Numerical simulation of rarefied gas flow in micro and vacuum devices
Date
2014-01-22
Authors
Rana, Anirudh Singh
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Abstract
It is well established that non-equilibrium flows cannot properly be
described by traditional hydrodynamics, namely, the Navier-Stokes-Fourier
(NSF) equations. Such flows occur, for example, in micro-electro-mechanical
systems (MEMS), and ultra vacuum systems, where the dimensions of the
devices are comparable to the mean free path of a gas molecule. Therefore,
the study of non-equilibrium effects in gas flows is extremely important.
The general interest of the present study is to explore boundary value
problems for moderately rarefied gas flows, with an emphasis on
numerical solutions of the regularized 13--moment equations (R13). Boundary
conditions for the moment equations are derived based on either
phenomenological principles or on microscopic gas-surface scattering models,
e.g., Maxwell's accommodation model and the isotropic scattering
model.
Using asymptotic analysis, several non-linear terms in the R13 equations are
transformed into algebraic terms. The reduced equations allow us to obtain
numerical solutions for multidimensional boundary value problems, with the
same set of boundary conditions for the linearized and fully non-linear
equations.
Some basic flow configurations are employed to investigate steady and
unsteady rarefaction effects in rarefied gas flows, namely, planar and
cylindrical Couette flow, stationary heat transfer between two plates,
unsteady and oscillatory Couette flow. A comparison with the corresponding
results obtained previously by the DSMC method is performed.
The influence of rarefaction effects in the lid driven cavity problem is
investigated. Solutions obtained from several macroscopic models, in
particular the classical NSF equations with jump and slip boundary
conditions, and the R13--moment equations are compared. The R13 results
compare well with those obtained from more costly solvers for rarefied gas
dynamics, such as the Direct Simulation Monte Carlo (DSMC) method.
Flow and heat transfer in a bottom heated square cavity in a moderately
rarefied gas are investigated using the R13 and NSF equations. The results
obtained are compared with those from the DSMC method with emphasis on
understanding thermal flow characteristics from the slip flow to the early
transition regime. The R13 theory gives satisfying results including flow
patterns in fair agreement with DSMC in the transition regime, which the
conventional Navier-Stokes-Fourier equations are not able to capture.
Description
Keywords
Kinetic Theory of Gases, Moment equations, Non-equilibrium Thermodynamics, Rarefied Gas Flows, Regularized 13 (R13) moment equations