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    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 in-

    vestigation. 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 simula-

    tions are performed to determine the level of model so-

    phistication needed to correctly predict the effects of the

    device. The current simulations correctly capture both

    the levels and characteristics of the acoustic signal gen-

    erated by the bare muzzle and suppressor configura-

    tions. These findings support the use of computational

    models in the suppressor design process.

    Introduction

    Devices for the suppression of overpressures from fire-

    arms have been known and utilized for some time dating

    back to the work of Maxim around the turn of the centu-

    ry [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 over-

    pressure suppression is to reduce the effects of blast on

    structures and supporting vehicles. The design process

    of the suppression devices has relied heavily on exper-

    imental work and the development of empirical data-

    bases [2, 3]. Some computational efforts have been un-

    * Associate Professor, Member AIAA.

    Research Associate, currently at NASA Jet Propulsion Lab

    Professor and Chairman, Associate Fellow AIAA.

    [

    ]

    wDoctoral Student, Member AIAA.

    Copyright E 1996 by M. Keith Hudson. Published by theAmerican Institute of Aeronautics and Astronautics, Inc.with permission.

    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, particular-

    ly to reduce the acoustic pressure levels from small arms

    firing to address hearing loss disability. Interestingly,

    while suppression for hearing loss reduction has re-

    ceived 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 regu-

    lation 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 ex-

    periments and a cutandtry procedure. Unlike the large

    caliber work, no significant computational effort has

    been undertaken. Therefore, the goal of the currentstudy 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 overpressur-

    es and pressure signals. These two factors are key to the

    acoustic signature of the suppressor and need to be cap-

    tured by any computational code to be used for suppres-

    sor 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 baffledesign used to evaluate the computational code. The re-

    mainder of this document first discusses the experimen-

    tal details and highlights some of the predominate

    physical occurrences identified. Next the computational

    model is reviewed and the simulations for the cylindri-

    cal baffle suppressor are presented and discussed. Con-

    clusions are then drawn as to the utility of computational

    codes in small caliber suppressor design and the driving

    physics behind the acoustic signal.

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    Experimental Investigation

    1. Experimental Setup and Description

    Firearms suppressor data collection requires that the re-

    searcher have a sound insulated laboratory with ade-

    quate 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 envi-

    ronment to make sound measurements. All testing has

    been performed with the instrumentation sheltered from

    direct sunlight, but with the firearms muzzle and micro-

    phone 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 equip-

    ment used includes a Competitor Corp. 38 Special cali-

    ber action for all nominally 38 caliber / 9 mm testing anda AMT Lightning rifle for all 22 LR testing. Both ac-

    tions have been modified to allow fitting of a commer-

    cial suppressor shell, utilizing a GEMTECH Model Vor-

    tec 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 cylindri-

    cal 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 en-

    sure 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 sup-

    ply. 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 tri-

    pod and positioned between 3 and 20 inches from the

    muzzle. The firearm is then positioned to a point paral-

    lel to the microphone, and then pulled back up to 10 in-

    ches from the microphone to establish a grid of measure-

    ments (Table 1). The microphone is read by a LeCroyModel 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 fir-

    ings 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 di-

    minish 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 spread-

    ing. The large single peak seen with the bare muzzle is

    gone, replaced typically by a set of peaks of similar in-

    tensity, 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 sup-

    pressor configuration, the smaller peaks which appear

    as ringing type peaks in the bare muzzle tests are rela-

    tively 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, mini-mizing 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 objec-

    tionable 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 genera-

    tion 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

    J Qt )

    J F

    c ) J G

    h ) J H + 0 (1)

    where the dependent variable and flux vectors are

    Q +

    rrurv

    rEra1

    LraNS*1

    , F +

    rU

    ruU ) cxPrvU ) cyPUrE ) Pra1U

    LraNS*1U

    ,

    G +

    rVruV ) hxPrvV ) hyPVrE ) Pra1V

    LraNS*1V

    , H + 1y

    rvruv

    rv2

    vrE ) Pra1v

    LraNS*1v

    .

    (2)

    The dependent variable ai is the mass fraction ofith spe-cies with the fluid being defined by NS total species.

    Note that the mass fraction of the NSth species is not ex-

    plicitly modeled since the total density is included and

    the relationship r + NS

    i+1

    rai holds.

    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

    J + xcyh * xhycU + cxu ) cyvV + hxu ) hyv

    . (3)

    The effects of the projectile are included in the simula-

    tion by making a constant velocity assumption and de-

    termining 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-

    able surface boundary conditions are applied to model

    the projectiles 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]

    P + rRuTNS

    i+1

    aiMi

    (4)

    The temperature during the calculations must be ex-

    tracted from the conserved quantity of internal energy

    using the relationship

    e + NS

    i+1

    aihi *Pr

    hi + ho

    fi ) T

    TR

    CpidT

    (5)

    where TR is the reference temperature for the gas prop-

    erties. 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 sophistica-

    tion 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, thetemperatures at each point in the field can be extracted

    by solving a simple equation while introducing the ef-

    fects of varying specific heats.

