ML17053A353
| ML17053A353 | |
| Person / Time | |
|---|---|
| Site: | Nine Mile Point, Susquehanna, Columbia, Limerick, LaSalle, 05000000, Zimmer, Shoreham, Bailly |
| Issue date: | 12/28/1978 |
| From: | Anderson C Office of Nuclear Reactor Regulation |
| To: | Borgmann E, Curtis N, Brian Lee CINCINNATI GAS & ELECTRIC CO., COMMONWEALTH EDISON CO., PENNSYLVANIA POWER & LIGHT CO. |
| References | |
| NUDOCS 7901080338 | |
| Download: ML17053A353 (44) | |
Text
MEETING
SUMMARY
DISTRIBUTION ocket Files NRR Reading CSB Reading NRC PDR Local PDR TIC E.
Case R.
Boyd D.
Ross D. Vassallo D. Skovholt W. Gammill J. Stol z R. Baer
- 0. Parr S.
Varga C. Heltemes L. Crocker D. Crutchfield F. Williams R. Mattson D. Muller Project Manager
- Attorney, ELD E. Hylton IE (3)
ACRS (16)
L. Dreher L. Rubenstein R. Denise NRC Participants C. Anderson NRC Attendees R. Tedesco W. Butler I. Peltier J.
Kudrick T.
SU C. Grimes
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UNITED STATES NUCLEAR REGULATORY COMMISSION WASHINGTON, D. C. 20555 DEC 2 61978 Docket Nos.:
50-358, 50-352/353, 50-367, 50-373/374, 50-387/388, 50-322, 50-397 APPLICANT:
Members of Mark II Owners Group
SUBJECT:
MEETING WITH MARK II OWNERS GROUP TO DISCUSS THE STAFF'S MARK II CONTAINMENT ACCEPTANCE CRITERIA RELATED TO SUBMERGED STRUCTURE DRAG LOADS - NOVEMBER 15, 1978 Back round The Mark II Owners Group notified the staff at a meeting held on October 19, 1978 of certain exceptions they would propose with respect to our pool dynamic loads acceptance criteria.
The purpose of the meeting on November 15, 1978 was to discuss their proposed exceptions to our criteria related to submerged structure drag loads and the bases for these exceptions.
An attendance list and meeting handouts are enclosed.
~Sumnar Exceptions to our acceptance criteria for submerged structure drag loads were proposed in a number of areas, including:
1)
LOCA/SRV water jet loads; and 2)
LOCA/SRV air bubble loads.
For our criteria related to LOCA water jet loads, the Mar k II owners provided the results of their analyses to determine the significance of the acceleration drag loads.
These analyses include a disturbance of the jet flow field by the target such that a zero normal boundary condition is satisfied.
This is in contrast to the staff's criteria which assumes that the flow field is not disturbed by the target.
Their treatment of the flow field shows a potential for a large reduction in the staff's criteria for LOCA jet induced acceleration drag loads.
However, the staff raised a number of questions regarding assumptions implicit in this new methodology.
We require that these questions be resolved before these loads can be considered negligible.
Mark II Owners Group The Nark II owner s showed films of scaled tests to support their argument that the penetration of the water jet is limited, since the jet assumes a
mushroom shape upon entrance into the pool.
They maintain that a substantial fraction of the kinetic energy of the jet is converted into vorticity.
Thus they conclude that a good representation of the flow field can be generated by an analytical model based on the movement of a vor tex ring.
This model is currently under, development by the Mark II owners.
The staff stated that this approach appears promising.
However, it is doubtful that we would receive documentation describing the model in time for its use by the lead plant applicants.
The Mark II owners also proposed to take exception to several of our criteria associated with LOCA air bubble submerged structure drag loads.
These included acceleration drag coefficients, the equivalent uniform flow velocity and modification of drag coefficients to account for interference effects.
A summary of our related discussions is provided below.
Our criteria for acceleration drag coefficients used in the calculation of air bubble associated drag loads are based on a bounding approach.
