1). Then it is believed that the insta- diagonally into four pieces, as shown in Fig. 2 and 3. In bility waves or vorticities generated in the jet shear layer the area critical to aeroacoustic feedback loop around the interact with the plate and produce acoustic waves. As jet core, the grid sizes are Ax = 0.05 and Ar = 0.025 these acoustic waves propagate upstream to the nozzle to ensure enough resolution.

exit where the shear layer receptivity is the highest, they trigger a new cycle of instability waves and thus com- 3.1 Initial Conditions plete the feedback loop. Initially, the flow of the entire domain is set at the am-The impinging jet problems are set up following the bient flow conditions, i.e., (using nondimensional vari-configuration in Henderson's experiment [4 - 7]. The ables)

NASA/CR-2005-213426 3

1 Pa = 1, Pa = -, Ua =0, Va =O.

to bounda here, the subscript a stands for 'ambient'.

3.2 Boundary Conditions At the inlet boundary, the conservative flow variables and their spatial derivatives are specified to be those of the ambient flow, except at the nozzle exit, where an N P elevated pressure is imposed, i.e., the jet is underex-L panded, as in the experiments. As the jet flow at the L A nozzle exit is choked (M, = 1), and the ratio of stag-0 T nation (plenum) pressure p0 to the ambient pressure Pa, W NPR = Po/Pa = 4.03, by using the ideal gas isentropic E relations, it follows that P= [- ]- =1.893, or pe=2.12 8 9pa Pe 2J Other nondimensional flow variables at the nozzle exit, with Me = 1 (choked flow with convergent nozzle), are no e wall given by *(-y + 1)Pe nozzle exit Pe= 2T,.

symm. axis ( 2Tr )1/2 C where T, is the reservoir (plenum) temperature. We will also follow the experimental cold-flow condition where the reservoir temperature equals the ambient one, i.e.,

T, = 1.

At the symmetry axis, i.e., y = 0, a simple reflective boundary condition is applied. At the top boundary, the Type I CE/SE non-reflecting boundary conditions as de-scribed in the next subsection are imposed. The no-slip boundary condition is applied on the nozzle walls and the end plate.

3.3 Non-Reflecting Boundary Conditions As the spatial derivatives of the conservative flow vari-ables are also considered as unknowns, the CE/SE scheme supports a simple but robust non-reflecting boundary condition (NRBC). Details and proof of the new NRBC can be found in [14]. The following is the Type I NRBC employed in this paper.

For a grid node (j, n) lying at the outer radius of the domain the non-reflective boundary condition (Type I) requires that Figure 3: a: Typical computational domain and grid (with buffer/sponge zone at the top) for a large end plate; (U*)7 = (Ui)7 = 0, b: an enlargement of the grid around the nozzle exit. while U7 is kept fixed at the initial steady boundary value. At the downstream outflow boundary, the non-reflective boundary condition (Type II) requires that

( )- = 0, NASA/CR-2005-213426 4

schlierens

    • numerical Figure 4: Plots 1-8: isobars at different time steps in a Figure 5: Plots 1-8: numerical schlierens showing the cycle, showing oscillations of the shock cell, the plate cyclic movements of the shock cell and plate shock.

shock, the radiating acoustic waves and the vortices in the wakes in the small plate case.

h=1.65D, where D=2.54 cm is the jet diameter at nozzle exit. The ratio of stagnation pressure to ambient pressure while U* and (U,)i' are now defined by simple extrap- is set at NPR = 4.03.

olation from the nearest interior node j', i.e.,

4.1.1 The unsteady oscillating flow Figure 4 Uj = Uý'7 (Uon = (Uw n 1. illustrates the isobars at different time steps in about a cy-cle, after 1.47 million steps were already run. It is clearly As will be observed later, these NRBCs, when combined displayed that the toroidal instability vortical waves grow with the buffer zone, are robust enough to allow a clean along the jet shear layer upstream of the plate cylinder, near field computation without disturbing or distorting and then interact with the bow shock (plate shock) and the flow and acoustic fields.

more importantly with the edge of the plate cylinder. The 4 Numerical Results vortices are deflected and convect downstream with the As sketched in Fig. 1, when the jet hits the plate, a flow, while the interaction generates acoustic waves that radial wall jet is formed along with the instability waves. propagate in the field. As the waves reach the nozzle exit It is believed that when the instability waves interact with lip, where the receptivity is the highest, another cycle of the flat plate and generate acoustic waves that propagate vortices is triggered and the feedback loop is thus com-upstream via either the jet shear layer or the jet exterior to pleted. In our view, the situation is somewhat similar to the nozzle lip and complete the acoustic feedback loop. the feedback loop of a high speed cavity noise problem, In this section, the cases of a small plate and a large plate although the situation may be different for a larger plate are considered. diameter.

Figure 5 is the numerical schlierens showing the cyclic 4.1 Jet Impinging on a Small Plate movements of the shock-cell, in particular, the shock cell Consider a supersonic underexpanded jet from a conver- shocks and the plate shock. The strong oscillation of the gent nozzle. With a small plate of diameter d placed shocks indicates strong, nonlinear waves in the near field.

downstream of the jet nozzle exit, the free jet becomes an impinging jet. The small plate is indeed a solid cir-cular cylinder aligned with the nozzle axis. According 4.1.2 Acoustic waves and frequency Fig-to the experiment [5], the small plate has a diameter d=D ure 6 shows the same isobar plots as in Fig. 4 but with and the distance between the jet nozzle exit to the plate is pressure limited between 0.6 -0.8 (non-dimensional val-NASA/CR-2005-213426 5

SPI. mdB Mt(-1. 3). sM* plate (d-1, h=1,65) 160.

4 C

4 140 120.

ý3A 5

-isobars 8

- p=0.6 -- 0.8 100 Frq. inHz Figure 7: SPL at (-1,2) (upstream of nozzle exit) for a small plate of d=D, binwidth = 80 Hz.

Figure 6: Plots 1-8: isobar contours with pressure limited within 0.6-0.8, showing acoustic waves generation and propagation.

ues). The generation and propagation of acoustic waves are clearly observed. The pressure history is recorded for a location (-1.5, 2) upstream of the nozzle exit. Fourier analysis is then performed to obtain the spectrum. Fig- I; ure 7 is the computed SPL (sound pressure level) plot 7

at this location. It is observed that the waves are strong (over 150 dB), as expected. The fundamental frequency is about 3,300 Hz with ample harmonics. This compares well with a similar but not exactly the same case in [4],

where h=1.65D but NPR=4.40 instead of 4.03, which has a fundamental frequency of 3,570 Hz.

09 4.2 Jet Impinging on a Large Plate (hiD = 1.4)

For the case of a jet impinging on a large normal flat 2 8 plate, the plate diameter is d=1OD (note that there is a buffer zone beyond d= 1OD in the computational do-main), and NPR=4.03. Two spacings between the noz-zle exit and the plate, namely, h=l.4D and h=2.5D, are considered. Figure 8 is the numerical schlierens at different time steps, the shock cell and the plate shock 9 (stand-off shock) are clearly displayed but their hydro- 3 dynamic movements are much weaker than the previous case. Figure 9 illustrates snapshots of a similar experi-Figure 8: Plots 1-9: numerical schlierens for large flat mental schlierens [6] for qualitative comparison.

plate case, the cyclic hydrodynamic movements of the With the pressure values limited in a narrow range of shock cell and plate shock are weaker than the previous 0.71 - 0.72, Fig. 10 demonstrates how the acoustic waves case of small plate.

are generated and propagate in a series of snapshots. Fig-ure 11 is a snapshot of isobars, giving particular details of NASA/CR-2005-213426 6

lAV In11 rwq!

Figure 9: Snapshots of experimental schlierens fora sim-ilar case with h/D =1.4, NPR=4.06(from [6 - 7])

the vortices along the jet and wall jet shear layers, which (isobars minmax: 0.71-0.72) are believed to be responsible for the noise generation.

Figure 12 shows the vortices around the jet and wall jet Figure 10: Wave generation in an impinging jet with a in experiment, for qualitative comparison with Fig. 11. large plate, h/D=l.4. Isobar values are limited within The computed SPL at a point upstream of the nozzle 0.71-0.72 in order the weaker acoustic waves can be dis-exit is shown in Fig. 13. The spectrum is calculated after played.

2.7 million time steps has run. The computed tone SPL is slightly greater than 110 dB, which means the waves are much weaker than in the case with a small plate. Also, there are ample harmonics, as described in Henderson's work [6].

4.3 Jet Impinging on a Large Plate (hiD = 2.5)

As the physical behaviors for this large plate case with large spacing between nozzle exit and the plate is similar to the previous case, only the SPL at a point upstream of the nozzle exit is presented in Fig. 14.

4.4 Comparison to Experimental Acoustic Data In addition to the above qualitative comparison of the structures of shock cell or vortical instability waves around the wall jet, comparisons of the computed fre-quencies in both small and large plate cases with sim-ilar experimental data show that they are similar. The comparisons are still somewhat qualitative, since we can only find similar experimental data under slightly differ-ent operating conditions. The experimental data are from Henderson and Powell [4] (figure 11 in their paper) and Alvi and Iyer [9] (Fig. 22 in their paper). Table 1 shows the comparisons. As the data are measured visually from the charts, a small error is inevitable. From Table 1, it is Figure 11: A snapshot of isobars showing presence of confirmed that the computed frequencies are in the right various vortical eddies around the jet core and wall jet range.

Although the sound producing mechanism in the im-NASA/CR-2005-213426 7

SPL at (-1, 2). h-2.50. NPR=4.03 120.

100.

eo.

60.

Freq. in 6z Figure 12: Experimental subtracted velocity vectors around the jet core and wall jet[6], showing the com-plicated vortical eddies there. (note that the flow is in Figure 14: SPL at (-1,2) (upstream of nozzle exit) for a large plate, h/D=2.5, NPR=4.03, binwidth = 80 Hz.

opposite direction in the experiment)

SPLat (-1.2). hD-1.4. NPR-4.03 120.

pinging jet is not fully understood, the numerical work 4350 HZ may shed some light on how the acoustic wave is gener-ated near a flat plate. Figure 15 shows a typical instan-taneous pressure field plus a velocity vector field on top 100. of it (Here h=2.5D with a large plate). Near the stagna-tion point of the plate, a high pressure bubble with di-ameter of about 1-1.5D is formed. Outside the bubble, the pressure quickly reduces to the ambient level. In the feedback loop, instability waves (vortices) are shed from

60. the nozzle lip and grow in strength and size along the jet shear layer. When the vortices pass through the tips of the shock in the jet core and the plate shock, and enter the high pressure stagnation bubble (Fig. 15), the entire flow experiences severe changes in terms of all the flow 60.
0. 10000. 20600. 300o0 ,oooovariables u, v, p and p. The vortices will be deformed and F int60. distorted, and an acoustic wave is thus generated. For ex-ample, when a vortex turns 90' inside the high pressure Figure 13: SPL at (-1,2) (upstream of no 8zzle exit) for a bubble and exits the bubble along with the radial wall jet h=80 Hz.

large plate, h/D-1.4, NPR=4.03, binwidtl stream, it interacts with high gradient compression wave or shock, and generates an acoustic wave. Outside the Table 1 comparison of tone freq uencies stagnation bubble, the acoustic wave appears to originate computed Henderson 41 Alvi [9] from a location near the plate but right outside of the (exp.) (exp.) stagnation bubble as sketched in Fig. 15. This also ex-small plate 3.3 kHz 3.57 kHz -- plains the experimental observation in [6] that the sound NPR=4.03 NPR = 4.4(0 - waves occur at a location of the plate 1.3D from the cen-d=D S4 mode terline (Fig. 12), because this location lies just outside large plate 4.4 kHz 5.1 Hz 4.2 kHz the high pressure bubble.

h=l.4D h=l.4D h=l.6D (case 1) NPR=4.03 NPR=4.40 NPR=3.70 5 Concluding Remarks

w. lift plate In this paper, we attempt to numerically simulate the large plate 5.43 kHz 5.38 kHz important phenomena of a supersonic underexpandedjet (case 2) NPR=4.03 NPR=4.40 impinging normally on flat plates, with emphasis on their h/D=2.5 h/D=2.5 aeroacoustic behaviors.

NASA/CR-2005-213426 8

[6] B. Henderson, J. Bridges and M. Wemet, "An In-vestigation of the Flow Structure of Tone Produc-ing Supersonic Impinging Jets", AIAA Paper 2002-shock plate high pres. 2529, 2002.

shock stagnation bubble

[7] B. Henderson, "An Experimental Investigation into the Sound Producing Characteristics of Supersonic Figure 15: Instantaneous pressure field and velocity vec-Impinging Jets", AIAA Paper 2001-2145,2001.

tor field, h=2.5D.

[8] A. Krothapalli, E. Rajkuperan, F. alvi and L.

The numerical method used is based on the re- Lourenco, "Flow field and noise characteristics of a cently developed CE/SE scheme solving the axisymmet- supersonic impinging jet", J. Fluid Mech. ol. 392, ric Navier-Stokes equations. As the scheme possesses pp. 155-181, 1999.

low dissipation while being capable of capturing shocks,

[9] F.S.Alvi and K.G.Iyer, "Mean and Unsteady Flow the numerical results compare favorably to both hydro-Field Properties of Supersonic Impinging Jets with dynamic and acoustic experimental findings [4 - 9] even given the two-dimensional axisymmetric approximation. Lift Plates", AIAA Paper 99-1829.

However, for jet impinging on a large plate, the sound

[10] S.1. Kim and S.O. Park, "Unsteady Simulation of genration mechanism is still not fully understood and Supersonic Impinging Jet", AIAA Paper 2003-621, we have put forward an explanation for the mechanism 2003.

based on the numerical results. More investigations are needed in the impinging jet problem to further validate [11] Y. Sakakibara and J. Iwamoto, "Oscillation of Im-the numerical work. pinging jet with generation of acoustic waves",

References Aeroacoustics, %ol. 1(4), pp. 385-402, 2002.

[1] A. Powell, "The sound-producing oscillations of

[12] Chang, S.-C., Wang, X.-Y. and Chow, C.-Y., "The round underexpanded jets impinging on normal Space-Time Conservation Element and Solution plates", J. Acoust. Soc. Am. %ol.83 (2), pp. 515-Element Method-A New High Resolution and 533, 1988.

Genuinely Multidimensional Paradigm for Solving

[2] C-M. Ho and N. Nosseir, "Dynamics of an imping- Conservation Laws," J. Comp. Phys. vol. 159, ing jet. Part I. The feedback phenomenon", J. Fluid pp.89-136 (1999).

Mech. vol. 105, pp. 119-142, 1981.

[13] Wang, X.-Y. and Chang S.-C., " A 2-D Non-splitting Unstructured Triangular Mesh Euler

[3] C.K.W. Tam andK.K. Ahuja, "Theoretical model of Solver Based on the Space-Time Conservation El-discrete tone generation by impinging jets", J. Fluid ement and Solution Element Method" C.F.D. J.

Mech. vol. 214, pp. 67-87, 1990.

vol. 8, pp. 309-325 (1999).

[4] B. Henderson and A. Powell, "Experiments Con-

[14] Loh, C. Y., "On a Nonreflecting Boundary Condi-cerning Tones Produced by an Axisymmetric tion for Hyperbolic Conservation Laws" AIAA Chok edJet Impinging on Flat Plates", J. Sound Vib.

Paper 2003-3975 (2003).

vol. 169(2), pp. 307-326, 1993.

[5] B. Henderson and A. Powell, "Sound Production [15] Loh, C. Y., Hultgren, L. S. and Chang S.-C.,

Mechanisms of the Axisymmetric Choke Jet Im- "Computing Waves in Compressible Flow Using pinging on Small Plates: the Production of Primary the Space-Time Conservation Element Solution El-Tones", J. Acoust. Soc. Am. %ol.99 (1), pp. 1996. ement Method," AIAA J., %ol. 39, pp. 794-801 (2001).

NASA/CR-2005-213426 9

[16] Loh, C. Y. and Zaman, K.B.M.Q., " Numeri-cal Investigation of Transonic Resonance with a Convergent-Divergent Nozzle", AIAA J., w1. 40, no. 12, pp. 2393-2401 (2002).

[17] Loh, C. Y., Hultgren, L. S., and Jorgenson, P. C. E.,

"Near Field Screech Noise Computation for an Un-derexpanded Supersonic Jet by the CE/SE Method",

AIAA Paper 2001-2252, (2001).

NASA/CR-2005-213426 10

REPORT DOCUMENTATION PAGE Fofm Apploved I OMB No. 0704-01 88 Public reporting burden for this collection of information is estimated to average 1 hour1.157407e-5 days <br />2.777778e-4 hours <br />1.653439e-6 weeks <br />3.805e-7 months <br /> per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

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4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Computation of Tone Noise From Supersonic Jet Impinging on Flat Plates
6. AUTHOR(S) WBS-22-781-30-69 NAS3-03072 ChingY. Loh
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13. ABSTRACT (Maximum 200 words)

A supersonic jet impinging normally on a flat plate has both practical importance and theoretical interests. The physical phenomenon is not fully understood yet. Research concentrates either on the hydrodynamics (e.g., lift loss for STOVL) or on the aeroacoustic loading. In this paper, a finite volume scheme-the space-time conservation element and solution element (CE/SE) method-is employed to numerically study the near-field noise of an underexpanded supersonic jet from a converging nozzle impinging normally on a flat plate. The numerical approach is of the MILES type (monotonically integrated large eddy simulation). The computed results compare favorably with the experimental findings.

14. SUBJECT TERMS 15. NUMBER OF PAGES 16
16. PRICE CODE Aeroacoustics; Impinging jet; CE/SE method
17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT Unclassified Unclassified Unclassified NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18 298-1 02

J. Fluid Mech. (1999), vol. 392, pp. 155-181. Printed in the United Kingdom 155

@ 1999 Cambridge University Press Flow field and noise characteristics of a supersonic impinging jet By A. KROTHAPALLI, E. RAJKUPERAN, F. ALVI AND L. LOURENCO Department of Mechanical Engineering, Florida A & M University and Florida State University, 2525 Pottsdamer Street, Tallahassee, FL 32310, USA e-mail: kroth@fmrl.fsu.edu (Received 24 June 1998 and in revised form 13 March 1999)

This paper describes the results of a study examining the flow and acoustic char-acteristics of an axisymmetric supersonic jet issuing from a sonic and a Mach 1.5 converging-diverging (C-D) nozzle and impinging on a ground plane. Emphasis is placed on the Mach 1.5 nozzle with the sonic nozzle used mainly for comparison. A large-diameter circular plate was attached at the nozzle exit to measure the forces generated on the plate owing to jet impingement. The experimental results described in this paper include lift loss, particle image velocimetry (PIV) and acoustic mea-surements. Suckdown forces as high as 60% of the primary jet thrust were measured when the ground plane was very close to the jet exit. The PIV measurements were used to explain the increase in suckdown forces due to high entrainment velocities.

The self-sustained oscillatory frequencies of the impinging jet were predicted using a feedback loop that uses the measured convection velocities of the large-scale coherent vortical structures in the jet shear layer. Nearfield acoustic measurements indicate that the presence of the ground plane increases the overall sound pressure levels (OASPL) by approximately 8 dB relative to a corresponding free jet. For moderately underexpanded jets, the influence of the shock cells on the important flow features was found to be negligible except for close proximity of the ground plane.

1. Introduction While hovering in close proximity to the ground, short take-off and vertical landing (STOVL) aircraft experience a suckdown force, commonly known as 'lift loss'. This lift loss is due to the entrainment flow associated with the lifting jets which induce low surface pressures on the airframe resulting in a force opposite to lift. The lift loss in hover increases in magnitude as the aircraft approaches the ground. When the aircraft is in vertical landing mode and is near touch down, in addition to lift loss, the impingement of the high-speed lifting jets on the ground plane lead to significant ground erosion (Margason et al. 1997). Increased overall sound pressure levels (OASPL) associated with the supersonic jets are also of concern with respect to sonic fatigue of structural elements in the vicinity of the nozzle exhaust. These problems become more severe when the jets operate at supersonic speeds, which is the case in the future generation STOVL aircraft (e.g. the Joint Strike Fighter). Very limited data are currently available in the literature to characterize accurately the supersonic jet induced effects in hover. Using the simple configuration shown in figure 1, a series of experiments is conducted aimed at providing some understanding of the flow physics and identifying the main effects contributing to the hover lift loss.

156 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco D

n h 1.Schematk FIGURE 1. Schematic of the experimental set-up.

With the exception of the lift plate, the configuration chosen for this investigation closely resembles that used by a number of other investigators (Marsh 1961; Neuwerth 1974; Ho & Noisseir 1981; Powell 1988; Tam & Ahuja 1990; Henderson & Powell 1993; Messersmith 1995; Kuo & Dowling 1996) for the study of discrete sound generation of normally impinging jets. One of the key findings of these investigations is that the oscillation of the jet becomes a dominant feature of the flow when the ground plane is in close proximity to the jet exit. These oscillations are accompanied by high intensity sound (-160 dB, when the ground plane is at a distance of approximately 10 diameters) whose spectrum is dominated by discrete tones. In the past, the focus has been upon characterizing these tones and their generation mechanisms, especially in subsonic jets.

1.1. The feedback mechanism The resonance-like behaviour of sound-producing oscillations is generally explained using a feedback loop that has its origins as far back as 1912. However, most of the current understanding of the feedback mechanism comes from the work of Powell (1953a,b). In his seminal paper (1953a), Powell not only discusses the physical mechanism governing feedback but also provides a simple feedback formula for predicting the frequencies of discrete tones so generated.

Although the formula proposed by Powell was mainly in the context of edge tones from high-speed jets, it applies equally well to impinging tones which, as pointed out by many investigators, including Powell himself (Neuwerth 1974; Ho & Noisseir 1981; Powell 1988; Tam & Ahuja 1990; Henderson & Powell 1993), are also generated by a feedback loop. Tam & Ahuja noted that the energy for the feedback loop is provided by the instability waves in the shear layers of the jet. These waves are generated by acoustic excitation in the region near the nozzle exit. The waves grow as they propagate downstream and manifest themselves as large-scale vortical structures that are commonly seen in flow-visualization pictures (cf. §3). Upon impingement on the wall, these large structures generate coherent pressure fluctuations, which result in acoustic waves with significant intensity, sufficient to render them visible in shadowgraph pictures. The acoustic waves travel through the ambient medium and upon reaching the nozzle exit, excite the shear layer of the jet, leading to the generation of instability waves thus closing the feedback loop. Krothapalli (1985) used the feedback-loop mechanism to predict the frequencies generated by an impinging supersonic rectangular jet, thus verifying its validity. When the impinging plate size is

Flow field and noise characteristicsof supersonic impinging jet 157 small (a few jet diameters), additional tones are observed (Powell 1988; Henderson &

Powell 1993) that relate to flow features associated with the oscillations of the normal standoff shock (cf. § 3). Such standoff shocks are observed in experiments using underexpanded jets. When the jets are 'highly underexpanded' the oscillations of the Mach disk also appear to play a role in the feedback mechanism (Glaznev 1977).

