Multispecies Reacting Flow Model for the Plasma Efflux of 

an ETC Igniter—Application to an Open-Air Plasma Jet 

Impinging on an Instrumented Probe 

by Michael J. Nusca, William R. Anderson, and Michael J. McQuaid 

ARL-TR-3227 July 2004 

Approved for public release; distribution is unlimited. 
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Destroy this report when it is no longer needed. Do not return it to the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-3227 July 2004 

Multispecies Reacting Flow Model for the Plasma Efflux of 

an ETC Igniter—Application to an Open-Air Plasma Jet 

Impinging on an Instrumented Probe 

by Michael J. Nusca, William R. Anderson, and Michael J. McQuaid 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
ii

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4. TITLE AND SUBTITLE 

Multispecies Reacting Flow Model for the Plasma Efflux of an ETC Igniter—

Application to an Open-Air Plasma Jet Impinging on an Instrumented Probe 

5c. PROGRAM ELEMENT NUMBER 

5d. PROJECT NUMBER 

6122618H8000 

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6. AUTHOR(S) 

Michael J. Nusca, William R. Anderson, and Michael J. McQuaid 

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U.S. Army Research Laboratory 

ATTN: AMSRD-ARL-WM-BD 

Aberdeen Proving Ground, MD 21005-5066 

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14. ABSTRACT 

The U.S. Army Research Laboratory (ARL) is investigating the electrothermal-chemical (ETC) gun concept. As part of this 

program, ARL has recently begun a comprehensive study on the interaction of the plasma efflux from an ETC igniter with solid 

propellant grains. The goal of this work is to elucidate the relevant physical, mechanical, and chemical mechanisms that 

underlie the observed ballistic effects in ETC guns that can lead to useful performance gains once an understanding of these 

mechanisms is achieved. This report describes the first phase of the modeling effort in support of this plasma-propellant 

interaction project. A time-accurate computational fluid dynamics code was used that included high-temperature 

thermodynamics, variable specific heats and transport properties (viscosity and thermal conductivity), and finite-rate 

(nonequilibrium) chemical kinetics. Validation of this code used a series of experiments with an ETC igniter fired into open air, 

generating an unsteady flowfield in which a measurement probe is placed. Computer simulations revealed important gas 

dynamic and chemical details of the plasma jet as it interacted with the probe and represented the first such detailed modeling of 

ETC plasma efflux. 

15. SUBJECT TERMS

gun charges, solid propellant, multiphase flow, computer simulation 

16. SECURITY CLASSIFICATION OF: 

19a. NAME OF RESPONSIBLE PERSON

Michael J. Nusca 

a. REPORT 

UNCLASSIFIED 

b. ABSTRACT 

UNCLASSIFIED

c. THIS PAGE 

UNCLASSIFIED

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OF ABSTRACT 

UL 

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OF PAGES 

30 

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410-278-6108 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18
iii

Contents 

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Description of Open-Air Plasma Jet Experiment 2

3. Previous Modeling Efforts 7

4. Multispecies Reacting Flow CFD Code 7

5. Results and Discussion 10

6. Conclusions 16

7. References 17

Distribution List 20 
iv

List of Figures 

Figure 1. ETC gun concept. ............................................................................................................1 

Figure 2. Schematic of plasma generator and pressure probe also showing computational 

domain........................................................................................................................................3 

Figure 3. Current and power histories.............................................................................................4 

Figure 4. Efflux density and velocity histories. ..............................................................................4 

Figure 5. Efflux pressure and temperature histories. ......................................................................5 

Figure 6. Efflux species histories....................................................................................................5 

Figure 7. Schematic of gas dynamic features in a highly underexpanded jet...............................10 

Figure 8. Computed Mach number contours. ...............................................................................12 

Figure 9. Measured and computed pressure at the probe tip. .......................................................13 

Figure 10. Computational results displayed in eight contour variables for 0.13 ms. ...................14 

Figure 11. Computational results displayed in eight contour variables for 0.22 ms. ...................15 

List of Tables 

Table 1. Species concentrations (moles/m3) at 0.22 ms and four locations along the 

centerline....................................................................................................................................6 
v

Acknowledgments 

The Plasma-Propellant Interaction Workunit, headed by Dr. Richard Beyer, at the U.S. Army 

Research Laboratory (ARL) funded this project. The Department of Defense Major Shared 

Resources Centers supplied supercomputer time at ARL and the Naval Oceanographic Office. 
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction 

Future military engagements will require weapons systems exhibiting longer range and greater 

accuracy. One of the technologies under investigation to achieve these goals is the 

electrothermal-chemical (ETC) propulsion concept, shown schematically in figure 1. In the ETC 

gun, energy which is stored either in batteries or in a rotating device is converted on demand into 

an electrically generated plasma (resulting from the ablation of polyethylene material in a 

capillary), which is then injected into the chamber in a howitzer or gun. This plasma energy is 

used to ignite the chemical propulsion charge (e.g., solid propellant) as well as enhance gun 

performance by taking advantage of a number of unique plasma characteristics. For example, a 

low-density plasma jet can more efficiently ignite charges of high loading density (HLD), can 

control propellant mass-generation rates (1), can reduce propellant charge temperature sensitivity 

(i.e., the variation of gun performance with changing ambient temperature [2, 3]) and can shorten 

ignition delay (i.e., the time interval between firing of the igniter and ignition of the propellant 

[4]). Plasma igniters also eliminate the conventional chemical igniter and can thus enhance the 

safety aspects of the overall gun propulsion system. All of these observations have a significant 

effect on the ballistics of ETC gun systems and can lead to a useful improvement in gun 

performance and accuracy. 

