In this paper, the expansion of xenon, argon, krypton, and neon gases through a Laval nozzle is studied experimentally and numerically. The pressurized gases are accelerated through the nozzle into a vacuum chamber in an attempt to simulate the operating conditions of a cold-gas thruster for attitude control of a micro-satellite. The gases are evaluated at several mass flow rates ranging between 0.178 mg/s and 3.568 mg/s. The Re numbers are low (8–256) and the estimated values of Kn number lie between 0.33 and 0.02 (transition and slip-flow regime). Direct Simulation Monte Carlo (DSMC) and continuum-based simulations with a no-slip boundary condition are performed. The DSMC and the experimental results show good agreement in the range Kn > 0.1, while the Navier-Stokes results describe the experimental data more accurately for Kn < 0.05. Comparison between the experimental and Navier-Stokes results shows high deviations at the lower mass flow rates and higher Kn numbers. A relation describing the deviation of the pressure drop through the nozzle as a function of Kn is obtained. For gases with small collision cross sections, the experimental pressure results deviate more strongly from the no-slip assumption. From the analysis of the developed function, it is possible to correct the pressure results for the studied gases, both in the slip-flow and transition regimes, with four gas-independent accommodation coefficients. The thrust delivered by the cold-gas thruster and the specific impulse is determined based on the numerical results. Furthermore, an increase of the thickness of the viscous boundary layer through the diffuser of the micronozzle is observed. This results in a shock-less decrease of the Mach number and the flow velocity, which penalizes thrust efficiency. The negative effect of the viscous boundary layer on thrust efficiency can be lowered through higher values of Re and a reduction of the diffuser length.

1.
D.
Hänel
,
Molekulare Gasdynamik
(
Springer-Verlag
,
Berlin, Heidelberg
,
2004
).
2.
J.
Maxwell
, “
On stress in rarefied gases arising from inequalities of temperature
,”
Philos. Trans. R. Soc. London
170
,
231
256
(
1879
).
3.
N.
Dongari
,
A.
Sharma
, and
F.
Durst
, “
Pressure-driven diffusive gas flows in micro-channels: From the Knudsen to the continuum regimes
,”
Microfluid. Nanofluid.
6
,
679
692
(
2009
).
4.
N.
Dongari
,
Y.
Zhang
, and
J.
Reese
, “
Modeling of Knudsen layer effects in micro/nanoscale gas flows
,”
J. Fluids Eng.
133
,
071101
(
2011
).
5.
R.
Deissler
, “
An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases
,”
Int. J. Heat Mass Transfer
7
,
681
694
(
1964
).
6.
J.
Maurer
,
P.
Tabeling
,
P.
Joseph
, and
H.
Willaime
, “
Second-order slip laws in microchannels for helium and nitrogen
,”
Phys. Fluids
15
,
2613
2621
(
2003
).
7.
D.
Stops
, “
The mean free path of gas molecules in the transition regime
,”
J. Phys. D: Appl. Phys.
3
,
685
696
(
1970
).
8.
H.
Brenner
, “
Navier-Stokes revisited
,”
Physica A
349
,
60
132
(
2005
).
9.
H.
Brenner
, “
Fluid mechanics revisited
,”
Physica A
370
,
190
224
(
2006
).
10.
F.
Durst
,
J.
Gomes
, and
R.
Sambasivam
, “
Thermofluiddynamics: Do we solve the right kind of equations?
,” in
Proceeding of the International Symposium on Turbulence, Heat and Mass Transfer, Dubrovnik
,
25–29 September 2006
(
Begell House Inc.
,
2006
), pp.
3
18
.
11.
Y.
Sone
,
Kinetic Theory and Fluid Dynamics
(
Birkhäuser
,
Boston
,
2002
).
12.
G.
Bird
,
Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(
Oxford University Press
,
New York
,
1994
).
13.
L.
O’Hare
,
D.
Lockerby
,
J.
Reese
, and
D.
Emerson
, “
Near-wall effects in rarefied gas micro-flows: Some modern hydrodynamic approaches
,”
Int. J. Heat Fluid Flow
28
,
37
43
(
2007
).
14.
D.
Lockerby
,
J.
Reese
,
D.
Emerson
, and
R.
Barber
, “
Velocity boundary condition at solid walls in rarefied gas calculations
,”
Phys. Rev. E
70
,
017303
(
2004
).
15.
R.
Balakrishnan
, “
An approach to entropy consistency in second-order hydrodynamic equations
,”
J. Fluid Mech.
503
,
201
245
(
2004
).
16.
X.
Zhong
,
R.
MacCormack
, and
D.
Chapman
, “
Stabilization of the Burnett equations and application to hypersonic flows
,”
AIAA J.
31
,
1036
1043
(
1993
).
17.
S.
Jin
and
M.
