Flow resistance over heterogeneous roughness made of spanwise-alternating sandpaper strips

The Reynolds number dependent flow resistance of heterogeneous rough surfaces is largely unknown at present. The present work provides novel reference data for spanwise-alternating sandpaper strips as one idealized case of a heterogeneous rough surface. Experimental data are presented and analysed in direct comparison with drag measurements of homogeneous sandpaper surfaces and numerical simulations. Based on the homogeneous roughness data the related challenges and sensitivities for the evaluation of roughness functions from experiments and simulations are discussed. A hydraulic channel height is suggested as an alternative measure for the drag impact of rough surfaces in internal flows.
For the investigated heterogeneous roughness it is found that turbulent flow does not exhibit a fully-rough flow behaviour, indicating that the assignment of an equivalent sand grain height as commonly applied for homogeneous roughness is not possible. A prediction of the drag behaviour of rough strips based on an average between rough and smooth drag curves appears promising, but requires further refinement in order to capture the impact of turbulent secondary flows and spatial transients linking smooth and rough surface parts.
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While turbulent secondary flow induced by the roughness strips yield significant spanwise variation of the mean velocity profile for the investigated rough strips we show that the spanwise averaged velocity profiles collapse reasonably well with a smooth or homogeneous rough wall flow. This allows to extract a global roughness function from the spanwise averaged flow field in good agreement with the one deduced from global pressure drop measurements.