ML18026A289

Submits Withdrawal of Expedited Review/Approval of Tech Specs/Bases 3/4.3.7.11 & 3/4.11.2.6 & Response to Request for Addl Info Re Offgas Sys Mods

ML18026A289
Person / Time
Site:	Susquehanna
Issue date:	05/22/1998
From:	Byram R PENNSYLVANIA POWER & LIGHT CO.
To:	NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM)
Shared Package
ML17159A348	List: ML17159A347 ML18026A289
References
PLA-4882, NUDOCS 9806020236
Download: ML18026A289 (76)

Text

CATEGORY 1

! REGULAT ii ~INFORMATION DISTRIBUTIO STEM (RIDS)

ACCESSION NBR:~ 9806020236 DOC.DATE: 98/05/22 NOTARIZED: NO DOCKET ¹ FACIL:50-387 Susquehanna Steam Electric Station, Unit 1, Pennsylva 05000387 50-388 Susquehanna Steam Electric Station, Unit 2, Pennsylva 05000388 AU'ZH.NAME AUTHOR AFFILIATION BYRAM,R.G. Pennsylvania Power & Light Co.

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RECIPIENT AFFILIATION Document Control Branch (Document Control Desk) ~~ w T(S

SUBJECT:

Submits withdrawal of expedited review/approval of Tech Specs/Bases 3/4.3.7.11 & 3/4.11.2.6 & response to request for addi info re offgas sys mods. A DISTRIBUTION CODE: A001D COPIES RECEIVED:LTR ENCL SIZE: T TITLE: OR Submittal: General Distribution E

NOTES: 05000387 6

RECIPIENT COPIES RECIPIENT COPIES ID CODE/NAME LTTR ENCL ID CODE/NAME LTTR ENCL PD1-2 LA 1 1 PD1-2 PD 1 1 NERSES,V 1 1 INTERNAL: ACRS 1 1 01 1 1 NRR/DE/ECGB/A 1 1 NRR/DE/EMCB 1 1 NRR/DRCH/HICB 1 1 NRR/DSSA/SPLB 1 1 NRR/DSSA/SRXB 1 1 NUDOCS-ABSTRACT 1 1 OGC/HDS2 1 0 TERNAL 6 NOAC NRC PDR 1 1 D NOTES: 1 1 U'

NOTE TO ALL "RIDS" RECIPIENTS:

PLEASE HELP US TO REDUCE WASTE. TO HAVE YOUR NAME OR ORGANIZATION REMOVED FROM DISTRIBUTION LISTS OR REDUCE THE NUMBER OF COPIES RECEIVED BY YOU OR YOUR ORGANIZATION, CONTACT THE DOCUMENT CONTROL DESK (DCD) ON EXTENSION 415-2083 TOTAL NUMBER OF COPIES REQUIRED: LTTR 15 ENCL 14

s I Robert G. Byram Senior Vice President Generation and Chief Nuclear Officer Tel. 610.774.7502 Fax 61 0.774.5019 E-mail:rgbyram@papl.corn PPSL, Inc.

Two North Ninth Street Allentown, PA 18101-1179 Tel. 610.774.5151 http:ltwww.papl.coml pp MAY 22 1998 U. S. Nuclear Regulatory Commission Attn.: Document Control Desk Mail Stop P 1-137 Washington, D. C. 20555 SUSQUEHANNA STEAM ELECTRIC STATION WITHDRAWALOF EXPEDITED REVIEW/APPROVAL OF TECHNICALSPECIFICATIONS/BASES 3/4.3.7.11 AND 3/4.11.2.6 PURSUANT TO ITS AND t

RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION- OFFGAS SYSTEM MODIFICATIONS Docket Nos. 50-387 PLA-4882 FILE R41-2 and 50-388

Reference:

I) R. G. Byram to USNRC "Expedited Review/Approval of Technical Speci Jication 'Sections/Bases 3/4.3.7.11 and 3/4.11.2.6 Pursuant to ITS, "dated March 27, 1997, (PLA-4564).

2) R G. Byram lo USNRC, "Deletion of Hydrogen Isolation in Technical Specificalion Bases,"

dated October 7, 1996, (PLA-4508).

3) R. G. Byram lo USNRC, "Proposed Amendmenl No. 205 to License NPF-14 and Proposed Amendment No. 170 to License NPF-22: Main Steam Line Radiation Monilor Setpoinl Change and Change to Radioactive Gaseous Event Monitoring System," dated March 16, 1998.

4) USNRC to R G. Byram, "Offgas System Modifications, Susquehanna Steam Electric Station (SSES), Units I and 2," dated March 20, 1998.

The purpose of this letter is to:

~ withdraw two PP&L, Inc. (PP&L) Technical Specification review and/or approval requests associated with the Susquehanna SES offgas system (references 1 and 2), and

~ respond to the NRC's Request for Additional Information related to offgas system modifications (reference 4).

The NRC reviews requested by references 1 and 2 are being withdrawn from co'nsideration because they have been superseded by the Technical Specification proposed amendment change identified by reference-3.

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FILE R41-2 PLA-4882 Document Control Desk The attachment to this letter provides the PP8'cL response to the NRC Request for Additional Information related to the offgas system modifications.

Also attached to this letter are the references requested during the May 6, 1998, telecon concerning the RAI response.

Ifyou have any questions please contact Mr. J. M. Kenny at (610) 774-7535.

Sincerely, R. . yra Attachments copy: NRC Region I Mr. K. M. Jenison, NRC Resident Inspector Mr. V. Nerses, NRC Sr. Project Manager

ATTACHMENTTO PLA-4882 Page 1 of 11 Response to Request for Additional Information Offgas System Modifications

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Back round Removal of the Offgas Isolation on High Hydrogen concentration is required to support the implementation of Hydrogen Water Chemistry (HWC). Implementation of this modification under 10CFR50.59 is contingent upon NRC approval of proposed amendment no. 205 to license NPF-14 and proposed amendment no. 170 to license NPF-22 submitted on March 16, 1998. This change in part will move/relocate the Main Condenser Offgas Treatment System Explosive Gas Monitoring System and Radioactive Effluents Explosive Gas Mixture to TS Section 6.0, FSAR Section 16.3 (Technical Requirements Manual) and controlling documents.

This modification is needed to avoid an offgas isolation following a loss of oxygen injection.

Under HWC, hydrogen gas is injected into the reactor vessel with feedwater. This reduces the radiolysis of water to hydrogen and oxygen by up to 90%. As a result, oxygen must be injected upstream of the recombiners to react with the hydrogen injected to feedwater. A loss

. of oxygen injection would cause hydrogen injection to shutdown, but would result in a high hydrogen transient downstream of the recombiner, until residual hydrogen in the steam cycle had been purged. With the current design, offgas would isolate and potentially cause a plant shutdown on loss of condenser vacuum. This modification will permit hydrogen to be passed through the offgas treatment system, to be diluted to well below the lower flammability limit by the turbine building vent flow.

As presently designed, the Offgas system will automatically isolate itself from the main condenser by closing the Offgas inlet valves to the first stage Steam Jet Air Ejectors (SJAE) when the hydrogen analyzers on the recombiner condenser outlet detect >2% hydrogen by volume (Hi-Hi hydrogen setpoint). This is intended to preclude'the formation of explosive gas mixtures in the downstream offgas treatment system. The setpoint is half of the lower flammability limit for hydrogen in air (4%), which is also the Susquehanna Technical Specification limit (TS LCO 3.11.2.6).

This design is one acceptable approach to eliminating the potential for release of activity to the environment as a consequence of a hydrogen explosion in the offgas treatment system. The other acceptable approach is to design the system to contain a hydrogen explosion. PPAL is committed to Branch Technical Position (BTP) ETSB No. 11-1 (Rev. 0) "Design Guidance for Radioactive Waste Management Systems Installed in Light-Water-Cooled Nuclear Power Reactor Plants." This BTP did not address requirements for explosive mixtures in gaseous radioactive waste systems. Subsequently, the BTP was superseded by Regulatory Guide

. (RG) 1.143. This RG was revised in October of 1979 to address this concern. RG 1.143 g806020236

ATTACHMENTTO PLA-4882 Page 2 of 11 Rev. 1 Section 2 "Gaseous Radwaste Systems" states "If the potential for an explosive mixture of hydrogen and'oxygen exists, adequate provisions should be made to preclude buildup of explosive mixtures, or the system should be designed to withstand the effects of an explosion".

To confirm whether or not the Susquehanna SES (SSES) offgas systems are hydrogen "detonation proof', General Electric (GE) has completed an evaluation titled "Evaluation of Susquehanna Offgas System Pressure Integrity for Hydrogen Detonation" (EC-072-1007). In summary, GE's analysis of the Susquehanna offgas system showed by calculation that the pressure boundary, consisting of piping and major components, is either capable of withstanding multiple hydrogen detonations or the system is designed to preclude the existence of a detonable gas mixture. PP&L has reviewed and concurs with GE's evaluation.

Therefore, automatic isolation is not necessary to preclude explosive gas mixtures.

Existing capabilities for hydrogen monitoring will be retained. Operating procedures will be modified using GE SIL 150 to provide guidance for responding to high hydrogen alarms.

Additionally, appropriate revisions will be made to the FSAR and other controlled documents.

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""" ' "' '"'"c Queslion i?1 The method of calculation in EC-072-1007 was based on GE report, NEDE-11146 with some modifications in determination of detonation peak pressure. In NEDE-11146, the detonation peak pressure is a function ofthe length lo diaineter ratio (LID).

For LID (7, the peak pressures are 17 tidies the initialpressure.

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For LlD 7, the peak pressures are 170 times the initialpressure.

EC-072-1007 uses 80 times the initialpressure as the peak pressure for an 8-inch diaineter piping with

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LID 7 in the SSES oggas system. This factor of80 is not supported by NEDE-11146 method.

The licensee indicated that the factor of 170 was developed based on the measirreinents in small diameter piping of 5 inches or less and that for piping diaineters of 8-inches and larger, both theory and measurements support a factor of two conservatism in the small bore piping data. The licensee further referred to the actual ineasurement ofa long 24-inch diaineter piping to support its argument.

The staff has reviewed the licensee 'sj ustifications and has the following questionsi (a) Explain why the measurement data from 24-inch diameter piping are more applicable than the data Poin 5-inch for the application of8-inch piping.

ATTACHMENTTO PLA-4882 Page 3 of 11 (b) Furthermore, the peak pressure is a fimction of (LID), notjust a function ofpiping diameter (D).

Explain why the licensee adjusted the factor from 170 to 80 based on the piping diameter alone?

(c) The licensee is required to provide applicable supporting documents in the measurements and theory regarding the factor of two'onservatism for the staff to review their applicability.

Otherwise, the licensee should use the methodin NEDE-11146 without modifications.

Res onseto uestionPI. a 8r, The design method of NEDE-11146 was modified by GE for the SSES evaluation to remove excessive design conservatisms known to exist in the original methods developed by GE, The strict application of the NEDE-11146 methods, while cost effective for new construction, would result in excessive overdesign and unnecessary expense ifapplied to an existing system. For this reason, GE researched existing data and theory regarding peak pressures developed in piping larger than S-inches, which formed the basis for the peak pressure ratio of 170 used in NEDE-11146 for all piping diameters. Reference 3 of calculation EC-072-1007 showed a maximum pressure ratio of approximately 80 for 24-inch piping. The data for 24-inch piping clearly supports the existence of lower pressure ratios in large diameter piping, but the data does not specifically address 8-inch piping. Therefore existing theory was quantified in support of the difficulty in achieving a uniform piston effect needed to achieve pre-detonation run-up as piping diameters increase.

To quantify the relationship between pipe diameter and pre-detonation run-up length (length of reaction zone from point of ignition or deflagation initiation to onset of fully turbulent conditions and detonation initiation), the relationship between peak pressure ratio and the ratio of pre-detonation length to piping length for acetylene detonation (Reference 1 of this attachment) was used. This relationship for acetylene, which exhibits pressure ratios up to about,400, was modified to represent the maximum peak pressure ratio of 170 observed for hydrogen detonation. Using this relationship and the pre-detonation run-up length for hydrogen of 70 centimeters (Reference 2 of this attachment), a relationship between pressure ratio and

'pipe length to diameter ratio for various piping diameters was developed (Reference Figure 1 of this attachment). Figure 1 is a graphic representation that shows the relationship between detonation pressures and pipe size for various gasses which was developed &om references 1 and 2 of this attachment. Therefore, the pressure values for hydrogen detonations cannot be directly compared to the data identified in calculation EC-072-1007. From this figure it is evident that the effect of pre-detonation cascading for 8-inch piping and larger, which shows a maximum pressure ratio of about 60, is very small compared to 4-inch piping. This same effect is explained in Example 4 of Reference 1 of this attachment, which cites the example of 12-inch piping. The example states that self-propagating detonations are very difficult to establish because "when a small ball of fire forms in a large volume of acetylene, it may not have sufficient available heat to raise the adjacent layer of cold gas to its ignition point." In other words, it is difficult to form the uniform deflagation front across the piping cross-section needed to produce the pre-detonation run-up or piston effect to compress the unburned gas ahead of the flame front. Therefore, based on the above information, the piping analysis for

ATTACHMENTTO PLA-4882 Page 4 of 11 Susquehanna offgas piping 8-inches diameter and larger was based on a pressure ratio of 80 (Reference 3 of calculation EC-072-007 for 24-inch piping) rather than 170.

Res onseto ucstion81. c Data for the 24-inch pipe pressure ratio of approximately 80 is found in Reference 3 of calculation EC-072-1007. Development of Figure 1 of this attachment is discussed in the responses to 1 (a) & (b).

Quese on 42'he initialpressures (Pg, used in Table 1, "Suinmary ofSusquehanna Piping Analysis, " appears to be the pressures corresponding to the normal plant operation. In Final Safety Analysis Report Table 11.3-8, it shows that the pressures corresponding to startup mode are higher. Explain why the analysis used the lower pressures.

Res onse to uestion 82 Offgas system normal pressures were used in the calculations because at low power

'conditions and high air flow rates present during startup, detonable offgas mixtures can not be present. The footnote to FSAR Table 11.3-8 notes that at startup conditions, negligible hydrogen is present. At low power conditions hydrogen will not be injected by the HWC system.

uestion i0 Section 2.0 of Calculation EC-072-1009 indicates that ANSI/ANS 55.4-1979 Appendix C provides an acceptable inethod for analyzing a hydrogen detonation in the offgas system. The summary discussion in Calculation EC-072-1007 further inrplies that tlie criteria were accepted in Regulatory Guide 1. 143.

However, the discussion in Regulatory Guide 1.143 indicates that the standard would be endorsed separately. Please provide the following information.

A specific reference that indicates the procedure specified in Appendix C ofANSI/ANS 55.4-1979 has been previously reviewed and approved by the staff.

b. Table 1 ofRegulatory Guide 1.143 lists the applicable equipment design codes. Describe how the criteria for determining wall thickness specified in Equation 2 of Appendix C of A1VSVANS in 55.4-1979 met the design code requirements specified Regulatory Guide 1. 143.

0 ATTACHMENTTO PLA-4882 Page 5 of 11 Res onseto uestion¹3 a There is no specific reference that indicates the procedure specified in Appendix C of ANSUANS 55.4-1979 has been accepted by the NRC. However, NUREG/CR-5973 (Rev 3) identified ANSVANS 55.4-1979 as a document that provides background information. The basic methodology used in the design of detonation-resistant BWR Offgas systems is 'described in Appendix C of ANSVANS 55.4-1979. That methodology, with slight variations between Architect - Engineers and industry equipment suppliers, has been followed since the early 1970's. This methodology was used in licensing of the Limerick Offgas system design.

Res onse to uestion ¹3 FSAR Table 3.2-1 "SSES Design Criteria Summary", Note 31, has been revised and now identifies the design criteria for the Gaseous Radwaste System per ESTB 11-1 Rev. 0. This revision will be incorporated into the next update to the FSAR. The design guidance in Table 1 of Regulatory Guide 1.143 is not applicable for detonation analysis purposes. Appendix C of ANSUANS 55.4-1979 is the applicable guideline to use for detonation analysis.

Qu~tioit S4 Section 2.0 of Calculation EC-072-1009 indicates that the design guidance documents do not require design for a hydrogen detonation simultaneous with a seismic event. However, ANSI/ANS 55.4-1979 Appendix C contains the following statement: "The method assumes the absence of simultaneous secondary events such as earthquakes." The statement does not indicate that additional load combinations are not required. Describe the design load combinations for mechanical equipment and piping that are applicable to the design ofthe offgas system. Reference the Susquehanna FSAR section that contains the load combination criteria.

