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Comprehensive Studies on Rarefied Jet and Jet Impingement Flows with Gaskinetic Methods

Part of: Rarefied gas flows, Boltzmann equation Time-dependent statistical mechanics (dynamic and nonequilibrium) Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  06 July 2017

Chunpei Cai ,
Xin He  and
Kai Zhang
Chunpei Cai*
Affiliation:
Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, Houghton, Michigan, 49931, USA
Xin He*
Affiliation:
Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, Houghton, Michigan, 49931, USA
Kai Zhang*
Affiliation:
Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, Houghton, Michigan, 49931, USA
*
*Corresponding author. Email addresses:ccai@mtu.edu (C. Cai), xinhe@mtu (X. He), kazhang@mtu.edu (K. Zhang)
*Corresponding author. Email addresses:ccai@mtu.edu (C. Cai), xinhe@mtu (X. He), kazhang@mtu.edu (K. Zhang)
*Corresponding author. Email addresses:ccai@mtu.edu (C. Cai), xinhe@mtu (X. He), kazhang@mtu.edu (K. Zhang)

Abstract

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This paper presents comprehensive studies on two closely related problems of high speed collisionless gaseous jet from a circular exit and impinging on an inclined rectangular flat plate, where the plate surface can be diffuse or specular reflective. Gaskinetic theories are adopted to study the problems, and several crucial geometry-location and velocity-direction relations are used. The final complete results include flowfield properties such as density, velocity components, temperature and pressure, and impingement surface properties such as coefficients of pressure, shear stress and heat flux. Also included are the averaged coefficients for pressure, friction, heat flux, moment over the whole plate, and the averaged distance from the moment center to the plate center. The final results include complex but accurate integrations involving the geometry and specific speed ratios, inclination angle, and the temperature ratio. Several numerical simulations with the direct simulation Monte Carlo method validate these analytical results, and the results are essentially identical. Exponential, trigonometric, and error functions are embedded in the solutions. The results illustrate that the past simple cosine function approach is rather crude, and should be used cautiously. The gaskinetic method and processes are heuristic and can be used to investigate other external high Knudsen number impingement flow problems, including the flowfield and surface properties for high Knudsen number jet from an exit and flat plate of arbitrary shapes. The results are expected to find many engineering applications.

Keywords

Kinetic theory of gasesrarefied gas flowsMonte Carlo methods

MSC classification

Secondary: 82C40: Kinetic theory of gases 76P05: Rarefied gas flows, Boltzmann equation 65C05: Monte Carlo methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 712 - 741
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Kun Xu

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