U.S. DEPARTMENT OF COMMERC 1Na•muai Tecl.ic! fnwifion Service

AD-AU25 502

ESTIMATES OF BLOWDOWN OF QUASI-STATIC PRESSURES

IN VENTED CHAMBERS

SOUTHWEST RESEARCH INSTITUTE

PREPARED FOR

EDGEWOOD ARSENAL

NOVEMBER 1975

y• 169080

EDGEWOOD ARSENAL CONTRACTOR REPORT

EM-CR-76029Report No. 2

ESTIMATES OF BLOWDOWN OF QUAS[-STATIC

PRESSURES IN VENTED CHAMBERS

by

W. E. Baker

G. A. Oldham

November 1975

SOUTHWEST RESEARCH INSTITUTEPost Office Drawer 28510, 8500 Culebra Road

San Antonio, Texas 78284

Couitract No. DAAAI5-75-C-0083 1-

DEPARTMENT OF THE ARMYHeadquarters, Edgewood Arsenal

Aberdeen Proving Ground, Maryland 21010

Approved for public release; distribution unlimitedREPROMICED BYNATIONAL TECHNICAL

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READ INSTRUCTIONS

REPORT.D UMENTATION PAGE BEFORE COMPLETIN(; FORM

1. REPORTNUMBER J2. GOVTACCESSIONNO. 3. RECIPIENTS CATALOG NUMBER'EM-.CR-76029

4. TITLE (andSubtitle) 5. TYPE OF REPORT & PERIOD COVEREDSESTIMATES OF.BLOWDOWN OF QUASI-STATIC Technical Report

E - FJanuary 1975 to March 1975PRESSURES IN VENTED CHAMBERS 6. PERFORMING ORG. REPORT NUMBER

Report No. 27. AUTHOR(s) S. CONTRACT ORGRANT NUMBER(s)

W.E. Baker DAAA 15-75.C-0083G.A. Oldham

9. PERFORMING ORGANIZATION NAME AND ADDRESSES' 10. PROGRAM ELEMENT. PROJECT, TASK

Southwest kesearch Institute AREA & WORK UNIT NUMBERS

P. 0. Drawer 28510 PA, A 5751264SaihAntonio, Texas ,78284

"11. CONTROLLING OFFICE NAME AND ADDRESS, 12. REPORT DATECommander, Edgewood Arsenal November 1975Attn: SAREA-TS-R 13. NUMBER OF PAGES

Aberdeen Proving Ground, MD 2 1010 1914 'MONITORING AGENJC" ;,AME & ADDRESS 15. SECURITY CLASS (of thii report)

(ij different from Ciontrolling Officer)Commander. Edgewood Arsenal UNCLASSIFIEDAttn: SAREA-MT.H"Aberdecr;Proving Ground, MID 21010 i. SCHEDUECLASSIFICATION/DOWNEGRADING

(CPO Mr. hiuca Jezek, 671-266i) NA16. DISTRIBUTION STATEMENT fof this Report)

Approved for public release; distribution unlimited

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18. SUPPLEMENTARY NOTES

'19. KEY WORDS (Continue on! reecr.b side' if mcceszrIr and identify. by block number)

Internal blast pressures Gas venting theoryBlast venting Blowdown from vented chambersSuppressive h, ieldsScaling of gas',intiIng

20. ABSTRACT (Contin'ue on .'etyrse side if necessary and Identify by block number)

This report presents recent analyses, and fits of experimental data to scaled parameters. for blowdownpressures in vented chambers. Theoretical predictions are made for time histories of blowdown pressures.and a scaling law is presented. Umited comparisons are made with experiment%

9

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JAN 73 UNCLASSIFIEDI SECURITY CLASSIFICATION OF THIS PAGE (It'hici Data Entered)

SUMMARY'

This report presents recent analyses, and fits ef experimental d'it4Ito saied parameters,for time histories of the relatively long duration pressures which 'ekxiZ;ter explosions invented chambers. A convenient form for combination o•fseverals,!-'cl4quantitiesvarisesrfrom'-the analysis. Curves oftvent:pressure tiffiehiitories and duratio.'w. p e.,,nted in the reportshould, however, be considered as tentative because of additional, a 'ent work on vented gaspressures in the Edgewood Arsenal suppressive structures progranm

PREFACE

The, investigation described inthis report was authorzzei- .,9r PA, A 4932, Project

5751264. The,work was performed at Southwest Research hi, ••'iute under Contract

IDAAA I 5-75-C-0083.