Res onse to uestion ¹4 ESTB 11-1 Rev. 0 "Design Guidance for Radioactive Waste Management Systems Installed in Light-Water-Cooled Nuclear Power Plants",Section II.a.(3) states that "for systems that operate near ambient pressure and retain gases on charcoal adsorbers, only the tank elements and the building housing the tanks are included, (e.g. charcoal delay tanks in a BWR)." The SSES offgas system charcoal adsorber tank elements and the building housing the tanks are designed to meet the requirements of ESTB 11-1 Rev.0, section V. There are no additional design load combinations for the SSES Offgas system and therefore, no section in the SSES FSAR contains specific load combination criteria. FSAR Table 3.2-1 "SSES Design Criteria Summary", Note 31, identifies the design criteria for the Gaseous Radwaste System.

ATTACHMENTTO PLA-4882 Page 6 of 11 guesliost iiS Calculation EC-072-1007 provides a summary of the evaluation of the offgas piping and equipment using the criteria in ANSVANS 55.4-1979 Appendix C. The summary indicates that the analysis demonstrates that inaterial yield stresses would not be exceeded following a detonation with the Susquehanna offgas systeni. Provide the followinginforniation.

a. Table 1 ofCalculation EC-072-1007 lists the yield stress values used in the evaluation. Provide the technical justification that the reported yield stress values are applicable to the piping at Susquehanna.

b. Table 1 of Calculation EC-072-1007 lists the straiir hardening exponents used in the evaluation.

Provide the technical justification that the reported strain hardening exponents are applicable to the piping at Susquehanna.

c. The procedure specified in ANSVANS 55.4-1979 Appendix C only applies to the hoop stress due to pressure. Discuss the potential for additional dynamic loads resultingPom the transient pressure wave propagation through the system as a result of the detonation. Describe the component and component sripport criteria diat are applicable to this scenario.

Res onse to uestion ¹5 a &

Yield values and strain hardening exponents for C1010 carbon steel are documented in References 2 and 5 of Calculation EC-072-1007 at temperatures of 70', 400', and 900'.

The yield strength values and strain hardening exponents in Table 1 of Calculation EC-072-1007 for carbon steel (A-106, Gr B) are linearly interpolated at the required temperature. The yield strength value and strain hardening exponents for stainless steel (SA-312, TP 316 and SA-213, TP 316) are from Reference 4 of calculation, Table 1 "Stress-Strain Properties in Simple Tension" for T-304 stainless steel. Based on subsequent reviews, the yield strength values and strain hardening exponents have been corrected in Table 1 of Calculation EC-072-1007 (attached) to reflect the values of Reference 4.

The yield stress and strain hardening exponent values used in the GE report, NEDE-11146 are dynamic values, i.e. they are values expected as a result of subjecting th'e materials in question to the high strain rates experienced during a detonation. These values are therefore not the normal values as are found in the codes, which are applicable to static or low strain rate conditions. The values used for high temperature carbon steel were derived from a report by A. Shultz, "Dynamic Behavior of Metals Under Tensile Impact," AFML-TR-69-76, Part 1, April 1969, which evaluated C-1010 carbon steel at high strain rates. The data in that report represent best fit values as determined from a series of approximately 20 experimental observations at each reported temperature.

I

ATTACHMENTTO PLA-4882 Page 7 of 11 The room temperature values for carbon steel were derived from a report by P. Randall and I.

Ginsburg, "Bursting of Tubular Specimens by Gaseous Detonation," Journal of Basic Engineering, December 1961, which again represents best fit values from a series of experimental results. The experiments were run for both hot-rolled carbon steel pipe and cold-drawn carbon steel tubing.

Values for stainless steel at room temperature were taken from a report by C. Costantino, "The Strength of Thin-Walled Cylinders Subjected to Dynamic Internal Pressures,"

Transactions of ASME, March 1965, and are believed to represent average 'or nominal values.

It should be stressed that the method and dynamic material properties as used in the Susquehanna analysis are the same as have been used by GE in the design of all offgas systems supplied by GE. Based on operating history at other BWR's with similar offgas systems no reported deformation or failure of the pressure boundary have occurred following an offgas system detonation. The GE desig'n method as used in NEDE-11146 has been adopted in ANSI-55.4, Appendix C for design of gaseous waste systems handling detonable hydrogen mixtures, and is endorsed in Regulatory Guide 1.143, Rev. 1. The GE design method is a static analysis utilizing dynamic material properties, and is known to contain considerable conservatism relative to a rigorous dynamic analysis. This conversatism has been estimated by GE to be a factor of two in terms of pipe wall thickness, and results from the fact that the detonation forces creating the piping hoop stresses are acting over a very short length of piping of less than 1 inch. The piping length reacting to the peak detonation pressure is determined by the extremely short width of the Chapman-Jouget reaction zone (usually less than 10 microseconds) (D.H. Edwards, et al, "Pressure and Velocity Measurements on Detonation Waves in Hydrogen-Oxygen Mixtures," Journal of Fluid Mechanics, April 1959, pp. 497-517) and the velocity of the detonation wave (about 9000 A/sec). Because the entire pipe length is not subjected to the peak pressure simultaneously, the short (<1 inch) hoop section subjected to the peak pressure is supported both upstream and downstream by adjacent piping material. This support effectively limits the stresses developed in the hoop section subjected to the peak detonation pressure, thus reducing the required wall thickness.

Res onseto uestion85 e Line Properties & Conditions in Table 1 of Calculation EC-072-1007 lists Po (Operating Pressure, psia), P (Peak Internal Detonation Pressure, psia) and other design parameters to calculate pipe thickness required (Reference 3 of this attachment) to sustain normal operating and peak detonation pressure. Based on these calculations and with an additional factor of safety of 1.15 (Reference Table 1 of Calculation EC-072-1007), there is enough pipe thickness margin left in the existing offgas piping system for Susquehanna Steam Electric Station, Units 1 & 2.

ATTACHMENTTO PLA-4882 Page 8 of 11 The stress in the pipe wall is a time dependent quantity; the pressure is applied suddenly but the pipe wall does not respond instantly because of its inertia (Reference 4 of this attachment). General engineering practices were used to design component and component support for Susquehanna Steam Electric Station, Units 1 & 2. Based on operating history at other BWRs with similar offgas systems where offgas detonations have occurred, no failure has occurred involving either component pressure boundaries or component supports.

Hence, existing component and component support designs for Susquehanna Steam Electric Station, Units 1 &, 2 are acceptable based on both operating experience and Calculation EC-072-1007.

In addition to hoop stress, which is addressed by the GE design method, impulse loading on the piping is expected as a result of detonation. This loading, which has been measured in a report by D. White, "On the Existence of Higher than Normal Detonation Pressures,"

GE Research Laboratory, Journal of Fluid Mechanics, July 1957, is approximately 1 lb-sec/in as measured at the end of a pipe filled with detonable hydrogen mixtures. For offgas systems supplied by GE, piping supports and hangers have been designed by the architect engineers, and GE has never required that the hangers be designed to withstand these additional detonation induced loads. While GE has not quantified these loads, GE believes them to be insignificant. For example, through years of BWR plant operating experience, no piping support or hanger damage has occurred following offgas detonation events. Because of the short duration (microseconds) of detonation induced loading and the inertia of the piping, the piping mass can not respond significantly to the detonation pulse.

Therefore, the additional load on piping supports and hangers is believed to be insignificant.

gsesllon N6 F

Following a postulated explosion ofthe offgas system, discuss the following concerns:

a. the equipment (such as hydrogen analyzers, radiation monitors... etc) survivability,

b. monitoring and controlling the release ofradioactivity, and

c. operator actions.

Res onseto uestion86 a The offgas hydrogen analyzers, pre-treatment radiation monitors and other instrumentation have the potential to fail following a detonation within the offgas pressure boundary. The offgas system and related instrumentation is not safety related. Failure of the equipment poses no personnel safety hazard. Additionally, as a backup to the offgas pre-treatment monitor, the Turbine Building SPING stack monitor will alarm and prompt operator action to prevent exceeding occupational and offsite dose requirements.

ATTACHMENTTO PLA-4882 Page 9 of 11 Res onse to ucstion ¹6 The release of radioactivity &om the Offgas system will be monitored by the Turbine Building SPING monitor. Control of releases from the Turbine Building SPING will be accomplished under the existing procedures.

Res onse to uestion ¹6 c Plant specific operator actions following an offgas detonation will be specified in plant operating procedures prior to removing the offgas high hydrogen trip. GE Service Information Letter (SIL) 150 provided licensees general recommendations for operator action following an indication of recombiner effluent hydrogen in excess of 4%. Key offgas system parameters including charcoal bed temperatures, offgas flow rate, recombiner temperatures, and pre-treatment radiation monitors will be evaluated in developing operating procedures.

Specific operator actions will depend upon whether an offgas ignition occurs and whether the ignition results in a sustained combustion. Operator actions following an ignition that will be evaluated include 1) shutdown and repair of failed components, or 2) addition of inert gas to dilute the mixture below the flammable limit.

References

1. H. B. Sargent, "How to Design a Hazard-Free System", Figure 2, Chemical Engineering, February 1957, pp 250-254.

2. B. Lewis and G. von Elbe, Combustion, Flames and Explosions of Gases, Academic Press, Third Edition, 1987.

3. ASME B&PV Code,Section VIII, ASME B&PV Code,Section III, and ASME/ANSI B31.1 Power Piping Code.

4. P. N. Randall and I. Ginsburg, "Bursting of Tubular Specimens by Gaseous Detonation",

Journal of Basic Engineering December 1961, pp 519-528.

5. D.H. Edwards, et al, "Pressure and Velocity Measurements on Detonation Waves in Hydrogen-Oxygen Mixtures," Journal of Fluid Mechanics, April 1959, pp. 497-517

6. D. White, "On the Existence of Higher than Normal Detonation Pressures," GE Research Laboratory, Journal of Fluid Mechanics, July 1957.

Table 1. Summary of Susquehanna Piping Analysis

>ne roper ies on <<ons ynannc rope les ic ness, Inc Line iltateriat dp ln t,in(1) Lin (2) po psia (3) p/po p, psia T,4F Sy, psi Sn, psi H H, Sensor SA-312, TP 316 0.086 15.0 17 110 3,800 171,000 2.00 0.72 1.15 0.041 0.009 Hs An yzcr SA-213, TP 31 0.375 >7 15.0 170 110 3 >800 17110 2.00 0.72 1.15 0.041 0.008 Where:

d = nominal pipe diameter, inches Su = ultimate dynamic stress, psi (Ref 4&5) t = pipe wall thickness, inch =

h dynamic load factor (Ref 2)

L/D = length to diameter ratio n = strain hardening exponent (Ref 4&5)

=

po operating pressure, psia F = arbitrary safety factor

=

p peak internal detonation pressure, psia H'= thickness at yield point, inch (Ref 2)

T = operating temperature, F = pdhF/[2.31(Sy- p) x 0.577']

Sy = dynamic yield stress, psi (Ref 4&5) H = permanent deformation thickness, inch (Ref 2)

= pdhF/[2.31(Su- p) x 0.577']

Notes:

1. Thickness includes corrosion allowance of 0.080" for carbon steel and 0.003" for stainless steel.

2. L/Ds are based on the Offgas system isometric drawings, Reference 6.

3. Pressures are from Reference 7.

Figure 1. Peak Pressure Ratio for Hydrogen Detonation 140 4" pipe 120 100 80 6" pipe 60 8" pipe 24" pipe 40 20 10 15 20 25 30 35 Pipe L/D

497 (44) Pressure and velocity measurements on detonation waves in hydrogen e.-.,ygen mixtures

'Ls would be iminate the By D H EDWARDS. G. T. WILLIAMS'ANDJ. C BREEZEt ature of the Department of Physics, University College of Wales, Aberystwyth ll sharp so

thwhile. It (Received 23 December 1958 and in revised form 18 April 1969) rent,< 1 is

!Onic speeds Measurements are described of the static pressures and velocities of detonation ntropy rise: waves in hydrogen-oxygen mixtures, together with the pressures arising on their s, and non- normal refiexion at the closed end of the explosion tube. Two explosion tubes, of es. The net diameter 10 and 1 6 cm, were employed to study the diameter effect on the wave

'.he limiting pressures. The experimental results are compared with,calculated values of the wave properties for a range ofhydrogen-oxygen mixtures initiallyat atmospheric pressure. In the 10 cm tube the static pressures and velocities are found to agree mcheti snd well with theory for mixtures with hydrogen content in the approximate range

.I equation, 50-75 /e; the evidence from pressure profiles and wave velocities indicates that mixtures outside this range may not be able to support ideal C-J waves.

Detonation waves in all the mixtures studied in the 1 6 cm tube are found to be subidesl. A, possible explanation, in terms of energy loss to the tube wall, of the

.'sondere bei discrepancy between experiment and theory is discussed. Spinning occurs in mixtures near the limits of detonation in the smaller tube; the measured as. J. Zluid frequencies are found to be in reasonable agreement with the values predicted bv the theories of 3Isnson (1947) and I~'ay (1952).

reacting gas

957.

s subject to

-2. l. Introduction y of viscous Of the various properties of gaseous detonation waves, the velocities have Order VII, been studied experimentally far more extensively than any other. Early" John Wiley investigators in this field were able to obtain tolerably'ood values for the wave velocities by means of chronoelectric methods (e.g. Berthelot S Uieille 1882) or 1'. 25, 279. from the records of the waves on moving photographic plates or film (e.g.

s subject to Mallard 8; Le Chatelier 1900). Since then, the considerable advancements which have been made in high-speed photography and in the application of electronic

'isco-elastic techniques to the measurement of time intervals enable wave velocities to be

.ctive Qow. measured to a high degree of precision. An example of such measurements is the study of the wave velocities in hydrogen-oxygen mixtures made by Berets, axing Quid. 8: Kistiakowsky (1950). 'reene In contrast to wave-velocity messuremcnts, pressure measurements have received far less attention; this fact is understandable since it is a more diincult quantity to measure with acouracy. Zarly work gave no more than a crude and

~ Now at M.O.S. Arm. Res. Dev. Estab., Fort Halstead.

t Now at'Department of Physics, University of Western Ontario, London, Ontario.

3+ Fluid Necb. 6

e 498 D. Z. Eduerd's, 8. 2'. 'fViQiams amE J'. O. Breeze uncertain measure of the peak pressures generated in detonation waves. Thus Dixon k Cain (1894) attempted to estimate the pressures generated from the known strengths of glass tubes which were just &actured by the impact of the wave, whilst Campbell, Littler 4 Whitworth (1932) noted. how metal foils of various thickness, placed across the end of an explosion tube, were ruptured. ~

The results of both investigations were very approximate in view of the uncer-tainties in the mechanisms of fracture or rupture. Similarly, the results of the crusher gauge experiments of Rimarski 8: Konschak (1934) and Henderson (1941) must be regarded, as unreliable.

The most significant measurements reported of detonation pressures in hydrogenwxygen mixtures appear to be those of Gordon (1949) and Davies, Mwards k Thomas (1950). Gordon employed tourmaline gauges, in which oil or soft wax was used to damp the crystal vibrations, and although the results he presents are few and some of the gauge records are marred by oscillations, quite good agreement is observed between the measured and the theoretical values of pressure for a few compositions. Davies d aL used both quartz crystal gauges and the Hopkinson pressure bar method in the electrical form devised by Davies (1948), and in a preliminary investigation obtained results which were promising, It was apparent, however, that a more satisfactory gauge design was required before completely reliable pressure measurement could be achieved.

