st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Graphical Analysis of LSD Wave Propagating Through a Diatomic Gas Using
Thermal Non-equilibrium CFD Results
H. Shiraishi1
1
Daido University, Nagoya, Japan
Abstract: Laser-supported Detonation (LSD), one type of Laser-supported Plasma (LSP), is
considered as one of the most important phenomena for laser propulsion systems; it can generate high pressure and high temperature, which are essential for propulsion, by absorbing a
laser beam. In this study, p-v graphical analyses using the thermal-non-equilibrium and
one-dimensional numerical results of LSD waves are performed for searching the detailed
LSD structure propagating through a diatomic gas ,which are abundant in the atmosphere.
Keywords: Numerical Analysis, Laser-supported Plasma (LSP), p-v Diagram
Nomenclature
D
propagation velocity of detonation wave
[m/s]
I
laser intensity [W/m3]
I0
incident laser intensity [W/m3]
h
enthalpy per unit mass [J/kg]
p
pressure [Pa]
p0
initial pressure of cold gas [Pa]
t
laser irradiation time [s]
T
temperature [K]
u
velocity in x direction [m/s]
x
x direction

heat capacity ratio
wavelength of incident laser beam


density [kg/m3]
0
initial density of cold gas [kg/m3]
Subscripts
e
0
case of LSC, the shock front propagates almost adiabatically because the heat transfer from the laser
absorption zone becomes much weaker. Therefore the
transition from LSD to LSC is a very important
theme for a laser propulsion system.
For studying 1-dimensional (1-D) steady propagation of
LSD, ZND (Zel’dovich-von Neumann-Doering) model,
the classic 1-D distribution, is very important.
Figure 1 and 2 show ZND model and p-v diagram of
chemical detonation, non-dimensionalized by initial state,
respectively. The point that both longitudinal axes indicate pressure makes easy to compare the two diagrams.
electron
initial cold gas
1. Introduction
A beam (laser or microwave) propulsion system is one
of the most promising next generation space propulsion
systems. Laser-supported plasma (LSP) is essential for
this system, because the laser energy is mainly absorbed
by hot plasma and then converted to the kinetic energy
that is necessary for propulsion. In this study, we investigate the use of laser supported detonation (LSD), a type
of laser supported plasma (LSP), in a repetitively pulsed
(RP) type laser propulsion system. LSD is also categorized as a type of hypersonic reacting flow, where
exothermicity is supplied by laser absorption and not by
chemical reaction. With the decrease in irradiative
laser beam by LSD expanding, the detonation can be
weaker and finally transform to LSC wave (Laser-supported Combustion- wave), in which the laser
absorption zone detaches from the shock front. In the
Fig. 1.
ZND Mmodel for Cchemical Detonation.
Fig. 2. p-v Diagram of Chemical Detonation.
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Fig. 3. Control Volume for Conservation Laws.
In the diagram, three characteristic lines: Rayleigh,
Poisson and Hugoniot curves exist. These lines derive
from the Rankine-Hugoniot relation, which is composed
by the conservation laws of mass, kinetic momentum and
energy. The coordinate system in the conservation lows is
shown in Fig.3.
The difference between Poisson and Hugoniot lines is
in the heat release value q[J/m3]. The Hugoniot line is
calculated as follows:
In the Poisson line, where q is equal to zero, therefore
Poisson line indicates no-heat release case. Therefore von
Nuemann state indicates the ignition delay where is no
heat release by combustion as shown in Fig.1.
As a practical case, Wang et al. [5] simulated LSD
propagating in the inner geometry of a laser propulsion
system, for example. Though some simulations for laser
propulsions are studied, there had been no case which
applies a detailed processes, such as multi-charged model
[1], as far as I know.
The objective of this study is to clarify the LSD propagation structure by applying p-v diagram to the simulation
results. Especially, to evaluate the difference between the
true distribution of LSD and the hypothetical ZND model
shown in Fig. 4. , is important.