Figure 1. ETC gun concept. 

Research has been carried out on a number of aspects of plasma and plasma/propellant 

interactions (5, 6). Because the plasma is at a temperature (typically >10,000 K) that is 

considerably higher than conventional chemical igniters (3000 K), the radiation properties of the 

plasma have also been considered. The high plasma temperature leads to radiation effects nearly 

100 times greater than that of chemical igniters (i.e., a T4

 effect) (5). Such radiation could lead 

to significantly different temperature profiles within the propellant, causing changes in 

combustion rates. Another significant characteristic of the plasma is a much lower density than 

P lasm a

C artridge

E n erg etic

W o rkin g Flu id

(P rop ellan t)

B arrel

C om bustion C ham ber

P rojectile

S w itch

P u lse Fo rm in g

N etw ork (P FN )

In term ed iate

S torage P rim e S to rage
2

the gases generated by a chemical igniter. The lower density plasma impacts the convective 

heat transfer to the propellant, as the plasma moves through the grains, as well as the velocity 

and mode of flamespreading within a propellant bed. It has been suggested that energy transport 

by convection may be as important as radiation transport in plasma-propellant interaction (PPI) 

(7, 8). 

The effects previously described can lead to significant changes in ballistic behavior and useful 

improvements in gun performance once an understanding of the underlying physical mechanisms 

is achieved. To this end, the U.S. Army Research Laboratory (ARL) has begun a comprehensive 

study on the interaction of the plasma efflux from a ETC igniter with solid propellant grains. 

The goal of this work is to elucidate the relevant physical, mechanical, and chemical mechanisms 

that underlie the observed ballistic effects. Various aspects of the experimental program for PPI 

are described elsewhere (9). The first phase of the modeling effort in support of this PPI project 

involves a time-accurate computational fluid dynamics (CFD) code that has been written to 

include high-temperature thermodynamics, variable specific heats and transport properties 

(viscosity and thermal conductivity), and finite-rate (nonequilibrium) chemical kinetics (the 

mechanism is described in reference [10]). A separate capillary model described by McQuaid 

and Nusca (11, 12) supplies boundary conditions for the CFD code in terms of the physical and 

chemical properties of the plasma capillary efflux. Validation of the capillary model and the 

CFD code, including coupled chemistry, uses a series of experiments wherein a plasma jet is 

generated from a plasma cartridge; pressures in the resulting unsteady flowfield are measured 

using a probe. 

2. Description of Open-Air Plasma Jet Experiment 

References (8) and (13) provide a full description of the experiment with a summary given 

herein. The general view of the plasma generator is shown in figure 2. The plasma capillary 

consists of standard polyethylene liner with dimensions of 102 mm in length and 6.35 mm in 

diameter. The nozzle consists of a circular tube of 2.9 cm in length and 1.3 cm in diameter that 

is directly adjacent to the end of the plasma capillary followed by another circular tube of 1.9 cm 

in length and 3.2 cm in diameter. As a result, the plasma efflux, generated by the capillary, is 

expanded through a step-configuration nozzle before emerging into the open air. A series of 

probes is positioned in the path of the plasma efflux; typically, a single-pressure probe is used 

(figure 2), but ongoing tests involve heat flux probes as well (13). To protect these probes, the 

plasma capillary is mounted behind a steel plate. The surface of this plate forms the upstream 

boundary for the numerical simulation, with a hole in the plate forming the inlet to the 

computational domain. 

The pressure probe is placed 15 cm away from the surface of the plate and aligned with the 

centerline of the cartridge. The data acquisition system was chosen for maximum frequency 

response (>1 MHz). The pressure gage was rated at 1.5 MHz and 0.2 μs. Care was exercised 
3

Figure 2. Schematic of plasma generator and pressure probe also showing computational domain. 

in shielding the gage from direct interaction with the plasma as were the cables and amplifiers 

(strong evidence of charged particle impact on the unshielded gage was found [8]). Even so, 

post-firing examination of the pressure gage indicated significant amounts of particulate in the 

plasma effluent (the plasma is generated by ablation) that contributed to noticeable variability in 

pressure histories from shot to shot. 

The electrical power supplied to the plasma generator used a five-stage, pulse-forming network 

(PFN) that could store up to 130 kJ (see reference [5]). The five stages could be charged to 

different voltages and fired at different times to obtain the desired power-pulse shape. The 

electrical data were recorded using a Rogowski coil for load current and a voltage divider and 

current transformer for load voltage. These data were used to generate load current, voltage, 

power, energy, and impedance as a function of time. Figure 3 shows the power and amplitude 

variation for a typical experiment. Given the amplitude/time and the physical characteristics of 

the capillary, the capillary model (11, 12) generates the range of density, velocity, pressure, 

temperature, and species distributions shown in figures 4–6. 

