Progress in the Development of a Multiphase Turbulent 

Model of the Gas/Particle Flow in a Small-Caliber 

Ammunition Primer 

by John R. Schmidt and Michael J. Nusca 

ARL-TR-3860 August 2006 

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-3860 August 2006 

Progress in the Development of a Multiphase Turbulent 

Model of the Gas/Particle Flow in a Small-Caliber 

Ammunition Primer 

John R. Schmidt and Michael J. Nusca 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
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Progress in the Development of a Multiphase Turbulent Model of the Gas/Particle 

Flow in a Small-Caliber Ammunition Primer 

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John R. Schmidt and Michael J. Nusca 

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14. ABSTRACT 

There is significant experimental evidence that burning particles of various chemical compositions and sizes are ejected from 

gun primers and that these particles interact with the propellant grains during main charge ignition. This explicit ignition 

phenomenon is thought to be incompatible with the implicit treatment of primer function in conventional interior ballistics 

codes and models. Generally, the primer efflux is treated as a hot gas that evolves from a specified region in the model’s 

representation of the gun chamber (usually along the chamber centerline and near the breech). What amounts to an igniter table

is arrived at by experimental means and by careful calibration of the interior ballistics simulation using gun firing data. With 

the advent of multidimensional, multiphase interior ballistics codes which employ coupled Eulerian-Lagrangian schemes to 

explicitly treat both the gas and solid phase, the time is ripe for a primer model that is commensurate with the availability of 

such an interior ballistics model. Progress in the development of a primer model that is compatible with the ARL-NGEN3 

interior ballistics code and small-caliber weapons is described herein. 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. 

15. SUBJECT TERMS

interior ballistics, turbulence, primer, CFD, two-phase flow 

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John R. Schmidt 

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iii

Contents 

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. The ARL-NGEN3 IB Code 5

3. Description of the Primer 6

3.1 Chemistry ........................................................................................................................6 

3.2 Description of the Primer Firing Event ...........................................................................7 

4. Formulation of the Primer Model 10

4.1 The Navier-Stokes Equation .........................................................................................10 

4.2 Overview of the One-Dimensional Turbulence Model.................................................11 

4.3 Particle Dynamics for a Perfect Sphere.........................................................................14 

4.4 Particle – Fluid Interactions ..........................................................................................15 

4.5 Particle – Wall Interactions ...........................................................................................15 

4.6 Model Implementation ..................................................................................................16 

5. Computational Results for a Small-Caliber Simulator 18

5.1 Parametric Scaling.........................................................................................................19 

5.2 Definition of the Deposition Velocity Vd

+

.....................................................................21 

6. Conclusions 22

7. Future Work 22

8. References 24

Appendix. Cheetah 4.0 Summary Sheet 29

Distribution List 32 
iv

List of Figures 

Figure 1. A cut away of large-caliber ammunition showing piccolo tube......................................2 

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

Figure 3. Small-caliber ammunition igniter; primer cup with anvil. ..............................................3 

Figure 4. Axial cross-section schematic of primer for a 5.56 ammunition.....................................3 

Figure 5. The procedure for implementing particle-eddy interactions which avoids double 

counting. Find ∆yp and ∆V, then add them to the original position and velocity. The 

resultant position and velocity are shown in (b). ....................................................................19 

Figure 6. Large-caliber gun primer tube concept..........................................................................23 

List of Tables 

Table 1. Chemical composition of the number 41 primer mixture.................................................6 

Table 2. Cheetah code gun calculation results................................................................................9
v

Acknowledgments 

The first author would like to thank Dr. Alan R. Kerstein, the inventor of One Dimensional 

Turbulence, for his continued help. The authors would also like to thank the following: Dr. 

Anthony Kotlar for his help and expertise with Nasa-Glenn thermodynamics code, Mr. Anthony 

Williams for keeping us apprised of the ongoing experiments, and Dr. Pamela Kaste for 

discussions on the analytical work on the primers. The Program Manager – Maneuver 

Ammunition Systems is acknowledged for continued support of this effort. This research was 

performed while the first author held a National Research Council Research Associateship at the 

U.S. Army Research Laboratory. 
vi

INTENTIONALLY LEFT BLANK.
1

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 

(known prior to 1992 as the Ballistics Research Laboratory) 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), which progress in both model complexity and 

dimensionality (i.e., 0-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 that has been paid less attention is 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. This phase was to mimic some 

effects of a true solid phase which would represent the particles that are a major part of most 

primer efflux and will be addressed in this report. 

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. Numerical investigation of this ignition phenomena was previously intractable using 

the NGEN code because the code utilizes an explicit, particle-based treatment of the propellant 

but not the igniter material. It would then follow that such an IB code could be upgraded to 

model the interaction of the discrete primer particles and the discrete propellant particles 

simultaneously. 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. Progress in the development of a primer model that is compatible with the ARLNGEN3 IB code is the subject of this report. 

The conventional ignition system for a large-caliber (120 mm, figure 1) gun consists of a long, 

narrow metallic tube that is mounted on the gun chamber breech and extends into the gun 

chamber along the centerline (11). The tube is perforated along its length, which allows venting 

(primarily in the radial direction) of igniter gases from burning igniter material loaded within. 

This energetic material generally consists of either long sticks of Benite or tightly-packed 

particles (black powder) designed to rapidly ignite and flamespread producing hot gases and hot 

solid particles. The efflux from the primer tube is used to ignite the solid propellant gun charge. 

Conventional modeling of this igniter tube generally consists of a tabular input of gaseous mass 
2

Figure 1. A cut away of large-caliber ammunition showing piccolo tube. 

flow rate as a function of time and, in some cases, axial distance. This table can have both radial 

and axial dimensions and is usually obtained from a set of careful experiments (such as Chang 

and Rocchio [12]). This type of primer model includes solely the gas phase and ignores any 

ignition enhancement that may exist when hot burning particles are ejected from the igniter tube. 

Nevertheless, this type of primer model has been used successfully to predict the performance of 

a number of large-caliber U.S. Army guns (6, 13, 14). 

Small-caliber ammunition (figure 2) is traditionally encased with a brass shell or casing; it has a 

metal jacketed lead projectile or bullet and has a ball powder propellant charge in the main 

chamber to discharge the projectile upon initiation from the pulling of the trigger. 

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

The conventional ignition system for a small-caliber (for example, 5.56 ammunition; see figures 3 

and 4) weapon consists of a metal cup primer (approximately 4.5 mm in diameter) with an interior 

anvil which when hit by a firing pin allows the ignited primer material to exit through the tubular 

primer flow channel (hereafter referred to as the flow channel) into the main chamber of the round 

and ignite the propellant charge (15). Conventional modeling of this primer charge system generally 

consists of a tabular input of igniter-gas mass flow rate as a function of time specified along a small 

radial region along the breechface. This table has solely a radial dimension. This type of primer 

model includes only the gas phase and ignores any charge ignition enhancement from ejected hot 

burning particles. It is widely recognized that this limited treatment of the small-caliber primer is not 

appropriate for IB modeling and has not been successfully used by anyone, to the authors’ 

knowledge. Hot particles play an important role in the propellant ignition in small-caliber 

ammunition (10, 16, 17 [page 66]). However, the present authors are unaware of hot particle 

enhancement of ignition being successfully implemented anywhere in the IB modeling literature. 

Presented in this report is the development of a one-dimensional model of the small-caliber 

primer with the hope that the model can be later extended to the large-caliber configuration. The 

non-linear terms in the Navier-Stokes equations and the pressure term make turbulent fluid flows 
3

Anvil 

Primer cup 

Pellet 

Figure 3. Small-caliber ammunition igniter; primer cup 

with anvil.

Model this section 

for input to NGEN 

Figure 4. Axial cross-section schematic of primer for a 5.56 ammunition. 

difficult to solve even on the fastest computers. With this in mind, people have made a varying 

number of simplifications commensurate with what their needs and available tools (such as 

computer speed) were. The model utilized in this report is based on a method of integrating the 

two-phase flow equations into the vector formulation of a One-Dimensional Turbulence (ODT) 

(18) model to simulate the flow channel which bridges the percussion primer and the propellant 

chamber in the 5.56 round (figure 4) as a steady-state particle-laden turbulent channel flow. 

The novel ODT model is an unsteady turbulent flow simulation model implemented on a onedimensional domain while preserving three velocity components, representing flow evolution as 

observed along a line of sight through a 3-D turbulent flow. Overturning motions representing 

individual eddies are implemented as instantaneous rearrangement events. They obey applicable 

conservation laws and emulate the multiplicative increase of strain and decrease of length scales 

associated with the turbulent cascade. Eddy occurrences are random, with likelihoods 
4

proportional to a local measure of shear kinetic energy. These events punctuate conventional 

time advancement of viscous transport. The ODT model has been used successfully to simulate 

two-phase flow, one-way coupling, in a fully developed turbulent channel. Verification was 

achieved by comparison with direct numerical simulation (DNS), measurements, and large eddy 

simulation (LES) over a wide range of friction Reynolds (180 ≤ Reτ ≤ 1200) and a wide range of 

Stokes numbers, based on wall units, (0.3 ≤ St ≤ 55,000) (19). 

Other methods such as LES, DNS, and Reynolds-Averaged Navier-Stokes (RANS) could be 

(and in many cases have been) applied successfully to solve similar two-phase flow problems. 

Unlike LES, ODT would resolve the scales necessary to capture the smallest eddies in the one 

dimension (transverse to the flow) which ODT keeps track of. In addition, LES needs a subgrid 

model to account for energy losses due to such things as viscosity. Since ODT keeps track of the 

smallest eddy scales, the standard viscous dissipation equation takes care of this. An additional 

consideration is that the LES method would need a subgrid model to account properly for the 

two-phase flow portion of the model. Because ODT captures the smallest scales, no additional 

assumptions are needed for implementation into ODT. As Pope (20) points out, when defining 

LES as resolving 80% of the energy in the grid, the high turbulent Reynolds numbers are still 

beyond the reach of the largest main frames. (This Reynolds number boundary is continuously 

being moved higher.) To add to this restriction, the fact that particle-laden LES requires a 

significant increase in computer resources (over fluid only LES) indicates that ODT is an 

acceptable alternative to LES. 

