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AIAA 96­3020

CFD APPROACH TO FIREARMS SOUND SUPPRESSOR DESIGN M. Keith Hudson* and Chris Luchini[ Department of Applied Science University of Arkansas at Little Rock, Little Rock, Arkansas J. Keith Clutter] and Wei Shyyw Department of Aerospace Engineering, Mechanics & Engineering Science, University of Florida, Gainesville, Florida

Abstract

Suppression of muzzle blast is important in both large and small caliber gun designs. Key goals in the case of small caliber systems are the reduction in the incidence of hearing loss due to the acoustic signal and signature reduction for military applications. Various devices have been used to reduce the muzzle blast and the design of these devices have relied heavily on experimental investigation. The current study evaluates the utility of computational models in the design of suppressors for small caliber guns. Experimental measurements are made for a representative suppressor design and simulations are performed to determine the level of model sophistication needed to correctly predict the effects of the device. The current simulations correctly capture both the levels and characteristics of the acoustic signal generated by the bare muzzle and suppressor configurations. These findings support the use of computational models in the suppressor design process.

dertaken [4, 5, 6] but have been limited primarily to large caliber gun systems. In the case of small caliber guns, suppressors have been widely used as clandestine devices in sniper and other roles in warfare to avoid detection of the shooter. While this role has been widely accepted for many years other applications of suppression are being sought, particularly to reduce the acoustic pressure levels from small arms firing to address hearing loss disability. Interestingly, while suppression for hearing loss reduction has received some study, there has been little reported in the open literature over the many years that these devices have seen use. This is most likely due to strict US regulation of these devices in civilian applications. As in the case of the large caliber suppressors, the design process for the suppressors has depended heavily on experiments and a cut­and­try procedure. Unlike the large caliber work, no significant computational effort has been undertaken. Therefore, the goal of the current study is to determine the applicability of computational tools developed for the large caliber suppressors to the small caliber suppressors. Of primary concern is the scaling of the blast phenomena and the identification of the driving physics which dictates the peak overpressures and pressure signals. These two factors are key to the acoustic signature of the suppressor and need to be captured by any computational code to be used for suppressor design. This report summarizes the initial experimental and computational investigation into suppressors for 22 and 38 caliber / 9 mm guns. The experimental effort tested a commercial suppressor as well as a cylindrical baffle design used to evaluate the computational code. The remainder of this document first discusses the experimental details and highlights some of the predominate physical occurrences identified. Next the computational model is reviewed and the simulations for the cylindrical baffle suppressor are presented and discussed. Conclusions are then drawn as to the utility of computational codes in small caliber suppressor design and the driving physics behind the acoustic signal.

Introduction

Devices for the suppression of overpressures from firearms have been known and utilized for some time dating back to the work of Maxim around the turn of the century [1]. Currently, suppressors are used on both large and small caliber guns for somewhat different purposes. In the case of large caliber guns, the primary goal of overpressure suppression is to reduce the effects of blast on structures and supporting vehicles. The design process of the suppression devices has relied heavily on experimental work and the development of empirical databases [2, 3]. Some computational efforts have been un* Associate Professor, Member AIAA. [ Research Associate, currently at NASA Jet Propulsion Lab ] Doctoral Student, Member AIAA. w Professor and Chairman, Associate Fellow AIAA. Copyright E 1996 by M. Keith Hudson. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

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Experimental Investigation 1. Experimental Setup and Description

