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Empirical slip and viscosity model performance for microscale gas flow
Author(s) -
McNenly Matthew J.,
Gallis Michael A.,
Boyd Iain D.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1012
Subject(s) - microscale chemistry , mechanics , slip (aerodynamics) , computational fluid dynamics , viscosity , flow (mathematics) , materials science , geology , thermodynamics , physics , mathematics , mathematics education
For the simple geometries of Couette and Poiseuille flows, the velocity profile maintains a similar shape from continuum to free molecular flow. Therefore, modifications to the fluid viscosity and slip boundary conditions can improve the continuum based Navier–Stokes solution in the non‐continuum non‐equilibrium regime. In this investigation, the optimal modifications are found by a linear least‐squares fit of the Navier–Stokes solution to the non‐equilibrium solution obtained using the direct simulation Monte Carlo (DSMC) method. Models are then constructed for the Knudsen number dependence of the viscosity correction and the slip model from a database of DSMC solutions for Couette and Poiseuille flows of argon and nitrogen gas, with Knudsen numbers ranging from 0.01 to 10. Finally, the accuracy of the models is measured for non‐equilibrium cases both in and outside the DSMC database. Flows outside the database include: combined Couette and Poiseuille flow, partial wall accommodation, helium gas, and non‐zero convective acceleration. The models reproduce the velocity profiles in the DSMC database within an L 2 error norm of 3% for Couette flows and 7% for Poiseuille flows. However, the errors in the model predictions outside the database are up to five times larger. Copyright © 2005 John Wiley & Sons, Ltd.