The state-of-the-art DNS modeling of turbulent flows is restricted by the maximum Re allowable 

due to the memory and speed of the fastest computers available. The memory requirement for 

DNS goes as the number of grid points needed to resolve fully the turbulent (Kolmogorov) scale 

raised to the third power. Since ODT keeps track of only one dimension, the required memory 

scales directly with the number of grid points needed to resolve the turbulent scale. Though 

progress to bring DNS to the high Re regime continues on all fronts, there is still much work to 

be done in order to use DNS for practical industrial or military applications. Since the ODT 

model capitalizes on the symmetry of the flow and utilizes innovative methods to model threedimensional turbulent behavior on a one-dimensional domain, it is the model of choice for this 

highly turbulent flow configuration. 

RANS based models have also been used to predict two-phase-flow problems (21). Call and 

Kennedy (22, 23) have shown that stochastic separated RANS models do a poor job in capturing 

the behavior of evaporating droplets in turbulent flow. They suggest that the treatment of droplet 

vaporization may be problematic. The multi-physics involved (the coupling between the droplet 

evaporation, the drag, and the turbulent eddies on the droplet trajectory) indicates that the 

instantaneous gas temperature profile is also of primary importance when droplets are 

undergoing vaporization since the variations in the gas phase temperature directly correspond to 

variations in the droplet temperature profile. Since ODT keeps track of the instantaneous 
5

velocity and temperature profiles, it has a distinct advantage in the long run over RANS, which 

does not automatically correlate the velocity and temperature fluctuations. There are authors 

who have attempted to add models which will do such correlations, but they do so by adding 

more models to the RANS structure. The present authors believe that working with ODT rather 

than RANS will make the results less model dependent. 

In the present report, initial results are shown for the primer model run as a stand-alone code and 

are compared to the on-going experiments with small-caliber primers being conducted by 

Williams et al. (24). Some aspects of our work are compared to Kuo et al. (25). Plans for 

coupling the present primer model to the ARL-NGEN3 code and extensions of the model to 

large-caliber primers are discussed. 

2. The ARL-NGEN3 IB Code 

Since one of the primary motivations for the present work is to develop a primer model that is 

compatible with the ARL-NGEN3 IB code, a brief description of this code is included for 

completeness. For further details the reader is referred to papers by Gough (4, 5) and Nusca (5, 6). 

The Army’s NGEN3 code is a multi-dimensional, multi-phase CFD code that incorporates threedimensional continuum equations along with auxiliary relations into a modular code structure. 

On a sufficiently small scale of resolution in both space and time, the components of the interior 

ballistic flow are represented by the balance equations for a multi-component reacting mixture 

describing the conservation of mass, momentum, and energy. A macroscopic representation of 

the flow is adopted using these equations derived by a formal averaging technique applied to the 

microscopic flow. These equations require a number of constitutive laws for closure including 

state equations, intergranular stresses, and interphase transfer. The numerical representation of 

these equations as well as the numerical solution thereof is based on a finite-volume 

discretization and high-order accurate, conservative numerical solution schemes. The spatial 

values of the dependent variables at each time step are determined by a numerical integration 

method denoted the continuum flow solver (CFS), which treats the continuous phase and certain 

of the discrete phases in an Eulerian fashion. The Flux-Corrected Transport scheme is a suitable 

basis for the CFS since the method is explicit and has been shown to adapt easily to massively 

parallel computer systems. The discrete phases are treated by a Lagrangian formulation, denoted 

the large particle integrator (LPI), which tracks the particles explicitly and smoothes 

discontinuities associated with boundaries between propellants yielding a continuous distribution 

of porosity over the entire domain. The manner of coupling between the CFS and the LPI is 

through the attribution of properties (e.g., porosity and mass generation). The size of the grid as 

well as the number of Lagrangian particles is user prescribed. The solid propellant is modeled 

using Lagrange particles that regress, produce combustion product gases, and respond to 

gasdynamic and physical forces. Individual grains, sticks, slab, and wrap layers are not resolved; 
6

rather, each propellant medium is distributed within a specified region in the gun chamber. The 

constitutive laws that describe interphase drag, form-function, etc., assigned to these various 

media determine preferred gas flow paths through the media (e.g., radial for disks and axial for 

wraps) and responses of the media to gasdynamic forces. Media regions that are encased in 

impermeable boundaries which only yield to gasdynamic flow after a prescribed pressure load is 

reached act as rigid bodies within the chamber. The use of computational particles to represent 

the propellant charge permits a host of other modeling features that enhanced the representation 

of charge details. 

3. Description of the Primer 

3.1 Chemistry 

The composition of Army small-caliber primers is well known (15) and unchanged for many 

years (table 1). This primer composition is used in all of the Army’s small- and medium-caliber 

ammunition. 

Table 1. Chemical composition of the number 41 primer mixture. 

Name Formula Weight-Percent

± Weight-Percent 

Deviation Primary Purpose 

Lead styphnate H3 C6 N3 O9 Pb 37 5 Primary explosive 

Barium nitrate Ba (N O3)2 32 5 Oxidizer 

Antimony sulfide Sb2 S3 15 2 Fuel, slow 

Aluminum powder Al 07 1 Fuel, fast 

Tetracene H8 C2 N10 O 04 1 Primary explosive 

PETN C5 H8 N4 O12 05 1 High explosive 

Lawrence Livermore National Labs developed a thermodynamics code for explosives called 

Cheetah (26) which includes the option for a gun calculation. The gun calculation is done under 

conditions of constant specific volume and enthalpy, which are meant to simulate a gun firing. 

Of special interest to the IB community is the ratio of specific heats (frozen) called γ, along with 

the thermodynamically predicted temperature and pressure. 

Primary explosives detonate or explode upon shock or added heat. High explosives detonate 

under the influence of the shock of the explosion of a suitable primary explosive. Explosives do 

not necessarily combust; in some cases, explosives do not have the necessary ingredients to 

combust. Propellants are materials which contain sufficient amount of oxygen to burn without 

exploding, but provide gas which thereafter may produce an explosion. Fuels are similar to 

propellants, but they need oxygen from another source to burn. Oxidizers are materials with 

excess oxygen which when liberated can be used by a fuel. 
7

The lead styphnate and tetracene are primary explosives meant to convert the shock induced by 

the firing pin into the initiation of the primer material. Tetracene is the more impact sensitive of 

the two (10, 27) and is important in order to keep stability in the sensitivity of the small-caliber 

primer (28). Davis (10) points out that as little as 2 weight-percent is enough to improve the 

sensitivity of primers. The impact sensitivity of tetracene is given as 1 N-m, and lead styphnate 

as 2.5–5 N-m (27). 

The PETN (pentaerythritoltetranitrate) is a high explosive added to the primer mix to increase 

brisance (the shock produced) and heat produced. The impact sensitivity is given as 3 N-m (27). 

The aluminum powder increases the heat produced upon ignition, i.e., the enthalpy of 

combustion of aluminum raises the peak temperature of the explosive event. (The added effect is 

dependent on the Al particle size.) The aluminum powder is assumed to sequentially oxidize, 

but first the encapsulating Al2O3 coating must be disturbed to allow oxygen to the elemental Al 

in the core of the powder. This can be done by melting the oxide (2045 °C, melting point), 

melting the interior elemental Al (660 °C, melting point), or vaporizing the interior Al (2057 °C, 

boiling point). It is interesting to note that an explosive mixture consisting of only liquid oxygen 

and porous aluminum was invented in 1895 (10, page 355), the products of which are only solid 

aluminum oxide, the excess oxygen gas, and much heat. The aluminum powder is a fuel which 

burns quickly once ignited due to a cascading effect of the large amount of heat released. 

The barium nitrate is an oxidizer which undergoes a chain of decomposition reactions which first 

produce NOx and barium peroxide. The NOx goes into the gas phase where it can supply oxygen 

to the fuels. The barium peroxide decomposes to barium oxide with further heating during the 

primer initiation. Barium nitrate produces a green flame when burned in air. 

3 2 2 () () ( ) () 2 heat Ba NO BaO NO S S XG ⎯⎯⎯→ + . (1) 

2 2 () () ( )

1

2

heat BaO BaO O S SG ⎯⎯⎯→ + . (2) 

The antimony sulfide, also known as stibnite, is a slow fuel. Davis (10, page 454) describes, as 

an constituent of percussion primers, “antimony sulfide (a combustible material which maintains the 

flame for a longer time) ...” Antimony sulfide produces a blue flame when burned in air. 

3.2 Description of the Primer Firing Event 

The action of the firing pin hitting the primer cup causes the detonation of the primary explosives 

(tetracene and lead styphnate) and the high explosive (PETN). The aluminum is a fuel which 

burns very quickly. The outer surface of the Al powder is actually Al2O3, up to 30 % by weight. 

Burning occurs when the inner Al (that is not oxidized) is exposed to oxygen. This can be done 

by either melting the solid particles or vaporizing it (sublimation). Oxide cracking would also 

provide an avenue for oxygen to reach the aluminum. The convection currents in the melted Al 

particles would assure fresh un-oxidized aluminum would be supplied to the surface. Once at the 
8

surface it would react with available oxygen and release a generous amount of heat. This heat 

would increase the convection currents supplying more un-oxidized aluminum at the surface, and 

a cascading effect takes place. After a suitable amount of energy is produced by this process the 

particles could then vaporize, which would burn (oxidize) in the vapor phase. The first reaction 

of aluminum with oxygen produces AlO. The largest spectral signature from burning aluminum 

powder is Al O (29). 

2

1

2 Al O Al O + → . (3) 

From the open-air experiments and analysis of Williams et al. (24), the aluminum containing 

particles are mostly in the submicron size range. This indicates that the aluminum containing 

particles nucleated from the vapor phase into the solid phase upon cooling. This supports the 

supposition that the aluminum powder is a fast burning fuel. 

The barium nitrate is an oxidizer with the primary purpose of ensuring that the fuels have enough 

oxygen containing compounds in the vapor phase to react to completion. The decomposition of 

barium nitrate is highly endothermic (17, page 263) and burns with a green flame (30, page 29). 

The decomposition process is described in detail by Bordon and Campbell (31). As previously 

stated, the barium nitrate decomposes with heat to oxygen containing nitrogen compounds which 

can then give up their oxygen in the gas phase. The barium peroxide will (with additional 

heating) decompose to barium oxide and oxygen. The oxygen is then available for the fuels in 

the gas phase. The analysis (24) indicates that there may be some BaO present after the open air 

firings, but that was inconclusive. Kaste’s analysis of the products of the closed chamber packed 

with inert propellant grains, primer firing showed a marked decrease in the nitrates. This is 

consistent with the higher pressure, temperature, and time of exposure to which the primer 

products (including barium nitrate) would be exposed in a closed chamber with an inert 

propellant bed. 