A value of three times the standard drag coefficient was chosen to bound both the situation of uniform flow characteristic of most pool swell phenomena and the oscillating flow that is characteristic of SRV actuation.
The Mark II owners proposed a modification to our criteria wherein they would specify separate criteria for uniform and oscillating flow fields.
For uniform flow fields, unpublished data of Sarpkaya was referenced which indicates that an upper bound of 1.4 can be justified for the standard drag, multiplier.
For oscillating flow fields, they propose direct application of the Keulegan-Carpenter corrections for standard drag coefficients.
The staff stated that the proposed approach appeared reasonable and that the unpublished date of Sarpkaya should be submitted to substantiate their proposed uniform flow field criteria.
The staff's criteria specify that the maximum velocity "seen" by the structure should be used in submerged structure drag calculations.
The Mark II owners proposed use of the velocity at the center of the structure.
The results of their analyses were provided to support their view that this methodology satisfies our criteria.
In addition, they discussed problems they would have in applying our criteria.
The flow field may be very complicated due to the presence of multiple sources and sinks.
- Thus, determination of the point of maximum velocity may be very costly.
They proposed that sensitivity studies be performed by each A/E to define a multiplier that may be easily applied to the velocity calculated at the target
Mark II Owners Group 3 w WP et ~
C 4
geometric center.
The staff identified several problems associated with this approach.
- First, we stated that their argument for the velocity at the center of the target being a maximum did not cover the case of offset targets.
The approach of establishing a simplified approach such as defining a multiplier to the velocity at the center of the target appears reasonable'.
- However, we stated that this should be pursued generically instead of on a plant unique basis.
The staff criteria specifies that for certain conditions, a multiplier of 4 times the standard drag coefficient be used to account for interference of nearby structures.
The Mark II owners proposed performing analysis on a plant unique basis.
Data were referenced to substantiate their view that our criteria is unrealistically high.
The staff stated that an alternate approach to our interference criteria, based on references to available data, appeared reasonable.
However, the references should be clearly specified.
In addition, generic guidelines should be developed to cover those cases which involve extrapolation to conditions outside those tested.
Again we stated that exceptions to our criteria should be approached on a generic r ather than plant unique basis.
The staff stated the need for a follow up meeting on this topic of submerged structure drag loads, to enable us to resolve some of the concerns raised in this meeting.
Enclosure:
As Stated Clifford Anderson, A-8 Task Manager Containment Systems Branch Division of Systems Safety Office of Nuclear Reactor Regulation cc:
See attached pages
P
Mr. Earl A. Borgmann Vice President - Engineering The Cincinnati Gas and Electric Company P. 0.
Box 960 Cincinnati, Ohio 45201 CC:
Troy B. Conner, Jr.,
Esq.
- Conner, Moore I% Corber 1747 Pennsyania
- Avenue, N.
W.
Washington, D.
C.
20006 Mr. William J.
Moran General Counsel The Cincinnati Gas and Electric Company P.
0.
Box 960 Cincinnait, Ohio 45201 Mr. William G. Porter, Jr.
- Porter, Stanley, Arthur and Platt 37 West Broad Street
- Columbus, Ohio 43215 Mr. Peter H. Forster, Vice President Energy Resources The Dayton Power and L'.ght Company P.
0.
Box 1247 Dayton, Ohio 45401 J.
Robert Newlin, Counsel The Dayton Power and Light Company P. 0.
Box 1034
- Dayton, Ohio 45401 Mr. James D. Flynn
- Manager, Licensing Environmental Affairs The Cincinnati Gas and Electric Company P. 0.
Box 960 Cincinnati, Ohio 45201 Mr. J.
P.
Fenstermaker Senior Vice President - Operations Columbus and Southern Ohio Electric Company 215 North Front Street
- Coulubus, Ohio 43215 David B. Fankhauser, PhD 3569 Nine Mile Road Cincinnati, Ohio 45230 Thomas A. Luebbers, Esq.
