Analytical Modeling of Turbine Cascade Leading Edge Heat Transfer Using Skin Friction and Pressure Measurements

The flow near the leading edge stagnation line of a plane turbine cascade airfoil is analyzed using measurements, analytical modeling, and computational fluid dynamics modeling. New measurements of skin friction and pressure are used to show that the aerodynamics of the leading edge, within what we call the stagnation region, are well described by an exact analytical solution for laminar stagnation-point or Hiemenz flow. The skin friction measurements indicate the extent of the stagnation region. The same parameters that characterize Hiemenz flow also characterize stagnation-point potential flow. The thermal resistance of the laminar momentum boundary layer in Hiemenz flow is absent in the inviscid solution. Consequently, the heat transfer in stagnation-point potential flow is greater than the heat transfer in Hiemenz flow. Based on measurements from an earlier study, the highest heat transfer levels in the cascade occur along the leading edge stagnation line. Stagnation-point potential flow provides a close, upper bound for the measured heat transfer at this small but critical location within the stagnation region. This paper describes how to apply the analytical model for predicting cascade stagnation-line heat transfer using only surface pressure calculations.