American Institute of Aeronautics and Astronautics
1
Physical Aspects of Rarefied Gas Flow in Micro to Nano
Scale Geometries Using DSMC
Ehsan Roohi
1
, Masoud Darbandi
2
, Vahid Mirjalili
3
Sharif University of Technology, P. O. Box 11365-8639, Tehran, Iran
Gerry E. Schneider
4
University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Rarefied gas flow in micro/nano electro mechanical systems (MEMS/NEMS) does not
perform exactly as that in macro-scale devices. The main goal in this study is to investigate
mixed subsonic-supersonic flows in micro/nano channels and nozzles and to provide physical
descriptions on their behaviors. We use DSMC method as a reliable numerical tool to extend
our simulation. It is because the DSMC provides accurate solution for the Boltzmann
equations over the entire range of rarefied flow regime or Knudsen numbers. As is known,
the appearance of oblique/normal shocks at the inlet of a channel or a nozzle adds to the
complexity of internal flow field analyses. We found some very unique physical aspects of
micro/nano flows including mixed supersonic-subsonic flow regimes in constant area ducts
and the attenuation of emitted shocks, which are attributed to the strong viscous forces and
dominant rarefaction effects in micro/nano scales. We simulated nozzle flow under different
flow conditions including different Knudsen and Reynolds numbers and inlet-outlet pressure
ratios. It was observed that as the Knudsen number increases, the viscous dissipation forces
increase and the flow in nozzle would not be choked at its throat and no supersonic flow is
observed in the divergent part. Contrary to the classical gas dynamics, no shock stands in
the divergent part despite specifying a back pressure at the outlet. Alternatively, we
observed that multiple expansion-compression waves would be generated and amplified as
the back pressure was decreased.
I. Introduction
icro and nano channels are widely used in Microelectromechanical and Nanoelectromechanical Systems
(MEMS and NEMS). In order to enhance the design and performance of such systems, it is mandatory to
achieve a deeper understanding of flow and heat transfer behavior through them. The magnitude of gas rarefaction
is known as a main parameter to assess such systems if the Knudsen number is sufficiently high [1-2]. In such
conditions, the solutions have to be established based on the kinetic principles such as those in treating the
Boltzmann equation. However, the exact solution of the Boltzmann equation can be derived for a limited number
of free-molecular flows and simple geometries. Thus, the non-equilibrium gas flow problems occurring in
complex geometries need the numerical treatments of the Boltzmann equation. However, the complexity in
Boltzmann equation promotes the use of alternative tools such as direct simulation Monte Carlo (DSMC). It is
claimed that the DSMC is one of the most successful particle simulation methods in treating rarefied gas flows
[3].
The DSMC method has been widely used to simulate both supersonic and subsonic micro flows. Oh et al. [4]
coupled DSMC with monotonic Lagrangian grid (MLG) to study the supersonic flow behavior in microchannels.
They specified the back pressure at the outlet benefiting from a virtual region outside the channel. They applied the
variable hard sphere (VHS) model [3] to simulate the molecular collision and simulated the flow at three Knudsen
numbers of 0.07, 0.14, and 0.19. Their results showed that the downstream variable magnitudes would qualitatively
agree with those of Fanno theory. They also found that the velocity slip and temperature jump would increase at the
1
Graduate student, Department of Aerospace Engineering.
2
Professor, Department of Aerospace Engineering.
3
Graduate student, Department of Aerospace Engineering.
4
Professor, Department of Mechanical and Mechatronics Engineering, AIAA Associate Fellow.
M
39th AIAA Fluid Dynamics Conference
22 - 25 June 2009, San Antonio, Texas
AIAA 2009-3583
Copyright © 2009 by Professor M. Darbandi. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.