Note that figure 3 shows a pulse forming network (PFN) pulse width of ~0.45 ms, but 

figures 4–6 show efflux histories spanning ~0.275 ms. The current/time data up to 0.027 ms 

and between 0.40 and 0.45 ms were ignored by the capillary model; the relatively small current 

levels during these times caused a divergence in the capillary model because a relatively small 

amount of plasma was being generated. As a result, the efflux histories were shifted to 

zero-time, and the CFD computation was started with efflux properties that characterized an 

abrupt rather than a more gradual start to the efflux; the computed time-of-arrival of the jet on 

the pressure probe will be shorter than measured (see section 5). A more amenable resolution to 

this problem is being formulated for future simulations. Figure 6 shows that there are five 

prominent species in the plasma efflux among a total of 31 species that were considered in the 

capillary model (11, 12) and 38 species in the CFD simulations (7 species were added for 

reaction with air). For a complete list of species, see table 1. 

SWITCH

 PLASMA

PFN CARTRIDGE

CAPILLARY LINER

POLYETHYLENE

EXPLODING WIRE

ANODE CATHODE

CARTRIDGE

NOZZLE

PRESSURE PROBE

PROTECTIVE PLATES

DATA

COLLECTION

COMPUTATIONAL DOMAIN
4

Figure 3. Current and power histories. 

Figure 4. Efflux density and velocity histories. 
5

Figure 5. Efflux pressure and temperature histories. 

Figure 6. Efflux species histories. 
6

Table 1. Species concentrations (moles/m3) at 0.22 ms and four locations along the centerline. 

Species Inlet X = 1 cm X = 9 cm X = 15 cm 

(Probe Tip) 

Electrons 0.0022 0.0026 0.0021 0.0435 

C 0.0061 0.0048 0.0038 0a

C+ 0.0017 0.0019 0.0015 0.0327 

C++ 0a 0a 0a 0a 

C– 1.07E-06 1.09E-06 8.53E-07 2.38E-07 

CH 3.32E-06 2.38E-06 1.19E-06 6.66E-07 

CH+ 1.90E-06 1.99E-06 1.55E-06 4.27E-07 

CN 9.48E-11 5.29E-11 4.32E-11 1.41E-11 

CN+ 9.16E-12 8.63E-12 6.79E-12 1.99E-12 

CO 2.58E-10 3.41E-10 5.42E-10 0.0017 

CO+ 3.27E-11 2.59E-06 2.07E-06 0a 

C2 2.12E-06 1.27E-06 1.03E-06 4.05E-07 

C2+ 9.12E-07 8.16E-07 6.45E-07 1.95E-07 

H 0.0152 0.0126 0.0099 0.0462 

H+ 5.40E-04 7.61E-04 5.80E-04 0.0429 

H- 2.40E-06 2.78E-06 2.15E-06 5.57E-07 

H2 4.28E-06 3.52E-06 2.82E-06 9.22E-05 

H2+ 5.43E-07 7.46E-07 5.71E-07 1.34E-07 

N 9.25E-08 7.60E-08 6.03E-08 7.17E-08 

N+ 5.34E-09 7.62E-09 5.81E-09 1.33E-09 

NH 4.98E-11 3.78E-11 3.02E-11 4.45E-12 

NH+ 1.14E-11 1.44E-11 1.11E-11 2.72E-12 

NO 0a 1.03E-16 5.80E-17 3.92E-12 

NO+ 3.31E-16 2.68E-11 2.14E-11 5.17E-08 

N2 0a 1.95E-18 3.82E-12 0.0061 

O 1.33E-07 2.70E-06 2.15E-06 0.0767 

O+ 4.32E-09 6.24E-09 5.02E-09 0.0014 

OH 6.80E-11 1.10E-10 1.09E-10 2.02E-04 

OH+ 1.33E-11 1.67E-11 1.28E-11 3.17E-12 

O2 0a 4.98E-16 6.26E-10 0a 

O2+ 2.72E-17 8.96E-13 7.39E-10 0a 

H2O 0a 1.08E-15 1.06E-15 1.46E-08 

HO2 0a 0a 0a 0a 

H2O2 0a 0a 0a 0a 

HNO2 0a 0a 0a 0a 

NO2 0a 0a 0a 0a 

CO2 0a 2.72E-21 1.21E-20 1.35E-08 

O3 0a 0a 0a 0a 

Density (mol/m3) 0.0274 0.0194 0.0153 0.0894 

Pressure (atm) 31.7 21.1 22.7 62.8 

Temp (K) 13950 13560 16770 8310 

a

Quantity is <1.0 × 10–50. 
7

3. Previous Modeling Efforts 

ARL, in cooperation with the Naval Research Laboratory (NRL), had conducted a computational 

study of open-air plasma discharges from 1997 to 1998 (14–16). This computational study was 

