RD-R69 365 DEPENDENCE OF FREE-FIELD IMPULSE ON THE DECRY TIE OF illENERG Y EFFLUX FOR A JET FLON(U) ARMY BALLISTIC RESEARCHLAS ABERDEEN PROVING GROUND MD K S FANSLER MAY 86

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MEMORANDUM REPORT BRL-MR-3516

DEPENDENCE OF FREE-FIELD IMPULSEON THE DECAY TIME OF ENERGY EFFLUX

FOR A JET FLOW

-,,m s.DTICKevin S. FanslerDTIC ELECTE

UN9 1986

C._) May 1986

CAPPROVED FOR PUUUC MIEA= 0=0mR oN M4UMED.

US ARMY BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

86 6 o14

Destroy this report when it is no longer needed.Do not return it to the originator.

Additional copies of this report may be obtainedfrom the National Technical Information Service,U. S. Department of Commerce, Springfield, Virginia22161.

The findings in this report are not to be construed as an officialDepartment of the Army position, unless so designated by otherauthorized documents.

The use of trade names or manufacturers' names in this reportdoes not constitute indorsement of any commercial product.

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MEMORANDUM REPORT BRL-MR -3516

&. TITLE (amd mbetle) S. TYPE OF REPORT & PERIOD COVERED

Dependence of Free-Field Impulse on the Decay FinalTime of Energy Efflux for a Jet Flow 6. PERFORMING ORG. REPORT NUMBER

S. PEFORMNG OG. REORT UMEE

7. AUTHOR(&) 4. CONTRACT OR GRANT NUMBER(a)

Kevin S. Fansler

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

U.S. Army Ballistic Research Laboratory AREA& WORK UNIT NUMBERS ." .--

ATTN: SLCBR-LF RDT&E 1Ll61102AH43Aberdeen Proving Ground, Maryland 21005-506611. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

U.S. Army Ballistic Research Laboratory May 1986ATTN: SLCBR-DD-T 13. NUMBER OF PAGES

Aberdeen Proving Ground, Maryland 21005-5066 3514. MONITORING AGENCY NAME A ADORESS(l different fom Cotolling Office) IS. SECURITY CLASS. (of thls report)

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IS. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side it necear ad identify by block number)

Gun Muzzle Blast,Shock WavesBlast Wave ScalingDimensional Analysis "

*"7r*ACr (=0CAR diev aide2 0610 negor m ftdaWf9, by block (er

"' Until now, the peak energy efflux at the jet exit was considered the sig-nificant parameter in a scaling approach to estimate the peak overpressure, time- %

of-arrival, and positive phase duration from guns and shock tubes. The result-ing predictions for the peak overpressure and timeofzarrival were satisfactorybut the positive phase duration prediction was poor. This predicted value ofthe positive phase duration is used with the peak overpressure prediction to ob-tain an estimate of an important quantity: the impulse. Here we investigate the

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characteristic exhaust decay time for the energy efflux at the jet exit as apossible additional significant parameter that might be used to improve pre-dictions for the impulse. Numerical simulation was used to establish that theimpulse value depends upon this parameter. Comparison between simulation andexperiment is satisfactory. This additional parameter was used to correlatethe available impulse data. It was determined that the additional parametersignificantly improves the prediction capability of the scaling method for pre-dicting the impulse. An idealized wave form together with the predicted peakoverpressure can be used to obtain an estimate of the positive phase duration.This approach yields less satisfactory agreement with the duration data butthis fact is relatively unimportant since the impulse is the quantity of im-portance. 3 - / '

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TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS ........................... .................... 51%'

I. INTRODUCTION ..................................... 7

II. BACKGROUND AND SCALING DEVELOPMENT ........... 8

III RESULTS AND DISCUSSION ...................... ............ 12

IV. SUMMARY AND CONCLUSIONS ........... o................................. 15 .1

REFERENCES ....... .. . ... . . ... .o. ......... ......... 29

DISTRIBUTION LIST. ................................................... 31

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LIST OF ILLUSTRATIONS1P

Figure Page

1 Positive Phase Duration Data from 30mm Firings and AccompanyingCurve Fit of Reference 6 .............................................. 16

