Monte Carlo simulation of nonequilibrium flow in a low-power
hydrogen arcjet
Iain D. Boyd
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
͑Received 17 September 1996; accepted 9 June 1997͒
A particle-based Monte Carlo numerical method is developed for computation of flow in a
low-thrust hydrogen arcjet. The method employs the direct simulation Monte Carlo technique to
compute the nonequilibrium fluid mechanics and thermochemical relaxation. Simulation of plasma
effects is included at a simple level that ensures charge neutrality. A new model is developed to
include Ohmic heating in the simulation. Results are presented for a flow condition that has been
studied experimentally with a number of different diagnostic techniques. A strong degree of thermal
nonequilibrium is found in the flow. It is demonstrated that Ohmic heating is important, and that the
Monte Carlo model captures the important physics very well. The predicted results are in very good
agreement with most of the experimental data. © 1997 American Institute of Physics.
͓S1070-6631͑97͒01510-9͔
I. INTRODUCTION
Arcjets operated at a power level of about 1 kW are an
attractive candidate for use as electric propulsion devices on
spacecraft. They offer substantial increases in specific im-
pulse compared with chemical rockets and resistojets. Unfor-
tunately, the performance of arcjets remains poor with pro-
pulsion efficiencies in the range of 30 to 50%. There is a
need for accurate numerical simulation of the flows gener-
ated by these devices both for improving their performance,
and for analysis of potential spacecraft interaction effects
such as contamination. There are many coupled physical
phenomena at work in an arcjet that makes numerical simu-
lation difficult. Nonequilibrium kinetic processes include ro-
tational and vibrational relaxation, and several chemical
mechanisms including dissociation, recombination, and ion-
ization. In addition plasma effects are important.
A hydrazine arcjet has been developed and flown in
space. In terms of basic research, however, hydrogen arcjets
have received considerable attention. Several experimental
studies have been conducted on an arcjet designed and fab-
ricated at NASA Lewis Research Center. A schematic dia-
gram of this thruster is shown in Fig. 1. The NASA Lewis
hydrogen arcjet has been used in experimental investigations
to determine its performance
1
and flow fields.
2–9
Of consid-
erable importance is the fact that several different diagnostic
techniques have been applied to these flows yielding mea-
surements that include translational and rotational tempera-
ture, velocity, and number densities of atomic and molecular
hydrogen. These data offer excellent opportunities for de-
tailed calibration of modeling efforts. Several models for de-
scribing flow in arcjets have been developed that are based
on continuum formulations.
10,11
There are two problems with
the continuum approach. First, there is a significant degree of
thermal and chemical nonequilibrium in these flows. Second,
it is very difficult to extend the continuum simulations out to
the plume produced by the arcjet. This means that these
methods cannot be used to predict spacecraft interference
effects.
In this paper the development of the direct simulation
Monte Carlo method ͑DSMC͒ for application to a hydrogen
arcjet is described. In satellite propulsion, the DSMC tech-
nique has been applied and successfully verified to the plume
of a hydrazine thruster,
12
and to the nozzle and plume flows
of both a nitrogen resisto-jet
13
and a cold flow of hydrogen
through an arcjet.
14
In this paper, a description is provided of
collision and chemistry models developed for the application
of the DSMC technique to an ignited arcjet flow. In addition,
the implementation of plasma effects is discussed. In particu-
lar, in this study a new model for the computation of Ohmic
heating is described using the DSMC technique. Results are
presented to illustrate the general nonequilibrium nature of
the arcjet flows and a comparison is made with experimental
data.
II. NUMERICAL METHOD
The direct simulation Monte Carlo method
15
͑DSMC͒
uses the motions and collisions of particles to perform a di-
rect simulation of nonequilibrium gas dynamics. Each par-
ticle has coordinates in physical space, three velocity com-
ponents, and internal energies. A computational grid is
employed to group together particles that are likely to col-
lide. Collision selection is based on a probability model de-
veloped from basic concepts in kinetic theory. The method is
widely used for rarefied nonequilibrium conditions and finds
application in hypersonics, materials processing, and micro-
machine flows.
The extension of the technique for the application to
arcjet flows requires the development of a number of new
physical models. Arcjets are characterized by high tempera-
tures ͑as high as 30,000 K͒ which give rise to strongly ion-
ized flows ͑as much as 30% ionized͒. In terms of intermo-
lecular collisions, mechanisms must be included in the
numerical model to account for ͑1͒ momentum transfer; ͑2͒
rotational excitation; ͑3͒ vibrational excitation; ͑4͒ disso-
ciation/recombination; and ͑5͒ ionization/recombination. The
relatively high level of ionization requires modeling of
plasma effects at some level. Each of these modeling issues
is discussed in the following.
3086 Phys. Fluids 9 (10), October 1997 1070-6631/97/9(10)/3086/10/$10.00 © 1997 American Institute of Physics