Table of contents

This paper reports an analytical study of an unsteady heat and mass transfer flow induced by an instantaneous concentrated point source in an unbounded fluid. Assuming the thermal Rayleigh number to be small, analytical solutions are obtained for the flow field, temperature and species concentration in the form of series expansions of the dependent variables in terms of the Rayleigh number. The impact of species diffusion on the buoyancy induced heat and fluid flow has been highlighted. Streamlines are drawn to demonstrate the evolution of the flow field at different times. Even though heat was specified to be one of the two diffusion mechanisms, the results apply as well to the case where the source generates simultaneously two different chemical components.

The present paper is concerned with the penetration of jets into fluidized beds. Simple models are developed and compared with data from the author's experiments and those from the literature. Differentiation is made between three jet flow regimes: jetting, bubbling and the transition between these two. Jet penetration length is found to increase as the orifice gas velocity increases, and the rate of increase is a function of the particular flow regime. This appears to be one of the main reasons for the large disagreement between the various correlations available in the literature. It is also found that the bed gas velocity has a first-order effect on the jet penetration length, something which is overlooked by most correlations in the literature. A simple analysis has been used successfully to define the extent of the transition zone.

The effect of Mach number on communication between regions of a shear layer is analyzed in the limit of geometric acoustics. Communication is quantified in terms of the acoustic intensity emitted by a point source and received by an observer moving with the flow. The generalized Snell's law is used to trace the sound rays which are shown to be highly distorted because of the Mach-number gradient. Sound-intensity calculations reveal that the influence of the source on the surrounding medium becomes confined to a smaller area as the mach number increases. The zones of influence on the Lagrangian observer are funnel-shaped and become narrower with increasing Mach number. Communication is inhibited primarily in the axial direction, both upstream and downstream, and to a lesser extent in the transverse direction. Hindrance of communication may be the fundamental reason for enhanced stability at high Mach numbers.

We give a general solution of Stokes equations for an incompressible, viscous flow past a sphere with mixed slip-stick boundary conditions. The Faxén's law for drag and torque on the sphere is also given and illustrated with an example.

In this paper we provide examples, by numerical simulation using the Navier-Stokes equations for axisymmetric laminar flow, of the `leapfrogging' motion of two, initially identical, vortex rings which share a common axis of symmetry. We show that the number of clear passes that each ring makes through the other increases with Reynolds number, and that as long as the configuration remains stable the two rings ultimately merge to form a single vortex ring.