The antimony sulfide is also a fuel similar to the aluminum powder, but the reaction takes a 

longer time. The solid antimony sulfide melts with added heat; the liquid drops must absorb 

more heat to vaporize, only once it reaches the vapor phase can the antimony sulfide produce 

appreciable amounts of antimony oxide. The analysis of both the open air and inert propellant 

experiments of Williams et al. (24) indicates that this reaction is slow, as no antimony oxide peaks 

were detected by Fourier Transform InfraRed (FTIR), which would have been readily apparent if 

there were any substantial amounts. It is possible that the antimony sulfide also serves a secondary 

purpose during the initiation phase of the primer. That is while the firing pin is impinging on the 

primer cup, the secondary purpose is to make the mixture more sensitive to percussion. A similar 

function is provided by ground glass in some percussion primers (10, page 455). Of note is that 

high-speed films of the no. 41 primer open air firings (24) were compared to the open air firings of 

a primer without antimony sulfide as an ingredient. The primer no. 41 firing showed a definite 

blue hue near the end of the firing event, where the primer without stibnite failed to show a blue 

hue. This indicates that there was some burning of the antimony sulfide. 
9

For the present work, the proposed model is that the primary and high explosives detonate first, 

with the aluminum powder burning quickly after. The barium nitrate decomposes after some 

heating, which takes longer than the aluminum. The antimony sulfide first melts and vaporizes 

before it can react, which takes the longest time due to heat transfer and kinetic constraints. 

In order to properly supply the NGEN code with information on the efflux from the primer spit 

hole (see figure 4), we propose that particles of barium nitrate and antimony sulfide are heated in 

the flow channel. The flow channel is represented by a particle-laden fully turbulent channel 

flow. Some of these particles melt due to heat conduction from the hot turbulent gas flow 

through the primer flow channel produced in the detonation event. 

Gun thermodynamic calculations were performed using the Cheetah code (26) with the 

components tetracene, lead styphnate, PETN, and aluminum powder to simulate the gas phase 

equilibrium conditions. The aluminum powder was assumed to be 30% by weight Al2O3 and the 

balance elemental Al. The results can be found in table 2. In this model, the stibnite and barium 

nitrate are only heat sinks (absorbing energy from the flow) while in the primer tube. To account 

for the heat loss, an estimate of energy needed to bring these solid particles from room 

temperature to the thermodynamically determined final temperature (as predicted by a Cheetah 

gun calculation) was subtracted from the heat of formation of one of the components (lead 

styphnate). Only some of the heat capacities and heats of fusion for barium nitrate and antimony 

sulfide were available in the literature. Utilizing the heat capacity of solid stibnite, the amount of 

energy needed to take the compound from room temperature to its melting temperature of 819 K 

was calculated. The heat of fusion (33 cal/g) was then used to compute the heat necessary to 

melt the stibnite. The heat capacity of liquid antimony sulfide could not be found. As an 

approximation, the heat capacity of liquid antimony was used in its stead. Therefore, an estimate 

of the energy necessary to bring antimony sulfide from room temperature to 2312 K was 

computed. The energy needed to heat the barium nitrate was assumed to be identical. The 

experimental observations (24) and the Cheetah calculations both indicate that the flow inside 

the primer tube is highly turbulent. The gun calculation was done with a loading density of 

0.0139 g/cm3

. This was computed from the mean pellet weight (0.025 g) as specified in the 

military drawing M855TDP for the 5.56 primer pellet and the empty chamber volume of 1.8 cm3

. 

The input and output files for Cheetah can be found in the appendix. Based on the assumption 

that the stibnite and barium nitrate remain in the solid phase and the condensed phase from the 

Cheetah calculation, this model estimates a condensed phase of greater than 60%. Note that this 

is inconsistent with the Kuo et al. (25) computed estimate of 40% condensed phase. 

Table 2. Cheetah code gun calculation results. 

Temperature Pressure Impetus Molecular Weight Covolume Gamma, Frozen 

2797 K 7.4 MPa 530 J/g 44 g/g-mol 0.635 cm3/g 1.176 
10

4. Formulation of the Primer Model 

The pertinent work of Williams et al. (24) as related to this primer model consisted of a set of 

open-air primer experiments recorded with time-lapse photography and analysis of the blast via a 

witness plate and subsequent SEM/EDAX/FTIR analysis. Additional experiments were 

performed in a closed chamber with inert balls meant to simulate the primer action as 

realistically as possible without the ignition of a propellant bed. 

A fundamental motivation behind the production of this model is the conjecture that the hot 

particles ejected into the propellant bed are essential to capturing the initiation and flame 

spreading phenomena. 

The pictures indicate that the explosion event consists of hot gases and particles being ejected 

from the flow channel at high velocities. This motivated the development of a primer model 

concentrating on the flow channel. With proper attention to detail, the output of this primer tube 

can be feed into the NGEN code. NGEN calculations can then be made to carry these gases and 

particles to the proper ignition of the propellant bed with minimal changes to NGEN. 

The primer tube is modeled as a fully turbulent steady-state particle-laden fluid channel flow. 

The particles are chosen to be Ba(NO3)2 and Sb2S3 based on the thermochemical calculations and 

the results from Williams et al. (24). Particles are released into the simulation of the flow 

channel at room temperature and allowed to absorb heat from the turbulent channel. Upon 

heating the particles melt. The hot particles which leave the spit hole are carried by the NGEN 

simulation into the propellant bed (see figure 4). There they release heat conductively to the 

propellant and can aid or even cause ignition of the propellant. 

4.1 The Navier-Stokes Equation 

Du 2 P ug Dt ρ = −∇ + ∇ + μ ρ    . (4) 

The Navier-Stokes equation simply says that the mass per unit volume times the acceleration 

(which is the Left Hand Side [LHS]) is equal to the pressure force on said element per unit 

volume (first term on the Right Hand Side [RHS]) along with the viscous force on the element 

per unit volume plus the body forces per unit volume (the last term on the RHS). Note that even 

though g is used, equation 4 is not restricted to only gravitational forces. Vectors are denoted by 

a tilde “~” above, ρ is the density of the fluid, μ is the viscosity, P is the pressure, t is time, and u

is the fluid velocity vector. 
11

4.2 Overview of the One-Dimensional Turbulence Model 

Kerstein developed a one-dimensional Monte Carlo modeling technique for turbulent mixing of 

velocity and scalar fields. A subsequent extension (18) keeps three velocity components on the 

ODT domain. This allows for the introduction of an ODT analogy of pressure scrambling. The 

fields defined on the one-dimensional domain evolve by two mechanisms: molecular diffusion 

and a stochastic process representing advection. The ODT approach represents turbulent 

advection by a random sequence of “eddy” maps applied to a one-dimensional computational 

domain. Profiles of the velocity components (ui) and the advected scalars evolve on this domain. 

Equations for the turbulent flow field are not solved explicitly; rather, the viscous and diffusive 

equations are solved: 

( ) ( ) ( ) ( )

2

2

2

2 , , , , , 1

y

y t

t

y t

dx

dp

y

u y t

t

u y t i i

∂

∂ = ∂∂ − ∂

∂ = ∂∂ θ

κ

θ

ρ

ν , (5) 

where t is time, ν is the kinematic viscosity, ρ is the density, θ can be any advected scalar (e.g., 

temperature, species concentration, etc.), and κ is the corresponding diffusion coefficient. Note 

that the dp/dx term in equation 5 is an imposed mean pressure gradient in the streamwise 

direction. 

In order for ODT to be used there must be a minimum of one homogeneous direction. There 

should be a predominantly streamwise direction. The one dimension in the ODT model is 

transverse to the mean flow. The ODT model implements triplet maps or eddies as instantaneous 

rearrangements of the velocity ui(y, t) field. 

The events representing advection may be interpreted as the model analogue of individual 

turbulent eddies. However, this interpretation is not essential to the analysis; it merely provides 

an intuitive basis for presenting the model. Essentially, each ‘eddy event’ has three properties: a 

length scale l, a time scale τ, and a measure of kinetic energy. 

The vector (three-component) form of ODT has eddy events consisting of two mathematical 

operations. The first is a measure-preserving map representing the fluid motions of a turbulent 

eddy. The other is a modification of the velocity profiles in order to account for energy transfers 

between velocity components. 

u ( ) y u ( f (y)) c K(y) (y) ( f (y)) i → i + i , . (6) θ →θ

The fluid at location f(y) is moved to location y by the mapping operation. This mapping is the 

vector ODT analog of the advection operator v · ∇ of the Navier-Stokes equations. This 

mapping is applied to all fluid properties. The additional term ciK(y), which is only applied to 

the velocity components, is the ODT analogue of pressure-induced energy redistribution among 

the velocity components. This also takes care of velocity changes due to pressure gradients or 

body forces. 
12

The triplet map has a starting point yo and a length l which are sampled randomly from an eddy 

distribution rate. The mapping rule y Æ ⎯y for a triplet map is given by 

( )

( )

( )

1 1

3 3

21 1 2

33 3 3

21 2

33 3

o o oo

o oo o

o oo o

y yy y y y l

y l yy y l y y l

y

y l yy y l y y l

y otherwise

⎧ + − << + ⎪

⎪

⎪ + − − + << + = ⎨

⎪ + + − + << + ⎪

⎪⎩

, (7) 

where ⎯y is the y profile after the instantaneous rearrangement. 

The desired attribute of the triplet map is to provide a means of mimicking the increase in strain 

intensity, the decrease in strain length scale, and the increase in mixing due to eddies in physical 

turbulent flow. This mapping rule assures that closest neighbors after the spatially discretized 

mapping event were no more then three cells (or fluid elements) apart before the mapping event. 

Hence, the increased strain rate and shortening length scale is attained without undue 

introduction of discontinuities. Using the continuous analog to describe the triplet map, the 

original scalar profile is reduced by a factor of three, and a copy is placed in both the first third 

and the last third of the eddy domain. For the middle third, the reduced image is inverted. 

Though there are other mappings which could be used, this implementation of the triplet map is 

the simplest which obeys three key physical conditions: (1) measure preservation (the non-local 

analog of vanishing velocity divergence, this property is manifestly satisfied in the discrete 

numerical implementation, in which the map is a permutation of equal-volume fluid cells on the 

1D domain), (2) continuity (no introduction of discontinuities by the mapping operation), and 

(3) scale locality (at most order-unity changes in property gradients). The first two conditions 

are fundamental properties of incompressible fluid motion. The third is based on the principle 

that length-scale reduction in a turbulent cascade occurs by a sequence of small steps 

(corresponding to turbulent eddies), causing down-scale energy transfer to be effectively local in 

wavenumber. 