2 Positive Phase Duration Data Delineated into Subgroupings ............. 17

3 Energy Efflux versus Nondimensionalized Time for 30 mm WECOM Cannonwith Exponential Approximation ........................................ 18

4 Blast Wave Overpressure versus Time for Different Distances from theMuzzle. Simulation of 30mm Cannon with 40 Caliber Barrel Length ...... 19

5 Waveform Comparison for Different Energy Efflux Decay Times ........... 20

6 Positive Phase Duration versus Distance from Muzzle for DifferentEnergy Efflux Decay Times............................................. 21

7 Dimensionless Impulse versus Distance from Muzzle for DifferentEnergy Efflux Decay Times ............................................. 22

8 Impulse versus the Energy Efflux Decay Time ........................... 23

9 Comparison of Simulated and Experimental Values for the Impulse ....... 24

10 Scaled Impulse Data versus Scaled Distance for 30mm Cannon ............ 25

11 Reduced 30mm Impulse Data Compared with Present Prediction ............ 26

12 Reduced Positive Phase Duration Data Compared with CorrespondingPrediction. The Prediction Utilized Predicted Peak Overpressure andthe Friedlander Waveform .............................................. 27

13 Comparison of Two Predictions for the Positive Phase Durationversus the Polar Angle. Reference 7 Prediction was Derived fromShock Tube Data ... ... .. ... ... ... . .. . .. . .... 28 "-

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I. INTRODUCTION

Guns and shock tubes under operation generate large pressure waves thatcan be harmful to nearby personnel and equipment. Industry and the Armyemploy these devices extensively and need to be acquainted with the salientcharacteristics of these blast waves. For these devices, the magnitude of theenergy efflux from the tube exit and its history determine the characteristicsof the blast wave and the associated gas-plume structure. Two principal char-acteristics of blast waves are the peak overpressure and the impulse. The

impulse is the time integral of the pressure at a field point of interest.The positive phase duration is another often-used characteristic; it is thetime duration for the positive pulse of a blast wave to pass over the fieldpoint. If we know the peak pressure and the positive phase duration value,

the impulse for the wave can be estimated easily by assuming a simple expres-sion for the pressure as a function of time.

Scaling theory is used extensively to predict blast wave characteristics;this approach yields simple but powerful methods. The scaling theory for in-stantaneous-energy blast waves1 is well known and accepted. Reynolds2 used apoint blast scaling theory developed by Hopkinson 3 to treat gun-generatedblast waves. Later, Westine4 developed a scaling law from point blast theory

but, in addition, introduced the length of the barrel as an important param-eter. This modification permits his method to be applied successfully over avariety of weapons.

Smith,5 and more recently, Fansler and Schmidt, 6 have predicted the blastwave characteristices from gun weapons by applying scaling theory to blastsgenerated by constant energy efflux conditions. Schmidt and Duffy7 utilizedthe oreceding reference 6 to predict the blast characteristics from shocktubes. Smith5 and Fansler and Schmidt6 selected the peak energy deposition

1. Baker, W.E., Explosions in Air, U. Texas Press, Austin, 1973.

2. Reynolds, G.T., "Muzzle Blast Pressure Measurements," Report No. PMR-21,Princeton University, Princeton, NJ, April 15, 1944.

3. Hopkinson, B., British Ordnance Minutes, 13565, Royal Army Research DefenceEstablishment, Fort Halstead, England, 1915.

4. Westine, P., "The Blast Field About the Muzzle of Guns," The Shock and Vibra-tion Bulletin, Vol. 39, Pt. 6, pp. 139-149, March 1969.

5. Smith, F., "A Theoretical Model of the Blast from Stationary and Moving Guns,"ADPA 1st International Symposium on Ballistics, Orlando, FL, 13-15 November1974.

6. Fansler, K.S., and Schmidt, E.M., "The Relationship Between Interior Ballis-tics, Gun Exhaust Parameters, and the Muzzle Blast Overpressure," AIAA/ASME3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, St.Louis, Missouri, 7-11 Jone 1982.

