Heat Transfer Predictions for U-Shaped Coolant Channels With Skewed Ribs and With Smooth Walls

A computational study was performed for the flow and heat transfer in coolant passages with two legs connected with a U-bend and with dimensionless flow conditions typical of those in the internal cooling passages of turbine blades. The first model had smooth surfaces on all walls. The second model had opposing ribs staggered and angled at 45° to the main flow direction on two walls of the legs, corresponding to the coolant passage surfaces adjacent to the pressure and suction surfaces of a turbine airfoil. For the ribbed model, the ratio of rib height to duct hydraulic diameter equaled 0.1, and the ratio of rib spacing to rib height equaled 10. Comparisons of calculations with previous measurements are made for a Reynolds number of 25,000. With these conditions, the predicted heat transfer is known to be strongly influenced by the turbulence and wall models. The k-e model, the low Reynolds number RNG k-e and the differential Reynolds-stress model (RSM) were used for the smooth wall model calculation. Based on the results with the smooth walls, the calculations for the ribbed walls were performed using the RSM and k-e turbulence models. The high secondary flow induced by the ribs leads to an increased heat transfer in both legs. However, the heat transfer was nearly unchanged between the smooth wall model and the ribbed model within the bend region. The agreement between the predicted segment-averaged and previously-measured Nusselt numbers was good for both cases.