The present study is concerned with the sound produced by axisymmetric supersonic jets exiting either from a converging-diverging (C-D) nozzle or a converging choked nozzle at moderate nozzle pressure ratios (NPR), where NPR is defined as the ratio of the stagnation pressure to the ambient pressure. In the present experiments NPR is less than 6. The plate representing the ground plane upon which the jet impinges is very large compared to the jet diameter (4000d, where d is the nozzle throat diameter).

More details of the experimental hardware are discussed in § 2.

In the present context, it is believed that the phenomenon associated with discrete sound generation is governed by the simple acoustic feedback loop as discussed earlier. The impingement tone frequency fN is determined from the following formula proposed by Powell (1953a):

N + p _ hdh h fN+,P =Jf //+I (N = 1,2,3,...). (1)

Here h is the distance between the wall and the nozzle exit and Ci and Ca are the convection velocities of the downstream-travelling large structures and the speed of upstream-travelling acoustic waves, respectively. N is an arbitrary integer and p represents a phase lag due to the fact that the phases of the acoustic wave and of the convected disturbance are not always exactly equal at both the nozzle exit and the source of the sound.

In order to predict the impinging tone frequencies using the above formula, accurate values of the large-scale structure velocities are needed. Owing to the difficulty of measuring these velocities experimentally, especially in supersonic jets, most previous investigators assumed a constant value for Ci- usually in the range of 60% to 70% of the primary jet velocity. The results presented later will show that this is not always the case; rather, the propagation speeds of the large structures exhibit significant variation with plate height. For example, the measured convection velocity of identifiable vortical structures in the shear layer of the free jet was found to be about 0.6 Uj, where Uj is the fully expanded jet velocity, whereas, for an impinging jet, it was found to be about 0.5 Uj at h/D = 4. Karamcheti et al. (1969) also found such variation in the convection velocity in earlier low-speed edge tone experiments.

In this paper, we will verify the validity of the simple feedback formula using the present experimental data. The uniqueness of this comparison lies in the fact that the convection velocities of the downstream-travelling large-scale structures (CQ) used in the formula were obtained directly from velocity measurements using the PIV technique. Recent theoretical attempts by Tam & Ahuja (1990) and Kuo

& Dowling (1996), using linear stability analysis, provided better models for the frequency determination. The amplitude prediction of the tones, which are of primary interest in practical applications, still remains elusive. However, using computational tools, progress is being made by How & Tam (1998) to predict the amplitude of screech tones.

1.2. Broadband noise In addition to the discrete sound generated due to a feedback loop as described above, the broadband noise also becomes important as it contributes to an increase

158 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco in the OASPL for an impinging jet by approximately 10 dB, relative to a free jet. The full-scale noise investigations of Harrier aircraft by Soderman (1990) suggest that the strong jet oscillations discussed above may be an artifact of small-scale laboratory cold jets. However, when two jets are in close proximity, as is the case in the proposed Boeing Joint Strike Fighter (JSF) configuration, a strong flow-acoustic coupling occurs between the two jets resulting in violent oscillations. These oscillations may lead to sonic fatigue of the nearby structures.

When the jet approaches the ground, the OASPL levels increase significantly as will be shown in §3. In addition to the commonly known sources of sound from free supersonic jets, such as mixing noise and shock associated noise, the increased levels may also be attributed to the acoustic reflection from the ground, and the generation of additional noise sources in the jet impingement and wall-jet region of the flow field. The reflection of jet noise by the ground was modelled by Sutherland

& Brown (1972) using an array of image sources placed symmetrically with respect to the ground plane where both sources (due to the jet) and their images radiate into unbounded space. Acoustic amplifications of up to 14 dB were predicted using this simple model. However, experimental observations by Soderman (1990) indicate much lower amplification levels.

To the authors' knowledge, measurements regarding the aeroacoustic behaviour of full-scale supersonic impinging jets (heated or cold) are not currently available in open literature. However, investigations of small-scale supersonic heated free jets show the presence of screech tones governed by a feedback mechanism similar to the impingement tones of the present study (see Krothapalli et al. 1997 for more details and references). Typically, in high-temperature supersonic jets, the broadband mixing noise levels are high enough to disguise the discrete tones (Krothapalli et al. 1997) and, as a result, their contribution to the OASPL is minimal. In light of the presence of screech tones in hot model jets we believe that impingement tones may persist in full-scale STOVL aircraft, i.e. in full-scale, hot, supersonic impinging jets.

There is clearly a lack of high-quality data information in the literature necessary to accurately model the noise generated by a supersonic jet impinging on the ground.

In particular, the prediction of OASPL still remains elusive. The present study is an attempt to provide quality baseline data that can provide some insight into the flow physics as well as guidance for modelling efforts and their validation.

1.3. Hover lift loss The loss of lift in STOVL aircraft while in hover mode has been extensively studied for subsonic aircraft where the impinging jets are also subsonic or subcritical. A good discussion of this issue, especially for subsonic jets, may be found in Margason et al. (1997). Briefly, the entrainment of the ambient fluid by the primary lifting jet(s) induces low pressures on the lower surface of the airframe, which in the present configuration is represented by a circular lift plate. Additional entrainment by the radial wall jet formed because of the impingement of the lifting jet can further reduce the surface pressures on the lift plate. It is expected that the entrainment due to the wall jet will become more significant when the ground plane is in close proximity to the nozzle exit and the ambient region from which the fluid is entrained becomes increasingly confined. As a result of the low surface pressures, a force in a direction opposite to the jet thrust is created, leading to a lift loss. The magnitude of this suckdown force and lift loss increases as the ground plate approaches the nozzle exit.

As a consequence of the above mechanism responsible for lift loss, it is expected that increasing the jet entrainment would result in a higher lift loss. Based on extensive

Flow field and noise characteristicsof supersonic impinging jet 159 data, this fact has been established for subsonic jets which show that jets which decay rapidly in terms of the centreline velocity (presumably due to higher entrainment rates), induce increased flow along the lower surface of the lift plate, resulting in reduced surface pressures and an increased lift loss (Margason et al. 1997).

In contrast to subsonic flows, very few data are at present available for supersonic impinging jets in STOVL configurations. In a recent study, researchers observed a nonmonotonic lift loss as a function of jet NPR for a supersonic impinging jet (Levin & Wardwell 1997). From the flow-visualization data, they speculated that this nonlinear lift loss behaviour may be related to the jet shock cell structure; however, a more rigorous explanation remains elusive. One of the objectives of this study is to investigate the lift loss phenomenon for supersonic impinging jets and to examine the physical mechanism responsible for this behaviour. Among other parameters, the role of shock cells on lift loss will also be examined. It is also well-known that jets with self-excited oscillations at discrete frequencies decay more rapidly than their counterparts without the oscillations. Hence, it is of interest to establish whether there is a correlation between the oscillatory behaviour of the jet column and the hover lift loss. It should be noted that other ground effects associated with single and multiple impinging jets, such as: ground erosion; fountain flow; and pitching moment due to the roll-up of a wall jet into a horseshoe-shaped ground vortex in transition to forward flight, can also significantly affect aircraft performance (Kuhn 1997). However, these issues will not be addressed in the present paper.

Keeping the above observations in mind, a basic research program has been initiated to investigate the aeroacoustics of supersonic single and multiple impinging jets. In this paper, the results of an investigation of the near sound field and the lift loss characteristics generated by an axisymmetric supersonic jet issuing from a convergent and a C-D nozzle are presented.

2. Experimental apparatus and procedures The details of the hover test facility used for the experiments discussed in this paper are given by Wardwell et al. (1993). The facility was designed to obtain the jet-induced forces on STOVL model aircraft hovering in and out of ground effect. In order to simulate different heights above the ground, the ground plane is mounted on a hydraulic lift and can be moved relative to the model (figure 2). For the experiments described here, the ground plane was 2.44 m x 2.44 m and was centred under'neath the model. To obtain measurements in the ground plane for ground erosion studies, a secondary instrumented 2.54 cm thick, 1 m x 1 m Plexiglas plate was mounted on the larger ground plane.

Two different nozzles were used in this study. A converging axisymmetric nozzle with an exit diameter of 2.54cm was used to simulate an underexpanded choked jet.

A shock-free nearly ideally expanded jet was obtained using a C-D axisymmetric nozzle with a throat diameter of 2.54cm designed for an exit Mach number of 1.5.

The exit diameter of the C-D nozzle was 2.75 cm. The divergent portion of the nozzle was a straight conic section with a 30 divergence angle to mimic the realistic nozzle geometry used in practice. Several nozzles were made with different diverging angles to study its influence on the lift loss. However, the data in this paper is restricted to the 3' nozzle. The nozzle upstream of the throat was designed using a third-order polynomial with a contraction ratio of approximately 5.

A high-pressure blow-down compressed air facility was used to supply air to the nozzles. A high-displacement reciprocating air compressor drives the facility, which

160 A. Krothapalli, E. Rajkuperan, E Alvi and L. Lourenco FIGURE 2. Schematic of the PIV set-up.

is capable of supplying air at a maximum storage pressure of 160 bars. Large storage tanks provide a total capacity of 10im 3 and are capable of driving the Mach 1.5 jet continuously up to 40 min.

The nozzle was flush mounted with a circular lift plate of diameter D, as shown in figure 1. The lift plate diameter is 25.4cm (approximately ten times the nozzle exit diameter) and is instrumented with 17 surface pressure taps along a radial line.

The pressure taps are used to obtain detailed surface pressure distribution on the lift plate. The taps are more closely spaced near the nozzle exit where the mean pressure variations are expected to be more significant. The pressures were measured with a Validyne strain-gauge transducer mounted in a Scanivalve unit. At each port, several seconds of digitized data was recorded to obtain the mean surface pressure. The jet-induced mean surface pressure distributions were subsequently used to calculate the lift force on the plate.

A shadowgraph system with a field of view of 30 cm was used to visualize the flow field. It employed a conventional single-pass arrangement with a stroboscopic flash unit having a flash duration adjustable from 1.3 to 7 ps at five discrete settings. The frequency of the pulsed light source can be varied up to a maximum of 1 kHz.

In the particle image velocimetry experiments, the jet was seeded with small

(- 1 gm) oil droplets generated using a modified Laskin nozzle. The ambient air was seeded with smoke particles (- 5 pm in diameter) produced by a Rosco fog generator.

A schematic of the experimental arrangement of the PIV system is shown in figure

2. Because of the unique nature of the PIV measurements used in this study, a brief description of this technique is provided in the following section.

Near-field acoustic measurements were obtained using a 0.635 cm diameter B & K microphone oriented 90' to the jet axis and placed approximately 25 cm away from the nozzle exit. The conditioned signals from the microphone and the surface pressures on the lift plate were acquired using a National Instruments data acquisition system with associated 'LabView' software. For acoustic measurements, the nearby exposed metal surfaces were covered with 10 cm thick acoustic foam to minimize sound reflections.

Flow field and noise characteristicsof supersonic impinging jet 161 The main controlling parameters in the experiment were as follows: nozzle pressure ratio (NPR), which was varied from 1.5 to 5.5; the ground plate height h with respect to the nozzle exit, varied from 2.5d to 60d (d, diameter of the nozzle throat = 2.54 cm).

The jet stagnation temperature was nominally maintained at 20'C. A top-hat velocity profile with laminar boundary layers was maintained at the nozzle exit. The nominal exit Reynolds number was 7 x 105.

2.1. Particle image velocimetry The main feature of the particle image velocimeter used in this experiment is its ability to record two images in quick succession, from which the velocity field is derived using a cross-correlation algorithm. This is possible by integrating the PIV system's two main hardware components: the Kodak ES1.0 digital video camera and the dual Spectra Physics Nd-Yag laser illumination system, with a repetition rate of 15 Hz. At the heart of the camera is the CCD interline transfer sensor, KAI-1001 with a resolution of 1008(H) x 1018(V) pixels. Each square pixel measures 9 jim on the side with 60% fill ratio with a microlens, and a centre to centre spacing of 9 Jim. The camera is also equipped with a fast electronic shutter and outputs eight-bit digital images, via a progressive scan readout system, at a rate of 30 frames per second.

The arrangement described above makes it possible to acquire up to 15 image pairs per second. The fact that the image pairs are recorded in separate frames and that the image pair separation can be reduced to a few microseconds makes this instrument appropriate for high-speed flows. In the present experiments, a 2 PIs pulse separation was used. The image is acquired from the camera using an Imaging Technologies ICPCI board, which resides on a single slot of the PCI bus of a personal computer.

The computer CPU is an Intel 300 MHz Pentium with 256 Mbytes of RAM, running under the Windows NT operating system.

An image-matching approach is used for the digital processing of the image pairs to produce the displacement field. One of the shortcomings of the conventional processing scheme is the spatial resolution. This limitation is due to the averaging caused by the typical correlation window size, of the order of 162-322 pixels. Since the measurement represents an average over the correlation window, it can be weighted towards the areas of the window with higher seeding density and/or reduced velocity.

This weakness especially limits the use of this technique in flows with large velocity and/or seeding density gradients, e.g. reacting flows.

To achieve velocity data with high spatial resolution a novel processing algorithm was developed (Lourenco & Krothapalli 1998). With the new processing approach, the particle images themselves comprise the interrogation region, which have sizes ranging from 3 to 4 pixel square. Such a high-resolution scheme not only allows for accurate measurements of the gradient fields but also permit measurements in very close proximity of solid surfaces.

The displacement between image pairs was found in the usual manner by means of cross-correlation, and a velocity (displacement) vector is assigned at the mid-distance between image pairs. Therefore, each particle pair contributes to a second-order approximation of the velocity. However, in contrast to the traditional approach which uses structured grids, these velocities are evaluated in an unstructured grid. The flow field at any point is described by an analytical function using a least-squares-fitting algorithm. The function that is used is a second-order polynomial:

u = ax 2 + bx + cy 2 + dy + exy + f. (2)

The marked advantage of this approach is that the field is described at any point with

162 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco second-order accuracy, including the derivatives that are found by differentiating the previous equation, given as a u = 2ax + b

+ ey, a '(3) u= 2cy + d + ex.

Although an unstructured grid is used for calculating the velocity, for ease of visualization, the velocity field is usually presented at regular intervals. This new scheme is very efficient and incorporates a vector validation procedure, making it independent of operator intervention. The time it takes to compute a vector field depends on the computer hardware and it ranges from 1400 mesh points s-I on a 200 MHz dual Pro Pentium PC up to several thousand on a 500 MHz Alpha based PC.

Despite the use of the novel processing scheme described above, some particle lag always occurs, especially in regions with very high velocity gradients, such as in the vicinity of shock waves. A careful study examining the behaviour of particles in supersonic flows with shocks was conducted by Ross, Lourenco & Krothapalli (1994) using a similar PIV system. As expected, the particle relaxation time was found to be a strong function of the particle diameter and shock strength. Consequently, it is expected that the location of strong shocks will be somewhat 'smeared' owing to particle lag, a fact noted in a subsequent discussion of velocity profiles obtained from PIV measurements (cf. § 3.2, figure 133b). Similar particle lag will also occur in other regions with high velocity gradients such as the wall jet although this effect will be of a lesser degree than that across a shock. A more detailed investigation, which is outside the scope of this study, is required to assess the particle behaviour accurately in regions with large velocity gradients and highly rotational flows such as the large-scale vortical structures and the near-wall region of the wall. However, in the absence of shock cells the mean velocity field data obtained using PIV shows that the velocity of the particles is in very good agreement (+/-1%) with the exit velocity calculated using isentropic relations. Furthermore, instantaneous velocity field data, such as that shown in figure 8, clearly reveals that the PIV technique is capable of capturing the presence of large-scale structures in the primary jet and the wall jet. Despite the uncertainty introduced because of particle lag, it is expected that the effects of shocks and large-scale vortical structures do not significantly alter the conclusions reached in this investigation and are of ancillary importance in this study.

3. Results and discussion 3.1. Flow visualization A conventional shadowgraph technique was used to visualize the jet flow. The images were captured using an SVHS video camera. Selected images displaying important flow and acoustic features are shown in figures 3-5 and will be discussed in this section.

It is well known that the axisymmetric free-jet instability manifests itself in symmet-ric as well as helical and/or flapping modes depending upon the exit Mach number, NPR (i.e. over/under-expansion condition), and the exit boundary-layer characteris-tics. The mode type also depends upon the height of the ground plane with respect to the nozzle exit. The flow-visualization images of an ideally expanded free jet at

Flow field and noise characteristicsof supersonic impinging jet 163 (a) (b)

(c) (d)

FIGURE 3. Instantaneous shadowgraphs depicting helical and symmetric modes of an ideally expanded supersonic impinging jet at M = 1.5. (a) hid - 8; (b) hid - 6; (c) hid - 4; (d) hid - 3.

M = 1.5 (not shown here) suggest that this jet is dominated by the helical mode instability. When the impinging plate is present, the helical mode continues to dom-inate up to h/d - 8, as shown in figure 3(a). Note that, in these and subsequent images, the lift plate and the ground plane appear as dark horizontal lines on the top and bottom of the pictures, respectively. The two pictures included in figure 3(a) represent the jet at two different phases of the resonance condition. An examination of the continuous video record suggests that the acoustic modes allowed at these conditions are also asymmetric in nature. When the ground plane is moved closer to the jet exit to hid - 6, the axisymmetric mode begins to dominate, as shown in figure 3(b). The axisymmetric nature of the flow is also evident by the presence of the symmetric large-scale turbulent structures in the jet. The axisymmetric instability and acoustic modes persist until hid - 4 (figure 3c). A further decrease in ground plate distance results in the re-emergence of the helical mode, as shown in figure 3(d).

Also evident from figures 3(b) and 3(c) are the incident and reflected acoustic waves in the jet near field. The incident waves are concave upwards and travel upstream (relative to the primary jet flow) while the waves reflected by the lift plate are of opposite curvature and travel downstream in the ambient medium. Owing to the straight divergent section and finite nozzle lip thickness, a weak shock cell structure is present in the jet. The presence of only a weak shock cell structure precludes the generation of screech, a fact verified by the acoustic measurements.

A better illustration of the incident and reflected acoustic waves is seen in figure 4(a) where the ground plane is at hid - 4. Also seen clearly in the image are the downstream-propagating axisymmetric structures in the jet column. The source of the upstream-propagating acoustic wave system be identified in the picture by locating

164 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco Reflected wave (a)

Incident wave (b)

Standing wave MtGuRE 4. Instantaneous shadowgraphs depicting helical and symmetric modes of an ideally expanded supersonic impinging jet at M = 1.5. (a) h/d - 4; (d) hid - 5.5.

the centre of the arcs. This source location is found to be in the stagnation region on the ground plane. Additionally, under certain conditions, a standing wave pattern is also produced between the lift plate and the ground plane, as shown in figure 4(b).

The wavelength between the successive upstream-propagating acoustic waves roughly corresponds to a frequency calculated from the feedback loop (cf. §3.4). The standing wave pattern represented by the horizontal lines corresponds to another resonance frequency that depends upon the distance between the lift plate and the ground plane (Krothapalli & Hsia 1996).

When the jet is moderately underexpanded, at NPR = 5, a series of shock cells appears as shown in figure 5(a). To accentuate the features of the shock cell struc-ture, time-averaged (average of 17 instantaneous images) shadowgraph images are presented here. In the presence of a shock cell structure, when the ground plane is close to the jet exit, the most notable feature is the generation of a stand-off or plate shock which in some cases is accompanied by a local stagnation bubble in the impingement region. The stand-off shock can be seen in figures 5(b)-5(d) while the bubble can be observed in figure 5(c) and is indicated on the image for clarity.

Although the stand-off shock was not observed for hid > 8, it was not always present for all conditions corresponding to hid < 8; in fact its size, shape and presence is a strong function of NPR and h/d. The appearance and disappearance of the shock and the associated separation or stagnation bubble may play an important role in determining the local aerodynamic and acoustic field, thereby affecting the lift loss and acoustic loading (cf. §3.3 and 3.4). The oscillations of the underexpanded jet were quite similar to those observed in figure 4 and both axisymmetric and helical modes

Flow field and noise characteristicsof supersonic impinging jet 165 (a)

(b)

(c) (d)

Stand-off shock RGURE 5. Mean shadowgraphs of an underexpanded supersonic jet at NPR = 5.0 for M = 1.5 C-D nozzle. (a) h/d - 60; (b) hid - 6; (c) hid - 4; (d) hid - 3.4.

of oscillation were observed. Henderson & Powell (1993) considered the stand-off shock distance from the ground plane and different disturbance convection velocities upstream and downstream of the stand-off shock region to calculate the self-excited oscillation frequency (cf. §§ 3.4). The flow associated with the stand-off shock has been the focus of several investigations (Lamont & Hunt 1980). The detailed discussion of this aspect is outside the scope of the present paper, since it is more pertinent to the ground erosion problem.

3.2. PJV flow-field measurements A detailed investigation of the jet characteristics was carried out using the PIV technique. All the measurements are confined to the central plane of the jet. Typical double exposure images of the free jet and the impinging jet are shown in figure 6.

The main jet is seeded with the oil droplets while the ambient medium is seeded with smoke particles. The flow field produced by the jet impingement consists of three flow regimes: the free jet upstream of the ground plane, the impingement region and the wall jet. Donaldson & Snedeker (1971) provide a very good discussion of the basic flow characteristics of these regions, especially, the mean flow. The focus of the PIV measurements is the unsteady characteristics of the flow field and their effect on lift loss. Hence, little attention is paid here to the radial wall-jet flow field on the ground plane. However, a companion investigation is currently underway to investigate the impingement and the accompanying wall-jet regions (Alvi & Iyer 1999).

For the case of a free, nearly ideally expanded jet, shown in figure 6(a), there are no discernible large-scale organized structures such as those found in figure 6(b) which corresponds to an impinging jet at hid = 4. The large structures appear to be nearly symmetrical, corresponding to the axisymmetric nature of this flow, also observed

166 A. Krothapalli, E. Rajkuperan, E Alvi and L. Lourenco (b) I1 d I-(c) (d)

- Radial wall jet Impinging region Stand-off shock FIGURE 6. Instantaneous PIV images for M = 1.5 C-D nozzle. (a) Ideally expanded free jet, NPR = 3.7; (b) ideally expanded impinging jet, NPR = 3.7, h/d = 4, vertical dotted line is measurement location for entrainment velocity, q; (c) underexpanded free jet, NPR = 5.0; (d) underexpanded impinging jet, NPR = 5.0, h/d = 4.

earlier in figure 3. Upon impingement on the ground plane, the structures move laterally in the radial wall jet without losing much of their coherence. In the case of an underexpanded jet at NPR = 5 (figure 6c), the vortical structures appear to be smaller and much less organized relative to those shown in figure 6(b). The stand-off shock, a prominent feature of this flow, is indicated by an arrow in figure 6(d).