Cincinnati City Solicitor Room 214, City Hall Cincinnati, Ohio 45202 Mr. Stephen Schumacher Miami Valley Power Project P. 0.
Box 252 Dayton, Ohio 45401 Ms. Augusta Prince, Chairperson 601 Stanley Avenue Cincinnati, Ohio 45226
Mr. Norman W. Curtis Vice President
- Engineering and Construction Pennsylvania Power and Light Company 2 North Ninth Street Allentown, Pennsylvania 18101 cc:
Mr. Earle M. Mead Project Manager Pennsylvania Power 5 Light Company 2 North Ninth Street Allentown, Pennsylvania 18101 Jay Si lberg, Esq.
- Shaw, Pittman, Potts Trowbridge 1800 M Street, N. W.
- 0. C.
20036 Mr. William E. Barberich, Nuclear Licensing Group Supervisor Pennsylvania Power 5 Light Company 2 North Ninth Street Allentown, Pennsylvania 18101 Edward M. Nagel, Esquire General Counsel and Secretary Pennsylvania Power 8 Light Company 2 North Ninth Street Allentown, Pennsylvania 18101 Bryan Snapp, Esq.
Pennsylvania Power 8 Light Company 90'1 Hamilton Street Allentown, Pennsylvania 18101
Mr. Byron Lee, Jr.
Vice President Comnonwealth Edison Company P. 0.
Box 767 Chicago, Illinois 60690 cc:
Richard E. Powell, Esq.
Isham, Lincoln h Beale One First National Plaza 2400 Chicago, Illinois 60670
Niagara Mohawk Power Corporati,on ccs:
Ar vin E. Upton,'sq.
- LeBoeuf, Lamb, Leiby 8 MacRae 1757 N Street, N.
W.
Washington, D. C.
20035 Anthony Z. Roisman, Esq.
Natural Resources Defense Council 917 15th Street, N.
W.
Washington, D. C.
20005 Mr. Richard Goldsmith Syracuse University College of Law E. I. White Hall Campus
- Syracuse, New York 13210 T. K. DeBoer, Director Technological Development Programs New York State Energy Office Swan Street Building Core 1 - 2nd Floor Empire State Plaza
- Albany, New York 12223 Niagara Mohawk Power Corporation ATTN:
Mr. Gerald K. Rhode, Vice President System Proj ect Management 300 Erie Boulevard West
- Syracuse, New York 13202
Northern Indiana Public Service C~iy ccs i Meredith Hemphill, Jr. Esq.
Assistant General Counsel Bethlehem Steel Corporation 701 East Third Street Bethlehem, Pennsylvania 18016 William H. Eichhorn, Esq.
Eichhorn, Morrcw & Eichhorn 5243 Hohman Avenue
Mr. H. P. Lyle, Vice President Electric Production 5 Engineering 5265 Hohman Avenue HarnMnd, Indiana 46325 Hayward W. Osann, Jr., Esq.
Wolfe, Hubbard, Leydid, Voit & Osann, Ltd.
Suite 4600 One IBM Plaza Chicago, Illinois
~u611 Robert J. Vollen, Esq.
109 North Dearborn Street Chicago, Illinois 60602 Porter County, Izaak Walton League of America, Inc.
Bax 438 Chesterton, Illinois 463u4 Michael I. Swygert, Esq.
25 East Jackson Boulevard Chicago, Illinois 60604 Richard L. Roobins, Esq.
Lake Michigan Peaeration 53 West Jackson Boulevard Chicago, Illinois 60604 Maurice Axelrad, Esq.
Lcwenstein, Naeen, Reis
& Axelrad 1025 Connecticut Avenue, N. W.
Washington, Q. C. 2u036 JBHRs N ~ Cahan p Esqe Russell Eggert, Esq.
Office of the Attorney General 188 Randolph Street Chicago, Illinois 60602
Long Island Lighting Company ccs:
Edward M. Barrett, Esq.
