Theses and Dissertations

Issuing Body

Mississippi State University


Hodge, B. Keith

Committee Member

Taylor, Robert P.

Committee Member

Hudson, Susan T.

Committee Member

Briley, W. Roger

Date of Degree


Document Type

Dissertation - Open Access


Mechanical Engineering

Degree Name

Doctor of Philosophy


College of Engineering


Department of Mechanical Engineering


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 considers heat transfer from a rough surface to be 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 roughness composed of sparse, ordered, and deterministic elements. Modifications made to the discrete-element roughness method to extend the validation to real surface roughness are detailed. These modifications include accounting for the deviation of the roughness element cross sections from circular configurations, determining the location of the computational "surface" that differs from the physical surface, and accounting for temperature changes along the height of the roughness elements. 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. Two randomly-rough surfaces, two elliptical-analog surfaces, and two cone surfaces were generated for wind-tunnel testing using a three-dimensional printer. 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 planorm area and eccentricity. The cone surfaces were generated by placing conical roughness elements on a flat plate to create surfaces with equivalent values of centerline-averaged height or root-mean-square (RMS) height as the randomly-rough surfaces. The results of the wind tunnel skin friction coefficient and Stanton number measurements and the discrete-element method predictions for each of the six surfaces are presented and discussed. For the randomly-rough surfaces studied, the discrete-element method predictions are within 7% of the experimentally measured skin friction coefficients. The discrete-element predictions are within 16% of the experimentally measured Stanton numbers for the randomly-rough surfaces.