The instantaneous velocity field was obtained by the method described in §2.1, with interrogation regions of 8 x 8 pixels corresponding to a physical dimension of 0.8 x 0.8 mm. The data was obtained using a 120 x 80(x, r) Cartesian grid. Typical instantaneous velocity fields corresponding to the images in figure 6 are shown in figure 7. The magnitude of the out-of-plane component of the vorticity shown in colour contours is superimposed on the velocity field. In this fashion, the identity of large-scale vortical structures in the shear layer of the jet can be accentuated. Forty such instantaneous velocity fields were obtained for each of the condition tested.

One of the key parameters in the frequency prediction formula given in § 1.1 is the convection velocity of the large-scale structures, C1 . In the absence of any direct measurements of the convection velocity, many of the previous investigators estimated its value to be between 0.6 and 0.7 U1 (Uj: mean jet exit velocity). From the velocity field data, it is possible to identify the regions of concentrated vorticity. For example, a typical region of high vorticity corresponding to a coherent vortical structure is shown in figure 8. Once a structure is identified, its convection velocity can be obtained easily

Flow field and noise characteristicsof supersonic impinging jet 167 from the velocity data. Free-jet convection velocities of 0.6 Uj were measured in this fashion. However, in the case of an impinging jet, the convection velocity varies as a function of the plate height and the NPR. Figure 9 shows the convection velocities measured from individual PIV images, each represented by a single data point on the plot. Obviously, the location of the large-scale vortical structures (given on the x-axis) varies from one PIV image to another. The solid line in the plot represents the average value of the convection velocity, which in this case is equal to 0.52 Up Because of the non-uniform variation of the centreline velocity owing to the presence of the shock cell structure, Uj is substituted here by a mean velocity, U,,,,,, obtained from averaging the centreline velocity of the free jet within the first five diameters.

As the plot in figure 9 shows, measurement of the convection velocities, Ci of large-scale structures were obtained only for x <_ 75 - 80 mm. This is typical for all the cases presented in this paper, where the convection velocity measurements could not be obtained in regions close to the wall. This is due to the presence of the impingement zone and the wall jet in the near-wall region which makes it very difficult, if not impossible, to identify large-scale structures and obtain reliable data for Ci. We suspect that the lack of this data may somewhat bias the average convection velocities towards higher values since one would expect the structures to slow down as they approach the ground plane. However, since the region where this occurs is relatively small, we expect the bias to be small and the convective velocities presented here to be fairly accurate. The variation of the average convection velocity with the plate height is shown in figure 10 for three different NPR. For example, for an ideally expanded jet (NPR = 3.7), the convection velocity increases linearly with h1d from 0.52 Uj at h1d = 4 towards the free-jet value. Figure 10 also shows that for a fixed h1d, the presence of shock cells increases the convection velocities of the vortical structures. From the flow visualization pictures (see figure 6) and PIV data, it appears that these vortical structures are much smaller in the presence of shock cells and are located mostly towards the high-speed side of the shear layer. The convective Mach number of the large structures, M,, (M, = (U,,,. - Qlai; aj is speed of sound in the jet) at NPR = 5 was found to vary from 0.73 at h1d = 10 to 0.66 at h1d = 4. These values are consistent with the measurements of Powell (1988) who derived them from the flow-visualization pictures.

The magnitude of the surface pressures on the lift plate is closely linked to the jet entrainment velocities in the near hydrodynamic field, especially when the jet is confined by two solid boundaries (lift plate and the ground plane). These velocities can be obtained easily from the PIV data. Typical instantaneous velocity variation with downstream distance at a radial location of 1.5d is shown in figure 11. Included in the figure are the data for a free jet and the impinging jet at two different pressure ratios.

The magnitude of the near-field instantaneous entrainment velocity, q(q = (u2 +v2)1/2) for a free jet is about 8 m s-', while for the impinging jet, it can be as high as 50 rn s-', as indicated by the peaks in the velocity plot. Such large velocities in the near hydrodynamic field correspond to the presence of large vortical structures which can be clearly seen in figure 7. These high entrainment velocities will result in suction pressures on the bottom surface of the lift plate resulting in a downward force (lift loss), details of which are discussed in the next section. The entrainment field is quite unsteady as seen from three different instantaneous velocity profiles at the same radial location, shown in figure 12. The large velocities seen in the region x > 75 mm correspond to the radial wall jet. The thickness of the radial wall jet changes with time as suggested by the location of the peak velocity magnitude close to the ground plane x > 75 mm. (figure 12). From the examination of a number of instantaneous

168 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco (a) 0 (b) 0

-10 -10

-20 -20

-30 -30

-40 -40

-50 -50 U,, = 300 m s-'

-60 -60 S2 (s-1)

~--70 -70

-80

-80 76000

-90 -90 S.. 38000

-100 - -100 . . .

-50 -25 U Z) 50 -50 -25 0 25 50 0 (c)_0 (d) 0

-10 -10

-76000

-20 -20

-30

-30 E -40 E -50 -40

-60 -50

-70 -60

-80 -70

-90

-100 -80

-110 -90

-120 -100 "

-50 -25 0 25 50 -50 -25 0 25 50 r (mm) r (mm)

FIGURE 7. Instantaneous velocity fields corresponding to images shown in figure 6.

80 NPR = 3.7 MAd=1.5 h/d 4 Urf =300 m s-1 70 E

i: 76000 38000 60 10 20 I 0

-38000

-76000 r (mm)

FIGURE 8. Details of the large-scale vortical structure. Underexpanded impinging jet, M = 1.5 C-D nozzle, NPR = 3.7, h/d = 4.

Flow field and noise characteristicsof supersonic impinging jet 169 1.0 0.8 P 0.6 mmE mm 0.4

--,m, , , ,, ,.. , ,, ,,U U, . , ,E , , ,, , ,

0.2 0 20 40 60 80 100 x (mm)

FIGURE 9. Instantaneous convection velocities of large-scale vortical structures obtained from PIV data. Ideally expanded impinging jet, NPR = 3.7, hid = 4.

0.60

/

f /A 0.58 ,, A,"

0 - U S A"-

0.56

- - k

/

0.54 /

./-

//

//

0.52 /

/

/

0.50 0 5 10 15 hid FIGURE 10. Variation of the normalized convection velocity of the large vortical structures with ground plane distance. 0, NPR=5.0; *, 3.7; A, 2.5; 0, Free jet hid = 60.

170 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco 100 80 60 40 20 25 50 75 100 x (mm)

FIGURE 11. Instantaneous entrainment velocity for free and impinging jets at r/d = 1.5 (see figure 6). NPR=5.0: 0, freejet; A, h/d = 4; NPR=3.7: D, free jet; A, hid = 4.

100 80 60 C-40 20 25 50 75 100 X(mm)

FIGURE 12. Instantaneous entrainment velocities at three different instances at rid = 1.5.

Underexpanded impinging jet, NPR = 5.0, hid = 4.

velocity fields, it is observed that the wall jet is primarily characterized by the large vortical structures that orginate in the jet shear layer.

The mean velocity field was obtained by averaging 40 instantaneous velocity fields.

The number of samples used here is not sufficient to obtain a true mean velocity field. However, the trends provided by the averaged data are adequate to observe the

Flow field and noise characteristicsof supersonic impinging jet 171 (a) 600 500 400 300 200 100 0 20 40 60 80 100 (b) 600 500 400 300 x (mm)

FIGURE 13. Mean centreline velocity variation for.free and impinging jets. (a) NPR = 3.7; A, h/d = 4; 0, free jet; (b) NPR=5.0; A, free jet; 0, h/d = 4.

significant changes due to the impingement process. Figure 13 shows the centreline velocity variation with downstream distance for free and impinging jets. For the impinging jet, the ground plane was located at x = 101.6 mm (x/d = 4). The variation in the averaged centreline velocity in the free jet is primarily due to the shock cell structure. The spatial mean centreline velocity U,,,, calculated using the data from x/d = 0.2 to x/d = 5 for a free jet, is depicted by the solid line. For an impinging jet at NPR = 3.7, the mean centreline velocity remains nominally constant up to x/d - 3.

172 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco 0.7-0.6-0.5 0.4.

. 0.3 A 0.2-0.1A 0-1 2 4 6 8 10 hIdj FIGURE 14. Lift loss variation with ground plane distance. 0, Mach 1.5, NPR=3.7; U, Mach 1.0, NPR=3.7; A, Levin & Wardwell (1997), NPR=2.75.

Further downstream, the flow gradually decelerates, presumably through a system of compression waves, until it reaches sonic velocity. An examination of figure 13(a) reveals that the sonic condition occurs at x = 86 mm (x/d ,- 3.4) which corresponds to a change in axial velocity gradient. In contrast, the centreline mean velocity profile of the underexpanded jet (NPR = 5), shown in figure 13(b), displays a more drastic deceleration downstream of x 84mm (x/d - 3.3), indicating the presence of a much stronger shock than the ideally expanded case. Indeed, as pointed out earlier, the flow visualization clearly indicates the presence of this normal shock, commonly referred to as stand-off shock. Ideally, the velocity gradient across a normal shock will be extremely high. However, owing to particle lag inherent in PIV measurement, the velocity gradient across strong shock will be somewhat smeared, as evident in figure 13(b).

From the examination of all the instantaneous velocity fields, it is observed that critical changes in the jet flow field primarily occur in the vicinity of the jet impinge-ment region (figure 6). This region extends as much as one jet diameter upstream of the ground plane. The behaviour of the flow field in this region is essential for understanding the ground erosion problem, a topic that is outside the scope of this paper but is the subject of an ongoing study (Alvi & Iyer 1999).

3.3. Hover lift loss The negative jet-induced lift force that acts on the lift plate in the vicinity of the ground plane was obtained from the measurements of mean surface pressure. The estimation of the magnitude of this force becomes important as the ground plane approaches the nozzle exit. Typical variation of the negative lift force with h/dj (dj is the fully expanded jet diameter) is shown in figure 14. The lift force is normalized with the jet thrust calculated using one-dimensional isentropic equations. Included in the plot are the data of an underexpanded jet issuing from a conical nozzle. As the ground planes approach the lift plate, a large downward force is generated. For example, at x/d = 2, the magnitude of the lift loss is about 60% of the primary jet thrust. This force decreases rapidly in magnitude with increasing h/d and approaches an asymptotic value of the free jet, as shown in the figure. A comparison of the lift loss behaviour between the ideally expanded and underexpanded jet indicates that

Flow field and noise characteristicsof supersonic impinging jet 173 2

l0-I 5

-Y

-2 10)-2 3 5 100 h /(D-d)

FRGURE 15. Lift loss correlation at NPR = 3.7. e, Mach 1.5 nozzle; o, Mach 1.0 nozzle; 0.02 x 2 2 4 .

0.5 0.4 F

.=

0.3

? 0.2 k 0.1 3

U U p -

0 2 3 4 5 6 NPR FIGURE 16. Lift loss variation with NPR for a sonic nozzle. 0, h/d = 2.5; E, 3; V7,5; 0, 10.

the shock cells appear to play an insignificant role, except when the ground plane is in close proximity to the jet exit. This issue will be further explored later. Also included in the figure is the data for an underexpanded jet (NPR = 2.75) taken from Levin &

Wardwell (1997). Their measurements were obtained directly using a thrust balance and a sonic nozzle. The agreement between the two sets of data provides confidence in the present data which were obtained from integrated surface pressure profiles on the lift plate.

Figure 15 shows the same data plotted in coordinates that are commonly used in the literature related to this subject. The data shows a linear variation which can be described by the following simple relation:

(L - Lf)/T = 0.02 (h/(D - d))-224.

Here, L is the downward force on the plate; Lf is the downward force on the plate for a free jet; T is the jet thrust, D is the diameter of the lift plate and d is the nozzle throat diameter. This relationship is very similar to that obtained by Levin &

Wardwell (1997).

The dependence of lift loss on NPR was further explored to investigate the role of

174 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco 150 140 130 X 120 a- 110 90 80 80 .103

. 1046 Frequency (Hz)

FIGURE 17. Near-field narrowband frequency spectra for M = 1.5 nozzle with and without the lift plate ... , NPR=3.7, free jet, no lift plate; - -, 3.7, free jet, with lift plate; -, 5.0, free jet, with lift plate.

the shock cell structure at small values of hid. A summary of these measurements for the sonic nozzle is provided in figure 16. This plot confirms the earlier assertion that the shock cells are only relevant for small h/d. Measurable variations in lift loss with NPR are only observed for h/d < 3. As alluded to in § 1 this nonlinear loss in lift was also observed by previous investigators (Levin & Wardwell 1997). It is speculated that the NPR range over which these variations are observed are, in part, related to the appearance of the stand-off shock and associated bubble. For small h/d, the scale and the unsteady characteristics of this stand-off shock are likely to influence the local entrainment velocities, thereby affecting the surface pressure and the resulting lift loss. Furthermore, at such small lift-to-ground plane separations, the entrainment properties of the high-speed (transonic to supersonic) wall jet are likely to play an important role in determining the local pressure field and lift loss.

3.4. Acoustic characteristics 3.4.1. Screech tone characteristics It is well known that the noise from a supersonic jet existing from a C-D nozzle, operating away from the design condition, exhibits discrete tones commonly known as screech tones. The characteristics of these tones have been the subject of intense investigations; a summary of these studies can be found in review articles by Tam (1991, 1995). The mechanism for screech-tone generation is a feedback loop that is well understood. The presence of sound-reflecting surfaces in the immediate neigh-bourhood of the jet will alter the screech characteristics (Poldervaart, Wijnands &

Bronkhorst 1973). In addition, a thick nozzle lip increases the screech intensity by about 10 dB (Norum 1983). Hence, the lift plate at the nozzle exit is expected to influence the screech tones. The near-field noise spectrum was measured for the free jet, with and without the lift plate, to examine its influence on the screech frequency and amplitude.

Figure 17 shows a typical narrowband spectrum of a near-field microphone signal, for a free jet at NPR = 3.7 (nominally ideally expanded). As expected, the spectrum shows no discernible discrete tones corresponding to screech. A broad peak corre-

Flow field and noise characteristicsof supersonic impinging jet 175 1.2

1.0 S0.8 E 0.6

"* 0.4 i i 0.2 0

2 4 5 6 7 NPR FIGURE 18. Free-jet screech tone variation with NPR. 0, Mach 1.5 nozzle, no lift plate; 0, Mach 1.5 nozzle, with lift plate; 0, Mach I nozzle, no lift plate; N, Mach 1 nozzle, with lift plate; -, Tam's prediction.

sponding to the broadband shock-associated noise (generated because of the presence of the weak shock cell structure) is present at this condition. However, in the presence of the lift plate, a distinct tone appears in the spectrum, as shown in the figure.

Consistent with previous observations, the presence of the lift plate increased the amplitude of the screech tone. When the jet is underexpanded, the tones will become much stronger, resulting in several harmonics, as shown in the figure for NPR = 5.0.

The tones measured in the present study are compared with the prediction formula given by Tam (1991), which has been thoroughly validated against a number of ear-lier measurements. Figure 18 shows a comparison of the data with Tam's prediction.

Tam's formula only accounts for the helical mode, hence, in jets where symmetric or toroidal modes are present, primarily at NPR below 3, the data deviate from the curve. The good agreement of the data with the theoretical prediction for higher NPRs suggests that, although its magnitude is enhanced, the screech Strouhal number is not measurably altered by the presence of the lift plate. The effect of impingement on the screech frequency will be discussed in the following section.

3.4.2. Impinging tones In addition to the screech tone, another dominant discrete tone appears when the jet impinges on the ground plate. These tones are commonly referred to as impinging tones (Krothapalli 1985; Powell 1988). Several different prediction formulae exist in the literature for the frequency prediction of these tones. Using the present experimental data, and in light of the measurements of the convection velocity of the large-scale vortices in the shear layer of the jet, the feedback loop will be further examined in this section.

Typical near-field narrowband spectra of an impinging jet at NPR = 3.7 for three different h/d are shown in figure 19. For the sake of clarity, the h/d = 4 and 4.25 spectra are displaced relative to the h/d = 3.75 spectra as follows: h/d = 4 by 10 dB and h/d = 4.25 by 20dB. The shock cell structures are very weak at this NPR, as indicated by the PIV measurements. The spectra show the presence of several distinct tones, and a slight change in hid can result in a significant change in the magnitude and frequency of these tones. In order to identify the origins of these tones,

176 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco 170 V.d C-104 Frequency (Hz)

FIGURE 19. Near-field narrowband spectra for M = 1.5 impinging jet ... , NPR = 3.7, h/d = 3.75;

- -, NPR = 3.7, h/d = 4; NPR = 3.7, h/d = 4.25.

3 3 4 5 6 7 8 910 hidj FIGURE 20. Impinging tone variation with ground plane distance for an ideally expanded jet, NPR = 3.7, M1 = 1.5. Comparison with -, the feedback formula assuming phase lag, p = 0.

e, amplitude dominant tones.

a summary plot of their variation as a function of h/d is shown in figure 20 where the solid symbols represent the amplitude-dominant tones. The data fall roughly along parallel lines, in accordance with the well-known staging behaviour. Such a variation of frequency with the impinging plate height suggests that a feedback mechanism is governing the flow. Also shown in the figure, is the free-jet screech frequency, indicated by the dotted line. From the data, it appears that, in most cases, the dominant tones do not lie on the free-jet screech line. This suggests that the majority of the tones are generated because of jet impingement.

In order to predict the frequency variation with h/d shown in figure 20, the feedback-loop formula (equation (1)) was used. The convection velocities used in the

Flow field and noise characteristicsof supersonic impinging jet 177 formula are obtained from the PIV measurements and a phase lag of zero, i.e. p = 0 was assumed. The solid lines shown in figure 20 represent the predicted frequencies using the feedback formula. They clearly do not agree with the measured tones.

This is in contrast to the observations made for subsonic jets where, assuming a zero phase lag, the feedback formula predicts the tones reasonably well. To account for this discrepancy in the measured and predicted frequencies, one must re-examine the use of the feedback formula and ask whether any significant physical mechanisms responsible for generating impinging tones have been neglected. One such candidate was suggested by Henderson & Powell (1993) for underexpanded jets where they propose that oscillations of the stand-off shock play an important role in the generation of tones.

Accordingly, Henderson & Powell (1993) proposed a modified feedback formula which accounts for stand-off shock oscillations. However, in the present case, the flow-visualization pictures and the PIV data indicate that the sound emanates from the jet impingement region and there is no appearance of a stand-off shock. This is because only weak shock cells are present in the jet, and the flow approaching the plate transitions through a series of compression waves, as indicated by the smooth variation of the centreline velocity in the impingement region ('figure 13a). Hence, it is suggested that the feedback model of Powell (1988) which includes stand-off shock oscillations as a dominant source of sound may not be valid here. Consequently, a different source for this discrepancy had to be accounted for in the feedback mechanism.

The mechanism by which instability waves are produced by the incident sound wave at the nozzle exit is assumed to be quite simple in arriving at the feedback formula given earlier. A strong coupling between the sound wave and the instability waves takes place over the distance of a few instability wavelengths immediately downstream of the nozzle exit. A comprehensive discussion of this aspect can be found in Tam (1978) and Ahuja & Tam (1982). In the present case, the presence of the lift plate generates reflected waves (figure 4). These reflected waves, along with the upstream propagating waves, are expected to interact with the shear layer near the nozzle exit to generate instability waves. Consequently, this interaction between these acoustic waves and the shear layer near the nozzle exit may be much more complex and requires further investigation. As mentioned earlier, Powell argued that the phases of the acoustic wave and of the convected large-scale disturbances do not necessarily exactly correspond to each other at the nozzle exit and the source. This may be accentuated in this particular case by the reflective surface at the nozzle exit.

It is suggested that the complex interaction between the instability waves and the acoustic waves will lead to a phase lag. Therefore the assumption of a zero phase lag, p = 0, is probably incorrect and the likely source of discrepancy between predicted and measured frequencies in figure 20. Good agreement with the prediction formula is obtained when the phase delay is accounted for using p = -0.4. The agreement can be clearly seen in figure 21 in which data from figure 20 is replotted using this value of P.

To examine the effect of shock cells on the tones, a limited number of data for an underexpanded jet at NPR = 5 (M = 1.5 nozzle) were also obtained. Similar to behaviour observed for the ideally expanded case (NPR = 3.7), there is a significant discrepancy between the predicted and measured impingement tones when a zero phase lag is assumed. As before, assuming the same value of p = -0.4 resulted in good agreement between the predicted and measured frequencies. This suggests that either the stand-off shock oscillations play a minor role or their effect is accounted for in the phase lag, p. Another reason for this difference may be due to the under-

178 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco N

5 S.creech 2

2 3 4 5 6 7 8 9 10 h/dj FIGURE 21. Impinging tone variation with ground plane distance for an ideally expanded jet, NPR = 3.7, Md = 1.5 (same as figure 20). Comparison with -, the feedback formula assuming phase lag, p = -0.4. e, measured tones.

prediction of the convection velocities of the large-scale structures, as pointed out in the discussion of figure 9 (§ 3.2). Note that the particular value of the phase lag used here was not obtained from a rigorous analysis, rather this value of p simply provided the best agreement with the predicted frequencies over a wide range of conditions. Unfortunately, the relative contributions of the stand-off shock oscillation, under-prediction of convective velocities and the actual phase lag, to the total value of p used here cannot be determined. It should also be noted that for highly underexpanded jets, the stand-off shock oscillations are likely to play more significant role in determining the feedback loop.

Because of the confined nature of the geometry formed by the lift plate and the ground plane, some of the oscillatory modes can be strengthened. In cases where the screech or the impinging tone frequency matches the 'duct' mode, standing waves can be produced (Krothapalli & Hsia 1996). Such waves can be seen clearly in figure 4(b).

Messersmith (1995) also made similar observations.

3.4.3. Overall noise From the near-field narrowband spectra, overall sound pressure levels were calcu-lated and plotted as a function of NPR in figure 22. A comparison of the M = 1.5 free jet, with and without the lift plate, shows that the plate has negligible influence on OASPL. However, in the presence of the ground plate, a significant increase in the OASPL was observed. For example, at the nearly ideally expanded condition at NPR = 3.7, an increase of about 8 dB is observed. The magnitude of the increase in OASPL owing to the impingement is consistent with the full-scale measurements obtained by Soderman (1990). A comparison of h/d = 3 and 5 shows that the location of the ground plate height for small h/d does not produce significant variations in OASPL.

4. Conclusions The understanding of the oscillatory nature of impinging supersonic jets and their associated noise is of paramount importance for predicting the mean and

Flow field and noise characteristicsof supersonic impinging jet 179 160 156 0

0

  • "152 0 o0 C0 it i
  • C 144 0 140 , I 1 2 3 4 5 6 NPR FIGURE 22. Near-field over all sound pressure level variation with NPR for M 1.5 nozzle.

0, h/d = 3; 0, h/d = 5; 0, free jet, no plate; 0, free jet, with plate.

unsteady loads on the airframe from which the jets are issuing. The experimental results described in this paper include lift loss, whole field velocity and acoustic measurements. Considered as a whole, these complementary measurements provide a coherent picture of the flow field associated with the oscillatory impinging supersonic jets and their near-field acoustic characteristics.

