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

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 seriesexpansion 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.

Compressible two-phase boundary-layer flow with finite particulate volume fraction

“…For this reason, it is difficult to determine which model is physically accurate. In addition, no direct comparisons with the works of Singleton [11] and Wang and Glass [12] are possible since their results are applicable for particle-phase stress-free and variable particle-phase density.…”

“…Solution of the fluid-phase equations at s t =0 is governed by the Blasius solution of incompressible flow past a semi-infinite flat plate. In contrast, Wang and Glass [12] employ solutions produced by the asymptotic expansion method as the initial profiles of flow properties to start the finite-difference procedure and to avoid the singularities associated with the leading edge of the plate. Another advantage of the modified Blasius transformations is that they convert the computational domain from semi-infinite in x (0 -x < oo) to finite in st (0 -< st -< 1).…”

“…Some solved the problem using the series method [5,6], others used the integral method [7,8], and others employed finitedifference methods [9,10]. The compressible version of the same problem has been solved by Singleton [11], and Wang and Glass [12], and Chamkha [13]. Singleton [11] used the series expansion method while Wang and Glass [12], and Chamkha [13] employed the finitedifference technique.…”

“…The compressible version of the same problem has been solved by Singleton [11], and Wang and Glass [12], and Chamkha [13]. Singleton [11] used the series expansion method while Wang and Glass [12], and Chamkha [13] employed the finitedifference technique. In the work by Chamkha [13], general boundary-layer equations for the two-phase suspension are given.…”

Particulate viscous effects on the compressible boundary-layer two-phase flow over a flat plate

“…It is seen from Equations (6) through (8) that the particle phase is assumed to have viscous effects which are not present in the models reported by Singleton [1] and Wang and Glass [2]. These effects can model particle-particle interaction and particle-wall interaction.…”