Firearms suppressor data collection requires that the researcher have a sound insulated laboratory with adequate backdrop for projectile containment, or have the ability to set up on an outdoor range which has adequate facilities to support the planned experiment. A suitable range has been located which offerers a sheltered area with utilities, but provides an adequate acoustic environment to make sound measurements. All testing has been performed with the instrumentation sheltered from direct sunlight, but with the firearms muzzle and microphone located just outside of the shelter to avoid direct sound reflection effects on the collected data. Figure 1 shows the general layout of the equipment and tested firearm for all experimental trials. The equipment used includes a Competitor Corp. 38 Special caliber action for all nominally 38 caliber / 9 mm testing and a AMT Lightning rifle for all 22 LR testing. Both actions have been modified to allow fitting of a commercial suppressor shell, utilizing a GEMTECH Model Vortec 9 for 38 / 9 mm and a Vortec 2 for all 22 LR testing. Barrel length on the Competitor action is 10 inches while the 22 rifle has a length of 20 inches. The cylindrical baffle suppressor dimensions are given in figure 2. Handloaded ammunition has been used in the 38 / 9 mm unit consisting of a 160 grain Speer jacketed bullet in a 38 Special casing, over 8.6 grains of Alliance Blue Dot Powder. The 22 LR has used commercially available CCI Blazer brand ammunition. During firing, the 38 / 9 mm unit is held on a sandbag, while the 22 rifle is shoulder fired in the normal manner. Care is taken to ensure the same relative alignment of the pressure gages for each firing. Acoustic data is collected using a Bruel and Kjaer 4135 condenser microphone powered by a 2801 power supply. Calibration data indicated that this unit is accurate to 100 KHz and provides an output of 3.39 mV/Pa. The microphone is positioned upright (pointed up) on a tripod and positioned between 3 and 20 inches from the muzzle. The firearm is then positioned to a point parallel to the microphone, and then pulled back up to 10 inches from the microphone to establish a grid of measurements (Table 1). The microphone is read by a LeCroy Model 9400A, 175 MHz 8­bit digital storage scope. Computer readouts of the sound tracings during firings are not available so peak data is recorded by hand. If there appeared to be two major sound peaks, each peak is recorded. Measurements from three firings are made at each gage position. Firings are made with the bare muzzle in all positions, followed by a similar set of firings with the suppressor attached. For all experimental firings, the suppressors consisted of a right circular cyl-

inder body with one copper baffle held in place one third of the distance down the suppressor body by aluminum spacers (Figure 3). Limiting firing has been carried out using the commercial suppressor on the 22 to show the cylindrical suppressor to be used in the computational code evaluation produce similar pressure reductions.

2. Experimental Results and Discussion

All the experimental measurements are presented in Table 2 where ``Sup" denotes the cylindrical baffled suppressor and ``Com" the commercial suppressor. Scope traces from the unsuppressed firearms show a single high­intensity peak with only minimal ringing type peaks seen over the rest of the measurement period. This of course correlates with the sharp, high­intensity crack heard by the ear upon firearms discharge. For the positions further from the muzzle the sound is seen to diminish with distance from the microphone, as would be expected, and the tracing pattern remains essentially the same except for the overall intensity changes. Scope traces for the firearm firings using the cylindrical baffle suppressor show a characteristic intensity spreading. The large single peak seen with the bare muzzle is gone, replaced typically by a set of peaks of similar intensity, often by two peaks of almost the same amplitude especially in the 38 / 9 mm data. The values of the two peaks are given in Table 2 and are denoted with the 1 and 2 following the suppressor designation. Also for the suppressor configuration, the smaller peaks which appear as ringing type peaks in the bare muzzle tests are relatively larger when compared to the peak signals. This is in agreement with the suppressor acting to "spread" the discharge sound out over a larger time scale, minimizing the peak value, but giving a longer duration to the overall sound. Audibly, this is heard by the authors as a change in the characteristics of the sounds to less of a crack and more of a loud hissing noise. Also, audibly, the sound is suppressed to a level where it is not objectionable to the un­protected ear. The control firings made using the full commercial set of baffles is noted to be very quiet, although still sounding like a firearm in general. Another distinct acoustic signal noted during testing is the sonic crack generated by the supersonic bullet. This is especially true in the 22 LR trials.

Computational Model 1. Governing Equations

The computational model used for the current study is a finite volume based computational fluid dynamics (CFD) code developed to aid in the design of gun muzzle devices. The governing equations for the gun blast problem are the full Navier­Stokes equations for a multi­species chemically reacting flow. The current study focuses on the inviscid and real gas aspects of the

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problem to determine their relative role in the generation of the acoustic signature. Therefore, the equations to be solved are the Euler equations for a multi­species flow with variable specific heats. When discretized, the equations take the form

able surface boundary conditions are applied to model the projectile's surface.

2. Gas Properties

The equation of state is derived by assuming the ideal gas equation is valid for each species and has the form [7]

NS

J Q ) J F) J G)J H+ 0 h t c

where the dependent variable and flux vectors are

(1)

P + rR uT

i+1

r ru rv rE Q+ , ra 1 L ra NS*1 rV ruV ) h xP rvV ) h yP G + V rE ) P ra 1V L ra NS*1V

rU ruU ) c xP rvU ) c yP F + U rE ) P ra 1U L ra NS*1U rv ruv rv2 1 v rE ) P ,H + y ra 1v L raNS*1v ,

ai Mi

(4)

The temperature during the calculations must be extracted from the conserved quantity of internal energy using the relationship

NS

e+

i+1

a ih i * P r

T

(5)

(2)

hi + h

o fi

)

TR

Cp idT

.