7. Schmidt, E.M., and Duffy, S.J., "Noise from Shock Tube Facilities," AIAAPaper 85-0049, January 1985.

7

rate as the significant parameter. With a steady energy deposition rateassumed in the dimensional analysis, the nondimensionalized quantities of peakpressure, time-of-arrival and impulse depend only upon the distance divided bythe scaling length. For a given polar angle as measured from the axis, thisscaling length for the blast wave varies as the square root of the peak energydeposition rate. However, the blast waves are highly directional, with theirstrengths decreasing with increasing polar angle from the forward axis direc-tion. The form for the variation of peak overpressure with angle from theaxis is obtained from moving charge theory;s it possesses one free parameterthat determines how rapidly the overpressure falls off with the increase ofpolar angle. The assumed formulation for the peak overpressure generates twoother free parameters. One parameter is the exponent of the distance from thegun muzzle; it determines how fast the peak pressure falls off withdistance. The other parameter is the constant coefficient of the scalingexpression. The available data are then used with the given scaling relationto perform a least squares fit that establishes values for the three free

* parameters. Smith5 applied the scaling approach to a particular weapon.However, Fansler and Schmidt 6 assumed the resulting scaling expressions were

- universally applicable when using the initial energy-deposition rate as thecharacteristic value. The Fansler and Schmidt6 model successfully predictsthe peak overpressure and times-of-arrival for a variety of gun weaponsystems. On the other hand, the method predicts that the positive phaseduration increases with distance in a completely different fashion than forthe well-studied instantaneous energy deposition explosions. However, theoriginal generating method for the blast wave should have less relevance tothe behavior of the blast wave as it travels away from its origin. Thus, forthe larger distances, the behavior of the positive phase duration for the twocases should be quite similar.

It is the objective of this work to provide an improved prediction schemefor the impulse by modifying the scaling approach of Fans!er and Schmidt. 6

From the data already accumulated, it appears that the energy-deposition ratedecay affects the impulse. However, the waveforms obtained by experiment havesignificant amounts of noise generated by possible gage vibrations and turbu-lence; perhaps, the amount of turbulence can affect the impulse magnitude.The turbulence magnitude may in turn depend upon some other significant param-eter such as the velocity of the projectile, etc. Thus, it is difficult todetermine from the data whether the positive phase duration depends pre-dominantly upon the energy efflux decay rate. To study this relationship, weuse the Euler finite difference code, DAWNA, that calculates the blast wavefield along the boreline of a gun.8 It uses shock fitting, takes into accountthe decay rate of the energy efflux quantity, and executes much faster than anumerical axisymmetric scheme.

I. BACK'GROUND A449 SCALING DEVELOPMENT

As mentioned before, Fansler and Schmidt6 assumed that the blast wave

depended on the energy efflux. The functional dependence of the peak over-

8 Erdos, J., and del Guidice, F., "Calculation of Muzzle Blast Flowfields,"AIAA Journal, Vol. 13, No. 8, August 1975, pp. 1048-1056.

8

4

pressure is expressed as

P = P(rp.,a.,dE/dt) . (1)

Here r is the distance from the center of the explosion, p. is the ambient

density, a= is the ambient sound speed, and dE/dt is the characteristic valuefor the rate of energy deposition. For a spherical blast, we assume the idealequation of state; dimensional analysis yields a scaling length:

I -,(dE/dt)/(p-, _a.) (2)

and a nondimensionalized peak overpressure:

l= P/p= (3)= F (rlt)•

In this report the overbarred quantity is defined as the quantity non-dimensionalized by the significant quantities for the scaling analysis. Themomentum of the propellant gas results in the strength of the blast wave de-creasing markedly with polar angle. Smith 5 noted the similarity betweenmoving-charge blast waves and gun blast waves. From moving charge theory, heobtained a scaling length, X', for muzzle blast,

x'I = v cose + (1 - P2 sin 1/2 (4)

Here, u is the momentum index and is a measure of the directionality of theblast. It is a free parameter that is found by a least squares fit to experi-ment. With Equation (4), the resultant form of the overpressure relationshipis assumed as,

