Predicting Skin Friction and Heat Transfer for Turbulent Flow Over Real Gas Turbine Surface Roughness Using the Discrete Element Method

The discrete element method considers the total aerodynamic drag on a rough surface to be the sum of shear drag on the flat part of the surface and the form drag on the individual roughness elements. The total heat transfer from a rough surface is the sum of convection through the fluid on the flat part of the surface and the convection from each of the roughness elements. The discrete element method has been widely used and validated for predicting heat transfer and skin friction for rough surfaces composed of sparse, ordered, and deterministic elements. Real gas turbine surface roughness is different from surfaces with sparse, ordered, and deterministic roughness elements. Modifications made to the discrete element roughness method to extend the validation to real gas turbine surface roughness are detailed. Two rough surfaces found on high-hour gas turbine blades were characterized using a Taylor-Hobson Form Talysurf Series 2 profilometer. Two rough surfaces and two elliptical-analog surfaces were generated for wind tunnel testing using a three-dimensional printer. The printed surfaces were scaled to maintain similar boundary layer thickness to roughness height ratio in the wind tunnel as found in gas turbine operation. The results of the wind tunnel skin friction and Stanton number measurements and the discrete element method predictions for each of the four surfaces are presented and discussed. The discrete element predictions made considering the gas turbine roughness modifications are within 7% of the experimentally measured skin friction coefficients and are within 16% of the experimentally measured Stanton numbers.