A Two-Phase Boundary Layer and Its Drag-Reduction Characteristics

Abstract

Consideration is given to coexisting gas and liquid boundary layers which occur when a gas is injected at the surface of a flat plate into a free-stream liquid flow. It is postulated that the gas forms a continuous film over the plate surface. The problem can be formulated exactly within the framework of laminar boundary-layer theory. Solutions have been carried out for a range of values of blowing velocity and of a fluid property parameter (ρμ) L / (ρμ)g . It is demonstrated that the drag forces associated with the two-phase boundary layer are much smaller than those for the single-phase liquid flow. For example, for a blowing velocity which is 0.001 of the free-stream velocity and a gas Reynolds number of 105 , the over-all drag calculation yields a value which is 0.0205 of the single-phase drag force. The effect of evaporation at the gas-liquid interface is analyzed and found to be small at temperatures which are not too close to saturation.