= K (r/,-)n (5)

with the values of K=2.4, n=-1.1, and P=0.78 giving the best fit to the peakoverpressure data. These data were collected from a variety of guns.6 Theresulting expression, when cast in the interior ballistic formulation and whensome simplifying assumptions are made, resembles the form obtained by Westine.4

A further consequence of the dimensional analysis is that the positivephase duration should have the following functional dependence:

T = T a./," (6)

T z (r/x')

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,' . .. \, ; .., ,.. ,., ;.- - . .- .'..'.-'..',.'. '... .. ... ' .' - . • . .. • ., . . .- .- . ., .- . - ,. . . *-

Because of the general appearance of the 30mm data, 6 we used a linear fit toobtain the predictive curve forT.6 Figure 1 shows the fitted curve with thecorresponding data. There is considerable scatter of the data around thefitted curve. The data also do not show any tendency to go toward the far-field asymptotic relation; i.e., the positive phase duration increasesasymptotically as the square root of the log of the distance divided by someconstant. Figure 2 shows the 30mm data more clearly delineated with theparameters being the angular position and firing conditions. The impulsecould only be obtained directly from the set of experiments that was used toproduce the results of Figure 2. Only data from these experiments were usedto obtain the results of the present report. It is noted that some data sub-groups are clustered so that there is not much overlap between the sub-groups. These subgroups correspond to different polar angles or differentvalues of V/X. It is desirable to have substantial overlap of the subgroupsto improve the reliability of the data and thus the derived results. Thiscould have been accomplished by collecting data for larger distances. How-ever, the facilities and instrumentation did not allow data acquisition atthese larger distances.

Because the linear behavior of the data at the larger distances isclearly incorrect and the data are not well correlated by the curve fit, wedecided to searc.i for an additional significant parameter. A possiblesignificant parameter is the characteristic emptying time of the propellantfrom the gun barrel. As noted before, the peak overpressure for a givendistance and polar angle increases slowly, but insignificantly for mostpractical purposes, with increasing emptying time. However, the impulse mayhave a stronger dependence on the emptying time of the barrel.

A dimensional analysis performed with a characteristic emptying time, a,; as a significant variable yields the i group,

8 ' (a a.)/ • (7)

Corner9 discusses the barrel emptying time and its relationship with easily* observe( parameters. To a first approximation,

L/Vp (8)

With the proportionality substituted into Equation (7), the new working irgroupcan be defined as

0 = (a.L)/(WVp) . (9)

9. Corner, J., Theory of the Interior Ballistics of Guns, John Wiley, hY150.

10

1. ...... ....

This new parameter can be interpreted as the ratio of the emptying time of thetube to the characteristic time for the development of the blast wave. Weshall call the new parameter the nondimensional emptying time. Figure 3 showsthe normalized energy efflux versus the nondimensional time divided by thenondimensional emptying time constant for a 30mm cannon, or equivalently, thetime nondimensionalized by L/V If the first part of the emptying process is

deemed more important than the latter parts, we can assume an exponentialfunction to fit the first part of the data. This approximation to the curveshows that the efflux data values are high compared with the fitted functionfor the longer times. The approximation shows that the exponential emptyingtime constant is a = (L/Vp)/1.68. Thus, the exponential emptying time

constant divided by L/Vp is 0(1), which agrees with intuition. With the

nondimensional emptying time now assumed as a significant 7r grouping, thefunctional forms for the impulse and positive phase duration are

7 T(r/l,a), (10)

T = I a 0/(-p) (11)= T (r/97,B).

In the present paper, we have treated the impulse as the primary param-eter since it is used directly to assess vulnerability of actual or contem-plated structures. Previously, an assumed form for the positive phase dura-tion was correlated with available positive phase duration data and theimpulse was then obtained using the most primitive form of the Friedlanderwaveform,1 which is,

(p-p.)/p [1-(t-ta)/] exp-[(t-t a)/T] . (12)

Here, ta is the time of arrival of the blast wave front. However, the prior

approach introduces a source of inaccuracy in the predictive method becausethe assumption of a specific waveform is an approximation.

