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Performance Analysis of Microthrusters Based on Coupled Thermal-Fluid Modeling and Simulation J
OURNAL OF
P
ROPULSION AND
P
OWER
Vol. 21, No. 1, JanuaryFebruary 2005
Performance Analysis of Microthrusters Based on Coupled
Thermal-Fluid Modeling and Simulation
A. A. Alexeenko, D. A. Levin, D. A. Fedosov, and S. F. Gimelshein Pennsylvania State University, University Park, Pennsylvania 16802
and
R. J. Collins
§
University of Minnesota, Minneapolis, Minnesota 55455
Gas ow and performance characteristics of a high-temperature micro-electronically machined systems
(MEMS)-based thruster are studied using a coupled thermal-uid analysis. The material thermal response gov-
erned by the transient-heat-conduction equation is obtained by the nite element method. The lowReynolds
number gas ow in the microthruster is modeled by the direct simulation Monte Carlo approach. The effects of
Reynolds number, thermal boundary conditions, and micronozzle height are considered in detail. The predicted
thrust and mass-discharge coefcient of the three-dimensional microthruster under different ow conditions de-
crease with time as the viscous losses increase for higher wall temperatures.
Nomenclature
a
=
speed of sound
c
p
=
specic heat at constant pressure
h
=
height of nozzle
h
=
heat-conduction coefcient
k
=
thermal conductivity
m
=
mass ow rate
N
=
number of particles
P
=
inlet-to-outlet pressure ratio
p
=
pressure
q
a
=
conductive heat ux
q
c
=
convective heat ux
q
r
=
radiative heat ux
R
=
gas constant
Re
=
Reynolds number with respect to the throat dimension
T
=
temperature
u
=
X component of velocity
v
=
Y component of velocity
t
=
computational time step
x
=
cell size =
density =
accommodation coefcient
=
mean time between collisions res
=
mean residence time in a cell
=
domain of the nite element method (FEM) solution
Subscripts
o
=
stagnation
w
=
wall
Presented as Paper 4717-2003 at the Coupled Thermal-Fluid Modeling of
Micronozzles for Performance Analysis, Huntsville, AL, 2023 July 2003;
received 21 September 2003; revision received 4 June 2004; accepted for
publication 18 June 2004. Copyright
c
2004 by the American Institute of
Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper
may be made for personal or internal use, on condition that the copier pay
the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose-
wood Drive, Danvers, MA 01923; include the code 0748-4658/05 $10.00 in
correspondence with the CCC. Graduate thrusters-Based-on-Coupled-Thermal-Fluid-/' class='doin' >Student, Department of Aerospace Engineering. Member
AIAA. Associate Professor, Department of Aerospace Engineering. Senior
Member AIAA. Senior Research Associate, Department of Aerospace Engineering.
Member AIAA.
§
Professor Emeritus, Department of Electrical Engineering. =
linear size equal to local mean free path
= freestream
I.
Introduction
D
EVELOPMENTS in MEMS-based micropropulsion technol-
ogy are being considered for application in space propul-
sion, particularly by NASA for spacecraft formation ying. For-
mation ying of miniature spacecraft will demand a wide range of
propulsion maneuvers such as orbit raising, drag makeup, station-
keeping, and deorbit. thrusters-Based-on-Coupled-Thermal-Fluid-/' target='blank' class='doin' >Typically impulse bits on the order of mN s
will be required for such microspacecraft missions.
New propulsion systems are needed that are able to deliver precise
impulse bits while meeting strict mass, size, and power-usage lim-
itations. The advantages of MEMS-based propulsion devices for
such missions include lightweight materials, high degree of inte-
gration between different components, ability to provide versatile
thrust levels, and, nally, the potential to batch manufacture such
devices. A MEMS-based propulsion system might consist of arrays
of microrocket thrusters on a silicon chip with electronic circuitry
that controls the ring. Cold gas,
1
,2
catalytic decomposition,
3
va-
porizing liquid,
4
and mono and bipropellant
5
thrusters are among
the various micropropulsion concepts currently being evaluated.
The oweld of the typical lowReynolds number micronozzle
device cannot be calculated using conventional computational uid
dynamics techniques because the continuum assumption is not ap-
plicable throughout the ow.
6
The Knudsen number, based on the
MEMS nozzle throat diameter, is on the order of 10
3
and grows
several orders of magnitude at the nozzle exit. In this ow regime,
the direct simulation Monte Carlo (DSMC) method, a kinetic ap-
proach, provides the most accurate numerical oweld results.