The dependent variable ai is the mass fraction of ith species with the fluid being defined by NS total species. Note that the mass fraction of the NSth species is not explicitly modeled since the total density is included and

NS

the relationship r +

i+1

ra i holds.

where TR is the reference temperature for the gas properties. The specific heat, Cpi, of each species is a known function of temperature. The representation of specific heats can vary from assuming they remain constant to a quadratic dependence on T. If a high order function is used for Cpi then an iterative procedure must be used to extract the temperature in each cell at each time level. Here, a compromise between efficiency and sophistication is made by representing Cp as a linear function of T over the temperature range to be encountered during the simulations. By using the linear relationship, the temperatures at each point in the field can be extracted by solving a simple equation while introducing the effects of varying specific heats.

The suppressor design to be simulated are axisymmetric and therefore the axisymmetric form of the equations is used and the effects of the third dimension are included by incorporating the source term H. The grid Jacobian J and the contravariant velocities are defined as

3. Fluid Dynamics Operator

The fluid dynamics aspects of the problem are modeled using an explicit schemes. To maintain second­order accuracy, the fluid dynamics operator must be second order and here a prediction­correction scheme is used of the form [8]

J + x cy h * x hy c U + c xu ) c yv . V + h xu ) h yv

(3)

Q * + Q n * Dt 2

(1) ) cF

hG

(1)

) Hi , j

n *

Q n)1 + Q n * Dt

with

cF

(2) ) cF

(2) ) Hi , j hG

(6)

The effects of the projectile are included in the simulation by making a constant velocity assumption and determining at each time interval the appropriate location of the projectile. The cells which contain the projectile are identified and an additional source term is added to denote the appropriate volumetric change and imperme-

+ F i)1 , j * F i*1 , j

2 2

hG + G

i , j)2

1 * G

i , j*1 2

(7)

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and where the superscripts * and n denote the time level at which the fluxes are computed and the superscripts (1) and (2) denote the spatial order of the numerical fluxes. Note the fluxes in c and h are computed at the cell faces and the axisymmetric source term is computed based on the cell average. The scheme used to define the inviscid numerical fluxes is the Steger­Warming flux vector splitting algorithm which has been extended to model multi­species flows [9]. The flux vector splitting algorithm decomposes the inviscid fluxes into non­negative (K+) and non­positive (K­) components based on the eigenvalues of the Jacobian A + the form

The above formulation gives K=F when k=c and K=G when k=h. For the multi­species chemically reacting flow, c is the frozen speed of sound where c 2 + g P r and g is the effective specific heat ration. As indicated in equation 7, the fluxes are evaluated at the cell faces and are either 1st or 2nd order representations. The flux at the face is a function of the states in the neighboring cells and can be symbolically represented by

F and likewise for G. The split fluxes take Q

(8)

F

i)1 , j 2

+ F ) QL

i)1 , j 2

) F * QR

i)1 , j 2

(12)

K " + l " 1K 1 ) l " 2K 2 ) l " 3K 3

where the eigenvalues are

If a 1st order spatial representation is used, then Q L 1 + Q i , j , Q R 1 + Q i)1 , j . To achieve

i)2 , j i)2 , j

l " k + 1 lk " |lk| 2 l1 + bk l2 + b k ) c| k| l3 + b k * c| k|

with

(9)

2nd order accuracy, a MUSCL approached is used in which cell­center values are extrapolated to the interfaces [10]. Also, to guard against the interpolation introducing any nonphysical extremes into the field in the region of large gradients, a limiter must be used. The formula for the neighboring states takes the form

QL

i)1 , j 2

+ Qi , j ) F* 1 , j i)

2

QR 1 i)2 , j

+ Q i)1 , j * F ) 1

(13)

i)2 , j

q k + k xu ) k yv ky ~ ~ k kx + x ky + | k| | k| | k| + k2 x ) k 2 y

The split flux components are

~

~

where the limiting function is (10)

l i)1 , j mmod DQ ) i)1 , j, DQ * i)1 , j i)2 , j 2 li , j F* 1 , j + mmod DQ * i , j, DQ ) i , j i)2 2 F) 1 +

(14) with

r ru rv K1 +

2 g*1 r ht * c g g*1 ra 1 L ra NS*1

DQ ) i , j + DQ * i , j +

(11)

2 Q i)1 , j * Q i , j l i)1 , j ) li , j 2 Q i , j * Q i*1 , j l i , j ) li*1 , j

(15)

r r u " k xc r v " k yc K 2,3 + 1 2g r h t " q kc ra 1 L ra NS*1

~ ~

Here the popular minmod limiter is used where

mmod [X, Y] + sign(X) max[0., min(|X|, Ysign(X))] .