General Counsel Long Island Lighting Company 250 Old Country Road
- Mineola, New York 11501 Edward J. Walsh, Esq.
General Attorney Long Island Lighting Company 250 Old Country Road
- Mineola, New York 11501 J.
P. Novarro Project Manager Shoreham Nuclear Power Station P.
O. Box 618 Wading River, New York 11792 Jeffrey Cohen, Esq.
Deputy Commissioner and Counsel New York State Energy Office Agency Building 2 Empire State Plaza
- Albany, New York 12223 Howard L. Blau Blau and Cohn, P.
C.
380 North Broadway
- Jericho, New York 11753 Irving Like, Esq.
Reilly, Like and Schnieder 200 West Main Street
- Babylong, New York 11702
%$ Technical Associates 366 California Avenue Suite 6
Palo Alto, California 94306 Long Island Lighting Company ATTN:
Mr. Andrew W. Wofford Vice President 175 East Old Country Road Hicksville, New York 11801
Mr. Edward G. Bauer, Jr.
Vice President 5 General Counsel Philadelphia Electric Company 2301 Market Street Philadelphia, Pennsg1vania 19101 CC:
Troy B. Conner, Jr.,
Esq.
- Conner, Moore Ijl Corber 1747 Pennsylvania
- Avenue, N.
W.
Washington, D. C.
20006 W. William Anderson, Esq.
Deputy Attorney General Room 512, Main Capitol Building Harrisburg, Pennsylvania 17120 Frank R. Clokey, Esq.
Special Assistant Attorney General Room 218, Towne House Apartments P. 0.
Box 2063 Harrisburg, Pennsylvania 17105 Honorable Lawrence Coughlin House of Representatives Congress of the United States Washington, D. C.
20515 Roger B. Reynolds, Jr., Esq.
324 Swede Street Norristown, Pennsylvania 19401 Willard C. Hetzel, Esq.
312 Main Street East Greenville, Pennsylvania 18041 Lawrence Sager, Esq.
Sager h Sager Associates 45 High Street Pottstown, Pennsylvania 19464 Joseph A. Smyth Assistant County Solicitor County of Montgomery Courthouse 4orristown, Penosylvania 19404
Mr. Edward G. Bauer, Jr.
cc:
Eugene J. Bradley Philadelphia Electric Company Associate General Counsel 2301 Market Street Philadelphia, Pennsylvania 19101
Washington Public Power Supply System ATTN:
Hr. Kneil 0. Strand Managing Oirector 3000 George Washington May Richland Washington 99352 Joseph B. Knotts, Jr.,
Esq.
Oebevoise 4 Liberman 700 Shoreham Building 806 Fifteenth Street, N.
M.
Washington, O.
C.
20005 Richard Q. Quigley, Esq.
Washington Public Power Supply System P. 0.
Box 968 Richland, Mashington 99352
NRC/Mark II Owners November 15,> 1978 Attendance List Name E.
A.
W.
K.
C.
G.
C.
L.
L.
0.
P.
F.
W.
S.
M. Mead R. Smith M. Davis G. Hazifotis Economos Bienkowski Ander son M.
Su A. Kudrick E. Lasher S.
Dukelow C.
S.
Nieh E.
Bush D. Hedgecock C. Rally M. Davis B. Mucciacciaro L.
T.
Guaquil G. Peterson M. Whitcomb J.
M. Raymont Lum R.
I.
K.
Kohrs Domashovetz J.
Green J.
S.
Abel H.
Chau Vitay Chandra L.
H. Frauenholz Affiliation PPSL Co.
NRC/DSS/CSB NRC/DSS/CSB NRC/DSS/CSB GE Sargent 8 Lundy SKW WPPSS WPPSS GE GE SKW Stone
& Webster GE EBASCO GE GE BKR Bechtel GE (Mk I Program)
Sargent 5 Lundy SSL Commonwealth Edison Lilco
Name R. L. O'Mara J.
S.
Hsieh Dale Roth D.
M. O'onnor M. G. Michail T.
Y.
