Rough-wall Boundary Layers Research Articles

Reynolds number and roughness effects on turbulent stresses in sandpaper roughness boundary layers

Multicomponent turbulence measurements in rough-wall boundary layers are presented and compared to smooth-wall data over a large friction Reynolds number range (δ+). The rough-wall experiments used the same continuous sandpaper sheet as in the study of Squire et al. [J. Fluid Mech. 795, 210 (2016)JFLSA70022-112010.1017/jfm.2016.196]. To the authors' knowledge, the present measurements are unique in that they cover nearly an order of magnitude in Reynolds number (δ+≃2800-17400), while spanning the transitionally to fully rough regimes (equivalent sand-grain-roughness range, ks+≃37-98), and in doing so also maintain very good spatial resolution. Distinct from previous studies, the inner-normalized wall-normal velocity variances, w2, exhibit clear dependencies on both ks+ and δ+ well into the wake region of the boundary layer, and only for fully rough flows does the outer portion of the profile agree with that in a comparable δ+ smooth-wall flow. Consistent with the mean dynamical constraints, the inner-normalized Reynolds shear stress profiles in the rough-wall flows are qualitatively similar to their smooth-wall counterparts. Quantitatively, however, at matched Reynolds numbers the peaks in the rough-wall Reynolds shear stress profiles are uniformly located at greater inner-normalized wall-normal positions. The Reynolds stress correlation coefficient, Ruw, is also greater in rough-wall flows at a matched Reynolds number. As in smooth-wall flows, Ruw decreases with Reynolds number, but at different rates depending on the roughness condition. Despite the clear variations in the Ruw profiles with roughness, inertial layer u, w cospectra evidence invariance with ks+ when normalized with the distance from the wall. Comparison of the normalized contributions to the Reynolds stress from the second quadrant (Q2) and fourth quadrant (Q4) exhibit noticeable differences between the smooth- and rough-wall flows. The overall time fraction spent in each quadrant is, however, shown to be nearly fixed for all of the flow conditions investigated. The data indicate that at fixed δ+ both Q2 and Q4 events exhibit a sensitivity to ks+. The present results are discussed relative to the combined influences of roughness and Reynolds number on the scaling behaviors of boundary layers.

Rough-wall turbulent boundary layers with constant skin friction

A semi-empirical model is presented that describes the development of a fully developed turbulent boundary layer in the presence of surface roughness with length scale$k_{s}$that varies with streamwise distance$x$. Interest is centred on flows for which all terms of the von Kármán integral relation, including the ratio of outer velocity to friction velocity$U_{\infty }^{+}\equiv U_{\infty }/u_{\unicode[STIX]{x1D70F}}$, are streamwise constant. For$Re_{x}$assumed large, use is made of a simple log-wake model of the local turbulent mean-velocity profile that contains a standard mean-velocity correction for the asymptotic fully rough regime and with assumed constant parameter values. It is then shown that, for a general power-law external velocity variation$U_{\infty }\sim x^{m}$, all measures of the boundary-layer thickness must be proportional to$x$and that the surface sand-grain roughness scale variation must be the linear form$k_{s}(x)=\unicode[STIX]{x1D6FC}x$, where$x$is the distance from the boundary layer of zero thickness and$\unicode[STIX]{x1D6FC}$is a dimensionless constant. This is shown to give a two-parameter$(m,\unicode[STIX]{x1D6FC})$family of solutions, for which$U_{\infty }^{+}$(or equivalently$C_{f}$) and boundary-layer thicknesses can be simply calculated. These correspond to perfectly self-similar boundary-layer growth in the streamwise direction with similarity variable$z/(\unicode[STIX]{x1D6FC}x)$, where$z$is the wall-normal coordinate. Results from this model over a range of$\unicode[STIX]{x1D6FC}$are discussed for several cases, including the zero-pressure-gradient ($m=0$) and sink-flow ($m=-1$) boundary layers. Trends observed in the model are supported by wall-modelled large-eddy simulation of the zero-pressure-gradient case for$Re_{x}$in the range$10^{8}{-}10^{10}$and for four values of$\unicode[STIX]{x1D6FC}$. Linear streamwise growth of the displacement, momentum and nominal boundary-layer thicknesses is confirmed, while, for each$\unicode[STIX]{x1D6FC}$, the mean-velocity profiles and streamwise turbulent variances are found to collapse reasonably well onto$z/(\unicode[STIX]{x1D6FC}x)$. For given$\unicode[STIX]{x1D6FC}$, calculations of$U_{\infty }^{+}$obtained from large-eddy simulations are streamwise constant and independent of$Re_{x}$when this is large. The present results suggest that, in the sense that$U_{\infty }^{+}(\unicode[STIX]{x1D6FC},m)$is constant, these flows can be interpreted as the fully rough limit for boundary layers in the presence of small-scale linear roughness.