    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]

    Q* + Qn * Dt2 cF(1) ) hG(1) ) Hi , jn

    Qn)1 + Qn * DtcF(2) ) hG(2) ) Hi , j* (6)

    with

    cF + Fi)12

    , j* F

    i*12

    , j

    hG + Gi , j)1

    2

    * Gi , 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 thecell faces and the axisymmetric source term is com-

    puted based on the cell average.

    The scheme used to define the inviscid numerical fluxesis 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 Jaco-

    bian A + FQ and likewise for G. The split fluxes take

    the form

    K" + l"1K1 ) l"

    2K2 ) l"

    3K3 (8)

    where the eigenvalues are

    l"k+ 12lk" |lk|

    l1 + bkl2 + bk) c|k|l3 + bk* c|k|

    (9)

    with

    qk+ k~

    xu ) k~

    yv

    k~

    x +kx

    |k| k~

    y +ky

    |k|

    |k| k2

    x ) k2

    y+

    (10)

    The split flux components are

    K1 +g* 1g

    rrurv

    rht * c2g* 1ra1L

    raNS*1

    K2,3 +12g

    r

    ru " k~ xcrv " k~ ycrht " qkc

    ra1L

    raNS*1

    (11)

    The above formulation gives K=F when k=c and K=Gwhen k=h. For the multispecies chemically reactingflow, c is the frozen speed of sound where

    c2 + g Pr and g is the effective specific heat ra-tion.

    As indicated in equation 7, the fluxes are evaluated at

    the cell faces and are either 1st or 2nd order representa-tions. The flux at the face is a function of the states in

    the neighboring cells and can be symbolically repre-

    sented by

    Fi)1

    2, j+ F)QL

    i)12

    , j) F*QR

    i)12

    , j (12)

    If a 1st order spatial representation is used, then

    QLi)1

    2, j+ Qi , j , Q

    R

    i)12

    , j+ Qi)1 , j . To achieve

    2nd order accuracy, a MUSCL approached is used in

    which cellcenter values are extrapolated to the inter-

    faces [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

    QLi)1

    2, j+ Qi , j )F

    *i)1

    2, j

    QRi)1

    2, j+ Qi)1 , j *F

    )i)1

    2, j

    (13)

    where the limiting function is

    F)i)1

    2, j+

    li)1 , j

    2mmodDQ)i)1 , j,DQ*i)1 , j

    F*i)1

    2, j+ li , j

    2mmodDQ*i , j,DQ)i , j

    (14)

    with

    DQ)i , j +2Qi)1 , j * Qi , j

    li)1 , j ) li , j

    DQ*i , j +2Qi , j * Qi*1 , j

    li , j ) li*1 , j

    (15)

    Here the popular minmod limiter is used where

    mmod [X, Y] +sign(X) max[0.,min(|X|, Ysign(X))] . (16)

    Note li,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 beperformed on either the dependent or primitive vari-

    ables. 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 muzzleexit 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 experi-

    ments so some assumptions had to be made as to the

    boundary conditions. The exact boundary conditions

    achieved during the experiments may vary somewhatfrom those assumed, however, the relative effects of the

    muzzle device should be evident in the simulations.

    The particular boundary conditions used for the simula-

    tions 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 atmo-

    spheric 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

    N2found 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 combus-

    tion 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

    aF+ .64 and aN2+ .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 fur-

    ther combustion is included in the modeling [6].

    5. Results and Discussions

    The only experimental data available for code evalua-

    tion 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 sup-

    pressors in reducing the pressure levels and in turn the

    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 pres-

    sures and the acoustic signals. The data from the experi-

    ments 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 sup-

    pressor 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 larg-

    er 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 pre-

    dicted overpressures and the same results would be ex-

    pected if there is error in the projectile velocity. Howev-

    er, 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 cali-

    ber 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 overpressur-

    es for the bare muzzle case, the values are lower than

    those measured at all gage locations. This indicates ei-

    ther 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 chemi-

    cal reaction processes higher overpressures are seen insimulations for gun blast [6]. However, before adding

    reaction for the cases in the current study, a closer as-

    sessment 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 pres-

    sures and in turn lower sound levels. However, the simu-

    lated peak pressure values are somewhat larger than the

    measurements for gages 3 and 6. Again it is believed

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    that some of the discrepancy is due to the assumed pro-

    jectile 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 mea-

    surements for the 22 also showed a coupling of highpressure 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 pre-

    dominate peak was followed by a lower peak or plateau

    in pressure (figure 7) much as the case for the 38 simula-

    tions. 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 around1 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 suppressors internal flow field is viewed, it is evi-

    dent 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 pres-

    sure signature.

    Conclusions

    Many types of muzzle devices are used to reduce theoverpressures generated during the gun firing process.

    An example of these type devices is the baffle configu-

    ration tested here. Both the experiments and simulations

    show such a design reduces the level of overpressures.