(16)

Note l i,j , the cell­length, is used to provide weighting for nonuniform grid spacing. The same extrapolation procedure is carried out for the fluxes in h and can be performed on either the dependent or primitive variables. Previous investigations have shown that using primitive variables gives better performance for flows

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with strong shocks and this is the method used here [10].

4. Boundary Conditions

The present predictive code has been designed to model the launch phase of the ballistics problem and therefore, it is assumed that boundary conditions near the muzzle exit are known. This alleviates the need to recompute the interior ballistics phase for each computations which reduces the computational time when conducting design studies for muzzle devices. Typical boundary condition information needed includes temperature, pressure, and velocity time histories near the muzzle exit as well as the gun propellant used. This information can be obtained either from an interior ballistic code or from experimental measurements. For the current study, the simulations were carried out in parallel to the experiments so some assumptions had to be made as to the boundary conditions. The exact boundary conditions achieved during the experiments may vary somewhat from those assumed, however, the relative effects of the muzzle device should be evident in the simulations. The particular boundary conditions used for the simulations of the 38 / 9 mm are a peak pressure of 6,000 psi, peak velocity of 1000 fps, and a peak temperature of 2400 F. It is assumed that all quantities decayed to atmospheric conditions over a time period of approximately 4 ms. For the 22, the peak pressure is lowered to 2,000 psi but the remaining variables were kept the same. The simulations presented here model the flow field as a combination of three species, these being the O2 and N2 found in the ambient air and the gun propellant gas. The properties for oxygen and nitrogen are available in various sources [11]. The gun propellant is known to be composed primarily of the active agents CO and H2 as well as the inert N2 and to a smaller extent the combustion products H2O and CO2 resulting from the interior ballistic process. Therefore, the properties used for the gun propellant (F) are formulated to represent a mixture of CO and H2 and the boundary conditions imposed near the muzzle exit specify the mass fraction to be a F + .64 and a N2 + .36. These assumptions which simplify the gun gas composition are done to reduce the number of governing equations. Similar processes have been used previously with good results even when further combustion is included in the modeling [6].

acoustic signal. This data can also be used to determine if the inviscid and real gas effects being modeled are dominate players in the determination of the peak pressures and the acoustic signals. The data from the experiments and simulations are presented with respect to the gage location. The locations of the gages are given in table 1. The distances are measured from the exit of the muzzle in the cases with no suppressor and from the exit of the suppressor when it is used. A comparison between the simulated and measured pressures for the bare muzzle 38 / 9 mm is presented in figure 4 as well as data for the 38 / 9 mm with the suppressor present. The curves denoting the experimental measurements are fit to the average of the three firings made for each configuration and gage location. During the firing with the suppressor, two distinct peaks were measured by the gages and these are denoted wave 1 and wave 2 with wave 1 being the peak which arrived first. Likewise, the simulations showed the initial peak to be accompanied by a second peak or plateau (figure 5). However, in the simulations the larger of the two peaks always arrived first where as in the experiments the larger of the two peaks arrived second. This discrepancy may results from the assumptions about the projectile flight velocity since the interaction of the projectile with the pressure field as it is evolving in the suppressor can effect the resulting pressures. Previous studies [6] have shown that neglecting the projectile can affect the predicted overpressures and the same results would be expected if there is error in the projectile velocity. However, the simulated pressure levels agree quite well with the experiments and do indeed convey the effect of the suppressor in reducing the pressure and in turn the level of sound generated. The peak pressures from the simulation for the 22 caliber case are presented in figure 6 with the nomenclatural the same as earlier. The first observation is that even though the simulation captures the trend in overpressures for the bare muzzle case, the values are lower than those measured at all gage locations. This indicates either the pressure assumed for the boundary conditions in the simulation was somewhat lower than those achieved during the experiments or the inviscid non­ reacting flow model is not capturing some of the driving physics. It has been shown that by including the chemical reaction processes higher overpressures are seen in simulations for gun blast [6]. However, before adding reaction for the cases in the current study, a closer assessment of the true boundary conditions should be made. The simulations of the 22 with suppressor do capture the general trend of the baffle design producing lower pressures and in turn lower sound levels. However, the simulated peak pressure values are somewhat larger than the measurements for gages 3 and 6. Again it is believed

