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Newtonian flow theory for slender bodies in a dusty gas

Published online by Cambridge University Press:  20 April 2006

R. M. Barron  and
J. T. Wiley
R. M. Barron
Affiliation:
Department of Mathematics, University of Windsor, Ontario, Canada N9B 3P4
J. T. Wiley
Affiliation:
Department of Mathematics, University of Windsor, Ontario, Canada N9B 3P4
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Abstract

Hypersonic small-disturbance theory is extended to consider the problem of dusty-gas flow past thin two-dimensional bodies. The mass fraction of suspended particles is assumed to be sufficiently large that the two-way interaction between particle phase and gas phase must be considered. The system of eight governing equations is further reduced by considering the Newtonian approximation γ → 1 and M∞ → ∞. The Newtonian theory up to second order is studied and the equations are solved for the case of a thin wedge at zero angle of attack. Expressions for the streamlines, dust-particle paths, shock-wave location and all flow variables are obtained. It is seen that the presence of the dust increases the pressure along the wedge surface and tends to bend the shock wave towards the body surface. Other effects of the interaction of the two phases are also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 147 - 157
Copyright
© 1981 Cambridge University Press

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References

Barron, R. M. & Wiley, J. T. 1979 Remarks on dusty hypersonic wedge flow. A.I.A.A. J. 17, 317–318.Google Scholar
Carrier, G. F. 1958 Shock waves in a dusty gas. J. Fluid Mech. 4, 376–382.Google Scholar
Cole, J. D. 1957 Newtonian flow theory for slender bodies. J. Aero. Sci. 24, 448–455.Google Scholar
Marble, F. E. 1970 Dynamics of dusty gases. Ann. Rev. Fluid Mech. 2, 397–446.Google Scholar
Peddieson, J. 1975 Two-phase flow in supersonic shock layers. Developments in Mechanics, vol. 8, Proc. 14th Midwestern Mech. Conf., pp. 467–482.
Peddieson, J. & Lyu, C.-H. 1973 Dusty hypersonic wedge flow. A.I.A.A. J. 11, 110–112.Google Scholar
Peddieson, J. & Lyu, C.-H. 1974 Supersonic two-phase flow past a cone. Proc. 10th Southeastern Seminar on Thermal Sciences.
Probstein, R. F. & Fassio, F. 1970 Dusty hypersonic flows. A.I.A.A. J. 8, 772–779.Google Scholar
Spurk, J. H. & Gerber, N. 1972 Dust collection efficiency for power law bodies in hypersonic flight. A.I.A.A. J. 10, 755–761.Google Scholar
Van Dyke, M. D. 1954 A study of hypersonic small-disturbance theory. N.A.C.A. Tech. Note 1194.Google Scholar
Waldman, G. D. & Reinecke, W. G. 1971 Particle trajectories, heating and breakup in hypersonic shock layers. A.I.A.A. J. 9, 1040–1048.Google Scholar