A Wall-Function Approach to Incorporating Knudsen-Layer Effects in Gas Micro Flow Simulations

Abstract

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flowfield and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a wall-function model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction.

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Document Details

Document Type
Technical Report
Publication Date
Jul 13, 2005
Accession Number
ADA447232

Entities

People

  • D. A. Lockerby
  • J. M. Reese
  • M. A. Gallis

Organizations

  • King's College London

Tags

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Boundaries
  • Boundary Layer
  • Compressible Flow
  • Engineering
  • Equations
  • Flow
  • Flow Fields
  • Fluid Dynamics
  • Gas Flow
  • Knudsen Number
  • Mean Free Path
  • Mechanical Engineering
  • Navier Stokes Equations
  • Shear Flow
  • Simulations
  • Temperature Gradients

Fields of Study

  • Physics

Readers

  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.