Duck, P.W. and Hewitt, R.E. and Foster, M.R. (2004) On the spatial development of a dusty wall jet. Journal of Fluid Mechanics, 514. pp. 385-411.

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Abstract

We consider the flow of an incompressible particle-laden fluid through the application of the so-called �dusty-gas� equations, which treat the fluid/particle suspension as two continua. The two phases are described by their individual field equations and interact through a Stokes-drag mechanism. The particular flow we consider is of boundary-layer type, corresponding to the downstream development of a Glauert-type jet adjacent to a horizontal boundary (the inclusion of the particulate phase requires the flow to be non-self-similar). We solve the governing boundary-layer equations through a numerical spatial marching technique in the three distinct cases of (i) weak gravitational influence, (ii) a jet �above� a wall under the action of gravity and (iii) a jet �below� a wall under the action of gravity. The qualitative and quantitative features of the three cases are quite different and are presented in detail. Of particular interest is the development of a stagnation point in the particle velocity field at a critical downstream location in case (i), the development of fluid/particle flow reversal in case (ii) and the development of �shock� solutions and particle-free regions in case (iii). Asymptotic descriptions are given of the critical phenomena, which support the numerical results. It is found that inclusion of a Saffman force has no substantial effect on either the location or structure of the stagnation-point region.

Item Type: Article
Uncontrolled Keywords: particle-laden flow, multiphase flow, jet flows
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics
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