Flow in additively manufactured super-rough channels

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 mu m). These super-rough channels pose previously unseen challenges for experimental measurements, data interpretation and roughness modelling. First, it is not clear if measurements at a particular streamwise and spanwise location still provide accurate representation of the mean (time- and plane-averaged) flow. Second, we do not know if the logarithmic layer survives. Third, it is unknown how well previously developed rough-wall models work for these large-scale roughnesses. To answer the above practical questions, we conduct direct numerical simulations of flow in additively manufactured super-rough channels. Three rough surfaces are considered, all of which are obtained from computed tomography scans of additively manufactured surfaces. The roughness' trough to peak sizes are 0.1h, 0.3h and 0.8h, respectively, where h is the intended half-channel height. Each rough surface is placed opposite a smooth wall and the other two rough surfaces, leading to six rough-wall channel configurations. Two Reynolds numbers are considered, namely Re-tau = 180 and Re-tau = 395. We show first that measurements at one streamwise and spanwise location are insufficient due to strong mean flow inhomogeneity across the entire channel, second that the logarithmic law of the wall survives despite the mean flow inhomogeneity and third that the established roughness sheltering model remains accurate. Impact Statement Surface roughness, whose representative element size is comparable to the hydraulic diameter, incurs a significant drag penalty. This large-scale roughness is usually removed in conventional subtractive manufacturing, making small-scale roughness that occupies a few per cent of the boundary layer the rule in fluid engineering. It is therefore not surprising that most rough-wall boundary-layer theories and models are developed for small-scale roughness. The use of new engineering technologies leads to new flow problems, to which conventional theories do not apply. Here, flow in additively manufactured super-rough channels is such a new problem. This paper is the first direct numerical simulation (DNS) study of flows in additively manufactured super-rough channels. We compare our DNS results with the existing theories/models and show where the existing theories and models fail and succeed. In addition to providing benchmark data for a new engineering models they can/cannot trust when dealing with large-scale roughness. This work also impacts fundamental research: our findings, e.g. that the logarithmic law of the wall survives large-scale roughness, motivate revisions of the conventional rough-wall boundary-layer theories.