    The fact that the current simulations captures this phe-

    nomena infers that the reduction in sound by muzzle de-

    vices 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 en-

    couraging to the engineer tasked to design muzzle de-

    vices 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 includingthe 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 ac-

    companied 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 lev-

    el these aspects need to be modeled for engineering ap-

    plications. To correct some of the discrepancies identi-

    fied here in the prediction of pressure and sound

    generation, more attention should be paid to the projec-

    tile 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 sophis-

    tication should be weighed against its robustness and ef-

    ficiency 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 109Progress in Astronautics and Aeronautics, AIAA,Washington D.C., 1988 pp. 183259.

    [3] G Klingenberg, J.M.Heimerl, Gun Muzzle Blastand Flash, Vol 139 Progress in Astronautics and Aero-nautics, AIAA, Washington D.C., 1992 pp. 197338.

    [4] G.C. Carofano, Blast Field Contouring UsingUpstream Venting, ARCCBTR93009, US ArmyArmament Research, Development and EngineeringCenter, March 1993.

    [5] G.C. Carofano, A Note On The Blast Signatureof a Cannon, ARCCBTR92014, US Army Arma-ment Research, Development and Engineering Cen-ter, March 1992.

    [6] J.K. Clutter, G. Abate, W. Shyy, & C. Segal StudyOf Fast Transient Flow Phenomenon For MunitionApplication, 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 Numeri-cal Methods for Hyperbolic Conservation Laws withStiff Source Terms, Journal of Computational Phys-

    ics, 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 Com-putational Physics, Vol. 87, 1990 pp 124.

    [10] J.S. Shuen Upwind Differencing and LU Factor-ization for Chemical Nonequilibrium NavierStokesEquations, Journal of Computational Physics, Vol99, 1992, pp 233250.

    [11] Stull, D.R. and Prophet, H., JANAF Thermo-chemical Tables, NSRDSNBS 37, June 1971.

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    Caliber Gage X (in) Y (in)

    22 1 0 7.5

    22 2 3.5 7.5

    22 3 7 7.5

    22 4 0 1022 5 5 10

    22 6 10 10

    38 1 0 10

    38 2 5 10

    38 3 10 10

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

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

    Cal Y X Bare Sup (1) Sup (2) Com (1) Com (2)

    22 7.5 0.0 1.0505 1.0074

    22 7.5 3.5 1.0604 1.0098 1.0125

    22 7.5 3.5 1.0658 1.0119 1.0113

    22 7.5 3.5 1.0621 1.0106 1.0135

    22 7.5 7.0 1.0757 1.0123 1.0169 1.0082 1.0061

    22 7.5 7.0 1.0749 1.0124 1.0130 1.0071 1.0053

    22 7.5 7.0 1.0782 1.0124 1.0139

    22 10.0 0.0 1.0387 1.0048 1.0056

    22 10.0 0.0 1.0391 1.0055 1.0053

    22 10.0 0.0 1.0366 1.0051 1.0043

    22 10.0 5.0 1.0511 1.0092 1.0097

    22 10.0 5.0 1.0532 1.0087 1.0098

    22 10.0 5.0 1.0536 1.0075 1.0094

    22 10.0 10.0 1.0501

    22 10.0 10.0 1.0583 1.0128

    22 10.0 10.0 1.0600 1.0109

    22 10.0 10.0 1.0565 1.0128

    38 10.0 0.0 1.1500 1.0300 1.0416

    38 10.0 0.0 1.1636 1.0266 1.0281

    38 10.0 0.0 1.1670 1.0203 1.0237

    38 10.0 5.0 1.1936 1.0479 1.0542

    38 10.0 5.0 1.2105 1.0392 1.0532

    38 10.0 5.0 1.1922 1.0489 1.0523

    38 10.0 10.0 1.1704 1.0610 1.0987

    38 10.0 10.0 1.1554 1.0629 1.0799

    38 10.0 10.0 1.1626 1.0658 1.0842

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    Figure 1. Schematic of experimental layout.

    Oscopepreamp

    y distance

    x distance

    Microphone

    (vertical)

    suppressorsandbagfirearm

    table

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

    L

    L / 3

    Center Line / Line of Fire

    Di

    DeDe

    WeWi

    L = 4.316 6.373

    Di = .749 .995

    De = .263

    .22 .38

    .442

    Wi = .25 .25

    We = .36 .36

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

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

    1

    1.05

    1.1

    1.15

    1.2

    1.25

    1.3

    1.35

    1.4

    1 2 3

    P(atm)

    gage

    38_bare.dat38_sup_wave_1.dat38_sup_wave_2.dat

    38.sim38_sup_wave_1.sim38_sup_wave_2.sim

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

    0.95

    1

    1.05

    1.1

    1.15

    1.2

    1.25

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

    P(atm)

    time (~ms)

    38_bare38_sup

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

    1

    1.02

    1.04

    1.06

    1.08

    1.1

    1.12

    1 2 3 4 5 6

    P(atm)

    gage

    22_bare.dat22_sup_wave_1.dat22_sup_wave_2.dat

    22.sim22_sup.sim

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

    0.98

    0.99

    1

    1.01

    1.02

    1.03

    1.04

    1.05

    1.06

    1.07

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

    P(atm)

    time (~ms)

    22_bare22_sup

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

    (b)

    (a)

    Scale : .5 3. atm