c 

Interior Ballistic Simulations of the 

Bulk-Loaded Liquid Propellant Gun 

I James DeSpirito 

ARL-TR-2316 JANUARY 2001 

2001030542 

Approved for public release; distribution is unlimited. 
The findings in this report are not to be construed as an official Department of the Army position 

unless so designated by other authorized documents. 

Citation of manufacturer’s or trade names does not constitute an official endorsement or approval of 

the use thereof. 

Destroy this report when it is no longer needed. Do not return it to the originator. 
ERRATA SHEET 

RE: ARL-TR-2316, “Interior Ballistic Simulations of the Bulk-Loaded Liquid Propellant 

Gun,” by James DeSpirito of the Weapons & Materials 

Research Directorate, U.S. Army Research Laboratory 

The last line of page 15 is repeated at the top of page 16. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-23 16 January 2001 

Interior Ballistic Simulations of the BulkLoaded Liquid Propellant Gun 

James DeSpirito 

Weapons & Materials Research Directorate 

Approved for public release; distribution is unlimited. 

1 
Abstract 

ii 

The objective of this study was to determine the feasibility of 

modeling the interior ballistic processes of the bulk-loaded liquid 

propellant gun. A modified version of the CRAFT’ Navier-Stokes 

code was used to perform simulations of bulk-loaded liquid 

propellant gun firings that employed two different chamber 

configurations. The simulation accurately captures the longitudinal 

wave structure present in the experimental data, but a combustion 

delay present at the start of the ballistic cycle was not present in the 

simulations. The simulations showed the development of a cavity that 

penetrated the bulk-liquid column as it accelerated toward the 

projectile, leaving an annulus of unburned liquid propellant along the 

chamber wall. High gas temperatures were noted in this gas cavity 

region, possibly attributable to isentropic compression caused by the 

unique conditions in the bulk-loaded gun. The simulation of the 

second chamber configuration compared well with the experimental 

data, while the simulation of the first chamber configuration did not 

capture the experimental pressure-time profile. In general, the 

simulations showed an insensitivity to chamber geometry that is not 

observed in experimental firings. The limitations of the simulations 

were attributed to the lack of complete physical sub-models, such as 

a droplet formation/combustion model and detailed chemical 

kinetics. The model has the potential to be a useful tool in the analysis 

of- experimental data. However, predictive capability is unlikely 

without the development of better physical sub-models. 

’ not an acronym 
ACKNOWLEDGMENTS 

The author would like to thank Michael Nusca and Todd Rosenberger of the U.S. 

Army Research Laboratory for reviewing the manuscript; Ashvin Hosangadi of 

Combustion Research and Flow Technology, Inc., for modifications of the CRAFT 

code and for his help and many useful discussions during this effort; and Robert 

Talley and John Owczarczak of Veritay Technology, Inc., for supplying the 

experimental data used during this study. 

This work was supported in part by a grant of high performance computing time 

from the Department of Defense High Performance Computing Center at Aberdeen 

Proving Ground, Maryland. 

. . . 

111 
INTENTIONALLY LEFT BLANK 

iv 
. 

Contents 

1. Introduction ...................................... 

2. Numerical Technique ............................... 

3. Experimental Fixture. ............................... 

4. Results and Discussion .............................. 

4.1 Simulation Procedure .............................. 

4.2 Simulation of Standard Four-Stage Chamber .............. 

4.3 Simulation of Modified Four-Stage Chamber .............. 

4.4 Discussion of Results .............................. 

5. Summary ......................................... 

References ............................................. 

Distribution List ........................................ 

Report Documentation Page ............................... 

Figures 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

Phenomenological Model of the BLPG Interior Ballistics Proposed by 

Comer, Shearer, and Jones (1963) . . . . . . . . . . . . . . . . . . . . . 

Standard Four-stage Combustion Chamber . . . . . . . . . . . . . . . 

Modified Four-stage Combustion Chamber . . . . . . . . . . . . . . . 

Initial Grids Used in Simulations of the (a) Standard and the 

(b) Modified Four-stage Combustion Chambers . . . . . . . . . . . . . 

Contours of Combustion Product Mass Fraction for Simulation of 

Standard Four-stage Chamber at 0.255, 0.535, 0.695, and 0.923 ms 

Contours of Vorticity Simulation of Standard Four-stage Chamber 

at 0.255, 0.535, 0.695, and 0.923 ms . . . . . . . . . . . . . . . . . . . 

Pressure at Pl Location From Simulation (solid line) and From 

Test No. 130 (dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . 

Pressure at P2 Location From Simulation (solid line) and From 

Test No. 130 (dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . 

Pressure at I?5 Location From Simulation (solid line) and From 

Test No. 130 (dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . 

Contours of Combustion Product Mass Fraction for Simulation of 

Modified Four-stage Chamber at 0.205, 0.545, 0.706, and 0.866 ms . 

Pressure at I’1 Location From Simulation (solid line) and From 

Test No. 155 (dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . 

1 

4 

6 

8 

8 

11 

15 

15 

21 

23 

27 - 

29 

3 

7 

8 

9 

12 

12 

13 

14 

14 

16 

16 

V 
12. 

13. 

14. 

15. 

Pressure at P2 Location From Simulation (solid line) and From 

Test No. 155 (dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . 

Pressure at P2 Location From Simulation of Test No. 130 (solid 

line) and From Test No. 155 (dashed line) . . . . . . . . . . . . . . . . 

Contours of Temperature (K) for Simulation of Standard (top) and 

Modified (bottom) Four-stage Chamber . . . . . . . . . . . . . . . . . 

Comparison of Pressure at Pl Location From Simulation Using 

Cylindrical Chamber Geometry (solid line) and From Simulation 

Using Modified Four-stage Chamber Geometry (dashed line) . . . . . 

