Mean flow measurements of turbulent boundary layers over porous walls (permeable and rough) with varying pore size (s), permeability (K) and thickness (h) are presented across a wide range of friction Reynolds numbers (Reτ ≈ 2000−18000) and permeability based Reynolds numbers (ReK ≈ 1.5 − 60). The mean wall shear stress was determined using a floating element drag balance and the boundary layer profiles were acquired using hot-wire anemometry. Substrate permeability is shown to increase the magnitude of the mean velocity deficit. The use of a modified indicator function, assuming "universal" values for von-Karman constant (κ = 0.39) supports previous results where a strongly modified logarithmic region was observed. The indicator function was also used to estimate the zero-plane displacement (y d ), the roughness function (∆U + ) and equivalent sandgrain roughness (ks). At high Reynolds numbers, the roughness function data collapses on to the Nikuradse's fully-rough asymptote. However, at low roughness Reynolds numbers (k + s < 100), we observe the flow to be transitionally rough, evolving with Nikuradse-type behaviour. The equivalent sandgrain roughness ks for each substrate appears to include roughness and permeability contributions. These two contributions can be separated using data obtained from the same substrates with different thickness. This may allow us to model the porous wall as a combination of rough and permeable wall.

Abstract

Indirect methods to estimate surface shear stress are commonly used to characterise rough-wall boundary-layer flows. The uncertainty is typically large and often insufficient to carry out quantitative analysis, especially for surface roughness where established scaling and similarity laws may not hold. It is, thus, preferable to rely instead on independent measurement techniques to accurately measure skin friction. The floating element was one of the first to be introduced, and still is the most popular for its features. Although its fundamental principle has remained unchanged, different arrangements have been suggested to overcome its inherent limitations. In this paper, we review some of these designs and further present an alternative that is able to correct for extraneous loads into the drag measurement. Its architecture is based on the parallel-shift linkage, and it features custom-built force transducers and a data acquisition system designed to achieve high signal-to-noise ratios. The smooth-wall boundary-layer flow is used as a benchmark to assess the accuracy of this balance. Values of skin-friction coefficient show an agreement with hot-wire anemometry to within 2% for Re = 4 × 10 3 up to 10 4. A rough surface of staggered distributed cubes with large relative height, ∕h ≃ 10 , is also investigated. Results indicate the flow reaches the fully rough regime, at the measurement location, for the entire range of Reynolds number. Furthermore, the values of skin friction agree with existing estimations from alternative methods.

In-plane velocity measurements from PIV are used to estimate the pressure field above and within the canopy of two staggered arrays of cuboids, with distinct height distributions, via 2D-RANS and 2D-TH. The viability of this approach is examined by first comparing the mean drag profiles against reported wind-tunnel measurements that were carried out under similar test conditions and numerical simulations (LES and DNS). The surface drag is extrapolated from the nearest data point surrounding the roughness elements. Second, estimates of the friction velocity U p and the zero-plane displacement height d p are obtained by integrating the axial pressure difference across each individual obstacle, assuming it is spanwise uniform. These are compared against direct measurements of the wall-shear stress from a floating-element balance and a pressure-tapped cube, as well as against estimates from indirect methods. In addition to mean pressure maps, snapshots of the pressure field are obtained via 2D-TH, based on Taylor's Hypothesis, which are used to compute the RMS of the pressure fluctuations on the surface of a cube. The results indicate that 2D-RANS and 2D-TH perform adequately, providing reasonable estimates of the mean pressure distribution and of the boundary-layer flow parameters, outperforming indirect methods which rely on equilibrium assumptions that are often not verified.

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