Application of a sensitivity equation method to turbulent flows with heat transfer

Abstract

This paper presents a continuous sensitivity equation method (SEM) for incompressible turbulent heat transfer. The k– ɛ model of turbulence with wall functions is used to model turbulence. Heat transfer is handled using an eddy conductivity. The SEM formulation accounts for complex parameter dependence and is suitable for a wide range of problems. It is applied to turbulent flow over a heated backward facing step and to turbulent flow over a heated flat plate. Several uses of the SEM are demonstrated: fast computation of nearby flows, identification of key parameters controlling the flow, and uncertainty analysis. Sensitivities are used to cascade input data uncertainties through the CFD code to yield uncertainty estimates of the skin friction and Stanton number. The SEM also provides detailed information about the contribution of each parameter to the global uncertainty.