The self-sustained oscillatory behaviour of the impinging supersonic jet generates large-scale coherent vortical structures in the flow. These structures play a primary role in determining the entrainment properties of the jet and the acoustic field. From a practical perspective, knowledge of the entrainment flow is essential towards an understanding of the lift loss mechanism. Similarly, an understanding of the acoustic properties is important for predicting the unsteady acoustic loads on the airframe. A unique contribution of this study is the use of a novel high-resolution PIV technique to obtain the velocity field information with a high degree of accuracy. The velocity data clearly show that, as the ground plane approaches the nozzle exit, large-scale vortical structures of the increasing strength are generated. As a result, the jet entrainment velocities in the vicinity of the lift plate are significantly increased. This leads to lower pressures on the lift plate, followed by a suckdown force or lift loss. In the present study, suckdown forces as high as 60% of the primary jet thrust were measured.

A significant reduction in thrust loss can be accomplished by eliminating the self-sustained oscillations of the jet. For example, the impinging tone could be suppressed and stopped by placing a small plate normal to the centreline of the jet in the outside ambient flow region (Karamcheti et al. 1969; Elavarasan, Venkatakrishnan &

Krothapalli 1998).

The self-sustaining oscillation frequencies of the jet are frequently predicted using a feedback mechanism. Models describing this mechanism require a knowledge of the convection velocity of large-scale vortices in the shear layer. Using the vorticity

180 A. Krothapalli, E. Rajkuperan, F. Alvi and L. Lourenco as a tracer quantity, the convection velocities of the large structures in the impinging jets were accurately measured. It was found that when the jet is operating in close proximity to the ground plane, the convection velocity of the structures is smaller than that of free jets (0.52 Uj; Uj is the jet exit velocity). Using the measured convection velocities in a feedback formula, an accurate prediction of the measured frequencies was obtained. However, the amplitude determination remains elusive.

Near-field acoustic measurements indicate that the presence of the ground plane increases the OASPL by approximately 8 dB over a corresponding free jet. This increase was relatively insensitive to variations in the nozzle pressure ratio (NPR) for NPR>3.

This study briefly addressed the role of shock cells on the features discussed above.

The convection velocities of the vortical structures was found to increase in the presence of shock cells. Except for very close ground plane proximity, the shock cells have a negligible influence on the suckdown force. For moderately underexpanded jets, the feedback mechanism appeared to be unaffected by the shock cells. When the jets are operating at highly underexpanded conditions, a strong highly unsteady shock cell structure is present. A detailed study is currently underway to examine its effects on the features discussed in this paper.

We would like to thank the continued support of NASA Ames Research Centre through a grant monitored by Mr Douglas Wardwell. Dr R. Elavarason and Dr L.

Venkatakrishnan, helped us immensely in acquiring and processing the PIV data.

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MESSERSMITH, N. L. 1995 Aeroacoustics of supersonic and impinging jets. AIAA Paper 95-0509.

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NORuM, T. D. 1983 Screech suppression in supersonic jets. AIAA J. 21, 235-240.

POLDERVAART, L. J., WIJNANDS, A. P. J. & BRONKHORST, L. 1973 Aerosonic games with the aid of control elements and externally generated pulses. AGARD Conf Proc. 131, Noise Mechanisms, pp. 20.1-20.4.

POWELL, A. 1953a On edge tones and associated phenomena. Acoustica 3, 233-243.

POWELL, A. 1953b On the mechanism of choked jet noise. Proe. Phys. Soc. Lond. B 66, 1039-1057.

POWELL, A. 1988 The sound-producing oscillations of round underexpanded jets impinging on normal plates. J. Acoust. Soc. Am. 83, 515-533.

Ross, C., LOURENCO, L. & KROTHAPALLI, A. 1994 PIV measurements in a shock-containing super-sonic flow. 32nd Aerospace Sciences Meeting, AIAA Paper 94-0047.

SODERMAN, P. T. 1990 The prediction of STOVL noise-current semi-empirical methods and comparisons with jet noise data. NASA Tech. Mem. 102833.

SUTHERLAND, L. C. & BROWN, D. 1972 Prediction method for near field noise environments of VTOL aircraft. AFFDL-TR 71-180, AD 900405.

TAM, C. K. W. 1978 Excitation of instability waves in a two-dimensional shear layer by sound. J.

Fluid Mech. 89, 357-371.

TAM, C. K. W. 1991 Jet noise generated by large-scale coherent motion. Aeroacoustics of Flight Vehicles: Theory and Practice,NASA RP 1258, vol. 1, pp. 311-390.

TAM, C. K. W. 1995 Supersonic jet noise. Ann. Rev. Fluid Mech. 27, 17-43.

TAM, C. K. W. & AHUJA, K. K. 1990 Theoretical model of discrete tone generation by impinging jets. J. Fluid Mech. 214, 67-87.

WARDWELL, D. A., HANGE, C., KUHN, R. E. & STEWART, V. R. 1993 Jet-induced ground effects on parametric flat-plate model in hover. NASA Tech. Mem. 104001.

AIAA 2001-2145 AN EXPERIMENTAL INVESTIGATION INTO THE SOUND PRODUCING CHARACTERISTICS OF SUPERSONIC IMPINGING JETS Brenda Henderson*

Kettering University, Mechanical Engineering Department, 1700 W. Third Ave., Flint, MI 48504 Abstract For NPR less than, or equal to 2.73, large plate tones The results of an experimental investigation into the jet occur for plate diameters greater than or equal to 1/2/2 the structure associated with the production of sound by a nozzle exit diameter. Multiple discrete frequency tones supersonic impinging jet are presented. A convergent are often produced simultaneously and are associated nozzle operated at nozzle-pressure ratios (NPR) with multiple jet oscillation modes. Staging behavior between 3.38 and 4.47, where NPR is the ratio of the about the choked jet screech frequency is also common stagnation pressure to the pressure at the nozzle lip, for larger plate spacings. At higher pressures, large exhausted onto a square plate with side dimensions plate tones occur for plate diameters greater than, or equal to 12 nozzle exit diameters. Results from random equal to, 2 nozzle exit diameters. Single discrete and phase-locked shadowgraph photographs indicate frequency tones usually occur and are associated with that tonal production ceases when the first or second symmetrical jet disturbances.

shock waves develop a conical shape. When tones are produced, the standoff shock wave oscillates and Small plate tones are produced at pressure ratios greater periodic changes in the impingement and near wall than, or equal to, 3.04 and for plate diameters less than, flows occur. Sound is produced in the near wall region or equal to, 2 nozzle exit diameters. Two classes of and is associated with changes in the flow caused by the small plate tones have been identified. Primary small standoff shock wave motion. Unstable flow usually plate tones are associated with large shock wave occurs when the central portion of the flow is subsonic oscillations3 and secondary small plate tones are upstream of the standoff (annular) shock wave. produced by the interaction of jet disturbances with the standoff shock wave and shock waves in the deflected

1. Introduction flow along the plate 6 .

The impingement of a jet on a flat plate produces ground effects including surface erosion, non-uniform The production of large plate impinging tones by surface heat transfer, lift loss, and acoustic loading. underexpanded jets is not well understood due to the Intense discrete frequency sound is often produced with complicated flow structure of these jets. A number of sound pressure levels exceeding the local broadband flow phenomena have been associated with large plate levels by more than 10 dB. Although a number of impingement such as a recirculation zone in front of the studies have documented the oscillatory nature of the plate7"., oscillating shock waves4,7,8,101112, and .vortex flow, the connection between the oscillating flow acceleration in the impingement region. However, the structures and the production of intense acoustic operating conditions very significantly in the reported radiation is not well understood for impingement on experiments and the connection between these flow large plates. features and the production of sound has not been systematically studied.

The production of discrete frequency sound by a supersonic impinging jet depends highly on plate size Discrete frequency sound has been reported for ideally and moderately on nozzle-to-plate spacing and nozzle- expanded supersonic impinging jets despite the lack of pressure ratio (NPR),'z3" 4, where NPR is the ratio of the a strong shock cell structure 3. Although there has been stagnation pressure to the pressure at the nozzle lip. no direct comparison between the tonal characteristics Tones produced by impingement on small plates have of the ideally expanded and underexpanded supersonic significantly different tonal characteristics than those impinging jets, studies indicate that the radiation from produced by impingement on large plates. twin jets issuing from ideally expanded jets is more intense than that issuing from underexpanded jets' 4 .

"Associate Professor, Mechanical Engineering Department, member AIAA Copyright C 2001 by Brenda Henderson. Published by the American Institute of Aeronautics and Astronautics, Inc.

with permission.

236

The present study investigates the structure of tone- The tones falling along the LI line are associated with producing moderately and highly underexpanded symmetrical jet disturbances2 .

supersonic impinging jets. Far-field acoustic Despite the differences in the flow structure of the measurements are coupled with random and phase- ideally expanded and underexpanded jets, there are locked shadowgraph photographs. The oscillation some similarities in the two sets of data. Both types of cycle associated with the production of tones is jets produce impinging tones that display staging documented and a sound production model is presented. behavior. However, staging behavior is much more common for the ideally expanded jet. The frequencies

2. Experimental Apparatus produced by both jets often fall along the LI line for The experiments were conducted in the Acoustic Jet 1.5 < h/d < 3.5, although multiple tones appear to be Flow facility at NASA Glenn Research Center. A more common for the ideally expanded jet.

schematic of the facility is shown in Fig. 1.

Compressed air passed through a 200 mm pipe The most notable difference in the data from equipped with acoustic treatment and flow straightening Krothapalli et al.13 and the present study is the devices. A round convergent nozzle with a 25.4 mm occurrence of 'zones of silence' for underexpanded exit diameter was operated at NPR between 3.38 and flow that are not present for shock free flows. 'Zones 4.74. The jet impinged on a 305 mm x 305 mm of silence' where no tones are produced are indicated in aluminum plate placed perpendicular to the jet axis and Fig. 3. Data for h/d greater than 5 were taken by located between 2.54 cm and 12.7 cm from the nozzle Henderson and Powell 2 and it was found that regions of exit. tonal activity occurred at larger nozzle-to-plate spacings for NPR equal to, or greater than, 3.72 but these tones Acoustic measurements were taken in the far field with displayed staging behavior around the choked jet a calibrated B & K type 4135 microphone and analyzed screech frequency. The tones produced at larger with an Ono Sokki type CF-5200 spectrum analyzer. spacings are assumed to be related to the choked jet screech phenomenon and will not be addressed in this The shadowgraph system consisted of a Photonics study. Since the shock wave structure is significantly Analysis Pal Flash with a 1-2 lisec spark duration, two different for ideally and underexpanded jets, it appears 152 mm diameter spherical mirrors with 152.4 cm focal that the production of tones is affected by the shock lengths, two collecting lenses, one focussing lens, and a wave structure.

35 mm camera body. Phase-locked photographs were triggered by the far field microphone signal. The An instability plot indicating the regions where tones microphone signal was filtered then displayed on a are produced is shown in Fig. 4. The nozzle-to-plate digital oscilloscope. A trigger delay signal was spacing has been normalized by the first cell length in generated by the oscilloscope and sent to a the free jet, A. The limiting nozzle-to-plate spacing programmable waveform generator used to send a beyond which impinging tones are not produced is single pulse to the light source. The signal from a slightly greater than two cell lengths of the free jet.

photodiode was recorded on the oscilloscope to This is close to the plate position where the second determine the exact location in the cycle where the shock wave forms in the freejet location. For NPR less photographs were obtained. The photographs were than 3.8, the first unstable zone ends when the first taken in different oscillation cycles. shock wave develops a conical shape. The formation of a Mach disk appears to be important to the sound

3. Results production process for underexpanded impinging jets.
3. (a) Acoustic Measurements Discrete impingement tones are typically greater than 3. (M) Random shadowyrash photographs 10 dB above the local broadband noise. In this section, Figure 5 shows a series of random shadowgraph acoustic data were plotted for the fundamental photographs taken at NPR = 4.06 for a range of nozzle-frequency tones with amplitudes exceeding the local to-plate spacings. Two shadowgraph photographs were broadband noise by 5 dB. taken at random points in the oscillation cycle for operating conditions where tones were produced and a The acoustic data from the present study and the data single photograph was taken when no tones were from the study of Krothapalli et al.13 are shown in Fig. produced. Discrete frequency tones falling along the
2. In the experiments of Krothapalli et al., acoustic data Ll line in Fig. 2 are produced by the operating were only presented for the ideally expanded jet. The conditions associated with Figs. 5 (a) - (c), and 5 (e).

acoustic wavelength, X, and the nozzle-to-plate spacing, h, have been normalized by the nozzle exit diameter, d. A low frequency sound wave centered on the near wall region and high frequency sound waves centered on the 237

first shock wave and the standoff shock wave are in the free jet and is located close to its axial position in observed in the photographs of Fig. 5 (b) and (c). the free jet. A third stable shock wave is also present.

Although the high frequency sound waves appear to be intense, their frequencies are beyond the detection The results obtained from Fig. 5 indicate that tonal range of the microphones used in the experiments. production is associated with unsteady motion of the These tones are not the focus of the present paper. standoff shock wave. During the oscillation cycle, the standoff shock wave moves axially, changes shape, and, The photographs in Fig. 5 (a) show that when the plate for some operating conditions, periodically disappears.

is located near the end of the first free jet cell length, The end of the first unstable region occurs when the the first shock wave forms close to the nozzle and the plate position is such that the first shock wave is located diameter of the first Mach disk is larger than it would near its position in the free jet and a second dome be in the free jet. During portions of the cycle, a second shaped shock wave appears near the plate. As the plate shock wave forms in front of the plate and the shape spacing is increased, the second shock wave begins to and diameter of the first Mach disk change. As the oscillate and develops a slight conical shape for plate is moved downstream into the second free jet portions of the oscillation cycle. A further increase in shock cell (see Fig. 5 (b)), the diameter of the Mack the nozzle-to-plate spacing causes the second shock disk decreases and the first shock wave moves wave to be positioned near the free jet location and downstream. During the oscillation cycle, the first tonal production ceases. This occurs for plate spacings shock wave changes shape, the standoff shock wave approximately equal to 2.1 - 2.2 free jet cell lengths.

moves along the jet axis, and a wave is observed in the For all greater spacings, the second shock wave is central region of the jet between the first shock wave nearly conical.

and the standoff shock wave. When the plate is located near the end of the first unstable region as shown in Fig. A plot of the shock wave locations in the impinging jet 5 (c), the axial distance between the nozzle and the end for a range of nozzle-to-plate spacings and NPR is of the first shock wave is approximately 88 % of the shown in Fig. 6. The results from this'figure indicate distance to the first cell ending in the free jet. The that the shock locations depend highly on the location second shock wave develops a nearly conical shape for of the plate in the free jet cell structure and only slightly a portion of the oscillation cycle as it does in the free on NPR. In general, the first shock wave forms in the jet. A third shock wave also appears in front of the free jet location for nozzle-to-plate spacings greater plate for portions of the oscillation cycle. than, or equal to, approximately 1.8 cell lengths. The second shock wave forms in the free jet location for The photograph in Fig. 5 (d) was taken for a nozzle-to- nozzle-to-plate spacings greater than, or equal to, plate spacing falling between the first and second approximately 2.1 - 2.2 cell lengths which is close to unstable zones in Fig. 4. No discrete tones are the plate position where discrete tones are no longer produced at this operating condition. The first shock is produced (see Fig. 4).

located in the free jet position and, because of the small diameter of the Mach disk, the flow rapidly accelerates 3. (c) Phase-locked shadowgraph studies to supersonic speeds downstream due to the expansion Phase-locked shadowgraph photographs were taken for fan developed at the end of the first shock wave. A nozzle-to-plate spacings ranging from 0.9 to 1.6 free jet second dome shaped shock wave forms close to the cell lengths and for NPR equal to 3.72 and 4.06 plate. A third (annular) shock wave appears in the supersonic flow behind the second shock wave. Phase-locked shadowgraph photographs for a nozzle-pressure ratio of 3.72 and h/A = 1.35 are shown in Fig.

When the plate is located just in front of the second free 7. Figure 7 (a) has been arbitrarily selected as the jet cell ending, the second unstable region is reached beginning of the oscillation cycle. Although the and the photographs in Fig. 5 (e) are obtained. The photographs were taken in different cycles, the time second shock wave changes shape throughout the delay, t, between Fig. 7 (a) and subsequent photographs oscillation cycle and develops a slightly conical shape is measured as a fraction of the period, T, in one cycle.

at some positions in the cycle. At times, a third (annular) shock wave appears in front of the plate. Near the beginning of the oscillation cycle as shown in Fig. 7 (a), the standoff annular shock wave is in its most Photographs taken for plate spacings greater than the upstream location and a weak moving shock wave is second free jet cell length Figs. 5 (f) and (g). No tones located along the central regions of the jet behind the are produced beyond approximately h/A = 2.1. The first Mach disk. Relative to the moving shock wave, stable second shock wave has a conical shape as occurs the flow behind the first Mach disk must be supersonic.

As shown in Figs. 7 (b) and (c), the wave in the central 238

region of the jet moves upstream and the standoff indicated in the plot, the pressure is higher in the annular shock moves slightly downstream as time impingement region and drops off rapidly at progresses. In Fig. 7 (c), the moving shock wave in the approximately 1.2 jet radii. The higher pressure in the central region of the jet is replaced by a series of sound impingement region may be associated with plane wave waves. Jet disturbances are observed near the first motion in the impingement region, a result consistent shock wave and the radius of the first shock wave with the observed wave motion along the central region decreases. The standoff shock wave begins to move of the jet in Fig. 7. The increase in the pressure downstream in Fig. 7 (d). The photographs in Fig. 7 (e) amplitude near 1.6 jet radii may be associated with and (f) indicate that, near the end of the cycle, the motion of the expansion and compression regions in the standoff shock wave moves toward the plate, near wall jet as the standoff shock wave oscillates.

disappears, and is replaced by a series of compression and expansion waves. The angle of the first shock 4. Proposed sound source mechanism wave decreases dramaticafly when the standoff shock The experiments reported here focussed on moderately wave disappears. and highly underexpanded jets impinging on large plates. Although Mach disks do not occur in the free jet An intense sound wave radiates from the near wall below NPR = 3.8, Mach disks occur in the impinging region and is observed near the nozzle exit in Fig. 7 (d). jet for NPR less than, or equal to, 3.38 for h/d less than High frequency sound waves visible in Figs. 7 (b), (c), approximately 1.5 free jet cell lengths. linpinging jets and (e) appear to originate from the standoff shock operating in this pressure range predominantly produce wave the first shock wave and are most likely produced tones associated with symmetrical disturbances, display by jet disturbances, visible in Fig. 7 (c), interacting with zones of silence, have Mach disks along the central the first and standoff shock waves. portion of the jet for the first unstable region (based on nozzle-to-plate spacing), and become stable when the A plot of the shock wave motion over one cycle for the first or second shock waves develop a conical shape.

operating conditions used in Fig. 7 is shown in Fig. 8. Low frequency "impinging" tones are produced'in the The axial position of the first shock wave changes only near wall region and higher frequency tones are slightly while the axial position of the standoff shock sometimes produced in the jet at the first shock wave wave increases throughout the cycle until a position is and standoff shock wave locations.

reached where the standoff shock wave briefly disappears. The standoff shock wave reforms upstream The instability of these jets appears to be confined at the beginning of the next cycle. predominantly to the impingement and near wall regions. The first shock wave remains relatively The point in the oscillation cycle where sound is stationary, a result in direct contrast to small plate tones produced is indicated in Fig. S. This point was where the first shock wave exhibits large axial calculated by measuring the distance from the near wall oscillations. A comparison made between small plate region to the sound wave in Fig. 7(d), then calculating impingement and large plate impingement at the same the propagation time from the near wall region. The NPR and nozzle-to-plate spacing indicates that, when a sound appears to be emitted near the point in the large plate is used, the first shock wave forms oscillation cycle where the standoff shock wave downstream of the greatest axiaJ distance to the first disappears. shock wave occurring in small plate impingement flow.

3. (d) Plate pressure measurements Large plate impinging tones are part of a feedback loop Unsteady plate pressure measurements were conducted to the nozzle. Jet disturbances created at the nozzle exit by Henderson" for NPR 4.06 and h/A = 1.05. A PCB travel downstream and interact with the first shock type 105A transducer was mounted on a sliding arm so wave causing shock wave and expansion fan that the transducer could be moved incrementally distortions, changes in the slip stream location, and the across the diameter of the plate. For these operating production of sound waves in the flow. The sourid conditions, a single tone falling along the L I line in Fig. waves and stream disturbances travel downstream and 2 is produced affect the slip stream and standoff shock wave. The sound waves reflect from the plate with no phase shift The data from the experiments of Henderson" are and travel upstream in the subsonic flow along the presented in Fig. 9. Only the amplitudes associated central region of the jet. The creation of a large Mach with the LI tone are plotted in the figure. The plate disk in the first shock wave and a plate location that is pressures are normalized by the pressure at the plate reasonably close to the first shock wave causes the flow center. The plot only reflects unsteady pressures in the downstream of the Mach disk to remain at subsonic jet since steady jet pressures occur at 0 frequency. As speeds. As the sound waves move upstream, the slip 239

stream and intersecting expansion fan change causing region (see Morch's). Although wave motion is changes in the supersonic flow in the peripheral regions observed in the central subsonic flow, the process must of the jet. The motion of the stream disturbances and be forced from upstream most likely when the jet the sound waves within the jet cause the standoff shock disturbances and first shock wave interact. As the wave to move along the jet axis and sometimes stream disturbances and sound waves travel disappear. For NPR less than, or equal to 3.72, sound downstream, the slip stream distorts and causes the ceases when the plate distance increases and the first standoff shock wave to oscillate.

Mach disk disappears causing the entire flow behind the first shock wave to remain at supersonic speeds. Tones A better understanding of the flow along the central also cease for higher pressures when the second shock regions of the jet and in the impingement and near wall wave develops a conical shape at approximately b/A = regions is necessary to develop a more precise feedback

2.2. model

and a better understanding of the sound production mechanism. The relative importance of the A 'zone of silence' occurs at intermediate spacings for stream. disturbances and the sound waves in the NPR = 4.06 when the second shock wave forms close subsonic flow to the distortion of the slip stream is not to the plate and is dome shaped. For this situation, the known'. Although Carling and Hunt16 found that, the flow behind the first shock wave accelerates before occurrence of a stagnation bubble did not significantly reaching the second shock wave. Sound .wave motion effect Ithe wall jet in steady flow, an oscillating can only occur in the limited impingement region flow stagnation bubble may be important in an unstable jet and a strong resonance is not produced. This is and this aspect of the flow should be investigated presumably due to the fact that the sonic line is close to further. The nature of the unsteady wall jet also needs the jet boundary and wave motion in the impingement further attention. Unsteady plate pressure region does not significantly effect the location of this measurements indicate that an unsteady region of line or the supersonic flow in the peripheral regions of pressure occurs at approximately 1.6 nozzle radii which the jet. When the distance between the second shock appears to be close to the location where impinging wave and the plate increases slightly, the flow velocity tones are created in the flow. A better understanding of behind the second shock wave increases and the the flow in this region of the wall jet will enhance the standoff shock wave oscillates. development of a more precise sound production model.

