Turbulent Flows Over Rough Surfaces

Reliable prediction of drag due to rough wall-bounded turbulent fluid flow remains a challenge in the energy and transportation industry. At the moment, the only accurate methods that predict drag are computationally expensive direct numerical simulations (DNS) or customised experimental rigs that implement the exact wall surface of interest. These solutions are not practical. The aim of my PhD is to investigate the underlying physics to lay the foundations for a predictive model.
When the surface is only slightly rough, the velocity profiles away from the wall are smooth wall like and the drag increase can be calculated and modelled using the concept of virtual origins. However, when the wall is very rough, the velocity profiles are altered relative to the smooth-wall case. Therefore, the concept of virtual origins is not sufficient to model the drag increase.

The time-averaged flow around an individual roughness element looks like the flow around a bluff body. The effect of this flow caused by the individual roughness elements propagates away from the wall. For my PhD, I want to investigate whether this time-averaged flow can be used to predict the change in the velocity profiles relative to the smooth-wall case. Not only would this change the way we think about rough wall-bounded flows, but it would also reduce the computation time of drag prediction significantly.