5. Results and Discussions

The only experimental data available for code evaluation is the peak pressures measured in the experiments. Therefore, the only judgement as to the utility of the computational code that can be made is whether the code correctly simulates the general effect of the suppressors in reducing the pressure levels and in turn the

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that some of the discrepancy is due to the assumed projectile velocity but further investigation is needed. Even given these regions of over prediction, the simulation does capture the effects of the baffle design in reducing the pressure levels and in turn the sounds generated. As in the case of the 38 / 9 mm with suppressor, the measurements for the 22 also showed a coupling of high pressure peaks. But here the variation in the magnitudes were much less and the larger of the two was not always the peak which arrived first. In the simulations, the predominate peak was followed by a lower peak or plateau in pressure (figure 7) much as the case for the 38 simulations. As mentioned earlier, when fired the baffle design generates a sequence of pressure waves emitted from the suppressor with magnitudes larger than the ringing noted in the bare muzzle case. This phenomena is also seen in the simulations and can be seen in Figure 8 which shows a pressure contour at one instance in time during the firing of the 22 with suppressor. The contour levels have been set to highlight the pressure spectrum around 1 atmosphere. Evident in the figure is a sequence of pressure pulses emitted from the suppressor. Points A,B, and C denote the peaks of the pulses where A is a pulse just being emitted while B and C are pulses which have traveled outward into the field. If the time evolution of the suppressor's internal flow field is viewed, it is evident that shocks are continuously reflecting off the face of the suppressor walls normal to the line of fire. This is most likely the driving force behind the pulsating pressure signature.

plications. To correct some of the discrepancies identified here in the prediction of pressure and sound generation, more attention should be paid to the projectile flight parameters with one option being to use the simulated pressures on the projectile to dictate its flight velocity. However, any increase to the model sophistication should be weighed against its robustness and efficiency for the task at hand. The current study does show the utility of computational modeling in the design process of suppressors which is needed to reduce the reliability on empirical databases and the expensive cut­and­try procedure.

Acknowledgements

The authors wish to thank Armond Tomany for work in modifying the firearms to accept the suppressor units and to Philip H. Dater, M.D., of GemTech Division of Gemini Technologies and Antares Technologies for supplying the suppressors used in this study.

References

[1] E.C. Ezell, Small Arms of the World, 12th Ed., Barnes and Noble, New York, 1993. [2] L. Stiefel, Gun Propulsion Technology, Vol 109 Progress in Astronautics and Aeronautics, AIAA, Washington D.C., 1988 pp. 183­259. [3] G Klingenberg, J.M.Heimerl, Gun Muzzle Blast and Flash, Vol 139 Progress in Astronautics and Aeronautics, AIAA, Washington D.C., 1992 pp. 197­338. [4] G.C. Carofano, ``Blast Field Contouring Using Upstream Venting," ARCCB­TR­93009, US Army Armament Research, Development and Engineering Center, March 1993. [5] G.C. Carofano, ``A Note On The Blast Signature of a Cannon," ARCCB­TR­92014, US Army Armament Research, Development and Engineering Center, March 1992. [6] J.K. Clutter, G. Abate, W. Shyy, & C. Segal ``Study Of Fast Transient Flow Phenomenon For Munition Application," AIAA Paper 96­0829. [7] J. Anderson, Hypersonic and High Temperature Gas Dynamics, McGraw­Hill New York, 1989. [8] R.J. LeVeque and H.C. Yee, ``A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms," Journal of Computational Physics, Vol 86, 1990, pp 187­210. [9] M.S. Liou, B. Van Leer, and J.S. Shuen, ``Splitting of Inviscid Flues for Real Gases," Journal of Computational Physics, Vol. 87, 1990 pp 1­24. [10] J.S. Shuen ``Upwind Differencing and LU Factorization for Chemical Non­equilibrium Navier­Stokes Equations," Journal of Computational Physics, Vol 99, 1992, pp 233­250. [11] Stull, D.R. and Prophet, H., "JANAF Thermochemical Tables," NSRDS­NBS 37, June 1971.

