Rough Flow Research Articles

Comparison of statistical behavior of wall-attached motions in rough and smooth open channel flows

A set of high-resolution, time-resolved particle image velocimetry measurements were conducted in an open channel, with closely arranged glass spheres of 6 mm used to rough the bed, at low to moderate Reynolds numbers (Reτ≈ 600–2000) and intermediate to high relative submergences (h/ks = 6.3–14.7, where h is the flow depth and ks is the equivalent roughness height). Analyses of the wall-attached motions (WAMs) in rough-wall open channel flows (OCFs) are performed using linear coherence spectra at various wall-normal positions, and results of two smooth-wall OCFs are also included for comparison (Reτ≈ 500 and 900). The WAMs in rough-wall OCFs exhibit self-similar properties in the region of 0.2 <y/h< 0.8 (y is the wall-normal position and h is the flow depth), where the critical wavelength of WAMs (denoted as λxWA) increases linearly with y. Furthermore, WAMs in rough OCFs have larger streamwise wavelengths (λxWA≈ 25 y) and inclination angles (θuuWA≈ 18°) compared to their smooth-wall counterparts (λxWA≈ 18.3 y, θuuWA≈ 14°). The strength of WAMs in rough OCFs was lower than that in smooth OCFs, due to the effects of rough wall elements.

Flow-Sediment Interaction and Formation Mechanism of Sediment Longitudinal Streaky Structures in Rough Channel Flows

Flow-Sediment Interaction and Formation Mechanism of Sediment Longitudinal Streaky Structures in Rough Channel Flows

Performance study on a new solar air heater for space heating: A numerical and experimental study

The need to address energy challenges and environmental pollution has led researchers to focus on utilizing solar energy. In this study, a new solar air heater collector system was developed that incorporates arc-shaped wire roughness and external airflow recycling. The system performance was evaluated under various conditions using energy conservation equations and a semi-analytical method for modeling. The results were validated, confirming the method’s accuracy. The findings revealed that the hybrid system significantly improved energy and exergy efficiencies at lower mass flow rates. Increasing the airflow recycle ratio up to 3 in conditions of constant roughness and low mass flow rates enhanced collector performance. However, at high flow rates and recycle ratios, exergy efficiency decreased due to increased pressure drop, despite a rise in energy efficiency, making it less effective than a simple collector system. The results show that the temperature increase is not so much from a mass flow rate of more than 0.05 kg/s. The existence of considered artificial roughness has caused an increase in temperature, especially in mass flow rates of less than 0.035 kg/s.

Transition to turbulence in rough plane Couette flow

This DNS study considers transition to turbulence in plane Couette flow (pCf) with a rough stationary wall and a smooth moving wall. The roughness elements are square ribs of height $k=0.2h$ (where $h$ is the half-channel height). Two different pitch separations, $\lambda =2k$ and $10k$ , are considered, i.e. d-type and k-type roughness, respectively. The transition in both rough pCf cases takes place through a stage of alternate laminar–turbulent bands aligned in an oblique fashion. However, roughness causes a shift in the transitional Reynolds number ( $Re$ ) range. In the k-type roughness, stable bands are observed in the range $Re \in [300, 325]$ , which is a downwards shift from the transitional $Re$ range for the smooth pCf ( $Re \in [325,400]$ ). The d-type roughness, on the other hand, surprisingly shifts the transitional $Re$ range upwards to $Re \in [350,425]$ . This peculiar behaviour is associated with the ability of the ribs to shed and regenerate vorticity. Large-scale components extracted using a filtering process relate to the transition bands and flow parallel to the oblique laminar–turbulent boundaries. Counter-rotating vortices are present in the turbulent regions of the flow field, which exist in tandem with the high- and low-velocity streaks. Another interesting observation is the secondary Reynolds shear stresses, $-\overline {v^{\prime }u^{\prime }}$ and $-\overline {w^{\prime }v^{\prime }}$ , which are non-zero in the transitional regime, in contrast to the turbulent regime where they are negligible.

Modeling of non-equilibrium suspended sediment transport process in open channel flows with vegetation

A mathematical model based on advection-diffusion theory is established to study the non-equilibrium sediment transport process in vegetated channels. The effects of vegetation on velocity distribution and sediment diffusion coefficients were considered, respectively. Validation against experimental data from flume studies confirms the model's ability to accurately predict the longitudinal sediment deposition rate and the vertical distribution of suspended sediment concentration (SSC). A comparative analysis of three sediment diffusion coefficient formulations indicates that the linear-exponential formula provides a more precise estimate of εsz, and the linear-exponential formula performs well in predicting the turbulent diffusion coefficients of both rigid and flexible vegetation when gently swaying. Moreover, the distance required for SSC to regain equilibrium is influenced by the submergence level of the vegetation canopy. At lower submergence levels, the canopy shear vortices significantly affect the vertical exchange of sediment, and the sediment diffusion coefficients exhibit pronounced stratification near the vegetation canopy. An increase in vegetation density at these lower submergence levels intensifies the shear vortices, thereby extending the distance needed for SSC to reach equilibrium. At higher submergence levels, the impact of canopy shear vortices is lessened, which reduces sediment diffusion coefficient stratification characteristics, and the flow is similar to rough boundary layer flow. An increase in vegetation density increases flow resistance, which shortens the distance required for SSC to attain equilibrium. However, further efforts are required to explore turbulent characteristics with highly flexible vegetation motion and the grain size distribution of non-uniform sediments in vegetated flows.

