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 NavierStokes solution in the noncontinuum nonequilibrium regime. In this investigation, the optimal modifications are found by a linear leastsquares fit of the NavierStokes solution to the nonequilibrium 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 nonequilibrium cases both in and outside the DSMC database. Flows outside the database include: combined Couette and Poiseuille flow, partial wall accommodation, helium gas, and nonzero 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:
 (University of Michigan, Ann Arbor, MI)
 Publication Date:
 Research Org.:
 Sandia National Laboratories
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 961660
 Report Number(s):
 SAND20043305J
Journal ID: ISSN 02712091; IJNFDW; TRN: US200923%%153
 DOE Contract Number:
 AC0494AL85000
 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; NAVIERSTOKES 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. 2004.
"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 NavierStokes solution in the noncontinuum nonequilibrium regime. In this investigation, the optimal modifications are found by a linear leastsquares fit of the NavierStokes solution to the nonequilibrium 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 nonequilibrium cases both in and outside the DSMC database. Flows outside the database include: combined Couette and Poiseuille flow, partial wall accommodation, helium gas, and nonzero 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 = 2004,
month = 7
}

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