based on the NRL CFD code FAST3D (17) and sponsored by the Department of Defense 

Common High-Performance Computing Software Support Initiative program. The ARL openair plasma firing was chosen as a test case for the FAST3D CFD code because the plasma jet is 

of a very high velocity and temperature, but of a very low density. The plasma jet was assumed 

to be an ideal neutral single-component gas with density, temperature, ratio of specific heats (γ), 

and velocity characteristics identical to the plasma discharge. The multicomponent nature of the 

plasma, consisting of various neutral species, ions, electrons, and its chemical reactivity was not 

considered in those studies. The augmentation of plasma-air mixing, caused by viscosity and 

turbulence, was also excluded in these studies. The time-dependent gas properties, along with jet 

velocity and γ, were determined using a plasma capillary code developed at ARL by Powell and 

Zielinski (18). Overall, these CFD simulations captured the major features of the plasma jet as 

photographed by White et al. (5). Alternating bright-dark structures in the photos were identified 

as the shock structures in the jet. A precursor shock caused by the high-velocity/low-density 

plasma effluent (a feature not easily observed or photographed) was captured. Comparisons 

between computed and measured pressures in the jet were encouraging but pointed to the need 

for a variable γ multicomponent-reacting flow model. 

4. Multispecies Reacting Flow CFD Code 

The high-temperature, nonideal chemically reacting gas flowfield within the capillary efflux jet 

is numerically simulated using CFD. The NSRG2 code, written by Nusca (19–21), solves the 

two-dimensional (2-D)/axisymmetric, unsteady real-gas Navier-Stokes equations, including 

submodels that represent finite-rate (nonequilibrium) chemical reactions, multispecies diffusion, 

as well as variable specific heats, viscosity, and thermal conductivity. These partial differential 

equations are cast in conservation form and converted to algebraic equations using a finitevolume formulation. Solution takes place on a mesh of nodes distributed in a zonal fashion 

throughout the flowfield such that sharp geometric corners and other details are accurately 

represented. The conservation law form of the equations ensures that the end states of regions of 

discontinuity (e.g., shocks) are physically correct even when smeared over a few computational 

cells. The Navier-Stokes equations for 2-D/axisymmetric (x, y coordinates), reacting (N species), 

and unsteady (time, t) flow are written in nondimensional form (19). The dependent variables 

are density (ρ), velocity (V and components u, v), energy (e), and species mass fraction (ci). 

Pressure and temperature are p and T, whereas L is a characteristic lengthscale for the flowfield. 
8

+ + + H = 0 , y

G

x

F

t

U

∂

∂

∂

∂

∂

∂ (1) 

where 

U y , uy , vy , ey , c y , , c y = { , 1 ......... N } α αααα α ρρ ρ ρ ρ ρ

2

1 11 1

( + σ ) 

( + τ ) 

( + σ + τ + )

( – Λ ( ) – Γ ( ) ) 

.

.

.

( – Λ ( ) – Γ ( ) ) 

xx

xy

xx xy x

x x

N N Nx N x

ρ u y

ρ uy

ρ u v y

ρ u e u v q y

F ρ u c c ln T y

ρ u c c ln T y

 

 

=    

 

α

α

α

α

α

α

 , 

2

1 11 1

( + τ ) 

( + σ ) 

( + σ + τ + )

( – Λ ( ) – Γ ( ) ) 

.

.

.

( – Λ ( ) – Γ ( ) ) 

yx

yy

yy xy y

y y

N N Ny N y

ρ v y

ρ vu y

ρ vy

ρ v e v u q y

G ρ v c c lnT y

ρ v c c ln T y

                =  

               

α

α

α

α

α

α

.

1

.

0

0

0

 ,

N

w

.

.

.

w

H

+

       σ        = −                − 

α

2 2 ( ) ( ) σ = L =

3 xx T

yu yv u Le Pr y p + – , k , e , y Re Re x RePr Sc x y

  ∂ ∂ ∂   + Λ= Γ= Λ

∂ ∂ ∂  

α α

α

α

μ μμ ,

2 2 ( ) ( ) σ = =

3

p

yy

yu yv v VL c

y p + – , Sc Re , Pr , y Re Re y D K x y

  ∂ ∂ ∂   + = = ∂ ∂ ∂  

α α

α

α

μ μ μρ μ , ρ μ

( ) ( ) 2 2 2–

σ = =

3 + xy yx

yu yv v V u v

p + – , , E , y Re Re y y Re h x y y x

  ∂ ∂  ∂ ∂    + Γ =Γ = = +   ∂ ∂  ∂ ∂   

α α

α αα

μ μμ ,

1 1

– L and L

N N

i i

x iy i

i i

c c –K q = – eh , q – eh . RePrE x RePr x RePrE y RePr y = =

∂ ∂ ∂ ∂ = ∂∂ ∂∂ ∑ ∑ ΚΤ μ Τ μ

The diffusion coefficient, D, is understood to be the multicomponent coefficient, Dim (specie i

into the mixture), which is related to the binary diffusion coefficient, Dij (specie i diffusing into 

specie j), 

3/2

1/2 2

1 – 0.00266 2 , , , Ω 1 1

i

ij ij ij

j ij ij ij D i j j

X T DD M

X /D p M /M /M == = ∑ σ +

 (2) 

where Xi is the mole fraction and Mi is the molecular weight of species i, ΩD is the collision 

integral and σij is the collision diameter (available in the literature). The thermal diffusion ratio, 

kT, is assumed to be 1.0. 

