- A. Beskok, and G. E. Karniadakis, Models and Scaling Laws
for Rarefied Internal
Gas Flows Including Separation ,
Presented at the 48th Annual Meeting of the American Physical Society
Division of Fluid Dynamics, Irvine, California, 19-21 November 1995 (Submitted to
Journal of Fluid Mechanics).
Rarefied gas flows in channels, pipes and backwards-facing steps are studied in
a wide range
of Knudsen number (Kn) with the objective of developing continuum-based
simplified models.
Such flows are encountered in micro-electro-mechanical-systems (MEMS) and in
low-pressure
environments. A new general boundary condition that accounts for the reduced
momentum exchange with wall
surfaces is proposed and its validity is investigated. It is shown that it is
applicable in the entire Knudsen range and
it is second-order accurate in $Kn$ in the slip flow regime. Firstly,
channel and pipe flows in the slip flow and transition flow regimes are simulated
using the DSMC
method. Corresponding spectral element discretizations of the compressible Navier
-Stokes equations subject to various
slip models are also performed for Kn<1.
DSMC based solutions as well as solutions of the linearized Boltzmann
equations are used to test the accuracy of the macroscopic models.
A universal scaling for the velocity profile is obtained, which is used to develop
a unified model predicting the mass flowrate
with good accuracy in the entire flow regime (0 < Kn < oo).
A rarefaction coefficient is
introduced into the model to account for the increasingly reduced intermolecular
collisions in the
transition and free-molecular regime.
This model
also predicts correctly the well known Knudsen's minimum in the transition flow
regime as verified by
experimental results and the DSMC data.
Secondly, the effect of rarefaction on separated flows is studied by considering
the
backwards-facing step geometry in the slip flow regime. The multiple length scales
and the sudden
change in rarefaction conditions at the step expansion introduce substantial
complexity in this case.
First- and higher-order slip boundary
conditions are employed in the continuum simulations and the results are compared
against corresponding
DSMC simulations. Good agreement is achieved suggesting that the more efficient
continuum-based approximations
are valid in the slip flow regime even for separated rarefied flows.