17 

17 

18 

20 

vi 
INTERIOR BALLISTIC SIMULATIONS OF THE BULKLOADED LIQUID PROPELLANT GUN 

1. Introduction 

The use of liquid propellant (LP) in guns has been the focus of recurrent research 

efforts for nearly 50 years (Morrison, Knapton, & Bulman 1988; Klingenberg, 

Knapton, Morrison, & Wren 1997). The interior ballistic processes in liquid 

propellant guns are much different from those in conventional solid propellant 

guns. In conventional guns, the interior ballistics are controlled by the combustion 

of solid propellant grains, which are manufactured with a predetermined 

propellant formulation and grain geometry. The propellant formulation and the 

grain geometry control the gas generation rate by affecting the linear burning rate 

and the total burning surface area of the grain, respectively. In contrast, the 

interior ballistics of the liquid propellant gun are determined by either the rate of 

injection of LP into the combustion chamber, as in the regenerative liquid 

propellant gun, or the hydrodynamics of the combustion gas-liquid propellant 

mixing process, as in the bulk-loaded liquid propellant gun (BLPG). In the 

regenerative liquid propellant gun, the surface area required to bum the 

propellant is determined by the break-up of the liquid jet as it enters the 

combustion chamber. In the BLPG, the propellant surface area is generated by the 

break-up of the gas-liquid interface separating the bulk liquid and the gaseous 

combustion products. 

The primary focus of LP-related research over the past 15 years was on the 

regenerative liquid propellant gun, which was shown to offer control and 

repeatability of the ballistic cycle (Morrison, Knapton, & Bulman, 1988; 

Klingenberg, Knapton, Morrison, & Wren 1997). The last large caliber research 

program to develop a BLPG ended in the 1970’s after several catastrophic 

failures. Research interest in the BLPG was revived in the early 1990’s (Talley & 

Owczarczak 1991, 1994; Rosenberger, Stobie, Knapton, 1995a, 1995b; Talley, 

Owczarczak, & Geise 1997). The concept is attractive because it is less complex 

than the regenerative liquid propellant gun and offers some advantages for small 

and medium caliber direct fire weapons. However, the interior ballistic process in 

the BLPG is not as well understood and the modeling tools are not as advanced 

as they are for the regenerative liquid propellant gun. 

Several interior ballistic models were developed during the height of the BLPG 

work in the 1970’s. These ranged in complexity from simple, zero-dimensional 

(O-D) (Edelman 1974; Burnett 1976) and one-dimensional .(1-D) models 

(Edelman 1976) to two-dimensional (2-D), axisymmetric solutions of the NavierStokes equations (Edelman, Phillips, & Wang 1983). The O-D and 1-D models 

required empirical information and were based on the phenomenological model 

1 
of Comer, Shearer, and Jones (1963). This phenomenological model, which was 

proposed to be consistent with the physical situation and the experimental data, 

is illustrated in Figure 1 and is presented as follows. First, the ignition process 

creates a bubble or cavity of hot combustion products at the axial position of the 

breech (rear) end of the gun. Such a gas cavity can be generated by venting hot 

gases from an external igniter directly into the fluid in the combustion chamber. 

The ignition process causes the development of pressure waves, predominantly 

longitudinal. These pressure waves are believed to cause the gas-liquid interface 

at the cavity to spall, increasing the rate of mixing of propellant and hot 

combustion products. After the projectile begins to move, the high-pressure gases 

in the cavity accelerate both the projectile and the “slug” (i.e., column or volume) 

of LP between the projectile and cavity. This situation is similar to the 

hydrodynamic instability of accelerated liquid surfaces analyzed by Taylor 

(1950). The growth of this instability leads to the development of a “Taylor” 

cavity, which penetrates the liquid column’until it reaches the projectile. After the 

cavity reaches the projectile base, an annulus of liquid is believed to remain on 

the chamber wall, with combustion gases flowing through the center. This leads 

to the Kelvin-Helmholtz type instability at the gas-liquid interface, with an 

increased combustion rate attributable to enhanced turbulent mixing. This 

phenomenological model can be used to explain many of the phenomena 

observed in experimental BLPG data. However, another mechanism may be 

responsible for achieving the very high burning rates necessary to explain some of 

the experimental data, especially when anomalies occur. Pressure-time traces 

qualitatively similar to experimental results were produced with these early O-D 

and 1-D models, and some insight was gained from the results. Although some of 

these models were used with some success in analyzing experimental data, they 

had little predictive capability. 

The 2-D axisymmetric model of Edelman, Phillips, and Wang (1983) was an 

attempt to model the hydrodynamic and chemical processes present in the 

BLPG. The model included the framework to treat the processes in the BLPG: 

turbulence (algebraic and two-equation models), droplet formation, and finite 

rate chemical kinetics. With a simplified, one-step combustion mechanism, a 

favorable comparison between predictions of chamber pressure and experimental 

data was shown. The development of the Taylor cavity was also observed in the 

simulation. Development of this model for this application apparently ended 

with the conclusion of BLPG research in the late 1970’s. 

Another model to describe the interior ballistics of the BLPG was proposed by 

Kuo, Cheung, and Chen (1989). This was another 2-D axisymmetric formulation 

that also included mechanisms of droplet dispersion and Helmholtz instability 

to estimate the liquid entrainment rate and droplet distribution. Numerical 

calculations were not reported, but the methods presented were later used in a 

model of the liquid propellant electro-thermal-chemical (LPETC) gun (Chen, Kuo, 

& Cheung 1992) that compared well with experimental data. 

2 
/ LIQUID PROPELLANT 

GAST>: -PROJECTILE 

t 

Figure 1. Phenomenological Model of the BLPG Interior Ballistics Proposed by 

Comer, Shearer, and Jones (1963). 

A more recent model by Macpherson, Bracuti, and Chiu (1994) was based on the 

BLPG operating in supercritical conditions. Rather than follow the traditional 

model of Comer, Shearer, and Jones (1963), they assumed that the LP was 

supercritical throughout the process, and they included heat transfer in the fluid 

as well as chemical kinetics. The combustion results from a thermal wave 

moving through the fluid, starting from an initial hemispherical “ignition 

bubble” that was specified as a boundary condition. The model compared 

reasonably to a specific set of experimental data used to calibrate the model. 

The issue of supercritical conditions was also considered by Edelman, Phillips, 

and Wang (1983), who suggested the possibility that a gas-gas (i.e., combustion 

gas-supercritical “fluid”) type mixing might be applicable. Most, if not all, earlier 

BLPG models considered gas-liquid interactions. 

The experience gained in developing the 2-D BLPG model was later used to 

model the LPETC gun (Hsiao, Phillips, & Su, 1992), which is similar to the BLPG. 

