Investigation of Small-Caliber Primer Function Using a 

Multiphase Computational Model 

by John R. Schmidt and Michael J. Nusca 

ARL-TR-4514 July 2008 

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Army Research Laboratory 

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ARL-TR-4514 July 2008 

Investigation of Small-Caliber Primer Function Using a 

Multiphase Computational Model 

John R. Schmidt and Michael J. Nusca 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
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Investigation of Small-Caliber Primer Function Using a Multiphase Computational Model 

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14. ABSTRACT 

This report describes further development in the formulation of a primer model that is compatible with the ARL-NGEN3 code and smallcaliber weapons that takes in account multidimensional, multiphase interior ballistics codes, which employ coupled Eulerian-Lagrangian 

schemes to explicitly treat both the gas and solid phase. The model is based on the One Dimensional Turbulence modeling approach that has 

recently emerged as a powerful tool in multiphase simulations. Initial results are shown for the model run as a stand-alone code and are 

compared to recent experiments with small-caliber primers. Integration of the primer model with the Army’s ARL-NSRG computational fluid 

dynamics code is presented and the results are compared to experiments with small-caliber primers fired into empty test chambers. It is 

proposed that this further progress sets the stage for coupling the primer model to the ARL-NGEN3 code. 

15. SUBJECT TERMS

Interior ballistics, Turbulence, Primer, CFD, two-phase flow 

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19a. NAME OF RESPONSIBLE PERSON

John R. Schmidt 

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Prescribed by ANSI Std. Z39.18 
Contents 

List of Figures iv 

Acknowledgments v 

1. Introduction 1 

2. Previous Work 2 

3. Small-Caliber Ammunication Chamber Simulator 3 

4. Multi-Species, Multi=Phase Flow CFD Code 5 

5. Primer Model and Interface to CFD Code 6 

6. Results and Discussion 9 

7. Conclusions 17 

References 19 

Acronyms 22 

Distribution 23 

iii 
List of Figures 

Figure 1. Cut away of a 5.56-mm small-caliber round. ..................................................................2

Figure 2. Primer No. 41 open air firing. .........................................................................................3

Figure 3. The 5.56 ballistic simulator, where the channel between the primer (on the left) 

and the simulator is .203 cm in diameter and .165 cm deep, respectively, and the 

simulator volume is 1.45 cc. ......................................................................................................4

Figure 4. A measured pressure time curve of the empty ballistic simulator chamber (with and 

without a 15-kHz low-pass filter). .............................................................................................4

Figure 5.  Average and instantaneous ODT velocity profiles for Re_τ = 356; the 

instantaneous profile was randomly chosen to demonstrate the difference between mean 

velocity, computed for an ensemble and arbitrary instantaneous velocity profile. ...................7

Figure 6.  ODT wall-normal profiles of wall-normalized stream-wise velocity U for copper 

shot (τp = 790), glass beads (τp = 120), and lycopodium spores (τp = 10) for Re_τ = 180. ....8

Figure 7. ODT wall-normal profiles of wall-normalized stream-wise velocity for barium 

nitrate (τp = 19,600) for Reτ = 356. ............................................................................................8

Figure 8. Computational mesh used for the simulation of the small-caliber ammunition 

simulator, as shown in figure 3; partial grid shown for clarity. Note the stretching 

(~1.5×) of the figure in the transverse. ....................................................................................10

Figure 9. Schematic of gas dynamic features in a highly underexpanded jet. ..............................11

Figure 10. Computed color pressure contours and selected velocity vectors for 0.008 and 

0.022 ms from initiation of the primer efflux. .........................................................................12

Figure 11. Computed color Mach number contours (with contour lines added) for 0.022 ms 

from initiation of the primer efflux. .........................................................................................12

Figure 12. Computed color pressure contours and selected velocity vectors for 0.037 and 

0.072 ms from initiation of the primer efflux. .........................................................................13

Figure 13. Computed color pressure contours and selected velocity vectors for 0.101 and 

0.144 ms from initiation of the primer efflux. .........................................................................13

Figure 14. Computed pressure histories at four wall locations in the chamber, with colorcoded lines that correspond to the locations noted in figures 10–13. ......................................14

Figure 15. Computed color porosity contours (indicating location and density of solid 

particles) and selected velocity vectors for 0.004 and 0.006 ms from initiation of the 

primer efflux. ...........................................................................................................................16

Figure 16. Computed color porosity contours (indicating location and density of solid 

particles) and selected velocity vectors for 0.008 and 0.010 ms from initiation of the 

primer efflux. ...........................................................................................................................16

Figure 17. Computed color porosity contours (indicating location and density of solid 

particles) and selected velocity vectors for 0.016 and 0.022 ms from initiation of the 

primer efflux. ...........................................................................................................................17

iv 
Acknowledgments 

Program Manager – Maneuver Ammunition Systems (PM – MAS) is acknowledged for 

continued support of this effort. The initial research was performed while the first author held a 

