Improvements in turbulent scalar mixing modeling for trailing edge slot film cooling geometries [electronic resource] : a combined experimental and computational approach
Keywords: Mechanical Engineering.

Gas turbine blades require active cooling systems to prevent structural failure. Pressure-side film cooling slots have gained widespread usage for cooling the thin trailing edge of the blade. To maximize engine efficiency and blade lifetime, both the flow through these slots and the heat transfer into the blades should be minimized. The turbulent mixing of the coolant flow with the main flow decreases the coolant concentration at the blade surface, and thereby degrades the film cooling performance. Current steady Reynolds-Averaged Navier Stokes (RANS) computational fluid dynamics (CFD) models drastically under-predict the mixing between the coolant flow and the main flow and are therefore not useful in heat transfer predictions. More complex simulations, such as Detached Eddy Simulations, Scale-Adaptive Simulations, and Large Eddy Simulations, while more accurate, are highly sensitive to inlet conditions and wall models. There is significant demand for improved models for trailing edge slot film cooling flows that are easy to implement and robust. This research employed a dual experimental and computational approach with the goal of establishing a framework for more efficient design and testing of advanced airfoil trailing edge configurations. On the experimental side, Magnetic Resonance Imaging (MRI) was used to obtain 3D velocity and concentration data for a range of trailing edge configurations. Configurations with varying land taper angles and internal structures were investigated. It was shown that the land taper angle affects the secondary flow structures and coolant distribution both on the breakout surface and in the wake of the trailing edge. These MRI data sets provided an extensive database for the development and validation of improved turbulent mixing models. When combined with the work of a previous doctoral student, they included variation in Reynolds number, slot width, blowing ratio, land configuration and internal geometry. These studies not only broadened understanding of how these features impact the film cooling performance, but also served to challenge new turbulence models to ensure their generality across flow configurations. Computational efforts were aimed at using the MRI data sets to improve turbulence modeling of trailing edge slot film cooling flows. Because MRI provides a full volumetric velocity field, this field could be used as an input to the Reynolds Averaged Advection Diffusion equation, along with a specified turbulent diffusivity function, to calculate the mean coolant concentration distribution. The difference between the calculated and experimentally measured concentration distributions could be minimized to yield an optimized turbulent diffusivity function. This approach enabled the determination of the key features which a scalar flux model must capture in order to accurately model trailing edge slot film cooling flows. It was demonstrated that if the correct turbulent diffusivity magnitude and spatial variation are prescribed, then the simple isotropic gradient diffusion hypothesis is sufficient to accurately predict the coolant concentration distribution. Analysis of the optimal turbulent Schmidt number over different regions of interest revealed that the Reynolds analogy was inappropriate in the near wall region. Based on these results, a new near wall correction was proposed which consisted of removing the Van Driest damping function from the turbulent diffusivity formulation. This correction was shown to significantly improve adiabatic effectiveness predictions and to generalize well across the experimental database.