Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer

Abstract

Experiments described here show that the rate of heat transfer in a supersonic, turbulent, boundary layer on a concave wall is increased by the streamwise curvature of the wall. For the arrangement investigated, the pressure is kept constant along the wall, and the increase of about 20% is therefore only due to the wall curvature. For a convex wall, a comparable decrease was found, also with constant pressure along the wall.It is likely that this change in heat-transfer rate is mainly due to an increase or decrease of turbulent mixing by the effect of the curvature. The increase on a concave wall can in principle also be explained by large-scale vortices with axes in the flow direction (Gortler vortices). However, disturbances of this type cannot explain the decrease observed on the convex wall. They cannot therefore be the only cause.A simple criterion indicating the effect of curvature on the turbulent motion normal to the wall is given. It is derived from an inviscid-flow analysis. The criterion shows that, for most Mach numbers and wall temperatures of practical interest, the change in mixing depends mainly on the velocity gradient normal to the wall. For high supersonic and hypersonic Mach numbers, however, there is a layer near the outer edge of the boundary layer where the change depends mainly on the temperature (density) gradient.