Fluid parcels or elements are moved instantaneously during the triplet map from one y location 

to another. The momentum and passive scalar properties of each fluid particle or cell are 

preserved and remain unaffected (at first) by the instantaneous rearrangement. Subsequently 

energy redistribution among the three velocity components is implemented. This is represented 

by the ci term in equation 6. In equation 6, the K term is a kernel function that is defined as 

K(y) = y – f(y). Hence, its value is equal to the distance the local fluid element is displaced. 

Therefore, it is by definition non-zero only within the eddy interval l. The kernel integrates to 

zero so that the ‘eddy event’ does not change the total (y-integrated) momentum of individual 

velocity components. 
13

As mentioned, each eddy event has a time, a length scale, and a measure of kinetic energy 

associated with it. The kinetic energy of an individual velocity component i is 

( ) 1 2

2 E u y dy i i ≡ ρ ∫ . (8) 

(The density ρ, assumed constant, is defined here as mass per unit length.) The amplitudes ci in 

equation 6 are determined for each individual eddy subject to two constraints: (1) the total 

kinetic energy remains constant and (2) the energy removed from any individual velocity 

component by the kernel mechanism cannot exceed the energy available for extraction (18). 

In ODT, eddy events are instantaneous in time and occur with frequencies comparable to the 

turnover frequencies of corresponding turbulent eddies. Events are therefore determined by 

sampling from an event-rate distribution that reflects the physics governing eddy turnovers. 

Flow properties (e.g., velocity variations) affect the eddy rate distribution and the successful 

eddy events (based on sampling using a rejection method) affect the velocity distribution (and 

passive scalars). This creates a feedback by increasing the strain rate which allows more triplet 

maps to occur. The event rate, λ, is shown (18) to be 

( ) ( ) ∑ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ≡ = j

j K

j

K

o

o Z

u l

T

u l

l

C

l y l t

C

y l t

2

,

2,

2

2,

2 4 , ; , ;

ν

α

ν

ν

τ

λ , (9) 

where the matrix T assures invariance under axis rotation; all other new variables are defined 

shortly. If the quantity in the radical of equation 9 is negative, the eddy is deemed to be 

suppressed by viscous damping and λ is taken to be zero for that eddy. In the square root term, 

the quantities preceding Z involve groups that have the form of a Reynolds number. As such, Z

can be viewed as a parameter controlling the critical Reynolds number for eddy turnover. 

There are three free parameters in the ODT model proper: C, α, and Z. The free parameter C

determines the strength of the turbulence; hence, C allows fine adjustments to the eddy rate 

distribution. The transfer coefficient α determines the degree of kinetic energy exchange among 

components. (The matrix T in equation 9 depends on α.) The viscous cutoff parameter Z

determines the smallest eddy size for given local strain conditions. 

These three parameters, along with the initial and boundary conditions of the flow and the 

physical conditions of the fluid (density, viscosity, etc.), constitute the complete inputs for the 

vector ODT model proper. One additional free parameter is needed for the two-phase flow 

application. 
14

4.3 Particle Dynamics for a Perfect Sphere 

The full equation of motion for a particle suspended in a fluid (32): 

( )

( ) ( )

3

3 3

2

0

3

6 6 12

3 ' ' ' , 2 '

p pf

p p pf

t

p

f ei

i

dV du du dV D

D DuV D

dt dt dt dt

du dV D dt dt dt F

t t

ρπ π ρ π

πμ ρ

πρ μ

⎛ ⎞

= −+ + − ⎜ ⎟ ⎝ ⎠

−

+ + − ∑ ∫

     

 

(10)

where the LHS is the mass times the acceleration term, or the change in particle inertia. The first 

term on the RHS is Stokes force due to viscous drag. The second term on the RHS is due to 

pressure gradient in the fluid surrounding the particle, caused by acceleration of the gas by the 

particle. The third term on the RHS is the force required to accelerate the apparent mass of the 

particle relative to the fluid (that is the “added mass” term, the force needed to accelerate the 

fluid displaced by the sphere). The fourth term on the RHS is called the Basset history integral; 

this accounts for the force arising due to the deviation of the fluid velocity from steady state (or 

one can view this as accounting for the increase in viscous drag due to flow unsteadiness). The 

fifth and last term on the RHS is simply the summation of the body forces, or the buoyancy 

forces. Note that the particle velocity vector is V, the subscript p is a for particle property, the 

subscript f is for a fluid property, and Dp is the diameter of the particle. 

This equation has a long history (see Stock [33]) and is known as the BBO equation, for BassettBoussinesq-Oseen equation (see Maxey and Riley [34]). It is the general Lagrangian equation of 

motion for particles in an unsteady flow. 

Luckily, many of the terms drop out if the density of the particle is much greater than the density 

of the air, as long as the diameter of the particle stays below the smallest turbulent eddy scale. 

This equation can be simplified to equation 11 (35). Note that equation 11 can also be derived 

by a simple force balance around a particle. The drag law, equation 11, may seem too simple 

when compared to equation 10, but Sirignano (36) states that good engineering analysis can be 

performed using only modified Stokes drag and the gravitational force. A majority of the stateof-the-art publications in the area of two-phase flow use the simplified drag force to compute the 

motion of particles. 

( ) V

dt

f dX

u V

m

F

dt

dV

p p

G ~ ~

, ~ ~ ~ ~= + − = τ

, (11) 

2

0.687

1

, , Re . 18 1 0.15Re

p p g pp g

p

g

D Stokes law rV u

f non linear

ρ ρ

τ

μ μ

⎧ − == = ⎨

⎩ + −

  (12) 
15

4.4 Particle – Fluid Interactions 

The development of two-phase flow models with a turbulent gas phase is traditionally broken 

into three categories: one-way coupling, two-way coupling, and four-way coupling. The 

simplest is one-way coupling, or passive particle transport. In one-way coupling the turbulent 

contribution of the dispersed phase is negligible. The turbulent field is much more likely to gain 

kinetic energy from the gas flow rather than from the flow of the dispersed phase. Here, the fluid 

affects the particle, but the particle does not affect the fluid. This is often symbolized as follows: 

fluid Æ particle (one arrow). 

The two-way coupling flows are the next complicated. In this case the volume fraction of the 

dispersed phase is high enough that the mean flow of the particles can induce turbulent motion in 

the fluid. (Also, as in the one-way coupling, the turbulent fluid motion induces motion in the 

particles. Hence the title, two-way coupling.) This is symbolized as follows: fluid Å Æ

particle (two arrows). 

The most complicated of the flows is referred to as four-way coupling. In this case, the volume 

fraction of the dispersed phase is so large that the dispersed phase particles not only affect the 

fluid flow, but also affect each other by way of collisions or near collisions (wake or boundary 

layer interactions). This is symbolized as follows: fluid Å Æ particle Å Æ particle (four 

arrows). Elghobashi (37, 38) shows the range in which the three types of coupling are of 

importance. 

The present model utilizes the one-way coupling, or passive transport assumption. A Lagrangian 

framework for the particle is used with the key forces on the particle considered to be a modified 

Stokes drag and gravity. A majority of the state-of-the-art publications in the area of two-phase 

flow use the one-way coupling assumption along with a drag force to compute the equation of 

motion of particles. 

4.5 Particle – Wall Interactions 

In real world experiments (such as the flow in the primer firing), there are many contributing 

factors which make the two-phase flow modeling a difficult task. A short discussion on some of 

the main points of consideration when modeling particle-wall interactions is here presented. 

The main considerations for collisions are elastic vs. inelastic and all particles bouncing off vs. 

all particles sticking to the wall vs. some combination of any of these. There are other important 

considerations, such as (1) what happens if the particles are nonspherical (39) (will wall 

collisions cause the particles to spin and hence create Magnus forces), (2) the difference between 

free slip and no slip surfaces (40), and (3) re-entrainment mechanisms in turbulent flow as a 

function of particle size (41), to name but a few, but these are left for future work. 

A particle which hits a surface in the real world would either bounce off or stick to the surface. 

It must do one or the other, unless the particle somehow breaks apart and one part sticks to the 
16

wall while the other is re-entrained into the fluid flow. For obvious reasons, particle break up is 

too complicated for the scope of the present project. 

Particles which hit the wall and bounce off are most likely affected by the wall roughness. Many 

experimenters go to great pains to make the surfaces smooth relative to the particle size they are 

interested in or to characterize the surface roughness. 

Particles which bounce off a surface are not only affected by the roughness of the wall, but they 

also bounce off in an inelastic manner. Many surfaces, however, can closely match the behavior 

of flat walls with totally elastic collisions for all practical purposes. 

For the present work all collisions with a wall stick to the wall. For future work, the 

determination is based on the physical state of the particles: if a particle is in the solid phase, it 

bounces off the wall; if a particle is in a liquid phase, it sticks to the wall. This, of course, cannot 

hope to totally capture real experiments, since real experiments have much more physics than 

either of these two cases. Note however that many researchers use spectral reflection (42–44) for 

studying particle behavior in turbulent channel flow. Many other researchers investigate 

turbulent particle deposition by particles sticking to the wall as soon they get within one particle 

radius of the wall (45–49). 

4.6 Model Implementation 

To implement particle-laden flow into ODT is not straightforward because fluid motion 

(displacement by eddy events) and fluid velocity are distinct in ODT. This problem was first 

overcome by Schmidt (50), where a particle-eddy interaction mechanism was introduced. The 

net outcome is a particle-eddy interaction that obeys correct limiting behaviors (infinite inertia 

and vanishing inertia) and transitions smoothly between these limits. A second difficulty arises 

because the fluid velocities are being tracked in a Eularian reference frame but the particles are 

tracked in a Lagrangian reference frame. If the velocity of the particle is much greater than the 

bulk velocity of the fluid, the particle would move a distance X downstream in a much shorter 

time than the flow would move that same distance. This is compensated for by setting the 

particle time line to account for the velocity difference between the particle and the fluid. 