Chow D. Toner W.
R. Butler Affiliation S&W S&W PP&L Bechtel Bechtel S&W Lilco NRC/DSS/CSB
NRC'NARK II L'EAO PLANT ACCEPTANCE CRITERIA LEL 11/15/78
C g
CSS0'UT IN e
LOCA MATER Jv 9
LOCA AiR BuaacE 1
LOCA HATER JET NRC CRITERIA L'EAD PLANT POSITION III A,l, (A)
ACCELERATION DRAG IMPINGNENT FACTORs RA/ ~
6 S
(A) ftORE REALISTIC BOUNDARY CONDITIONS ~IVE RA/S ~
-5/64 (B)
(C)
POTENTIAL TO ACCOUNT FOR NOVING JET FRONT (B),
(C)
POTENTIAL FROM RING VORTEX tjODEL LEL 11/15/78
ACCELERATION DRAG"PRIOR"TO INPACT OF"A STRUCTURE AND"TRANSLATING SPHERE U.
FLOW FIELD UNDISTURBED BY STRUCTURE l RA/S ~
6 FLOW FIELD SATISFIES ZERO NORf'lAL VELOCITY BOUNDARY CONDITIONS'A/s
~ -3/64 LEL 11/15/78
t'IATER JET EXPERINENTS e
0 FILMS OF 1/15 5
AND 1/4 SCALE TESTS SHOW NUSHROOM NOT BULLET.
f l l)i t
t l l
)tl g II i I )
lillfi
~
JET KINETIC ENERGY CONVERTED INTO VORTICITYc NOVEMENT OF VORTEX RING PRODUCES FLOW FIELD IN POOL.
COf'lCL'US I'ON'l RING VORTEX MODEL CAN BE EXPECTED TO DRED ICT VENT CLEAR ING i LEL 11/15/78
t TE J T CON USIOtlS 6
A."." LERATION ORAG FACTOR AT IflPINGENE,l IS 128 SNALLER THAN CRITERION AND IS ATTRACTIVE.
FLOW FIELD GENERATED BY RING VORTEX f'IODEL APPROPRIATE FOR LOAD CALCULATIONS'
LOCA AIR BUBBLE (I)
NRC CRITERIA LEAD PLANT POSITION (A)
INCREASED LOAD FROM BUBBLE ASYMMETRY>
(A)
CONSENT (B) tlOD I FY DRAG COEFFICIENT BY CD/CD =
(B)
USE =X. ERIMENTAL LITERATURE TO DETERMINE APPRO. REATE VALUE OFCD/CD LEL 11/15/78
100 fb
$0 co NRC I
I I CRITERION
//////////,
///
JI I
/.
//I/
10
///
//
/,/.
//'
//
0 (p
8 CP C
G Ca Ex PhR IMENTAL STcAOY C
'o=3 60 io lg Fimps f. ToWFo~ on Cylinder, ~niAeeeiareion (R~ku~ and Gun&an, 7953J LEL 11/15/78
r-P1 f
Vl OO PLATES bg CO Cg PLATES
~CYLlNDERS CYLINDERS 0 0 IO 20 30 UMT/0 FIGUfK C-1 ACCELERATION CORRECTION FOR STANDARD DRAG COEFFICIENT
QSTF RESULTS"FOR LOCA"AIR BUBBLE TARGET NODEL" P RED I CTION(LBF)
QSTF 'NEASURENENTS(LBF)
B 50 50 290 65 TARGET-LOCATIONS IN"QSTF LEL 11/15/78
LOCA 'AIR BUBBLE LOADS CONCLUSIONS 0
ANALYTICALl'lODEL VERY CONSERVATIVE ANALYSIS OF APPLICABLE EXPERIMENTAL DATA INDICATES THAT 1.0 IS AS UPPER BOUND FOR CD/CP (RATHER THAN 5)
I APPROPRIATE FACTORS HILL BE CALCULATED DEPENDENT UPON INDIVIDUALPLANT GEONETRYe USE OSCILLATING FLOW RESULTS AT CORRESPONDING KEULEGAN-CARPENTER I'lUNBER FOR POOL-SWELL e PUBLISHED AND UNPUBLISHED HORK OF T s SARPKAYAe LEL 11/15/78
LOCA AIR BUBBLE (II)
NRC CRITERIA LEAD PLANT POSITION III B,l, (C)
TAKE NAXINUN VALUES OF FLOW FIELD SEEN BY STRUCTURE (C)
USE CENTER LOCATION FOR ACCELERATION.