National Research Council Research Associateship at the U.S. Army Research Laboratory. 

v 
INTENTIONALLY LEFT BLANK. 

vi 
1. Introduction 

Numerical simulation of the interior ballistics (IB) of large-caliber guns has steadily progressed 

over the last few decades. As a testament to this progress, the U.S. Army Research Laboratory 

(ARL) (known prior to 1992 as the Ballistics Research Laboratory (BRL)) has played a major 

role in the development and popularization of a number of IB codes, such as IBHVG2 (1), 

NOVA (also known as XKTC) (2, 3), and NGEN (4–6), with progress in both model complexity 

and dimensionality (i.e., 0-dimensional (D), 1-D, and 2-D/3-D, respectively). A good review of 

the utility of this suite of IB codes is given by Horst and Nusca (7). Through this ambitious and 

successful progression of IB code development, one area of research has been given less 

attention: the fidelity with which the ignition system (i.e., the primer in small-caliber guns, the 

primer and flashtube in medium-caliber guns, and the primer and igniter-tube in large-caliber 

guns) is represented. One notable exception is an igniter sub-model implemented in the NOVA 

code for a 105 mm tank gun charge of low vulnerability gun propellant (8, 9). In this model the 

primer efflux was treated as gaseous with an added condensing phase, which increases the heat 

transfer coefficient to the propellant. 

There is significant evidence that burning particles of various chemical compositions and sizes 

are ejected from gun primers (10–12) and interact with the propellant grains during charge 

ignition. It is perhaps due to this phenomenon that upgrades to IB codes in this regard have had 

to wait until IB codes were made to utilize an explicit, particle-based treatment of the propellant. 

It follows that such an IB code could be made to model the interaction of the discrete primer 

particles and the discrete propellant particles. With the advent of the ARL-NGEN3 IB code, 

which employs a coupled Eulerian-Lagrangian scheme to explicitly treat both the continuous 

(gases) and discrete (solid) phases, the time is ripe for a primer model that is commensurate with 

the availability of such an IB model. 

Such a primer model has been developed, has been described previously (13, 14), and will be 

summarized herein. As a first stage of testing, calibrating, and ultimately validating this primer 

model, this report describes an effort to couple this model to a general purpose computational 

fluid dynamics (CFD) code called ARL-Navier-Stokes Real Gas (NSRG), and then shows how 

this combined model is used to simulate data gathered in a carefully designed ballistic simulator 

for the small-caliber ammunition. The lessons learned will assist in guiding the ultimate goal of 

coupling the primer model to the ARL-NGEN interior ballistics code for the purpose of a 

complete simulation of small-caliber ammunition (figure 1). 

1 
Figure 1. Cut away of a 5.56-mm small-caliber round. 

2. Previous Work 

Previous reports (13, 14) detailed the initial work toward the development of a small-caliber 

primer model. Provided herein is a summary of that work. 

A literature search was performed to understand the function of the percussion primer and glean 

the importance and purpose of each of the ingredients in the No. 41 primer. Overall chemical 

reactions for the species were derived. National Aeronautics and Space Administration (NASA)-

Glenn thermodynamic calculations were performed as a check of all the major species formed at 

one atmosphere pressure. Cheetah thermodynamics calculations were preformed under gun 

conditions to determine the ideal combustion state for the exploded primer. These conditions are 

needed for IB calculations. This state was used to estimate physical constants of the gas phase, 

which were used for the particle-laden One Dimensional Turbulence (ODT) simulations. It was 

proposed that the primer could be satisfactorily modeled as a highly turbulent statistically steadystate constant density particle-laden channel flow using one-way coupling. The material coming 

out of the primer tube, before the propellant is ignited, was determined to be (1) the gas phase, 

consisting of the combustion products of lead styphnate, Tetracene, pentaerythritoltetranitrate 

(PETN), and aluminum; (2) the solid phase, determined to be the uncombusted barium nitrate 

and antimony sulfide; and (3) a condensed phase, indicated by a thermochemical calculation. 

It was determined that only the drag terms of the particle equation of motion were significant and 

particles hitting the wall would stick to the wall rather than bounce off the wall. A channel flow 

with a bulk Reynolds number (Re) of approximately 12,000 was chosen to simulate the flow. A 

brief overview of vector ODT with two-phase flow as it pertains to this application was given. 

The deposition velocity Vd

+

 was calculated for small particle size and compared to literature 

values for Vd

+

. Excellent agreement was achieved for the small radii simulations, but a new 

diameter dependence of Vd

+

 was noted. Mean particle velocity profiles across the ODT channel 

yielded close agreement with measured particle velocities.

2 
3. Small-Caliber Ammunition Chamber Simulator 

The modeling phase of this project was done in close coordination with the experimentation of 

Williams et al. (15, 16). Their work consisted of the following: 

1. They performed open air primer firing events with high-speed digital photography (figure 

2). From this, they were able to measure particle exit velocities. Analysis of the 

photograph revealed a spreading angle of ~70°. Two yellow lines were placed in the 

photograph to show the 70° spreading angle. 