The particle-fluid interaction during continuous evolution follows conventional approaches to 

drag law implementation, except that (1) to preserve the tracer limit only the x and y components 

of the gas velocity are nonzero and (2) to preserve proper time development of the particle, 

particle time is set equal to continuous time, t, divided by one plus the slip velocity in the x 

direction divided by the bulk fluid velocity also called the plug flow velocity: 

1 1 1

p

pf

t

t

V u

U

= − +

. (13) 
17

Particle interaction with a triplet map requires a novel approach, albeit in the spirit of existing 

particle-eddy interaction models. This interaction occurs when the particle and triplet map 

occupy the same space-time. The particle drag law as written is not applicable to ODT particleeddy interactions because triplet maps are instantaneous in time, yet the particle-drag law 

requires an interaction time to cause a change in the particle velocity or position. 

The logical solution to this difficulty is to assign an interaction time to the particle-eddy 

interaction. The interaction time coordinate is called T. This coordinate is introduced so that the 

particle drag law can have an effect on the particle without time advancing the flow solution. 

Particle evolution during this interaction is governed by the y, x, and z components of the particle 

drag law recast as follows: 

( ) ( ) ( )

Gz

p

Gx

p

Gy

p

E f A V u

dT

dV f A V u

dT

dV f A V v

dT

dV

+ − + = − − + = − − = − τ τ τ

2 2 1 1 1 3 3 3 , , ; (14) 

where T is the interaction time coordinate; vE is the fluid y component velocity induced by the 

triplet map; u1 and u3 are the x and z velocity components of the fluid cell which contains the 

particle center at the onset of the particle-eddy interaction; AGx , AGy, and AGz are the 

accelerations due to all body forces in the x, y, and z directions; and all other terms are as 

previously defined. In this formulation, vE is defined so that tracer particles behave correctly; 

that is, they mimic the motion of the fluid cell which surrounds them. 

ODT proper has a time scale associated with every eddy τ(yo, l; t). Accordingly, the eddy 

lifetime is taken to be a constant times that eddy timescale. The definition chosen for vE is 

( ) , ;

E

o

h

v

βτ y lt = , (15) 

where h is the displacement of a fluid element and a free parameter β has been introduced. This 

definition is chosen because it yields the correct tracer-particle limit of equation 14. 

As discussed in Kerstein et al. (18), in the analytical formulation of the triplet map, three images 

of the original fluid interval are formed, so there are three distinct fluid displacements h

corresponding to the three images generated by the triplet map. For the fluid, the three 

displacements correspond to subdivision of a given fluid element into thirds, with application of 

a different displacement to each third. Unlike fluid elements, individual particles cannot be 

subdivided, so determination of vE requires a determination of which one of the three h values 

associated with a fluid element applies to a given particle within the fluid element. The h for a 

particle is determined randomly from among the three choices. 

An eddy exists in a defined space (three-dimensional) space for a defined lifetime. Particle-eddy 

interactions occur while the particle occupies the same space-time (x, y, z, t) as the eddy and 

ceases the first time the particle leaves the ODT space time (x, y, z, t), which the eddy is 

idealized to occupy. Additional details on this aspect can be found in Schmidt (19). 
18

A problem arises when comparing the integration done in interaction time over a time period T

and the conventional particle-time integration of the drag law subsequent to the particle-eddy 

interaction over a comparable time interval ∆t. Comparison of equations 11 and 14 indicates that 

the equations contain similar terms and therefore the resultant actions of integrating them over 

the same time period are in fact double counting acceleration effects. To overcome this problem, 

the particle trajectories with and without the effect of the eddy are computed. This is achieved 

by integrating both during continuous evolution and interaction time concurrently over the period 

Τ and determining the difference in the ending yp position and the ending V velocities. 

( ) ( ) , ( ) ( ) in in

pp p ∆ = − ∆= − y yT yT V VT V T . (16) 

These computations define the perturbations felt by the particle due to the eddy, where the 

superscript i (for interaction) denotes the results based on equation 14 and the superscript n (for 

no interaction) denotes using equation 11. 

This procedure is pictorially represented in figure 5a. The perturbation distance, ∆yp, 

(demarcated with a “}”) and the perturbation velocity, ∆V, are then added to the particle’s 

original position and velocity (respectively) at the instant it first encounters the triplet map. On 

this basis, the particle location yp’ and y velocity V’ resulting from the particle-eddy interaction 

are yp’ = yp + ∆yp, V’ = V2 + ∆V, where yp and V2 are the values at the instant the particle 

encounters the eddy (prior to the interaction). With double counting thus eliminated, continuous 

evolution resumes. Results of this procedure are shown in figure 5b. No adjustments in xp, zp, 

V1, or V3 are made for a particle-eddy interaction. Since interaction time exists only during 

particle-eddy interactions, the initial particle velocity, Vo, during interaction time is set equal to 

the final particle V3 velocity from the last time that the particular particle was involved in a 

particle-eddy interaction. That way Vo matches the end V3 velocity of that same particle the 

instant it ended the last particle-eddy interaction. 

5. Computational Results for a Small-Caliber Simulator 

Returning to the problem at hand, recall that figure 4 highlights the channel separating the primer 

from the main chamber of the ammunition. 

The channel half height h was taken to be equal to the nominal radius of the primer flow channel 

tube as given in the military technical description package M855TDP as 0.1016 cm with a 

deviation of 0.00508 cm, which gives a cross-sectional area of 3.24 × 10-6 m2

. 

The channel length is taken to be the equivalent length based on the volume if the primer 

chamber did not undergo a sudden contraction. 
19

V

Y 

T1

V’ = V2+ Vi-Vn

0 0 

Vi

∆ yp

Vn

(a) (b)

Trajectory without eddy interaction. 

Trajectory with 

eddy interaction. 

Interaction Time Particle Time 

∆ yp

Y

Figure 5. The procedure for implementing particle-eddy interactions which avoids double counting. Find ∆yp and 

∆V, then add them to the original position and velocity. The resultant position and velocity are shown 

in (b). 

Particle sizes are taken as a nominal size based on the military specification for the raw materials 

(stibnite and barium nitrate) used in preparation of the no. 41 primer. Particle distributions are 

possible, but left to future work. 

Presently, all particles are released into the channel at the same instant in time. However, 

staggering the release time can be done easily, but is left to future work. 

5.1 Parametric Scaling 

In order to completely capture particle-laden channel flow in a computer simulation there needs 

to be dimensional similarity in the Reynolds number of the flow, the Stokes number of the 

particle, and the ratio of radius of the particles to the channel height h. In addition, the initial and 

boundary conditions of the fluid and the particles must be the same. Particle-laden ODT (PODT) 

is capable of meeting all of these conditions. 

The bulk Reynolds number of the flow through the primer tube was computed by equation 17 

with the (incompressible fluid) plug flow or bulk velocity Upf defined in equation 18. The 

volume of the chamber Vc (1.5 cm3

) and the duration of the primer firing event t (9.55 ms) was 

taken from Williams (51) . This gave a plug flow velocity of ~ 48.4 m/s. The viscosity of the 

fluid is unknown; an estimate was taken by searching the thermophysical properties of 

compressed air in the region given by the Cheetah code (2800 K and 7.4 MPa) and looking for 

agreement with the density (0.12 kg/m3

). Reasonable agreement with the density was found in 
20

the area between 6 and 8 MPa and 2500 K. A value of 8.17 × 10–5 kg/m/s was estimated for the 

primer products. This leads to a bulk Re ~ 12,000. 

Re f pf

f

ρ U D

μ = . (17) 

*( )

c

pf

V U

t cross sectional area = − . (18) 

The properties of compressed air were used in a fully developed ODT channel flow simulation to 

obtain a mean flow velocity of 48 m/s. This was considered close enough to the 48.4 m/s 

previously calculated. Particles representative of stibnite particles were put into the simulation, 

utilizing a Stokes drag law (equations 11 and 12) with the gravitational force set to zero, and 

allowed to reach pseudo-steady-state. When particles travel to within one radius of the wall they 

were allowed to deposit on the wall. The average of all particle streamwise velocities were taken 

and found to be just over 47.5 m/s. Williams et al. (24) gives a measured value of 45 m/s. This 

was considered good agreement. 

It is well known that near the wall the kinematic viscosity ν and the wall shear stress τw are 

important parameters of the flow. A time scale, called wall time t

+

, can be defined from these 

and the fluid density (see equation 19). The Stokes number τp

+

, as defined by equation 20, 

relates the relative importance of the aerodynamic response time to the wall time. The wall 

velocity Uτ and the friction Reynolds number Reτ are also defined. 

w

t

νρ

τ

+ = . (19) 

p

p t

τ

τ+ = + . (20) 

w Uτ

τ

ρ = . (21) 

Re hUτ

τ ν = . (22) 

Within the channel the nondimensionalized gravitational constant G in wall units is given in 

equation 23. The Froude number Fr is the ratio of the inertial force to the gravitational force and 

can be computed by multiplying G by the Stokes number and taking the reciprocal, as shown in 

equation 24. The larger the Fr number the less important gravity is in the simulation. For this 

simulation G = 3.6 × 10-6 and Fr = 9. This indicates that for this simulation, gravity is not as 

important as the inertia, but probably not negligible. For the primer firings in open air (24) the 

particles seem to congregate predominately in the lower half of the explosion event. This would 

indicate that gravitational forces are important in the open-air firings. 
21

3

g G

Uτ

ν = . (23) 

3

p

U Fr

g

τ

ντ+ = . (24) 

5.2 Definition of the Deposition Velocity Vd

+

To ensure proper mass balance across the flow channel requires a knowledge of the number of 

particles which enter the tube (based on the number of particles in the original primer mix) and 

the number of particles which hit the channel wall due to both gravitational effects and turbulent 

effects. In order to properly account for mass loss to the walls the so called deposition velocity, 

Vd, is introduced. It is not a velocity at all, but rather a deposition rate constant which has units 

of distance per time, the same units as a velocity. Because of this it was called a deposition 

velocity, but has nothing to do with the velocity of the particle at the time of impact. Some may 

confuse the deposition velocity with the wall normal velocity of a particle at impact, but there is 

no correlation whatsoever. The definition of the deposition velocity is 

d

N V

c = , (25) 

where c is the mass of the particles per unit volume in the channel and N is the mass flux. All 

simulations done in this work are done with monodisperse particles so that 

p c mn = (26) 

and 

N mj = p , (27) 

where n is the number of particles per unit volume, j is the number flux of particles that deposit 

on the channel walls, and mp is the mass of a single particle. It is useful to define the 

dimensionless deposition velocity in wall units. Combining these equations and making the 

result non-dimensional yields 

d

d

V j V

U nU τ τ

+ = = . (28) 

While investigating the deposition of particles on channel walls with small nondimensionalized 

radii (r/h), Schmidt et al. (52) demonstrated that the steady-state deposition velocity is 

independent of Reynolds numbers for Stokes numbers τp

+

 from values of 10 to 25000. Above 

25000 there is a slight Reynolds number dependence, with the highest Re having the greatest 

deposition. 
22

For a first approximation a stibnite particle with a small r/h and a St τp

+

 of 30000 was simulated 

in PODT at two different bulk Reynolds numbers around 12000 to compare to Schmidt et al. 