An expansion fan occurs at the intersection of the jet boundary and the standoff shock wave. The waves 5. Conclusions from the fan reflect from the sonic line behind the Low frequency impingement tones produced by standoff shock wave as compression waves. The moderately and highly underexpanded supersonic jets reflected compression waves reach the jet boundary and are produced in the near wall region of the jet. The are reflected as expansion waves. A successive pattern tones cease when the second shock wave is located in of compression and expansion continues in the wall jet the free jet position which occurs for a nozzle-to-plate for a few jet radii. In steady jets, local separation has spacing of approximately 2.1 - 2.2 free jet cell lengths.

also been observed in the near wall region (see Carling 'Zones of silence' appear to be associated with the and Hunt' 6) for some operating conditions. As the formation of conical shock waves in the flow. Discrete standoff shock wave oscillates, changes occur in the frequency sound is produced in the near wall region and downstream expansion fan and in the compression and is associated with oscillations of the standoff shock expansion regions in the wall jet. Oscillations of the wave and motion of the expansion and compression wall jet boundary result. Oscillatory separation of the regions in the near wall jet.

flow along the plate may also enhance the motion of the jet boundary. The oscillatory motion of the flow in the Acknowleftements near wall region produces sound that travels back to the This work was supported by NASA Glenn Research nozzle to create stream disturbances, thus closing the Center through the Summer Faculty Researcher feedback loop. Glaznev's' 7 sound production model program. I would like to thank James Brides of NASA which treats the oscillating jet boundary as an Glenn Research Center and J. Panda of Modem oscillating conical membrane may apply to large plate Technologies Corporation for their assistance and tones although his experiments were conducted on support of this project.

small plates.

The feedback loop must include jet disturbances created at the nozzle. Strong resonance is not produced by one-dimensional wave motion confined to the impingement 240

References 14. Wlezien, R. W., and Ferraro, P. J. (1990).

1. Powell, A. (1988). "The sound-producing "Aeroacoustic environment of an advanced oscillations of round underexpanded jets impinging STOVL aircraft in hover," AIAA 90-4016.

on normal plates," J. Acoustic. Soc. Am. 83, 515- 15. Henderson, B. (1993). Sound Source Mechanisms 533. of the Axisymmetric Supersonic Impinging Jet, Ph.

2. Powell, A., and Henderson, B. (1990). "On the D. Dissertation, University of Houston.

tones of round underexpanded jets impinging on 16. Carling, J. C. and Hunt, B. L. (1974). "The near normal plates, AIAA-90-3985. wall jet of a normally impinging, uniform,

3. Henderson, B. and Powell, A. (1993). axisymmetric, supersonic jet," J. Fluid Mech. 66, "Experiments concerning tones produced by an 159-176.

axisymmetric choked jet impinging on a flat plate," 17. Glaznev, V. N. (1977). "Sound field of an J. Sound Vib. 168(2), 307-326. underexpanded supersonic jet impinging on a

4. Glaznev, V. N., and Popov, V. Y. (1992). "Effects barrier," Soy. Phys. Acoust. 23, 142-145.

of the face dimensions of a flat barrier on the self- 18. Morch (1964). "A theory for the mode of oscillations generated in the interaction with a operation of the Hartmann air jet generator," J.

supersonic underexpanded jet," Translated from Fluid Mech. 20, 141-159.

Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza 6, 164-168.

5. Henderson, B. and Powell, A. (1996). "Sound producing mechanisms of the axisymmetric choked jet impinging on small plates: The production of Acoustic primary tones," J Acoust. Soc. Am. 99, 153-162.
6. Henderson, B., and Powell, A. (1997). "The use of an array to explain the sound characteristics of secondary small plate tones produced by the impingement of an axisymmetric choked jet," J.

Acoust. Soc. Am. 102, 1454-1462.

7. Gubanova, 0. I., Lunev, V. V., and Plastinina, L.

N. (1973). "The central breakaway zone with interaction between a supersonic underexpanded jet and a barrier," Fluid Dynamics 6, 298-301 (Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza 2, 13 5-138 (1971)).

8. Ginzburg, I. P., Semiletenko, V. N., and Uskov, V. Camera N. (1975). "Experimental study of underexpanded jets impinging normally on a plane baffle," Fluid Mechanics-Soviet Research 4(3),93-105. Figure 1. A schematic of the experimental facility at
9. Alvi, Iyer (1999). "Mean and unsteady flowfield NASA Glenn Research Center.

properties of supersonic impinging jets with lift plates," AIAA 99-1829. 10

10. Nakatogawa, T., Hirata, M. and Kukita, Y. (1971).

"Disintegration of a supersonic jet impinging normally on a flat plate," J. Spacecraft 8(4), 410- "~ ~ _,LI a ~

411. k4:3 ' NPR 4.40

11. Semiletenko, B. G., Sobkolov, B. N., and Uskov, VJd I NPR4 *.06 g D4+

V. N. (1974). "Features of unstable interaction 0 0 o NPR3.72 between a supersonic jet and infinite baffle," Fluid NPR 3.38 Mechanics-Soviet Research 3(), 90-95. Krothapalli

12. Back and Sarohia (1978). "Pressure pulsations on a flat plate normal to an underexpanded jet," J. 0.1 AIAA 16(6), 634-636.

I 10

13. Krothapalli, A., Rajkuperan, E. Alvi, F., and h/d Lourenco, L. (1999). "Flow field noise characteristics of a supersonic impinging jet," J.

Fluid Mech. 392, 155-181. Figure 2. The acoustic data from the present study and from Krothapalli et al.'3 .

241

O Primary Tone

  • Secondary Tone
  • Tertiary Ton*

- -Cell End

-Free Jet mNo Tones I h/d 10 Figure 3. The acoustic data for NPR = 4.06.

Second Shock Forms in Free Jet Location 2

/, /,/ , "/ / "

,XirAt -SKCkFQrWs-.gFreeMetL-ocgtImqn /-

Conical Shock - "' /

,/'i  !/Uastable

' / /'/ /// i7 / "7 /,/// ,,. '.,,. .. 7 3 4 NPR 5 6 Figure 4. The unstable regions where discrete impinging tones are produced.

(d)

Figures 5 (b), (c), (d). See next page for caption.

(a)

Figure 5 (a). See next page for caption.

242

2.80 c"NPR 3388 x3 Cell 3 Shocks DI 2.40 toNPR3.7?

ANPR 4.066&-ý- xi,*- *= --

2.00  :. x x

[oNPR4.4 - 4 *  ;

x/A 1.60 1.20 Z -x 0.80 0.40 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 h/A Figure 6. The axial locations of the first, second, and third shock waves.

Figure 5. Shadowgraph photographs taken at NPR =

4.06 and (a) h/A 0.95 (f= 10 kHz), (b) h/A 1.38 (f=

7.9 Hz), (c) h/A 1.61 (f-= 6.75 Hz), (d) h/A = 1.78 (no tones), (e) h/A = 1.90 (f= 5.75 Hz), (f) h/A 2.13 (no tone), and (g) h/A = 2.60 (no tones).

243

1.6 1.5 1.4 X-1.3 X X4

- 1.2 0.9 p * -*___Sound Xxjx Generation 0.9 cation 0_lR 08v 0 0.2 0.4 0.6 0.8 1 Time/Period Figure 8. Shock wave motion over one oscillation cycle for NPR = 3.72 and h/A = 1.35.

1 0.8 4 0.6 pc/pc 0.4 +

0.2 4 0

0 1 2 3 4 5 6 x/r Figure 9. Root-mean-square plate pressures at radial locations along the plate, where x is the distance from the center of the plate to the pressure tap, and r is the nozzle exit radius.

ýe) (t)

Figure 7. Phase-locked photographs taken at NPR =

3.72 and h/A = 1.35 for (a) t/T = 0, (b) t/T = 0.12, (c) t/T = 0.28, (d) t/T = 0.48 (e) t/T = 0.60, and (f) tUT 0.78.

244

Fluorescence Imaging Study of Impinging Underexpanded Jets Jennifer A.(Wilkes) Inman*, Paul M. Danehyt, Robert J. Nowak', and David W. Alderfert NASA Langley Research Center, Hampton VA, 23681-2199 An experiment was designed to create a simplified simulation of the flow through a hole in the surface of a hypersonic aerospace vehicle and the subsequent impingement of the flow on internal structures. In addition to planar laser-induced fluorescence (PLIF) flow visualization, pressure measurements were recorded on the surface of an impingement target. The PLIF images themselves provide quantitative spatial information about structure of the impinging jets. The images also help in the interpretation of impingement surface pressure profiles by highlighting the flow structures corresponding to distinctive features of these pressure profiles. The shape of the pressure distribution along the impingement surface was found to be double-peaked in cases with a sufficiently high jet-exit-to-ambient pressure ratio so as to have a Mach disk, as well as in cases where a flow feature called a recirculation bubble formed at the impingement surface. The formation of a recirculation bubble was in turn found to depend very sensitively upon the jet-exit-to-ambient pressure ratio. The pressure measured at the surface was typically less than half the nozzle plenum pressure at low jet pressure ratios and decreased with increasing jet pressure ratios. Angled impingement cases showed that impingement at a 600 angle resulted in up to a factor of three increase in maximum pressure at the plate compared to normal incidence.

Nomenclature D, = nozzle exit diameter Dimp = impingement distance, measured from nozzle exit plane to impingement target JPR = jet pressure ratio (ratio of nozzle exit to ambient pressure)

NO = nitric oxide Po = nozzle plenum pressure Pa = test chamber (ambient) pressure Pe = static pressure at nozzle exit Pma = maximum (peak) pressure PLIF = planar laser-induced fluorescence Reexit = Reynolds number at nozzle exit RTF = Return to Flight lVe = velocity at nozzle exit

/re = dynamic viscosity at nozzle exit Oimp = impingement angle A = density at nozzle exit I. Introduction in the wake of the loss of the Columbia orbiter due to a breach in the leading edge of its left wing, a series of tests were conducted in an effort to better understand the flowfields resulting from breaches in the outer structure of reentry vehicles. Penetration of hot gas through breaches could impact internal structures, causing failure of the Research Scientist, Advanced Sensing and Optical Measurement Branch, MS 493, AIAA Member Research Scientist, Advanced Sensing and Optical Measurement Branch, MS 493, AIAA Associate Fellow Research Scientist, Aerothermodynamics Branch, MS 408A, AIAA Member Research Scientist, Advanced Sensing and Optical Measurement Branch, MS 493 1

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vehicle. These tests were conducted in support of the Orbiter Aerothermodynamics Working Group as part of NASA's Shuttle Return to Flight (RTF) effort. A subset of these tests used planar laser-induced fluorescence (PLIF) of nitric oxide (NO) to visualize the flow issuing from a nozzle into a low-pressure chamber. The flow environments encountered in these tests include regions of low static pressure, turbulent and/or three-dimensional flow structures, and regions of interest with both strong and weak density gradients. Such conditions, though frequently encountered in aerospace simulation facilities, cannot be satisfactorily visualized using traditional path-averaged techniques such as schlieren and shadowgraph, which rely on sufficiently strong density gradients. An alternative approach was therefore required in order to satisfy the objectives of these tests to characterize the features of these nozzle flows. PLIF is a flow visualization technique that provides non-intrusive measurements with sub-millimeter spatial resolution and flow-stopping (1 gis) temporal resolution in many of these challenging testing regimes'. PLIF images reveal the size and location of flow structures. Additionally, these images can be used to identify the laminar or turbulent state of these flows 2. We have previously reported the use of PLIF to investigate free (non-impinging) underexpanded sonic jets3 and have compared a subset of these results with computational fluid dynamics (CFD)4 . This paper will focus on the results of the test cases in which the nozzle flow was directed onto the surface of a flat plate (hereafter referred to as the "impingement target") at various distances and angles. A future paper will report the results of these tests in regards to the effect of jet impingement upon the process of transition to turbulence. This paper will mainly focus upon the test cases involving steady, laminar, impinging jet flows.

A major difference between this work and the majority of previous investigations of similar impinging flows by others is that this work focused on relatively low Reynolds numbers, spanning from many fully laminar test cases to transitional and turbulent cases. By contrast, other investigations have generally involved higher Reynolds numbers-up to three orders of magnitude higher than the very highest Reynolds numbers investigated in the present work and well within the turbulent flow regime. Table 1 gives a summary of test conditions for several past investigations.

Another distinction is that Me Reexit JPR Pa Dimp O Type(s)

T of these previous studies have (pip') (atm) / m (I measurements generally been concerned with De (deg) - near-field impingement, on the AMl & lyer 5 1 1.9E6 2.6 1 1.5-2 90 PIV, shadowgraph, order of a few jet diameters. The (1999) acoustic, surFace impinging jet configurations in the present work, with the Donaldson & 0.57,1 1.9E5- 1-3.57 1 1.90- 15-90 Pltot & surface Snedeker 6.7 1.3E6 39.1 pressure, grease closest impingement distance (1971) streak heat transfer being about 10.5 nozzle 8 diameters and the furthest being Kim et al. 1 9.7E5- 1.1-3.7 1 1.8-2 90 Computational (3D (2003) .7E6 unsteady NS) 39.5 nozzle diameters, are all Lamont & 2.2 4.0E0- 1.2,2 1 0.75-15 30-90 Shadowgraph, relatively far-field compared to Hunt 9 8.7E6 surface pressure the studies listed in Table 1 (with (1980) the exception of Stitt." Note also Love & Lee 10 1-3 1.7E5- 0.25-19, 1: 5e-S NA NA Schlieren, method of that, even though the (1958) 5.7E7 60- characterislics investigations of Donaldson and 41,820 calculations Snedeker6'7 had some limited Stitt 11 1-9.85 3.7E4- 545- 4.7E-4 0.4-40 90 Schlieren, surface data at about 40 nozzle (1961) 2.7E7 1.51E5 pressure, surface erosion diameters, the vast majority of Present work 1,2.8 170- 1-37 1.3E-3 10.5- 90, 60, PLIF, surface their data were within about 15 3.6E4 -0.094 39.5 45 pressure nozzle diameters). In rocket Table I. Comparison of previous underexpanded jet studies with the present plume/ground interaction investigation. The quantities compared here are, from left to right: nozzle exit Mach applications, ground erosion was number, exit Reynolds number, jet (nozzle-exit-to-ambient) pressure ratio, ambient a primary concern, and the near pressure of test section, impingement distance in nozzle diameters, impingement angle, field was thus of greatest and type of study and/or measurements. significance. Many of these studies were conducted at atmospheric pressure. Of the studies listed in Table 1, only those of Stitt1" and Love and Lee 'o investigated flows into sub-atmospheric pressure environments. For those studies, the intended application was rocket and thruster operation in the vacuum of space, and so the ambient pressures used were one to two orders of magnitude lower than those of the present study, the conditions of which were designed to be relevant to the reentry conditions experienced by the space shuttle orbiter.

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In addition to flow visualization, pressure measurements were recorded on the surface of the impingement target.

The observed pressure profiles along the centerline of the target were found to fall into two broad categories: those with the maximum pressure corresponding to the centerline of the jet axis, and those with the maximum pressure occurring in an annular ring, away from this axis. PLIF images helped to elucidate the characteristics of the resulting pressure profiles by highlighting the flow structures corresponding to distinctive features of these pressure profiles.

II. Experimental Description A. Facility and Hardware Tests were conducted at the NASA Langley Research Center using the test section of the 15-Inch Mach 6 Air Tunnel as a vacuum chamber. For a detailed description of the facility and hardware, see Ref. 12. A schematic of the layout is PI Laser shown in Fig. 1. Nitrogen or helium sheet seeded with 0.5% nitric oxide was plumbed into a heated stainless steel Gas cabinet plenum, through a nozzle, and into the -

vacuum chamber. Mantroloer asfo le..

Two different nozzles were used. The geometry of these nozzles is illustrated in Fig. 2. The first was a converging nozzle with a nominal exit Mach number of 1,.

This nozzle is hereafter referred to as the sonic nozzle. The second was a Mass flow converging/diverging nozzle with a nominal exit Mach number of 2.6, hereafter called the supersonic nozzle. ZVacuum chamber Mass flow controllers controlled the flow Figure 1. PLIF system and experimental hardware. Gas is plumbed rates, which indirectly controlled the through a heated plenum and nozzle into a vacuum chamber. A laser sheet plenum pressure upstream of the nozzle. enters the top of the vacuum chamber and excites nitric oxide molecules in the Optics directed a 100mm wide by flow. An intensified CCD camera positioned at right angles to the laser sheet

--0.2mm (FWHM) thick laser sheet images the fluorescence.

vertically downward through a window in the top of the test chamber.

The laser sheet was oriented 0.,8 /0.8' in a plane perpendicular to 0.6 " 06* "

the nozzle exit plane. The 0.4 0.4 sheet forming optics were 9 0.2 ' o021 mounted to a translation = o 0 stage. A stepper motor ...9 -0.2 90.21 attached to the translation -0.4 -0.4 stage allowed fine -0.6 'o. ,

adjustment of the spanwise 08

-. o.08 position of the laser sheet. 0 0.5 1 1.5 0 0.5 1 1.5 2 diameter inches inches A 4-inch stainless steel impingement Figure 2. Sonic and supersonic nozzle geometries. The design exit Mach numbers for disk was positioned at these two nozzles are 1 and 2.6, respectively.

various distances and angles downstream of the nozzle exit. Figure 3 shows a diagram of this apparatus. The center of this disk included 32 pressure taps. They were spaced 0.045 inches apart, and had an inside diameter of .021 inches. The taps were oriented in a vertical plane (the plane of the laser sheet), on the jet centerline. From the camera's viewing angle, the jet flow was from left to right.

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B. Model Configuration Parameters Impingement distance was continuously variable from 0 to 6 inches and impingement angle' was continuously variable from 90' to 00, though the minimum impingement distance at non-normal impingement angles was limited by the physical size of the target. In practice, changing impingement distance or angle required approximately a half day of down time, and so a limited number of discrete distances and angles were included in the test matrix. For the majority of cases, the impingement disk was oriented normal to the jet axis (which is defined to be a 900 impingement Figure 3. Stainless steel plenum and impingement target hardware. The angle). Two configurations included impingement angle and distance were continuously variable. A close-up view oblique impingement angles of 450 and shows the orientation of the 32 pressure taps in the center of the impingement disk. 601. For these cases, the target was rotated clockwise, as viewed from the camera viewing angle, about the horizontal axis perpendicular to the jet axis.

For each hardware configuration, two flow parameters were varied: the exit Reynolds number (Reei,) and the jet pressure ratio (JPR). Reexi, was defined in terms of the nozzle exit diameter, De, and the density pe, velocity Ve, and dynamic viscosity ,/at the nozzle exit, as given by (1).

Reexi,- Pe Ve D, (1)

Re*xi, was varied by changing the mass flow rates and nozzle plenum temperature. JPR was defined as the ratio of the static pressure at the nozzle exit, pe, to the ambient pressure in the test chamber, p., according to (2), and was varied by changing the test section pressure for a given Reynolds number (and therefore, a fixed pe).

JPR =- P (2)

Pa C. Planar Laser-Induced Fluorescence (PLIF) Flow Visualization Technique The PLIF laser system includes a tunable Nd:YAG-pumped dye laser followed by doubling and mixing crystals.

The resulting output, at 226.256 nm, was tuned to excite the strongly fluorescing spectral lines of NO near the Qi branch head (Q denotes a change in rotational quantum number equal to zero). Optics formed the beam into a laser sheet that was 100 mm wide x -0.2 mm thick (FWHM) in the measurement region. Fluorescence was imaged onto a gated, intensified CCD at a viewing angle normal to the laser sheet. Images were acquired at 10 Hz with a l ts camera gate and a spatial resolution of between 3 and 7 pixels/mm, depending on the required field of view for a given hardware configuration. This system is detailed in Refs. 3, 4, and 12. The PLIF system is also capable of pressure-sensitive and velocity-sensitive flow imaging.

IlI. Analysis Methods: Flow Visualization Image Processing Sets of 100 single-shot images were acquired for a range of unit Reexit (177 to 35,700) and JPR (1.8 to 38). So-called background images were also acquired on each day of testing for a range of vacuum chamber pressures.

During the acquisition of these background images, the laser was fired but no gas was flowing through the nozzle.

Any nonzero intensity in these background images is attributed to either camera dark current or the laser scatter and room light not blocked by the filter in front of the camera lens. Averaged background images were created from the average of 100 single-shot images in order to smooth out random shot-to-shot variations in background intensity.

Single-shot images were processed to correct for background scattered light and camera dark current as well as mean spatial variations in laser sheet intensity. Conveniently, jet gas containing nitric oxide diffused relatively uniformly into the test chamber in regions away from the jet, but still imaged by the camera. The fluorescence from 4

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the diffuse nitric oxide in these regions provided a convenient laser-energy reference, allowing the spatial variation in the laser intensity to be corrected. This was accomplished on a shot-by-shot basis by first selecting an area of the image above the core of the jet flow and then establishing the average pixel intensity along each column in that region.

Raw images were 512 x 512 pixels; images presented in this paper have been cropped top and bottom to show the regions of greatest interest. In some of the earlier runs, the spatial resolution was determined by imaging a ruler in the same plane as the laser sheet. This process was improved midway through this set of tests, after Run 200. A dotcardwas used in place of a ruler. Dotcards consisted of a rigid metal plates covered with a sheet of paper. The paper was white with black squares printed in a regular grid pattern. Spatial resolution was calculated by capturing images of a dotcard positioned in the same plane as the laser sheet. The optical access in these experiments permitted perpendicular viewing of the measurement plane and no significant perspective or lens distortion was found in the images.

IV. Results Table 2 shows the range of conditions and hardware configurations for which data were taken during the impinging jet Supersonic Nozzle Sonic Nozzle study. Reynolds numbers and jet pressure ratios were calculated 1mP#VO-m*nt FV/VI V P pFV/V V' P conflgw.bon based on nozzle exit conditions. The table list the number of cases 1"@90" 25 5 that were studied for each combination of hardware configuration 175090 25 2221 5 and type of PLIF imaging that was investigated in these tests. For 2,5"@90' 22 19:21 24 each flow visualization case, 100 single-shot images were 250@60- 18 acquired. The laser sheet was also swept spanwise through the flow, providing slices of the flow field, though these results are 3.7..45 23.

not shown here. The velocity-sensitive, pressure-sensitive, and 53 90" 22 density-sensitive imaging data are not presented in this paper, with (freejet) 88 11 12 53 8 the exception of one pressure-sensitive image in Fig. 9. Re,,' 600-14,000 2,400-35,000 JPR 1-16 3-27 A. Characteristic Flow Structures

1. Sonic andsupersonicfreejet structures Table 2. Matrix of configurations for which data were acquired in the impinging jet cases.