The use of trade names in this report does not cdnstitu' official endorsement orapproval of the use of such cOmmercial hardware or soft•ar . 'This report may not be cited-Worthe purposes of advertisnement.

The information in ;ihis-dvcument has been cleared f&c,'-elease imothe'general public.

Preceding page blank

TABLE OF CONTENTS

S! Page

1 . INTRODUCTION. ....... .. .. .. .......... .......... .......7

SII. THEORY ........... ............... ........... 7

Ill. COMPARISON WITH!DATA ............................... 14

IV. DISCUSSION ............ ....................... .... 16

V. CONCLUSIONS ............ .......................... 18

REFERENCES ............ . ........................... 19

S.p

S~Preceding page blank

LIST OF ILLUSTRATIONS

:Figure. Page

I Idealized Vessei'Blowdown ............ ......... 8

2 Semi-Log Plot of ScaledzBlowdown Pressure Versus Scaled Time, 3y = 1.4 . I

3 Linear Plot of Scaled Blowdown Pressure Versus Scaled Time, y = 1.4 12

4 ScaledBlowdown Durations ..... ... ................... .. 13

5 Scaled Blowdown Durations for Suppressive Structures ........... .. 15,

6 Sc'ied-Gas Pressure Impulse Versus Scaled Initial Pressure .... ........ 7

t.

6

ESTIMATES OF: BLODOWN OF OJrASI-STATIC PRESSURESIN VENTEDCHAMBERS

1. INTRODUtTION

"In earlier work on estimating quasi-static presrares within vented structures, a dimnensional-analysis was made and scaled curves generated ba',ed-on empirical fits to data for pr.,k quasi-static pri:gsures'andblowdown times (see Fig.B5 and B6 in Ref. '). Data fromrnReferences 2and3 were fitted to an empirical combination-of scaled parameters whichseemed-to fit-the-data-best.

To describe more completely the internal pressures applied to vented structures duringthe blowdownof these relatively long-term pressures (long term compared to initial reflected

,shock pressures), it would be desirable to be able to estimate the time histories, including theircharacter for structures which were better vented thart those reported in References 2 and 3.Reference 3 reports some data for impulse in the quasi-static phase, as well as peak quasi-staticpressure-and blowdown-times, Thcse authors (Keenan-and-Tancreto)-also-note that they 16b-"3/2tained~no measurable quasi-static pressure rises for values of (AentI/V) of 0.678 or greater.No measurements have apparently been made in the range

0.0775 g \'--t] < 0.678

This report includes additional studies on blowdown of pressures resulting'from explosionsin'veifited structures, with particular emphasis on prediction of the details of these pressures fordesign of suppressive structuresý The work was performed for the Edgewood Arsenal suppressive,structures progprt under Contiact DAAA! 5-75-C-0083.

II. THEORY

An Analysis is available in the literature'which can be applied with some modification tothis problem. Oivczarek, 4 on pp. 254-255, considers the problem of prediction of pressurewith time in a tank initially filled with gas at high pr-ssure, and then emptied by the suddenopening of a convergent nozzle in the tankLvall. He'assumes* a quasi-steady flow process, aperfect gas, no heat transfer, and isentropic expansion in thehnozzle. Two flow regimes apply,for back pressure po less than, and equal, -or-greater than, critical pressure for the nozzle.Schematically,,this situation is shown in Figure 1.

*Elsewhere in-Referce'4, Owczarek also considers this same problem with shocks and rarefactionfs in the tank.