The relations for species enthalpy, mixture energy per unit volume, and pressure are given by the 

following state equations. It should be noted here that appropriate state equations for a 
9

high-temperature plasma, which are somewhat more complex than these, are at the same time not 

widely available in the literature. The present choice of these relations will affect the results. 

2 2

1 1

( ) , ,, 1 2

N N o i

i i i i fi

i i i

p uv c h e R T e c H p RT M

ρ ρ ρ

γ = =

+ =+ = + + ∆ = − ∑ ∑ (3) 

where ∆Hi

o

 is the formation heat for species i. The ratio of specific heats is γ = cp /cv , where cp

and cv are the mixture specific heats. The species values are computed using polynomials with 

coefficients α1–α7 (22). The specific gas constant is Ri (the universal constant is R), and the 

heats can be related using = – CCR vi pi i . 

1 1

 , 

N N

i

p pi i i

i i p

c c cc h = = T

  ∂

= +     ∂ ∑ ∑ 

and 

( ) 2 1 234

1 2 34 5 6 7 . pi i c R aT aT a aT aT aT aT − − = + ++ + + + (4) 

Likewise, viscosity and thermal conductivity coefficients are given by polynomials with 

coefficients A, B, C, and D given in reference (22) (coefficients for each specie are different for 

each variable and each specie). The mixture values of viscosity and thermal conductivity are 

computed using empirical mixture rules discussed in reference (19). 

() () () () 2 2 , and . ii ii

i ii i

BC BC ln A ln T D ln A ln T D

TT TT μ= + + + κ= + + + (5) 

Chemical reactions can be expressed in a general reaction equation. Xi represents the symbol for 

specie i, and ν is the stoichiometric coefficient for species i (primed for reactant and 

double-primed for product) in the reactions (10). The chemical source terms that appear in the 

H array for equation 1 (i.e., w) are computed using a general reaction rate equation. The reaction 

rates for each reaction, k (“f” for forward and “b” for backward), are usually expressed in 

Arrhenius form (see reference [19] for details) but often include corrections for high-pressure 

effects (see reference [10] for reaction rate data). The backward rate coefficients are computed 

from the forward values and the equilibrium constant for each reaction (19). 

( ) ' ' ' ' . ' ' ' ' ' '

1 1

 , and – – . f i i

b

N N N N

k

i i ik i i ii i f i b i

i i i i

X X w M kC kC ν ν

= =

 

↔ =     ∑ ∑ ν ν νν ∏ ∏ (6) 

The Navier-Stokes equations (equation 1) are written in integral form and then re-expressed in a 

semi-discrete fashion using a finite-volume discretization technique. The numerical 

computations proceed by solving the semi-discrete equation on each computational cell using 

central and upwind numerical differences along with flux-limiting. Once properly discretized, 

the resulting set of algebraic equations is solved in a coupled manner in time, using an explicit 

time-accurate method. The numerical time-step is computed using the CFL condition. A 

separate chemical time-step is computed as well. The final time-step is based on the smallest of 

these. Nusca (19–21) offers a complete treatment of the numerical scheme. 
10

5. Results and Discussion 

The computational domain chosen to be used to simulate the experiment and sketched in figure 2 

extends from the protective plate to a small distance along the pressure probe (0.18-m total 

length) and from the centerline of the capillary (and probe) to a small radial distance 

(0.08-m total radius). This region was discretized using 277 axial grid cells and 160 radial grid 

cells, distributed in essentially an even spacing throughout. The boundary conditions for this 

region are symmetry on the axis (Y = 0), outflow at X = 0.18 m and Y = 0.08 m, 

no-slip/no-penetration on the plate surface (X = 0, 0.0159 < Y < 0.08 m) and the probe surface, 

and specified inflow at the capillary exit (X = 0, 0 < Y < 0.0159 m). The inflow conditions 

follow from those displayed in figures 4–6 (note: see table 1 for a complete list of species 

specified at the inlet). Initially, the entire flowfield is filled with air (0.8 mole fraction of N2 and 

0.2 mole fraction of O2). 

To aid in the interpretation of computational results for the plasma jet, figure 7 shows a 

schematic of the expected gas dynamic features as have been observed in highly underexpanded 

supersonic jets (23, 24). The efflux of plasma from the inlet generates a weak precursor shock 

(A) that expands spherically. Behind this shock is air; the plasma is entirely contained by this 

shock and is separated from the air by an irregularly shaped contact surface (B) across which 

pressure and velocity are preserved, but entropy changes discontinuously. Expansion waves (C), 

generated at the inlet, travel to the precursor shock (A), are reflected as weak compression 

waves, and coalesce into a strong oblique shock or barrel shock (D) within the plasma jet. This 

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

barrel shock (D), it’s reflection (F), and a normal shock (G) or Mach disk. Whereas the 

precursor shock (A) is relatively weak and diffuse, producing a mildly supersonic flow, the 

barrel shock (D) and Mach disk (G) are strong shocks that enclose a fully supersonic flow 

region. 

