Parameters Affecting Adiabatic Effectiveness and Turbulence in Film Cooling

Gas-turbine engines use film cooling to actively cool turbine components and keep thermal loads on the materials at acceptable levels for structural integrity and service life. The turbulent mixing between the film-cooling jet and the crossflow decreases the coolant temperature, which reduces the cooling performance. This turbulent mixing is sensitive to parameters such as density ratio (DR), blowing ratio (BR), velocity ratio (VR), and momentum-flux ratio (MR) and understanding the effects of these parameters on the turbulent mixing is critical for improving film cooling.

This research seeks to improve understanding by using large-eddy simulation (LES) as a tool to analyze the turbulence of film cooling. With this knowledge it is possible evaluate more fundamental turbulence modeling assumptions utilized by Reynolds-Averaged Navier-Stokes (RANS) approaches as they apply to film cooling. This analysis can provide insight regarding how to improve turbulence models.

The film-cooling problem studied involves the cooling of a flat plate, where the cooling jets issued from a plenum through one row of circular holes of diameter $D$ and length 4.7$D$ that are inclined at 35$^\circ$ relative to the plate. Parameters studied include BR = 0.5 - 1.3, DR = 1.1 - 2.1, VR = 0.3 - 0.9, and MR = 0.16 - 0.9. For LES, two different boundary layers upstream of the film-cooling hole were investigated - one in which a laminar boundary layer was tripped to become turbulent from near the leading edge of the flat plate, and another in which a mean turbulent BL is prescribed directly without any superimposed turbulent fluctuations. For RANS, two different turbulence models were investigated - realizable $k$-$\epsilon$ and $k$-$\omega$ shear-stress-transport (SST). The wall-resolved LES solutions generated are extensively verified and validated using analytical, DNS, and experimental measurements to ensure high quality.

LES results obtained show that having an upstream boundary layer that does not have turbulent fluctuations enhances the cooling effectiveness significantly at low VRs when compared to an upstream boundary layer that resolved the turbulent fluctuations. However, these differences diminish at higher VRs. Instantaneous flow reveals a bifurcation in the jet vorticity as it exits the hole at low VRs, one branch forming the shear-layer vortex, while the other forms the counter-rotating vortex pair. At higher VRs, the shear layer vorticity is found to reverse direction, changing the nature of the turbulence and the heat transfer. Results obtained also show the strength and structure of the turbulence in the film-cooling jet to be strongly correlated to VR.

RANS results obtained show the turbulent and thermal structure of the jets predicted by the two RANS models to differ considerably. However, both models are consistent in underpredicting the spread of the film-cooling jet. The counter-rotating vortex pair dominates the interaction of the jet and crossflow in the near-wall region, and neither RANS model could predict the strength and structure of this interaction. The gradient-diffusion and Boussinesq hypotheses were evaluated by using the LES data. Comparing LES and RANS results shows that $k$-$\epsilon$ tends to overpredict eddy viscosity, while SST tends to underpredict the eddy viscosity. Additionally, both models predict very low values of eddy viscosity near the wall which leads to incorrect Reynolds stresses. While regions of counter-gradient diffusion and stress-strain misalignment were identified in the near-wall region, further above the wall, the jet behaved according to the hypotheses.

The turbulence scaling when VR is fixed at 0.46 and 0.63 was investigated. The LES results show that separation and spreading of the film-cooling jet increase as BR, DR, and MR increase while VR remains constant. For a given VR, the LES predicts an absolute difference between the minimum adiabatic effectiveness of the lowest and highest MRs to be 2 to 5 times greater than those predicted by RANS. This is because RANS with either model cannot respond appropriately to changes in MR. However, RANS can correctly predict that adiabatic effectiveness decreases as VR increases. The LES results show the turbulent kinetic energy and Reynolds stresses near the film-cooling hole to change considerably with MRs at a constant VR, while turbulent heat flux changes negligibly. This suggests that while improved turbulence models for heat flux can improve RANS’ prediction of spreading, capturing trends, however, requires improved modeling of the Reynolds stresses.