As mentioned in the introduction, noise from turbulence and other sourceswere superimposed upon the waveforms. Such factors introduced difficulty inascertaining that the emptying time was a major significant variable. More-over, the limited range of distances over which the data were taken also makesit difficult to assert what the significant variables are with confidence. Toisolate the effect of the emptying time from other possible significant param-eters, we use numerical simulation. We chose the DAWNA code,3 which computesthe flow properties of the blast wave along the gun boreline. Although themethod calculates the flow properties along the centerline, by the assumptionsof the scaling approach, the results are applicable to the gun blast for arbi-trary polar angle. In the jet plume portion, the property distribution of asteady jet is assumed along the centerline and the shock layer between theMach disc and the blast wave front is computed with a finite differencemethod. The discontinuities are obtained using a shock fitting technique.

14

The method executes rapidly compared to an axisymmetric code and the positionof the discontinuities are determined exactly whereas shock capturing schemesportray discontinuities as more or less steep rises or falls in the calculatedgasdynamic quantities.

III. RESULTS AND DISCUSSION

The simulation performed was for the 30mm cannon firing the projectile at572 m/s with a peak pressure of 8600 kPa. These conditions are for one of thefiring conditions used in an earlier study.10 To investigate the relationshipbetween the dimensionless emptying time and the impulse, the value of a wasvaried from 1.37 to infinity, or equivalently, the barrel length was variedfrom 10 calibers to infinity. For a 40 caliber length barrel, the energyefflux history is shown in Figure 3. As discussed before, the time is pro-portional to the barrel length. Figure 4 shows overpressure versus time atdifferent distances from the muzzle for the above conditions. The valueof 8 is 5.47 or equivalently, the barrel length is 40 calibers. The wavegenerally resembles waves generated by instantaneous energy explosions.Figure 5 shows calculated waveforms with various barrel emptying times for adimensionless distance of 4.54 calibers from the muzzle. The waveforms forlarger emptying times result in larger values for the positive phase dura-tions. Furthermore, the shape of the wave does not maintain geometric oraffine similarity as the emptying time is increased. Thus, the similaritybetween the waves generated by instantaneous energy explosions and waves forfinite energy explosions should become weaker as the dimensionless emptyingtime increases. In fact, for this position, the positive phase duration forthe barrel of infinite length is longer than for the times calculated. Ineffect, the jet appears to be sustaining a positive pressure at some fieldpositions, as one might intuitively expect.

The positive phase duration versus the distance from the muzzle for dif-ferent values of the dimensionless emptying time is shown in Figure 6. Forfinite values of the emptying time, the positive phase duration at first in-creases rapidly and then starts to level off. This behavior occurs since atearly times the blast wave strength is large and the front of the wave thentravels at speeds appreciably greater than the speed of sound while the partof the wave where the overpressure is zero is traveling near the speed ofsound. As the wave travels from the muzzle, the peak overpressure decreasesand the wave front speed approaches the ambient sound speed. In the asymp-totic limit, the positive phase duration involves a logarithmic term. Forconstant energy efflux, the positive phase duration increases rapidly withdistance to very large values, as was noted from Figure 5.

Figure 7 gives the simulated impulse as a function of the distance fromthe muzzle for various values of the dimensionless emptying time. The impulseappears to decrease rapidly which we should expect since the overpressure is

10. Fansler, K.S., and Keller, G.E., "Variation of Free-Field Muzzle Blast witth

Propellant Type," ADPA 6th International Symposium on Ballistics, Orlando,

FL, OctobJer +.-12

rUK'

decreasing more rapidly than the inverse power of the distance and the posi- IItive phase duration is increasing relatively slowly. Figure 8 shows that theimpulse increases slowly but significantly with the barrel exhaust time.Figure 9 shows a comparison between the simulated values of the impulse andsome experimental values for comparable values of the dimensionless emptyingtime. These data were obtained from the primitive waveform data for anearlier study.10 The utilization of this additional parameter produces amarked improvement over the original predictive model of Fansler and Schmidt. 6

Although the comparable emptying times are smaller for the simulation, theypredict higher values for the impulse. The simulated curves also show asteeper decline of the impulse with distance but this would be expected sincesimulations predict a steeper decline in peak overpressure than actuallyoccurs. The reason for the steeper decline is not known. Considering thatthe simulation is based on a model that is a gross simplification of themuzzle blast flow, the agreement is quite good.