7

y

nPO

P, , eaAee

1.FIGURE I. IDEALIZED VE.!.SEL BLQO'• , N

Owczarek's *,lutions give time't as a function of ratio ofpress.usa't this time to outsideambient pressure.t

SNPt) ,"(tPo (I)

LIa These solutions are:

A (I 1)"2 y- I , ~l2, -1)1K Pt )(' WI)/. i\2. = " "(" - I(2)S~A,.(-IR,0 )v ( 2y II W

for ýP(,,t,),,,,, (3)

k, and

[,v ty 1/2 / 1)/ 0(27)1 r='7-l'•----\2 (7R 1)J [":4932

-- (2xW + S)(.. 2 + It 2 (X + (4)

8 81 Tv~l 4

for

I •PI(2 P<(5)S\+ l

In Eq. (4), t* is the time at which P first equals the upper limit in Eq. (s), and x is a dimension-less group

X = [p4., - 1)/, 1] 1" (6)tin this analysis, all pressures arcabsolute pressures.

8

In these equations. ,-is exit area of the nozzle-.the symbol "'" indicates sound velocity.'y is ratio ofspecific heats for gas within the chamber, R. is the universal gas constant- and.other quantities have been defined. The perfect gas law requires that

a2 - (7)P

So the quantity

('yR ,O)12 =at (8)

i.e.. the initial sohnd velocity withinthe Vessel. The set of Eqs.•(2) and.(4) applies on&i., forinitial pressure ratio PT geater tha:Phac- limit in Eq. (5).

With some asu.umptions. adaptation anidrearringement, we can apply Owczarek's equa-tions to venting of suppressive structures. Let us assume-that the nozzle exit area

Ae =,e4is (9)

The inlet s6und velbcity a, is aw important parameterin Eqs. (2) and (4). In suppressivestructures, this is not 'known exactly because the gas being vented is heated air mixed withexplosion products. 'gut. from work of Proctor and Filler;2 it-is appaint that the-great

majority of the pressure rise within a'vessel containinganh explosion is~caused by addition-ofthe heat energy of the explosive to'air,-rather than aiddition of tools ofdexplosive products.Assuming thatno appreciable venting Occurs during the initial stages with shock reflections.this process represents4a constant volume heat addition. Such a process raises the absoluteteinperature of a perfect gas in direct proportion wiCh the absolute p ssure rise. From Eq.,(3). we then see tilat

(a.) (T,)" 2 ('P, ,12

- - 1 ) ('10)

Equations (2) and (4) can be rearranged in dimensionless form. Let:

i"-- I- ta, t \ 1 ) (0 1)

'whwre,? is a dimensibnless time. Then, Eqs. (2) and (4),become

2 J y + I\ ) ( -Y + + 1 ) 1 + ( 7 - I )( ( 2 i 1) ( )

(y o1)-\2 / --

for P>l( 3 -1/

-- 4 9

p1 _X-(2r

2I40 + 5)(.2 + )I":

88

Thewe equations express dimensionless time~as a functibnof dimensionless pressure Vind ratio-of specific heMs. They are explicit and allow solution for any initial pressure ratio P, and -f.Plots-are iW•ion for ajrange of Ai andy •'1.4 in Figures2 and 3. From these figures. one can

see'thatP = i1 for finitWalues of ?. ie..blowdown times are finite. Scaled durations of-blow-down fmax can be obtaihed from Eq. (2a) and (4a) for any P, by determining *, and settingx = 0. Values for scaled duration of blowdown, fm,. and time to reach critical pressure 7,are shown in Figure.4 as funtions of P,.

=Thcsceq uations~change-the definition:9jf ?iinEq. 11.)to

I(o -A5\ p 02 /2/ (12)V\1 2/) P-0 \9v1/)7

where a0 is sound velocity,in the outside air. A, is internal surface area of:the strlmcture..anda, is as 0efined in Reference i. Frbm Figure 4 and our previous discussibn. we note that

fma% is'ii unique function of P,. say

However, from Eq. (12)

T -' - J2 t:, " (14)

F.,rthermore. we can define,• simpler eombination'of.paraneters as-a scaled time. i.e..

