Use of the Adiabatic Wall Temperature in Film Cooling to Predict Wall Heat Flux and Temperature

The adiabatic wall temperature is generally assumed to be the driving temperature for heat transfer into conducting gas turbine airfoils. This assumption was analyzed through a series of FLUENT simulations using the standard k-ω turbulence model. Adiabatic effectiveness and heat transfer experiments commonly documented in literature were mimicked computationally. The results were then used to predict both the heat flux and temperature distributions on a conducting flat plate wall and the predictions were compared to the heat flux and temperature distributions found through a flat plate conjugate heat transfer simulation. The heat flux analysis was compared to previously published work using the realizable k-ε turbulence model. The same conclusions could be drawn for both turbulence models despite differences in simulated adiabatic effectiveness and heat transfer coefficient distributions. Agreement between heat flux predictions and the heat flux from the conjugate simulations correlated well with how closely the adiabatic wall temperature approximated the over-riding gas driving temperature for heat transfer into the wall. In general, the driving temperature for heat transfer was represented well by the adiabatic wall temperature and the heat flux was well predicted. However, in some locations, the heat flux was over-predicted by up to 300%. Since wall temperature is ultimately the parameter of interest for industrial gas turbine design, the conducting flat plate temperature distribution was also predicted. This was done by using the adiabatic effectiveness and heat transfer coefficients found with the standard k-ω turbulence model as boundary conditions in a three dimensional solid conduction simulation. Then metal temperatures predicted in the solid conduction simulation were compared to those found through conjugate analysis. Despite deviations in predicted heat flux and the conjugate model heat flux of up to 300%, deviations in the predicted and the conjugate model non-dimensional metal temperatures were less than 10%. Thus, use of the adiabatic wall temperature as the driving temperature for heat transfer to predict temperature on the surface of a conducting wall results in relatively small errors.