Unsteady Analysis of Blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes

The effect of the upstream wake on the time averaged rotor blade heat transfer was numerically investigated. The geometry and flow conditions of the first stage turbine blade of GE’s $E3$ engine with a tip clearance equal to 2% of the span were utilized. The upstream wake had both a total pressure and temperature deficit. The rotor inlet conditions were determined from a steady analysis of the cooled upstream vane. Comparisons between the time average of the unsteady rotor blade heat transfer and the steady analysis, which used the average inlet conditions of unsteady cases, are made to illuminate the differences between the steady and unsteady calculations. To help in the understanding of the differences between steady and unsteady results on one hand and to evaluate the effect of the total temperature wake on the other, separate calculations were performed to obtain the rotor heat transfer and adiabatic wall temperatures. It was found that the Nusselt number distribution for the time average of unsteady heat transfer is invariant if normalized by the difference in the adiabatic and wall temperatures. It appeared though that near the endwalls the Nusselt number distribution did depend on the thermal wake strength. Differences between steady and time averaged unsteady heat transfer results of up to 20% were seen on the blade surface. Differences were less on the blade tip surface.