The need for a study of the pressure distribution in the detonation wave,, in addition to a measure of its velocity, may be appreciated from the following considerations, (Contrary to strict usage the term detonation wave will fre-quently be employed in the present paper to denote the shock front, the reaction zone together with the non-steady regime of the rarefaction wave,) In the case of the ideal detonation wave the Chapman-Jouguet (C-J) plane is identified in the hydrodynamic theory with the plane of complete chemical and thermal equilibrium. Kirkwood 4 Wood (1954), however, have shown that thermo-dynamic equilibrium at the C-J plane is not an essential requirement in the generalized theory. Deviations from complete equilibrium at the C-J plane would be expected to give rise to diiferences between the observed detonation wave parameters and those computed on the assumption of equilibrium. Thus ifthe rate of release of chemical energy within the reaction zone is lowered, for example by cooling of the reacting gases at the walls of the confining vessel, then the rate of evolution of useful energy may drop below the level required for the propagation of the ideal C-J wave. In this case, the velocity of the wave =

will be less than the ideal value and the C-J condition, V~ ~ ~+g, will now hold for the plane in which the energy required to propagate the wave (i.e. useful energy) is just balanced by the evolution of chemical energy, Berets et aL (1950) suggest that the excellent agreement which is usually'bserved between theoretical and experimental velocities may be due to the stabilizing action on the detonation velocity of the largely dissociated reaction systems, in which exothermic and endothermic reactions, involving both mole increment and decrement, are proceeding simultaneously. This interpretation appears to have been rejected later by Kistiakowsky 4 Zinman (1955), and agreement between experiment and equilibrium calculations is taken as proof of the attainment of

I Pressure and velocity measurements on detonation leaves 499 thermodynamio equilibrium in the C-J plane. In the view of the present authors, the original hypothesis of the buffering effect of the reactants on the wave f the velocity is of some importance, and consequently an examination of the velocity ils of alone does not provide a sufficiently strong criterion to establish whether ared. equilibrium has been achieved in the C-J plane. IIoreover, the measurement of ncer- any othor parameter, such as pressure, density or temperature, for the same f tho reason, would equally be insensitivo to small departures from strict equilibrium

~

rson at the C-J plane. If, however, the pressure-time or density distribution (Kistiakowsky, &; Kydd 1955) in tho wave are known in conjunction with the s in velocity, then the two parameters give a more complete description of the wave vies, than is obtained from the measurement of the wave velocity alone. Further-h ol moro, a comparison of the detonation pressure with the theoretical value should ililts provide a far more sensitive criterion of the validity of the C-J hypothesis itself ons, than a measure of the velocity. This fact can be verified from an examination of

'ical theoretical data (e.g. Nanson 1947); for ifit is assumed that, the end point of the stal detonation moves away from the C-J point along the Ra'nhine-Hugoniot curve 1 by for complete reaction, the corresponding changes in pressure'ap, for small vere deviations, several times as large as the resulting changes in veloc t .

sign In this paper, results are presented of measurements of the static dad refiexion ed. pressures in detonation waves in various hydrogenwxygen mixtures=conflned in

~,in tubes; measurements of the wave velocities were made simultaneously with the ing pressure measurements. Since no systematic,investigation appears t'0 have been carried out previously on the effect of explosion tube diaineter'on the wave pressures, comparable to the lvork of Berets et aL,(1950) on the wayne velocity, pressure measurements have been obtained for two explosion tubes of different diameter.

2. The numerical calculations he no Tho best results arailable of tho theoretical properties of detonation waves in on hydrogen-oxygen mixtures are those of Berets et aL (1950), who employed the us most recent thermochemical data given by the National Bureau of Standards

'or (1949). Their calculations were made for an initial gas pressure of 1 atm. at el, a standard temperature of 25 'C. The'ambient temperatures normally found in

'or our laboratories are, however, nearer 18'C, and whereas wave velocities are ve comparatively insensitive to small changes in initial gas temperatures, a signifi-ilv cant dopendenco on such changes is found for the values of the wave pressures.

'ul Furthermore, to the authors'nowledge, no results have been reported of the i)) properties of the shock wave arising on normal refiexion of a plane detonation

'll wave at a rigid surface. For these reasons, a new series of calculations have been

~n made of the properties of both the detonation ware and normally refiected h- shock wave.

d. 2.1. The detonatiml anve e In the computation of the properties of the detonation wave, it is assumed. that ll the burnt gases obey the ideal gas law (see Schmidt 1941; Kistiakowsky, Knight if &c Malin 1952), and the C-J plane is defined as the plane of thermodynamic 32.2

'I I

0

500 D. H. Er/u;ards, g. T. Williams and J. ( . Breeze equilibrium over which the condition U, = u~+g obtains, where Uu, and ct are the wave, mass and sound velocities, respectively. Moreover, Brinkley 8 Richardson (1953) and. Eirkwood R VFood (1954) have shown that the sound velocity, cat the C-J plane must be evaluated at the instantaneous frozen composition (i.e. the total mole number being regarded as independent of pressure and temperature) and not, as had been previously assumed, for mobile equilibrium. Following Berets et aL (1950) allowance has been made in the calculations for the following equilibria:

)H,=H,

$ 0, 0, Hz+kO, H,O, kH,+SO, OH.

Mass Pres- Den- Velo- Velo- velo- Total Initial Temp. sure sity city city city Final Composition ( je) mole compo-sition T, (~) ratio Vg cr

('K.) (atm.) (p,/p,) (m/s) (m/s) (m/s) H,O H 0 number Ha Os OH SHq+ 0~ 271V 14 53 1 V4 3802 2186 1615 24 70 7382 000 0 ll 136 000 8 060 4'+ Og 3Ha+ Os 3439 3607 1V 79 18 44 1 76 3426 1.V7 3197 1942 1807 1483 1390 42 48 V4 97 4516 31 GS 0.15 0 89 337 7 20 816 S VS 041 1 48 4 270 3 365 2Hg+ Og 3675 18 59 1 VV 2853 1610 1243 53 00 16 V2 513 1285 817 413 2 493 H,+0, 3467 17 63 1 77 2333 1318 1015 47 o9 414 2634 1345 265 583 1 673 H,+20, 3029 15 VS 1.76 1941 1103 838 34 76 062 5567 G22 034 249 2 687 Hl+ 30a 2662 14'14 1 76 1759 1QQG 752 26 92 011 GS 77 243 004 072 3 538 Taszx l. The detonation wave. Initial pressure, 1 atm.,'initial temperature, 18 'C.

The method adopted for the solution of the detonation wave and reflected shock wave equations closely follows that used by Huff, Gordon 8r, Morrell (1951) for the computation of the equilibrium composition and temperature of chemical reactions. This method, when applied to the detonation and reflected shock wave equations arranged in a suitable form, gives a rapidly convergent solution and has been found suitable for use with a desk calculator and for programming on an electronic digital computer. The calculated values of the parameters at the C-J plane and their values behind the leading shock of the detonation wave, termed the 'on ¹umann'peak, are given in tables 1 and, 2. In addition to.the symbols already defined, p, p and T denote the pressure, density and temperature respectively, and the subscripts 0, 1 and 2 are used to define their values in the unburnt gases, behind the incident detonation front, and behind the reQected A

shock front, respectively; the peak values of the parameters are designated by a circumflex accent.

s r ofd 2.2. The rejected shock unde int The computation of the reflected shock wave properties has been divided into shc two parts: per (a) The computation of the properties of the shock wave obtained on reflexion ruE of the von Neumann peak, in which it is assumed that, immediately on reflexion, in(

Pressure and velocity measurements on detonation uuves 501 the shook wave moves into a medium which is at the conditions prevailing at the ey k von Neumann peak of the incident detonation wave, and for which the boundary

')und condition at the reflecting wall is ua = 0.

oxen (6) A similar computation to the above has been made for the C-J plane in tt of which it is assumed that the boundary condition for the reflexion is fata = 0.

obile

. the Mass Temp. Pressure Density Velocity velocity Initial >x Px ratio Us composition (oK.) (atm.) Pt/Po (m/s) (m/s)

SHs+Os 1505 26 68 5 16 3802 3065 4Hs+ Oa 1739 32 69 5 47 3425 2799 3Hs+Oa 1778 33 89 555 3197 2621 2Hs+ Os 1774 34 16 561 2853 2344 Ha+Os 1678 32 43 5 63 2333 1919 Ha+ 20a 1521 29 10 5 57 1941 1593 H,+30a 1391 26 06 545 1759 1437 Total Txnm 2. Tho von Zeumann peak in tho detonation wave.

mole Initial pressure, 1 atm.; initial temperature, 18 'C.

number 0 n

) 00 8060 , ReAocting wall

)

'13 41 48 427Q 3 365 2 493

/k""

l83 1673 Po~ Po. Zo iacidettt

."4 2 587 1l ~Q shock-r 53S ock for plan ical I

- -- e

/

ock lst reflected Ideal detonation r ~ " ~ shock ion wave,reactionendittg e

,ing at C- Jconditinns t at Distance

.ve, Rear end of detonation tube the Tittle ure Ftovaa 1. Diagram of the proposed construction of tho rotlexion of an idoal detonation the wave at a rigid surface. Particle paths, W .

ted A possible construction of the reflexion process of an ideal detonation wave at by a rigid surface has been suggested to the authors by ilfr C. K. Thornhill. In order to simplify the geometry the device is adopted of compressing the reaction into an instantaneous event, a short finite time after the passage of the causal

'Lto shock; i.e. the detonation wave is replaced by an initial shock followed by a short period of steady state at peak conditions and ending in a 'reaction ihto the C-J state. This construction is shown, in a qualitative fashion, shock'unning ion on, in the diagram of figure l.

502 D. H. Edicarde, G. T. Williams and J'. C. Breeze From the diagram it is seen that the present computation refers to conditions at the point P, on the dividing particle-path PQ, mhich represents the point of intersection of the refiected shock and incident C-J plane, assuming that the mass fiow us is reduced almost to rest at this point. The point P is at a distance of the order of the width of the reaction zone of the incident detonation mave away from the refiecting wall; for gaseous mixtures initially at atmospheric pressure, the reaction time is of the order of 1 ps and the thickness of the reaction Total Den- Velo- mole Initial Temp. sure sity city Final composition (c~) num-com- Ti pi ratio Ui ber, position ('K) (atm.) pi/pi (m/s) HiO Hi- Os OH H 0 n SHi+ Oi 3136 34 31 2 02 1581 24 10 72 08 0 00 0 40 3 40 001 816 4Hi+ 0, 42 22 078 439 Hi+30'res-3H,+0, 3773 3915 43'79 2

2 10 12 1343 1239 39 28 44 20 44 01 31 86 0 27 1'14 4 95 10 70 9 00 ll 6S 212 347 2Hi+Oi 3971 44 18 2 13 1100 47 64 17 89 5 18 14 63 9 63 502 258 Hi+f4 3763 41 83 2 12 902 43'37 5'01 24'79 15'91 3 56 737 172 Hi+ 20i 3345 3729 210 747 3214 098 5321 888 066 4 12 264

. 3016 3331 20o 715 2533 027 6794 450 015 1 81 358 Tenez 3. The retiectcd shock wave. Initial pressure, 1 atm.;

initial temperature, 18 'C.

Temp. Pressure Density Velocity Initial 2'i pi ratio Ui composition ('K) (atm.) pi/p, (m/s)

SHi+ 0, 2783 175 4 3 55 1200 4Hi+Oa 3243 226 6 3 72 1030 3H +0 3322 237 8 3 76 951 2H +0 3315 241 7 3 79 841 H,+0, 3128 229 9 3'80 685 H +20 2819 203 7 3 78 573 Hi+ 30i 2559 178 6 3 73 527 Tant'. Tho peak values in the reQocted shock wave. Initial pressure, 1 atm.;

initial temperaturo, 18 'C.

zone is 1mm (Kistiakowsky &: Kydd, 1956). An important feature of the construction is the hypothesis that a pressure and velocity balance is achieved at the dividing particle-path PQ by the existence of a second shock front which is refiected at the point B in the diagram a finite time after the arrival of the first shock at the refiecting mall; experimental evidence in support of tins proposition is discussed later. Calculated, values of the parameters at the point P are given in table 3 and their peak values at the mall in table 4.

2.3. The effect of initial temperature Several calculations were carried out for the stoichiometric mixture assuming different values of initial temperature. In figure 2 graphs are shown of the percentage deviation of the detonation velocities and pressures, from their

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504 D. H. ECkearhls, G. T. 1Villiahns and J. C. Breeze ionization 3 2. 2'he pressure gauges and yro6es A pressure gauge has been developed in this Laboratory ivhich employs an X-cut quartz disk to measure the average stress over the cross-section of l.

a duralumin rod. The construction and behaviour of this gauge is described by C Edwards (195S} who has shown that, it gives satisfactory records of the pressure profile in gaseous detonation waves. Pressure bars of $ and 4 in. diameter have C been used in the present investigation, the former for the measurement of the r reflexion pressures and the latter for thc static pressures in the waves. The time e interval over ivhich the gauge will record is determined by the length of bar i) used; in most instances a gauge capable of recording over an interval of 220 ps was adequate, but when recordings were required. over longer intervals a gauge d

li ll f(

cl IS 03 Ch tl fii le FrohhRE 3. Oscillogram obtained with $ in. gauge when set to measure the reflexion oi pressure due to a shock wave in air. Shock Mach number: 1 75. Timing marks: 20 Ihs. V(

pi of greater length was employed which responded to pressure pulses of approxi- ac mately 1 1 ms duration. The pressure gauges could be set to measure the static ge and reflexion pressures by screwing the gauge head into bushes, one is placed in the cylindrical wall of the tube at a distance of 30 cm from the end of the tube TR and another is placed centrally in the end-plate. In order to reduce the trans- thi mission of stress waves propagated in the explosion tube wall to the gauge, ste these bushes are constructed of polythene. The m'easuring.end of the static Af pressure gauge is machined to the same radius as the internal wall of the tube so fill that when the gauge is mounted in position this face is flush with the internal Tb wall surface. Similar care is taken to ensure that the reflexion pressure gauge is mK flush with the end-plate. of The manner in which the gauges are calibrated by a ball impact method has fix been described by Edwards (1958). In addition to this method, the gauges were dhl calibrated by the impact of shock waves in air, generated in a 5 cm diameter Fa shock tube. 4 typical record obtained when a $ in. diameter gauge is set to adl measure the reflected shock pressure is shown in figure 3. It is seen that vol oscillations due to dispersion of the stress waves in the gauge bar occur im-mediately after the initial rise. The average voltage level, however, remains constant over an interval of 220 ps before the return of the pulse of tension

r Pressure and uehcity measurenients on detonation uuues oOo from the free end of the pressure bar. Values of the gauge constant can be determined from these records to an accuracy of within 1%.

Velocity measurements on the detonation waves are made by the ionization probe technique. The design of the probes and. of the associated electrical

>y circuitry used in the 10 cm diameter tube closely resemble those described by re IQ>ight 4 DuK (1955).-Twelve probes are fitted into the tube wall in:two groups of six, the probes in each group being placed a4 intervals of 10'and 20 cm, ie respectively. In the 1 6 cm tube 10 mm sparking plugs are used as probes, their ie ends having been slightly modified so that no part protrudes into the tube and interferes with the gas flow. 4 I

!S

e 3.3.. 2'he recording apparatus.,'..

any circuit external to the pressure gauge must possess a suSciently high input inipcdance ifleakage of charge from the gauge is to be kept low during the time in which the gauge signal is being recorded. For this purpose,'a cathode-followcr is used which has an input impedance of 20 3IQ and whose frequency characteristics are constant up to 2 31%. The signal from the cathode-follower is fed by a coaxial cable into a recording room where it is amplified and displayed on a c.r.o., a Solarscope Type CD 513, and recorded on a stationary plate caniera. The time-base of the c.r.o. is initiated at a predetermined interval before the arrival of the pressure gauge signal by a pulse from an ionization probe.

Two methods are available for recording the ionization probe signals. In the first, when it is desired to follow the variation of the ware velocity along the length of the tube, the voltage pulses, after appropriate shaping, are displayed on a c.r.o. and recorded photographically. Alternatively, if only the average velocity over a particular length of tube is desired, the pulses from two selected probes are employed to trigger a 'Cintel'icrosecond chronometer. The accuracy obtainable by these methods in the measurement of velocity is generally k jp.

3.4. Preparation of the gas mixtures The driving and test sections of the explosion tube are evacuated simultaneously, the pressure in the tube being measured by a mercury manometer and a 'Vacu-stat'auge; a residual pressure of 0 1 mm of mercury is considered satisfactory.

After evacuation the tube is isolated from the vacuum pump and each section is filled in turn, the constituent gases being obtained from commercial cylinders.

The partial pressure of each component gas is measured by means of the mercury manometer, which can be read to the nearest 0 05 cm. The test section of each tube is filled first and in the case of the 10 cm diameter tube a coarse grid, fixed near the end of the driving section, provides support for the diaphragm during this operation. A minimum time of 12 h is allowed for the gases to mix.

Facilities are available for pre-mixing the gases in large cylinders. before admitting them into the 1 6 cm tube; in this way errors in metering small volumes of gas are avoided.

506 D. H. Edwards, G. T. lYilliams and J'. C. Breeze to 4.1. The 10 cm diameter tube rec I

In all the experiments performed in this tube, the gaseous mixture was initially of:

the at atmospheric pressure and at room temperature which was within a degree or lim two of 18 'C. In the preliminary work, the cellophane diaphragm separating the be driving and test sections was absent, the detonation being initiated by electrically ray firing copper acetylide matchheads. The pressures obtained, however, even with the more strongly detonating mixtures, were substantially higher than the theoretical values and, the measured velocities in all mixtures were between 3 and 4% below those calculated. After carefully checking the recording apparatus it was concluded that even after a run of approximately 5m in mixtures near the stoichiometric composition, a stable wave was not established by this method of initiation. It was, therefore, abandoned in favour of the shock wave method of initiation, the shock waves being generated by detonating a stoichiometric acetylene-oxygen mixture, at an initial pressure of 1 atm.,

contained in the driving section.