In the LPETC gun, the combustion of a liquid propellant is initiated and 

(potentially) controlled by the injection of a plasma generated from the discharge 

of electrical energy. In the BLPG, the liquid propellant is only initiated by the 

injection of hot gas from an igniter. Several other 2-D models of the LPETC gun 

were also developed (Cook, Dyvik, & Chryssomallis 1989; Chen, Kuo, & Cheung 

1992; Hosangadi, Sinha, & Dash 1995). Results from these models compared 

quite well to specific experimental data. 

3 
The sensitivity of various BLPG design parameters, such as igniter location, 

igniter output, and boundary conditions, has been largely unexplored because a 

validated, predictive computer model does not exist. This is primarily because of 

the difficulty in identifying, through diagnostic experimentation, the physical 

processes that occur at gun pressures as great as 700 MPa. Many of these 

difficulties remain. However, the codes developed for the LPETC gun also 

contain the framework for simulating the combustion processes in the BLPG and 

provide a good starting point for developing a model of the BLPG. 

For this study, the CRAFT’ Navier-Stokes code (Sinha, Dash, & Hosangadi 1992) 

was used to model two BLPG concepts that were also investigated 

experimentally. The goal of this study was to evaluate the effectiveness of using 

state-of-the-art numerical techniques to model the BLPG process via relatively 

simple physical models for LP combustion and mixing. If reasonably successful 

results with these simple models were obtained, then the feasibility of 

developing more advanced physical models could be estimated. A minimum of 

two experimental configurations was chosen to determine the sensitivity of the 

simulation results to changes in combustion chamber geometry. This report 

describes the results obtained via the CRAFT code to simulate two BLPG 

concepts and the comparison of those results with experimental data. 

2. Numerical Technique 

The CRAFT code is based on the TUFF’ aerodynamic code developed by Molvik 

and Merkle (1989). It is a 3-D, finite volume code that uses an implicit, upwind 

scheme based on that of Roe (1981). The total variation-diminishing (TVD) 

technique of Chakravarthy and Osher (1983) was used to obtain higher order 

accuracy without spurious oscillatory behavior. A large-eddy simulation (LES) 

approach was used for turbulence modeling, i.e., the large-scale turbulent 

structure was directly simulated by the flow solver, while the small-scale (on the 

order of the grid cell size) dissipative structures were modeled. In the code 

version used in the present study, a third order accurate TVD scheme, second 

order time integration, and a simple small-scale (sub-grid) turbulence model 

were used. A summary of the CRAFT code numerics and modifications for short 

duration transient, chemically reacting, multi-phase flows was provided by 

Hosangadi, Sinha, and Dash (1995). They also presented several fundamental 

numerical validation studies that demonstrate the capability of the CRAFT code 

to analyze problems involving finite rate combustion, turbulence with largescale vertical structures and transient wave processes particular to gun 

propulsion systems. The CRAFT code was successfully used to simulate flows in 

the electro-thermal-chemical gun and the regenerative liquid propellant gun 

1 

not an acronym 

4 
(Hosangadi, Sinha, & Dash 1995; Hosangadi, Kenzakowski, Sinha, & Dash 1996; 

Madabhushi, Hosangadi, Sinha, & Dash 1995), and unsteady jet flow fields 

(Sinha, Dash, & Madabhushi 1993). All calculations were performed in serial 

mode on the Silicon Graphics, Inc., Power Challenge Array (SGI-PCA) system at 

the Department of Defense High Performance Computing Center at Aberdeen 

Proving Ground, Maryland. 

The version of the CRAFT code used for the LPETC gun simulations was 

modified to perform 2-D axisymmetric simulations of a BLPG. This version of 

the code uses a mixing length, turbulent eddy viscosity, sub-grid stress model 

for the finer scales of turbulence. The numerical formulation in the CRAFT code 

allows for generalized fluid mixtures of gas and bulk liquid. In addition, an 

equilibrium formulation is used, in which at a given location, the gas and liquid 

phases have identical velocities, pressures, and temperatures. The combustion 

model is an Arrhenius-type formulation in which the kinetic rate is based on 

temperature. The combustion of the bulk liquid propellant, a monopropellant, is 

modeled as a two-step process. First, the bulk liquid is converted to an 

intermediate gaseous form (LP vapor). Second, the single, gaseous intermediate 

species then burns to generate the product species. The numerical values of the 

rate coefficients are estimated by numerical simulations of earlier liquid 

propellant closed chamber combustion experiments (DeSpirito 1988); the rate of 

pressure rise is then matched. These rate coefficients are only estimates and are 

considered adequate since it is known that this combustion model does not fully 

describe the combustion process in the BLPG, as discussed in the following 

paragraphs. 

The temperatureSbased combustion model was chosen for these investigations 

instead of a pressure-dependent propellant bum rate equation. The latter is used 

in conventional (solid propellant) interior ballistic analyses and requires 

knowledge of the propellant burning surface area, which is calculated from the 

geometry form function. In contrast, in the BLPG, the propellant surface area is 

generated as a result of the fluid dynamic shear stress between the gas and 

liquid and is therefore very difficult to calculate. A model of droplet formation, 

based on shearing at the gas-liquid interface, is required for a pressuredependent formulation. The temperature-based combustion model should 

provide acceptable results if the combustion process in the BLPG is dominated 

by turbulent mixing, i.e., the combustion rate is much faster than the mixing rate. 

This condition was found in the LPETC gun (Hosangadi, Sinha, & Dash 1995). 

The forcing of temperature equilibrium between the gas and the liquid in each 

cell led to a dependence of the combustion rate on the cell size. Since the 

temperature of the gas is much greater than that of the liquid, it is believed that 

the larger cells cause a larger amount of the total liquid to heat at a given time 

step than would occur on a finer grid. This leads to a faster combustion rate with 

the large cell size. This problem was noted and new reaction rate coefficients 

5 
were estimated by the closed chamber numerical study with a finer grid spacing 

comparable to that used for the BLPG simulations. A two-temperature 

formulation appears to be more appropriate and should be implemented into the 

code in the future. 

It was realized at the outset that some aspects of the experimental pressure-time 

curves would not be captured by this combustion model formulation. For 

example, the combustion enhancement attributable to pressure wave interaction 

at the gas-liquid interface is expected to significantly increase the surface area by 

increasing the rate of droplet formation. Without a droplet formation model, this 

effect will not be simulated. The CRAFT code contains a Lagrangian solver for 

tracking droplets, and a pressure-dependent burn rate combustion model could 

be implemented. Unfortunately, the appropriate rate constants are not available 

because empirical models of droplet formation are calibrated at much lower 

pressure and velocity. Therefore, droplet formation was not modeled. 