(52). Excellent agreement with Schmidt et al. was achieved, thereby verifying the use of this 

method to simulate the primer tube particles. 

The simulation was repeated for a single Re with the radius of a representative stibnite particle 

actually used in the primer mix (r/h = 0.036). The larger diameter particle caused a higher 

deposition velocity. This is a phenomena not previously demonstrated in the literature. 

6. Conclusions 

Based on the experiments of Williams et al. (24), the corresponding Cheetah code gun 

calculations which assume stibnite and barium nitrate remain in the solid phase provides 

reasonable agreement. Verification of the PODT model in the range of interest to primer no. 41 

simulations, with known deposition velocities, was achieved. A new diameter dependence on 

deposition velocity was noted. The PODT model has been assessed to be reasonably well suited 

to serve as an input to the NGEN code for small-caliber ammunition simulations. The PODT 

model predicted streamwise particle velocities inside the steady-state flow channel to be 

47.5 m/s, where measurements just outside of the primer tube (24), in an open-air firing, yielded 

45 m/s. 

7. Future Work 

The extension of PODT to large-caliber ignition systems is of interest. As can be seen in 

figure 1, the conventional ignition system for a large-caliber (120-mm) gun consists of a long, 

narrow metallic tube that is mounted on the cartridge case base (housing the igniter), which 

extends into the gun chamber along the chamber centerline and is sealed at the other end. Along 

its length, this primer tube is perforated with regularly spaced holes which allow radial and 

azimuthal venting of igniter gases. The tube contains an energetic material that generally 

consists of tightly-packed grains (smaller in diameter than the primer tube holes) designed to 

rapidly ignite and flamespread producing hot gases and hot solid particles. The efflux from the 

primer tube is used to ignite the solid propellant gun charge. 

Primer models that include first-order effects (i.e., gas generation in a tabular form) have been 

used successfully to predict the performance of a number of large-caliber Army guns but are 

somewhat inconsistent with the multiphase Lagrangian approach used to model the solid 

propellant charge in the Army's NGEN code. It has long been considered a viable task to 

upgrade the treatment for the primer tube in a manner consistent with the NGEN code in a way 
23

that explicitly treats the multiphase nature of the energetic material in the primer. Though the 

primer tube is essentially three-dimensional by its nature, an attempt has been made to develop a 

one-dimensional numerical model which will capture enough of the essential physics to predict 

semiquantitatively the burnout of these primer particles yet to be simple enough to be useful in 

providing the flow rates of gas and particles through the primer holes. The fate of the 

gas/particles from the primer efflux will then be determined using the NGEN IB model, i.e., the 

primer model would be in some fashion linked to the IB model. 

Large-caliber ignition systems can be viewed as an array of particles in a turbulent channel 

which are allowed to leave the domain through a vent hole. PODT can be used to model this by 

adding many particles to the channel flow ODT code using one-way coupling to simulate a 

simple packed bed. Combustion of the particles would be simulated by igniting one end of the 

packed bed and allowing flame spreading down the bed. Particles would be allowed to heat up 

until the temperature was high enough to start combustion. The rate of combustion and 

combustion chemistry would be commensurate with current state-of-the-art IB modeling. Each 

representative particle would be tracked individually. A schematic of the piccolo tube primer 

model can be seen in figure 6. Each particle has an individual temperature, mass, velocity field, 

and position. As such, the particles can be ensemble averaged to produce look-up tables which 

may be used in NGEN or for simpler IB codes. 

x 

y 

Walls of piccolo 

tube with vent 

holes shown as 

breaks 

Figure 6. Large-caliber gun primer tube concept. 
24

8. 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. 

3. Minor, T. C.; Horst, A. W. Theoretical and Experimental Investigation of Flamespreading 

Processes in Combustible-Cased Stick Propelling Charges; BRL-TR-2710; U.S. Army 

Ballistic Research Laboratory: Aberdeen Proving Ground, MD, February 1986. 

4. Gough, P. S. Modeling Arbitrarily Packaged Multi-Increment Solid Propellant Charges of 

Various Propellant Configurations. Proceedings of the 33rd JANNAF Combustion Meeting, 

November 1996, CPIA publication no. 653, 1, pp 421–435. (See also Gough, P. S. 

Formulation of a Next-Generation Interior Ballistic Code; ARL-CR-68; U.S. Army 

Research Laboratory: Aberdeen Proving Ground, MD, September 1993.) 

5. Nusca, M. J.; Gough, P. S. Numerical Model of Multiphase Flows Applied to Solid 

Propellant Combustion in Gun Systems; AIAA Paper No. 98–3695, July 1998. 

6. Nusca, M. J. High-Performance Computing and Simulation for Advanced Armament 

Propulsion; ARL-TR-3215; U.S. Army Research Laboratory: Aberdeen Proving Ground, 

MD, June 2004. 

7. Horst, A. W.; Nusca, M. J. The Charge Designer’s Workbench: A Range of Interior 

Ballistic Modeling Tools. Proceedings of the 53rd JANNAF Propulsion Meeting, Monterey, 

CA, 5–8 December 2005. 

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

of the 22nd JANNAF Combustion Meeting, October 1983, CPIA publication no. 432, 1, 

Pasadena, CA. 

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

York, NY, 1943. 
25

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: 

Aberdeen Proving Ground, MD, June 1955, p 9. 

12. Chang, L.; Rocchio, J. J. Simulator Diagnostics of the Early Phase Ignition Phenomena in 

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

Aberdeen Proving Ground, MD, March 1988. 

13. Keller, G. E.; Anderson, R. D.; Horst, A. W. The Influence of Ignition Stimulus on the 

Interior Ballistic Performance of High-Performance Tank Gun Ammunition; ARL-TR-292; 

U.S. Army Research Laboratory: Aberdeen Proving Ground, MD, October 1993. 

14. Nusca, M. J. Application of the NGEN Code to Solid Propellant Charges of Various 

Propellant Configurations. Proceedings of the 33rd JANNAF Combustion Meeting, CPIA 

publication no. 653, November 1996, pp 421–435. 

15. Encyclopedia of Explosives and Related Items; Vol. 8; Picatinny Arsenal: Dover, NJ, 1978. 

16. Chamot, E. M. The Microscopy of Small Arms Primers. Cornell University Press: Ithaca, 

NY, 1922. 

17. Ellern, H. Modern Pyrotechnics, Fundamentals of Applied Physical Pyrochemistry. 

Chemical Publishing Co., Inc.: New York, NY, 1961. 

18. Kerstein, A. R.; Ashurst, W. T.; Nilsen, V.; Wunsch, S. E. One-Dimensional Turbulence: 

Vector Formulation and Application to Free Shear Flows. J. Fluid Mech. 2001, 447, 

85–109. 

19. Schmidt, J. R. Stochastic Models for the Prediction of Individual Particle Trajectories in 

One Dimensional Turbulence Flows. Ph.D. Dissertation, University of Arizona, Tucson, 

AZ, 2004. 

20. Pope, S. B. Turbulent Flows. Cambridge University Press: New York, NY, 2000. 

21. Young, J.; Leeming, A. A Theory of Particle Deposition in Turbulent Pipe Flow. J. Fluid 

Mech. 1997, 340, 129–159. 

22. Call, C. J.; Kennedy, I. M. Droplet Dispersion, Velocity and Vaporization in Heated and 

Unheated Jets. 31st Aerospace Sciences Meeting and Exhibit, AIAA 93-0904, Reno, NV, 

1993. 

23. Call, C. J.; Kennedy, I. M. Measurements of Droplet Dispersion in Heated and Unheated 

Turbulent Jets. AIAA Journal 1994, 32, 874–875. 

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

Ignition in 5.56 Ammunition. Proceedings of the 53rd JANNAF Propulsion Meeting, 

5–8 December 2005, Monterey, CA. 
26

25. Kuo, K. K.; Moore, B. B.; Chen, D. Y. Characterization of Mass Flow Rates for Various 

Percussion Primers. Gasdynamics of Detonations and Explosives, Bowen, J. R., Manson, N., 

Oppenheim, A. K., Soloukhin, R. I., Eds.; AIAA Progress Series, 75, pp 323–337, 1981. 

26. Fried, L. E.; Glaesemann, K. R.; Howard, W. M.; Souers, P. C.; Vitello, P. A. Cheetah 

Code, Version 4.0, UCRL-CODE-155944, 2005. 

27. Meyer, R.; Kohler, J.; Homburg, A. Explosives; 5th ed.; Wiley-VCH Publishing Co.: 

Germany, 2002. 

28. Fox, W.; Vogelsang, K.; Harris, J.; Lathrop, A. Invesigation of Tetracene Decomposition 

Variation Using Taguchi Methodology. In Military Mathematical Modeling (M3); 

Arney, D. C., Ed.; Department of Mathematical Sciences: United States Military Academy, 

West Point, NY, 1998. 

29. McNesby, K. U.S. Army Research Laboratory. Personal communication, 11 November 

2005. 

30. Brauer, K. Handbook of Pyrotechnics; Chemical Publishing Co., Inc.: New York, 1974. 

31. Bordon, S.; Campbell, C. Differential Thermal Analysis of Inorganic Compounds, Nitrates 

and Perchlorates of the Alkali and Aldaline Earth Groups and Their Subgroups, Analytical 

Chemistry; 27, 1102–9, 1955. 

32. Hinze, J. O. Turbulence. McGraw-Hill Book Company; 2nd ed.; 1975. 

33. Stock, D. E. Particle Dispersion in Flowing Gases–1994 Freeman Scholar Lecture. 

Transactions of the ASME 1996, 118, 4–17. 

34. Maxey, M. R.; Riley, J. J. Equation of Motion for a Small Rigid Sphere in Nonuniform 

Flow. Phys. Fluids 1983, 26, 883–888. 

35. Wells, M. R.; Stock, D. E. The Effects of Crossing Trajectories on the Dispersion of 

Particles in a Turbulent Flow. J. Fluid Mech. 1983, 136, 31–62. 

