Table of contents

The propagation of normal rarefaction waves in dusty gases has been investigated numerically, using the modified random choice method with operator splitting technique. The effects of the dust parameters on the flow properties inside and behind the rarefaction wave are studied. The results are compared with those appropriate to a dust-free gas.

The effect of the various flow parameters, namely: the diameter of the solid particles, the material density of the solid particles, and the loading ratio of the solid particles on the flow field which is obtained when two normal shock waves collide head-on in a two phase dust-gas suspension has been investigated numerically, using the modified random choice method (RCM). The results were compared with those appropriate to the dust physical parameters used recently by Elperin, Ben-Dor and Igra in their study of the head-on collision of normal shock waves in dusty gases.

The influence of slip velocity and transverse magnetic field on a horizontal composite (porous/electrically conducting fluid) layer is investigated analytically and numerically. The analytical method is based on a perturbation technique while the numerical simulation is based on a finite difference scheme. Several important characteristics of the conducting flow as well as the concentration fields in the composite layer are reported. Also, the dependence of these characteristics on the dimensionless parameters of the problem are described graphically. The results of the present analysis are compared with similar results of viscous flow in the absence of a magnetic field and good agreement is found.

Direct numerical simulation of two-dimensional Navier-Stokes equations at large Reynolds numbers is made by the spectral method with 1364² modes starting from a high-symmetric random initial velocity field. Two wavenumber ranges, governed by different similarity laws are observed after the enstrophy dissipation rate η(t) takes the maximum value. At small wavenumbers the energy spectrum is stationary in time, while at larger wavenumbers it decays according to the similarity law predicted by the enstrophy cascade theory, and the shape of the energy spectrum E(k,t) is expressed by E(k,t) = Aη(t)^1/6v^3/2(k/k_d)^-3exp[ –√2A(k/k_d)], where k is the wavenumber, t the time, v the kinematic viscosity of fluid, k_d = η(t)^1/6v^1/2 the dissipation wavenumber, and A ≈ 1.6. Concerning the enstrophy dissipation rate the following properties are observed: (i) As the Reynolds number R increases, the time of maximum enstrophy dissipation rate is delayed, probably in proportion to ln R. (ii) It approaches finite positive values in the inviscid limit if the above-mentioned time-lag is taken into account, (iii) It decays inversely proportionally to the cubic of time, so that the enstrophy is expressed as a sum of a constant term and a term which decays inversely proportionally to the square of time. This paper discusses why power laws of the energy spectrum observed in most of previously reported direct numerical simulations of two-dimensional periodic flows were steeper than k^-3.