Another consideration is that the operating conditions in the BLPG may be 

above the critical state of the LP. Accurate values of the critical pressure and 

temperature of the LP (described in the next section) being used in the 

experimental studies (Talley & Owczarczak 1994; Rosenberger, Stobie, & 

Knapton 1995a, 1995b; Talley, Owczarczak, & Geise 1997) are unknown. An 

estimate of a critical pressure of 250 MPa was made by Faeth, Lee, and 

Kounalakis (1987); however, the authors attributed an error of as much as 50% to 

that value. In any case, it is possible that the flow and combustion processes in 

the BLPG occur above the critical state for a portion of the ballistic cycle. In view 

of the uncertainties, the gas-liquid formulation was chosen to model the 

experimental data. This is consistent with the previous BLPG and LPETC 

modeling efforts. 

3. Experimental Fixture 

The approach of this study was to perform 2-D axisymmetric simulations of two 

30-n-m BLPG firings performed in accordance with a U.S. Army contract at 

Veritay Technology, Inc. (Talley, Owczarczak, & Geise 1997). The objective of the 

BLPG experimental program was to evaluate the effectiveness of combustion 

chamber geometry in controlling the interior ballistic variability and overall 

shape of the pressure-time curves. Figures 2 and 3 show two of the “stepped 

chamber” configurations that were investigated. It was postulated that by 

properly configuring the diameter and length of each section, the progressivity 

and stability of combustion in the chamber could be controlled. It was believed 

that one mechanism for achieving this was by the promotion of turbulence via 

the addition of steps in the combustion chamber. The experimental results 

showed that some control of the ballistic process could be achieved with this 

6 
. 

. 

concept, as compared to standard, single-diameter chambers. However, the 

empirical data indicated the potential for a lack of control late in the ballistic 

cycle, when the Taylor cavity is expected to extend beyond the stepped region in 

the chamber. 

Figure 2 shows the standard four-stage, stepped chamber. The combustion 

chamber consisted of four sections that “step” in diameter from 1.6 to 2.0, 2.4, 

and 2.8 cm, respectively. The gun barrel section, which becomes part of the 

chamber wall after the projectile moves, was 3.0 cm in diameter. The location of 

the pressure gauge ports, Pl, P2, and P5, is also shown in Figure 2. The 

combustion chamber was initially completely filled with LP and was 14.2 cm 

long. The mass of the LP was 85.0 g and the mass of the projectile was 394 g. The 

process was initiated by the ignition of a small solid propellant charge loaded in 

the “igniter chamber” (see Figure 2). The igniter charge burned at high pressure 

and injected hot gas into the combustion chamber, initiating the LP combustion. 

The size of the igniter chamber orifice was 1.32 mm. 

(x=7.7 cm) 

P5 

(x=1 7.4 cm) 

Pbarl 

(~~23.8 cm) 

Chamber Insert 

Gun Chamber Housing 

NOT DRAWN TO SCALE. 

Figure 2. Standard Four-stage Combustion Chamber. 

Figure 3 shows a modified version of the four-stage combustion chamber. The 

diameter of the fourth stage of the chamber was increased to 3.8 cm and then 

was tapered to 2.8 cm with a 12” taper. The mass of the LP was 114 g and the 

mass of the projectile was 357 g. The purpose of this design was to increase the 

ballistic performance (i.e., projectile muzzle velocity) by increasing the LP charge 

without adversely affecting the stability of the pressure-time curve. Past 

experience showed that increasing the LP charge by simply increasing the length 

of the chamber could lead to unrepeatable pressure-time traces. These 

unrepeatable results usually showed two pressure peaks, with the second peak 

7 
likely attributable to the portion of the LP charge that travels with the projectile 

and burns in the gun barrel, late in the ballistic cycle. If this characteristic were 

repeatable, it could provide a performance enhancement because of the higher 

pressure near the projectile. However, this effect was not repeatable and usually 

led to undesirable variability in muzzle velocity. 

1 Pbarl 

1 (x=23.8 cm) 

Chamber Insert 

Gun Chamber Housing 

NOT DRAWN TO SCALE 

Figure 3. Modified Four-stage Combustion Chamber. 

The propellant used in the gun firings was the monopropellant XM46 (formerly 

designated LGP.1846). The weight-percent composition of XM46 is 19.2% 

hydroxylammonium nitrate, 60.8% triethanolammonium nitrate, and 20.0% 

water. The basic thermodynamic properties of XM46 (at 0.2 g/cm3 loading 

density) are a flame temperature of 2469 K, an impetus of 898.3 J/g, a molecular 

weight (product gas) of 22.848, and a frozen specific heat ration (fi of 1.2225 

(Freedman 1988). 

4. Results and Discussion 

4.1 Simulation Procedure 

Two simulations were performed with the chamber configurations shown in 

Figures 2 and 3. The grids for these two chamber configurations are shown in 

Figure 4. The simulation was performed as 2-D axisyrnmetrical, as shown in 

Figure 4. The lower boundary represents the axis of the combustion chamber. To 

form the stepped region of the chamber, a grid-blanking procedure was used to 

remove sections of the grid from the computations. The initial grid sizes were 

8 
. 

. 

47 by 66 and 47 by 67, respectively. The right boundary represented the rear face 

of the projectile and was modeled as a solid, moving boundary. As the projectile 

moved, a grid-embedding procedure was used to add ceils to the computational 

domain. A cell was added at the last location in the axial direction if the length 

of the cell became greater than 3.14 mm. Grid embedding was stopped after 

propellant “burn-out.” The last section of the domain (starting 9.3 cm in 

Figure 4a and at 13.9 cm in Figure 4b) was then allowed to expand for the 

remainder of the computation, i.e., during the gas expansion process. The 

maximum number of nodes in the axial direction at the completion of grid 

embedding was 144 in the configuration of Figure 4a and 157 in the 

configuration of Figure 4b. 

0.020 

0.015 

z 0010 

aY . 

0.005 

0.000 

0.020 

0.015 

E 0010 

IY ‘ 

0.005 

0.000 

Standard 4-Stage Chamber 

Modified 4-Stage Chamber 

0.00 0.05 

Travel(m) 

0.10 0.15 

Figure 4. Initial Grids Used in Simulations of the (a) Standard and the 

(b) Modified Four-stage Combustion Chambers (units are in meters). 

