Surface Tension Flows Induced by a Moving Thermal Source

Abstract

Surface tension flows induced by a thermal source moving over an otherwise stationary liquid layer are investigated. Such flows are important for fire spread over flammable liquids at sub-flash temperatures. The flow structure and parameter dependence are obtained with the aid of numerical solutions of the energy and vorticity transport equations in two space dimensions. Convergence of the solutions is established by successively refining the spatial grids. Results are presented for a range of surface tension parameters (25 ≤ S ≤ 250), Prandtl numbers (1 ≤ Pr ≤ 100) and Reynolds numbers (10 ≤ Re ≤ 2500). The Reynolds number (Re = Uh/v) is based on thermal source speed (U) and layer depth (h). The induced flow takes the form of a captured eddy just below the surface. The rate of fluid circulation in the eddy (dimensional) is found to depend linearly on S, to be essentially independent of Pr and to be functionally dependent on h. Viscous and boundary-layer flow regimes are found for small and large values of h, respectively and compare favorably with available analysis.