Fu Fxoaas 4. Oscillogram of the response of the $ in. gauge to the static pressure in a detonation wave in 2H~+0~ in the 10 cm diameter tube. Timing marks: 20 pe.

A typical oscillogram, obtained with the 4 in. pressure gauge, of the static pressure in 2Hz+Os is shown in figure 4 and the pressure-time distributions derived from three such records are given in figure 5. The oscillations appearing have been smoothed out so that the general trend of the profile can be appre-ciated more readily. It willbe observed that the rise time of the pressure to the peak value is 7 0 ps, which exceeds the time of traverse of the wave across the reI end of the pressure gauge of 4 45 ps. This discrepancy in the two values arises slo from the distortion of the pulse due to the dispersion of the stress pulse as it pr travels along the pressure-bar; this has the effect of roundingwff sharp pressure th<

variations and lengthening the rise-times (see Davies 1948). The peak pressure is observed in the records is attributed to the partial re'sponse of the gauge to the 18=

von Neumann peak pressure within the detonation wave. That this peak is not for due to a gauge effect may be verified by comparing the r'ecords with the record of figure 3 obtained for the shock waves in air, in which the characteristic over- st shoot of the pressure bar signal due to dispersion is seen to be markedly different on

C Pressure and velocity measurements on detonation ueves 507 to the response for the detonation wave. The average value obtained fro'm four records for this peak pressure is 27 I atm. compared with the theoretical value "ally of 34 16 atm. An exact response to the peak pressure is not to be expected since

'B or the reaction zone of the wave is extremely narrow and is obviously outside the

the limit of resolution obtainable with the gauge; the significance of this peak will

.ally be discussed later. Following the peak value the pressure on the records falls with rapidly, until after an interval of 5.ps the pressure begins to lovel out and the 30

,veen Mixture: 2H2+ 02 ding

n in Tube diam.: 10 au shed 10

tho

.sting ltm.,

I 10 1

0 0 30 60 90 120 150 Time (ps)

Frol:Irr. 6. Pressure.time distributions obtained from three recordings with a $ in. gauge set to measure tho static pressure in 2Hs+O.. Tube diameter: 10 cm.

Average Peak prcssure Average pressure 20-SO ps pressul'0 Risc time (obs.) (obs.) 100-200 ps (obs.)

'c rn (atm.) (atm.) (atm.) (m) 268 190 167 I'2o

~

,'la.

26 7 18 4 162 static 9 18:6 16 7 6.S

'Itions '71 1S 6 17 6 7.1

.'aring Tanm 6. Rcproducibility of the static pressures in 2H, + 0, in 10 cm diameter tube.

Peak pressure (theor.), 84 16 atm.; C-J pressuro (theor.), 18 69 atm.

lppre-to tho ss tho remains sensibly constant for the next S0-90 ps, and. thereafter it begins to decay arrses slowly under the infiuence of the following rarefaction wave. The average o as lt pressure over the period 'O-SO ps has been measured for comparison with the cssure theoretical value, and tho mean value found from four records for this mixture

'essuro is 18 6 atm. which is in excellent agreement with the computed C-J value of to the 18 59 atm. To illustrate the reproducibility of the static pressure records, values is not for the four records obtained with the stoichiometric mixture are given in table 5.

record Pressure-time curves for the non-stoichiometric mixtures investigated are

over- shown in figure 6. As before, the small amplitude irregular oscigations appearing fferent on the records have been smoothed out. The general shapes of the curves for all

)0

o08 D. H. Eduerds, G. T. )Vt'lliams and J. C. Breeze the mixtures are very similar except for Hz+302 which does not exhibit the m peak and ~

sharp initial rise found in the others. The values of the observed and theoretical pressures are given for each mixture in table 6, and the corre-sponding mave velocities in Table 7.

af be in ar 4'+ Og <<H)+Oq 20 lo IO 0

0 50 l00 l50 0 50 IOO ISO 3Hq+ Oq H~t 20.

10 IOO I 50 0 50 IOO I 50 2H~+ 0~ H.+ 30~

20 IO IO 0

0 0 IOO I 50 Time (ps)

Fravns 6. Statio pressure-time curves for various mixture compositions in the 10 cm diameter tube. Broken lines represent tho calculated C-J pressures.

Average Peak Peak prcssure pressure pressure 20-80 ps C-J pressure (obe.) 'the or.) (obs.) (theor.)

Mixture (atm.) (atm.) (atm.) (atm.)

4H,+0, '27 3 32 69 180 17 78 3H~+0, 28 1 33 89 184 18 44 2H,+0, 271 3416 186 18 59 H~+0, 261 3243 183 17 63.

H~+20s 250 29 10 16 7 16 79 H,+30, 249 2606 161 14 14 Tanrz 6. Static pressures in tho 10 cm diameter tube.

The pressure-time relationship obtained when the $ in. gauge is set to measure the pressure due to the normal reQexion of a detonation mave in 2Hs+ Os at the plate closing the end of the tube is shown in figure 7. As mould be expected the initial rise-time of 3 2 ps is shorter than the corresponding times on the statio records. Following the initialpeak, the pressure drops rapidly and after a further interval, ranging between ll and 19 ps, depending on the composition of the

Pressure and velocity measurements on detonation ueves 509 mixture, a second very sharp peak occurs which again rapidly decays; there-after, the pressure remains reasonably constant for the next l00 ps or so before beginning to rise slowly. Similar features are observed for the r'eQexion records in all the mixtures and consequently they are not reproduced; numerical values are given in table 8.

Velocity Velocity Standard Deviation (obs.) (thcor.) deviation trom theory Mixture (m/s) (m/s) (%) (0/)

4H,+0, 3344 3425 07 -23 3Hs+0, 3156 3197 02 -13 2H~+0, 2825 2853 05 -10 Hs+0, 2320 2333 05 -06 H~+20~ 1909 1941 03 16 Ht+ 30a 1691 1759 03 -'3 8 ThSLE 7, Detonation velocities in the 10 cm diameter tube Mixture: 2H>+ 02 60 Tube diam.: 10 cm 9e 40 I

P

~ 20 0

30 60 90 120 150

.Time (ps)

Flol'nE 7. Pressure-time curves of the reflexio pressuro for a detonation wave in 2H~+0~ in the 10 cm diameter tube.

Peak Peak Average C-J reflexion pressure pressure pressure pressure (obs.) (theor.)20-100 ps (theor.)

Mixture (atm.) (atm.) (atm.) (atm.)

4H,+0, 594 226 6 370 42 22 3H~+ 0~ o97 237 8 375 43 79 2H~+ 0~ 62 5 241 7 338 44 18 H~+ 0~ 606 229 9 380 41 82 H~+ 20, 203 7 343 37 29 tc H~+30~ 4 178 5 37 9 33 31 TABLE 8. Reflexion pressures in thc 10 cm diameter tube.

te

510 D. H. Edtterds, g. T. Williams and J. O. Breeze An in inl ref FIGURE 8. Oscillogram of static pressure in 2H,+0, in the 1 6 cm diameter I<<bc.

Timing marks: 20 ps.

8Hg+ Og H,+0, 20 Io Io 0

30 loo ISO 6Hg+ 0, H.+204 20 ISO'H~+

lo lo 8

0 ~

50 loo 0 SO IOO ISO 04 H~+ 304 20 lo lo 0 50 leo ISO 0 50 loo ISO 2H)+ 0. 40 H..

+40'o 20 0 0 0 50 IOO ISO loo l50 Time (ps)

Prove 9. Static pressure-time curves for various mixture compositions in the 1 6 cm diameter tube. llroken lines represent the calculated C-J pressures.

i Pressure aruE telocity measurements on detonation ueves 4.2. TJic 1 6 cm diameter explosion tube An oscillogram obtained in the 1 6 cm diameter tube for the detonation wave in oHs+ Os is shown in figure S; the initiating mixture again is CSHs+Os at an initial pressure of 1 atm. Pressure-time curves for each of the mixtures examined in this tube are given in figure 10; on the first four of these records the shock wave refiected from the closed einl of the tube has been recorded. The compositions Average Peak Poak pressure press uro pressure 20-80 ps C I'ressure (obs.) (theor.) (obs,) (theor.)

31ixture (atm.) (atm.) (atm.) (atm.)

8Hs+ Os 33 2 207 116 14 53 6Hs+ Os 242 294 123 15 85 4Hs+ Os 233 32 7 135 1778 2Hs+ Os 342 140 18 59 H,+0, 217 324 144 1703 Hs+ 20s 213 291 134 1579 Hs+ 30s '34 201 112 1414 H;+40, 434 242 102 12 60 TABLE 9. Static pressure in the 10 cm diameter tube.

Velocity Velocity Standard Doviation (obs.) (theor.) doviation from theory 31ixture (m/s) (m(s} ('/) (/0) 8Hs+ Os 3542 3802 05 -68 6Hs+ Os 3550 3750 04 -53 4Hs+ Os 3208 3425 03 -46 2H,+0, 2709 2853 10 -30 Hs+Os "315 2333 .02 -08 Hs+ 20s 1901 1941 0 2 -2.1 H,+3O, 1683 1759 02 -43 Hs+ 40s 152'680 02 -94 TABLE 10. Detonation velocities in tho I 0 cm diameter tube.

Avcrago Peak Peak pressure C 7 reQexion I)ressuro pressure 20-100 ps pressure (obs.) (theor.) (obs.) (theor.)

>Iixture (atm.) (atm.) (atm.) (atm.)

8Hs+ Os 814 175 4 219 3431 GHs+ Os 07 0 201 0 22.8 38 26 4Hs+ Os 2Hs+ Os 009 005 226 241 6

7 285, 309 4222 44 18 Hs+ Os 515 229 9 304 41 83 Hs+ 20 300 203 7 200 37 29 cm Hs+ 30s 104 9 178 5 282 33 31 Hs+4Os 118 0 153 3 233 2933 TABr.E 11. ReQexion pressures in tho I 0 cm diamctor tube.

olo D. H. EduerCk, G. T. II illiams nlld J. C. Breeze 100 8Hg+ Op H~+Oi 0 50 100 150 100 150 0Hg+ Or Hq+ 20' 0

8 0 5O lOO 150 0 50, 100 150 60 4Hg+Og 100 Hg+50g M

20 0 50 100 150 0 50 100 150 2H~+Or 100 . Hr+40g 40 20 0 0 0 50 100 150 0 50 100 150 Time (ps) reflexionpressure. l FtovnE 10. Pressure-time curves of tho reflexion pressures for various mixturo composi- C tions in the 1 6 cm diatneter tube. Broken lines represent the calculated (

1 Frequency X observed Frequency bohind Frequency ti Fundamental observed reflected observed on tt mode spin on static shock on reflexion t(

frequency gauge static gauge gauge a ilIixture (K%) (Kc/s) (K%) (K%)

SH~+ ot 807 76 799 1549 I

e 6H,+O, 762 138 0 143 5 4H,+0, 717 129 8 S 2Hz+os 594 110 2 t H,+0, 486 933 C H,+20, 407 765 t Ht+ 30~ 37 1 363 743 Ha+40'36 329 663 8.

t T.eau. 12. Frequoncics of vibrations observed on tho statio and reflexion prossuro records hl 1 6cm diameter tube.

I'ressure and velocity measuremsnts on detonation icaves 513 SH,+OH,+30, and H,+40, show pronounced regular oscillations; the periods of these oscillations have been measured and they i'llbe discussed later in connexion with the theory of spinning detonation. In all the records no pressure plateau occurs after the initial peak; the pressure drops relatively rapidly after the peak value and continues to do so throughout the duration of the record. However, since it is useful to compare the pressures of the detona-tion waves in the two tubes, the mean pressures over the interval 20-80 ps on the records are quoted in Table 9. Values of the velocities for the various mix-tures are y'ven in table 10.

Pronounced oscillations are found on all the reQexion pressure-time curves in the 1 6 cm tube which are given in flgure 10. The curves show an initial sharp pressure peak followed by a slow decay in pressure, but after approximately SO ps the pressure remains fairly constant for the remainder of the record.

Observed and calculated values for the reQexion pressures are given in table ll, and the frequencies of the oscillations in both the static and reQexion records in table 12.

5. Discussion 5.1. 2'Ae 10 cm diameter tube The static pressures observed in this tube (table 6) are in general agreement with the theoretical C-J pressures and for some of the mixtures the agreement is well within the experimental error. Most of the observed values, however, are somewhat higher than the theoretical values; the discrepancies, which are more pronounced for miztures containing excess oxygen, cannot be accounted for by systematic errors in measurement. Furthermore, the observed detonation velocities are all lower than the calculated values, the lack of agreement becoming more serious the further the gas composition is removed from stoichiometric. Berets et ai. (1950), in their investigation of the velocities of detonation waves in hydrogen-ozygen in a 10 cm tube, obtained good agree-ment with theory in the middle composition range, lower velocities in mixtures with excess hydrogen, and higher velocities in mixtures with excess oxygen.

During the course of later investigations Kistiakowsky 4 Zinman (1955) report that the high velocities observed in the excess oxygen mixtures were due entirely to overdriring of the mixture by the initiator. This interpretation would seem to imply that the low relocities, when excess hydrogen is present, are genuine and since in these mixtures the effects of overdrive would presumably have been present, it can only be inferred that the effect of its removal would be to yield even lower values than were originally observed. Even after allowing for the spread in the present measurements the conclusion cannot be escaped. that, for the extreme composition, the velocities are signiQcantly lower than those computed. At first it was thought that these low values could be attributed to the imperfections in the explosion tube wall; in view of the work ofKistiakowsky 8: Zinman on acetylene-oxygen mixtures however, this hypothesis would appear to be untenable since the 'waH-eKect's independent of the mixture composition.

Berets et ai. (1950) attribute the differences between experimental and theoretical velocities to energy losses to the explosion tube wall. Such losses 33 Flu/d Maob. B

514 D. H. Eduerds, 8. T. iVillianis and J. C. Breeze could arise in two ways: (1) by the instantaneous cooling of a layer of gas in C contact with the wall, and (2) by friction at the wall causing a reduction in mass th velocity in the proximity of the wall. Both effects would give rise to a rarefac- 18 tion wave which is propagated into the interior of the tube. If this occurs within> ~

pr<

the reaction zone, the resulting lowering of the temperature reduces,thy rate of be chemical reaction thereby causing a loivering of the detonation v'elocit1 . At the thl same time, this hypothesis necessarily implies a lowering of the pressure which is contrary to the experimental evidence. Thus although cooling and frictional effect are almost certainly present, they are alone insuflicient to ezplain the Th observed deviations of pressure, so that some further. mechanism must be reh present which maintains the pressure at a higher value. On close ezamination nol of the pressure profiles of figure 6, it is seen that the further the mizture com- Ptu position is removed from tho stoichiometric, the lon~er the pressure takes to dor doecay from its peak to the C-J equilibrium value.'ren though the gauge is reh incapable of reproducing faithfully the pressure variations which occur in times wax of a few microseconds, a comparison of the width of the peak in various miztures oft provides a relative measure of the duration of the reaction xone. It appears oft reasonable to assume that although the greater part of tho chemical reactio'n is turI completed within the first few microseconds, complete equilibrium is not thai attained in some miztures until SO ps after the onset of the detonation wave. it is This effect is more marked in mixtures away from stoichiometric composition gas ivhere the rate of chemical reaction is much lower owing to the lower tempera- the ture. Thus mixtures away from atoichiometric may not be able to support an encr ideal C-J wave at all; tho detonation waves in these mixtures corresponding to alaI the subideal waves of Brinkley R Richardson (1953). These wares hare been

'h 1

shown to propagate with velocities which are less than the ideal C-J values and ws v(

since tho rate of chemical reaction is low the pressure in tho wave will not decay Tl as quickly as in the ideal wave. Prom the present pressure and velocity measure- mixt ments it may be concluded that the hydrodynamic theory gives a correct frequ description of the detonation wave in hydrogen-ozygen mixtures haring i>Ians a hydrogen content in the range of approximately 50-Vo~/z. The agreement mode between experiment and theory, however, does not imply that the assumption cI an(

of chemical equilibrium at the C-J plane has been rigorously established. obser The first peak on the reflexion pressure records corresponds to the reflex on f vibrs tthe vvon Neumann peak of the incident wave; the magnitude of the peak cl bei pressures recorded. bears no resemblance to the calculated values due to the perah inadequacy of the gauge response. The interesting feature of these records is the has ir second sharp peak, which occurs in all tho mixtures studied in this tube, and been~

which appears to present strong evidence for the second reflected shock front whorl predicted by the construction shown in figure 1 for tho normal reflezion of flowe a detonation wave. It is certain that the second peak is not attributable to highe:

a property of the gauge, and tho time interval between its occurrence and the Thl first peak shows'a corresponding variation ivith the acoustic velocitr of the exhibi burnt gases of the mixtures. Further elucidation of the reflexion process, frequI however, must await a photographic investigation of waves in th' b quenc r

Moreover,

~ the values of the properties calculated on the assumption stated in spin fi

~ Pressure and uelocity measurements on detonation uaves o15

) 2.2 (6) are essentially the values obtaining at a plane a distance of the order of the width of the reaction zone in front of the reflecting wall; consequently there refac- is no strict basis for comparison between the calculated pressures and the vithin pressures measured at the wall. It is to be expected, however, that they would ate of be of the same order of magnitudo as the comparison, given in table 8, between Yt the the calculated and observed average pressures in the interval 20-100 ps shows.

