Development of a Design Model for Airfoil Leading Edge Film Cooling Free

Leading edge showerhead cooling designs represent an important feature of certain classes of high temperature turbine airfoils. This paper outlines a methodology for predicting the surface temperatures of showerhead designs with spanwise injection through an array of discrete holes. The paper describes a series of experiments and analyses on scaled cylinder models with injection through holes inclined at 20, 30, 45, and 90 degrees for typical radial and circumferential spacing-to-diameter ratios of 10 and 4, respectively. The experiments were conducted in a wind tunnel on several stainless steel test specimens in which flow and heat transfer parameters were measured over the simulated airfoil leading edge surfaces. Based on the experiments, an engineering design model is proposed that treats the gas-to-surface heat transfer coefficient with film cooling in a manner suggested by a recent Purdue-NASA investigation and includes the important contribution of upstream (coolant inlet face) heat transfer. The experiments suggest that the averaged film cooling effectiveness in the showerhead region is primarily influenced by the inclination of the injection holes. The effectiveness parameter is not strongly affected by variations in coolant-to-gas stream pressure ratio, freestream Mach number, gas-to-coolant temperature ratio and gas stream Reynolds number. This is appropriately reflected in the design model in which the increase in coolant side heat transfer coefficient (with blowing ratio) is essentially offset by a simultaneous increase in the gas side film coefficient. The model is also employed to determine (inferentially) the average Stanton number reduction parameter for a series of pressure ratios varying from 1.004 to 1.3, Mach numbers ranging from 0.1 to 0.2, temperature ratios between 1.6 and 2.0, and Reynolds numbers ranging from 3.5 × 10⁴ to 9.0 × 10⁴. Design capabilities of the analytical model are explored for typical high temperature first stage turbine vanes and rotor blades operating at rotor inlet temperatures in excess of 1644°K.