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Supersonic gas-particle two-phase flow around a sphere

Published online by Cambridge University Press:  26 April 2006

R. Ishii ,
N. Hatta ,
Y. Umeda  and
M. Yuhi
R. Ishii
Affiliation:
Department of Aeronautics, Kyoto University, Kyoto 606, Japan
N. Hatta
Affiliation:
Department of Mineral Science and Technology, Kyoto University, Kyoto 606, Japan
Y. Umeda
Affiliation:
Department of Aeronautics, Kyoto University, Kyoto 606, Japan
M. Yuhi
Affiliation:
Department of Aeronautics, Kyoto University, Kyoto 606, Japan
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Abstract

This paper describes supersonic flows of a gas-particle mixture around a sphere. The Euler equations for a gas-phase interacting with a particle one are solved by using a TVD (Total Variation Diminishing) scheme developed by Chakravarthy & Osher, and the particle phase is solved by applying a discrete particle-cloud model. First, steady two-phase flows with a finite loading ratio are simulated. By comparing in detail the dusty results with the dust-free ones, the effects of the presence of particles on the flow field in the shock layer are clarified. Also an attempt to correlate the particle behaviours is made with universal parameters such as the Stokes number and the particle loading ratio. Next, non-steady two-phase flows are treated. Impingement of a large particle-cloud on a shock layer of a dust-free gas in front of a sphere is numerically simulated. The effect of particles rebounded from the sphere is taken into account. It is shown that a temporal reverse flow region of the gas is induced near the body axis in the shock layer, which is responsible for the appearance of the gas flow region where the pressure gradient becomes negative along the body surface. These phenomena are consistent with the previous experimental observations. It will be shown that the present results support a flow model for the particle-induced flow field postulated in connection with ‘heating augmentation’ found in the heat transfer measurement in hypersonic particle erosion environments. The particle behaviour in such flows is so complicated that it is almost impossible to treat the particle phase as an ordinary continuum medium.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 453 - 483
Copyright
© 1990 Cambridge University Press

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References

Batchelor, G. K.: 1988 A new theory of the instability of a uniform fluidized bed. J. Fluid Mech. 193, 75–110.Google Scholar
Batchelor, G. K.: 1989 A brief guide to two-phase flow. In Theoretical Applied Mechanics (ed. G. Germain, M. Piau & D. Caillerie), pp. 27–56. Elsevier.
Belotserkovskii, O. M.: 1960 The calculation of flows past axisymmetric bodies with detached shock waves. J. Appl. Maths Mech. 24, 744–753.Google Scholar
Carlson, D. J. & Hoglund, R. F., 1973 Particle drag and heat transfer in rocket nozzles. AIAA J. 11, 1980–1984.Google Scholar
Chakravarthy, S. R. & Osher, S., 1985 A new class of high accuracy TVD schemes for hyperbolic conservation laws. AIAA paper 85–0363.Google Scholar
Chung, J. N. & Troutt, T. R., 1988 Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech. 186, 199–222.Google Scholar
Dunber, L. E., Courtney, J. F. & Mcmillen, L. D., 1975 Heating augmentation in erosive hypersonic environments. AIAA J. 13, 908–912.Google Scholar
Fernández De La Mora, J. & Riesco-Chueca, P. 1988 Aerodynamic focusing of particles in a carrier gas. J. Fluid Mech. 198, 1–21.Google Scholar
Fernández De La Mora, J. & Rosner, D. E. 1982 Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers. J. Fluid Mech. 125, 379–395.Google Scholar
Fleener, W. A. & Watson, R. H., 1973 Convective heating in dust-laden hypersonic flow. AIAA paper 73–761.Google Scholar
Forney, L. J. & Mcgregor, W. K., 1987 Particle sampling in supersonic streams with a thin-walled cylindrical probe. AIAA J. 25, 1100–1104.Google Scholar
Gilbert, M., Davis, L. & Altman, D., 1955 Velocity lag of particle in linearly accelerated combustion gases. Jet Prop. 25, 26–30.Google Scholar
Godunov, S. K.: 1959 A finite difference method for the numerical solutions of the equations of fluid dynamics. Mat. Sb. 47, 271–306.Google Scholar
Henderson, C. B.: 1976 Drag coefficient of spheres in continuum and rarefied flows. AIAA J. 14, 707–708.Google Scholar
Ishii, R.: 1983 Shock waves in gas-particle mixtures. Mem. Fac. Engng Kyoto Univ. XLV-3, 1–16.Google Scholar
Ishii, R., Umeda, Y. & Yuhi, M., 1989 Numerical analysis of gas-particle two-phase flow. J. Fluid Mech. 203, 475–515.Google Scholar
Israel, R. & Rosner, D. E., 1983 Use of a generalized Stokes number to determine the aerodynamic capture efficiency of non-Stokesian particles from a compressible gas flow. Aerosol. Sci. Tech. 2, 45–51.Google Scholar
Lhuillier, D.: 1986 Mass and entropy transport in a suspension of rigid particles. J. Phys. Paris 47, 1687–1696.Google Scholar
Marble, F. F.: 1970 Dynamics of dusty gases. Ann. Rev. Fluid Mech. 2, 397–446.Google Scholar
Matsuda, T., Umeda, Y., Ishii, R., Yasuda, A. & Sawada, K., 1987 Numerical and experimental studies on choked underexpanded jets. AIAA paper 87–1378.Google Scholar
Matveyef, S. K. & Seyukova, L. P., 1981 Calculation of the flow of a dust-laden gas over a disk and flat end of a cylinder. Fluid Mech. Sov. Res. 10, 1–8.Google Scholar
Michael, D. H.: 1968 The steady motion of a sphere in a dusty gas. J. Fluid Mech. 31, 175–192.Google Scholar
Morioka, S. & Nakajima, T., 1987 Modeling of gas and particle two-phase flow and application to fluidized bed. J. Theor. Appl. Mech. 6, 77–88.Google Scholar
Park, H. M. & Rosner, D. E., 1989 Combined inertial and thermophoretic effects on particle deposition rates in highly loaded dusty-gas systems. Chem. Engng Sci. 44, 2233–2244.Google Scholar
Robinson, A.: 1956 On the motion of small particles in a potential field of flow. Commun. Pure Appl. Maths 9, 69–84.Google Scholar
Van Dyke, M. D. 1958 A model of supersonic flow past blunt axisymmetric bodies, with application of Chester's solution. J. Fluid Mech. 3, 515–522.Google Scholar