.vhich g.

ional 5.2. The 1.6 cm diameter tu6e n the Tho main features of tho static pressure records obtained in this tube are the st be relatively rapid decay of the pressure following the initial peak and the pro-ation nounced oscillations occurring in the miztures H2+ 302, H, + 402 and SH, + 02.

com- Furthermore, the measured velocities are all less than the ideal values, the es to deviations being greater for extreme compositions. To account for these low lge 18 velocities and the observed pressure profiles it must be assumed that all the

imes waves in the 1 6 cm tube aro subideal. It has been noted above that the effect tures ,

of the rarefaction wavo, which originates at the wall of the tube due to cooling lears of the gas, is to lower the pressure and the rate of chemical reaction which in on ls turn tends to'maintain the pressure at a higher value. XVhereas it was concluded not that in the 10 cm tube the latter effect is dominant, in the small diameter tube

.ave. it is reasonable to ezpect the lowering of the pressure due to cooling of the burnt ition gas to have the greater effect on the pressure profile of the wave. Consequently, lel'a- the low values of pressure found in tho 1 6 cm tube are probably due to the t an encroachment of the rarefaction wave into the reaction zone. If this were so,

~g to a large part of the energy released by the chemical reaction is lost to tho walls of 4 the tube since the reaction zone is spread out down the tube; this would lead to wavo velocities less than the theoretical values, which is borne out by experiment.

.'c The large'amplitudo oscillations occurring on the records of three of the ure- mixtures are attributed to spinning of the wave. Measured values of the spin

'rect frequencies are compared in table 12 with values derived from tho theories of "lng 31anson (1947) and Fay (1952), in which the frequency v of the fundamental lent mode of transverse vibration is related to the acoustic velocity in the burnt gas tion c, and 'the tube radius ro by v =', 1 S4112nro. The agreement between the observed and calculated frequencies leaves no doubt as to the nature of these nof vibrations; the observed values are, however, slightly lower due to the value of eak cl being lower than the ideal value assumed.. It is seen that these vibrations the persist behind the reflected shock wave in SH2+ 02 (figure 9), but their frequency the has increased slightly compared with the detonation wave. A similar effect has lnd been observed by I<night 8: Duff (1952), by means of light emission photographs, ont where the frequency of the transverse vibrations increased as the burnt gas

of flowed through the reflecte shock front. This fact may be accounted for by the

~

to higher temperature behind the reflected lvave giving a higher sound velocity.

the The reflezion pressure records for all the mixtures examined in this tube the ezhibit very regular non-sinusoidal pressure undulations whose recurrence

'ss, frequency given in table 12 are approximately twice the measured spin fre-be. quencies on the static pressure records. However, no evidence of a second mode in spin frequency is found on any of the static pressure records of the detonation 33.2

516 D. H. Edwards, G. T. 8'itliams and J'. 0, Breeze wave. In the record obtained with 6Hs+02 (figure 10), where the reflected shock wave has also been recorded by the static pressure gauge, the higher frequency oscillations are present although their amplitude is small. Schlieren streak photographs taken in this Laboratory of the reflexion of spinning waves at a rigid wall reveal that the pressure undulations recorded on the end pressure gauge are caused by the reflexion of longitudinal compression waves behind the detonation front. The recurrence frequency of the pressure crests of the longi-tudinal mode of vibration measured from these photographs agrees very well wit t e results obtained from the pressure records. The pressures set up by this mode of vibration are very small, but after reflexion they are sufficiently great to be detected not only on the end gauge but also on the side gauge. These vibra-tions pro ably correspond to the passage of pressure pulses upstream due to the chemical reaction proceeding in the rarefaction wave this mec h anism is essen-tially the same as that proposed by Brinkley &: Richardson (1953) to explain the build up of an ideal 0-J wave.

6. Conclusions I I

'l The lorn velocities observed in mixtures near the limits of detonation and with decreasing tube diameter are in general agreement with the results of previous K investigators. Decreasing the tube diameter also decreases the wave pressures; K t e pressure profile is found to be much more dependent on tube diameter than K velocity'. The hypothesis that energy is abstracted from the mave through the K formation of a rarefaction wave at the wall of thee tu b e is capa e not only of 31 explaining the lorn velocities observed but also thee s Iightly hig h pressures in the II.

10 cm tube and the rapid decay of the pressure in the 1 6 cm tube. Prom a con-sideration of the pressure and velocity data in thee 10 cm tu b e to together it is 50-V5'oncluded that mixtures with hydrogen content in p 'el i5 /o are able to support ideal waves; waves in mixtures outside these limits h

Rn are subideal in the sense the term. is defined by Bri'nkley k R'ic ar d son (1953). Sca Allthe detonation waves examinedin the 1 6 cm diam te r tu' b earesubidealandb'arne t near the caus cer tain mixtures energy losses to the wall are suKciently great to cause detonationlimitstospin;thesesamemixturesshowedwe no evi'd ence off spin in the is deduced from the vibrations, whose frequency is about t mod mo spin &equency, e recorded on the reflexion gauge in all

'h 10 cm tube. Further support for the subideal nature of the waves in the 1 6 cm tube f d mixtures; these are attributed to the reflexion of pressure pulses which are delivered upstream by the chemical reaction taking place in the rarefaction mave.

The authors are greatly indebted to Dr Z. %'. Maccoll, head of the Applied Mathematics Division, M.O.S. Arm. Res. Dev. Estab., Fort Halstead, or s interest in the numerical work and the use of the digital computer, to Mr H. Z.

Gawlik and Mr F. J'. Berry for their assistance duri'ng th e programming of the pro em, aand to Mr C. K. Thornhill for his valuable suggestions.

roblem

Pressure anil telocity Ineasttrements on detonation uaves

.ted der REFERENCES

ren BERETs, D. J., GREEvE, E. F. h: KISTrhzowszY, G. B. 1950 J..4mcr. Chem. Soc. 72, 1080.

ves BERTIIELoT, M. 8: VIEILLE,P..1882 C.R. Read. Sci., Paris, 94, 101, 149, 822; 95, 151, 199.

lure BRI fKLEY,S. R. JR. 4 RIOHARDsoN, J. 3L 1953 Fourth Symposium on Combustion, p. 450.

the Baltimore: Williams and AVilkins.

ngi- CAMFRELL, C., LITrLER, W. B. 8; WIIrnvoRTH, C. 1932 Proc. Roy. Sec. A, 137, 380.

well Dhvlzs, R. Af. 1948 Phil. Trans. A, 240, 375.

this DAVIEs, R. hL, EDWARDs, D. H. 8: Trloms, D. E. 1950 Proc. Roy. Soc. A, 204, 17.

reat DIKDN, H. B. dc CALv, R. S. 1894 .item. 3fanchceter Lit. Phil. Soc. p. 174:

EDWARDs, D. H. 1958 J. Sci. Inetrum. 35, 346.

bra-FAY, J. A. 1952 J'. Chem. Phye. 20, 942.

the GoRDov, W. E. 1949 Third Symposium on Combustion Flame and Explosion Phenomena, sen- p. o79. Baltimore: williams and Wilkins.

. the HEvDERsov, J. 1941 Proc. Pacijic Coast Gae rise. p. 32.

HUFF V. Ã., GoRDov, S. 8: 3foRRELL, V. E. 1951 V.A.C.A. Rcp. no. 1037. Washington t National Advisory Committee for Aeronautics.

KIRKwooD, J. G. Sc IVooD, EV. lV. 1954 J'. Chem. Phye. 22, 1915.

KISTlhzowszY, G. B., KNlolIT, H. T. h DIALING, 5L E. 1952 J. Cliem, Pliye. 20, 884.

.rith KISTIAKowszY, G. B. S. KYDD, P. H. 1955 J'. Chem. Phys. 23, 271.

Ious KISTrhzowszY, G. B. S: KYDD, P. H. 1956 J. Chem. Phye. 25, 824.

! res; KlsTlhzowszY, G. B. 8: Zlmshv, W. G. 1955 J. Chem. Phys. 23, 1889.

han KNlolIT, H. T. 8: DUFF, R. E. 1952 J. Chem. Phys. 20, 1493.

the KvIGHT, H. T. P. DUFF, R. E. 1955 Rec. Sci. Inetrum., 263, 257.

~IALLARD, E. 5: LE CHATELIER, H. L. 1900 C.R..4cad. Sci., Parie, 130, 1755; 131, 30.

~&vsov, 3; 1947 Propagation dee Dttonatione et dee Ddflagratione dane tce 3fetangee Gazcux. Paris: L'Office National O'Etudes et do Recherches Aeronautiquo et do con- 1'Institut Frangals des Pbtroles.

it is NATIovhL BURF KU oF SThvDARDs 1949 Selected Values of the ProPcrtiee of Hydrocarbons Inge and Related Compipunde. American Petroleum Institute.

mits RlsfhRsKI, S, 4 KoNscrrhz, L. 1934 ciutogene 31ctallbearb. 27, 209.

i53). ScnsIIDT, A. 1941 7~. phye. Chem. A, 189, 88.

and the

< the

ube ntal

. are I by ilietl his

f. J.

the

search was made for local bulgea The amount of plastic deforma-tion in each shotI a key quantity used in the analysis of the data, was obtained by averaging the two measurements of the diame-ter, taken at right angles to each other, at tho center of the sped-men. In addition to the measurements of diameter, careful measurements of waH thickness were made of the specimens be-fore testing and of the fragments after the specimen burst. These were required to obtain the amount of permanent deformation in the final shot, the one which burst the specimen. To,convert the reduction of thickness to circumferential strain, it was assumed that the strain in the thickness direction wss one half the circum-ferential strain. This is based on the assumption that the volume of metal remained constant during the plastic deformation and that the per cent reduction of length was equal to the per cent reduction of tbidmess. W Test Results The test results are presented in the form of photographs of burst specimens along with a tabulation of the results of each at Flg. 4 Photograph of oscilloscope trace showing pressure pvlses at 24 tempt to burst it. ?n general, several trials were run on each (rtght) and 10 (I (left) from spark plug. The htgh4requency oscillation specimen, starting with a low initial pressure and increasing the of trace ls caused by ringing of pressure pickup crystal. tn lower part of pressure about 30 per cent each time until the spedmen burst.

photograph, upper and lower light spots show dot!ection obtained by The calculated values of the stress at which yielding began snd

~ lectrlcally slmvlatlng a known pressure. Center spot has no slgnlllcanco the strain rate at that instant are given also, To explain how the stress and the strain rate value's were calcu-6 Fire the spark plug and start the oscinoscope trace to record lated, and to aid in interpreting the test results, a qualitative the detonation pressure. description. of the response of tubular specimens to detonation 7 Fill with COI. seems desirable. A mathematical description is given in the Ap-8 Exhaust to atmosphere. pendix.

In addition, there was an emergency switch which removed It can be shown that the detonation velocity and wave form are electric power from the shock tube and associated "circuitry, and such that the effect on the tube may be treated as a suddenly which automatically fined the shock tube with COs. appHed pressure, uniform along the length of the tube. This Fig. 4 shows typical pressure data. The trace proceeds from produces radial motion of the pipe waH, which is governed by its right to left with a speed of 0.87 minisec per cm on the film. A mass and its elasticity in the manner shown in Fig. 6. (The convenient measure of time is the ringing frequency of the quartr time scale is realistic for the specimens tested.) The stress in crystal pickup, each cycle of which represents 20 microsec. The the wall builds'up sinusoidany with tbne as the wall moves out.

first (right) vertical signal is from a pressure probe 2.6 ft from ward (bottom sketch) until it is sufficient to counterbalance the end. Notice the steep rise and the fairly rapid decay of the the'park pressure force. This value of the stress is called the static pres-.

pressure pulse. The next vertical signal (roughly at the middle sure stress. This is the position at which the pipe wall win of the illustration) is from a pressure probe 10 ft from the spark eventually come to rest, but at this instant the pipe wall has its end. Again the rise is steep, the amplitude is about the same but peak velocity; hence it goes by this position and undergoes an the decay is much slower than the decay at 2.5 ft. It was possible to vary the duration of the prcssure pulse by positioning the specimen holder at various distances from the spark plug.

A't the extreme left of the dlattxatn is a shock wave reffected from'he end of the tube and returning psst the pressure probe at 10 ft. The vertical line is somewhat skewed in this view because the camera alignment wss incorrect. This skewness afso has affected the vertical signals of the upper trace; they actuauy are much steeper than they appear to be in this figure.

The test temperature was obtained by blowing liquid nitrogen into the annular space between the rubber-lined shield and the specimen. Two perforated 0.25-in. copper tubes were mounted along the top and bottom of the specimen. They were connected, i0 O

through regulating valves and a wash-bottle arrangement, 'to a Tl OINO 15-liter Dewar Qask of liquid nitrogen. The Qow of Hquid was A FI.ASTIC STRAIN regulated manuauy by varying the gas pressure ui the Dewar Qask, the pressure required being only 1 to 5 pig. Temperatures were measured by reading three chromel-alumel thermocouples which were bound to the specimen with copper wire. The 8&

thermocouples were wrapped with friction tape to insulate them from the cold nitrogen gas to insure that they were indicating 0 Io Eo SO TIMEe MICROSECONOS specimen temperature. oon CIRCUMFERENTIAI. STRAIN Olt STRESSe Measurements of permanent deformation were made by.remov- ut EI.ASTIC RANCE ing the shield after each shot and measuring the specimen diame- Ptg.g titustratton of ttmoctependont response of a pipe to a detonotten ter with a micrometer. Readings were taken at six places, and a of suNctent pressure to cavso soma ptasttc deformatton of pipe woll Journal of Basic'nglneerfng DECEMSER 1951 / 521

'47~pcmRW~o'. ~

4k' iver t~

g q Sy g

PJ Jtr

@I tIY Fttt. 6 Spodmon machlnod from hobiollod, carbo~toot plpo 3.17 In.

OD X 0.03F ln. wall. Burct at +F5 F with 3 major axlatahoar fractures.

Conditions at instant yielding began>> Rtt, 7 Spoclmen machlnod from hotrollod carbotvstool plpo 3,21 ln.

Detonation Permanent OD X 0.04'I ln. walL Burat at 130 F.

pressure P, strain, Stress, Strain rate, psig Pffc/h per cent psi pcr sco 2400

• 100,000 10-20 100,000 600 Conditions at iastaat (approx) (approx) Detonation Permanent ~yielding began~

pressure P, strain, ~

Stress, Strain rate, psig , PI4/h per cent psi per second "elastic overshoot" vrhich momentarily doubles the stress unless 720o 27000 0 >54000 the yield-point stress is reached. If the test pressure is raised ~ 34000 0 >68000 900'300'800 49000 0 >98000 gradually in succeeding shots, the first yielding of the specimen 68000 0.09 113000 220 willbe produced during this overshoot This is illustrated by the 1800 68000 0.09 113000 220 solid curves ia Fig. 6. The deceleration curve (second from top) 2360 90000 0.44 117000 370 has a fiat spot, because the resistance to motion provided by 3540 135000 20 135000 900 stress in the pipe wall has become constant The velocity there- (approx) (approx) fore decreases linearly with time from the instant yielding begins Burst with 4 shear fractures, 3 of which changed to cleavage.

until the pipe wall is brought to rest The motion during this The surface was darkened by etchants in aa attempt to show Luders bands. A light polish with silicon~bide paper brought interval is the plastic deformatioa during this shot, which can be them out as light bands in the photograph. From the fracture measured, aad which is given by the area A in Fig. 6 (third curve appearance, the main fracture started as a shear fracture near the from top). The elapsed time before yielding bcyia, and the ac- piece that was cut out after failure, and changed to cleavage as it celeration and velocity at that instant, can be expressed in terms ran downward (in the photograph) bifurcatmg as it picked up of the unkaown yield stress. But the area A, which is knowa, speed+

also can be expressed in terms of the velocity when yielding began 'ested at -30 F.

and the acceleration (slope of velocity-time plot) at that instant..

