An Approximate Analysis of Gaseous Film Cooling With Constant Fluid Properties

Abstract

Presented herein is an analysis of the velocity and temperature fields for a constant-property turbulent flow downstream of a step-type injection slot. The flow field is considered to be in a developing condition and is quantitatively described with a two-layer model in which the outer region is dominated by large-scale turbulence typical of free shear layers. An approximate solution for the outer region is appropriately joined to an inner profile determined by the usual “law of the wall” so that one obtains both the correct profile shape for the complete viscous layer and the proper spatial positioning of velocity and temperature profiles. The latter are obtained from a linearized energy equation with unit turbulent Prandtl number and are employed, along with the velocity profiles, in an energy balance to determine the longitudinal variation of the effectiveness. A successful calculation technique is discussed and typical results are compared with existing experimental data. The analysis is shown to be competitive in accuracy with available correlation expressions while also yielding considerable insight into the interaction of various design parameters.