The movement of the right boundary, which represented the rear face of the 

projectile, was based on the equations of motion of a given projectile mass. The 

acceleration of the projectile was first calculated from the pressure and area at 

the right boundary and the projectile mass. The velocity and displacement of the 

right boundary were then calculated. The only loss included in the projectile 

equation of motion was the frictional force attributable to contact with the gun 

barrel. A simple resistive force profile was used, with an estimated projectile 

shot-start pressure of 30 MPa maintained for the first 0.5 cm of travel, decreasing 

9 
linearly to 5 MPa at 1.0 cm of travel and remaining at 5 MPa for the remainder of 

travel. The total projectile travel was 201.7 cm. 

The solid boundaries were treated as Euler reflecting boundaries, rather than 

viscous, no-slip walls. The latter condition would require a large degree of mesh 

refinement near the walls, including the steps, and was considered too 

computationally expensive for this study. This limitation was deemed 

acceptable, even though this boundary condition would have an effect on the 

near-wall turbulence. The effect on the solution would likely be most 

pronounced in the stepped region. 

Four species were used in the simulation: igniter gas, Ll? combustion products, 

LP vapor, and LP liquid. The chamber was initialized as all liquid propellant 

with the gas volume fraction parameter, 4. The igniter gas was only injected 

during the early part of the simulation and it was included in the combustion 

products in the plots of combustion product mass fraction. A value of 4 = 0.02 

was used for the liquid in the combustion chamber, and a value of C#I = b.99999 

was used for the incoming igniter gases. 

s 

The injection of hot combustion gases from the igniter chamber (see Figure 2) 

was simulated via experimental igniter chamber pressure-time data. This “inflow” boundary condition was centered at the left end of the axis of the chamber 

and consisted of the first five cells in the radial direction. The static pressure 

(from the experimental data), temperature, and velocity vector direction cosines 

were specified at this in-flow boundary. The in-flow velocity was calculated as 

part of the solution, with an allowance for choked flow. The properties of the 

igniter gas in the simulations were the same as Ll? combustion products, 

although in the experiments, a solid propellant was used. This was done for 

convenience only, since the igniter gas represents only a small percentage of the 

total energy. The temperature of the injected igniter gas was specified as 2000 K. 

The initial pressure and temperature in the chamber were set to 1 MPa and 

300 K, respectively. Although the initial pressure in the experiment was 

atmospheric (0.1 MPa), the initial pressure in the simulation was set higher to 

alleviate a numerical issue in the liquid equation of state calculation. Specifically, 

a very low pressure would lead to very little change in density and would cause 

a large round-off error in the iterative routine used to equate the liquid pressure 

to the gas pressure (equilibrium formulation). The chemical reactions 

(vaporization and decomposition) were not allowed to begin until the local 

temperature exceeded 400 K. In addition, a high temperature limit was put on 

the reaction rate coefficients. The reaction rates at temperatures above 700 K 

were set to those at 700 K. Without this limitation, the combustion rate was 

found to increase too much as the temperature increased. 

10 
. 

. 

After the simulation began with a value 0.1, the Courant-Friedrich-Levy (CFL) 

number was increased to 1.0 over the first 2000 iterations (about 0.080 ms). The 

solution proceeded with a CFL number of 1.0 until about 1.25 ms. The average 

time step during this time was about 6 x lOWa sec. After this time, with LP 

combustion almost complete, the CFL number was raised to 5.0, grid embedding 

was stopped, and the solution was continued until the projectile reached the 

maximum gun barrel travel. 

4.2 Simulation of Standard Four-Stage Chamber 

This simulation was initialized with the conditions of Veritay Test No. 130. One 

modification in the simulation was that the fourth stage diameter was made 

3.0 cm instead of 2.8 cm. This resulted in an increase in the mass of LP in the 

simulation from 85 g to 93 g-an increase of about 9%. The increase in diameter 

from the 2.8-cm chamber to the 3.0~cm gun barrel after the projectile moved 

would have required modification of the dynamic grid routine. It was decided 

that this was not necessary for these preliminary runs, and the increase in initial 

chemical energy would be considered when the simulation was compared to the 

experiment. 

Contours of combustion product mass fraction are shown in Figure 5, where the 

computational domain has been mirrored for illustration. The solution is 

presented at four times, showing the evolution of combustion and the 

development of the Taylor cavity. The top plot, at 0.255 ms, shows the 

development of the combustion gas bubble shortly before the igniter gases 

stopped venting. Only about 1.5% of the original LP charge combusted to this 

point. At 0.535 ms, the development of the Taylor cavity is observed. The tip of 

the cavity is penetrating the liquid at a velocity faster than the projectile velocity. 

About 17% of the charge has combusted to this point. At 0.695 ms, about 38% of 

the charge has combusted and there is no liquid left on the wall of the first two 

stages of the chamber. The cavity tip reaches the projectile base just before the 

plot shown at 0.923 ms. About 82% of the charge has combusted at this point. 

Contour plots of vorticity show eddy structures forming past the steps at 

0.535 ms, which are well defined at 0.695 ms. Figure 6 shows a contour plot of 

vorticity at 0.695 ms. It was not determined whether these were turbulent eddies 

or just laminar wake eddies. However, these eddies may evolve to turbulence 

that would not be present in the absence of the steps. 

In Figures 7 through 9, the simulated pressure-time history is compared with 

that of Test No. 130 at the Pl, P2, and P5 locations (see Figure 2). The P5 location 

is open to the chamber pressure after passage of the projectile. The experimental 

pressure-time curves shown here were filtered with a lo-kHz, low-pass filter. 

The unfiltered curves contained high frequency oscillations usually associated 

with LP combustion. In general, the simulated maximum mean pressure is 

higher and occurs later in time than in the experiment. The overall wider shape 

of the simulated pressure-time curve near peak pressure indicates that 

11 
combustion is likely progressing in a more stable manner than in the experiment. 

In the simulation, the gas cavity reaches the projectile at about 0.9 ms, which is 

the point at which the pressure begins to decrease (see Figure 8). This is in 

contrast to the traditional view of the BLPG process, which proposed that 

combustion enhancement would normally take place at this point. However, the 

Kelvin-Helmholtz mixing attributed to‘ 

simulation. 

this process is not included in the 

0.0 0.1 0.2 0.3 

X (m) 

0.00 0.20 0.40 0.80 0.80 1.00 

Figure 5. Contours of Combustion Product Mass Fraction for Simulation of 

Standard Four-stage Chamber at 0.255,0.535,0.695, and 0.923 ms. 

