Generalized roughness effects on turbulent boundary layer heat transfer. A discrete element predictive approach for turbulent flow over rough surfaces

A discrete element model for turbulent flow over rough surfaces has been rigorously derived from basic principles. This model includes surface roughness effects as a constituent part of the partial differential equations which describe momentum and energy transport in turbulent flows. The model includes the necessary empirical information on the interaction between the roughness elements and the flow around and between the elements in a general way which does not require experimental data on each specific surface. This empirical information is input via algebraic models for the local element drag coefficient and Nusselt number. These models have been calibrated by comparison with base data sets from surfaces with three-dimensional (distributed) roughness elements. Calculations using the present discrete element model are compared with experimental data from 118 separate experimental runs. The results of these comparisons range from good to excellent. The calculations are shown to compare equally well with both transitionally rough turbulent flow and fully rough turbulent flow without modification of the roughness model. In the course of the present work it was discovered that the definitive data set of Schlichting is flawed. Corrected values are presented for this data set.