Free (non-impinging) laminar jet cases are seen to exhibit FV/VI indicates flow-visualization and volume-flow structures that are similar to those of other cases having the imaging runs, V indicates velocity runs, P indicates same JPR2 . That is, two laminar cases with similar JPRs but pressure-sensitive runs, and p indicates density-different Reynolds numbers will appear more similar than two sensitive runs.

cases with the same Reynolds numbers but different JPRs. For sonic nozzle cases, flows can be divided into two major groups:

those with a repeating diamond shock structure, and those with a barrel shock structure, a Mach disk, and a streamwise high-velocity jet boundary (seen for flows with JPRs greater than about 3).2,3 The diamond shock structure is seen for JPRs less than about three, such as in Fig. 4, where several diamond shock cells can be seen in the first several jet diameters downstream of the nozzle exit. Figures 5 and 6 show higher JPR PLIF images resulting in an underexpanded jet issuing from a sonic nozzle. Key flow structures are labeled in these figures. Figure 5 shows the nozzle plenum, nozzle exit, and ambient conditions, as well as the major shock structures and relative Mach numbers in each region of the flow. Additional flow features are labeled in Fig. 6. The arrows within the high-velocity jet boundary qualitatively indicate Figure 4. Diamond shock pattern in flow from the velocity profile of the gas in this region. For a good sonic nozzle. This image is a 100-shot average of a flow with JPR = 1.9 and Re,,it = 417 (Run 5).

description of the flow features shown in these figures, see Refs. 5 The scales are in inches, with the smallest hash and 12. marks measuring 1/16th in.

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For cases with the Mach 2.6 supersonic nozzle, the division between repeating shock patterns and barrel shock/Mach disk patterns happens at a JPR of about 4. For smaller JPRs, a repeating pattern analogous to the diamond shock pattern is evident, with a chain-like pattern of alternating spatial minima (high-pressure nodes) and maxima (low-pressure antinodes).

This oscillating flow pattern can be seen for two cases in Fig. 7. As JPR increases, the wavelength of this oscillating pattern decreases. As a result, the number of cell structures within a fixed distance decreases for Figure 5. Ma jor flow structures of highly-underexpanded jets. The larger JPRs. Above a JPR of about 4, appearance of a Mach disk is associated with jet pressure ratios greater than high pressure nodes are no longer about 3 for the scinic nozzle and greater than about 4 for the supersonic nozzle.

evident, and as JPR continues to increase, the oscillations in the high-velocity jet boundary gradually decrease. Even larger JPRs lead to a modified barrel shock structure-elongated into a more egg-like shape than its comparable sonic jet counterpart-with a Mach disk and a streamwise high-velocity jet boundary, as shown in Fig. 8. In the upper image, note how the upper and lower jet boundaries appear parallel to one another. The lower image was acquired with greater magnification, and the shock and expansion reflections Figure 6: Detail in the high-velocity jet boundary image is from Rueu flow structures o0 ntgnhy-unuerexpano in 56 with JPR = 29.1 and Reek = 4,294.

(labeled in Fig. 6) are visible in this lower image.

2. Impingingjet structures Impinging jet flows can be divided roughly into three regions: the jet flow upstream of the impingement region, the impingement region, and the wall jet flow (where the flow has become parallel to the surface of the impingement target). For steady flows, the flow structures that are observed in the upstream region are essentially identical to those in free jet cases.

Impingement region flow structures are described below. In the wall jet region, several factors act to decrease the intensity of the fluorescence. First, mixing of the jet fluid with the ambient gas is enhanced by the physical dispersion of the jet gas. This results in a decreasing mole fraction of nitric oxide as the gas moves away from the jet centerline. This, in turn, tigure /. unuerexpanuea supersonic jets at iow pressure results in a reduction of fluorescence signal near the ratios. Images are 100-shot averages Top: Run 354, JPR =

plate, and so the details of the flow in the wall jet 2.0, Reex, = 4,605; bottom: Run 222, JPR = 3.0, Reexa = 3,370, region are not necessarily well-resolved. Arrows mark examples of flow minima and maxima. Scales are in inches; the smallest hash marks measure 1/16th in.

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Flows in the impingement region may exhibit several additional flow structures. When the flow impinging on the flat plate is supersonic, a normal shock parallel to the impingement surface, called a plate shock, may be formed.5 Under certain flow conditions, a high pressure bubble of gas may build up between this shock and the impingement surface, causing the shock to move further away from the surface.' '314 Choosing to excite pressure-sensitive spectral lines1 2 at a laser wavelength of 225.693 nm (in which the fluorescence signal is most strongly dependent on pressure, with much weaker dependence on temperature) makes identification of such a stagnation bubble (also called a recirculation bubble) and/or normal plate shock much easier, as the pressure rise inside the recirculation region results in a large increase in intensity compared to the free jet region. Figure 9 illustrates this, with two images of similar flows, taken with the laser at two different frequencies. Both images are averages of 100 single-shots of supersonic flows, taken at an impingement Figure 8. Supersonic free jets with Mach disks and parallel distance of 1.75 in. (10.7 nozzle diameters). The image high-velocity jet boundaries. Both images are 100-shot on the left was acquired with the laser tuned to flow averages. The first image is from Run 236, with JPR = 16.2 visualization lines (226.256 rim). The image on the right and Reex, = 13,104; the second is from Run 347 with JPR = 12.6 was taken with the laser tuned to pressure-sensitive lines and Re,, = 10,173. Scales are in inches; the smallest hash (225.693 nrm). Note the well-defined boundaries of the marks measure 1/16th in. Note the magnified scale of the lower recirculation bubble in the pressure-sensitive image as image. compared with the flow-visualization image. By contrast, note the lack of signal in the low pressure region inside the barrel shock in the pressure-sensitive as compared to the flow-visualization image, where there is signal throughout the flow and the jet boundary is more clearly defined.

Several studies in the literature have discussed the formation of recirculation bubbles for some combinations of jet pressure ratio and impingement distance. Alvi et Figure 9. Comparison of flow visualization and pressure-sensitive PLIF. Left: al. ' give a good description of JPR=3.1 (Run 363). Right: JPR=3.0(Run 451). Dim=/De=10.7 (1.75 in.) for both. The recirculation bubble formation.

scales are in inches, with the smallest hash marks measuring 1/16th in. Mackie and Taghavi"6 found that recirculation bubble formation was purely a three-dimensional phenomena; that is, two dimensional jets (quasi-two dimensional in experimental studies, or truly two-dimensional in computational studies) never resulted in recirculation bubble formation. This is less surprising in the experimental cases (which can never be truly two-dimensional), since the recirculation bubble is shaped like a bell, and requires the annular pressure "seal" around the ring where it intersects with the impingement plate in order to be a stable feature. The gas inside the recirculation bubble acts as a high-pressure reservoir, contained by the plate shock upstream, the high-velocity jet boundary impingement along the outer edge, and the impingement disk surface.

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B. Flow Structure Comparison with Pressure Profiles Consider an impinging jet flow with a uniform momentum profile throughout the core of the jet. One would expect the pressure profile of such a jet to resemble a top hat function, with roughly uniform pressure across the intersection of the jet with the 0 0.1 0.2 0.3 0.4 0.5 0.6 Ps Measured pressure (psi) impingement target, dropping to near ambient pressure away from the core of Figure 10. Pressure profile with a single, central peak. This profile is for the jet. Modifying the situation to supersonic nozzle Run 544 with JPR = 1.5, Reexk= 1,317, Op= 900 and 062 include viscous effects, one would Dir/De= 15.2, pa=0. psi. A dashed line indicates the ambient pressure. A single-shot PLIF image from this run is shown on the left. The scales on both expect to see a decrease in the image and the graph are in inches, with the smallest hash marks equal to momentum-and therefore a decrease in 1/16th in.

pressure on the impingement surface-along the edges of the jet. This modified pressure profile would be peaked in the center, smoothly dropping off to the ambient pressure toward the edges of the jet flow. In fact, for some cases, this describes the pressure profiles that have been measured. An example is shown in Fig. 10. The PLIF 0

image on the left and the graph of pa1h.05h0.1 0.15 Measured pressure 02 (psi) 0.25 measured impingement pressure on the right are shown aligned and equally Figure 11. Pressure profile with a double peak. This profile is for scaled, so that the vertical axis on the supersonic nozzle Run 536 with JPR = 5.4, Reexf= 2,302, Oinp= 900 and graphd, mothatc the vertical locionte DimWDe= 15.2, pa=0.03 5 psi. A dashed line indicates the ambient pressure. A graph matches the vertical location single-shot PLIF image from this run is shown on the left. The scale on the along the impingement plate in the image is in inches, with the smallest hash marks equal to 1/16th in.

image. All pressure profiles presented herein are time-averaged.

For some flow conditions, the pressure profiles are quite different than the smooth single-peaked profile predicted by the simple explanation. For example, some profiles typically exhibit a double-peaked structure, with the maximum pressure occurring away from the flow centerline. The peaks in pressure are found to coincide with the location of the impingement of the high-velocity jet boundary or with the intersection of the shock structure surrounding a recirculation bubble. Fluid mechanically, this can be understood because the high-velocity jet boundary carries with it a great 0 2 3 4 5 6 7 8 deal of the momentum and thus creates a larger Pa Normalized pressure (p/pa) pressure rise as it impinges on the flat plate, Figure 12. Relation of flow features to the maximum and compared to the slower jet core, which has passed minimum measured pressures. The PLIF image is a close-up of through a normal shock wave at the Mach disk. The the impingement region for the flow in Fig. It and is show to pressure between these peaks is often nearly scale with the graph. The smallest hash marks on the vertical constant, while the pressure outside these peaks scale of the graph are 1/16th in.

drops off toward-and sometimes dips briefly below-the ambient pressure. Figure 11 shows an example of this type of profile. The high-velocity jet boundary impinges on the flat plate, and is partly reflected. That is, the flow does not immediately become tangent with the wall, but rather first appears to reflect off the surface before becoming a pure wall jet. This results in an annular suction region beneath the place where the flow is skipping above the surface, where the pressure is actually lower than ambient. Figure 12 shows a close up of the flow in Fig.

11. This is a case with a strong suction ring. Arrows identify the regions of maximum and minimum pressure, 8

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clearly illustrating the connection between flow features and surface pressures. A dashed vertical line indicates the ambient pressure (the pressure has been normalized by this pressure). Note that the actual peak pressures may occur between pressure taps, and thus may be greater than the measured peak pressure.

0.3 C. Reynolds Number Effect on Pressure Profiles

-Re,,=1,675; Run739 Like their free jet counterparts, the shape of

" 0.25 -Re.xr=932; Run730 impinging jet flow structures are similar for those runs S Pa, Run739 that have similar JPRs (for a given nozzle type), so to 0,2

0) 2 p., Run73O long as the runs are all laminar. It is then not surprising that the shapes of the pressure distributions

.30.15 for runs with the same JPR have similar features.

However, for runs with matching JPR but different o .1 values of Reexit, the magnitude of the measured pressure co profiles increases with increasing Reexit. This is 4) 20.05 expected to be the case because, for constant gas

-1 -0.5.above centerline 0 00 1 Distance (inches) plenum temperatures, Reexit is proportional to plenum pressure (po). Self-similar pressure profiles can be Figure 13. Measured pressure profiles. Two impingement obtained for runs with the same JPR by normalizing all surface pressure profiles from laminar runs with the same jet pressure ratio but different exit Reynolds numbers are shown. the measured impingement disk pressures by either po or Pa.

"*2 Figures 13 and 14 graphically depict the effect of 1.8 L'-Re.,

J 1 =1,675;Run730 Run739 normalization by p.. Figure 13 shows pressure

-Re..i,=932; profiles from two runs with essentially the same JPR

0) 1.6 6 pa, R.n739 (2.8), but different values of Re,1 it (1,675 and 932).

1.4 P.Run73O p Figure 15 shows these same data after they have been normalized by the ambient pressure for either run. The

-o 1.2 two normalized profiles exhibit a high degree of N0.8 overlap.

01

-o1.

D. Jet Pressure Ratio Effect on Pressure Profiles The shape of the pressure profile was found to Z -1 Distance

-0.5 above centedine(inches) 0etdn 1nhsdepend heavily on the jet pressure ratio. To illustrate this, consider Figs. 15-17. In Fig. 15, the maximum Figure 14. Normalized pressure profiles. This shows the (peak) pressure (p,,m,) has been graphed versus JPR.

same impingement surface pressure data as Fig. 13, normalized Data have been included for both steady and unsteady by the ambient (chamber) pressure of each run. This normalization results in nearly self-similar profiles. laminar supersonic runs with an impingement distance (Dimp) of 15.2 nozzle diameters (2.5 in.) and 0.3 - impingement angle 0 imp of 900. In this graph, the JPR 02 1.0 pressures have been normalized by the nozzle plenum

  • . 0.25
  • 1.5 pressure (p0). Peak pressures are significant in
  • 2.0 aerothermal applications because they may be 0.2 2.0 42.8 associated with regions of peak heating. The maximum 0.15
  • 5.4 pressure, normalized by the plenum pressure, will be called the recovery pressure to indicate that this

.46 14.3 quantity represents the maximum plate pressure as a E 0.1 2 fraction of the stagnation pressure. Keep in mind that the discrete (as opposed to continuous) nature of the Z° 0.05 pressure taps results in measured peak pressures that are less than or equal to the actual peak pressure, which 0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 may occur between taps.

JPR, Jet Pressure Ratio In Fig. 15, notice that the recovery pressure for this nozzle/plate configuration is always less than 0.3.

Figure 15. Supersonic nozzle recovery pressure as a function of JPR for one impingement distance, 900 Next, notice that for JPRs of less than about 5, the impingement. Dimp / De =15.2 (2.5 in.). Data from runs having values are seen to exhibit relatively large variations exit Reynolds numbers ranging from 380 to 12,500 are included around the apparent mean. Above about 5, the value of in this graph. the recovery pressure is seen to decline smoothly, American Institute of Aeronautics and Astronautics

without these large fluctuations. The oscillations 528 52 that are seen for low JPRs are not simply noise in the data, but corresponds to variations in flow structures that are very sensitive to small changes in JPR in this region. The colored data points in Fig. 15 correspond to the PLIF images and their 0 0.15 0.3 associated pressure profiles shown in Fig. 16. The images are labeled by their JPR. The number of 544 cells (that is, the number of low-pressure antinodes or flow maxima) between the nozzle exit and the impingement target is seen to __

decrease for increasingly large JPR, from about 4 -.

cells in the second image, to about 2 1/2/2 cells in the 0 0.15 0.3 fifth image. In the sixth image, no high-pressure 540 nodes are evident. Instead, this image and the last image both show a flow with a barrel shock and normal Mach disk.

As a further illustration of the dependence of the recovery pressure on JPR, consider Fig. 17. 0 0.15 0.3 Here, pressure profiles are shown for two runs 3__

with very similar jet pressure ratios. The top profile has a double-peaked structure, whereas the bottom profile is single-peaked. This is due to the existence of a recirculation bubble in the top image, and the lack of such a feature in the bottom 0 0.15 0.3 image. The sudden emergence or disappearance 541 of a recirculation bubble that results for small changes in JPR is an effect known as staging.12 Staging behavior is the exhibition of non-continuous phenomena in a flow, or rather, discrete jumps from one continuous region (or 0.15 0.3 stage) to another. This staging behavior causes01 the oscillations shown in Fig. 15. Subsequent 536 peaks of these oscillations correspond to different numbers of nodes, and also correspond to swapping between single and double peaked pressure profiles. 0 0.15 0.3 For supersonic normal impingement cases with JPRs above about 4, a double-peaked pressure profile was always seen, even in cases with no 537 recirculation bubble. In such cases, the peak pressures were found to occur at the intersection of the high-velocity jet boundary with the impingement The behavior target.of the recovery pressure as a Nomlie Presur 0.3 function of JPR is shown in Fig. 18 for four Normalized Pressure pip0 supersonic normal impingement (Oimp=90°) Figure 16. Single-shot PLIF images and the corresponding configurations with different impingement normalized pressure profiles for the colored data points in Fig.

15. JPR are listed in white on each figure and run numbers are listed distances. All four configurations are similar to in black in the upper right-hand comer on each graph. All runs have that shown in Fig. 15 in that they all show 0.--=9 0 °, Dimp/De = 15.2 (2.5 in.). The smallest hash marks on the fluctuations in peak pressure for JPRs associated scales are 1/16e in.

with oscillating flow structures and show a lack of fluctuations for higher JPRs associated with flows having a Mach disk. Interestingly, the behavior appears to be relatively independent of impingement distance, at least for the range of impingement distances (10.7-30.5 nozzle diameters) in this study. A solid black line denotes a 10 American Institute of Aeronautics and Astronautics

Run 371 proposed empirical model for the mean behavior of the recovery pressure (neglecting the higher order oscillations around the mean). The equation for the empirical model is given by Eq.

(3):

P.x. 0.34 (3)

Run 377 P0 JPR This coefficient in Eq. (3) was found by performing a least squares fit to the data for JPR

> 1.5. Note particularly that, for impingement distances between about 10 and 30 nozzle diameters, this result does not depend on 0 2 4 6 8 10 impingement distance. This relation may not Normalized pressure (P/Pa) hold for arbitrarily large or small impingement Figure 17. Staging effect in impingement pressure profiles. distances, so caution is warranted in its Graphs show the sensitivity of profile features to small changes in application to flows outside the range of tested JPR, for two cases with 0 imp= 90' and Dip / De = 10.7 (1.75 in.). The configurations. But within this range, one can see upper image is for JPR = 1.7 (Run 371) and the lower images is for JPR = 1.8 (Run 377). Pressures have been normalized by the that the recovery pressure for supersonic (Mach ambient pressure, Pa. Scales on images and vertical scales on graphs 2.6) underexpanded (JPR >1.5) jets, the recovery are in inches, with smallest hash marks equal to 1/16e in. pressure will be less than 0.34 times the plenum pressure. The decrease in recovery pressure at large jet pressure ratios results partially from the increased surface area over which the jet flow impacts the impingement target. An additional effect may result from the pressure losses associated with normal shock waves (the Mach disk) at higher JPR versus the oblique shocks associated with oscillating flow structures at lower JPR.

Although Fig. 18 indicates that the peak pressure is found to be somewhat independent of distance for supersonic nozzle cases, the shape of the pressure profile does change with distance. This is illustrated in Fig. 19. Four single-shot PLIF images are shown for four runs with similar JPR but different impingement distances. Pressure profiles (normalized by Po) are shown on the same graph. Note that the pressure transducer at the -0.135 in. location was faulty and so it appears that the peak pressure was not captured on both sides of the jet for two of the cases. The pressure profiles are all double-peaked (as expected since these flows all have Mach disks and JPR > 5) and all have similar peak pressures. However, the pressure deficit near the jet centerline is more or less pronounced, depending on distance. One explanation for this is that the intersection of the jet with the

-'d 0.4-0.4 impingement target sometimes occurs e 10.7 noz dia (1.75 in)

X0.35 near a high-pressure node (flow Uo E

  • 15.2 noz dia (2.5 in) minima), but other times occurs at a

.$L 0.3 a lower-pressure antinode (flow a 22.9 noz dia (3.75 in)

S0.25 maxima). When the intersection occurs A 30.5 noz dia (5.0 in) at a node, the pressure difference 4 0.2 -Pmax / PO = 0.34 /JPR between the core and outer high-X0.15 velocity boundary of the jet is less than when the intersection occurs at an E 0.1 A antinode. A secondary effect may result from the loss in total pressure 90.05 N A 0 associated with the Mach disk.

Z 0 Immediately downstream of the Mach 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 disk, the centerline gas is subsonic (see Fig. 5). Further downstream, viscous JPR, Jet Pressure Ratio effects exert their influence through the Figure 18. Supersonic nozzle recovery pressures for four impingement inner shear layer (see Fig. 6), and the distances, 900 impingement. The black line shows a plot of Eq. (3). centerline velocity begins to recover.

Likewise, the impingement pressure is 11 American Institute of Aeronautics and Astronautics

reduced along the centerline immediately downstream of the Mach disk, but may gradually recover as the 0.08 impingement distance is 0.07 5.22.

52' in.).

I0.06 increased.

For sonic nozzle 0.04 cases, slightly different 0.05 trends are observed.

Figure 20 shows 0.01 recovery pressure as a

-075 -0.5 -0,25 0 0.25 0.5 0.75 function of JPR for four Distance away from oenterlineang plae surface (in.)

different impingement Figure 19. Similar supersonic jet conditions (JPR -5.7) at four impingement distances. distances. Like the Single-shot images are labeled according to the corresponding value of Dimp/De (nozzle supersonic nozzle cases, diameters). In order o0 increasing distance, they are 1.71 in. (Run304), 2.5 in. (Run553), 3.75 in. peak pressures are (Run578), and 5.0 in. (Run605). Note that the peak pressure in the 3rd and 4th cases probably observed to decrease occurred near the location of a faulty pressure transducer at -0.135 in.

with increasing JPR.

Additionally, oscillations n e 10.5 noz dia (1.0 in) are again observed for the region of low JPR

-0.6

  • 18.3 noz dia (1.74 in) (less than about 3), the same flow regime in 0 26.3 noz dia (2.5 in) which oscillating flow structures are C0.5 A39.5 noz dia (30.75 in) manifest. However, oscillations are not

= 0.4 observed for the two larger impingement U) distances (26.3 and 39.5 nozzle diameters).

0.3 It has been previously noted that the spatial wavelengths associated with sonic nozzle X

m 0.2 ii I,.. flows tended to be smaller than their E supersonic nozzle counterparts (on the order 0

0.1 A

A, q: of 2 nozzle diameters in length, versus 3 to 8 nozzle diameters in length in the case of a Z 0 supersonic nozzle), and that diamond shock 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 structures in low JPR sonic nozzle flows JPR, Jet Pressure Ratio tended to dampen out after 2 or 3 oscillations". So at larger impingement Figure 20. Sonic nozzle recovery pressures, 900 impingement. Smaller impingement distances are seen to result in larger recovery pressures, distances, flow oscillations are no longer especially for small JPR. No data were taken at JPR less than about 2.5, present (see Fig. 4, for example), and so do so the maximum possible recovery pressure was not determined. For not result in staging behavior of impingement small impingement distances and low JPR, it may approach the plenum pressure. The sonic cases also exhibit an pressure. inverse relationship of recovery pressure to JPR. However, unlike the supersonic cases, the sonic cases show a dependence on impingement distance, with larger recovery pressures associated with smaller impingement distances, especially for low JPRs. For these sonic impingement cases, no simple empirical model passes through all the data.

E. Angled Impingement In the literature, some studies (most notably, the experimental studies of Lamont and Hunt 9, as well as the computational studies of Wu et al.17 which simulated flows at conditions identical to those of Lamont and Hunt) found that the maximum impingement pressure on angled impingement targets could be much greater (up to a factor of three greater) than the maximum pressure in the corresponding normal impingement cases. In our experiments, we have observed results consistent with these observations. Figure 21 shows three single shot images from runs at three impingement angles and their associated normalized pressure profiles. Although 450 and 600 configurations were not tested at the same impingement distances, the results shown in Fig. 18 and described above suggest that a rough comparison might still be made among runs at different impingement distances.