0.02 

0.01 

0 

-0.01 

73000 

65000 

57000 

49000 

41000 

33000 

25000 

17000 

9000 

1000 

-7000 

-15000 

----- 

Figure 6. Contours of Vorticity Simulation of Standard Four-stage Chamber at 

0.255,0.535,0.695, and 0.923 ms. 
. 

600 

Simulation - 

Test No.130 ----. 

0.5 1 

TIMk~ms) 

2 2.5 

Figure 7. Pressure at I’1 Location From Simulation (solid line) and From Test 

No. 130 (dashed line). 

In Figures 7 and 8, it can also be seen that the travel of the blast wave from the 

igniter orifice (at t = 0.0) to the Pl and P2 locations was captured in the 

simulation. Also, in the simulation, the pressure, which is driven by the igniter, 

continues to rise quickly. However, there is a combustion delay of about 0.1 ms 

in the experiment. During this delay, which is not detrimentally long in this case, 

there is likely quenching of the igniter gases and a low-energy release, “fizzburn” of the LP. In the past, longer combustion delays have led to extremely 

high, undesirable pressures. As set up, the simulation will not capture this 

combustion delay. Figure 9 shows that the simulation captures the passage of the 

projectile by the P5 location at the proper time. 

The simulation does capture the predominantly longitudinal wave structure that 

was observed in the experiment. This wave structure is attributable to the 

pressure pulse caused by the igniter. Examination of contour plots of pressure 

showed some radial structure early, during the early growth of the gas cavity, 

but this quickly developed into the longitudinal structure. The longitudinal 

wave structure is expected with ignition that occurs at the end of the chamber. 

The frequency of the longitudinal wave structure was a little lower in the 

simulation. The period between the first two peaks (at about 0.5 ms) was 

0.164 ms in the simulation versus 0.149 ms in the experimental case. 

13 
700 I I I I I 

Simulation - 

Test No. 130 ----. 

600 

500 

l3 

ci 400 

i! 

2 

2 300 

B 

200 

100 

0 

0 0.5 1 1.5 2 2.5 3 

TIME (ms) 

Figure 8. Pressure at P2 Location From Simulation (solid line) and From Test 

No. 130 (dashed line). 

700 

600 

500 

2 

E 400 

E 

i 300 

200 

100 

0 

I I I 

Simulation - 

Test No. 130 ----- 

0 0.5 1 1.5 2 2.5 3 

TIME (ms) 

Figure 9. Pressure at P5 Location From Simulation (solid line) and From Test 

No. 130 (dashed line). 

The projectile muzzle vejocity in the simulation was 967 m/s, which is much 

higher (26%) than that measured in the experiment (769 m/s). The 9% increase in 

chemical energy in the simulation would only account for a small part of this 

difference because of the ballistic efficiency (projectile muzzle kinetic energy 

14 
divided by total chemical energy), which was 34% in Experiment No. 130. No 

heat transfer losses to the gun tube wall were considered in the calculation, 

although this would still only account for part of the difference. The velocity 

difference is attributable to the difference in the pressure-time history of the 

simulation, as compared to the experimental data. It is obvious that not all the 

physics of the combustion process are correctly modeled in this case. 

4.3 Simulation of Modified Four-Stage Chamber 

This simulation was set up with the conditions of Veritay Test No. 155. The rear 

of the projectile in this experiment was made of plastic and was hemispherical in 

shape; this was a design modification that alleviated but did not eliminate the 

adverse effects of the longitudinal wave problem (Talley, Owczarczak, & Geise 

1997). The hemispherical base was not modeled for this simulation. However, 

the length of the flat base design was adjusted so that the difference in volume 

was only 0.42 cm3 (1%). 

Contours of combustion product mass fraction are shown at four times in 

Figure 10. When compared to the previous simulation, the gas cavity is observed 

to reach the chamber wall in the third stage earlier. This is a result of the 

increased compressibility of the liquid column because of the increased volume 

in the fourth stage. This also results in a slower penetration of the cavity tip. 

The simulated pressure-time history is compared to that of Test No. 155 in 

Figures 11 and 12. The very large amplitude of the pressure waves in the 

experimental pressure-time curve in Figure 11 is likely an artifact attributable to 

amplification in the pressure gauge port cavity (Rosenberger 1994). The 

projectile muzzle velocity in the simulation was 1086 m/s versus 983 m/s in 

Test No. 155-a difference of 10%. This simulation compares better with the 

experimental data than the previous simulation. Comparing the two simulation 

results, shown in Figure 13, it is observed that the main differences are a shift of 

the peak pressure to a later time and a slightly higher pressure during the 

expansion part of the process. The better match with the data in the second 

simulation is more attributable to the difference in the experimental pressuretime curve, which is wider than in the previous experiment. One may consider 

that in the second case, Test No. 155, the combustion may have proceeded in a 

more stable manner, without the anomalous features not modeled in the 

simulation. 

4.4 Discussion of Results 

Figure 14 shows contour plots of temperature for the two simulations at about 

0.7 ms. The difference in cavity penetration between the two simulations can be 

observed. It was also observed that the maximum temperature in the gas cavity 

was about 3200 K, even though the flame temperature is 2469 K (at a loading 

density of 0.2 g/cm3). Adjusting for the higher loading density in the BLPG only 

15 
density of 0.2 g/cm”). Adjusting for the higher loading density in the BLPG only 

increases the flame temperature to about 2600 K. Temperatures higher than the 

flame temperature in interior ballistic calculations would normally indicate an 

error in the solution. One possible explanation is the use of a constant specific 

heat value. Although the CRAFT code allows for a variable specific heat, a 

constant value was used. The unique conditions in which the BLPG operates led 

to a search for a possible physical mechanism. The highest temperature is near 

the core of the gas cavity, not far behind the tip. The temperature in the 

combustion zone (gas-liquid interface) is at the flame temperature. One might 

expect the combustion zone to give the highest temperature if numerical error 

were the problem. 

0.020 

g %i 

uz :;:;:; 

0.00 0.05 0.10 0.15 0.20 0.25 0.30 

X (m) 

0.00 0.20 0.40 060 0.80 1 00 

Figure 10. Contours of Combustion Product Mass Fraction for Simulation of 

Modified Four-stage Chamber at 0.205,0.545,0.706, and 0.866 ms. 