2. Numerical Model and Assumptions
2. 1. Analysis model
Figure 5 shows the analysis model for the
1-dimensional study. The CO2 gasdynamic laser beam ( 
= 10.6μm) passes from the right to the left, and the LSD
wave propagates through hydrogen gas at room temperature (T0 = 300K). In order to simulate the laser-supported
plasma, a hot spot in which hot electrons are seeded, is set
up to imitate the initial plasma. This hot spot model imitates the hot electrons, which are generated on a metal
target by dielectric breakdown in an experiment [6]. In
this study, the hot spot is placed at the center at x = 2 mm.
The hot electron temperature is 30,000 K and the size of
the hot spot is 2 mm (200 points  0.01 mm). Only 1%
seeding rate is applied because the number of seeded
electrons has little effect on the LSD propagation results;
however, a high seeding rate is not good for the simulations.
Fig. 4. Hypothetical ZND Model for LSD.
Figure 4 shows the hypothetical ZND model for LSD.
Though the frame zone is displaced by the laser absorption zone, the ionization delay is not clarified because the
delay is remarkable only near the threshold condition in
the conclusion of the previous work [1].
For simulating LSD propagation, 1-dimensional (1-D)
steady and unsteady analyses [2] were performed at first,
using a CO2 gasdynamic laser into argon gas, where the
most important laser absorption mechanism for LSD
propagation is Inverse Bremsstrahlung: The laser energy
is transformed into the kinetic energy of free electrons by
photon absorption during collisions of electrons with ions
or neutral particles, which is re-distributed among heavy
particles through collisions. As a numerical method, TVD
scheme, which is taken into account of real gas effects, is
applied. Though Quasi-1-dimenmsional analyses [3] were
also performed, the dimension should be extended to axisymmetric 2-D model [4] for realistic cases.
Fig.5. One-dimensional Analysis Model.
2. 2. Assumptions
The assumptions for this analysis are the same as the
previous work [1] except for the propellant gas. They are
as follows:
(1) The propellant gas is always electrically neutral.
(2) Chemical reaction and laser absorption are considered.
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
The chemical reactions considered in this model are as
follows:
1500
1) H 2  H 2  H 2  2H
Numerical Result
Poisson
2) H 2  H　　2H  H
(3)
The
thermal
non
equilibrium
model
is
a
p/p0
1000
3) H  e  H   e  e
500
two-temperature model. The electron temperature related
to the electron-electronic excitation mode is separated
0
from the heavy particle temperature related to the other
modes.
(4)Transportation properties are considered.
2. 3. CFD method for graphical analyses
In this study, CFD results are derived from
one-dimensional Navier-Stokes solver using the
Harten-Yee non-MUSCL modified flux-type TVD scheme,
where the radiative energy transfer terms (Bremsstrahlung
and Inverse Bremsstrahlung) are treated implicitly [7].
2. 4. Laser absorption model
In the presence of absorption, the local radiation intensity I(x, t) is governed by the following equation:
dI ( x, t )
 I ( x, t )  ( K ea  K ei )
dx
(7)
0.4
0.6
v/v0
(a) I0 = 60MW/cm2
1500
0.8
Numerical Result
Poisson
1000
p/p0
With respect to the effective diffusion coefficient, the
ambipolar diffusion is also considered.
0.2
500
0
0.2
0.4
0.6
v/v0
0.8
(b) I0 = 55MW/cm2
Fig. 7. p-v Diagram in LSD and LSC-LSD threshold.
3. Results and Discussion
3. 1. Initial conditions
The physical conditions for analyses are shown in Table 1.
Table 1. Initial Conditions for Analyses.
Laser beam intensity
Pressure of cool gas
I0 = 50 - 65 MW/cm２
0.25atm
3. 2 Evaluation the difference between the LSD and
LSC-LSD threshold
Figures 7 shows the p-v diagrams in the case of (a) I0 =
5.5MW/cm2 , p0 = 0.2atm and (b) I0 = 4.9MW/cm2, p0 =
0.2atm. Here, we would like to emphasize again that the
main object of this study is to evaluate the LSD structure
by applying the simulation results, not simulation itself.