Figure 7. Schematic of gas dynamic features in a highly underexpanded jet.

CENTERLINE

A

B

CAPILLARY

AIR

PLASMA

PLASMA

E

C

F

D

G
11

Figure 8 shows the time history of the plasma jet from shortly after entrance into open-air 

(0.05 ms) to shortly after impact upon the pressure probe (0.24 ms). Note that the frames in 

figure 8 are not evenly spaced in time but are chosen to highlight the features of figure 7. Mach 

number contours are displayed in gray-scale from 0 (bright white) to 1.6 and above (dark black). 

As the low-density (0.08-kg/m3) plasma efflux enters the open-air, a precursor shock is formed. 

At this time, the jet is moving at ~5600 m/s, which is ~Mach 1.6, based on the local sound speed 

in the mixture (note that the plasma gas is of very low molecular weight, ~4.3). By ~0.20 ms, 

the predominant gas dynamic features in the jet have been established, including the intersection 

of the barrel shock with the Mach disk (X = 0.06 m) and a weak reflected shock. Due to the 

variable viscosity in the flowfield (see equation 5), the precursor shock is more diffuse than the 

normal shock of the Mach disk or the oblique “barrel” shock. Note the subsonic flow region 

between the normal shock and the precursor shock; within this region resides the contact surface. 

The precursor shock reaches the pressure probe at ~0.22 ms. Stagnation of supersonic flow on 

the probe tip causes a normal shock to standoff from the probe. By 0.24 ms, this tip shock is no 

longer required because the flow is subsonic in the probe’s near field. Figure 9 shows the 

measured and computed pressure at the probe tip. As was discussed in relation to figure 3, the 

computed pressure history has been shifted by 0.027 ms. Even so, the computed precursor shock 

arrives at the probe ~0.02 ms early and registers a pressure that is ~30% higher than measured. 

Computed pressure oscillations around the peak are due to the unsteady nature of the normal 

shock at the probe tip. The presence of particulates in the flow stream reported by 

White et al. (8) may account for some of this discrepancy as may the absence of both a true 

plasma equation of state (see equation 3) and radiation energy losses in the computations. At 

this point in time, the computation was halted until further investigations of the source of the 

pressure overprediction was discovered. 

Figures 10 and 11 show computed results for the plasma jet at 0.13 and 0.22 ms, respectively, in 

terms of eight variables. The pressure and temperature have been normalized by one atmosphere 

and 300 K, the values ahead of the precursor shock, respectively. The heat capacity (cp), thermal 

conductivity (κ), and viscosity (μ) have been nondimensionalized using the values for air; 

therefore, ahead of the precursor shock, these variables are 1.0. At 0.13 ms (figure 10), the 

precursor shock is indicated by the sharp pressure gradient at X = 0.09 m from the inlet (the 

spherical shape of this shock is distorted by the plotting scale). The normal shock (Mach disk) at 

X = 0.035 m is clearly visible in the pressure contour map, as is the high-pressure flow from the 

inlet. Behind the precursor shock and in front of the normal shock (i.e., 0.035 < X < 0.09 m), the 

pressure and temperature are quite high, indicating extreme compression of the flow due to these 

two shocks. The plots of heat capacity and thermal conductivity highlight the region of plasma 

(note the piston-like shape with expanded leading edge) in which these variables take on values 

that are much higher than those in ambient air. The plot of viscosity indicates that the plasma 
12

Figure 8. Computed Mach number contours. 
13

Figure 9. Measured and computed pressure at the probe tip. 

itself represents largely laminar flow (i.e., high value of viscosity). The plot of hydrogen (H) 

atom concentration confirms that the plasma consists mainly of H gas (figure 6) and electrons 

(the plot of electron concentration is qualitatively similar to the plot of H). In the high-pressure 

and high-temperature region, the density is also high and causes the largest local concentration of 

H away from the inlet. The formation of OH and CO2 will not take place until sufficient thermal 

and chemical conditions arise in the flowfield, as dictated by the detailed chemical kinetics 

mechanism (the reader is referred to reference [10]). The contour plots of these species indicate 

that such conditions do exist outside the plasma core region (0 < X < 0.055 m, 0 < Y < 0.018 m 

at this time) where mixing with air (i.e., O2 and N2) is sufficient. Space limitations do not permit 

the displaying of all chemical species distributions, but this information is being probed as a

means of characterizing the chemical nature of the plasma efflux. Figure 11 shows the same 

variables plotted for 0.22 ms in time, when the leading edge of the plasma jet (i.e., the precursor) 

has just reached the probe. Flow stagnation on the probe tip causes local compression, and a 

bow shock is generated on the tip (see pressure plot). Gas temperature (and density) also 

increases near the probe as does the concentration of H. Flow heating, species mixing with air, 

and chemical reactions cause increased concentrations of OH (especially) and CO2; this indicates 

increased levels of chemical reaction in the flowfield. Of course, the probe’s near-field 

properties continually change as subsequent regions of the jet flow impinge upon the tip 