The complete data set"0 that was used in seeking a correlating relation-

ship with the nondimensional emptying time is shown in Figure 10. The datacover a range over the nondimensional time from 3.23 to 32.3 which does notcompletely encompass the ranges occupied by gun weapons. Neverthelcss, a cor-relation was sought with extrapolation to these ranges that would hopefullynot result in large predictive errors. Further available data can later beadded to yield an improved prediction. It was decided to employ a simple formdevoid of any logarithmic expressions that the impulse might be tending toasymptotically. We have no data for performing a least squares fit in the farfield. The nondimensional impulse was assumed to have a form such that whenthe data were fitted and the free parameters determined, -

I = 0.50 B0.2 (r/-') " 0.6 (13) .%~

This form can easily be understood and used and shows that the impulse variesas a weak power law function of the barrel exhaust time and is consistent withhow the simulated values of the impulse vary with the efflux decay time. Aleast squares fit was also attempted with the addition of the polar angle asan explicit variable but very little improvement in the correlation wasobtained.

To display all the results on a plot, the function T must be transformedto a function depending on only one variable. Dividing T by the last factorin Equation (13), one obtains the reduced value of the impulse, Ir' that is no

longer dependent on the nondimensional emptying time. Figure 11 shows thereduced impulse data together with the prediction. The scatter of the reduced

data is significantly diminished by utilizing the barrel exhaust time in thecorrelation. Of course, some of the scatter can be attributed to random vari-ations. Nevertheless, we have need of a larger data set with measurementsperformed for longer distances from the muzzle.

Now that we have developed a predictive expression for the more importantquantity, the impulse, we can return to the positive phase duration and inves-tigate whether an adequate predictive expression can be easily obtained. Ofcourse, from Figure 5 we should expect that the impulse would not vary lin-

13

... . . . . ..

early with the positive phase duration. If we assume the Friedlander rela-tionship as given in Equation (12), a very simple relationship exists betweenthe nondimensional impulse and the nondimensional positive phase duration,

T = P T/e . (14)

Utilizing the expression forT in Equation (13) and the expression for P asgiven in Equation (5), we find by substituting into Equation (14),

= .5 0.2 (r/)0. 5 (15)

As before with the impulse, the dimensionless positive phase duration is* transformed to a function of the nondimensional distance. The positive phase

duration data are likewise divided by 0 ' 2 to obtain a reduced form. Thecomparison between the predictive curve and the reduced data is shown inFiqure 12. The data trend and the predictive curve have different slopes. Itappears that a more complicated wave shape than is possible from Equation(12) would be needed to generate excellent predictions of the positive phaseduration. However, attempts to obtain better agreement would seem to be

"" wasted effort since with data being digitized and processed with computers,the impulse can easily be directly determined for a wave.

Although the data used here were obtained from gun weapons, the resultsshould be applicable to any device that produces a jet flow with decayingenergy efflux. Schmidt and Duffy7 obtained pressure data in the field ex-ternal to the exit of the shock tube. They did not obtain the impulse butthey did measure the positive phase duration. They found that for r heldconstant:

T ~ exp(0.25 cose). (16)

Using Equation (15) and Equation (9),

~ (i/L) 0.3 (17)

A comparison of the two expressions is shown in Figure 13 and yields fairagreement even though the simple Friedlander waveform is used.

14

* • 2 . .- Ap . . . . . - ° . ° .- - -• . • . ° . . - . .-. -- - - . .. . . - -° - ,* .-.. . . . .