Figure 2. Primer No. 41 open air firing. 

Note: Taken from Williams et al. (16) with permission. 

2. They collected particles from the open air primer firings. Samples were collected on 

carbon tape and analyzed using Scanning Electron Microscopy/Energy-Dispersive X-ray 

spectroscopy (SEM/EDAX) Fourier Transform Infrared (FTIR) spectroscopy. The impetus 

behind these experiments was to try and find out what was coming out of the primer spit 

hole at the very beginning of the ballistic cycle. During the ballistic event, the primer 

efflux ignites the propellant, which increases the pressure and temperature inside the gun 

case. Firing primers into open air is, in effect, quenching the reaction just after the 

initiation, because the products are spit out of the primer tube into room temperature and 

pressure. Their conclusions were that the solids coming out of the primer tube were 

particles of barium nitrate and antimony sulfide with evidence of some melting and perhaps 

a small level of combustion. Traces of mostly sub-micron aluminum/aluminum oxide were 

noted, the authors of this report attribute this to the aerosol generation from the gaseous 

state due to the quenching of the hot gases as they were shot into the open air (which was at 

room temperature and pressure). 

3 
3. They developed a closed ballistic simulator made of clear acrylic, which was used to test 

the firing of the No. 41 primer into an empty chamber. Time dependent pressure 

measurements of the projectile end of the simulator were taken in conjunction with high 

speed photography of the firing event as could be seen through the acrylic sidewalls. A 

high frequency pressure wave was noted due to the complex interactions between multiple 

wave fronts reflecting between the two chamber ends. The signal was filtered. The 

chamber pressure reached a maximum value of about 3 MPa in a time of between 25 and 

35 microseconds. A schematic diagram of the primer and empty chamber is shown in 

figure 3. A pressure time curve is shown in figure 4. 

0.251 3.05

0.794 0.570 

2.77

Figure 3. The 5.56 ballistic simulator, where the channel between the primer (on the left) and the simulator is 

.203 cm in diameter and .165 cm deep, respectively, and the simulator volume is 1.45 cc. 

Note: All measurements in units of cm. 

Figure 4. A measured pressure time curve of the empty ballistic simulator chamber (with and without 

a 15-kHz low-pass filter). 

Note: The dashed line shows the filtered curve. Taken from Williams et al. (16) with permission. 

4. They utilized the closed ballistic simulator for experiments with both inert propellant and 

live propellant. Time dependent pressure measurements and high speed photography were 

performed. Analysis done postmortem on the inert propellant balls supported the 

supposition that the open air firing quenched the reaction soon after the primer firing. 

4 
Comparison of the analytical results of the open air firings and the closed chamber firings 

showed that there was further reaction in the closed chamber, which had a peak pressure of 

18.3 MPa as compared to the open air firings where the pressure was atmospheric 

(~0.1 MPa). This is consistent with the use of barium nitrate and antimony sulfide in 

primer to extend the life of the primer. That is, they continue to burn after the firing event 

to provide extra heat to ignite the propellant. The live propellant simulations will be used 

in future work to help verify the ARL-NGEN code extension to small-caliber IB. 

4. Multi-Species, Multi=Phase Flow CFD Code 

The ARL-NSRG CFD code is a time-accurate, multi-dimensional CFD code that has been under 

development and validation at ARL for over 10 years (17). This code has been successfully used 

for the simulation of unsteady, multi-component, turbulent, chemically reacting (nonequilibrium) 

flows (18–23). The code solves the unsteady Navier-Stokes equations, including 

multicomponent species diffusion, thermal conduction, viscosity (laminar and turbulent), and 

user-defined nonequilibrium chemical kinetics. The conservation-law form of the Navier-Stokes 

equations is used and a finite-volume discretization methodology is employed. The convective 

and transport fluxes are resolved using upwind and central-differencing along with flux-limiting 

methods. The chemical reactions are fully coupled to the gas dynamics and the numerical 

stiffness due to chemical source terms is mitigated by pre-conditioning techniques, thus 

permitting explicit time integration (i.e., a technique that accurately represents wave dynamics). 

Several kinetics mechanisms have been installed in the code using an Arrhenius formulation (the 

code admits other methods for computing the chemical source terms including pressuredependent and “falloff” reaction rates). Real-gas equations of state (e.g., Noble-Abel, JonesWilkins-Lee (JWL), and Peng-Robinson) are also available in the code. Although originally 

formulated for gas-phase modeling, the ARL-NSRG code has been recently upgraded to include 

a discrete phase, which can be either liquid or solid. This version of the code has been 

successfully used for the modeling of liquid rocket engines (22, 23). The multiphase version of 

the code includes governing equations to simulate particle dynamics (including interphase drag 

and heat conduction), particle heating and vaporization, as well as the participation of these 

particles in chemical reactions if so desired. 

