An Analytical Study of the Effects of Surface Roughness on Boundary-Layer Transition

Abstract : The effects of surface roughness on the transition of a laminar boundary layer are basically two-fold: (1) it can distort the mean velocity and temperature profiles thus altering the stability characteristics of the layer and (2) it can induce additional disturbances to the boundary layer which may lead to an earlier transition. Only the first of these effects is considered in this report. Three different types of surface roughness are investigated here; distributed roughness, surface waviness, and a single two-dimensional bump. An analytical model which describes the effect of distributed roughness on the mean flow and its stability is described. This model is further validated by comparison with Achenbach's experimental results and is then applied to the flow about an underwater body in order to illustrate the effects of surface roughness in a more realistic situation. Surface irregularities can play a dominant role in determining the practical limit for the application of boundary-layer control techniques. The present distributed roughness model as incorporated into the TAPS code can provide a reasonable prediction of its effect in the presence of boundary-layer control techniques (shaping, heating, suction) on the transition location for an underwater vehicle.