Towards a new roughness parametrization through the Effective Distribution function*

Many studies have explored the effects of different roughness shapes and distributions. Efforts have been aimed at finding a statistical descriptor of roughness geometry to replace the equivalent sand grain roughness k_s​, a hydraulic property estimable from the mean velocity profile. Despite advances in understanding of the flow over rough walls, a knowledge gap still remains, in particular how to parametrize the drag and roughness function. DNSs have been performed for a fully developed turbulent channel flow with triangular bars at Re_τ up to 790. For a fixed pitch to height ratio w/k=4 two sets of simulations varying roughness height were analyzed. The first set had 16 triangular bars equally spaced in the streamwise direction w/h=0.4with a constant roughness height k/h=0.1. The second set halved the number of bars but doubled the roughness height to k/h=0.2. Other cases modified the baseline to highlight features like protuberances and wakes affecting downstream roughness. Plotting total drag and roughness function against ES, Sk, or Ku showed significant variation, about 30-40%. The results indicated that parametrization must consider: contribution of elements in larger elements' wake to drag is negligible, pattern and distance effects of roughness elements and the impact of flat regions between rough elements on velocity distribution. These factors were included in the Effective Distribution (ED), revising ES and improving drag correlation by accounting for peaks above mean roughness, wake regions from the highest elements and distances between elements. To further corroborate our previous finding and validate the ED, we applied it to a more complex irregular rough wall generated through the superimposition of sinusoidal functions with random amplitudes showing consistent results with the presented correlation.