DEFINE t'lULTIPLIER TO BE APPLIED TO VELOC ITY AT CENTER LEL 11/15/78
EQUIVALENT"UNI'FORN FLOW" ACCELERATION P
Souaez
~&)
I
(~ooD Y'j F/< I 6r L~~]
p Axa~ Lj~
up EXAcT'oa J
LEL 11/15/78
EQUIVALENT UNIFORN FLOW VELOCITY USE OF I"lAXIMUMVELOCITY SEEN BY STRUCTURE IS IMPRACTICABLEe If FLOW FIELD NAY BE VERY COMPLICATED CONTAINS MULTIPLE SOURCES AND SINKS DETERMINATION OF POINT OF HAXIMUM VELOCITY f'lAY BE VERY COSTLY (SCHEDULE AND RESOURCES)
~
EACH A/E TO DO SENSITIVITY STUDY TO DEF I NE 'A NULTIPLIER THAT NAY BE APPLIED TO THE VELOCITY CALCULATED AT GEOMETRIC CENTER AND TO ASSESS THE IMPORTANCE OF THIS EFFECTS LEL 11/15/78
0 EauIVALENT uriIFORrs FLOW FIELD COi>>CLuSIO~SS O
ACCELERATION DRAG LOAD IS CONSERVATIVELY ESTIMATED BY USING ACCELERATION AT CENTER OF STRUCTUREs IMPRACTICABLE TO IDENTIFY NAXIMUM YELOCITY POINT FOR EACH STRUCTUREs 6
SENSITIVITY STUDY TO DEFINE, NULTIPLIER TO APPLY TO CENTER YELOCITYs LEL 11/15/78
LOCA AIR BUBBLE (III)
NRC CRITERIA LEAD PLAi4T POSITION III, B.
1 (D)
TO ACCOUNT FOR (E)
INTERFERENCE OF NEARBY STRUCTURES MULTIPLY CD AND'VA BY (D)
OETAILED ANALYSIS OF (E)
~ INTERFERENCE EFFECTS IS BEING PERFORMED (F)
CHANGE COEFFIENCT FOR FALL BACK LOAD (F)
CONSENT LEL 11/15/78
INTERFERENCE EFFECTS o
STANDARD DRAG DALTON AND SZABO EXPERIMENTS ON GROUP OF 5 CYLINDERS AT VARIOUS SPACINGS AND ORIENTATIONS SHOW CD ALWAYS BOUNDED BY 1 2 ~
ZDRAVKOVICH COMPREHENSIVE HISTORICAL REVIEW SHOWS THAT IN MOST CASES INTERFERENCE REDUCES STANDARD DRAGi IN NO CASE IS THE STANDARD DRAG INCREASED MORE THAN 3~/o EXCEPT FOR SIDE BY SIDE ARRANGEMENT OF CYLINDERS ALMOST TOUCHING ONE ANOTHER'HEN THERE IS A 9$ $ INCREASE 4
e ACCELERATION DRAG INTERTIA COEFFICIENT CAN BE INCREASED DUE TO P
I INTERFERENCE'ACH A/E IS DETERMINING A"PROPRIATE FACTORS LEL 11/15/78
INTERFERENCE EFFECTS CONCLUSION
~ 'I A DETAILED ANALYSIS OF INTERFERENCE EFFECTS IS BEING DONE AS SUGGESTED IN THE ACCEPTANCE CRITERIONe LEL 11/15/78
SRV AIR 'BUBBLE NRC CRITERIA LEAD PLANT POSITl01'l III, B, 2.
