Predicting Skin Friction for Turbulent Flow Over Randomly-Rough Surfaces Using the Discrete-Element Method: Part I — Surface Characterization

The discrete-element method for predicting skin friction for turbulent flow over rough surfaces considers the drag on the surface to result from the combination of the skin friction on the flat part of the surface and the drag on the individual roughness elements that protrude into the boundary layer. To adequately analyze flow over a randomly-rough surface using the discrete-element method, the blockage fraction and the roughness element cross-section area distributions as a function of height must be measured. Taylor, in 1983, proposed a method for evaluating the blockage fraction and cross-sectional areas distributions, assuming circular cross sections, using two-dimensional profilometer traces. With the advent of three-dimensional profilometery, the geometry of a randomly-rough surface can be completely characterized. Two randomly-rough surfaces found on high-hour gas-turbine blades were characterized using a Taylor-Hobson Form Talysurf Series 2 profilometer. A method for using the three-dimensional profilometer output to determine the geometry input required in the discrete-element method for randomly-rough surfaces is presented in this paper, Part 1. Part 2 extends the validation of the discrete-element roughness method to closely-packed, randomly-rough surfaces. The procedure for handling randomly-rough surfaces is described, and the characterizations for the surfaces used to validate the discrete element model in Part 2 are presented.