Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-22T08:02:01.267Z Has data issue: false hasContentIssue false
  • English
  • Français

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat plate

Published online by Cambridge University Press:  21 April 2006

B. Y. Wang  and
I. I. Glass
B. Y. Wang
Affiliation:
Institute of Mechanics, Academia Sinica, Beijing, China
I. I. Glass
Affiliation:
Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Downsview, Ontario, Canada, M3H 5T6
Get access Rights & Permissions [Opens in a new window]

Abstract

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions: the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a series-expansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 223 - 241
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, D. A., Tannehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. Hemisphere.
Blottner, F. G. 1970 AIAA J. 8, 193–205.
Digiovanni, P. R. & Lee, S. L. 1974 J. Appl. Mech. 41, 35.
Flügge-Lotz, I. & Blottner, F. G. 1962 AFOSR 2206.
Gear, C. W. 1971 Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall.
Gilbert, M., Davis, L. & Altman, D. 1955 Jet Propul. 25, 26.
Hamed, A. & Tabakoff, W. 1973 AIAA paper 73–687.
Jain, A. C. & Ghosh, A. 1979 Z. Flugwiss. weltraum forschung 3, 379.
Knudsen, J. G. & Katz, D. L. 1958 Fluid Mechanics and Heat Transfer. McGraw-Hill.
Liu, J. T. C. 1967 Astro Acta 13, 369.
Marble, F. E. 1963 Combustion and Propulsion, 5th AGARD Colloquium, Oxford. Pergamon.
Osiptsov, A. N. 1980 Fluid Dyn. 15, 512.
Otterman, B. & Lee, S. L. 1970 Proc. Heat Transfer and Fluid Mechanics Institute, Monterey. Stanford University Press.
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Prabha, S. & Jain, A. C. 1982 Proc. 13th Intl Symp. Space Technology and Science, Tokyo.
Rudinger, G. 1980 Fundamentals of Gas-Particle Flow. Elsevier.
Singleton, R. E. 1965 Z. angew. Math. Phys. 16, 421.
Soo, S. L. 1967 Fluid Dynamics of Multiphase Systems. Waltham: Blaisdell.
Soo, S. L. 1968 Z. angew. Math. Phys. 19, 545.
Tabakoff, W. & Hamed, A. 1972 AIAA paper 72–87.
Wang, B. Y. & Glass, I. I. 1986a UTIAS Rep. 310.
Wang, B. Y. & Glass, I. I. 1986b UTIAS Rep. 311.
Wang, B. Y. & Glass, I. I. 1986c UTIAS Rep. 312.
Wu, J. C. 1960 Douglass Aircraft Company Inc. Rep. SM-37484.