-Itao

so that"

Tmna\ kV--)•"maý 0,IY) (16)

-!0

• ,:o -•5.0'• • • -10.0

•. m0 & 0'• 0 50.0

I:C

•~6--

I -

0 1.0 2.0 3.0 4.0 0 6.0 7. 8.0 .0

S:; ~~~~~~~FIGURIF. SE S..%II-.LOG• PL.OT OFC S(,LEDI HI.OWD'•IOW'N PR ESSU RE" " VERSUS" " CA' LED" TIiMI, E. 1.4

?,o

; 'I

* * I •I ' I

4n

'U-

p..r.

0. CD

C0.0

C~

) 12

cao

A IA

-- ¼

4~

t0

13l-

Il1. COMPARISON'WITH DATA

The functionimax can be compared with measured blowdown times for vented structures,as from Reference 3. Theor.tical functional forms for fmax, are plotted versus P, in Figure 5,and data from Reference 3 cast into this form are also plotted. Because Reference'3 cites spreadin measurements, we can indicate this spread by width and height of each rectangie in ig'ure 5.The experimental data describe a different functional form than Owczarek's theory. (Note thatthe vertical scal' is greatly expanded, and that deviation'from the theoretical curve is always with-in a factor of two.)

Some data are reported in Reference 5 for blowdown times for cylindrical vessels with endplates having various sizes of holes. These investigatort give times to reach critical pressure, ratherthan atmospheric pressure. But, we can easily calculate scaled times corresponding to this pressure;they are 7. and 7., defined in the same manner as in Eqs. (12) and (16) respectively. These qv, an-tities are plotted on Figures 4 and 5. Scaled data for ?, from Reference 5 are shown on i-;£ure 5and fie generally below theexperimental valueszfor -mnax fromReference 3.

A much more approximate analysis of blowdown from vented structures has been made byKinney and Sewell. 6 Theyassumed that there was no regime for flow transition, and venting:

therefore occurred at sonic flow velocity down to outside atmospheric pressure. They alsoassumed an initialsource temperature independent of initial pressure. These assuimptions yieldeda simple differential equation for pressure change,

= AP (17)

Kinney and Sewell integrated this equation directly and obtained the solution*

A P=,o P, -CAt (18)

They chose\,' value for C 2379 ft/sec, giving C 2.130. Using our definition for

7= ,,, (19)

0 .(!8) becomes

P" AtP - 2.1307' (1l8a)

F} ~and it yields r-max by setting 1P= . This value is

7max = 0.4695 A P, (20)

It is plotted on Figure 5 as the line labeled "Theory, Kinney and Swevl", and apparently givesbeeter agreement with experiment than the more "exact" theory of Owczarek.

We have converted to dimensionless parameters, iith C = C/aO.

14

2.2 , * I I I •

KEY.

2.0- DATA FOR 'fmax

• 2.0 FROM KEENAN & TANCRETO (ref. 3)

o DATA FOR Y*o"1.8 FROM ZILLIACUS, etal (ref. 5)

1.6 -- EYE-FIT TO DATA FORT'%x

Ymax'

THEORY, Tmex

1.21 KINNEY'&k S EWELL (ref.v6)1. Z-• OTHEORY, Tmax

1.0-

0.8 0 THEORY. T.0WCZAREK(ref. 4)

0 0

2 4 6 10 20 40 60 100

FjIGURE S. SCALED BLOWI)OWN DURATIONS FOR SUPPRESSIVE STRUCTURES,

15

Iecause the theories of Owczarek or-Kinney-and Sewell predict complete time historiesof blowdown pressures, these histories can be integrated toyyield predictions of gas pressure-impulses, Ig. This was done graphically for, plots such is Figure 3 from Qwczalek's theory,

4, and analytically- for the simpler equation of Kinney and Sewell. The latter equation, indimnensionless form, is

i7g = 7 -ax-, T. ax (21)

'where

17 = 19 ) (22)

Both prediction curves are shown in'Figure 6, together with points from Keenan ind Tancreto.AAgain, the very approximate formula of Kinney and Sewell appears to fit the data better than-the~more "exact"_curve-based on Owczarek's equations.