0 0.5 1 1.5 2 2.5 3 

TIME (ms) 

Figure 11. Pressure at Pl Location From Simulation (solid line) and From Test 

No. 155 (dashed line). 

16 
600 

0 0.5 1 1.5 2 2.5 3 

TIME (ms) 

Figure 12. Pressure at P2 Location From Simulation (solid line) and From Test 

No. 155 (dashed line). 

700 

600 

500 

400 

300 

200 

100 

0 

I I I I I 

Simulation Test No. 130 - 

Simulation Test No. 155 ----’ 

0 0.5 1 

TIMkFms) 

2 2.5 3 

Figure 13. Pressure at I’2 Location From Simulation of Test No. 130 (solid line) 

and From Simulation of Test No. 155 (dashed line). 

17 
TEMP (K) 

3200 

2900 

-0.020 2600 

2300 

2000 

1700 

1400 

0.020 1100 

800 

0.010 500 

200 

E 0.000 

u 

-0.010 

-0.020 

0.00 0.05 0.10 0.15 0.20 0.25 

X (ml 

Figure 14. Contours of Temperature (K) for Simulation of Standard (top) and 

Modified (bottom) Four-stage Chamber. 

One possible explanation may be simply isentropic compression of the 

combustion gases during the ballistic cycle. The process begins when the igniter 

vents hot gas into an almost incompressible liquid. Relief will be achieved by 

movement of the projectile and the conversion of LP to gas combustion product. 

The projectile does not begin to move until about 0.2 ms and the pressure at the 

Pl location is already about 150 MPa by this time (see Figure 7). Therefore, 

compression of the igniter vent gases would occur very early. In combustion of 

solid propellant grains or LP droplets, only the local temperature near the 

combustion surface will be at the flame temperature. The temperature quickly 

drops as the combustion gases expand away from the combustion zone. The 

configuration of the BLPG is such that the combustion gas is surrounded by the 

combustion zone, which is at or near the flame temperature. In this case, it may 

be possible for the combustion gases to be compressed above the flame 

temperature. 

In order to check the plausibility of this hypothesis, the simulation of the 

standard four-stage chamber (Veritay Test No. 130) was examined in more 

detail. The value of the temperature and pressure in the region behind the cavity 

tip was extracted from the solution field at about 0.1~ms intervals. If isentropic 

compression were occurring during this time, assuming a perfect gas model, the 

relation Tp-(y.i)l should be constant. In this relation, T is the gas temperature, p is 

the gas pressure, and yis the ratio of specific heats. From about 0.3 ms to 0.9 ms, 

the period of highest temperature, the value of Tp-T/-l)p varied only about 3.6%, 

with a y value of 1.2226. Mass was being added to the system from the igniter 

18 
venting process before 0.3 ms. After 0.9 ms, the value of Tp-fr’J’Y decreased about 

9%, which coincided with a decrease in total mass of about 1.5%. This mass error 

occurred during the period of high projectile acceleration. It was likely 

attributable to both numerical error from the extrapolation used during the grid 

embedding process and the high CFL number used during this period. 

This result indicates that gas compression is a possible explanation -for the high 

gas cavity temperature. This phenomenon was apparently not encountered in 

previous BLPG modeling. It would not likely be noticed in LPETC gun modeling 

since the plasma is injected at temperatures above 15,000 K. Future studies 

should consider this phenomenon, both for added confirmation that it is 

physical and because of its potential effect on the combustion process. 

The results of the two simulations illustrate both the strengths and weaknesses 

in modeling the BLPG process. Solutions that compare favorably with 

experimental data can be made, such as in the second simulation. At the same 

time, other solutions, such as in the first simulation, demonstrate that some 

physical processes are not being modeled. To further illustrate this limitation, a 

third simulation was performed. This simulation was set up with the same LP 

charge volume and projectile mass as the modified four-step chamber 

simulation, 114 g and 357 g, respectively. However, in this case, a simple 

cylindrical chamber was considered, similar to the traditional BLPG chamber 

that was considered in earlier studies. The diameter of the chamber was 3.0 cm 

and the initial length was 11.3 cm, with an initial grid of 38 by 66. From the 

experimental point of view, this case would not be expected to have a pressuretime history similar to that of Test No. 155 (see Figures 11 and 12), at least not 

without proper tuning of the igniter. The pressure-time history was shown 

experimentally to be sensitive to the igniter orifice/chamber diameter ratio 

(Talley & Owczarczak 1991, 1994), which was the original basis for using the 

stepped chamber geometry. The resulting simulation did not show any grossly 

different features than the previous two simulations, thus indicating 

insensitivity to geometry, which does not follow the experimental observations. 

Figure 15 shows a comparison of the simulated pressure at the Pl location from 

this simulation and the modified four-stage chamber simulation (see Figure 11). 

The comparison illustrates some physically viable differences in the cylindrical 

chamber case, such as the lack of amplification of the longitudinal wave 

structure (discussed in the next paragraph); the slower initial rise rate because of 

the added compressibility of the increased volume of LP outside the igniter 

orifice; and the low-amplitude, high-frequency, radial wave structure. The 

combustion model used in the simulation does not provide the capability to 

simulate the physical instability mechanisms that appear in the experimental 

fixture. 

19 
600 

Cyl. Chamber - 

Modified 4-Stage Chamber ----. 

500 

400 

300 

200 

100 

0 

0 0.5 1 2 2.5 3 

Figure 15. Comparison of Pressure at Pl Location From Simulation Using 

Cylindrical Chamber Geometry (solid line) and From Simulation 

Using Modified Four-stage Chamber Geometry (dashed line). 

The limitations of the current model reduce its usefulness as a predictive tool. 

However, it may be useful in helping to analyze experimental data and even 

give insight for chamber design. For example, in many of the experimental data, 

high amplitude pressure waves were observed at the Pl location but at a much 

lower amplitude at the P2 location. It was interesting to see the same 

phenomenon present in the simulation. The phenomenon is apparently 

attributable to the wave interactions with the stepped geometry, amplifying the 

magnitude in the smaller volume, end section where Pl is measured. Although 

this may be intuitive from the geometry of the chamber, the pressure 

measurement technique at the Pl location was susceptible to amplification of the 

signal (Rosenberger 1994), leading one to question whether the magnitude of the 

pressure waves was reasonable. 

