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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)
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Abstract

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

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Footnotes

Communicated by Kun Xu

References

[1] Campargue, R., Historical account and branching to rarefied gas dynamics of atomic & molecular beams: A continuing and fascinating Odyssey commemorated by Nobel prizes awarded to 23 Laureates in physics & chemistry. 24th International Rarefied Gasdynamics Symposium, July, 2004.Google Scholar
[2] Sanna, G., and Tomassetti, G., Introduction to Molecular Beams Gas Dynamics, Imperial College Press, London, 2005.Google Scholar
[3] Maev, R., and Leshchynsky, V., Introduction to Low Pressure Gas Dynamic Spray, Wiley-Vch, Weinheim, Germany, 2008.Google Scholar
[4] Hastings, D., and Garrett, H., Spacecraft-Environment Interactions, Cambridge University Press, Cambridage, UK., 1996.Google Scholar
[5] Metzger, P., Rocket exhaust cratering: A serious challenge for space exploration. Proceedings of the 1st Workshop on Granular Materials in Lunar and Martian Exploration, KSC FL, Feb. 2-3, 2005.Google Scholar
[6] LeBeau, G.J., and Lumpkin, F.E., Application highlights of the DSMC Analysis Code (DAC) software for simulating rarefied flows, Comput. Method Appl. Math., 191(2011), pp.595–609. http://dx.doi.org/10.1016/S0045-7825(01)00304-8.Google Scholar
[7] Kannenberg, K.C., and Boyd, I.D., Three-dimensional Monte Carlo simulation of plume impingement, J. Thermophys. Heat Tr., 13(1999), No.2, pp.226–235. http://dx.doi.org/10.2514/2.6440.CrossRefGoogle Scholar
[8] Simons, G.A., Effects of nozzle boundary layers on rocket exhaust plumes, AIAA J., 10(1972), No.11, pp.1534–1535. http://dx.doi.org/10.2514/3.6656.CrossRefGoogle Scholar
[9] Vashchenov, P., Kudryavstev, A., Khotyanovsky, D., and Ivanov, M., DSMC and Navier-Stokes study of backflow for nozzle plumes expanding into vacuum. International Symposium on Rarefied Gas Dynamics (24th),Monopoli (Bari), Italy on 10-16, July 2004.Google Scholar
[10] Vincenti, W.G., and Kruger, C.H., Introduction to Physical Gas Dynamics, Krieger Publishing, Malabar, Florida, 1986.Google Scholar
[11] Noller, H.G., Approximate calculation of expansion of gas from nozzles into high vacuum, J. Vac. Sci. Tech., 3(1966), pp.202–207.Google Scholar
[12] Narasimha, R., Collisionless expansion of gases into vacuum, J. Fluid Mech., 12(1962), No.2., pp.294–308. https://doi.org/10.1017/S0022112062000208.CrossRefGoogle Scholar
[13] Woronowicz, M.S., and Rault, N., On jet flowfield analysis and simulation techniques. AIAA paper 1994-2048, 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, June 20-23, 1994, Colorado Springs, CO.Google Scholar
[14] Cai, C., and Zou, C., A gaskinetic study on planar collisionless jet impingement at a plate, Comm. Comput. Phys., 4(2013), pp.960–978.Google Scholar
[15] Cai, C., and Huang, X., High speed rarefied round jet impingement flows, AIAA J., 50(2012), pp.2908–2911. DOI: 10.2514/1.J051785.Google Scholar
[16] Cai, C., and He, X., Comprehensive investigations of high Knudsen number planar jet impingement on an inclined flat plate, Phys. Fluids, May, 2016.Google Scholar
[17] Cai, C., Gaskinetic modeling on dilute gaseous plume impingement flows, Aerospace, 3(2016), 43. DOI: 10.3390/aerospace3040043.Google Scholar
[18] Cai, C., and Boyd, I.D., Theoretical and numerical study of several free molecular flow problems, J. Spacecraft Rockets, 44(May-June, 2007), No.3, pp.619–624.Google Scholar
[19] Cai, C., and Boyd, I.D., Collisionless gas flow expanding into vacuum, J. Spacecraft Rockets, 44(2007), pp.1326–1330. DOI: 10.2514/1.32173.CrossRefGoogle Scholar
[20] Khasawneh, K., Liu, H., and Cai, C., Surface properties for rarefied circular jet impingement on a flat plate, Phys. Fluids, 23(2011), pp.1–6. DOI: 10.1063/1.3549934.Google Scholar
[21] Bird, G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press, New York, 1994.Google Scholar
[22] Boyd, I.D., Modelling of satellite control thruster plumes. Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, University of Southampton, Southmpton, England, 1998.Google Scholar
[23] Stark, J.P.W., and Boyd, I.D., Modelling of a small hydrazine thruster plumes in the transition flow regime, J. Propul. Power, 6(1990), No.2, pp.121–126. http://dx.doi.org/10.2514/3.23232.Google Scholar
[24] Roohi, E., and Stefanov, S., Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows, Phys. Reports, 656(2016), pp.1–38. http://dx.doi.org/10.1016/j.physrep.2016.08.002.CrossRefGoogle Scholar
[25] Liu, H., and Cai, C., An object-oriented serial and parallel DSMC simulation package, Comput. & Fluids. 57(2012), pp.65–75.Google Scholar
[26] Cai, C., Analytical solutions for free-molecular gas flow over a flat plate, 29th International Rarefied Gasdynamics Symposium, Xi’an, China, July 12th-19th, 2014.Google Scholar