Optimal Turbulent Schmidt Number for RANS Modeling of Trailing Edge Slot Film Cooling

Abstract

It has been previously demonstrated that Reynolds Averaged Navier Stokes (RANS) simulations do not accurately capture the mixing between the coolant flow and the main flow in trailing edge slot film cooling configurations. Most RANS simulations use a fixed turbulent Schmidt number of either 0.7 or 0.85 to determine the turbulent scalar flux, based on the values for canonical flows. This paper explores the extent to which RANS predictions can be improved by modifying the value of the turbulent Schmidt number. Experimental mean 3D velocity and coolant concentration data obtained using Magnetic Resonance Imaging techniques are used to evaluate the accuracy of RANS simulations. A range of turbulent Schmidt numbers from 0.05 to 1.05 is evaluated and the optimal turbulent Schmidt number for each case is determined using an integral error metric which accounts for the difference between RANS and experiment throughout a 3-dimensional region of interest. The resulting concentration distribution is compared in detail with the experimentally measured coolant concentration distribution to reveal where the fixed turbulent Schmidt number assumption fails. It is shown that the commonly used turbulent Schmidt number of 0.85 over-predicts the surface effectiveness in all cases, particularly when the k-omega SST model is employed, and that a lower value of the turbulent Schmidt number can improve predictions.