Wind resource assessment in heterogeneous terrain.

High-resolution particle image velocimetry data obtained in rough-wall boundary layer experiments are re-analysed to examine the influence of surface roughness heterogeneities on wind resource. Two different types of heterogeneities are examined: (i) surfaces with repeating roughness units of the order of the boundary layer thickness (Placidi & Ganapathisubramani. 2015 J. Fluid Mech.782, 541-566. (doi:10.1017/jfm.2015.552)) and (ii) surfaces with streamwise-aligned elevated strips that mimic adjacent hills and valleys (Vanderwel & Ganapathisubramani. 2015 J. Fluid Mech.774, 1-12. (doi:10.1017/jfm.2015.228)). For the first case, the data show that the power extraction potential is highly dependent on the surface morphology with a variation of up to 20% in the available wind resource across the different surfaces examined. A strong correlation is shown to exist between the frontal and plan solidities of the rough surfaces and the equivalent wind speed, and hence the wind resource potential. These differences are also found in profiles of [Formula: see text] and [Formula: see text] (where U is the streamwise velocity), which act as proxies for thrust and power output. For the second case, the secondary flows that cause low- and high-momentum pathways when the spacing between adjacent hills is beyond a critical value result in significant variations in wind resource availability. Contour maps of [Formula: see text] and [Formula: see text] show a large difference in thrust and power potential (over 50%) between hills and valleys (at a fixed vertical height). These variations do not seem to be present when adjacent hills are close to each other (i.e. when the spacing is much less than the boundary layer thickness). The variance in thrust and power also appears to be significant in the presence of secondary flows. Finally, there are substantial differences in the dispersive and turbulent stresses across the terrain, which could lead to variable fatigue life depending on the placement of the turbines within such heterogeneous terrain. Overall, these results indicate the importance of accounting for heterogeneous terrain when siting individual turbines and wind farms.This article is part of the themed issue 'Wind energy in complex terrains'.

Applicability of Taylor’s hypothesis in rough- and smooth-wall boundary layers

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number ($\unicode[STIX]{x1D6FF}^{+}\approx 12\,000$). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor’s frozen turbulence hypothesis (Proc. R. Soc. Lond. A, vol. 164, 1938, pp. 476–490). The same applies for the streamwise velocity spectra on rough walls. For the wall-normal velocity spectra, however, clear differences are observed between the true spatial and temporally convected spectra. For the rough-wall spectra, a correction is derived to enable accurate prediction of wall-normal velocity length scales from measurements of their time scales, and the implications of this correction are considered. Potential violations to Taylor’s hypothesis in flows above perturbed walls may help to explain conflicting conclusions in the literature regarding the effect of near-wall modifications on outer-region flow. In this regard, all true spatial and corrected spectra presented here indicate structural similarity in the outer region of smooth- and rough-wall flows, providing evidence for Townsend’s wall-similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956).

Turbulent boundary layer response to the introduction of stable stratification

The response of an initially neutral rough-wall turbulent boundary layer to a change in wall temperature is investigated experimentally. The change causes a localized peak in stable stratification that diffuses and moves away from the wall with downstream distance. The streamwise and wall-normal components of turbulent velocity fluctuations are damped at similar rates, even though the stratification only directly impacts the wall-normal component. The Reynolds shear profiles reveal the growth of an internal layer that scales approximately with the bulk Brunt–Väisälä frequency.