Thus the velocity aad stress at the instant yielding began can be computed. Knowing the velocity, the strain rate can be found Figs. 10, 12, and 13 present the results of the detonation tests ot simply by dividing by the radius of the pipe. Note that this is spccimeas cut from cotd~wa, carbonwtccl tubing. It will be not.the maximum strain rate imposed on the pipe wall as it noted in Fig. 10 that the specimen burst at +75 F required a moves outward, unless the static-pressure stress was just equal to prcssure ">3600 psig" to burst it. The specimea survived a the yield stress. detonation pressure of 3600 psig, but it was one of the Grat to,be The practical working of the foregoing analysis may be seen tested, aad the experimenters were then unwilling to subject the in the following tabulation ot test conditions aad results. Note apparatus, particularly the soleaoid valves, to a greater pressure.

that the photographs are mounted so the direction of travel The specimen finally was subjected to a rcficctcd detonation of the detonation is downward on the page. wave by placing it at the downstream end of the shock tube.

Consequently, the prcssure required to burst this specimen could Figs. 6-9 present the test results for the three specimens cut from hot rolled, carbon<teel llipe. As noted in the caption, the not be estimated as accurately as it was in the other teste, be-cause ot the added difficulty of estimating the pressure multipli-fractures were of the shear mode in the specimen tested at +76 F, cation produced by reficction.

Fig. 6. At -130 F, Fig. 7, shear fractures were formed initially, but they changed to cleavage as they propagated along the tube. Fig. 11 is included to give a comparison of the appearance ot a At -230 F, Figs. 8 aad 9, all of the maj or fracture's were cleavage tube burst by a gaseous detonation with that, of a tube burst by fractures. This specimen appears to have bulged before it broke, hydrostatic prcssure. In both cases, the fractures were shear but actually, it burst atter only about 1 pcr cent deformation, and fractures.

the loagitudiaal strips then were beat out against the inner sur- Fig. 12 shows the specimen tested at .130F, which failed by face ot the shield by the expanding gases. cleavage fractures, mixed with shear fractures, aad Fig. 13 shows

~~ l DRCEhLBBR 1961 Transactions of the "ASME

Flg. d Specimen machined from ho&rolled, carbo~teel pipe 3.2T ln, FI. 9 Crack fa pelal near ono ond of spedmon shown ln Flg. y, ofter OD X 0.04I In. wall. Burst at -230 F pollshlny and etching a plane at about mtd4htcknoss of the petaL The branchlny of the crack and tho lack of visible dlstortton ef the grains are Conditions at instant charactsrlstlc of a @savage fracture. Tho crack ran downwanl In tho Detonation - Permanent yielding began photogroph. Etched wllh nltal. X 250 pressure P, strain, Stress, Strain rate, psig PRs/h per cent psi per seo lQ20 3900Q 0 > 78000 1340 51000 0 " >102000 1880 72000 0 >144000 ~

2410 92000 0.06 167000 230 3810 145000 1.0 180000 600 (approx) (approx)

Burst with 3 major cleavage fractures (no major shee fractures).

Some Luders bands visible paralleling most fractures, in addition to a pattern similar to those shown in Fig. 7, but less prominent; see also Fig. 9. The symbols on the outer surface of the specimen were made with stamp-pad ink to faciutate the assembly of the fragments.

the specimen tested at -230 F, in which all the fractures ap-peared to be cleavage fractures.

The austenitic stainl~teel specimen, shown in Fig. 14, was tested erst at +75 F and at rather low pressures (rihots Nos. 1, 2,

, and 3) to determine the yield stress under these conditions. Then two additional shots (Nos. 4 and 5) were Gred at the same detona-tion pressure as shot No. 3. The amount of plastic deformation decreased each time and, consequently, by the analysis in the Appendix, the computed yield stress went up and the strain rate at the instant yielding began went down.

Dtscussfon of Results The detonation bursting pressures for these tubuhLr specimens were slightly higher, generally, than would be predicted by Ry. 10 Specimen cut fram cob&frown, carbo~teel tubtny ~d ln neglecting the dynamic etrects and assuming that fracture would OD X 0.0'n. wall. Burst at +F5 F with ono maior shoat fracture occur when the circumferential stress was equal to the static ten- and two secondary splits sile strength of the material at the test temperature. This com-Conditions at instant, parison is given in Table 1. The exception to this rule is the test ~yielding began~

of a coldWawn tube at -230 F, in which the detonation burst ing pressure was less than that precucted from the tensile data Another possible exception is the hot-rolled, carbon~teel speci-Detonation psig-pressure Pr

--PRc/h'760 66000 peTmanent

" perstrain, c'ent

0. 18 Stress, psi 96000

'erStrain rate, seo 250 men tested at -230 F. 'It may be signiflcant that these two 2780 66000 66000

0. 12 Q.Q6 104000 115000 220 180 specimens both failed in a very brittle. manner. The explanation 2780 3600 87000 0.22 130000 310 for the high strength of these specimens appears to be that the >3600 estimsted- 8.00 high strain rates induced by the detonations raised their fracture reflected shock lournal of Baste Ent,tneerfnt. DECEMBER I 9d T / 523

-I

+s ~

ci fK~~+>> $ 'Pi)

C> Q' v Flu 12 Spectmen cvt from cohtchawn, carbo~teel tvblns, 3'n. OD Rp. 'll DAI67 In.

Spectmen of col~wn, carbo~teel tubtny wall, burst hydrostatlcally at 3700 psltt 3'n. OD X pressure at +75 F X 0.067'n.

some cleayase, watt. Burst at -130 F with B malor fractures, some shear, Betonation pressure Pr Permanent strain r Conditions at instant yielding began Stress,

~

Strain rate, psig PRs/h per cent psl per sec 1950 49000 0 )98000 2500 62000 0.03 116000 130 3400 85000 0.09 146000 240 4300 108000 0.37 150000 400 4300 '08000 0.43 146000 400 4300 108000 0.3? 150000 400 stress (also shown in Table I) sufncientiy to mask the dynamic effect of the detonation on the stress produced.

A striking result tcas the high values computed for the yield stresses of the materials under the conditions induced by detona-tion. These are compared with static yieldwtress values at the test temperatures, in Figs. 15, 16, and 1?. For hot rolled carbon steel the increased strain rate during the detonation raised the yield stress about 60 per cent, and for coldMrawn tubing about

'o 30 per cent.

show that these values are in fair agreement with published data, Fig. 18 presents some taken from a paper by Hendrichon, Wood, and Clark'nd extrapolated to obtain a comparison with values for the calculated yidd stress for hot-roiled carbon steel in the detonation experimenta It also is of interest to compare the bursting-stress value of 180,000 psi which was reported for the specimen tested at -230 F, with the principal conclusion of Hendrickson, Wood, and Clark: "The results show that brittle

.RB. 13 Spechnen cut from colbchawn, carbo~test tubtntt at 3~ fracture is initiated in the material employed in this investigation In. OD X 0.067 In. wall. Burst at -230 F wtth 7 malar cleavase when a critical tensne stress of about 210,000 lb/in.s is attained."

fractures orISInatintt near the mlb4ensth of the tube. "Brittle fracture" is deened in their work, in which notched ten-Conditions at instant ' sile specimens were used, as fracture which occurs after some Detonation Permanent yielding began plastic How at the root of the notch, but before the sone of plasti-Pressure Pr strain, Stress, Strain rate, cally deformed metal penetrates to the center of the specimen psig PRs/h per cent psi per sec cross section.

3500 82000 0.03 164000 170 For the stainless specimen, the effect of strain "rate on yield 4600 108000 <0.6 160000 c J. A. Hendrichen, D.S. Wood, and D. S. Clarlr, "Tho Initiation

~ Not kaown accurately because of diaiculty in measuring the of Brittle Fracture in Mild'Steel," Tians., Arncrsosn aockttr for amount of plastic deformation. Metots, vol. 50, 195S, pp. 656-681.

524 / DECEMBER 196 I Transactions of the ASME

Rlf. 14 Spestmea machlneoi from hohrollerl, stalnlesmteel pipe, 341 In. OD g OA4Mn. wall!hlshness, tested at -330 p

'>'*tstrfvtsb Conditions at instant "t

~yielding began~

i r ~ ~ Detonationt.;> Permanent pressure Pr stralar Stress, Strain rate, psig PRo/h per cent JSl per seo

• 500'9500 670'6000 0.015 0.03 35000 50

~J~ f 840'3000 0.05 44000 54000 80 110 840'3000 840'3000 0.03 0.016 68000 61000 90 70 1230 48000 0.09 75000 170 1650 64000 0.16 96000 240

<<lP 2070 81000 1.75 87000 348 2690 105000 3.10 111000 450 4620 180000 28.

Specimen did not burst but deformed to such an extent that it ulled out of "upstream" Gaage as shown at top of photograph.

tress imposed during Inst shot is not given because deformatton was so great that assumption =

of constant stress during deforma-tion is probably not valid.

~ The test temperature vras +76 F for these testa Table 1 Summary of test results on bursting of tubes

~Bursting prcssure, psig Bursting stressr pta~ Per cent deformatfon~

Estimated Circum-Measured in from tensile Computed for Tensile ferential Ehtagation Type of specimen Test temp, detonation data detonation ultimate strain in m tensue deg F (1) (2) tests 'trength tubes test hiachined from hot rolled,. +75 (4)-2400 1600 100000 65000 10-20 30 carbon<teel pipe -130 2360-3540 2200 135000 85000 20 28

-230 241~810 2800 180000 107000 1 10 Cut from coldWawa, car- +76 (3) 3700 (3) 3400 93000 (3) 83000 28 (3) 12 bon<teel tubing +76

-130 368')

43844300 3400 >130000 83000 96000 8

1-2 12 16 (6) 3800 160000 ~

'16

-230 3500-4600 5000 160000 118000 0.6 II fachined from stainless-steel pipe -230 46~7) 175000 28 38 (1) The two values given are peak pressures of last two detonations; the one which burst the specimen and the previous one.

(2) Computation assumes that specimen burst when circumferential itress equalled tensile streagth at test temperaturer dynamic effects considered.

(3) Hydrostatic test.

(4) Burst on Grat shot.

(5) ReQected detonation vrave, prcssure unknown.

(6) Burst oa third trial at this pressure.

(7) Did not burst.

'his could not be avoided. The failure of an increase in ductility be explained as follows: From the analysis given ia the Appendix aad illustrated in Ftg. 5, it can be shown that, m order to produce 1 per cent plastic deformation in these specimens, the detonation stress is shown in Fig. 17. The Grat small amounts of yielding ia pressure'must be high enough to produce a static pressure stress the tube took place at about, the same stress as in the tensile speci- (PRo/h) of about 90 per cent of the yield stress under the test mens. However, at a strain of 0.4 per cent, the stress ia the tube conditions.,(The stress will reach the yield stress and plastic was nearly twice that in the tensile specimen. It appears that deformation 'will occur because of the inertia of the moving pipe strain-hardening in the stainless steel was moro drastic at walL) Yet, in order to produce 20 per cent deformation, the high strain rates than at low straia rates. However, the cal- detonation preisure need be only about 95 per cent of the yield culation of yield stress in the detonation experiments was based stress. It is assumed that the pressure pulse is of sufncieat on the assumptioa that yielding took place at constant stress.

duration 100 microseo or more. This effect can be seen quslita Hence for the stainless specimen, the calculated values given are tively in Fig. 6: When the yield stress is only slightly above the

'somewhat high, particularly for trials Nos. 7, 8, and 9. static pressure stress, the area A of the shaded triangle will be A rather disappointing Gnding in this investigation was the very sensitive to changes in the pressure. The pressure pulse relatively small effect of ductility on bursting pressure. This generated in the shock tube decayed to one half its initial value may be seen in Table 1. Changes in ductility were achieved by in about 500 microseo. Consequently, the amount of plastic testing at temperatures both above and belovr the transition tem- deformatioa was not limited by the duration of the pressure pulse perature. Temperature itself had some effect on strength, but in these testa In larger pipe or vessels, however, this may not be Journal of Basic Engineering DECEMBER 19451 / 525

7 Paleo IL ooo TSF 230 230 F 150 cn 50 STOIG STR Ess +TSF 01 Vl IL o YIELD STRESS ~S o too o 0 . cu ~

a2 as =. Oa as as PLASTC STRAIN; PERCENT Vl E Ftg. 17 Compattcon of s~hatn cutuee for stainless stool at two tem .

ao 50 petaturee with calculated ytefd itrecs.values tn successive detonattoni, T.S. plotted agatnst cvmutattve pfacttc sttatn,, '

" ~ ic 0 200 300 200 00 0 +loo TEMPERATURE, DEO. F

~ -230F Flg. 15 Compartson, with tendfe data (dashed Itnee), of yield and bumllng ctteccec (coltd tinea) catcutoted for ho&etted, carbon cteet tube e, l50 r+

~re spedmens ~

S-ISOF lu QO 30F I50 SURSTINO 5TRE55 I -200F w

o -I I 0 F e

o YIELD STRESS -23F 7- 50

/

o loo 25.

Ol ORDINARY Vl Y.S. TENSXE TEST w

IL' 0

50 lac lo lo IO' IO lee sTREss RATE.Lyso ut pER sEc STRATN RATE, INJIM. PER SEC 0 Rg. 1$ Replot and extrapetatton of published ytetctetrees data (coltd 300 200 loo 0 +loo floes) (3) for a to~urban stool for comparison with calculated values TENPERATURE, DEO. F from delonotlon expedments (open drctes)

Ftg, 16 Compoticon, wtlh tenstte data (dashed tines), of yletd and burcttng ctteccea (cottd tines) calculated for cotILchawn, cathe~teel tube specimens wss shghtiy higher> in most cases than the static bursting pres-sure, computed by inserting the tensile strength of the material at true, because the duration of the period of plastio deformatioa the test temperature into the usuai formula for stress in a thin-(the base of the shaded triangle in Fig. 6) varies linearly with the walled cylinder.

pipe radius. 2 The fracture stress in the carbonwteel specimens which were In cotre)sting these findings with service experience, it is burst by detonation exceeded the nominal tensile strength of the necessary to remember that the test specimens were free of material at the bursting, temperature. The stress required to macroscopic stress raisers. In fabricated piping and vessels, produce yielding in the pipe wss considerably higher than the ductility is necessary to prevent high stresses from building up at static yield stress of the material st that temperature.

notches of any hnd. 3 The amount of plastic deformation prior to fracture did not It is interesting and rather. surprising to compare the strain rate affect the bursting pressure of these specimens to any great de-in these tests with that in a Charpy test. Ca)culations show gree. In fact, the bursting pressure was highest for the speci-that an uanotched Charpy specimen, struck with the full 240-ft mens which failed by deavage, with little prior deformation.

lb blow. (hammer in the top position), suffers s rate of straia at the However, it should be noted that these specimens were small-teasion face of 200 in. per in. per eec. In a V-notched Charpy diameter pipes of smooth wall and were about 40 diameters down-specimen, the strain rate of the bottom of the notch is 160 in. per stream from the ignition point. The duration of the pressure in. per seo times the S~ncentration factor for the notch. pulse was long relative to the natural period of the pipe wsH in A value of 1000 in. per in. per seo is quoted in the literature.s For radial motion. For pipes or vessehl of larger diameter, the natural these teste, the median value of the strain rate at the instant period is increased in direct proportion to the diameter (but is not yielding began, in the trial which burst the specimen, was 600 in. affected by thickness) aad there is a greater probability that the per in. per sec. Hence it appears that the Charpy test duplicates pressure pulse willdiminish before the pipe has reached the critical quite weQ the strain rate imposed by gaseous detonations sufficient amount of deformation for fracture to occur. For pipes contain-to burst pipes of this size. In larger pipes and vessels the strain ing notches or other stress raisers, it geaerally is believed that rate would be less than it wss in these specimens. ductility is beneficial to strength, sad this work on smooth speci-mens docs not contradict that belief.

Coacfusfons 4 Specimens which faoed by shear formed very few frsgmeats.