IV. SUMMARY AND CONCLUSIONS

An older predictive scheme for blast waves generated from gun weaponsthat is based on a scaling approach has not produced entirely satisfactoryresults. For example, this older model, which utilizes the peak energy de-position rate as the significant parameter, predicts that the positive phaseduration increases linearly with the distance from the jet exit. However, forthe well-studied explosions that are generated by instantaneous energy de-position, this sort of behavior does not exist. For these explosions, thepositive phase duration at first increases steeply with the distance but therate of increase with distance falls off rapidly as the wave travels away fromits origin. It would seem that much the same behavior should exist for blastwaves generated by jet flows that exit from gun tubes or shock tubes. Thepuzzling linear relationship between the positive phase duration and thescaled distance from the jet exit could be caused by neglect of a significantparameter. A possible significant parameter could be barrel exhaust time forthe energy efflux passing the exit plane. To test this possibility, weemployed a numerical simulation scheme that calculates the fluid dynamicquantities along the boreline. Although the simulation scheme is limited tothe boreline direction, this is not a major impediment since the currentscaling approach allows application of the results to all polar angles. Thenumerical scheme also executes very quickly and allows for isolation fromturbulence and other phenomena occurring in the actual gun blast flow.

The simulation results show that the impulse increases with the decaytime of the energy efflux. Moreover, comparisons of experiment data withsimulation results show a similar dependence of the impulse upon the decaytime of the energy efflux. Thus, it is felt that the barrel exhaust time is asignificant parameter for improving the correlation of the impulse data. Wecorrelated the data utilizing the new variable and obtained a power law depen-dence of the impulse upon the nondimensional energy efflux exhaust time. Thepredicted impulse increases at a slower rate for the larger distances, as itshould. We can obtain corresponding positive phase duration values by usingthe most primitive Friedlander relation together with the predicted peakoverpressures to construct idealized waveforms. This approach generates asimple expression for the positive phase duration. Comparison with the phaseduration data yields different slopes and fair agreement. It is concludedthat the positive phase duration prediction should only be used when there areno impulse data to compare with. A case in point is the shock tube resultsobtained by Schmidt and Duffy,7 that had only the positive phase duration datareadily available. The results of the present prediction agree reasonablywell with the shock tube results even though we have used the simpleFriedlander relationship.

In conclusion, the impulse given to nearby structures by guns or shocktubes can now be more accurately predicted in a range of distances wherepossible injury can result to personnel and equipment. This relationship isnot applicable to very large distances from the gun or shock tube. Data havenot yet been collected for correlation to these distances and the presentfunction does not contain a logarithmic expression that is essential for theasymptotic form.

15

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REFERENCES

1. Baker, W.E., Explosions in Air, U. Texas Press, Austin, 1973.

2. Reynolds, G.T., 'Muzzle Blast Pressure Measurements," Report. No. PMR-21,Princeton University, Princeton, NJ, April 15, 1944.

3. Hopkinson, B., British Ordnance Minutes, 13565, Royal Army Research DefenceEstablishent, Fort Halstead, England, 1915.

4. Westine, P., "The Blast Field About the Muzzle of Guns," The Shock andVibration Bulletin, Vol. 39, Pt. 6, pp. 139-149, March 1969.

5. Smith, F., "A Theoretical Model of the Blast fram Stationary and MovingGuns," ADPA Ist International Symposium on Ballistics, Orlando, FL,13-15 November 1974.

6. Fansler, K.S., and Schmidt, E.M., "The Relationship Between Interior Ballistics,Gun Exhaust Parameters, and the Muzzle Blast Overpressure," AJAA/ASME 3rd JointThermophysics, Fluids, Plasma and Heat Transfer Conference, St..Louis, Missouri,7-11 June 1982.

7. Schmidt, E.M. and Duffy, S.J., "Noise fxn Shock Tube Facilities,"AIAA Paper 85-0049, January 1985.

8. Erdos, J., and del Guidice, F., "Calculation of Muzzle Blast Flowfields,"AIAA Journal, Vol. 13, No. 8, August 1975, pp. 1048-1056.

9. Corner, J., Theory of the Interior Ballistics of Guns, John Wiley, NY,1950.

10. Fansler, K.S., and Keller, G.E., "Variation of FreLe-Field Muzzle Blast withPropellant Type," ADPA 6th International Symposium on Ballistics, Orlando,FL, October 1981.

29

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