Micro-Flow is the name of a series of continuum based Navier-Stokes solvers that implements
the slip
boundary conditions to simulate transport in micro-scales. Since we have
used the dynamic similarity of the micro-flows with the low pressure
rarefied gas flows, our numerical models are appropriate for general rarefied gas
flow simulations. Here is a summary of the computational models we have developed in
the past five years.
We summarize all the computational models we have developed and implemented in the
spectral element code mu-Flow in the above table.
Mu-Flow uses a spectral element algorithm
for the solution of compressible, subsonic Navier-Stokes equations.
In addition to continuum based simulations, we use the DSMC code of Bird with
certain modifications for our geometries. This set of codes are used to analyze rarefaction,
compressibility, viscous heating, and thermal creep effects and their relative importance. In the current work we
use primarily the compressible model and DSMC simulations.
In the simulations, the limits in Knudsen number for the incompressible models are dictated by both the physics of the problem as
well as
by numerical stability considerations.
The first incompressible version of the flow solver (Incomp 1 in table above) solves the Navier-Stokes equations as well as energy
equation. It employs first-order slip and temperature jump and thermal creep
boundary conditions. It is general for two- and three-dimensional flows. Explicit (in time) implementation of the boundary
conditions results in a Knudsen number limit of typically Kn < 0.1. The second version of incompressible
model (Incomp 2 in the table) employs the slip boundary condition based on obtaining
the slip information one mean-free path away from the surface.
It is stable for high Kn flows, and
applicability is restricted with the flow geometry and the validity of the slip flow model. It does not
solve the energy equation, and therefore thermal creep effects are imposed by an assigned tangential
temperature gradient. In the compressible version (Comp in the table)
the general high-order slip boundary
condition
and temperature jump boundary condition are used. Its limitations
are based on the limitations of the slip flow theory. This version of the code is restricted to
shock-free flows, therefore it is used for subsonic and shock-free transonic flows.
Resolution tests and grid independent solutions have been verified for all
simulations.
Finally the DSMC
code is general enough to handle the slip conditions. It only requires
the accommodation coefficients (sigma_v, sigma_T) to simulate the interaction of the molecules
with the surfaces.
Although the DSMC methods are appropriate to simulate rarefied flows, they have some disadvantages.
One main disadvantage is that the error of the method is inversely proportional to the square-root of
number of simulated molecules. This is a slow convergence.
Other disadvantages of the DSMC method are that low subsonic flow simulations
require a large number of time averagings/samplings, making
the DSMC method very expensive. The reason for this is the smallness of mean flow properties (such as average flow speed)
for
low subsonic flows compared to the mean molecular magnitudes, which are in the order of speed of sound.
For this reason, our results are sampled for at least 500,000 time steps.
Back to Micro-Flow web pages.
Back to Ali Beskok's web pages.