The results are reassuring in that the strength exhibited by the Specimens which failed by cleavage at a temperature just below specimens was surprisingly high, even for those which failed in a the transitioa temperature formed fewer fragments than those brittle manner. Their brittleaess at the lower temperatures ap- which failed at lower temperatureIL The austeaitic stainiees-steel specimen bulged very severely, but did not burst as expected peared to be simply another manifestatioa of the transition tem-perature phenomenon. Some specifio conclusions follow: from the static tensile data.

6 The analysis of these test results has shown that the strain 1 The detonation pressure required to burst these specimens rates imposed by gaseous detonations in piping do not greatly s E. R. Parker, "Brittle Behavior of Engineerin Structures," exceed those imposed by Charpy impact tests.

John Wiley d: Sons, Inc., New York, N.Y., ~ 1967.~ 0 It is worth noting that cleavage fractures were produced ia SZ5 / DECEMSER 1961 Tfaosactloi)s of the ASME

very thin material (0.(Nb0.070 in.) in these tests. In many in- The natural period of a simple spring aad mass system of this vestigatioas, it has been difncult to get cleavage fractures, pre- type is ceded by small amounts of plastic defoi'iijition; in plates less than '/o in. thick. These tests show thrift'temperatures are T 2x(m/Zp'TrRo(p/gE) as low as -130 to ~230 F and if strain rates of the order of 200 in. '~'ithia the elastic region, the motion of the pipe wall will be per in. per sec are used, cleavage fractures are readily produced, governed by the following general equation:

even in smooth thin speciineas. " ~ ~

dor/dl' (P/m) (Zr/m)

Acknowledgment.... The solution of this equation, in terms of the time elapsed after The authors wish to acknowledge the'leadership of Dr. R. B. the application of the pressure pulse, describes the harmonic Jacobs, Managero and Drs C H. Samans aad L T. Wright, Asso- motion of the pipe wall in the radial direction as ciate Directors, of the Engineerin'g Research Department, Standard Oil Company (Indiana), in the coaduct of this research project. They also wish to acknowledge the shll of Messrs.

r~ 1 cos B. D. Penningtoa and H. G. J. Myers, who performed the tests.

The circumferential strain is simply the radial motion divided by Ro'I "and since the specimen is not stressed in the axial direc-tion, the circumferential stress is obtained by multiplying by E to give 0 I X" '. "

~

A P P E N ~

'omenclature d ~ 1 cos p ~ density, pci h ~ wall thickness, in.

g ~

T l ~

r ~

acceleration of gravity,. In/seer time,sec natural period, sec radial motion, in. R,(4 )

'a From this expression, the elapsed time until the end ofplastic action, i.e., until yielding begins is given by R.

'gEWo Ro ~ initial inside radius, in.

P ~ magnitude of pressure pulse, psig the term 'B being introduced for convenience in later manipula-E ~ Young's modulus of elasticity, psi tion. From trigonometric relationships, d ~ stress in pipe wau, psi d~ yield-point stress, psi K spring constant, lb/in.

m mass of unit area of pipe wall, lb seco/in.

Pstatic pressure which will produce yield point stress in Hence the velocity and acceleration at the instant yielding begins are given as follows:

B~ PRo 1 ~

pipe mall, psig dh (1 Bo) s/

Elast!c Motion of Pipe Wall The general equation of motion is that of a mass, the masy of a unit area of the pipe wall, acted upon by a suddenly applied Assuming that yieldiag begins during the elastic overshoot, the force, P, the pressure" pulse, aad by a restraining spring force, plastic extension of the radius, area A in Fig. 5, is obtained as which is the radial component of the hoop stress in a unit length follows: The time elapsed from the initiation of yielding until the of the pipe wall. These are illustrated in Fig. 19. pipe wall is brought to rest is Therefore Substituting, WIT AREA MASS, m I ~ A ~(B' PRoo 2Eh B 1)

Ry. 19 Dollnnlon okoloh ot pipe element Remembering that A is the measured permanent deformation of the tube radius, the quaatity (Bo 1)/B Is therefore known; The pipe wall is a spring of stiffness Z determined as follows: and the stress oat which yielding occurred can be obtained.

The radial motion caused by the pressure P (static) is The straia rate at the instant yielding began is obtained from the expression for velocity by dividing by Ro.

r ~ PRo'/Eh K ~ p/r ~ Eh/Roo (Straia rate)o ~

p /gEX'/o (1 B')'

Eh t,p)

( )

journal of Basic Englneerlng ,DECEMSKR 19dl / 527

DfSCUSSION It is hoped that the authors will be able to pursue this problem further.

D.B. Rossheims and j.J. Murphyr. Authors'losure The authors and the Standard Oil Company gndiana) deserve The discussion by Messm. D. B. Rossheim and J. J. Murphy the appreciation of the many engineers and industries concerned is appreciated very much. Their note of caution.piobably arises with gaseous detonation, and its avoidance for the safe operation from knowledge that many brittle fractures of engineering struo-of pressure and process equipment. The tentative indication tures have occurred at nominal stresses that seem very low, com-that ductility of carbon steel apparently has little infiuence on pared to the nominal fracture stress found for laboratory speci-bursting strength, and that maximum strain rate is less than in a mene. To explain this durerence, either some'unexpected weak-Charpy 'V" notch test, is of particular interest. Also, that ness of the material in the structure or a source:of high stress analysis indicates that the strain rate for larger diameter ves-must be found from dynsmio loading, from notches of some kind sels decreases; the pressure pulse would also be of shorter dura- (geometrical or metallurgical), or from,'residual stress.. Gen-tion for larger diameters when compared with the natural period erauy, the explanation also requires the assumption of low duc-of vibration which again is favorable with respect to larger di- tility.

ameters withstanding shock. With'out in any waydetracting from We have shown how'. to analyse the case of dynamic loading, the value of the data presented, caution is in order in their gen- for the simple geometry of a smooth pipe subjected to a gaseous eralisation or in arriving at conclusions, in view of the possible detonation, to get values of strerss and strain rate at the instant infiuence on numerical results, of the test'"configuration and the yielding begins. The results of the tests agree fairly weu with indicated sensitivity of deformation extent with respect to stress published evidenco that high strain rate raises the yield point of level, mild steel. They predict'that vessels burst by dyn'amic pressure The authors are careful to point out the absence of stress raisers loading will develop high nominal stress before fracture, unless and their potentially potent effect. The specimens carried no contain severe stress raisers or residual stresses. 'hey longitudinal pressure stress and were very thin; this leads to With regard to the eirect of the plate thickness on yield and specuhLtion as to whether thick plates would behave similarly. fracture stressos, the effects of detonations on vessels were studied first in the investigation of the bursting of refinery vessels. In

~ The M.W. Kellogg Company, New York, N.Y. Fellow ASME. our opinion, these vessels also developed high stress before frac-r The M. PP; Kellogg Company, New York, N. Y. Mem. ASME. ture. At present, no further studies are contemphLted.

528 / DKCEMSER 196 l Transactions of the ASME

Bursting of Tubular $ pecimeus Senior Resoatch Supervisor, L A Standard Oil Company ilndlana),

uaSeauS ueaOna LIOn WMtbtt, Inch The paper dcscribcs some cxpcrimcntal tvorh dcsigncd to invcsttgatc the bursting of I., GINSBURGH "

pips attd prcssure vcsscls by gaseous detonation. "--~test "spccimcns werc 3.25-in.0D sonlar ptaioct Supotstsa<e tubes, 12 in. long, and of 0.040 to 0.070-in. mall.lhtchncss.;, Thc spccimcns, cul fruit hot-rotted carbon-stccf pipe, and afso from dratvn carbon-stccl lubittg, urcrc tcslcd at scvcral tcmpcraturcs, tvhich tvcrc chosen to produce fat'fuics both above and bcrotv thc

, britttc transition tcmpcraturcs for the ttvo malcrials;

'n addition, an austcnilic shin-t fess-sled spccimcn tvas tcstcd under very scvcrc conditions in scvcraf unsuccessful i 'atlcmpls lo fragment it. ~ Vo

't "L I'n lntrudugtfun '1 t .1 ~. tion, a number of pieces of pipe were burst by detonation and the experimental results were analysed to give approximate values of S svsttsr recent occurrences !in<oil'"reflnerics have the bursting stress in the pipe'wan and also th'e stress and the revealed an unusual mode of failure for pipe a'nd prcssure vessels, strain rate at the instant yielding,begsn.

namely, bursting by the detonation of their gaseous contents. When a vessel or pipe hss fragmented with little sign of plastic From the technical literature, it is known that the magnitude of deformation, the question arises. '"Would a more ductile ma-the pressure puhe impend momentarily by a detonation is very terial ride with the punch ank survive the detonation prcssure much higher than the prcssure caused by slovr.combus'tion. It pulse without bursting at all, or possibly would it burst with-also is known that the front of the detonation wave is a pressure out the formation of dangerous fragments2" To answer thht discontinuity and that the detonation travels at a velocity of question, detonations were set off in csrbonwteel specimens at

'housands of feet per second. Thus a detonation imposes a shock temperature's both above and below their brittle transition tem-load on the pipe wall as it traverscs the pipe. A number of ques- perature. In addition, an austenitic stsinl~teel specimen was tions have been raised about the resulting eEects on the me- tested under very severe conditions to determine if it could be chanical properties of steel pipe and vessels". For example, in fragmented.

any investigation of detonation damage,'he'following questions are likely to be raised: "What prcssure did it take to burst, this feSf Equipment pipe or vessc12" "Was it more'or lees than the static bursting prcssure2" Two problems are involved-"here: p. The stress in in2.o.ftand@ftsectionswithintcrconncctingcarbonwteeifiangcs the ptpe wau is a t dependent q~tity; the'prtx ure is sp- fitbd mth rubber O.~K.. The sp imcn holder d~nb~ ht.r Plied suddenly, but.the PiPe wall does not resPond iristantly be- was assembled in the shock tube with 10 ft of tube extending cause of its inertia. 2 The high strain rate produced in the upstream from it to the end flange which carried the spark igniter ~

metal auects its yield and fracture properties. In this invcstiga- and the inlet piping connections, as shown in Fig. l. (Pressure measurcmcnts indicated this length to be an ample distance for Contributed by the Metals Ensinoetsns Divisloa'and presented the detonition wave to achieve its equiubrium form.) A 5-ft at the Winter Annual Meetinlt, New York, iV. Y.,'November 27- length of shock tube was mounted downstream from the sPeci-D~mb r 2, 1960, of T~ A stem Sects'r'icmutchL EN-clNEzas. >fanuscdpt receiv~ at As>fEiHcadqQpf+~ /pm 5 mcn holder, terminating in a heavy blind Qsnge which carried the 1960. Paper Na. 60  %'A-12., ,: ~t I'< .,' exhaust-piping connections.

THERMOCOUPLES E.

IO FT PttKSSURK PROSE PURGK AIR

'PARK IGNITKR EXHAUST OXYGEN FUEL SHOCK FLANGK SOLTs TUSE TYPICAL SPECIMEN Cos DILUTION PERFORATED FILLING TUSE INNER SHIELD TIE SAR sTYPICAI OUTER SHIELD Fl. 1 Shock&le tost oqutpmont Journal of Basic Engineering D E c E Ms E R 1 96 'I

/ 519

The gaseous fuel and oxygen were mixed in'the shock tube by K introducing first the fuel, then the oxygen, through a '/c-in~s-ter stsinl~ GHer tube, lying on the bottom of the'shock'ube.

This tube had a 0.015-in~meter hole every B in. along its length to admit the incoming gas in high-prcssure jete, for good mixing. This procedure "eliminated the danger involved in handling the detonable mixture outside of the shock tube.. The mixing tube wss lashed to a '/c-in~ster stainl~teel rod to prevent the mixing tube from being bent, folded, and rammed into the end of the shock tube by the detonation. The presence of the mixing tube and its support rod apparently did not interfere with the generation of the detonation.

O O

O

~ ~

Fftt. 3 Specimen holder after pcntlal dtcaceembty, foltowlntt the shot which burst the hohcotted, carbonsteel specimen at room temp<<aturo and the ends of the shock tube were covered by movable wooden l2 shields, 3 in. thick. 'hese were intended to catch any Qying pieces if one of the fittings attached to the ends of the shock Fltt. 2 Sketch of lect specimens machined from ho~tied, earhart<<l tube failed.'

pipe, and from etatntecvst<<l pipe mixture of 27 per cent methane, 73 per cent oxygen was used for most of the tests. The proportion of fuel wss made somewhat The specimens used in the preliminary work were cut from ress'han stoichiometric (33 per cent) because a lean mixture cold~wn carbo~teel tubing, 3.250-in. OD with 0.067-in. waH produced less soot. The choice of the initial pre.sure of the mix-tbickness. No machining was done on thcso specimens except ture was baaed on the expected pressure multiplication in the to turn the ends to Gt in the Qangca Hot rolled carbonwteel detonation and the desired peak stress in the specimen. Usually, specimens, which were used for later work, were machined from several trial were run on each specimen, starting with a premure 3-in. seamless pipe, Schedule 40, conforming to ASTM Spec.

which was expected to produce no yielding and increasing the A43, Grade 3. Final teste were made on hot rolled pressure about 30 per cent each trial until the specimen burst.

stainlesmteel specimens machined from 3-in. seamless pipe, The analysis given in the Appendix shows that the peak stress Schedule 40. A sketch of the machined specimen is given in produced in an clastic specimen by s detonation is twice Fig. 2. The stainless-pipe material was AISI Type 304 (18 per that produced by a slowly applied pressure.

cent chromium and 8 per cent nickel). The chemical analysis of the carbon<teel specimens was as foHows:t The desired initial pressure of the gas mixture is obtained by calculation from the desired peak pressure of the detonation, C Mn ~ P S Si Al using a pubHshed set of MoHier-type charts based on the ac-Colddrawn tube.... 0.22 0.50 0.012 0.032 0.19 0.02 cepted theory of detonation.'he Mach number of the detona-Hot rolled pipe..... 0.27 0.46 0.004 O.ON 0.04 0.02 tion, which is needed to obtain the pressure-multiplication ratio from the charts, was measured for each shot by making a pressure-A view of a specimen holder and an exploded specimen, which time record from two probes, mounted a known distance apart shows the method used for mounting the specimens in the shock along the shuck tube.

t'ube, is given in Fig. 3. The ends of'the specimen were sealed to The procedure for GHing the shock tube with fuel and oxygen the Ganges by rubber 'O-rmgs, the grooves for which can be seen was standardized and safeguarded against operator errors by inside the Gangs openings. Thus the pressure did not exert an axial thrust on the specimen as it docs in ordinary internal-pres- providing a single, multiposition, manual control switch which operated solenoid valves and electrical equipment in a controlled sure tests of a cylinder. The axial thrust was taken by the sequence. Also, the equipment wss designed to permit the hexagonal bars. The gas-GHing tube, referred to previously also operator to remain in a shielded control booth when the shock tube can be seen.

contained a detonable mixture. The following steps were re-Various methods were tried to contain any fragments produced.

quired to GH the shock tube and Gre it:

The most successful system utHixed two short lengths of pipe.

An austenitic stsinl~teel pipe of 0.25-in. waH thickness was 1 Test the shock tube for leaks.

placed inside the cage of hexagonal bars. It Gttcd tightly 2 Flush the gases of previous experiments from the tube, against the Ganges but had one small opening for thermocouple using oxygen.

leads and copper tubing carrying liquid nitrogen. The stainless 3 Put in the fuel, the amount being measured by the rise in shield was lined with'0.50-in-thick sponge rubber. At the low pressure in the shock tube.

test temperatures the rubber hardened and did an exccHent job 4 Put in the oxygen; thepressure at the end of this step is the of embedding and retaining the specimen fragments in their cor- initial pressure chosen for the "shot."

rect rchLtive positions. A second piece of pipe, 30 in. long, also 5 Activate electric measuring circuitry.

wss sHpped over'he Qanges to provide additional safety from Qying fragments snd to reduce the noise when a specimen broke. c L Qinsburgh, "Abnormally High Detonation Proeeuro in s Shook The shock tube was wrapped with two layers of '/c4n. steel cable c The values shown sro the weight por cent of osch olomoat in the Tube," Journal of Applied Phycfcc, vol. 29, 1958, p. 1881

~

T. Wolfeon snd R. G. Dorm gonorslicod Charts of Detona-tion Parameters for Qseoous Mixtures %Fright Afr Defence Com-steel. nisad Tcchnical Ro port 64486.

520 / DECEMBER 1961 Transacttons af the ASME

0 Rrprintrd from JocaNar. or Ft.vto iblacwwrcs, Vol. 2, Part 5, p. 513, July 1957 On the existenc'e of higher than,iiormal detonation

• pr sures ' ..'

