A Discrete-Ordinates Solution for the Strong Evaporation Problem in Rarefied Gas Dynamics
DOI:
https://doi.org/10.5540/tcam.2021.022.02.00201Keywords:
Rarefied gas dynamics, Kinetic model, ADO method, Strong evaporation.Abstract
In this work we solve the nonlinear strong evaporation problem in rarefied gas dynamics. The analysis is based on the BGK model, with three dimensional velocity vector, derived from the Boltzmann equation. We present the complete development of a closed form solution for evaluating density, velocity, temperature perturbations and the heat flux of a gas. Numerical results are presented and discussed.
References
C. S. Scherer, An analytical approach to the strong evaporation problem in rarefied gas dynamics, Z. Angew. Math. Phys., vol. 66, pp. 1821-1833, 2015.
L. B. Barichello and C. E. Siewert, A discrete-ordinates solution for a non-grey model with complete frequency redistribution, JQSRT, vol. 62, pp. 665-675, 1999.
P. L. Bhatnagar, E. P. Gross, and M. Krook, A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems, Phys. Rev., vol. 94, pp. 511-525, 1954.
M. D. Arthur and C. Cercignani, Non-existence of a steady rarefied supersonic flow in a half-space, Z. Angew. Math. Phys., vol. 31, pp. 634-645, 1980.
C. E. Siewert and J. R. Thomas Jr., Strong evaporation into a half space, Z. Angew. Math. Phys., vol. 32, pp. 421-433, 1981.
K. M. Case and P. F. Zweifel, Linear Transport Theory. Massachusetts:
Addison-Wesley, 1967.
C. E. Siewert and J. R. Thomas Jr., Strong evaporation into a half space. ii. the three-dimensional bgk model, Z. Angew. Math. Phys., vol. 33, pp. 202-218, 1982.
S. Chandrasekhar, Radiative Transfer. New York: Dover, 1960.
C. S. Scherer, J. F. Prolo Filho, and L. B. Barichello, An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. i. flow problems, Z. Angew. Math. Phys., vol. 60, pp. 70-115, 2009.
C. S. Scherer, J. F. Prolo Filho, and L. B. Barichello, An analytical approach to the unified solution of kinetic equations in the rarefied gas dynamics. ii. heat transfer problems, Z. Angew. Math. Phys., vol. 60, pp. 651-687, 2009.
C. S. Scherer and L. B. Barichello, An analytical approach to the unified solution of kinetic equations in rarefied gas dynamics. iii. evaporation and condensation problem, Z. Angew. Math. Phys., vol. 61, pp. 95-117, 2010.
T. Ytrehus, Theory and experiments on gas kinetics in evaporation, in 10th International Symposium on Rarefied Gas Dynamics, pp. 1197-1212, Aspen, 1976.
Y. Sone and H. Sugimoto, Strong evaporation from a plane condensed phase, in Adiabatic Waves in Liquid-Vapor Systems, (Berlin), Springer, 1990.
K. Aoki and N. Masukawa, Gas flows caused by evaporation and condensation on two parallel condensed phases and the negative temperature gradient: Numerical analysis by using a nonlinear kinetic equation, Phys. Fluids, vol. 6, pp. 1379-1395, 1994.
Y. Sone, S. Takata, and F. Golse, Notes on the boundary conditions for fluid dynamic equations on the interface of a gas and its condensed phase, Phys. Fluids, vol. 13, pp. 324-334, 2001.
C. E. Siewert, Heat transfer and evaporation/condensation problems based on the linearized boltzmann equation, Euro. J. Mechanics B/Fluids, vol. 22, pp. 391-408, 2003.
C. Cercignani, The Boltzmann Equation and its Applications. New York: Springer-Verlag, 1988.
M. M. R. Williams, Mathematical Methods in Particle Transport Theory. London: Butterworth, 1971.
C. S. Scherer, Efeitos de Evaporação em Gases Rarefeitos. PhD thesis, Programa de Pós Graduação em Engenharia Mecânica. Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, 2009.
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C.
Klema, and C. B. Moler, Matrix Eigensystem Routines - EISPACK Guide.
Berlin: Springer-Verlag, 1976.
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK User's Guide. Philadelphia: SIAM, 1979.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.