I. The Transient Boundary Layer Produced by a Sink on a Plane Wall. II. Flow of Dusty Gases

Citation

Parthasarathy, Shakkottai P. (1969) I. The Transient Boundary Layer Produced by a Sink on a Plane Wall. II. Flow of Dusty Gases. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GAFK-2R04. https://resolver.caltech.edu/CaltechETD:etd-04012009-085458

Abstract

Part I: The solution for the problem of the transient boundary layers generated by a sink on a plane wall is obtained by an integral method. The incompressible flow is similar and the similarity solutions are obtained for the two dimensional and axisymmetric cases. The velocity layer reaches a steady state and the thermal layer does not. For large times, when the thermal layer is much thicker than the velocity layer, a solution for the temperature field is obtained ignoring the velocity layer. With some approximations to the flow near the sink, similar solutions for compressible flow are also obtained. Part IIa: By using the integrated equations of motion, the development of a laminar, two-dimensional, dusty jet issuing from a slit is considered. The solutions are simple in the limits τ → 0 and τ → ∞, where τ is the particle relaxation time. For arbitrary τ, a numerical example is given. With some assumptions, the turbulent dusty jet is also considered. Part IIb: There are three parameters in the problem of steady motion of a dusty gas around a sphere. These are the Reynolds number R, particle parameter σ and the mass concentration of dust f[subscript ∞]. Solutions are obtained by the perturbation method by expanding in terms of R with σ or σ/R fixed, in the limit R → 0. Solutions are also obtained for the limit R tending to infinity with f < < 1. In both cases critical values of σ exist, below which the sphere does not capture dust. The efficiency of capture as a function of σ is calculated in both cases.

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