Particularly germane to the current application of the code is a similar application in which the 

ARL-NSRG CFD code was coupled to a model that predicted the efflux from the orifice of a 

capillary containing a solid material (polyethylene) that was vaporized when high-voltage 

current was applied to the leads of an included copper wire. The resulting efflux was a high 

velocity, high density, chemical mixture primarily composed of electrons, C, C+, H, H+, and 

other species. This efflux, in the form of a highly underexpanded jet, was exhausted into a 

chamber containing air and a solid propellant sample. The ARL-NSRG CFD code was used to 

5 
resolve this jet. Output of the capillary model was used as a boundary condition for the ARLNSRG, which produced resultant shock waves at the orifice (the classical barrel shocks, normal 

shock, and reflected shocks) and the subsequent series of shock wave reflections within the test 

chamber. Measured and computed pressure/time histories were compared. In this case, the code 

included a nonequilibrium chemical kinetics mechanism (air-plasma-JA2 propellant) and certain 

real fluid effects (Coulomb interactions) that are present for ionized gases. For further details on 

the model and results, refer to the work of Nusca, McQuaid, and Anderson (19–21). The overall 

plasma-propellant interaction research program is described by Shaw et al. (24). Clearly, the 

current application of the ARL-NSRG CFD code is quite similar to this previous case since a 

primer model will be used to supply the CFD code with the flow properties and conditions at the 

primer orifice that is issuing into a closed chamber as a boundary condition. 

5. Primer Model and Interface to CFD Code

There exist a number of challenges in order to couple the ODT two-phase flow model with the 

ARL-NGEN code. An important first step is the merging of the ODT with the ARL-NSRG 

code. Analysis of the Military (Mil) specifications (Mil-A-159, Class 1, 2, and 3) for the 

antimony sulfide and (Mil-B-162, Class 1 granulation A) for barium nitrate were performed. A 

log averaged mean diameter of 95 microns was found suitable for both antimony sulfide (Stokes 

number τp+ = 28,000) and barium nitrate (τp+ = 19,600). Assuming a 95 micron diameter 

particle, the total number of barium nitrate particles in an average No. 41 primer is calculated to 

be 5,493; for stibnite, the calculation yields 1,800 particles. 

Grid convergence studies were performed at 1,292 and 2,584 grid points. The statistical steadystate deposition velocity Vd+ was calculated and it was confirmed that 1,292 grid points were of 

sufficient resolution. 

An example of a Re = 356 steady-state fluid velocity profile across the channel is shown in 

figure 5, where the wall-normal direction is denoted y. Mean V and W fluid velocity profiles are 

zero. Also shown is a transient fluid U velocity profile for comparison. The channel half height 

h is equal to 0.1016 cm. The friction velocity Uτ is 2.81 m/s. The velocity at the centerline 

(y/h = 1) is equal to 55.7 m/s. 

6 
U / Uτ

0 5 10 15 20

y/h

0.0

0.5

1.0

1.5

2.0

ave

instantaneous

Figure 5. Average and instantaneous ODT velocity profiles for Re_τ = 356; 

the instantaneous profile was randomly chosen to demonstrate the 

difference between mean velocity, computed for an ensemble and 

arbitrary instantaneous velocity profile. 

Note: The mean profile is the smooth one. 

The Stokes number τp+ is the ratio of the aerodynamic time constant of the particle to the time 

constant (based on wall units) of the fluid. The closer the Stokes number is to 1, the more likely 

a particle is to follow the fluid. As the Stokes number becomes larger, the particle is less and 

less sensitive to its position across the channel, the wall-normal direction, here measured in wall 

units Y+ (24). Figure 6 shows the steady-state wall-normal profiles of particles with varying 

Stokes numbers: Lycopodium spores with τp+ = 10, glass beads with τp+ = 120, and copper 

shot with τp+ = 790. As can be seen in figure 5, the fluid velocity drops drastically near the 

wall. The Lycopodium spores with a Stokes number of 10 follow this trend quite readily. As the 

Stokes number goes up a factor of 10 (for glass), the slowing down of the particle’s U velocity as 

it approaches the wall is attenuated. For the copper shot, which has a Stokes number two orders 

of magnitude higher, the wall effects are much less evident. Therefore one would expect 

minimal wall effect in U velocities for the particles of interest in this study, barium nitrate and 

antimony sulfide, which have Stokes numbers three orders of magnitude higher than 

Lycopodium spores. 

7 
Y +

0.1 1 10 100

U / Uτ

0

5

10

15

20

copper

glass

lycopodium

Figure 6. ODT wall-normal profiles of wall-normalized stream-wise 

velocity U for copper shot (τp = 790), glass beads (τp = 120), 

and lycopodium spores (τp = 10) for Re_τ = 180. 

Note: Taken from Schmidt (25) with permission. 