12 American Institute of Aeronautics and Astronautics

As previously stated, measured peak pressures may be less than actual peak pressures, due to the finite nature of the pressure measurements performed, and compounded by several faulty pressure transducers. 0.16 Nevertheless, of the recorded 0.14 pressures, the graph in Fig. 21 shows that the normalized peak pressure in the 600 case is roughly twice that of the 450 I

case and roughly three times that of the 900 case, in .0.75 -0.5 -0.25 0 0.25 0.5 0.75 agreement with prior Distance away fonmoenlaetlnealong plate sutface (In) experimental 9 and Figure 21. Three impingement angles. Single shot images are shown for similar jet computational' 7 studies. By conditions (supersonic nozzle, JPR -5.7, Re00 ft -2,300), and Oj.p=900 (Run536), 60' closely examining the images (Run553), and 450 (Run630). For the first two, Dimp/De= 15 (2.5 in); for the third, associated with these runs, it is Di,,pD 0= 23 (3.7 in). Note that the peak pressure in the 450 case probably occurred near seen that in the 60' the location of a faulty pressure transducer at -0.135 in.

configuration, the high-velocity jet boundary along the bottom of the jet impacts the 0.4 impingement target at nearly normal incidence, which Q. S60 deg, 2.5 in.

likely results in a pressure maximum at that point. By 0.35 E

at. 45 deg, 3.7 in.

contrast, at 450, this part of the flow strikes the plate at S 0.3 a slightly more glancing angle. In both cases, the 0.25 upper boundary of the jet impacts the target at a gentler 0.2 angle, resulting in asymmetric pressure profiles with peak pressures below the jet centerline. Figure 22 ID 0.15 shows the recovery pressure plotted as a function of E 0.1

,~U .3.= 4.

  • JPR for all 450 and 60' supersonic impingement cases. o 0.05 The general trend is for increased recovery pressure for 0 0

60' cases relative to 450 cases for low values of JPR. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 JPR. Jet Pressure Ratio V. Conclusion Figure 22. Supersonic nozzle recovery pressures for 450 vs.

PLIF images have been used to visualize free and 600 impingement. Somewhat higher peak pressures are seen impinging underexpanded jet flows and have provided in the 600 cases.

detailed information about flow structures. The insights into flow structure characteristics provided by PLIF images have helped to elucidate the results of pressure measurements taken at the surface of a flat impingement target and have shed light on the features of the pressure distributions across the face of the target.

Under certain conditions, the shape of these pressure distributions was seen to be a very sensitive function of jet pressure ratio; under other conditions, the dependence was rather insensitive to JPR. In all cases, the absolute magnitude of the measured pressures was seen to be a linear function of plenum pressure, and therefore, of Reynolds number. The recovery pressure (that is, the peak pressure relative to the plenum pressure) was found to oscillate for low JPR and then decrease as the inverse of the jet pressure ratio for high JPR. In supersonic nozzle cases, this trend was found to be relatively independent of impingement distance for the cases studied. In sonic nozzle cases, it was found to depend inversely on impingement distance as well. Finally, it was found that recovery pressure was greater for angled impingement than for normal impingement with 600 impingement angle having three times higher peak pressure than normal incidence. These results, while providing good test cases for computations, demonstrate the significant contribution that flow visualization can provide in the understanding and interpretation of surface measurements.

13 American Institute of Aeronautics and Astronautics

Acknowledgments The authors wish to acknowledge the collaborative input of Scott Halloran of Rocketdyne, Don Picetti of The Boeing Company and Chris Glass of NASA Langley Research Center, as well as the technical assistance of David Alderfer, Stephen Jones, and Paul Tucker, also of NASA Langley Research Center. They also wish to acknowledge the image processing work done by A iyana Garcia, a graduatephysics student from The College of William and Mary and a NASA GSRP (Graduate Student Researchers Program) student. This work was funded as part of the Shuttle Return to Flight effort through Chuck Campbell of Johnson Space Center and Tom Horvath of NASA Langley Research Center. Support was also received from the Aeronautics Research Mission Directorate's FundamentalAeronautics Hypersonic Project,Experimental Capabilitiesdiscipline, under Robert Okojie.

References J. L. Palmer and R. K. Hanson, "Shock tunnel flow visualization using planar laser-induced fluorescence imaging of NO and OH," Shock Waves, vol. 4, pp. 313-323, 1995 2 J. A. Inman, P. M. Danehy, R. J. Nowak, and D.W. Alderfer, "Identification of Instability Modes of Transition in Underexpanded Jets," 38 th A1AA FluidDynamics Conference, Seattle, WA, 23-26 June 2008 (to be published).

3 J. A. Wilkes, P. M. Danehy, and R. J. Nowak "Fluorescence Imaging Study of Transition in Underexpanded Jets,"

Proceedings of the 21st International Congress on Instrumentation in Aerospace Simulation Facilities (ICIASF)

[CD-ROM], Sendai, Japan, 29 August - 1 September 2005, pp. 1-8.

4 J. A. Wilkes, C. E. Glass, P. M. Danehy, and R. J. Nowak, "Fluorescence Imaging of Underexpanded Jets and Comparison with CFD," 4 4th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2006-0910, Reno, NV, 9-12 January 2006.

5 Alvi, F.S. and K.G. lyer, "Mean and Unsteady Flowfield Properties of Supersonic Impinging Jets with Lift Plates,"

Yh 5 AIAA/CEASAeroacoustics Conference, AIAA 99-1829, Bellevue (Greater Seattle), WA, 10-12 May 1999.

6 Donaldson, C. D., and R. S. Snedeker, "A study of free jet impingement. Part 1. Mean properties of free and impinging jets," J FluidMech. 45, 1971, Part 2: 281-319.

7 Donaldson, C. D., R. S. Snedeker, and D. P. Margolis, "A study of free jet impingement. Part 2. Free jet turbulent structure and impingement heat transfer," J. FluidMech. 45, 1971, Part 3: 477-512.

8 Kim, Sung In, and Seung 0. Park, "Unsteady Flow Simulation of Supersonic Impinging Jet," 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2003-621, Reno, NV, 6-9 Jan 2003.

9 Lamont, P.J., and B.L. Hunt, "The Impingement of Underexpanded Axisymmetric Jets on Perpendicular and Inclined Flat Plates," Journalof FluidMechanics 100: 471-511, 1980.

'0 Love, E. S. and L. P. Lee, "Shape of Initial Portion of Boundary of Supersonic Axisymmetric Free Jets at Large Pressure Ratios," NACA TN 4195, January 1958.

1 Stitt, Leonard E., "Interaction of Highly Underexpanded Jets with Simulated Lunar Surfaces," Lewis Research Center, Cleveland, OH. NASA Technical Note D-1095, December 1961.

12 Inman, Jennifer A., "Fluorescence Imaging Study of Free and Impinging Supersonic Jets: Jet Structure and Turbulent Transition," Ph.D. Dissertation, Department of Physics, The College of William and Mary, Williamsburg, VA, 2007.

13Henderson, Brenda, "The connection between sound production and jet structure of the supersonic impinging jet,"

Journalof the Acoustical Society ofAmerica 111 (2): 735-747, Feb 2002.

14 Henderson, B., J. Bridges, and M. Wernet, "An experimental study of the oscillatory flow structure of tone-producing supersonic impinging jets," Journal of Fluid Mechanics, Cambridge University Press, 542: 115-137, 2005.

"5 Alvi, F.S., J.A. Ladd, and W.W. Bower, "Experimental and Computational Investigation of Supersonic Impinging Jets," A1AA Journal40 (4): 599-609, April 2002.

16 Mackie, S. and R. Taghavi, "Supersonic Impinging Jets: A Computational Investigation,"

4 0 ,h AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV. AIAA 2002-0671, 14-17 Jan. 2002.

17 Wu, J., L. Tang, E.A. Luke, X-L. Tong, and P. Cinnella, "A Comprehensive Numerical Study of Jet Flow Impingement over Flat Plates at Varied Angles," 3 9 th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2001-0745, Reno, NV, 8-11 Jan 2001.

14 American Institute of Aeronautics and Astronautics

Extended abstract to be submitted to: 4 6 th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 7-10 January 2008 Fluorescence Imaging Study of Impinging Underexpanded Jets Jennifer A. (Wilkes) Inman*t, Paul M. Danehy t , Robert J. Nowakt, and David W. Alderfert

  • email address: jennifer.a.inman(nasa.gov t NASA Langley Research Center, Hampton VA, 23681-2199 I. INTRODUCTION II. EXPERIMENTAL METHODS The tests that will be described in this paper were A. Facilityand Hardware designed to create a simplified simulation of the Tests were conducted at NASA Langley flow through a hole in the surface of a supersonic Research Center using the test section of the 15-aerospace vehicle and the subsequent Inch Mach 6 Wind Tunnel as a vacuum chamber.

impingement of the flow on internal structures. Nitrogen or helium seeded with 0.5% nitric They were conducted in support of the Orbiter oxide was plumbed into a heated stainless steel Aerothermodynamics Working Group as part of plenum, through a nozzle, and into the vacuum NASA's Shuttle Return to Flight (RTF) effort. chamber. Two different nozzles were used: the Planar laser-induced fluorescence (PLIF) of first-a converging nozzle with the exit at the nitric oxide (NO) is used to visualize the flow. smallest diameter, or throat, and hereafter PLIF images show the size and location of flow referred to as the "sonic" nozzle-had a nominal structures, and the laminar or turbulent state of exit Mach number of 1; the second-a these flows can also be ascertained from these converging/diverging nozzle, hereafter called the images. "supersonic" nozzle-had a nominal exit Mach The flow environments encountered in these number of 2.6. Mass flow controllers controlled tests include regions of low static pressure, the flow rates, which indirectly controlled the turbulent and/or three-dimensional flow plenum pressure upstream of the nozzle.

structures, and regions of interest with both A 4-inch impingement disk was positioned at strong and weak density gradients. Such various distances and angles downstream of the conditions, though frequently encountered in nozzle exit. The center of this disk included 32 aerospace simulation facilities, cannot be pressure taps. They were spaced 0.045 inches satisfactorily visualized using traditional path- apart, and had an inside diameter of .021 inches.

averaged techniques such as schlieren and The taps were oriented in a vertical plane (the shadowgraph, which rely on sufficiently high plane of the laser sheet), on the jet centerline.

static pressures and strong density gradients. An From the camera's viewing angle, the jet flow alternative approach was therefore required. was from left to right.

PLIF is a powerful flow visualization technique that provides a means of making non-intrusive B. Model ConfigurationParameters measurements with sub-millimeter spatial For the majority of cases, the impingement resolution and flow-stopping temporal resolution disk was oriented normal to the jet axis (which is in many of these challenging testing regimes [ I]. defined to be a 90' impingement angle). Two We have previously used PLIF to investigate configurations included oblique impingement underexpanded sonic jets [2] and have compared angles of 450 and 600. (For these cases, the a subset of these results with computational fluid target was rotated clockwise, as viewed from the dynamics (CFD) [3]. camera viewing angle, about the horizontal axis In addition to flow visualization, pressure perpendicular to the jet axis.) Impingement measurements were recorded on the surface of an distance was continuously variable from 0 to 6 impingement target. PLIF images helped to inches. In practice, changing impingement elucidate the characteristics of the resulting distance or angle required approximately a half pressure profiles by highlighting the flow day of down time.

structures corresponding to distinctive features of For each hardware configuration, two flow these pressure profiles. parameters were varied: the exit Reynolds number (Reexit) and the jet pressure ratio (JPR).

Reexit was defined in terms of the nozzle exit diameter, De, and the density oe, velocity Ve, and

Extended abstract to be submitted to: 46t"' AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 7-10 January 2008 dynamic viscosity pe at the nozzle exit, as given were acquired under these conditions, those by (1). results will be reported in a future paper.

Pe Ve,DD e Re ext = p, (1)

III. EXPERIMENTAL RESULTS Figure 1 shows the range of conditions and Reeil was varied by changing the mass flow hardware configurations for which data were rates and nozzle plenum temperature. JPR was taken during the impinging jet study. Reynolds defined as the ratio of the static pressure at the numbers and jet pressure ratios were calculated nozzle exit, pe, to the ambient pressure in the test based on nozzle exit conditions. The table list section, p., according to (2), and was varied by the number of cases that were studied for each changing the test section pressure for a given combination of hardware configuration and type Reynolds number (and therefore, a fixed p,). of PLIF imaging that was investigated in these (2) tests. For each flow visualization case, 100 JPR - Pe Po single-shot images were acquired. The laser sheet was also swept spanwise through the flow, C. PLIFFlow Visualization Technique The PLIF laser system includes a tunable providing slices of the flow field, a technique Nd:YAG-pumped dye laser followed by hereafter called "volume imaging." These slices doubling and mixing crystals. The resulting allow us to reconstruct cross-sections of the flow in planes perpendicular to the jet axis, as output, at 226.256 nm, was tuned to excite the strongly fluorescing spectral lines of NO near the described in the following section. As previously stated, we plan to report the results of Q, branch head (Q denotes a change in rotational quantum number equal to zero). Optics formed the velocity-sensitive, pressure-sensitive, and the beam into a laser sheet that was 100 mm density-sensitive imaging data in a future wide x -0.2 mm thick (FWHM) in the publication, but not in this paper.

measurement region. Fluorescence was imaged A. CharacteristicFlow Structures onto a gated, intensified CCD at a viewing angle normal to the laser sheet. Images were acquired The data show that free jet cases having the same JPR exhibit the similar flow structures, so at 10 Hz with a hls camera gate and a spatial long as the cases under consideration are all resolution of between 3 and 7 pixels/mm, laminar. For sonic nozzle cases, flows can be depending on the required field of view for a divided into two major groups: those with a given hardware configuration. This system is repeating diamond shock structure (seen for detailed in Ref. 2 and Ref. 3. The PLIF system flows with JPRs less than about 3), and those is also capable of pressure-sensitive and with a barrel shock structure, a Mach disk, and a velocity-sensitive flow imaging. Although data streamwise high-velocity jet boundary (seen for flows with JPRs greater than about 3)[2]. For Supersonic Noz. Sonic Nozzle cases with the supersonic nozzle, the division Impingement FV/VI V P p FV/VI V P configuration happens at a JPR of about 4. For smaller JPRs, a 1" @ 90g 25 5 repeating pattern, analogous to the diamond 1.75"@90g 25 22 22 1 25 shock pattern, is evident, with a chain-like 2.5"@9go 22 19 21 24 pattern of alternating spatial minima and 2.5" @ 60' 18 maxima. As JPR increases, the repeating pattern 3.75" @ 90° 23 23 becomes less pronounced. Larger JPRs lead to a 3.7" @ 450 23 modified barrel shock structure-elongated into 5" @ 90° 22 a more egg-like shape than its comparable sonic 8 (free jet) 88 11 12 53 8 8 jet counterpart-with a Mach disk and a Reexit 600-14,000 2,400-35,000 streamwise high-velocity jet boundary.

JPR 1-16 3-27 Sometimes these flow structures are more readily understood by using volume imaging Figure 1. Test matrix for impinging jet cases. FV/VI = flow data to reconstruct spanwise slices of the flow.

visualization and volume imaging; V = velocity-sensitive The full paper will describe this process in more imaging; P = pressure-sensitivc imaging; p = density-sensitive imaging. Because Reynolds numbers and jet detail. An example is shown in Figure 2. The pressure ratios were calculated based on nozzle exit top image in the figure shows a single-shot conditions, the range of Re and JPR for supersonic nozzle image from the centerline of the flow. The six cases is less than for sonic nozzle cases. The controlling images in the bottom of the figure are cross-limitation was the inability to achieve steady chamber pressures below 1or 2 Torr (0.2 - 0.4 psi).

lxtended absttract to be submitted to: 40" IA A Aerospace Science,) Meeitin mnd L'xhihbil, Reno. N',I. 7-10 .lniuarv 2f(l(t-sectional slices at various axial locations in the long as the runs are all laminar. It is then not 7 surprising that the shapes of the pressure distributions for runs with the same JPR have similar features. However, for runs with matching JPR but different values of Rexit,, the Eu.,..

16 100 200 300 400 500 Figure 2. PLIF volume imaging. The white lines on the magnitude of the measured pressure profiles increases with increasing Reexit. This is expected to be the case because, for constant gas plenum temperatures, Re 5xit is proportional to plenum pressure (po). Self-similar pressure profiles can upper single-shot centerline image show the axial locations be obtained for runs with the same JPR by for which reconstructed cross-sectional slices are shown. normalizing all the measured impingement disk The numbers below the cross-sectional images indicate the pressures by either Po or Pchmber.

column number in the original image, which is 512 columns Figure 3 graphically depicts the effect of wide.

normalization by Pchmbý. The upper image shows pressure profiles from two runs with B. Flow StructureRelation to PressureProfiles essentially the same JPR (2.8), but different Consider an impinging jet flow with a values of Reexit (4448 and 2476). The lower uniform momentum profile throughout the core image shows these same data after they have of the jet. One would expect the pressure profile been normalized by the plenum pressure for each of such a jet to resemble a top hat function, with run. The two normalized profiles show a high roughly uniform pressure across the intersection degree of overlap.

of the jet with the impingement target, dropping to near ambient pressure away from the core of the jet. Modifying the situation to include 0,3 Supersonic, Ocdeg, JPR=2.8, 1.75" viscous effects, one would expect to see a 0,25 -R- ,5,247, decrease in momentum-and therefore a decrease in pressure on the impingement S0.2 surface-along the edges of the jet. This modified pressure profile would be peaked in the center, smoothly dropping off to the ambient pressure toward the edges of the jet flow. In 0.1 fact, for some cases, this describes the pressure profiles that have been measured. 0.05 But for other cases, the actual profiles are -1 -0.5 0 0.5 1 location (inches) quite different. Such profiles typically exhibit a double-peaked structure, with the maximum pressure occurring away from the flow Supersonic, 90deg, JPR=2.8, 1.78" centerline. The pressure between these peaks is 2 often nearly constant, while the pressure outside these peaks drops off toward-and sometimes 1.8 dips briefly below--the ambient pressure. Flow 16 visualization images acquired in the present study have helped to elucidate the origin of these hallmark features by highlighting the flow 1:.

structures associated with presence of the impingement surface. These images also help to 0.8 explain the observed sensitivities (and insensitivities) of the pressure profiles to -1 -05 0 0.5 location (inches)

Reynolds number and jet pressure ratio, as explained further in the following two sections. Figure 3. Effect of Reynolds number on pressure profile. Both runs have a jet pressure ratio of 2.8. The red line is for a run C. Reynolds Number Effect on PressureProfiles with Re,.,, = 4448; the blue line, Rexi, = 2476.

Like their free jet counterparts, impinging jet flow structures are similar for those runs that have similar JPRs (for a given nozzle type), so

lIxtended abstract to he subnittled to: 46' AlAA Aerospace Sciences MIeeling ad IFxhibit Reno. NX\', 77-10IJanuary 2008 D. Jet PressureRatio Effect on Pressure maximum pressure occurring along the Profiles centerline of the flow). Then the profiles The shape of the pressure profile was found to broaden again, with a marked change around a depend heavily on the jet pressure ratio for JPR of about 2.7, including a sudden broadening laminar runs where the impingement target was and the reemergence of a double-peaked located in a region of large local spatial structure (with peak pressures occurring along variations. That is, JPR small variations in JPR the edges of the jet, and a flattened profile in the were seen to cause significant variations in the subsonic central region of the impingement).

pressure profile for flows where the spatial cross- Similar sensitivity was not seen for the sonic section is strongly varying with distance in the cases that were studied in these tests. This is streamwise direction. This can be explained by likely due to the impingement distances that considering that small changes in JPR are were chosen. The minimum impingement roughly equivalent to small changes in distance in the sonic nozzle cases was 1.0 inch.

impingement distance. Whereas the low JPR supersonic nozzle flows For supersonic cases, this sensitivity to JPR (with JPRs less than about 5) exhibited repeating was seen for flows with JPRs less than about 4. flow patterns (i.e. spatial frequencies) on the This effect is illustrated in Figure 4 and Figure 5. order of 0.5 to 1.25 inches, low JPR sonic nozzle Starting in the upper left of Figure 4, PLIF flows had much smaller spatial frequencies---on images show the flow structures associated with the order of 0.2 inches. PLIF images show that impinging supersonic axisymmetric jets for diamond shock structures tended to dissipate increasing JPRs, from about 1.7 to 2.9. In the within about 2 or 3 oscillations. Laminar first image, the jet impinges on the disk just impingement structures for the sonic cases were upstream of what would have been the third thus rather indistinct, with little sensitivity to spatial minimum of the flow (location where the changes in JPR.

jet diameter is smaller than locations immediately upstream and downstream of that Supersonic, Odcg, 1.75" location). As JPR increases in the next three 7 -287 images, the jet then impinges near the third flow 6 -285 maximum, then the second flow minimum, and 275 finally, just downstream of the second flow 228 4 214 maximum. Figure 5 shows normalized pressure 211 3

profiles from these four runs, as well as four 2 206

-1I8 additional runs with similar JPRs. As the JPR 1

increases from about 1.7 to about 2.14, the pressure profile becomes narrower and single- .1 -0.5 0 0.5 1 peaked (that is, with a single location of the loc&tion linches)

Figure 5. Pressure profile sensitivity to JPR. These pressure profiles have been normalized by the chamber pressure of the corresponding run.

IV. CONCLUSIONS PLIF images have been used to visualize free and impinging underexpanded jet flows. They have provided detailed information about flow structures and have allowed determination of the laminar, unsteady, or turbulent state of the flow (although the results reported in this paper will be restricted to laminar cases). The insights into flow structure characteristics provided by PLIF images have helped to elucidate the results of pressure measurements taken at the surface of a Figure 4 Sensitivity of impingement flow structures to jet flat impingement target and have shed light on pressure ratio (JPR). The chain-like flow structures seen here the features of the pressure distributions across are reminiscent of the familiar diamond shock pattern seen in the face of the target. Under certain conditions, sonic jets. Note: the top images are from flow visualization runs; the bottom images are from "pressure" runs, in which the the shape of these pressure distributions was fluorescence intensity is primarily a function of pressure. seen to be a very sensitive function of jet

Extended abstract to be submitted to: 4 6 th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 7-10 January 2008 pressure ratio; under other conditions, the dependence was rather insensitive to JPR. In all cases, the absolute magnitude of the measured pressures was seen to be a linear function of plenum pressure, and therefore, of Reynolds number. The full paper will include more cases, it will delve into greater detail about the relationship between flow structures and characteristics of pressure profiles (e.g. width, single or double peaks, location of maximum pressure), and it will attempt to place this work in context with the literature on previous studies by others.

