suppressor1消音器

AIAA 96–3020 1 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 Shyy� 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. � � � Doctoral Student, Member AIAA. Copyright � 1996 by M. Keith Hudson. Published by the American 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 cut–and–try 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 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 baffle design 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. AIAA 96–3020 2 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 and a 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 LeCroy Model 9400A, 175 MHz 8–bit 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 high–intensity peak with only minimal ringing type peaks seen over the rest of the measurement period. This of course correlates with the sharp, high–intensity 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 un–protected 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 Navier–Stokes equations for a multi–species chemically reacting flow. The current study focuses on the inviscid and real gas aspects of the AIAA 96–3020 3 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 multi–species flow with variable specific heats. When discretized, the equations take the form �J Q �t � �J F �� ��J G�� � J H � 0 (1) where the dependent variable and flux vectors are Q � ������ � � �u �v �E ��1 � ��NS�1 ������ � � , F � ������� � �U �uU � �xP �vU � �yP U �E � P ��1U � ��NS�1U ������� � � , G � ������� � �V �uV � �xP �vV � �yP V �E � P ��1V � ��NS�1V ������� � � , H � 1y ������ � �v �uv �v2 v �E � P ��1v � ��NS�1v ������ � � . (2) The dependent variable �i is the mass fraction of ith 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 � �� NS i�1 ��i 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 � x�y�� x�y� U � �xu � �yv V � �xu � �yv . (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 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] P � �RuT� NS i�1 �i Mi (4) The temperature during the calculations must be ex- tracted from the conserved quantity of internal energy using the relationship e �� NS i�1 �ihi � P � hi � hofi � � 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, the temperatures 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 second–order accuracy, the fluid dynamics operator must be second order and here a prediction–correction scheme is used of the form [8] Q* � Qn � �t2 ���F (1) ���G(1) � Hi , j� n Qn�1 � Qn � �t���F(2) ���G(2) � Hi , j� * (6) with ��F � Fi�12 , j � Fi�12 , j ��G � Gi , j�12 � G i , j�12 (7) AIAA 96–3020 4 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 � and � are computed at the cell faces and the axisymmetric source term is com- puted based on the cell average. The scheme used to define the inviscid numerical fluxes is the Steger–Warming flux vector splitting algorithm which has been extended to model multi–species flows [9]. The flux vector splitting algorithm decomposes the inviscid fluxes into non–negative (K+) and non–positive (K–) components based on the eigenvalues of the Jaco- bian A � �F�Q and likewise for G. The split fluxes take the form K� � ��1K1 � ��2K2 � ��3K3 (8) where the eigenvalues are ��k � 1 2 ��k � |�k|� �1 � �k �2 � �k � c|�k| �3 � �k � c|�k| (9) with k � k ~ xu � k ~ yv k ~ x � kx |�k| k ~ y � ky |�k| |�k| k2x � k2y� (10) The split flux components are K1 � �� 1 � ������� � � u v �ht � c2�� 1� �1 � �NS�1 ������� � � K2,3 � 1 2� �������� � � �u � k~ xc� �v � k~ yc� �ht � kc� �1 � �NS�1 �������� � � (11) The above formulation gives K=F when k=� and K=G when k=�. For the multi–species chemically reacting flow, c is the frozen speed of sound where c2 � � �P� � and � 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 F i�12 , j � F��QL i�12 , j �� F��QR i�12 , j � (12) If a 1st order spatial representation is used, then QL i�12 , j � Qi , j , QRi�12 , j � Qi�1 , j . To achieve 2nd order accuracy, a MUSCL approached is used in which cell–center 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 QL i�12 , j � Qi , j ���i�12 , j QR i�12 , j � Qi�1 , j ���i�12 , j (13) where the limiting function is �� i�12 , j � li�1 , j 2 mmod �Q�i�1 , j,�Q�i�1 , j ��i�12 , j � li , j 2 mmod �Q�i , j,�Q�i , j (14) with �Q�i , j � 2�Qi�1 , j � Qi , j� li�1 , j � li , j �Q�i , j � 2�Qi , 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 l i,j , the cell–length, is used to provide weighting for nonuniform grid spacing. The same extrapolation procedure is carried out for the fluxes in � and can be performed on either the dependent or primitive vari- ables. Previous investigations have shown that using primitive variables gives better performance for flows AIAA 96–3020 5 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 experi- ments 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 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 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 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 �F� .64 and �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 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