Figure 7 shows the steady-state U velocity profile for barium nitrate as a function of the wallnormal direction. As expected, the slowing down of the particle as it approaches the wall is 

minimal. The mean particle velocity profiles in the Y and Z directions, V and W, respectively, 

are zero if the particles are allowed to bounce spectrally on the walls. If the particles are 

absorbed on the wall, then the mean V velocity profile shows a slight velocity toward the wall in 

the near wall region. This is due to fact that if they bounced off the wall they would contribute a 

velocity component away from the wall, but since they are absorbed on the wall there is a V 

velocity toward the wall. The antimony sulfide particle behavior is similar in every way to the 

barium nitrate particle. Only the antimony sulfide particles have a larger Stokes number, which 

means that it is even less sensitive to slowing in the near wall region. 

Y +

0 100 200 300 400

U / Uτ

0

5

10

15

20

Figure 7. ODT wall-normal profiles of wall-normalized stream-wise 

velocity for barium nitrate (τp = 19,600) for Reτ = 356. 

8 
To model the flow out of the primer tube into the ballistic simulator, the mean velocity profile 

for half the channel width (h) was fed into the ARL-NSRG simulation. The mean velocity 

profile is symmetric around the channel center. The vector ODT model provides instantaneous 

velocity profiles in the X, Y, and Z directions. The ARL-NSRG program uses the axis 

symmetric coordinate system R, θ, Z. The Z coordinate in ARL-NSRG corresponds to the X 

coordinate in the ODT code. Hence the stream-wise (U) velocity from ODT is the Z velocity for 

ARL-NSRG. Since ARL-NSRG assumes an axis-symmetric velocity profile, the θ velocity 

component is assumed to be zero. The ODT program models a 1-D line of sight on which the 

turbulent velocity profile is kept track of in all three dimensions. The θ component in ARLNSRG corresponds in this case to the Z component in ODT. The R component in ARL-NSRG 

corresponds to the Y component in ODT. The V velocity profile corresponds to the R velocity. 

Particles in ODT are allowed to migrate in their own individual space time line, so they have 

their own X, Y, Z, t position; however, all particles are constrained to stay on the ODT 1-D 

domain. Since the particles have their own Y, Z positions, an attempt was made to map the 

particle position and velocity into the R, θ coordinates. A total of 1,260 particles were released 

and allowed to reach pseudo-steady-state. The particles were binned into 10 equal time 

increments and converted into R, θ coordinates. 

Particles in ARL-NSRG must be at least one diameter apart and cannot get within one radius of 

the walls. The ODT particles in each time bin were sorted in the R coordinate so that they were 

at least one radius apart. These efforts will hopefully bare fruit in future ARL-NSRG 

simulations. 

6. Results and Discussion 

The computational domain chosen to simulate the ARL small-caliber ammunition experiment (as 

shown in figure 3) is shown in figure 8. The computational domain extends from the exit plane 

of the primer orifice (i.e., entrance to the simulator chamber) on the left, to the afterbody of the 

5.56 ammunition mounted on the chamber sealing wall on the right (3.05 cm) and within the 

cylindrical wall of the chamber (which were made from a semi-transparent Lexan)—a diameter 

of 0.794 cm. This region was discretized using 304 axial grid cells and 40 radial grid cells 

(79 across the diameter), distributed with essentially even spacing throughout, as shown in figure 

8 (partial grid deployed for clarity). Some degree of radial grid clustering was used among the 

chamber walls in order to more accurately resolve viscous effects. The boundary conditions for 

the region are non-slip/no-penetration on all solid walls along with specified inflow at the primer 

orifice (0.102 cm < Y < 0.102 cm at X = 0). Initially, the entire flowfield is filled with air 

(0.8 mole fraction of N2 and 0.2 mole fraction of O2) at standard pressure and temperature. 

During the simulation, a two-phase flow was fed into the chamber using the parameters 

described in section 5. 

9 
Figure 8. Computational mesh used for the simulation of the small-caliber ammunition simulator, as shown in figure 

3; partial grid shown for clarity. Note the stretching (~1.5×) of the figure in the transverse. 

The efflux from the 5.56 caliber ammunition primer into an empty chamber is postulated to 

resemble that of a high-speed, high-pressure jet that is said to be highly “underexpanded.” To 

aid in the interpretation of computational results for the primer jet, figure 9 shows a schematic of 

the gas dynamic features expected in highly underexpanded supersonic jets (21). The efflux of 

primer from the inlet generates a weak precursor shock (A) that expands spherically. Behind this 

shock is air; the primer gases are entirely contained by this shock and are separated from the air 

by an irregularly shaped contact surface (B) across which pressure and velocity are preserved but 

entropy changes discontinuously. Expansion waves (Mach cone), generated at the inlet (C), 

travel to the precursor shock (A), are reflected as weak compression waves, and coalesce into a 

strong oblique shock, or barrel shock (D), within the primer jet. This barrel shock (D) terminates 

in an irregular reflection that forms a triple-point (E) joining the barrel shock (D) its reflection 

(F), and a normal shock (G) or Mach disk. Whereas the precursor shock (A) is relatively weak 

and diffuse, producing a mildly supersonic flow, the barrel shock (D) and Mach disk (G) are 

strong shocks that enclose a fully supersonic flow region. 