Slemrod
, “
Regularization of the Burnett equations via relaxation
,”
J. Stat. Phys.
103
,
1009
1033
(
2001
).
18.
H.
Struchtrup
and
M.
Torrilhon
, “
Regularization of grads 13 moment equations: Derivation and linear analysis
,”
Phys. Fluids
15
,
2668
2680
(
2003
).
19.
D.
Lockerby
and
J.
Reese
, “
On the modelling of isothermal gas flows at the microscale
,”
J. Fluid Mech.
604
,
235
261
(
2008
).
20.
J.
Moriñigo
and
J.
Hermida-Quesada
, “
Analysis of viscous heating in a micro-rocket flow and performance
,”
J. Therm. Sci.
17
,
116
124
(
2008
).
21.
W.
Louisos
and
D.
Hitt
, “
Transient simulations of 3-d supersonic micronozzle flow
,” in
Proceedings of the FEDSM-ICNMM2010, Montreal
,
1–5 August 2010
(
American Society of Mechanical Engineers
,
2010
), pp.
491
501
.
22.
R.
Bayt
,
A.
Ayon
, and
K.
Breuer
, “
A performance evaluation of mems-based micronozzles
,” in
Proceedings of the 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Seattle
,
7–9 July 1997
(
American Institute of Aeronautics and Astronautics
,
1997
).
23.
A.
Alexeenko
,
D.
Levin
,
D.
Fedosov
, and
G.
Gimelshein
, “
Performance analysis of microthrusters based on coupled thermal-fluid modeling and simulation
,”
J. Propul. Power
21
,
95
101
(
2005
).
24.
A.
Alexeenko
,
D.
Fedosov
,
S.
Gimelshein
,
D.
Levin
, and
R.
Collins
, “
Transient heat transfer and gas flow in a MEMS-based thruster
,”
J. Microelectromech. Syst.
15
,
181
194
(
2006
).
25.
A.
Alexeenko
,
D.
Levin
,
S.
Gimelshein
,
R.
Collins
, and
G.
Markelov
, “
Numerical simulation of high-temperature gas flows in a millimeter-scale thruster
,”
J. Thermophys. Heat Transfer
16
,
10
16
(
2002
).
26.
A.
Giovannini
and
R.
Abhari
, “
Rarefied flow expansion in linear aerospikes
,”
Phys. Fluids
27
,
062003
(
2015
).
27.
A.
Alexeenko
,
R.
Collins
,
S.
Gimelshein
,
D.
Levin
, and
B.
Reed
, “
Numerical modeling of axisymmetric and three-dimensional flows in microelectromechanical systems nozzles
,”
AIAA J.
40
,
897
907
(
2002
).
28.
A.
Alexeenko
,
S.
Gimelshein
,
D.
Levin
, and
R.
Collins
, “
Numerical modeling of axisymmetric and three-dimensional flows in mems nozzles
,” in
Proceedings of the 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Huntsville
,
16–19 July 2000
(
American Institute of Aeronautics and Astronautics
,
2000
).
29.
A.
Kurganov
and
E.
Tadmor
, “
New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
,”
J. Comput. Phys.
160
,
241
282
(
2000
).
30.
VDI
,
VDI-Wärmeatlas
(
Springer Vieweg
,
Berlin, Heidelberg
,
2013
).
31.
W.
Sutherland
, “
The viscosity of gases and molecular force
,”
Philos. Mag.
36
,
507
531
(
1893
).
32.
A.
Clarke
and
E.
Smith
, “
Low-temperature viscosities of argon, krypton, and xenon
,”
J. Chem. Phys.
48
,
3988
3991
(
1968
).
33.
A.
Clarke
and
E.
Smith
, “
Low-temperature viscosities and intermolecular forces of simple gases
,”
J. Chem. Phys.
51
,
4156
4161
(
1969
).
34.
J.
Kestin
,
K.
Knierim
,
E.
Mason
,
B.
Najafi
,
S.
Ro
, and
M.
Waldman
, “
Equilibrium and transport properties of the noble gases and their mixtures at low density
,”
J. Phys. Chem. Ref. Data
13
,
229
303
(
1984
).
35.
S.
Chapman
and
T.
Cowling
,
The Mathematical Theory of Non-Uniform Gases
(
Cambridge University Press
,
1970
).
36.
F.
Sharipov
and
J.
Strapasson
, “
Benchmark problems for mixtures of rarefied gases. I. Couette flow
,”
Phys. Fluids
25
,
027101
(
2013
).
37.
W.
Rae
, “
Some numerical results on viscous low density nozzle flows in the slender-channel approximation
,”
AIAA J.
9
,
811
820
(
1971
).
38.
J.
Anderson
,
Fundamentals of Aerodynamics
(
McGraw-Hill Science/Engineering/Math
,
New York
,
2001
).
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