Skin friction and heat transfer for combined roughness and mass addition

A finite-difference solution to the boundary layer equations for flow over rough surfaces with mass addition is presented. The equivalent sand-grain roughness height is not needed, but rather the actual roughness height and spacing is used. The boundary layer equations are cast in a form to account for the blockage effects of roughness elements. The roughness effect is described by a sink (form drag) term in the momentum equation and a source term in the static enthalpy equation. A two-layer algebraic mixing-length model that contains very little empiricism but yet is capable of accounting for roughness height, spacing, geometry, and mass addition is presented. Good agreement is shown to incompressible and compressible flat-plate data with combined roughness and blowing.