Gcncrrd Ekctrr'c Company Rctcarch Lahoratoryr SduncctadyI Nero- York

\I ~

(Rcccir)cd 25 March 1957}

With the increasing 'popularity of combustion driving in strong shock.

tube experiments, the possibility of detonation must be considered seriously.,

In addition to the extreme and relatively vtell-known conditions associated with a detonation, there exists a phase during the t'ransition from,a flame to a detonation during. which pressures and velocities of propagation. can exist which are higher than those associated with the fullyformed detonation.

This has been discussed theoretically by Oppenheim (1952) and has been shown experimentally by several workers. A luminous front having a higher than detonation velocity has been observed by Bone, Fr'aser 8c Wheeler (1936) and others. J. B..Smith (1949), using calibrated burst diaphragms at the end of a pipe, has observed reflected pressures in fuel gas-air, acetylene-air, ~

~

and hydrogen-air mixtures which were approximately four times greater than those associated with a reflected normal detonation." Turin Bc Huebler (1951), using quartz pressure transducers in the side of a tube, observed, pressures during this transition process about three and'a half ttmcs.higher.

V than those at a later time when detonation was fully developed. They with Toledo natural gas. Mooradian 8 Gordon (1951) also haye- 'orked dear indications of this phenomenon with hydrogen-air mixtures: "'" "" "

~

t,p 1 1

tr tr Tube Time to half Peak pressure maximum pressure Impulse length 24 ft. no detonation 32 ft., 2600 lb /in.s 200 mictcsec 0 8 lb. sec/in.s harv 47 ft. 710 lb./in.s 1000 microsec 1 0 lb. sec/in.s

~ s,t.

Table 1.

,c Several experiments have been run in this laboratory using a quartz pressure transducer (SLM model PZ 14) mounted in the end flange of a 3$ in. square tube. A stoichiometric hydrogen-air mixture at atmos heric pressure on the other end of thc tube was measured as a function of time.

This prcssure record was then integrated between the time of impact and I~ ~ ~

thc time the pressure dropped to 1501b./in sabs. to obtain the impulse

~

~ J ~

I 'pplied to the end of the tube during this interval. The pressure level I

'% corresponding to constant volume combustion is about 120 lb./in. ab's., ~

ag) c )~

~

~ . and that due to a reflected normal detonation wave is on the order of 500

~ I,  ; or 600 lb./in.a. Our measurements arc given in table l. a

)

~

r t ~.

J i".

eIt ~:g ,t ~ ~ 4

.~ I,i p n' [1 ~ r.

s ~ ~

~ ~

r r

.I.C v <I,

514 Donald R. N'hite The 32 ft. len th was mar inal with res 'ect to occurrence of, this over-detonation when the i nition was at the extreme cnd. However movin the s ark lu 32 in. from the end resulted in this over-detonation on each 0

substantial noise than was detonation, like the difference between blows by a sledge hammer and a carpenter's hammer.

This over-detonation phenomenon may have escaped the attention of some experimenters using combustion driving in shock tube experiments."

It must be noted that not only are the limits for the occurrence of detonation rather uncertain, but also that the first departure from the expected constant volume combustion may result in a pressure loading much more severe than that which would result from a fully developed detonation. The long distances noted above do not offer comfort since the use of oxygen instead of air greatly reduces the formation distance for detonation. This hazard may be reduced by using a number of points of ignition and by choosing a gas loading sequence such that the mixture does not go through a condition which is more readily detonable than the final mixture desired (i.e. loading of hydrogen last).

Rmzamczs Bolts W A ~ FRASEay R P & WHEELER' H 1936 PhK Trans Ay 235> 29 MooaaMaN, A. J. & GoanoNy W E 1951 g Chem Phd 19'166.

OPPENHEIMp A. K. 1952 Gas dynamic analysis of the development of gaseous detonation and its hydraulic analogy. Fourth Sympotium on Combuttion,

p. 471. Williams & Wilkins.

SMLTH, J. B, 1949 Explosion pressures in industrial piping systems. Paper pre-sented before the International Acetylene Association; copies available from Eng. Div., Factory Mutual Labs, Boston, Mass.

TURtN, J. J. & Hvsstza, J. 1951 Report Comm. Induttr. Commer. Got Res., Project I.G.R-59. Amer. Gas Assn.

ltofjIsE 'tIjlS cttit orett] c7clii tIh stan'fQpfQf ljtt g1 jIj/ls I eras t (4~a i ~ w lr~fc'e)

T}ie Strength of Thin-Walled Cylinders C. J. COSTANTING Subjected to Dynamic Internal Pressures Research Enplnaarc IIT Rasaarch Institute, Chtca pa, III Thc cqualion of motion got(crning lhc rcsponsc of kng (infinite) cylir(dcrs to dynamic internal prcssurcs is dcrit(cd. Since large disphccmcnts and spall-thinning cgccts are taken inla account, chstic bchapior of thc material is ncglcctcd. The material is as-sumed to bc rigid-phstic, T((ith strain-hardcnsng being taken into account through lhc Ludt((ik pat((cr strain-hardening iato. Numerical results are prcscnlcd for a range of hardening constants from 0.01 to 1.0, cot(cring the range applicable to most materials of intcrcst. Thc form of lhc dynamic'prcssure consHcrcd is an initially pcakcd, linearly decaying prcssure pulse. Cliarts arc prcscntcd gitnng thc prcssure and duration rcquircd to produce a git(cnpnal radius of lhc cyhndcr.

P t std purpose of this study has been to obtain an ap- (r ~ (roF(c) proximate measure of the response of containment shells sub-where P is some function of the effective strain determined by jected to blast type (dynamic) internal pressures. Such informa-tion would be of value when attempting to evaluate the protec- experiment. For the state of biaxial stress associated with thin-shen problems, the effective stress and strain reduces'o tion afforded by the structure against an accident (nuclear excur-sion, coolant leak, and so on).

Within this framework, the bursting strength of thin-waHed in-a - la,s seas + ass}'f (2)

+ csos + cs } II 2

finite cylinders subjected to internal pressures is obtained in- ces corporating the renewing assumptionst 43 1 Elastic disphcements of the shell are negligible as compared where the subscripts 1, 2 designate the principal directions.

to the hsrge displacements obtained at burst. The material is assumed to be incompressible, or 2 The shell material deforms as an ideally plastic( strain-as+ as+ ce ~ 0 (3) hardening soHd satisfying the maximum octahedral yieldwtrcss will be made that the materia

'he criterion of Miscs'nd the subsequent displacementa are deter assumption is characterize mined from the associated fiow hsw. " by the Ludwnc power law strain-hardening, or 3 Thc applied internal pressure is a function of time only, but, P(c) ~ 8" (4) not of the radius (internal volume) of the shell. This assumption is actually an approximation to the loading felt by the shell as it in equation (1), where n is the strain-hardening cvponcnt.

deforms.

'4 Dynamic effects on the stree(Httrain properties of the ma- Static Solution terial can be accounted for by an appropriate choice of the con- The prcssure-radius relationship for infinite cylinders subjcctccf stants in the static stree(Httrain hws postuhsted for the material. to monotonicanyincrcasinginternal static pressures has been given previously.'his solution will be outlined briefiy. For this Stialn-Hardening Law case, subscript 1 refers to the circumferential direction, subscript 2 the axial direction, and subscript 3 the through-thickness direc-In general, the strcmHttrain behavior of any ductile material tion. The following system of equations is used to obtain the may be described analytically as solution:

1 R. HIII, The ltfa(homcstlcat Theory of Ptastici(t(, Oxford Univaraity (a) Strain&splaccmcnt relations (finite strains)

Press,'ondon, England, 1956. 'R Contributed by tba Applied Mechanics Divirion and prasantad at tha Winter Annual Mooting, Naw York, N. Y., November 29- log log r Ro December 3, 1964, of Tests hscsnscaN Socsxvr or MxcsrANTcas.

~

ENotN88(ss. (5) cl I Discussion of this papar should be addrecsacf to the Editorial De- ~ log H ~

cs log h part(nan, ASME, United Engineering Center, 345 East 47th Street, Ho Naw York, N. Y. 10017, and will ba, accepted until April 10, 1965.

Discussion received after the ciocnng date will be returned. Manu- sN. L. Svanson, "The Bursting Pressure of Cynndricai and script received by ASME Applied Mechanics Division, December Spherical Vassals," JotraNAT or Arruxo hf rcttamca, vol. 25, TnsNs.

4, 1963. Paper No. 64 Wh/APM-16. ASME, vol.80, 1958, pp. 82-96.

Neceeecletece H ~ shen thickness, in. Po ~ initial peak dynamic pres [yRo /2(roj', time factor Ho initial shell thicknc(N, in. sure, psi 8CC h ~ H/Hw dimensionlcas sheH p PRo/rroHo dimensionlcss dynamic load duration, acr:

thickness prcssure ratio unit mass ol material 8 ~ efi'ective strain n ~ strain-hardening exponent R shen radius, in.

occ cec es principal strains Pc ~ applied dynamic internal Ro initial shen radius, in. a ~ cffccttve stress pst cc PrCssutec Pst r R/Ro, dimcnsionlcss shen cro ~ strength measure psi

'I P, ~ applied static internal prce- lad((le Cree 0'ec O'S ~ principal stresses I

surec Pst t ~ time, seo r~ t/T, dimcnsionlcss time scale,

[04 / MARCH 1965 Transactions of the ASME

(I>} Incon>pressibility, equation (3) where asterlaked quantities refer to quantities at instability.

s:

This rehLtionahip is shown graphicauy in Fig. l.

r~]/h tet ]>lane-strain condition in axial direction Dynamic Solution (7) The equation of motion for the system can be written as

~ I ~ '0 ~ a

'4)..i~is ..ilC~> t.

I II I (d} Flow Iaw associated with )>fises yield condition d'R O

P,) 2rRHy , 'rR(Ps (13) 0 20> 0>

Or II .( .. "

fs re s> 20> 0'r 2 which in dimensionleas form becomes CI is cs-(s) Effective stress and strain, equation (2}

ough the

~or>gc of v'S 2 drr drs 2h 1

(ps p.) (14) crials of 0' 0>>

2 Iir>surly where pz and p, are the dimenaioniess applied pressure and static required Stress<train Iaw, equations (1) and (4) resistance, respectively. Substituting equation (6) into equation

< 0 (14) the equation of motion becomes 0' 0o

(=

43 ]ogre (10) r

-(ps - p) (15) drs 2 (g} Equilibrium condition

,uned by ith thin- a PR Solutions of Dynamic Problems H The problem at hand is to determine the maximum displace-I ment that the shell achieves when a given inten>al pressure pulse Thrse equations are combined to lead to the dimenaionless pres-Ia applied. Since only plaatio defonnations are being considered, sure-radius rehtion (2) it is necessary to determine the displacement when the shell velocity Grat becomes aero.

The dynamic pressures to be considered here are initially

'.rections. peaked, linearly decaying pressure pulses of the form (3) and po (12) ps

]--) To for Ogr<ro (16) acterized 0 for To+T ro ~ ceo where po is the initial peak pressure and ro is the pulse duration.

II

>ubjected xn given 1.0 For this subscript 0

!ss dlrec

>tain the lO nn 0.0 0 0.8 0.]

Ae 0.2 (5) n 0.6 C 0.3 0

I ricnl and Lit>a oj ]nota 5, TsxNs. .b 0.4 0

0.6 0.8 e factor 0. 2 cion, aec al 1.0 1.2 1.3 1.4 l. S 1.6 1.7 Dimension]ess Radius, r Ra. l Proaooroondlos rois>ion for vorloos vnlooo ot hordonlnu ~ >q>ononl e ASME journal of Appllelf. Mechanics MaaCH li>45 /105

?able 1 Slreomlraln properljeo ln ojnlpl~ lenolon Strength coefficient, Hardening Yield stress, Material Irol psi exponent, ro pei A212 Grade B Grebox steel.... 155,000 0.245 32,000 A285 Grade B Grebox steel...: 117,000 0.2?8 2?,500 T404 stainless steel.......... 171,000 0.724 36I800 A302 steel. 133,000 0.197 02,190 USS T-1 steel................ 178,700 0.087 119I800 0.15 percent carbon steel...... 108,000 0.285 32,700 Although this is a rather approximate idealization of the actual raaI 2 a+I lego+Ir pressure that would be felt by the shell, it allows for a representa- (20) tive evaluation of the relative effects of the load parameters po and To on the resPonse. The remaining integral in equation (19) cannot be evaluated in A Grst integral to equation (15) can be obtained from the re- closed form, and numerical'integration techniques must in general lation be useL For particular loading cases, however,. complete solutions can be obtained, these being the ext'reme cases of a step pulse (g ~ 0) and the impulse (g ~ 1). For an impulsive load applied to the This leads to the relationship shell, equation (17) reduces to r praea (r')' r! pc[1 g(T)) p,}dr + (ro')'17) (ro')' (21) 1 J1 where primes designate differentiationjwith respect to T ro's where the impulse is related to the initial velocity by the initial shell velocity, snd I 2't~Ho P/To for 0<T<To (22) g(T) ~ (18)

( 1 for To+T If a linearly decaying pressure pulse of peak nmgnitude, pl, and

't the maximum radius, r~ duration To is applied to the shell, and it is further assumed that rl ~0 this pulse is sppliedimpuhlively (actually it is applied overs Gnite so that time To), the total impulse applied to the shell (area under the po Se f 1 rau rpgr (ro')l rg(T) dr (19) pressure-time curve) is (23)

Equating equations (22) and (23), the initial velocity is found to where T is the dimensionless time at which the maximum radius be is reached. Thus, equation (19) yields the peak dynamic pres-sure required to achieve s given Gnsl radius. For power law- ro' pITo (24) hardening, 4 1.0

0. 6 l

T I "

j 0.4 I e I

/

, I

0. Z e I

I 7;," 7 l i I aa 4

0. 1 I ~, I "

I 1,.0 e:III I

~ u 0.0 I e I

0. 0 e I I e

0. 0

0. OI 77 ~ e

0. 01 0.0Z 0. 0O a06 0.0 0. Z 0. O 0.6 1.0 1 o 6 10 PI Wo RS. 2 Valuoo ot jIIro ao a function ot lllaldlnuln onaln

~ a ee CJl r ~, HI -e Ieeea<< Hea~ raaeeaaaloaeea e

'c l1a 0 II % ~ C'

L. 0

~ II~QWI5$

$$ ~1~r% ~~~$

I ~

0. 0 i ills 0.4 I ~

0.1

~ 1.0 ' I 0.5.

0. 1 FfLI 3 Valaos of ps as a fiiiIcLIon of I 0. 1 0. 01 maxlmam slrala (20)

I, 0.0 Lated in

0. 04

, generLLl ss lolls cnn (55

- 0) 0. 01 d to the E

0. 01 0.01 0.04 0.05 .0.1 O.X 0.4 0.6 no 1 4 0 'LO (21) Ps 100 100 0 = 0,0@i na 0,1 I ~ ~ 1. 086 ~ I ~ I pa = .78 6

l. 'I (22) 0.30, ~

's

~

<<sili

~

I 0.30 '"

O. 20' I 'iL0.20

. pI, nnd 10 ned that 0.10 0.'llew 5'0 ra 6nite 0. 05 I I I

. I I ~,

Po s

!>>!I'I

~

nder the p1 'I ls . I I ! Is! ~ I I I ~ i' ;iv

• I'l

. 0.1 I;I I I I INill, 0.

I Ll

,10 I~

100 0,1 10 100 1 RLL. 4 Damoeo pros (24) swo saLlos 100 100 n = 0.5. na 110~

p 0. 245 ASM'.OL po 10 ""'"0.05'i'c 'o.'fo'I 0,2p II 0.'lo'..

". I I I "IIII 10 I

=

0. 20 Ii' I I'l)

P

( ~ I III l l ii;i:I ss I-'

I I ) I I I svl; ~

i: II

~

0.1 i j lILii Ii,.;I I ji p I I IL 0.1 1. 100 0:1 100

~a 10 1 vl 10 Substituting into equation (21) we obtain This equatiNL does not, however, completely solve the problem for the step pulse. By refemng to Fig. 1, we note that the static pL Ls re (25) strength of the cylinder decreases for r > ro.- From the equation of motion, tbs shell acceleration is proportional to the difference For the case of a step pulse of magnitude ps applied to the shell, between the dynamic pressure and the static strength. There-the solution from equation (19) is foLe, if r > r'nd if ps > p the shell will continue to accelerate LL I'Ls ~

and never stop. The maximum value of a step puhLe that can be p- (r 2

1) JL (20) tolerated may be found by satisfying simultaneously both equa-tion (26) and the condition ie lourllal of Applied Mechail?cs MARcH 19ds / ~01

t p 4

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