Smooth- and rough-wall boundary layer structure from high spatial range particle image velocimetry

Two novel particle image velocimetry arrangements are used to make true spatial comparisons between high Reynolds number smooth- and rough-wall boundary layer flows across a very wide range of streamwise scales.

Inner–outer interactions in rough-wall turbulence

ABSTRACTHere we revisit the inner–outer interaction model (IOIM) of Marusic et al. (Science, vol. 329, 2010, pp. 193–196) that enables the prediction of statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows from a large-scale velocity signature measured in the outer region of the flow. The model is characterised by two empirically observed inner–outer interactions: superposition of energy from outer region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale ‘universal’ signal (u*), which in smooth-wall flows is Reynolds number invariant. In the present study, the inner–outer interactions in rough-wall turbulent boundary layers are examined within the framework of the IOIM. Simultaneous two-point hot-wire anemometry measurements enable quantification, via the model parameters, of the strengths of superposition and amplitude modulation effects in a rough-wall flow, and these are compared to a smooth-wall flow. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer region similarity. Using the model parameters obtained from the two-point measurements, predictions of inner region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u* signal does depend on roughness Reynolds number (k+s), but is robust to changes in friction Reynolds number (δ+). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number. The implications of the present results on the suitability of the IOIM as a predictive tool in rough-wall turbulence are discussed.

Large eddy simulations and parameterisation of roughness element orientation and flow direction effects in rough wall boundary layers

ABSTRACTWe conduct a series of large eddy simulations (LES) of turbulent boundary layers over arrays of cuboidal roughness elements at arbitrary orientation angles (non-frontal orientations with the incident flow). Flow response to changing roughness orientation is systematically studied at two ground coverage densities, λp = 0.06 and 0.11. As expected, the effective roughness heights zo measured from LES are higher for λp = 0.11 than for λp = 0.06, although appreciable changes both in zo and wall shear stress (friction velocity) are observed at both ground coverage densities as the roughness orientation angle changes. This suggests the necessity of accounting for detailed rough wall topology (including more information than just λp, λf) when relating rough wall morphology to its aerodynamic properties. To this end, a recently developed analytical rough wall parameterisation is used to predict the aerodynamic properties of the simulated rough surfaces. In this rough wall model, wake interactions among roughness elements are explicitly modelled using the concept of sheltering height and exponential attenuation coefficient. As a result, the parameterisation is responsive to detailed ground roughness arrangements and flow conditions, including roughness height variations, element orientation, incident flow direction, transverse displacements, etc. Model-predicted effective roughness heights, wall stress, mean velocity at the height of the roughness, and in some cases displacement height, are compared against the LES measurements from this study as well as numerical/experiment measurements from other authors. The predictions from the model are found to agree well with the measurements both in trends and in absolute values, thus extending the applicability of the analytical rough wall model to more general surfaces than those previously tested.

High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

A scaling law for the shear-production range of second-order structure functions

Dimensional analysis suggests that the dissipation length scale ($\ell _{{\it\epsilon}}=u_{\star }^{3}/{\it\epsilon}$) is the appropriate scale for the shear-production range of the second-order streamwise structure function in neutrally stratified turbulent shear flows near solid boundaries, including smooth- and rough-wall boundary layers and shear layers above canopies (e.g. crops, forests and cities). These flows have two major characteristics in common: (i) a single velocity scale, i.e. the friction velocity ($u_{\star }$) and (ii) the presence of large eddies that scale with an external length scale much larger than the local integral length scale. No assumptions are made about the local integral scale, which is shown to be proportional to$\ell _{{\it\epsilon}}$for the scaling analysis to be consistent with Kolmogorov’s result for the inertial subrange. Here${\it\epsilon}$is the rate of dissipation of turbulent kinetic energy (TKE) that represents the rate of energy cascade in the inertial subrange. The scaling yields a log-law dependence of the second-order streamwise structure function on ($r/\ell _{{\it\epsilon}}$), where$r$is the streamwise spatial separation. This scaling law is confirmed by large-eddy simulation (LES) results in the roughness sublayer above a model canopy, where the imbalance between local production and dissipation of TKE is much greater than in the inertial layer of wall turbulence and the local integral scale is affected by two external length scales. Parameters estimated for the log-law dependence on ($r/\ell _{{\it\epsilon}}$) are in reasonable agreement with those reported for the inertial layer of wall turbulence. This leads to two important conclusions. Firstly, the validity of the$\ell _{{\it\epsilon}}$-scaling is extended to shear flows with a much greater imbalance between production and dissipation, indicating possible universality of the shear-production range in flows near solid boundaries. Secondly, from a modelling perspective,$\ell _{{\it\epsilon}}$is the appropriate scale to characterize turbulence in shear flows with multiple externally imposed length scales.

