Revision as of 10:22, 1 July 2010

Unsteady Near-Field Plumes

Free Flows

Underlying Flow Regime 1-07

Description

Introduction

Free vertical buoyant plumes and free-jets are related phenomena, both having a core region of higher momentum flow surrounded by shear layers bounding regions of quiescent fluid. However, whereas for jets the driving force for the fluid motion is a pressure drop through an orifice, for plumes the driving force is buoyancy due to gradients in fluid density. Plumes can develop due to density gradients caused by temperature differences, for example in fires, or can be generated by fluids of different density mixing, such as hydrogen releases in air. There are many flows of both engineering and environmental importance that feature buoyant plumes, ranging from flows in cooling towers and heat exchangers to large geothermal events such as volcanic eruptions. There has been considerable attention paid to the mean flow behaviour of plumes in the far field, e.g. Chen & Rodi [5] or List [6] [7], which are examined in a companion UFR. However, there has been less study of the near-field unsteady dynamics of plumes.

In the present work, only non-reacting plumes are considered. This choice has been made in order to avoid the additional complexities associated with combustion, soot production and radiation in fire plumes. For helium plumes, the difference in density between helium and air is a factor of seven which is similar to that in fire plumes [8]. The principal difference between fire and helium plumes arises from the fact that heat is released locally from the flame in fire plumes whereas in helium plumes the buoyancy is produced only near the source where there are large concentration gradients.

The near-field of buoyant plumes features two key instabilities. The first is the Rayleigh-Taylor instability related to the presence of dense fluid above less-dense fluid. The two layers of different-density fluid are in equilibrium if they remain completely plane-parallel but the slightest disturbance causes the heavier fluid to move downwards under gravity through the lighter fluid. At the interface between the two fluids, irregularities are magnified to form fingers or spikes of dense fluid separated by bubbles of lighter fluid. The size of these irregularities grows exponentially with time and the smaller the density difference, the larger the wavelength of the instability. There has been considerable research into the dynamics of Rayleigh-Taylor instability (e.g. [9][10] [11][12]) as a consequence of its importance in nuclear weapons, atmospheric flows and astrophysics. Figure 2 shows the classic spike and bubble flow structures characteristic of R-T instability produced by two fluids of different density mixing, taken from Cook et al. [13].