In the case (a), the line from the numerical result gets into
touch with the Poisson line except for the initial state.
According to the p-v diagram of Fig. 2, this resembles the
von Neuman state in the chemical detonation. This indicates the LSD propagation resemble the Hypothetical
ZND Model for LSD in Fig. 4. On the other hand, the
diagram of the case (b) intersects the Poisson line. As the
laser absorption, which corresponds to the heat release in
the chemical detonation, makes the line upper right, the
energy loss in the case (b) excesses the laser absorption at
the shock front. This energy loss is derived from dissociation and ionization. Therefore LSC-LSD threshold
progagation will not be sustained in the weaker laser
power.
4. Conclusions
In order to studying the transition structure from LSD
to LSC propagation, p-v diagraming from l-dimensional
simulation is performed by applying the multiply-charged
ionization model. The conclusions are as follows:
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
(i) The p-v diagraming makes clarify the structure of
laser absorption because the same discussion of the heat
release as in the chemical detonation, which is induced by
the Rankine-Hugoniot relation, is effective.
(ii) The ionization delay length exposes in the typical
LSD threshold in the diatomic gas. Therefore the LSD
structure resembles the hypothetical ZND model for LSD,
which is assimilated by that for chemical detonation, in
the normal LSD propagation.
(iii) In the LSC-LSD threshold, p-v diagram intersects
the Poisson line. This differs from in the typical LSD case
and indicates the energy loss derived from dissociation
and ionization excesses the laser absorption at the shock
front. Therefore LSC-LSD threshold propagation will not
be sustained in the weaker laser power.
5. References
[1] Shiraishi, H. and Kumagai. Y., Numerical Analysis of
Threshold between Laser-Supported Detonation and
Combustion Wave Using Thermal Non-Equilibrium
and
Multi-Charged
Ionization
Model,
TRANSACTIONS OF THE JAPAN SOCIETY FOR
AERONAUTICAL AND SPACE SCIENCES,
AEROSPACE TECHNOLOGY JAPAN, Vol.10
iste28 (2012), pp.Pb_59-Pb_63.
[2] Shiraishi, H., Fujiwara, T.: Thermal Nonequilibrium
Analysis of 1-Dimensional Laser-supported Detonation Using a 2-Temperature Model, Proceedings of
22nd ISSW, July 18-23, 1999, pp.339-344.
[3] Shiraishi, H.: Fundamental Properties of
Non-equilibrium Laser-Supported Detonation Wave,
Proceedings of 2nd Int. Symp. on Beamed Energy
Propulsion, 2003, pp.68-79.
[4] Shiraishi, H.: Numerical Analysis on Laser-Supported
Plasma for Laser Propulsion Systems, The Journal of
Space Technology and Science,
23 (2007),
pp.20-29.
[5] Wang, T.-S., Chen, Y.-S., Liu, J., Myrabo, L. N., and
Mead, F. B., Jr.,: Advanced Performance Modeling of
Experimental Laser Lightcraft, Journal of Propulsion
and Power, 18 (2002), pp. 1129-1138.
[6] Stuermer, E. and von Allmen, M.: Influence of laser-supported detonation wave on metal drilling with
pulsed CO2 lasers, Journal of Applied Physics, 49
(1978), pp.5648-5654.
[7] Numerical Analysis on Thermal Non-equilibrium and
Multidimensional Laser-Supported Detonation Wave
Propagating
Through
a
Diatomic
Gas,
TRANSACTIONS OF THE JAPAN SOCIETY FOR
AERONAUTICAL AND SPACE SCIENCES,
SPACE TECHNOLOGY JAPAN, Vol. 7 (2009) ,
ists26 (ISTS Special Issue: Selected papers from the
26th International Symposium on Space Technology
and Science), Pb_141-Pb_146, 2009.