Comparison of four different two-equation models of turbulence in predicting film cooling performance

The capabilities of four two-equation turbulence models in predicting film cooling effectiveness were investigated and their limitations as well as relative performance are presented. The four turbulence models are: the standard, RNG, and realizable k-ε models as well as the standard k-ω model all found in the FLUENT CFD code. In all four models, the enhanced wall treatment has been used to resolve the flow near solid boundaries. A systematic approach has been followed in the computational setup to insure grid-independence and accurate solution that reflects the true capabilities of the turbulence models. Exact geometrical and flow-field replicas of an experimental study on discrete-jet film cooling were generated and used in FLUENT. A pitch-to-diameter ratio of 3.04, injection lengthto-diameter ratio of 4.6 and density ratios of 0.92 and 0.97 were some of the parameters used in the film cooling analysis. Furthermore, the study covered two levels of blowing ratio (M = 0.5 and 1.5) at an environment of low free-stream turbulence intensity (Tu = 0.1 %). The standard k-ε model had the most consistent performance among all considered turbulence models and the best centerline film cooling effectiveness predictions with the results deviating from experimental data by only ±10% and about 20-60% for the low (M = 0.5) and high (M = 1.5) blowing ratio cases, respectively. However, centerline side-view and surface top-view contours of non-dimensional temperature for the standard k-ε cases revealed that the good results for film cooling effectiveness η compared to the experimental data were due to a combination of an over-prediction of jet penetration in the normal direction with an under-prediction of jet spread in the lateral direction. The standard k-ω model completely failed to produce any results that were meaningful with under-predictions of η that ranged between 80 and 85% for the low blowing ratio case and overpredictions of about 200% for the high blowing ratio case. Even though the RNG and realizable models showed to have better predicted the jet spread in the lateral direction compared to the standard k-ε model, there were some aspects of the flow, such as levels of turbulence generated by cross-flow and jet interaction, that were not realistic resulting in errors in the η prediction that ranged from -10% to +80% for the M = 0.5 case and from -80% to +70% for the M = 1.5 case. As a result of this study at this point it was concluded that the standard k-ε model have the most promising potential among the two-equation models considered. It was chosen as the best candidate for further improvement for the simulation of film cooling flows.