10 
 

A

Figure 9. Schematic of gas dynamic features in a highly underexpanded jet. 

Figures 10–13 show the time history of the primer efflux jet from shortly after entrance into the 

chamber (0.008 ms) to sometime after impact upon the opposite chamber wall and reflection 

back to the primer (0.144 ms). Note that the frames in figures 10–13 are not plotted to scale. 

Pressure contours are displayed in color-scale from 0 (blue) to 0.35 or 0.50 and above (red). 

Velocity vectors (not all vectors are displayed for clarity) are superimposed in order to indicate 

the magnitude (length of the vector) and direction of the local gas velocity. Mach number (local 

velocity normalized by the local sound velocity) contours (figure 8) are displayed in color-scale 

from 0 (blue) to 2.2 and above (red) with grey contour lines superimposed for emphasis. 

As shown in figures 10 and 11, the high density and high pressure primer efflux enters the 

chamber as a highly underexpanded jet. Although not immediately evident in this scale, an 

expansion wave forms at the primer exit. A precursor shock is also formed from a mixture of air 

and primer gases (local molecular weight of about 30 g/mole) as the jet is moving at about 

550 m/s at this time, about Mach 1.12 based on the local sound speed in the mixture. The primer 

gas from the orifice is of very high molecular weight, about 44 g/mole. The precursor shock is 

initially curved and shock reflections form on the chamber wall. By 0.022ms the leading edge of 

the precursor shock is nearly flat and the predominant gas dynamic features of the 

underexpanded jet have been established as seen more clearly when plotted at Mach number 

contours in figure 11. Curved barrel shocks emanate from the primer orifice terminating in a 

small Mach disk (at about 0.007 m in figure 11) and weak reflected shocks (the “X” patters near 

0.007 m in figure 11). Supersonic flow resides within the barrel shocks and Mach disk (red color 

in figure 11). Due to the variable viscosity in the flowfield, the precursor shock is more diffuse 

than the normal shock of the Mack disk or the oblique barrel shock. Note the near sonic (i.e., 

Mach numbers subsonic to slightly supersonic) flow region between the normal shock and the 

precursor shock (green color); within this region resides the contact surface. Note that all of 

these features can be made more evident with a more highly refined computational mesh. The 

precursor shock impinges onto the projectile afterbody at about 0.037ms (figure 12) and reaches 

the end of the chamber before 0.072ms. In each case, a reflected shock is generated that 

CENTERLINE

B

Air

CAPILLAR PLASM

PLASM

E

C

D

G

F

Primer Gases 

Primer Primer Gases 

11 
coalesces and moves back toward the primer, leaving behind near flow stagnation (note the 

absence of velocity vectors in the high pressure region shown in figure 12 for 0.072ms). A new 

high pressure flow region is formed on the chamber centerline at about midsection (see figure 12 

for 0.072 ms) that results from the interaction of the Mach disk generated by the primer efflux 

and the receding reflected shock. Figure 13 shows the ultimate interaction of the reflected shock 

with the primer efflux jet near the jet orifice; the underexpanded jet is disturbed and then nearly 

reestablished by 0.144 ms. Note the formation of reverse flow along the chamber walls, forward 

flow along the chamber centerline and recirculation regions near the primer orifice at 0.101ms in 

figure 13. The primer jet is terminated at about 0.15 ms and subsequent gas dynamics in the 

chamber take the form of reflected waves and a steady buildup of pressure within the vessel. 

Eventually, the chamber flow is nearly uniform at a high level of pressure (not shown in these 

figures). 

Figure 10. Computed color pressure contours and selected velocity vectors for 0.008 and 0.022 ms from initiation of 

the primer efflux. 

Figure 11. Computed color Mach number contours (with contour lines added) for 0.022 ms from initiation of the 

primer efflux. 

12 
Figure 12. Computed color pressure contours and selected velocity vectors for 0.037 and 0.072 ms from initiation of 

the primer efflux. 

Figure 13. Computed color pressure contours and selected velocity vectors for 0.101 and 0.144 ms from initiation of 

the primer efflux. 