It is possible that other physical phenomena may be simulated through the 

adjustment of some parameters. For example, the combustion delay early in the 

ballistic cycle might be reproduced by increasing the temperature at which 

decomposition from LP vapor to combustion products takes place. This would 

allow the accumulation of LP vapor, which would not increase the pressure very 

much and would combust rapidly when the decomposition temperature was 

exceeded. Although this may increase the likelihood of capturing features of the 

experimental pressure-time trace and may be helpful in understanding the 

physical processes, it does not necessarily lead to better predictive capability. 

20 
The inclusion of better physical models, such as liquid droplet formation and 

more detailed chemical kinetics, is probably required before a predictive code 

can be developed. Unfortunately, this is a difficult task, since the applicability of 

formulations from other work, such as the spray combustion area, is difficult to 

validate at very high gun pressures. The evaluation of more detailed physical 

sub-models will require time-consuming comparisons with a good set of 

experimental data. The evaluation should also be made with various chamber 

geometry variations, such as the Veritay data, which include several other 

chamber concepts not discussed in this report (Talley, Owczarczak, & Geise 

1997). 

5. Summary 

A modified version of the CRAFT Navier-Stokes code was used to perform 

simulations of firings that employ two different bulk-loaded liquid propellant 

gun chamber configurations. The resulting pressure-time history at several 

locations in the chamber and gun tube was compared to experimental data 

obtained in a separate study. 

The simulations showed the development of a Taylor cavity that penetrated the 

bulk-liquid column as it accelerated toward the projectile. This was very similar 

to the traditional description of the BLPG interior ballistic process described by 

Comer, Shearer, and Jones (1963). An annulus of unburned liquid propellant 

remained along the chamber wall in the last section of the four-stage chamber. 

Eddy structures’ formed after the steps in the combustion chamber. The 

simulations also capture the longitudinal wave structure present in the 

experimental data. 

A comparison of the simulation of the first chamber configuration with 

experimental data showed that the shape of the pressure-time curve was 

different and the predicted pressure was higher in the simulation. The earlier 

pressure peak in the data indicated that the combustion occurred faster than the 

simulation predicted. A combustion delay present in the experimental data was 

not present in the simulation. An over-prediction of projectile muzzle velocity of 

26% followed from the difference in pressure-time history. 

The simulation of the second chamber configuration showed a much better 

match to the overall shape of the pressure-time curve of the experimental data. 

The peak pressure in the simulation was still too high and the projectile muzzle 

velocity was over-predicted by 10%. Since the overall shape of the pressure-time 

curve in both simulations was similar, the better match with data in the second 

experimental case was attributed to the processes in the second experiment 

proceeding in a more stable manner, similar to that modeled in the simulation. 

21 
Temperatures higher than the LP flame temperature were observed in the gas 

cavity region. It was proposed that isentropic compression was a plausible 

explanation for the phenomenon. Further study of this phenomenon is 

warranted. 

The model does not yet contain sufficient physics present in the BLPG to be a 

predictive tool but may be useful as a tool to help analyze experimental data. 

These results confirm that numerical tools are available and are capable of 

providing solutions to this very complex physical system. However, the 

emphasis in future work should be on the inclusion of the missing physical 

models, such as droplet formation and combustion and liquid propellant 

chemical kinetics. 
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c 

Chakravarthy, S.R., and S. Osher, “Numerical Experiments with the Osher 

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24 
Roe, P.L., “Approximate Reimann Solvers, Parameter Vectors, and Difference 

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Propellant Gun Concepts.” ARL-CR-127, U.S. Army Research Laboratory, 

Aberdeen Proving Ground, MD, April 1994. 

, 

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25 
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 

January 200 1 Final 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

Interior Ballistic Simulations of the Bulk-Loaded Liquid Propellant Gun 

PR: 626 18AH80 

6. AUTHOR(S) 

DeSpirito, J. (ARL) 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS 8. PERFORMING ORGANIZATION 

REPORT NUMBER 

U.S. Army Research Laboratory 

Weapons & Materials Research Directorate 

Aberdeen Proving Ground, MD 210055066 

3. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS 10. SPONSORING/MONITORING 

U.S. Army Research Laboratory AGENCY REPORT NUMBER 

Weapons & Materials Research Directorate ARL-TR-23 16 

Aberdeen Proving Ground, MD 2 1005-5066 

Il. SUPPLEMENTARY NOTES 

12a. DlSTRlBUTION/AVAIlABILITY STATEMENT 12b. DISTRIBUTION CODE 

Approved for public release; distribution is unlimited. 

13. ABSTRACT (Maximum 200 words) 

The objective of this study was to determine the feasibility of modeling the interior ballistic processes of the bulk-loaded liquid 

propellant gun. A modified version of the CRAFT Navier-Stokes code was used to perform simulations of bulk-loaded liquid 

propellant gun firings that employed two different chamber configurations. The simulation accurately captures the longitudinal 

wave structure present in the experimental data, but a combustion delay present at the start of the ballistic cycle was not present in 

the simulations. The simulations showed the development of a cavity that penetrated the bulk-liquid column as it accelerated 

toward the projectile, leaving an annulus of unburned liquid propellant along the chamber wall. High gas temperatures were noted 

in this gas cavity region, possibly attributable to isentropic compression caused by the unique conditions in the bulk-loaded gun. 

The simulation of the second chamber configuration compared well with the experimental data, while the simulation of the first 

chamber configuration did not capture the experimental pressure-time profile. In general, the simulations showed an insensitivity to 

chamber geometry that is not observed in experimental firings. The limitations of the simulations were attributed to the lack of 

complete physical sub-models, such as a droplet formation/combustion model and detailed chemical kinetics. The model has the 

potential to be a useful tool in the analysis of experimental data. However, predictive capability is unlikely without the 

development of better physical sub-models. 

4. SUBJECT TERMS 15. NUMBER OF PAGES 

BLPG interior ballistics 35 

computational fluid dynamics liquid propellant gun 16. PRICE CODE 

7. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION lg. SECURITY CLASSIFICATION 20. ,LIMITATION OF ABSTRACT 

OF REPORT OF THIS PAGE OF ABSTRACT 

Unclassified Unclassified Unclassified 

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std. 239-18 29 

298-102