Conclusions

Many types of muzzle devices are used to reduce the overpressures generated during the gun firing process. An example of these type devices is the baffle configuration tested here. Both the experiments and simulations show such a design reduces the level of overpressures. The fact that the current simulations captures this phenomena infers that the reduction in sound by muzzle devices such as the baffle design are due in a large part to the inviscid aspects of the flow. This as well as the good comparisons with the measured peak pressures is encouraging to the engineer tasked to design muzzle devices since all these simulations have been carried out modeling only the inviscid and real gas aspects of the problem. Further accuracy can be achieved by including the chemical reactions and turbulence and this would be required to model muzzle flash. Also, phenomenon such as suppressor erosion would require some accounting for the particle loading and heat transfer to the walls. Any investigation into these phenomena should be accompanied with a more detailed model of the internal flow field to include the modeling of the turbulence. Further investigation is needed to determine to what level these aspects need to be modeled for engineering ap-

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Caliber 22 22 22 22 22 22 38 38 38

Gage 1 2 3 4 5 6 1 2 3

X (in) 0 3.5 7 0 5 10 0 5 10

Y (in) 7.5 7.5 7.5 10 10 10 10 10 10

Table 1. Placement of pressure gages for the experiments and simulations.

Cal 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 38 38 38 38 38 38 38 38 38

Y 7.5 7.5 7.5 7.5 7.5 7.5 7.5 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

X 0.0 3.5 3.5 3.5 7.0 7.0 7.0 0.0 0.0 0.0 5.0 5.0 5.0 10.0 10.0 10.0 10.0 0.0 0.0 0.0 5.0 5.0 5.0 10.0 10.0 10.0

Bare 1.0505 1.0604 1.0658 1.0621 1.0757 1.0749 1.0782 1.0387 1.0391 1.0366 1.0511 1.0532 1.0536 1.0501 1.0583 1.0600 1.0565 1.1500 1.1636 1.1670 1.1936 1.2105 1.1922 1.1704 1.1554 1.1626

Sup (1) 1.0074 1.0098 1.0119 1.0106 1.0123 1.0124 1.0124 1.0048 1.0055 1.0051 1.0092 1.0087 1.0075 1.0128 1.0109 1.0128 1.0300 1.0266 1.0203 1.0479 1.0392 1.0489 1.0610 1.0629 1.0658

Sup (2) 1.0125 1.0113 1.0135 1.0169 1.0130 1.0139 1.0056 1.0053 1.0043 1.0097 1.0098 1.0094

Com (1) Com (2)

1.0082 1.0071

1.0061 1.0053

1.0416 1.0281 1.0237 1.0542 1.0532 1.0523 1.0987 1.0799 1.0842

Table 2. Experimental measured peak pressures in atmospheres for all configurations.

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O­scope

pre­amp

Microphone (vertical)

y ­ distance

table

x ­ distance firearm sandbag suppressor

Figure 1. Schematic of experimental layout.

L L/3 Wi Di Center Line / Line of Fire De De .22 .38 L = 4.316" 6.373" Di = .749" .995" De = .263" .442" Wi = .25" .25" We = .36" .36"

We

Figure 2. Schematic of cylindrical baffle suppressors cross section and specific distances.

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Figure 3. Picture of the cylindrical baffle suppressor and 38 action used in the tests.

1.4 '38_bare.dat' '38_sup_wave_1.dat' '38_sup_wave_2.dat' '38.sim' '38_sup_wave_1.sim' '38_sup_wave_2.sim'

1.35

1.3

1.25

P (atm)

1.2

1.15

1.1

1.05

1 1 2 gage 3

Figure 4. Comparison of peak pressures from the experiments and the simulations for the 38 / 9 mm with and without suppressor.

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1.25 '38_bare' '38_sup' 1.2

1.15

P (atm)

1.1

1.05

1

0.95 0 0.2 0.4 0.6 0.8 1 time (~ms) 1.2 1.4 1.6 1.8 2

Figure 5. Simulated pressure time history at gage location 3 for the 38 with and without suppressor.

1.12 '22_bare.dat' '22_sup_wave_1.dat' '22_sup_wave_2.dat' '22.sim' '22_sup.sim'

1.1

1.08

P (atm)

1.06

1.04

1.02

1 1 2 3 gage 4 5 6

Figure 6. Comparison of peak pressures from the experiments and the simulations for the 22 with and without suppressor.

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1.07 '22_bare' '22_sup' 1.06

1.05

1.04

P (atm)

1.03

1.02

1.01

1

0.99

0.98 0 0.2 0.4 0.6 0.8 time (~ms) 1 1.2 1.4 1.6

Figure 7. Simulated pressure time history at gage location 2 for the 22 with and without suppressor.

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Scale : .5 ­ 3. atm (a)

(b) Figure 8. Simulated pressure contour at one instant in time for the 22 with suppressor. In (b) the scale has been set to highlight the pressure spectrum around 1 atm. Pressure peaks are denoted with A, B, and C.

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