Effects of small isolated roughness elements on turbulent boundary layers.

A series of six equilibrium turbulent boundary layer flows hais been established with values of H from 1.3 to 2.3, and measurements made in them of the effect on the boundary layer development of a single two- dimensional roughness element of mainly square cross-section mounted near the start of the equilibrium region. It is shown that the local increment of the momentum thickness caused by the element is well-predicted by the flat-plate correlation of Gaudet and Johnson, a correlation which is here shown to be universally valid and that, for all flows except for the most adverse pressure gradient, a satisfactory prediction of the subsequent boundary layer development can be made with the aid of relationships proposed by Professor Bradshaw, for the change in H at the roughness element. For the flow with the largest value of H the prediction method for the development fails even in the absence of the element which, in fact, hats little influence on the flow. The discrepancy between calculation and experiment is much larger than can be accounted for by normal stress terms and the reasons for this discrepancy are not entirely evident. However, the essential outcome of the experiment is clear that the incremental drag of a roughness element depends on wall variables. In consequence, the effect of an element which is of small height compared with the boundary layer thickness is negligible in flows with strongly adverse pressure gradients. It is also demonstrated that the length of the separation region behind small roughness elements decreases as the pressure gradient increases adversely.