7 - INVISCID MULTIPHASE FLOWS: BUBBLING BEDS

Abstract

This chapter discusses multiphase flows in bubbling beds. To understand multiphase flow phenomena, such as bubble formation near the grid for uniform flow, simpler models are frequently useful. In single-phase fluid mechanics, the representation of the Navier–Stokes equation in terms of a vorticity transfer equation is often useful. With such an approximation normally made in free convection heat transfer, the stream function and the vorticity remain the same as in single-phase flow, as porosities only change where they occur as differences. Analytical solutions to such a linearized equation are used to describe solids tracer injection into fluidized beds. An analysis with more simplification can be used to show that a point source of gas injected into a two-dimensional fluidized bed will produce a circular bubble. In one dimension, the basic variables are the pressure, the porosity, and the gas and the solids velocities. In homogeneous flow, as in compressible single phase pipe flow, the variables reduce themselves to just the velocity and the pressure determined by their respective conservation of mass and momentum equations. The bubble frequency is obtained by counting the total number of bubbles and the total number of movie frames. From the known filming rate, the bubble frequency is determined.