On transport in turbulent wakes: methane wakes

Abstract

An approximate treatment is given for turbulent diffusion of buoyant fluids in the wake of a falling body. The treatment is developed in detail for the case when a body falls through a uniform region of one fluid, across an interface, into a uniform region of a second fluid which is denser than and freely miscible with the first. This problem has relevance to the ignition of methane in coal mines, where a stone might fall from the top of a roof cavity filled with methane and draw down behind it an inflammable column into the air below: hence the name methane wake. A model theory is developed from very simple mixing assumptions which have already proved extremely useful in the investigation of buoyant plumes. The resulting equations can be solved without difficulty for the case of forced convection when buoyancy forces are negligible, and this solution is used to show that once the body has passed through the interface, upper fluid is transported down in the wake through only apart of the distance between interface and body. Thus there is a clearly defined mixture front in the wake separating regions of relatively low and relatively high concentration of the upper fluid. A numerical solution is necessary in the case where buoyancy forces are significant, and this mixed convection solution is developed to show that in suitable circumstances the region above the mixture front may divide because of buoyancy, and the upper parts return towards the interface. Some preliminary experiments are described and the results are shown to be in moderate agreement with the theoretical predictions.