Wall-drag measurements of smooth- and rough-wall turbulent boundary layers using a floating element

The mean wall shear stress, $$\overline{\tau }_w$$ , is a fundamental variable for characterizing turbulent boundary layers. Ideally, $$\overline{\tau }_w$$ is measured by a direct means and the use of floating elements has long been proposed. However, previous such devices have proven to be problematic due to low signal-to-noise ratios. In this paper, we present new direct measurements of $$\overline{\tau }_w$$ where high signal-to-noise ratios are achieved using a new design of a large-scale floating element with a surface area of 3 m (streamwise) × 1 m (spanwise). These dimensions ensure a strong measurement signal, while any error associated with an integral measurement of $$\overline{\tau }_w$$ is negligible in Melbourne’s large-scale turbulent boundary layer facility. Wall-drag induced by both smooth- and rough-wall zero-pressure-gradient flows are considered. Results for the smooth-wall friction coefficient, $$C_f \equiv \overline{\tau }_w/q_{\infty }$$ , follow a Coles–Fernholz relation $$C_f = \left[ 1/\kappa \ln \left( Re_{\theta }\right) + C\right] ^{-2}$$ to within 3 % ( $$\kappa = 0.38$$ and $$C = 3.7$$ ) for a momentum thickness-based Reynolds number, $$Re_{\theta } > 15{,}000$$ . The agreement improves for higher Reynolds numbers to <1 % deviation for $$Re_{\theta } > 38{,}000$$ . This smooth-wall benchmark verification of the experimental apparatus is critical before attempting any rough-wall studies. For a rough-wall configuration with P36 grit sandpaper, measurements were performed for $$10{,}500< Re_{\theta } < 88{,}500$$ , for which the wall-drag indicates the anticipated trend from the transitionally to the fully rough regime .

Crosshatch roughness distortions on a hypersonic turbulent boundary layer

The effects of periodic crosshatch roughness (k+ = 160) on a Mach 4.9 turbulent boundary layer (Reθ = 63 000) are examined using particle image velocimetry. The roughness elements generate a series of alternating shock and expansion waves, which span the entire boundary layer, causing significant (up to +50% and −30%) variations in the Reynolds shear stress field. Evidence of the hairpin vortex organization of incompressible flows is found in the comparative smooth-wall boundary layer case (Reθ = 47 000), and can be used to explain several observations regarding the rough-wall vortex organization. In general, the rough-wall boundary layer near-wall vortices no longer appear to be well-organized into streamwise-aligned packets that straddle relatively low-speed regions like their smooth-wall counterpart; instead, they lean farther away from the wall, become more spatially compact, and their populations become altered. In the lower half of the boundary layer, the net vortex swirling strength and outer-scaled Reynolds stresses increase relative to the smooth-wall case, and actually decrease in the outer half of the boundary layer, as ejection and entrainment processes are strengthened and weakened in these two regions, respectively. A spectral analysis of the data suggests a relative homogenizing of the most energetic scales near Λ = ∼ 0.5δ across the rough-wall boundary layer.