(i.e., after the precursor shock, the contact surface, and the Mach disk containing a region of 

supersonic flow). 
14

Figure 10. Computational results displayed in eight contour variables for 0.13 ms. 
15

Figure 11. Computational results displayed in eight contour variables for 0.22 ms. 
16

After looking at these results, one can suppose that the physical and chemical nature of the 

plasma efflux in the vicinity of the probe is very different from that near the capillary. Gas 

dynamic expansion in open air has caused the generation of various shocks and mixing layers 

that have combined the plasma species with air and have resulted in chemical reactions. Table 1 

lists the species considered in the present model and provides the concentrations for a time of 

0.22 ms (i.e., displayed in figure 11) and at three locations along the centerline of the jet: at the 

inlet (i.e., capillary exit plane), just outside of the inlet, just ahead of the Mach disk, and within 

the precursor shock at the stagnation region on the probe tip. It is interesting to note the 

increased concentrations of various species at the probe tip, especially those species that are not 

predominant at the capillary (CO, NO+, N2, O, O+, OH, H2O, CO2), and those abundant in the 

plasma that have collected on the tip (H, H+

, C+, electrons). The C atom, abundant in the plasma 

efflux at the capillary, is absent at the probe tip (possibly combined in CO and CO2). These 

results confirm the supposition. The ultimate goal is to understand how the propellant responds 

to the plasma jet both mechanically (i.e., pressure and thermal loading from the shock system) 

and chemically. This information concerning the pressure, temperature, and chemical conditions 

at the probe tip are necessary starting conditions for subsequent modeling of solid propellant 

combustion in the plasma stream. 

6. Conclusions 

A time-accurate CFD code has been applied to the modeling of the high-temperature, chemically 

reactive plasma efflux from an ETC igniter fired into open air. The CFD code has been linked to 

a plasma capillary model for purposes of specification of the exit conditions of the igniter. The 

major features of this efflux have been resolved by numerical simulation revealing a highly 

underexpanded jet with a strong precursor shock, a barrel shock that reflects at a triple-point, and 

a normal shock or Mach disk. Impact of the jet upon a probe generates an intermittent bow 

shock on the probe tip that is dissipated in the low-velocity flow ahead of the Mach disk and is 

then re-established with the passage of this normal shock. The presence of this shock system has 

important implications for mechanical damage to solid propellant exposed to the plasma efflux. 

Chemical conditions at the probe are quite different from those at the ETC igniter. These 

computer simulations represent the first such detailed modeling of ETC igniter plasma efflux. 
17

7. References 

1. Del Güercio, M. Propellant Burn Rate Modification by Plasma Injection. Proceedings of 

the 34th JANNAF Combustion Subcommittee Meeting, West Palm Beach, FL, 1997; CPIA 

Publication 662, Vol. 1, 35–42. 

2. Perelmutter, L.; Sudai, M.; Goldenberg, C.; Kimhe, D.; Zeevi, Z.; Arie, S.; Melnik, M.; 

Melnik, D. Temperature Compensation by Controlled Ignition Power in SPETC Guns, 

Proceedings of the 16th International Symposium on Ballistics, San Francisco, CA, 1996; 

NDIA, Vol. 1, 145–152. 

3. Dyvik, J. A.; Katulka, G. L. ETC Temperature Compensation; Experimental Results of 

120-mm Test Firings, Proceedings of the 33rd JANNAF Combustion Subcommittee Meeting, 

Monterey, CA, 1996; CPIA Publication 653, Vol. 3, 111–119. 

4. Katulka, G. L.; Dyvik, A. Experimental Results of Electrical Plasma Ignition in 120-mm 

Solid Propellant Tank Gun Firings, Proceedings of the 33rd JANNAF Combustion 

Subcommittee Meeting, Monterey, CA, 1996; CPIA Publication 653, Vol. 3, 103–110. 

5. White, K. J.; Katulka, G. L.; Khuan, T.; Nekula, K. Plasma Characterization for 

Electrothermal-Chemical (ETC) Gun Applications; ARL-TR-1491; U.S. Army Research 

Laboratory: Aberdeen Proving Ground, MD, September 1997. 

6. Perelmutter, L.; Goldenberg, C.; Sudai, M.; Alimi, R.; Furman, M.; Kimhe, D.; 

Appelbaum, G.; Arie, S.; Zeevi, Z.; Melnik, D. Experimental Study of Plasma Propagation 

and Ignition of Solid Propellant in a Gun Chamber, Proceedings of the 16th International 

Symposium on Ballistics, San Francisco, CA, September 1996. 

7. Nusca, M. J.; White, K. J. Plasma Radiative and Convective Interactions With Propellant 

Beds, Proceedings of the 34th JANNAF Combustion Subcommittee Meeting, West Palm 

Beach, FL, 1997; CPIA Publication 662, Vol. 1, 21–42. 