36. Sirignano, W. A. Fluid Dynamics and Transport of Droplets and Sprays. Cambridge 

University Press: United Kingdom, 1999. 

37. Elghobashi, S. Particle-Laden Turbulent Flows: Direct Simulation and Closure Models. 

Appl. Sci. Res. 1991, 48, 301–314. 

38. Elghobashi, S. On Predicting Particle-Laden Turbulent Flows. Appl. Sci. Res. 1994, 52, 

309–329. 

39. Zhang, H.; Ahmadi, G.; Fan, F.-G.; McLaughlin, J. B. Ellipsoidal Particles Transport and 

Deposition in Turbulent Channel Flows. Int. J. Multiphase Flow 2001, 27, pp 971–1009. 
27

40. van Haarlem, B.; Boersma, B. J.; Nieuwstadt, F. T. M. Direct Numerical Simulation of 

Particle Deposition Onto a Free-Slip and No-Slip Surface. Physics of Fluids 1998, 10, 

2608–2620. 

41. Zhang, H.; Ahmadi, G. Aerosol Particle Removal and Re-Entrainment in Turbulent Channel 

Flows—A Direct Numerical Simulation Approach. J. Adhesion 2000, 74, 441–493. 

42. Rouson, D. W.; Eaton, J. K. On the Preferential Concentration of Solid Particles in 

Turbulent Channel Flow. J. Fluid Mech. 2001, 428, 149–169. 

43. Wang, Q.; Squires, K. D. Large Eddy Simulation of Particle-Laden Turbulent Channel 

Flow. Int. J. Multiphase Flow 1996, 22, 667–683. 

44. Segura, J. C.; Eaton, J. K.; Oefelein, J. C. Predictive Capabilities of Particle-Laden Large 

Eddy Simulation; Mech. Engng. Dept. Rep. TSD-156; Stanford University: Stanford, CA, 

2004. 

45. McLaughlin, J. B. Aerosol Particle Deposition in Numerically Simulated Channel Flow. 

Phys. Fluids 1989, A 1, 1211–1224. 

46. Chen, M.; McLaughlin, J. B. A New Correlation for the Aerosol Deposition Rate in Vertical 

Ducts. J. Colloid Interface Sci. 1995, 169, 437–455. 

47. Ounis, H.; Ahmadi, G.; McLaughlin, J. B. Dispersion and Deposition of Brownian Particles 

from Point Souces in Simulated Turbulent Channel Flow. J. Colloid Interface Sci. 1991, 

147, 233–250. 

48. Wang, Q.; Squires, K. D. Large Eddy Simulation of Particle Deposition in a Vertical 

Turbulent Channel Flow. Int. J. Multiphase Flow 1996, 22, 667–683. 

49. Wang, Q.; Squires, K. D.; Chen, M.; McLaughlin, J. B. On the Role of the Lift Force in 

Turbulence Simulations of Particle Deposition. Int. J. Multiphase Flow 1996, 23, 749–763. 

50. Schmidt, J. R. Trajectories of Evaporating Droplets in a Turbulent Combustor Using the 

One Dimensional Trubulence Model. Masters Thesis, University of Arizona, 2000. 

51. Williams, A. W. U.S. Army Research Laboratory. Personal communication, November 

2005. 

52. Schmidt, J. R.; Went, J. O. L. W.; Kerstein, A. R. Effects of Inertia on Wall Deposition in 

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28

INTENTIONALLY LEFT BLANK. 
29

Appendix. Cheetah 4.0 Summary Sheet 

######################################################################## 

# # 

# CHEETAH 4.0 SUMMARY SHEET # 

# Energetic Materials Center # 

# Lawrence Livermore National Laboratory # 

# Technical Contact: Dr. Laurence E. Fried # 

# Copyright 2004, Regents University of California # 

# All Rights Reserved # 

# # 

######################################################################## 

Product library title: the blake product library 

Reactant library title: # Reactant library 4.0 by W.M. Howard. Fri Nov 25 15:01:13 EST 2005 

The composition: 

Name % wt. % mol % vol Heat of Mol. TMD 

 formation wt. (g/cc) 

 (cal/mol) 

petn 9.43 4.97 14.23 -127151 316.13 1.78 n 4 c 5 h 8 o 12 

tetrazene 7.55 6.68 11.91 45172 188.15 1.70 c 2 n 10 o 1 h 8 

al 9.25 57.07 9.19 0 26.98 2.70 al 1 

al2o3 3.96 6.47 2.66 -399092 101.96 3.99 o 3 al 2 

lead styph 69.81 24.82 62.01 -260277 468.30 3.02 o 9 n 3 pb 1 c 6 h 3 

library file, blake.chl 

composition, petn, 9.43, tetrazene, 7.55, al, 9.25, al2o3, 3.96, lead styph, 69.81, weight 

gun, 0.0139, 0.05, 0.0139 

CHEETAH version 4.0 

Energetic Materials Center 

Lawrence Livermore National Laboratory 

Technical contact: Dr. Laurence E. Fried 

Copyright 2004 Regents University of California 

All Rights Reserved 

The time is Wed Jan 18 14:35:10 2006 

Version Tag: 280 

Code build date: 18 Jan 2005 

Code date = 2005/01/15 00:10:57 

 

This appendix appears in its original form, without editorial change. 
30

Library Title: the blake product library 

Executing library command: gas eos, virial 

Input>library file, blakejrs.chl 

Product library title: the blake product library 

Executing library command: gas eos, virial 

Input>composition, petn, 9.43, tetrazene, 7.55, al, 9.25, al2o3, 3.96, lead styph, 69.81, weight 

Reactant library title:# Reactant library 4.0 by W.M. Howard. Fri Nov 25 15:01:13 EST 2005 

 The Composition 

Name % wt. % mol %vol. Heat of Standard Standard Mol. Formula 

 Formation volume entropy wt. 

 (cal/mol) (cc/mol) (cal/K/mol) 

Petn 9.43 4.97 14.23 -127151 177.80 0.000 316.13 n4c5h8o12 

Tetrazene 7.55 6.68 11.91 45172 110.68 0.000 188.15 c2n10o1h8 

al 9.25 57.07 9.19 0 9.99 0.000 26.98 al1 

al2o3 3.96 6.47 2.66 -399092 25.55 0.000 101.96 o3al2 

lead styph 69.81 24.82 62.01 -260277 155.07 0.000 468.30 o9n3pb1c6h3 

Heat of formation = -562.799 cal/gm 

Standard volume = 0.373 cc/gm 

Standard entropy = 0.000 cal/k/gm 

Standard energy = -562.808 cal/gm 

The elements and percent by mole 

 n 17.519 

 c 20.343 

 h 18.226 

 o 33.601 

 al 7.612 

 pb 2.698 

The average mol. wt. = 166.476 g/mol 

Input>gun, 0.0139, 0.05, 0.0139 

GUN calculation: 

 Rho Temp Pressure Impetus Mol Wt. Covol Frozen Phi 

 g/cc K MPa J/g Gas cc/g Cp/Cv 

1.) 0.0139 2797.1 7.4 526.75 44.153 0.635 1.176 1.009 

Product concentrations 

 Name Phase (mol/kg) (mol gas/mol explosive) 

 co Gas 1.096e+001 1.825e+000 

 n2 Gas 4.838e+000 8.054e-001 

 h2 Gas 4.252e+000 7.079e-001 

 pb Gas 1.482e+000 2.466e-001 

 h2o Gas 7.313e-001 1.217e-001 

 co2 Gas 2.726e-001 4.539e-002 

 h Gas 9.275e-002 1.544e-002 

 opb Gas 9.166e-003 1.526e-003 

 oh Gas 4.559e-003 7.589e-004 

 hcn Gas 1.634e-003 2.720e-004 

 nh3 Gas 5.180e-004 8.624e-005 
31

 no Gas 4.265e-004 7.101e-005 

 cho Gas 3.140e-004 5.227e-005 

 alho2 Gas 2.544e-004 4.235e-005 

 ch2o Gas 8.735e-005 1.454e-005 

 o Gas 6.164e-005 1.026e-005 

 hnco Gas 4.291e-005 7.143e-006 

 al Gas 4.170e-005 6.943e-006 

 nh2 Gas 3.852e-005 6.412e-006 

 ch4 Gas 1.204e-005 2.004e-006 

 al2o Gas 9.490e-006 1.580e-006 

 formac Gas 9.379e-006 1.561e-006 

 ch3 Gas 6.115e-006 1.018e-006 

 nh Gas 4.697e-006 7.819e-007 

 o2 Gas 4.237e-006 7.053e-007 

 n Gas 4.196e-006 6.985e-007 

 cn Gas 3.702e-006 6.163e-007 

 c2h2 Gas 1.092e-006 1.818e-007 

 hno Gas 7.174e-007 1.194e-007 

 nco Gas 4.343e-007 7.230e-008 

 ch2 Gas 2.759e-007 4.593e-008 

 ketene Gas 2.201e-007 3.664e-008 

 n2o Gas 9.607e-008 1.599e-008 

 halo Gas 8.573e-008 1.427e-008 

 alo2 Gas 4.223e-008 7.029e-009 

 h2o2 Gas 3.165e-008 5.269e-009 

 ho2 Gas 3.137e-008 5.223e-009 

 ch2oh Gas 2.178e-008 3.626e-009 

 ch4o Gas 2.112e-008 3.517e-009 

 c Gas 5.157e-009 8.586e-010 

 c2h4 Gas 3.822e-009 6.363e-010 

 no2 Gas 2.088e-009 3.476e-010 

 hno2 Gas 1.137e-009 1.892e-010 

 ch3cn Gas 9.338e-010 1.555e-010 

 al2o3 liquid 2.102e+000 3.500e-001 

 *pb liquid 0.000e+000 0.000e+000 

 *pb solid 0.000e+000 0.000e+000 

 c(s) solid 0.000e+000 0.000e+000 

 al2o3 solid 0.000e+000 0.000e+000 

 Total Gas 2.265e+001 3.770e+000 

 Total Cond. 2.102e+000 3.500e-001 
NO. OF 

COPIES ORGANIZATION 

32

 1 DEFENSE TECHNICAL 

 (PDF INFORMATION CTR 

 ONLY) DTIC OCA 

 8725 JOHN J KINGMAN RD 

 STE 0944 

 FORT BELVOIR VA 22060-6218 

 1 US ARMY RSRCH DEV & 

 ENGRG CMD 

 SYSTEMS OF SYSTEMS 

 INTEGRATION 

 AMSRD SS T 

 6000 6TH ST STE 100 

 FORT BELVOIR VA 22060-5608 

 1 INST FOR ADVNCD TCHNLGY 

 THE UNIV OF TEXAS 

 AT AUSTIN 

 3925 W BRAKER LN 

 AUSTIN TX 78759-5316 

 1 DIRECTOR 

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 2800 POWDER MILL RD 

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 3 DIRECTOR 

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 2800 POWDER MILL RD 

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ABERDEEN PROVING GROUND

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NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