Shared dynamical features of smooth- and rough-wall boundary-layer turbulence

The structure of smooth- and rough-wall turbulent boundary layers is investigated using existing data and newly acquired measurements derived from a four element spanwise vorticity sensor. Scaling behaviours and structural features are interpreted using the mean momentum equation based framework described for smooth-wall flows by Klewicki (J. Fluid Mech., vol. 718, 2013, pp. 596–621), and its extension to rough-wall flows by Mehdiet al.(J. Fluid Mech., vol. 731, 2013, pp. 682–712). This framework holds potential relative to identifying and characterizing universal attributes shared by smooth- and rough-wall flows. As prescribed by the theory, the present analyses show that a number of statistical features evidence invariance when normalized using the characteristic length associated with the wall-normal transition to inertial leading-order mean dynamics. On the inertial domain, the spatial size of the advective transport contributions to the mean momentum balance attain approximate proportionality with this length over significant ranges of roughness and Reynolds number. The present results support the hypothesis of Mehdiet al., that outer-layer similarity is, in general, only approximately satisfied in rough-wall flows. This is because roughness almost invariably leaves some imprint on the vorticity field; stemming from the process by which roughness influences (generally augments) the near-wall three-dimensionalization of the vorticity field. The present results further indicate that the violation of outer similarity over regularly spaced spanwise oriented bar roughness correlates with the absence of scale separation between the motions associated with the wall-normal velocity and spanwise vorticity on the inertial domain.

Self-preservation in a zero pressure gradient rough-wall turbulent boundary layer

A self-preservation (SP) analysis is carried out for a zero pressure gradient (ZPG) rough-wall turbulent boundary layer with a view to establishing the requirements of complete SP (i.e. SP across the entire layer) and determining if these are achievable. The analysis shows that SP is achievable in certain rough-wall boundary layers (irrespectively of the Reynolds number$Re$), when the mean viscous stress is zero or negligible compared to the form drag across the entire boundary layer. In this case, the velocity scale$u^{\ast }$must be constant, the length scale$l$should vary linearly with the streamwise distance$x$and the roughness height$k$must be proportional to$l$. Although this result is consistent with that of Rotta (Prog. Aeronaut. Sci., vol. 2 (1), 1962, pp. 1–95), it is derived in a more rigorous manner than the method employed by Rotta. Further, it is noted that complete SP is not possible in a smooth-wall ZPG turbulent boundary layer. The SP conditions are tested against published experimental data on both a smooth wall (Kulandaivelu, 2012, PhD thesis, The University of Melbourne) and a rough wall, where the roughness height increases linearly with$x$(Kamedaet al.,J. Fluid Sci. Technol., vol. 3 (1), 2008, pp. 31–42). Complete SP in a ZPG rough-wall turbulent boundary layer seems indeed possible when$k\propto x$.

Recycling inflow method for simulations of spatially evolving turbulent boundary layers over rough surfaces

ABSTRACTThe technique by Lund et al. to generate turbulent inflow for simulations of developing boundary layers over smooth flat plates is extended to the case of surfaces with roughness elements. In the Lund et al. method, turbulent velocities on a sampling plane are rescaled and recycled back to the inlet as inflow boundary condition. To rescale mean and fluctuating velocities, appropriate length scales need be identified and for smooth surfaces, the viscous scale lν = ν/uτ (where ν is the kinematic viscosity and uτ is the friction velocity) is employed for the inner layer. Different from smooth surfaces, in rough wall boundary layers the length scale of the inner layer, i.e. the roughness sub-layer scale ld, must be determined by the geometric details of the surface roughness elements and the flow around them. In the proposed approach, it is determined by diagnosing dispersive stresses that quantify the spatial inhomogeneity caused by the roughness elements in the flow. The scale ld is used for rescaling in the inner layer, and the boundary layer thickness δ is used in the outer region. Both parts are then combined for recycling using a blending function. Unlike the blending function proposed by Lund et al. which transitions from the inner layer to the outer layer at approximately 0.2δ, here the location of blending is shifted upwards to enable simulations of very rough surfaces in which the roughness length may exceed the height of 0.2δ assumed in the traditional method. The extended rescaling–recycling method is tested in large eddy simulation of flow over surfaces with various types of roughness element shapes.

A new method for measuring turbulent heat fluxes using PIV and fast-response cold-wires

A new method for measuring turbulent heat fluxes using a combination of particle image velocimetry and a nanoscale fast-response cold-wire is tested by examining a rough-wall turbulent boundary layer subject to weakly stable stratification. The method has the advantages of simple calibration and setup, as well as providing spatial correlations of velocity and temperature and their associated integral length scales. The accuracy of using Taylor’s hypothesis when employing a large field of view is investigated. Heat flux, velocity–temperature correlation coefficients and turbulent Prandtl number profiles, as well as spatial velocity and temperature correlations, are presented.