Because of the reduced physical size of microthrusters, surface
effects such as friction and heat transfer can dominate the gas ow in
microdevices and, in a high-temperature microthruster, may neces-
sitate the cooling of its structure. The concept of a micromachined
bipropellant rocket engine with regeneratively cooled walls was in-
troduced in Ref. 5. In that work, it was emphasized that the heat-ux
and heat-load limits are two major physical-design constraints for
such micropropulsion devices.
The nozzle wall temperature and heat uxes are major factors
that inuence the gaseous ow dynamics and thruster performance,
yet the temporal variation of the thruster temperature is often an
unknown in the system design. The burn time of the thruster is
an important design parameter that determines the impulse bit that
will be available for spacecraft propulsion maneuver. Yet the heat-
ing of the microthruster structure by heat transfer between the
95 96
ALEXEENKO ET AL.
high-temperature supersonic ow in the nozzle and thruster walls
imposes time limits on its operation.
To expand micropropulsion-system design capabilities, a general
method for modeling coupled, time-dependent uid and thermal be-
havior in microcombustion devices was developed.
7
In that work,
a coupled uid and thermal model was applied for the rst time to
high-temperature gas ow in a MEMS device. The developed com-
putational tool allows the accurate computation of wall heat uxes,
temporal variation of the gas ow, and other system parameters
without having to specify the unknown wall temperature. The noz-
zle material thermal response can be expected to have an impact on
micronozzle integral quantities such as thrust, specic impulse ef-
ciency, and system specications such as the maximum operational
burn time. The model and computational approach were applied
to two- and three-dimensional models of a prototype micropropul-
sion system being designed and tested at NASA Glenn Research
Center
8
10
for Re
= 35 and 175, corresponding to chamber pressures
of 0.1 and 0.5 atm. Two limits of the true thermal environment were
considered. The rst thermal boundary condition was that of a ther-
mally insulated condition; the convective and conductive heat uxes
were assumed to be zero. The second thermal boundary condition
corresponded to that of nozzle actively cooled by a liquid ow at
300 K over the outer surface of the thruster.
A number of signicant conclusions may be drawn from that
work.
7
There exists a major difference between the gas owelds
inside the three- and two-dimensional models of the microthruster,
due to the impact of the sidewall boundary layer present only in the
three-dimensional case. The predicted thrust and mass discharge
coefcients of both the two- and three-dimensional micronozzles
decrease in time as viscous losses increase for higher wall and gas
temperatures. The decrease in thrust and mass discharge coefcient
as a function of time is greater for the three-dimensional than for
the corresponding (thermal boundary condition) two-dimensional
cases, again due to the presence of the third surface viscous losses.
Reference 7 also introduced a number of new issues regarding the
modeling and simulation of coupled high-temperature micronozzle
ows and performance. It is the purpose of this paper to address
these important numerical and operational issues. First, let us con-
sider the important issue of numerical accuracy. As mentioned, the
gas oweld is simulated using the DSMC particle method. The
correct use of this technique requires one to ensure that the simu-
lations are converged with respect to the number of particles in the
computational domain, number of particles per cell, correct choice
of time step, and adequate spatial resolution (or number of cells).
When multiple ow solutions have been examined with respect to
variations of these numerical parameters, the accuracy of the ow
simulation and hence nozzle operating parameters may be assessed.
In performing the calculations discussed in Ref. 7, it was found that
oweld solutions obtained with the stagnation pressure of 0.1 atm
for both two- and three-dimensional nozzle models and with the
stagnation pressure of 0.5 atm for the two-dimensional nozzle were
rigorously converged with respect to the aforementioned numerical
parameters.
However, this was not the situation for the second stagnation pres-
sure considered, that of 0.5 atm for the three-dimensional nozzle.
A detailed numerical study xing the thermal boundary condition
(and wall temperature) will be presented for the three-dimensional,
0.5-atm pressure case and the implications for modeling of such
micronozzle systems with DSMC will be discussed.
Second, the work of Ref. 7 demonstrated that for the lower
Reynolds number condition, stagnation pressure of 0.1 atm, the
viscous losses were greatest (particularly for the three-dimensional
nozzle). Hence in this work we consider a nozzle optimization study
for the lower stagnation pressure and the adiabatic thermal (the more
stressing) boundary condition. The ow and thermal simulations
will be fully coupled, as in ear