8. White, K. J.; Williams, A. W.; Nusca, M. J. Plasma Output and Propellant Radiation 

Absorption Characteristics, Proceedings of the 35th JANNAF Combustion Subcommittee 

Meeting, Tuscon, AZ, 1998; CPIA Publication 680, Vol. 1, 237–246. 

9. Kaste, P. J.; Birk, A.; Del Güercio, M. A.; Lieb, R.; Kinkennon, A. Surface Phenomena of 

Plasma-Treated Propellant Samples, Proceedings of the 36th JANNAF Combustion 

Subcommittee Meeting, Cocoa Beach, FL, 1999; CPIA Publication 691, Vol. 2, 77–98. 

10. Anderson, W. R.; Schroeder, M. A. Chemical Mechanism for ETC Plasma Interaction With 

Air, Proceedings of the 36th JANNAF Combustion Subcommittee Meeting, Cocoa Beach, 

FL, 1999; CPIA Publication 691, Vol. 2, 43–54. 
18

11. McQuaid, M. J.; Nusca, M. J. Calculating the Chemical Compositions of Plasmas Generated 

by an Ablating-Capillary Arc Ignition System, Proceedings of the 36th JANNAF Combustion 

Subcommittee Meeting, Cocoa Beach, FL, 1999; CPIA Publication 691. 

12. McQuaid, M. J.; Nusca, M. J. Calculating the Chemical Compositions of Plasmas 

Generated by an Ablating-Capillary Arc Ignition System; ARL-TR-2046; U.S. Army 

Research Laboratory: Aberdeen Proving Ground, MD, 1999. 

13. Williams, A. W.; White, J. Plasma-Propellant Interaction Studies: Measurements of 

In-Depth Propellant Heating by Plasma Radiation; Investigation of Possible 

Plasma-Induced Propellant Erosion, Proceedings of the 36th JANNAF Combustion 

Subcommittee Meeting, Cocoa Beach, FL, 1999; CPIA Publication 691, Vol. 2, 67–76. 

14. Nusca, M. J.; White, K. J.; Young, T. R.; Landsberg, A. M. Computational Simulation and 

Experimental Visualization of an Open-Air Plasma Discharge, Proceedings of the 34th 

JANNAF Combustion Subcommittee Meeting, West Palm Beach, FL, 1997; CPIA 

Publication 662, Vol. 1, 43–56. 

15. Nusca, M. J.; White, K. J.; Landsberg, A. M.; Lind, C. A.; Young, T. R. Computational 

Simulations of ETC Igniters and Plasma Discharge Experiments, Proceedings of the 35th 

JANNAF Combustion Subcommittee Meeting, Tuscon, AZ, 1998; CPIA Publication 680, 

Vol. 1, 219–227. 

16. Nusca, M. J.; White, K. J.; Williams, A. W.; Landsberg, A. M.; Young, T. R.; Lind, C. A. 

Computational and Experimental Investigations of Open-Air Plasma Discharges, 37th AIAA 

Aerospace Sciences Meeting, Reno, NV, January 1999; AIAA Paper 99-0865. 

17. Boris, J. P.; Landsberg, A. M.; Oran, E. S.; Gardner, J. H. LCPFCT – A Flux-Corrected 

Transport Algorithm for Solving Generalized Continuity Equations; NRL MR 93-7192; 

Naval Research Laboratory: Washington, DC, 1993. 

18. Powell, J.; Zielinski, A. Theory and Experiment for an Ablating-Capillary Discharge and 

Application to Electrothermal Chemical Guns; BRL-TR-3355; U.S. Army Ballistic Research 

Laboratory: Aberdeen Proving Ground, MD, June 1992. 

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

Nonequilibrium Chemically Reacting Flows. Computers and Fluids 1998, 27 (2), 217–238. 

20. Nusca, M. J. Numerial Simulation of the Ram Accelerator Using a New Chemical Kinetics 

Mechanism. Journal of Propulsion and Power 2002, 18 (1), 44–52. 

21. Nusca, M. J.; Dinavahi, S. P. G.; Soni, B. Grid Adaptation Studies for Reactive Flow 

Modeling of Propulsion Systems, American Institute of Aeronautics and Astronautics, 37th 

AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; AIAA Paper 99-0970. 
19

22. McBride, B. J.; Gordon, S. Computer Program for Calculation of Complex Chemical 

Equilibrium Compositions and Applications II. Users Manual and Program Description; 

NASA RP 1311; NASA: Cincinnati, OH, June 1996. 

23. Wilson, D. E.; Raja, L. L.; Petviashvili, N. Theoretical Analysis of the External Pulsed 

Propellant and Plasma Jets, American Institute of Aeronautics and Astronautics, 36th AIAA 

Aerospace Sciences Meeting, Reno, NV, January 1998; AIAA Paper 98-1000. 

24. Schmidt, E. M.; Shear, D. D. Optical Measurements of Muzzle Blast. AIAA Journal 1975, 

13 (8), 1086–1091. 
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