33

 1 DIRECTOR 

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 AMSRD ARL D 

 J MILLER 

 2800 POWDER MILL RD 

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 D MANN 

 R SHAW 

 TECH LIB 

 PO BOX 12211 

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 27709-2211 

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 W CHEW 

 C DOLBEER 

 J S LILLY 

 M LYON 

 J M FISHER 

 B P MARSH 

 R S MICHAELS 

 D THOMPSON 

 REDSTONE ARSENAL AL 35898-5249 

 2 PM MAS 

 SFAE AMO MAS 

 LTC M BUTLER 

 PICATINNY ARSENAL NJ 07806-5000 

 2 PM CAS 

 SFAE AMO CAS 

 PICATINNY ARSEBAL NJ 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR EMB 

 R CARR 

 BLDG 1 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 SFAE AMD CAS 

 R CIRINCIONE 

 BLDG 171

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEE W 

 S EINSTEIN 

 BLDG 382 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEE W 

 P HUI 

 BLDG 382 

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 1 US ARMY ARDEC 

 AMSRD AAR D 

 J LANNON 

 BLDG 1 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 B MACHAK 

 AMSRD AAR ATD 

 BLDG 1 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEE W 

 S NICOLICH 

 BLDG 3022 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 P O REILLY 

 BLDG 3022 

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 1 US ARMY ARDEC 

 J O REILLY 

 BLDG 382 

 J RUTKOWSKI BLDG 171M 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 A SABASTO 

 BLDG 94 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEE W 

 J SHIN 

 BLDG 382 

 PICATINNY ARSENAL NJ 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEE W 

 R SURAPANENI 

 BLDG 3022 

 PICATINNY ARSENAL NJ 07806-5000 
NO. OF NO. OF 

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34

 1 COMMANDER 

 RADFORD ARMY AMMO PLANT 

 SMCAR QA HI LIB 

 RADFORD VA 24141-0298 

 1 RAYTHEON MISSILE SYSTEMS 

 D BLANCHARD 

 8634 E OLINGA CT 

 TUCSON AZ 85747 

 8 DIR BENET WEAPONS LAB 

 M AUDINO 

 R DILLON 

 R FISCELLA 

 R HASENBEIN 

 E KATHE 

 K MINER 

 S SOPOK 

 J MCNEIL 

 WATERVLIET NY 12189-4000 

 1 COMMANDANT 

 USAFC&S 

 ATSF CN P GROSS 

 FT SILL OK 73503-5600 

 2 CDR NAVAL RSRCH LAB 

 TECH LIBRARY 

 J BORIS 

 WASHINGTON DC 20375-5000 

 1 OFFICE OF NAVAL RSRCH 

 J GOLDWASSER 

 875 N RANDOLPH ST RM 653 

 ARLINGTON VA 22203-1927 

 6 CDR 

 NAVAL SURFACE WARFARE CTR 

 R DOHERTY R2A 

 C GOTZMER TM3 

 C MICHIENZI R22 

 S MITCHELL OPA 

 S C SMITH R3A 

 TECHLIB 

 INDIAN HEAD MD 20640-5000 

 5 CDR 

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 J FRAYSEE G33 

 R FRANCIS T08 

 T C SMITH 

 T TSCHIRN G30 

 TECHLIB 

 DAHLGREN VA 22448-5000 

 3 CDR 

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 A ATWOOD 

 S BLASHILL 

 T PARR 

 CHINA LAKE CA 93555-6001 

 1 AIR FORCE RESH LAB 

 MNME EN MAT BR 

 B WILSON 

 2306 PERIMETER RD 

 EGLIN AFB FL 32542-5910 

 1 AIR FORCE OFC OF SCI RSRCH 

 M BERMAN 

 875 N RANDOLPH ST 

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 1 NASA LANGLEY RSRCH CTR 

 D BUSHNELL 

 MAIL STOP 110 

 HAMPTON VA 23681-2199 

 1 DIR SANDIA NATL LABS 

 M BAER DEPT 1512 

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 ALBUQUERQUE NM 87185 

 2 DIR LAWRENCE LIVERMORE NL 

 L FRIED 

 M MURPHY 

 PO BOX 808 

 LIVERMORE CA 94550-0622 

 1 CENTRAL INTELLIGENCE AGNCY 

 J BACKOFEN 

 RM 4PO7 NHB 

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 1 BATTELLE EAST SCI & TECH 

 A ELLIS 

 1204 TECHNOLOGY DR 

 ABERDEEN MD 21001-1228 

 2 JHU CHEM PROP INFO AGNCY 

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 10630 LITTLE PATUXENT PKWY 

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35

 1 OUSD (AT&L)/STRAT & TACT 

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 T MELITA 

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 1 BRIGHAM YOUNG UNIV 

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 M BECKSTEAD 

 PROVO UT 84601 

 1 CALIF INSTITUTE OF TECHLGY 

 F E C CULICK 

 204 KARMAN LAB 

 MS 301 46 

 1201 E CALIFORNIA ST 

 PASADENA CA 91109 

 2 UNIV OF ILLINOIS 

 DEPT OF MECH INDUSTRY ENGRG 

 H KRIER 

 R BEDDINI 

 144 MEB 1206 N GREEN ST 

 URBANA IL 61801-2978 

 5 PENNSYLVANIA STATE UNIV 

 DEPT OF MECHANICAL ENGRG 

 K KUO 

 T LITZINGER 

 G SETTLES 

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 1 ATK ORDNANCE 

 4700 NATHAN LANE 

 PLYMOUTH MN 55442 

 3 ATK AMMO & ENERGETICS 

 D A WORRELL 

 W J WORRELL 

 S RITCHIE 

 RADFORD ARMY AMMO PLANT 

 RT 114 PO BOX 1 

 RADFORD VA 24141-0299 

 4 ATK THIOKOL 

 P BRAITHWAITE 

 T B FARABAUGH 

 W B WALKUP 

 R WARDLE 

 PO BOX 707 

 BRIGHAM CITY UT 84302-0707 

 1 ATK ELKTON 

 J HARTWELL 

 PO BOX 241 

 ELKTON MD 21921-0241 

 1 BAE ARMAMENT SYS DIV 

 JAHN DYVIK 

 4800 EAST RIVER RD 

 MINNEAPOLIS MN 55421-1498 

 2 GEN DYNAMICS ORD/TACT SYS 

 N HYLTON 

 J BUZZETT 

 10101 DR M L KING ST N 

 ST PETERSBURG FL 33716 

 3 GENERAL DYNAMICS ST MARKS 

 J DRUMMOND 

 H RAINES 

 D W WORTHINGTON 

 PO BOX 222 

 SAINT MARKS FL 32355-0222 

 1 GENERAL DYNAMICS ARM SYS 

 J TALLEY 

 128 LAKESIDE AVE 

 BURLINGTON VT 05401 

 1 HICKS AND ASSOCIATES SAIC 

 I MAY 

 7990 SCIENCE APPLIC CT 

 VIENNA VA 22182 

 1 PAUL GOUGH ASSOC INC 

 P S GOUGH 

 1048 SOUTH ST 

 PORTSMOUTH NH 03801-5423 

 3 VERITAY TECHGY INC 

 R SALIZONI 

 J BARNES 

 E FISHER 

 4845 MILLERSPORT HWY 

 EAST AMHERST NY 14501-0305 
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 1 SRI INTERNATIONAL 

 PROPULSION SCIENCES DIV 

 TECH LIB 

 333 RAVENWOOD AVE 

 MENLO PARK CA 94025-3493 

 1 SAIC 

 M PALMER 

 1410 SPRING HILL RD 

 STE 400 

 MCLEAN VA 22102 

 1 NETWORK COMPUTING SERVICES 

 S RAY 

 1200 WASHINGTON AVE S 

 MINNEAPOLIS MN 55415 

 1 SANDIA NATIONAL LABS 

 A KERSTEIN 

 PO BOX 969 MS 9051 

 LIVERMORE CA 94551-0969 

ABERDEEN PROVING GROUND

 1 CDR USAATC 

 CSTE DTC AT SL 

 APG MD 21005 

 66 DIR USARL 

 AMSRD ARL WM B 

 C CANDLAND 

 J B MORRIS 

 J NEWILL 

 M ZOLTOSKI 

 AMSRD ARL WM BA 

 G BROWN 

 B DAVIS 

 D HEPNER 

 G KATULKA 

 T KOGLER 

 D LYON 

 AMSRD ARL WM BC 

 M BUNDY 

 G COOPER 

 J DESPIRITO 

 J GARNER 

 P PLOSTINS 

 J SAHU 

 S SILTON 

 P WEINACHT 

 AMSRD ARL WM BD 

 W R ANDERSON 

 R A BEYER 

 A L BRANT 

 S W BUNTE 

 L M CHANG 

 T P COFFEE 

 J COLBURN 

 P J CONROY 

 N ELDREDGE 

 B E FORCH 

 B E HOMAN 

 AW HORST 

 S L HOWARD 

 P J KASTE 

 A J KOTLAR 

 C LEVERITT 

 R LIEB 

 K L MCNESBY 

 M MCQUAID 

 A W MIZIOLEK 

 J E NEWBERRY 

 M J NUSCA (6 CPS) 

 R A PESCE-RODRIGUEZ 

 S PIRAINO 

 G P REEVES 

 B M RICE 

 R C SAUSA 

 J SCHMIDT (6 CPS) 

 A W WILLIAMS 

 AMSRD ARL WM BF 

 R D ANDERSON 

 W OBERLE 

 D WILKERSON 

 AMSRD ARL WM EG 

 E SCHMIDT 

 AMSRD ARL WM M 

 S MCKNIGHT 

 AMSRD ARL WM SG 

 W CIEPIELA 

 T ROSENBERGER 

 AMSRD ARL WM T 

 B BURNS 

 AMSRD ARL WM TB 

 P BAKER