Figure 14 shows the computed pressure-time histories as recorded at four wall-mounted pressure 

“taps” in the computational domain. Note the four colored “dots” in each of figures 10 through 

13. At these locations, pressure was recorded while the simulation was executing; the line color 

13 
of figure 14 corresponds to these color dots. The pressure tap location, represented by the 

“black” dot, corresponds to the actual location of an experimental pressure tap with the data 

displayed in figure 4 and discussed in section 3. The arrival of the precursor shock onto the 

pressure tap mounted on the projectile afterbody (black curve in figure 14) is about 0.04 ms at a 

pressure level of about 2.6 MPa. Comparing these results to those displayed in figure 4, it can be 

said that the timing is similar and the computed pressure is about 13% low (measured value has 

an average value of 3 MPa). This indicated that perhaps the density of the primer efflux, used in 

the simulation, is too low. The other curves displayed in figure 14 provide an indication of the 

unsteady gas dynamics within the chamber as shock waves are generated and reflect from both 

radial and axial surfaces. Subsequent shock wave arrival and reflection from the pressure tap 

mounted on the projectile afterbody are evident in both the measured (figure 4) and computed 

(figure 14) results; however the computed results show a continual increase in pressure to a 

steady value of about 3.4 MPa at 4 ms, while the measured results show a steady or mean 

pressure level of about 1.5 MPa. It is postulated that some of this discrepancy is owed to heat 

losses to the walls and leaks or venting in the chamber during the experiment. These 

investigations will be the subject of future reports. Williams et al. (15) recorded optical images 

of the empty ballistic simulator which are consistent with the shock wave and its reflections as 

shown in the ARL-NSRG simulation figures 10–14. 

Figure 14. Computed pressure histories at four wall locations in the chamber, with color-coded 

lines that correspond to the locations noted in figures 10–13. 

14 
In order to gain an understanding of the dynamics of the 95 micron solid particles generated by 

the primer, computed results for the solid phase of the simulations are displayed in figures 

15–17. These results are designed to be compared to the photographic evidence of the particles 

as given in figure 2. Since the model presently is not equipped with a way to graphically display 

the individual particles, a value of porosity is computed and graphed. In forming the porosity 

map for each point in time, each computational cell is interrogated for the presence of particles 

and since the diameter of these particles is known and is unchanging (in the current simulation 

the model’s subroutines governing particle combustion are deactivated) the porosity is the ratio 

of cell volume occupied by the particles to the empty cell volume and then subtracted from unity. 

As a result, the red color (values approaching zero) of figures 15–17 indicates a high density of 

particles while the blue color (value of unity) of figures 15–17 indicates the absence of particles. 

Examining the time progression of figures 15 and 16 one observed a high density of particles that 

is quickly dispersed in a “fan”-like structure following the gas dynamic expansion and then is 

turned from the chamber wall as the flow features of the underexpanded jet are formed 

(discussed previously). Analysis of figure 15 time 0.006 ms shows a spreading angle of 72°. 

This is in good agreement with the measured spreading angle (yellow lines) of 70° shown in 

figure 2. Since the spreading angle is compared to an open air firing it was important to take 

measurements before the wall effects could influence the particle spreading angle. Figures 16 

and 17 show that a small number of particles reach the chamber wall (and become trapped in the 

low velocity of the wall boundary layer) but most of the particles flow along with but lag the 

precursor shock. It should be noted that the individual “streamers” or “fingers” of particle are 

expected to coalescence in reality, but the fact that they do not is partially an artifact of the 

computational mesh used and mostly the fact that the particles are all given the identical initial 

conditions, with a zero velocity. The desire of the authors was to capture bulk flow properties of 

the particles in this simulation. Further simulations using particles and fluid with transient initial 

conditions are planned in the future. The expectation is that the finger structure, which is so 

evident in figures 15–17, will merge into a continuous distribution with turbulent initial 

conditions. 

15 
Figure 15. Computed color porosity contours (indicating location and density of solid particles) and selected 

velocity vectors for 0.004 and 0.006 ms from initiation of the primer efflux. 

Figure 16. Computed color porosity contours (indicating location and density of solid particles) and selected 

velocity vectors for 0.008 and 0.010 ms from initiation of the primer efflux. 

16 
Figure 17. Computed color porosity contours (indicating location and density of solid particles) and selected 

velocity vectors for 0.016 and 0.022 ms from initiation of the primer efflux. 

It is believed that the particle dynamics displayed in the modeling results are quite similar to 

those photographed (figure 2). However, additional quantitative work will be the subject of 

future reports, including a comparison of the computed and measured accumulation of particles 

deposited onto the projectile afterbody and the far axial wall of the chamber. 

7. Conclusions 

Analysis yielded a log-mean diameter of 95 microns for both the antimony sulfide and the 

barium nitrate. The primer tube was modeled at a steady-state turbulent channel flow with a 

Reτ = 356. An analysis of particle behavior across the channel was consistent with trends shown 

in the literature; the higher the Stokes number the less sensitive the particles are to wall effects. 

Particle simulations were performed and converted to R - θ coordinates suitable for the ARLNSRG code. 

