Calculation of a Turbulent Boundary Layer Downstream of a Step Change in Surface Temperature

Abstract

Mean temperature and heat flux distributions in a thermal layer that develops within a momentum boundary layer subjected to a step change in surface temperature are calculated using two different methods. The method of Bradshaw and Unsworth, which uses the method of Bradshaw, Ferriss and Atwell to determine the mean velocity and Reynolds shear stress distributions and then assumes a constant turbulent Prandtl number for the heat flux calculation, yields heat flux distributions that are significantly different than the available experimental results at small distances from the step. Good agreement between calculations and experimental values is achieved when the distance x from the step is about 20 δ0, where δ0 is the boundary layer thickness at the step. To obtain good agreement with measurements of heat flux and mean temperature near the step, estimated distributions of turbulent viscosity and effective Prandtl number have been derived using an iterative updating procedure and the calculation method of Patankar and Spalding. These distributions are compared with those available in the literature. Calculated heat flux distributions show that the internal thermal layer is only likely to reach self-preserving conditions when x exceeds 40 δ0.