Advanced Reentry Aeromechanics. Volume I. A Reynolds Stress Model for Boundary Layer Transition with Application to Rough Surfaces

A theory based on the use of second-order moment equations is presented for transitional and turbulent boundary layer flows. The technique yields accurate predictions for various fully turbulent boundary layers, including those affected by pressure gradients and surface roughness. Although the model has yet to be adequately developed for treating transition induced by free-stream turbulence, a method is presented that addresses wall-roughness dominated transition. Using an idealized representation of distributed roughness elements, the disturbances introduced by the elements are described by wake relations and are handled as distributed source or sink terms in the governing relations for mean momentum and fluctuating energy. Representation of actual roughness distributions should be feasible in computations performed with this model. The effects of roughness size and shape on transition are evaluated, and transition is found to be most sensitive to the location of the peaks of the roughness elements. Calculations performed to date compare satisfactorily with the transition measurements on sand paper-roughened flat plates in low speed flow. See also Volume 2, ADA019517.