ACKNOWLEDGEMENTS The authors wish to acknowledge the collaborative input of Scott Halloran and Don Picetti of The Boeing Company and Chris Glass of NASA Langley Research Center, as well as the technical assistance of David Alderfer, Stephen Jones, and Paul Tucker, also of NASA Langley Research Center. They also wish to acknowledge the image processing work done by Aiyana Garcia, a graduate physics student from The College of William and Mary and a NASA GSRP (Graduate Student Researchers Program) student. This work was funded as part of the Shuttle Return to Flight effort through Chuck Campbell of Johnson Space Center and Tom Horvath of NASA Langley Research Center.

REFERENCES

[I] J. L. Palmer and R. K. Hanson, "Shock tunnel flow visualization using planar laser-induced fluorescence imaging of NO and OH," Shock Waves, vol. 4, pp.

313-323, 1995

[2] J. A. Wilkes, P. M. Danehy, and R. J. Nowak "Fluorescence Imaging Study of Transition in Underexpanded Jets," Proceedings of the 21'"

International Congress on Instrumentation in Aerospace Simulation Facilities(1CIASF) [CD-ROM],

Sendai, Japan, 29 August - 1 September 2005, pp. 1-8.

[3] J. A. Wilkes, C. E. Glass, P. M. Danehy, and R. J.

Nowak, "Fluorescence Imaging of Underexpanded Jets and Comparison with CFD," 4 4 th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2006-0910, Reno, NV, 9-12 January 2006.

F 6/2.

EXPERIMENTAL STUDY OF PIPE REACTION FORCE AND JET IMPINGEMENT LOAD AT THE*PIPE BREAK LI . . K. KITADE, T. NAKATOGAWA MAPI Engineering Center. Mitsubishi Atomic'Power Industries.

Inc.. 2-1, Taito 1-chintm, Taiio-ku, Tokyo, Japan A,* "  : H. NISHIKAWA, K.. KAWANISHI, C. TSURUTO  %

Takasago Technical Institute, Mtubishi Heavy IndustrieS. Ltd.,

2-chome, Arai-cho, Takasago-City. Hyogo. Japan IE BREAK " TEST In the design of a light-water reactor nuclear power plant, the extreme loads which are caused as the result of hypothetical pipe break, accident have recently become the most se-vere factors. for the structure and equipment design of the plant. '

In this paper, we describe the results of ex ients about reaction forces and let u-pingement loads in the pipe breaý accident conditions. Experiments were carried out for the kinds of jets, that is steam jet and subcooled water jet.

  • For the steam jet experiment, the steady state saturated steam was range of 10 2 ejected at pressure

- 40 Kg/cm G through the pipe of inner diameter of 9.4 im. into the atnospheric condition. . In the jet impingement experiments, the steam jet impinged vertically on the flat plate, varying the distance H in the range of 0.59 H/D to 6.6 H/V (D: pine diameter).

The results are as' follo"s:

11) The reaction forces T is proportional to the reservoir pressure P and 0 the area of the pipe opening, that is, T=rp'A . formula is applicable. The thrust coeffi-cient K was 1.12 in our experiments, and this is slightly smaller than Moody's

-. prediction.

(2) The stagnation pressure P. at the centre of the pressure distribution on the'plate, is estimated by following formula.

Ps P- I-2 Pu -0.65 (-1_

(()A configuration of the pressure distribution on the plate and the area of it depend mainly on HID.. We could classify the configurations of the pressure die-tribution to three types in this experiments.

' The subcooled water jet experiments were carried cut under the condition of initial 2 2

.Pressure of 70 Kg/cm breakcs were simulated by' means of the rupture disks. The jet uas ejected upward into t~ir.

G and 150 Kg/CM C5 with subcoolinq diameters of 'the 'ejection opening were from 10.5 to .43.1temperature si.the of 13 741-C.

instantaneous guillotine The nd impinged vertically on the plane board. -atmosphere l .. : " .. "" . : reaks ofr timlae thebrek ad d m ubsquetl br " eas the rupture.dss'Te*t*

dereaesgradually. A thrust coefficient jce slightlypaditdepends /":: ".".. -

on a.

pessre resrvor raniens aterthe break and is approximately, between 1.2 and 1.4.

d'ist....r.i:b.

io. ofp the ureons the prespreads to it's mnaximum area just after the break.

0""' ..the* e haendtnhe stagnaton / pressure on the plate has its maxinum value after a some" F 6/1*

i": . . . ,1 ..

i. Introduction *'* .. *'..

r in atdesign of a light-water reactor nuclear power plant, the extreme loads which are caused as the result of hypothetical pipe break accident, have recently become the most se-vere factors for the structure and equipment design of the plant. Especially the evaluation of these reaction force and jet impingement load is essential for the design of the piping systems and:the structures.

in this paper, experimental results of the reaction force, the impingement load and the jet pressure distribution on the flat target on which the jet impinges'vertically, are de-scribed.. The experiments were performed for the two kinds of jet, that is steam jet and subcooled water jet-.

For the steam jet experiment, the steady state saturated steam was ejected at. the pres-2 sure range of 10 -. 40 Kg/cm G through the pipe of inner diameter of 9.4 =. into the atmcs-

  • pher. condition. In the jut i=pingemener iments, the steam jet impinged vertically on the flat plate, varying the distance H in the range of 0.59 H/D to 6.6 H/D (D: pipe diameter).

sucooled water jet

,The experiments ware carried out under the condition of the initial 2 2 pressure of 70 Kg/cm G and 150 rg/cn G with subcooling temperature of 13 -. -C. The dia-meters of the ejection opening were simulated by means of rupture disks. The jet was ejected upward into the atmosphere and impinged vertically on the plate.

. Data about the impingement jet which is practically useful for the design of the piping Isystems and structures have been obtained.

" 2. Impingement Jet of Saturated Steam 2.1 Apparatus I. A schematic 6f experimental apparatus is shown in Fig. 1. Saturated steam was ejected into the atmosphere through a straight nozzle as shown in Fig. 1. Inner diameter of the .

nozzle was 9.4 mi. The steam was supplied through a 1 inch pipe from a boiler. Quality of I steam was more than 99 per cent. It is considered that the flow was choked and the exit Mach number was unity. The ejected steam impinged vertically on a flat target plate which had a pressure tap. The target was made to traverse vertically and horizontally in order to measure the pressure. distribution on the target. The whole jet was intercepted by the 4

a*target.

. .periment Strain gauge type pressure transducers were used for pressure measurement.

was carried out at the ejection pressure of steam of 10 -

2 The ex-40 Kg/cm G and a distance between the nozzle opening and . the. target was from 5.5 mm to 62 mm.

ILLI in 2.2 Pressure Profile on a Taroet such a simple. manner.

Moody discussed about a jet expansion assuming a flat pressure profile.

Results of the pressure profile on the target in BSt it is the case of sot e -  :

". " tion pressure of 41 Kg/cm2 are shown in Fig. 2 typically. 'H is a distance between the tar-get and. the nozzle exit and D is a diameter of the nozzle exit. In this case D is 9.4

. P and P. are the impingement pressure on the target and the ejection (total) pressure of

. steam, respettively. r is a radial distance on the target from the center of the impinge-ment jet.

"" "The configurations of the pressure profile on the target are not same at all the loca-I tions. Within the limit of this experiment, the pattern of the pressure profile could be classified to three types. They varies with the location H. " .

- 2 612

type 1; In a region that H/D is smaller than 1.5, the pressure profiles are similar and is loads which are expressed as eq. (2.1)

-come the most se- 2

" Psp-- - sech (O.s88 rl/. (2.1) tlly the evaluation 7 . 1/2 *" "." .

  • ign.of the piping where Ps is a stagnation pressure on the target at the center of impingement jet, P_ is an ambient pressure, and ri/2 is a half value "radius.
ement
load and the
  • type 2; In a region that H/D is about 4, the pressure'profile becomes to the distorted con-rtically, are de-
stea lJet and figuration.
  • type 3; In a region that H/Dfis larger than about 6, the profile is concave and a position of the iaximum pressure on the target is not center.

jected at the pres-.

a. into the atmos- - These types of pressure profile and the jet spread are related to each other as described in iged --ertically on section" 2.3.

The stagnation pressure on the target at the center of the impinging jet are shown in D (L. I diameter).

Fig. 3. In the region H/> 1, the experimental results are summarized as correlation eq.

tic the initial i

-. (2.2)

The din-The jet was ejected SP, - P ý - 0 1)-2 P - o 0.65 . (2.2)

Po0 esign of the piping Assuming that normal shock wave occurs slightly upstream from the target and that the flow is isentropic upstream the shock wave, the righthand side of eq. (2.2) is approximately ex-pressed as eq. (2.3) by using a relation for total pressure. change across the normal shock wave for ideal gas [1).

1 *.

t steam was ejected 1 2 P, -1 r+x MhE s-h_ r (x+l)H 1 (2.3) diameter of the P0 20+1

,oiler. Quality of where x is a ratio of specific heats and s is a aFch number at the axial position of interest.

ed and the exit Oween et.al. (4) calculated the axial profile of the Mach number in the centsrof highly un-
argot plate which der-expanded free jet of which a nozzle exit Mach number was 1.008. The calculated stagna-
ontally in order to tion pressure on the target using eq., (2.3) and the Mach number calculated by Oween et.al.
cepted by the is shown by a broken line in Fig. 3. In addition, experimental result for air by Stitt (31

,asurement. -The ex-

'cm2G and a distance .is shown in Fig. 3. Experimental values are in good agreement with the calculated results.

When the pressure profile is type 3, the pressure is maximum on a circular line on the target. This maximum pressure (the secondary stagnation pressure) seems to be independent upon the ejection pressure and HID in this type.

le. "ut it is not un the case of ejec-2.3 Spread of Jet '

As Moody described in his work, the jet expands rapidly near the exit to the aetos-

a between the tar-pheric pressure surrounding it. After this initial expansion, the jet would remain at a Case D is 9.4 am.

Constant diameter if there were no mixing or shear force interaction with the environment.

al) *pressure of Dependence of the spread of the pressure profile on the target upon the impingement dis-ar of the impinge-tance would be in same manner. The experimental results of the spread of the pressure pro-file are shown in Fig..4, where rl/ is a half value radius. The spread of the pressure us et all the boca- 2 Profile is characterized by the half radius. The results are as follows.

profile could be (1) The spread of the pressure profile can be divided into three regions.

(2) Region 1 extends from the nozzle exit to the distance where H/D is 1.8. In this F 6/2 -- 3-- F 6/2

region, the half value radius slightly increases. as H/D increases and the pres- .

sure profile is type 1.

.(3) In the region 2; the half value radius increases in proportion to H/D and the pressure profile is type 2. It should be noted that the half value radius is independent on the ejection pressure in region 1 and 2. .

(4) In the region 3, the half value radius remains constant. The pressure profile.

is type 3. In this region, the half value radius increases in proportion to the square root of the ejection pressure Po as expressed by eq. (2.4) j1/2 =0.43 Po Dp

)0.5 . (2.4) where D is the nozzle diameter and P- is the ambient pressure. -

2.4 -Reaction Force o i x i t f o (5 TGenerally, the reaction force is expressed in the form of eq. (2.5)

T =.K P- A (2.5) where T is a reaction force and A is a discharge area. K is a coefficient which is called thrust coefficient.' For calculating the reaction force, saturated steam is usually treated as an ideal gas. If the flow is further considered isentpic, the-mst coefficient is the 1.26 when Po,:. P ' [21 . . . . . .;. . .

Tthe thrust coefficient w ohic has been obtained is 1.12 less than 1.26. Friction loss upstream from the exit would reduce "

  • FE the thrust coefficient.

An upstream restriction which limits flow reduces the reaction force, too. '[61 In this apparatus, the length of the stight nozzle is 120 m. The effect of the frictional loss would be small. But there is a sudden contraction with a sharp edge at the entrance of the nozzle. Therefore, there may be a possibIlity that the flow contracion occurred at the X S. .entrance of the.nozzle. If the flow contraction occurs, the discharge flow and the pressure 4 at the nozzle exit may decrease. Moreover, the pressure loss at the entrance decreases the reaction force. it is not clear from the results of this experiment About these two effects.

V"It is necessary that the effects of the configuration of the nozzle entrance and the fric-tional loss are confirmed experimentally in future.

' 3 Blowdown of Pressurized Hot Water 3.1 Equipment shown schematically in Fig. 6. Electric heater (1920kW) e

" Equipment used in experiment is

.1 . . is equipped in a heating vessel, which is used'to heat water. Slowdown piping (i.d. 190 m) 3 is contained in a blowdown vessel (140 m ).. A straight pipe nozzle is mounted at the end of

," the blowdown piping. Detail is shown in Fig. 7. Three different nmzoles are used. mea I diameters of the nozzles are 12.3 mnm, 21.2 mm and 43.1 mm respectively. They have the round "i inlets. Rupture disk is mounted at the exit of the nozzle. The rupture disk was broken by electric arc in order to simulate instantaneous guillotine.break. The water is circulated until blowdown starts so that the temperature of the water in the nozzle may be kept as high

~ I,* as in the loop.

I"

' 4 . +" 1 " -6/2

I Jet is .ejected upward and hits a target plate Perpendicularly. There are seven pres-and the pres-sure taps by which the pressure distribution on the target is measured. The locations of the pressure taps are as shown in Fig. 7. The target is supported by three rods with load*

H/D and the cells. Impingement load and Reaction force are measured by load cells. Natural frequency ue radius is of the system are 46 Hz.

ssure profile 3.2 Test Procedure 7oportion to the The test loop was initially filled with demineralized water and the water was heated to the starting conditions. When the initial condition was achieved, the circulation pump was then stopped and the valves VP-7 and VP-8 were closed and the rupture disk was broken.

(2.4) Nine tests were conducted. The initial conditions and the diameters of the nozzles used in each run are shown in Table 1.1.

3-3 Experimental Results Typical pressure history in the blowdown pipe after the break is shown *in. Fig. S. As the initial temperature of water is subcooled, the pressure decreases rapidly to near the satu-.

i 5) rated condition. An undershoot is observed. This seems to be due to time delay of evapo-ration.

which is called Examples of the reaction forces are shown in Fig. 9. The reaction force and the in-a usually treated pingement "load were measured simultaneously; These two forces are equal within the ex-coefficient is perimental error.

The reaction force has a-maximum value just after the break and .then decreases rapidly t coefficient which as the pressure in the blowdown pipe decreases. Such a peak of the reaction force is dis-exit would reduce tinguished when the initial subcooling is large. Probably, such a peak may diminish if the initial subcooling is zero..

too. 161 The ,experimental result of thrust coefficiant defined by eq. (2.5) was nearly constant t of the frictional with respect to time. The thrust coefficient seems to depend slightly on the stean quality at the entrance of of the mixture in the.blowdown pipe.

.on occurred at the The steady state reaction force is given by eq. (3.1)

  • w and the pressure 2

rce decreases the .T

  • G VE 9 (3.1).

A E 9

  • these two effects.

Lce and the fric-

  • where A is. an area of the break, PE is a pressure at the exit (critical pressure), G is a

-discharge mass flow rate, VE is a specific volume of discharge flow at the exit and g is (r' gravitational acceleration. Assuming an isentropic flow, and substituting PE, G and VE calculated by Moody's method E53 into eq. (3.1), the steady state frictionless thrust co-efficient can be obtained. The predictions for steady state saturated water are shown by

ric heater (1920kw) a broken line in Fig. 10. The experimental results of the thrust coefficient is from 1.2 to Lping (i.d. 190 mm)
  • 1.4 which is slightly greater than Moody's prediction as shown in Fig! 10.

inted at the and of A configuration of the'pressure distribution on the target varies considerably with time.

are used. The The typical history of the pressure distribution is shown in Fig. 11. In the early stage of the rhey .have the round period of blowdown, the configuration of the pressure distribution is flat and the spread of lisk was broken by jet is wide. The pressure at the center was rather low. As time goes on after break, the ter is circulated spread becomes narrow and the pressure at the center becomes high and then low. Therefore, nay be kept as high the pressure on the target plate is maximum in a short time after the break. The spread of the pressure distribution on the target is shown in Fig. 12, where P is a pressure in the F. 6/2 -- 5-- F612

IdIF, 2

The dependence on the pressure at more than 40 Kg/cm is blowdown pipe during blowdown.

2 different frot one at lees than 40 Kg/cm . It seems that the lower the steam quality of the discharge mixture i.s, the larger the spread of jet is. It is interesting that when the blow-down pressure becomes low (the steam quality is high) the spread of the pressure distriba-tion is similar to one for the saturated steam.

4. Conclusion (A] For the steady saturated steam jet, followingresults were obtained.

(1) The configuration of the pressure distribution on the impinged plate depends strongly on the distance between the platr and the pipe exit. The configuration are divided into three types according to the distance. The stagnation pressure of the jet at the center of the pressure distribution can be estimated by eq.

(2.2), which agrees well with the analytical results derived from the relation of the total pressures across the shock wave.

(2) -The value of reaction force for steam jet we obtained was smaller than that of Moody's prediction which assumed the frictionless isentropic flow. This dis-agreement seems to be due to the friction loss and/or flow contradiction at the entrance of the nozzle. Further investigation is necessary to clarify "this effect.

This results, however, shows that it is conservative to evaluate the reaction force by Moody's prediction.

(8] For the subcooled water jet, following results vere obtained.

(1) In the case-of the initially subcooled water, the peak reaction force and the of the rupture disk.

peak impingement load are observed just after the break These phenomena are considered to be due to the sudden decreasing of the system pressure.

(2) The thrust coefficients. obtained in this experiment kept constant value during blowdown. The values of the thrust coefficients were in the range of 1.2 to 1.4.

bldown*

(3) The spread of the jet is large at the early stage of the water phase On the other hand, the pressure on the impinged plate takes maxdimu value after a some period of time. This phenomena seemed to be complex. The pressure on the target depends on the impingement distance, the steam quality and the system pres-sure..

References

[i] Liepmann, H.W. and Roshko, A., "Elements of Gasdynamics," John Wiley & Sons, Inc.

2 oy , "Prediction of Slowdown Thrust and Jet Force,' ASME 69-HT-31, (1969)

[31 Stitt, L.E., "interaction of Highly Underexpanded Jet with Simulated Lunar Sur-faces., NASA TN D-1095, (1961) 141 Owen. P.L., and Thornhill, C.K., "The Flow inBrit., an Axially - Symmetric Supersonic Jet from a Nearly Sonic Orifices into a Vacuum" A.R.C. Technical Report, R & M 2616 (1952)

(5 o* F.., "Maximum Flow Rate of a Single Component Two-Phase Mixture," Journal of Heat Transfer, ASME, Series C, Vol. 87, (1965) t6l Moody, F.J., "Time-Dependent Pipe Forces Caused by Slowdown and Plow Stoppage,"

Journal of Heat Transfer, Trans. ASHE, Vol. 95. Series 1, No.3, (1973)

V, 6 F 6/

2 40 Kg/cm is Table I EspeImmml cwdil sam quality of the that when the blow- RanN. prmsr Perw. ;l*Mt w HiD 0

0 To -C U & Is POWeei HD 1 reseure distribu-ljKT2Ol 67 255 25 43 21.2 290 13.7 202 14V 299 41 as 21.2 290 13.7 203 150 313 23 112 21.2 210 13.7 I 204 60 268 s1 53 1.'7 ned. - 290 27.1 25 14 309 31 95 10.5 290 27.6 late depends 206 6 25 1s so 20I no I m he configuration 207 4527 1113 55] 4oz4"55 gnation pressure 05 70 2W4 21 50 2.5 1 .1 imated by eq.

20,2 63 2 21 ' 49 392.21 150 3.93 ISthe relation r 'at of 4w. s dis-adiu.on at the

  • larify this effect. 0 .0 0- f% 1- . 46 00 A i the reaction 0

30.042 -

I. l,%.M *pip- C51 7. T-,5. ph-1 -3 -2 .l-1 force and the a 1 2 3 2upture disk.

2.Vab.,i

4. N-z..

A. .P...

9I. L-md.IIe wII1 ig of the system

6. V.4.I/, l it valus during .0 Fig. I Sketch of experimental apparatus ige of 1.2 to 1.4. (steam blo.aown)

)hase blowdown.

mum value after a pressure on the id the system pros-

.0 y -as Inc.

I I

a j-HT-31. (1969)

!d Lun.r Sur-

.c Sup.rsonic Jet

. Report, R & M

-9" pk. f- ý "t 01-.a 6-. .o--I.od tO 5/D

ture," Journal Fig. 2 Examples of radial pressure profile Fig. 3 Stagnation pressure of saturated on target (steam) steam jet on target iw Gtoppage,"

)73)

F 6/2 F 6/2 A

om Memeqqqw. MIJ, . .........

':'~~~~~~~ . . . . "-*.. .i '" . . .... ~~~~

OL Fig.'4 Half value radius of pressure profile on target for steam jet.

40 U

Fig. 7 Details of water blowdown piping

- 00 0 eu I5 o X r o0 0 0-Fig. 5 R esulta of st~eamreacetion force U'0 0.3 01 00 o 0.05 0.1 0.15 Ial WHOl~

wddml&w-lvolwl ONl 6,A, WXTI 1 F ........

-1q h..hIa..,Ia~a 4100t005ow)ow IDI*

0 3t 10 " IS 20 iS 3

-,n TI- (S-o)

.11l.r 4...

r~ig. Typical history of pressure a0 ino bloIwdown pipe A

-* Co 4t'i 0

410 10

,,. Cfo) r 0

N r -I.'

0

_ I

___ 0 0 iii I

11

.0 I

S T11- CS.)

t; Fig. 9 Typical histories of reaction force during water blowdown Fig. 10 Reaction force just after initial 1OL- -ý depressurization (water blowdown) 2 -_ P_ NO N.*15 0 a fl-a aftw hod P 2 P4ftw ot - 0,o 0 2-. 81 k a/. G /.W 0

3- tD 13..2I.21 04 72 0.05

& v OA a 014 16 0.20 MKT= 150 112 21.2 13-a 2 MC 28*

A

  • __010 _3 103 6.6 a  !. ~ , **h ~ ~ *~ -L "56 AO.1 -1.9.95
  • L. 1 C

~1

.0 0 I0 Locaffm m ft%,i plý-frm ý r 100 e IA.T F 1 .h.2 -!1 49 30.2 3.93o 44 Fig. 11 Typical radial pressure profile 5 S waer lw.o " 21.2 3 . of two-phase impingement jet 0

-e 05 --

a

  • 0 u
  • 0 0

.0 44 S 10 100 I

'0

- ý 9t4 --- P (414/4420) M4 OC, Fig. 12 Jet diameter at half-maximUM p ressure on target

  • (water blowdown)

F 6/2 -- 9-- F 6/2

  • *",,=mml-Docket No.52-021 MHI Ref: UAP-HF-10356 ATTACHMENT 1 FILES CONTAINED INCDs CD 1: Technical Report, MUAP-10017-P (RI) "Methodology of Pipe Break Hazard Analysis (Proprietary)"

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