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Title: Empirical slip and viscosity model performance for microscale gas flows.

Abstract

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{sub 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.

Authors:
;  [1];  [1]
  1. (University of Michigan, Ann Arbor, MI)
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
961660
Report Number(s):
SAND2004-3305J
Journal ID: ISSN 0271-2091; IJNFDW; TRN: US200923%%153
DOE Contract Number:
AC04-94AL85000
Resource Type:
Journal Article
Resource Relation:
Journal Name: Proposed for publication in the International Journal for Numerical Methods in Fluids.; Journal Volume: 49; Journal Issue: 11
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; GAS FLOW; FLOW MODELS; VISCOSITY; SLIP FLOW; COUETTE FLOW; LAMINAR FLOW; NAVIER-STOKES EQUATIONS; MONTE CARLO METHOD; KNUDSEN FLOW

Citation Formats

Gallis, Michail A., Boyd, Iain D., and McNenly, Matthew J. Empirical slip and viscosity model performance for microscale gas flows.. United States: N. p., 2004. Web.
Gallis, Michail A., Boyd, Iain D., & McNenly, Matthew J. Empirical slip and viscosity model performance for microscale gas flows.. United States.
Gallis, Michail A., Boyd, Iain D., and McNenly, Matthew J. Thu . "Empirical slip and viscosity model performance for microscale gas flows.". United States. doi:.
@article{osti_961660,
title = {Empirical slip and viscosity model performance for microscale gas flows.},
author = {Gallis, Michail A. and Boyd, Iain D. and McNenly, Matthew J.},
abstractNote = {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{sub 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.},
doi = {},
journal = {Proposed for publication in the International Journal for Numerical Methods in Fluids.},
number = 11,
volume = 49,
place = {United States},
year = {Thu Jul 01 00:00:00 EDT 2004},
month = {Thu Jul 01 00:00:00 EDT 2004}
}