(A)
INCLUDE STANDARD DRAG t'IAGNITUDE CHECK (A)
CONSENT (B)
APPLY APPROPRIATE CONSTRAINTS DISCUSSED NITH LOCA AIR BUBBLE (B)
USE OSCILLATING FLOW RESULTS TO OBTAIN CD, POSITION IS SANE ON OTHER CONSTRAINTS AS IN LOCA AIR BUBBLE DISCUSSION LEL 11/15/78
I I
Ul 00
- PLATES, I
j-I co Cp PLATES
~CYLINDERS CYLINDERS 0 0 IO VMT/D 20 FIQK C-1 ACCFLERATION CORRECTION FOR STANDARD DRAG COEFFICIEtIT
SRV AIR BUBBLE CONCLUSIONS e
USE OSCILLATING FLON RESULTS AT APPROPRIATE KEULEGAN CARPENTER NUMBER TO DETERMINE CD/C ll I
LOCA AIR BUBBLE CONCLUSIONS ON EQUIVALENT UNIFORM FLOW FIELD AND INTERFERENCE EFFECTS APPLY HERE ALSO LEL ll/15/78
RATIO OF ACCELERATION TO STANDARD DRAG FOR JETS It is evident from the quarter-scale model tests and the pictures taken at the Stanford Research Institute that the LOCA water jet does not, travel as a bullet.
For the sake of argument, if the jet were to be modelable by a moving source of varying intensity, then the equation (1) of the reviewer (Reference
- 1) is correct.
However, the subse-quent arguments lead to overlyconservative results.
The force on a target at the time the jet front touches the target, if calculated as proposed by the reviewer, does not account for the presence of the target.
To incorporate the correct target boundary conditions, one must represent the target with appropriate singularities and take the mutual images of these singularities in the axisymmetric half body (representing the jet slug) and the target.
Nithout such a procedure, the condi-tion of no flow through the target boundary is not satisfied.
Let us demonstrate the use of a correct procedure for a doublet approaching a rigid sphere.
This corresponds to the case of two spheres approaching each other along the lines joining their centers, or to the case of one sphere approaching the other.
This case has been treated in the literature (see e.g.,
References 2 and 3).
b Figure l The correct fomulation of the potential function through
-the use of many image doublets yields the kinetic energy,
Now assume that sphere "b" is at rest, i.e.,
Ub =
0 then 7- = ~E~ gz (i+ saV)
(2)
The use of the equation of Lagrange (Reference
- 3) together with Equation (2) yields the force at the time of the touching of two spheres, i.e.,
when x = a + b.
(3)
Assuming, for the sake of simplicity, a = b, one has (4) 4 3
In terms of the acceleration volume V
= l. 5 W a, one has A
3
. 2q+g~
Jsb (5)
The standard drag for a uniform velocity U
past sphere"b",
a would have been (6)
The ratio of the forces is RA~S (7)
Et should be noted in passing that the sphere "a" is repelled by the sphere "b".
Let us now assume that the flow field created by the sphere "a" is not disturbed by sphere"b".
Then the potential for a moving sphere "a" is given by Ua CoS O g 92I'8)
The velocity V is 'calculated from r
a 0Q U~<'as&
Vf'p QS Also 0 k - -3~V. U+ g Q~
Q. pe Q 0r
~r (9)
At the time of contact
= +
3 U
/a the force would have
>Vr
'=
gg (sU~)/a, (10)
When compared with the standard
- drag, one would have
Equation
{11) is quite comparable to the Equation (5) of the reviewer, but it is overly conservative for the reasons cited above.
REFERENCES l.
Bienkowski's Review of General Electric Reports, NED0-21730, NEDE-21472, and NED0-21471.
2.
- Streeter, Fluid D namics, McGraw-Hill, 1948.
3 ~
Milne-Thomson, Theoretical H drod namics, MacMillan, 1960.