IV. DISCUSSION

From the analysis presented here, it seems apparent that time histories of pressures withinvented explosion containment structures can be scaled, and perhaps can be estimated, based ona simple gas dynamic analysis by Kinney and Sewell, 6 or a more complex analysis by Owczarek.4

The scaling (dimensionless) parameters involved are

I -a

(23)

' p_

Owczarek's analysis predicts that

. =f, (,,,v27,y (24)

and gives this functional dependence (see Figs. 2 and 3 for a 'y = 1.4). The combination ofscaled parameters in the second term in the parentheses is alio a scaled time,

16

-u

LAJ.

0'

z

cl--

zn ma)a0I

cm%

'0 C~J 017

=,jl2 (I 2a)

Becausep appears in this term, a more useful scaled combination is probably

(14a)

This combination also appears in Kinneyand Sewell's simple analysis.

Both prediction equations predict finite blowdown durations, so maxima for rand fcanbe easily calculated. These maxima and scaled times toreach critical pressure are shown asfunctions of P, in Figures 4 and 5 and data from Reference 3 and Reference 5 are comparedto the theoretical predictions in Figure 5. The scaled pressure-time histories can be integratedt6give scaled gas impulse 1g, which is plotted in Figure 6 as a function of P1. This parameteris defined as

7g ; (OAsao) (25=*

Limited experimental data indicate better agreement with the simple equation of Kinney andSewell than with the more exotic solution of Owczarek. Both, of course, are approximationsto the complex situation occurring during venting.

V. CONCLUSIONS

More venting pressure data should soon become available from BRL tests in the Applied

Technology Program. Also, conversations with J. Proctor of NSWC White Oak indicate that

there is a body of Norwegian data not noted here. NSWC is also looking at the venting processin much more detail. For these reasons, curves such as Figures 2 and 3 should be considered astentative. aind should only be used for interim estimates of venting pressures. gas impulses, anddurations. We feel that the primary value of the information presented in this.reoprt lies indevelopment of an improved method of piesentation of Venting data in dimensinbiess form.and in presentation of some curves and formulas which give preliminary estimates of ventingfor structures with la4e vent area ratios.

REFERENCES

I. W.E. Baker, P.S. Westine, P.A. Cox and E.D. Esparza. Southwest Research Institute.San Antonio, Texas. Tech. Rep. No. 1. Contract DAAD05-74-c-075 1. Analysis andPreliminary Design of a Suppressive Structure for it Melt Loading Operation.4 March 1974.

18

2. J.FX.Proctor and'W.S. Filler, A Computerized Technique for Blast Loads fromConfined

ExpIlosions, 14th Annual Explosives Safety Seminar, New Orleans, La., 8-10 Novemer,

1972, pp. 99-124.

3. W.A. Keenan and J.A. Tancreto, Tech. Rep. 51-027. Blast Environment from Fully and

Partially Vented Explosions in Cubicles, Civil Engineering Lab., Naval ConstructionBattalion Center. Port Hueneme, Ca., February 1974.

4. J.A. Owczarek, Fundamentals of Gas Dynamics, hit. Textbook Co., Scranton, Pa., 1964.

5. S. Zilliacus, W.E. Phyiliaier, and P.K.-Shorrow, Naval Ship R&D Center Report 3987,The Response of Clamped Circular Plates to Confined Explosive Loadingg. NSRDC,Bethesda, Md., Feb. 1974.

6. G.F. Kinney and R.G. S. Sewell, NWC Technical Memorandum 2488. Venting ofExplcsions. Naval Weapons Center, China Lake, Calif., July 1974.

I 1

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