Coupling of the ARL-NSRG code with the statistically steady-state fluid phase velocity profile 

across the channel yielded characteristics of a classical under-expended jet. Simulated pressure 

taps showed properties that are consistent with measurements. An average measured peak 

pressure of 3 MPa was recorded between 0.03 and 0.04 ms. This simulation showed a peak 

pressure of 2.6 MPa at 0.04 ms; this was considered acceptable agreement considering the 

assumptions made. The experimental data showed a rapid decay of pressure levels to a steady 

value that was notably lower than the computed value; the computed pressure shows a gradual 

rise to a steady pressure. The discrepancy between measured and computed results is mostly 

17 
18 

mental 

ream of particles was fed into the ARL-NSRG simulation with identical zero initial 

lations indicating an ordering of the particles that is 

ned by Williams et al. (15) are 

attributed to the fact that the experiment had heat losses to the surroundings, but the simulation

was adiabatic. Also, the fact that the experimental chamber reverted back to atmospheric 

pressure shortly after the firing event probably indicates that there were leaks in the experi

apparatus. 

A steady st

conditions. The particles were evenly distributed across the opening. Analysis of the initial 

particle spreading angle yielded a close match to the measured spreading angle of an open air

firing, 72° compared to 70°, respectively. 

Finger-like structures were seen in the simu

not considered realistic. The finger structure is attributed to (1) the mesh size and (2) the ordered

initial conditions. The introduction of particles with transient initial conditions (via the ODT 

simulation) is expected to alleviate most of this artifact. 

The optical images of the empty ballistic simulator obtai

consistent with the ARL-NSRG simulations. 
References 

1. Anderson, R.; Fickie, K. IBHGV2 – A User’s Guide; BRL-TR-2829; U.S. Army Ballistic 

Research Laboratory: Aberdeen Proving Ground, MD, July 1987. 

2. Gough, P. S. Interior Ballistics Modeling: Extensions to the XKTC Code and Analytical 

Studies of Pressure Gradient for Lumped Parameter Codes; ARL-CR-460; U.S. Army 

Research Laboratory: Aberdeen Proving Ground, MD, February 2001. 

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MD, June 2004. 

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Ground, MD, May 2006. 

8. Gough, P. S. Modeling Chemical Interactions in Ignition of Gun Propellants. Proceedings of 

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October 1983. 

9. Keller, G. E.; Horst, A. W. The Two Phase Flow Simulation of LOVA Propellant Interior 

Ballistic Behavior Using the XNOVAK Code; BRL-TR-2796; U.S. Army Ballistic Research 

Laboratory: Aberdeen Proving Ground, MD, April 1987. 

10. Davis, Tenney L. The Chemistry of Powder and Explosives, John Wiley & Sons, Inc.: New 

York, 1943. 

19 
11. Ekstedt, E. E.; Vest, D. C.; Emerson, V. C.; Dean, L. W. Pressure Studies of Artillery 

Primers Fired Statically; BRL Report No. 938; U.S. Army Ballistic Research Laboratory: 

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in a 105-mm Tank Gun Chamber; BRL-TR-2890; U.S. Army Ballistic Research Laboratory: 

Aberdeen Proving Ground, MD, March 1988. 

13. Schmidt, J. R.; Nusca M. J. Progress in the Development of a Multiphase Turbulent Model 

of the Gas/Particle Flow in the Primer Tube for Small Caliber Ammunition. Proceeding of 

the 53rd JANNAF Propulsion Meeting, CPIAC JPMCD05, Monterey, CA, December 2005. 

14. Schmidt, J. R.; Nusca M. J. Progress in the Development of a Multiphase Turbulent Model 

of the Gas/Particle Flow in a Small Caliber Ammunition Primer; ARL-TR-3860; U.S. Army 

Research Laboratory: Aberdeen Proving Ground, MD, August 2006.

15. Williams, A. W.; Brant, A. L.; Kaste, P. J.; Colburn, J. W. Experimental Studies of Primer 

Ignition in 5.56-mm Ammunition. Proceeding of the 53rd JANNAF Propulsion Meeting, 

CPIAC JPMCD05, Monterey, CA, December 2005.

16. Williams, A. W.; Brant, A. L.; Kaste, P. J.; Colburn, J. W. Experimental Studies of the No. 

41 Primer and Ignition of 5.56-mm Ammunition; ARL-TR-3922; U.S. Army Research 

Laboratory: Aberdeen Proving Ground, MD, August 2006. 

17. Nusca, M. J. Numerical Simulation of Electromagnetic Wave Attenuation in 

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21 

22. Nusca, M. J.; Mathis, N. P.; Michaels, R. S. Modeling Hypergolic Ignition in the Army’s 

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Arizona 2004.
Acronyms 

ARL U.S. Army Research Laboratory 

BRL Ballistics Research Laboratory 

CFD computational fluid dynamics 

D dimensional 

EDAX Energy-Dispersive X-ray spectroscopy 

FTIR Fourier Transform Infrared spectroscopy 

IB interior ballistics 

JWL Jones-Wilkins-Lee equation of state 

MAS Maneuver Ammunition Systems 

Mil Military 

NASA National Aeronautics and Space Administration 

NSRG Navier-Stokes Real Gas 

ODT One Dimensional Turbulence 

PETN pentaerythritoltetranitrate 

PM Program Manager 

Re Reynolds number 

SEM Scanning Electron Microscope 

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