Predicting Skin Friction for Turbulent Flow Over Randomly-Rough Surfaces Using the Discrete-Element Method: Part II — Skin Friction Validation

The discrete-element method for predicting skin friction for turbulent flow over rough surfaces considers the drag on the surface to be the sum 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. The discrete-element method has been widely used and validated for roughness composed of sparse, ordered, and deterministic elements. This paper extends the validation of the discrete-element to include real (random and closely packed) surface roughness. To analyze flow over a randomly-rough surface using the discrete-element method, the roughness element blockage fraction and the roughness element cross-section area distributions as a function of height must be determined from surface profilometer measurements. The technique developed for determining these distributions was described in Part 1. This paper, Part 2, describes the modifications that were made to the discrete-element roughness method to extend the validation to real surface roughness. These modifications include accounting for the deviation of the roughness element cross sections from circular configurations and the determination of the location of the computational “surface,” that differs from the physical surface. Two randomly-rough surfaces, two analog surfaces were generated using a three-dimensional printer for wind-tunnel testing. The analog surfaces were created by replacing each random roughness element from the original randomly-rough surface with an elliptical roughness element with the equivalent plan area and eccentricity. The results of the wind tunnel skin friction measurements and the discrete-element method predictions for each of the six surfaces are presented and discussed. For each randomly-rough and analog surface studied, the discrete-element method predictions are within 7% of the experimentally measured skin friction coefficients.