Generating an artificially thickened boundary layer to simulate the neutral atmospheric boundary layer

We aim to generate an artificially thickened boundary layer in a wind tunnel with properties similar to the neutral atmospheric boundary layer. We implement a variant of Counihan's technique which uses a combination of a castellated barrier, elliptical vortex generators, and surface roughness to create a thick boundary layer in a relatively short wind tunnel. We demonstrate an improved spanwise uniformity when compared to Counihan's original design by using a tighter vortex generator spacing with a smaller wedge angle which keeps the frontal area approximately constant while keeping the turbulence intensity and power spectral density unchanged. With this arrangement we were able to generate a 1:1000 scale atmospheric boundary layer at Reθ∼106 displaying logarithmic mean velocity behavior, a constant stress region, and turbulence intensities consistent with atmospheric boundary layer measurements and high Reynolds number laboratory rough-wall boundary layers. In addition, the power spectral density of the longitudinal velocity fluctuations agrees well with von Kármán's model spectrum, and the turbulence integral length scale agrees well with data from atmospheric boundary layer measurements.

Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers

Large-scale secondary flows can sometimes appear in turbulent boundary layers formed over rough surfaces, creating low- and high-momentum pathways along the surface (Barros &amp; Christensen, J. Fluid Mech., vol. 748, 2014, R1). We investigate experimentally the dependence of these secondary flows on surface/flow conditions by measuring the flows over streamwise strips of roughness with systematically varied spanwise spacing. We find that the large-scale secondary flows are accentuated when the spacing of the roughness elements is roughly proportional to the boundary layer thickness ${\it\delta}$, and do not appear for cases with finer spacing. Cases with coarser spacing also generate ${\it\delta}$-scale secondary flows with tertiary flows in the spaces in between. These results show that the ratio of the spanwise length scale of roughness heterogeneity to the boundary layer thickness is a critical parameter for the occurrence of these secondary motions in turbulent boundary layers over rough walls.

Drag of a turbulent boundary layer with transverse 2D circular rods on the wall

In this paper, we present the results of a turbulent boundary layer developing over a rod-roughened wall with a spacing of \(\lambda /k = 8\) (\(\lambda\) is the spacing between two adjacent roughness elements, and \(k\) is the rod diameter). Static pressure measurements are taken around a single roughness element to accurately determine the friction velocity, \(U_\tau\) and the error in the origin, \(d_0\), which are the two prominent issues that surround rough-wall boundary layers. In addition, velocity measurements are taken at several streamwise locations using hot-wire anemometry to obtain \(C_\mathrm{f}\) from the momentum integral equation. Results showed that both methods give consistent values for \(U_\tau\), indicating that the contribution of the viscous drag over this rough wall is negligible. This supports the results of Perry et al. (J Fluid Mech 177:437–466, 1969) and Antonia and Luxton (J Fluid Mech 48(04):721–761, 1971) in a boundary layer and of Leonardi et al. (2003) in a channel flow but does not agree with those of Furuya et al. (J Fluids Eng 98(4):635–643, 1976). The results show that both \(U_{\tau }\) and \(d_0\) can be unambiguously measured on this particular rough wall. This paves the way for a proper comparison between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.

Effects of upstream roughness and Reynolds number on separated and reattached turbulent flow

This paper presents experimental investigation of upstream roughness and Reynolds number effects on the recirculation region over a smooth forward facing step. The upstream rough wall was produced from 1.5 mm sand grains and the Reynolds number based on step height, Reh, was varied from 2040 to 9130 for both the upstream smooth and rough walls. For the smooth wall, the reattachment length increased monotonically with Reh to an asymptotic value of 2.2 step heights for Reh ≥ 6380. Upstream roughness reduced the reattachment length by 44% because of larger momentum deficit and higher turbulence level in the rough wall boundary layer. The mean velocities and Reynolds stresses were also reduced by roughness. The Reynolds shear stress and production of turbulent kinetic energy showed high negative values at the leading edge of the step indicating counter-gradient diffusion. The implications of these results for standard eddy viscosity models are discussed.