Relative size matters: Spawning substrate roughness size and spacing affect egg dislodgement and retention in the benthos

AbstractThe consequences of hydrodynamic effects on survival of embryonic benthic organisms remain unknown. This is because the interaction of hydrodynamics and substrate roughness is complex, but it can be conceptualized in two dimensions by roughness flow regimes (isolated, wake interference, and skimming flow) or roughness types (k‐ and d‐type). We examined the effect of different roughness flow regimes/roughness types and roughness heights (k) on the dislodgement of walleye (Sander vitreus) eggs (2 mm diameter, ⌀) using a wall jet apparatus. We expected that lower wall shear stress (τw) would be required for dislodgement in more‐exposed/less‐sheltered roughness type/flow regimes (i.e., k‐type/isolated roughness flow) and when k ≤ ⌀. Surprisingly, the opposite was found, indicating that other mechanism(s) are also responsible for egg dislodgement on these rough surfaces. Hydrodynamic sheltering occurred when flow was directed over exposed eggs (k ≤ ⌀) adjacent to roughness elements effectively increasing their width, and thus requiring higher τw for rolling and then ejection. When k > ⌀, eggs dislodgement likely occurred via the lower pressure in the eddies recirculating in the groove width between roughness elements, rather than due to τw. These results indicate the relevance of heterogeneous sorting and sizing of substrate elements to provide suitable spawning habitats in benthic environments.

Electromagnetohydrodynamic flow and thermal performance in a rotating rough surface microchannel

Rough surfaces in microchannels effectively enhance liquid mixing, thermal performance, and chemical reactions in electrically actuated microfluidic devices. Rotation of the microchannel with surface roughness intensifies this enhancement. We investigate the combined effects of electromagnetohydrodynamics and surface roughness on transient rotating flow in microchannels. We present a mathematical model considering the variable zeta potential, heat transfer characteristics, and entropy generation within the microchannel. We obtain analytical solutions using the separation of variables method and Fourier series expansion. The surface roughness of the microchannel, when combined with rotation, impacts the temperature enhancement. Higher rotation rates result in the formation of multiple vortices. The secondary flow pushes the primary velocity toward the boundary layer, which affects the flow pattern. Surface roughness and electroosmotic flow significantly affect secondary flow, resulting in complex flow patterns and reversals. The interaction between centrifugal and viscous forces results in maximum velocities at the boundary layers. Higher roughness and electromagnetic effects enhance temperature by intensifying fluid-solid friction and joule heating. Surface roughness causes an increase in wall shear stress and friction factor, resulting in a higher Poiseuille number. Moreover, surface roughness increases entropy production by enhancing fluid mixing and internal friction despite improved heat transfer. Higher rotation also elevates entropy generation due to additional vortices induced by secondary flow.

Revisiting wave friction factors for rough turbulent flow

The wave friction factor 𝑓𝑤 and the phase lead of the seabed shear stress over the free stream velocity 𝜑 for rough turbulent flow are revisited by utilizing the similarity theory used by Myrhaug (1989). Results are obtained for 𝑓𝑤 and 𝜑 by determining the similarity coefficients using the Dixen et al. (2008) data for large bed roughness. Comparisons are made with other experimental data and wave friction factor formulae. As a result, an approximation for 𝑓𝑤 by disregarding the phase 𝜑 is recommended covering a wide range of amplitude-to-roughness ratios.

Numerical Simulation of Non-Matching Rough Fracture Seepage

Natural rock fractures often exhibit non-matching characteristics at certain scales, leading to uneven aperture distributions that significantly affect fluid flow. This study investigates the impact of the mismatch between the upper and lower surfaces on the flow through three-dimensional rough fractures. By applying fractal theory, a rough upper surface of the fracture is generated, and different degrees of mismatch are introduced by adding random noise to this surface. This approach enables the construction of a variety of three-dimensional rough fracture flow models. Numerical simulations, which involve directly solving the Navier-Stokes equations, are used to simulate flow through a rough single fracture, assessing the effects of various degrees of mismatch between the surfaces. The study also examines how the inclusion of the matrix alters flow characteristics. The results demonstrate that the Forchheimer equation accurately describes the nonlinear flow behavior in fractures with different degrees of mismatch. The increased mismatch intensifies the uneven distribution of fracture apertures, causing the flow velocity to shift from uniform to discrete and the streamlines to become increasingly curved. The overall tortuosity of the flow path increases and the formation of ‘concave’ and ‘convex’ areas leads to vortex zones, promoting nonlinear seepage. The correlation between both viscous and inertial permeability with the degree of mismatch is negative, whereas the impact of matrix permeability on the flow capacity of the fracture shows a positive correlation with a mismatch.

Pressure-Angle Polars Obtaining Flow Field of Rotating Detonation

ABSTRACT Rotating detonation engines have been studied experimentally and numerically due to a higher thermal efficiency in theory. Numerical simulations of the flow field inside the engine cost more since the flow is unsteady and contains shock waves, detonation waves, and contact surfaces. Thus, a two-dimensional theoretical study with the method of pressure behind a shock wave or a rarefaction wave as a function of deflection angle of flow was carried out to predict the flow field and reduce the cost. Numerical simulations with a premixed inviscid model were also carried out to verify the theoretical results. The flow field at an equivalence ratio of 0.8 has a curved contact surface, whereas it has a plane contact surface at equivalence ratios of 0.9–1.2 because the RDW is stronger and more stable. Comparisons between the theoretical and numerical results show the theoretical method can be used to obtain a rough flow field inside the RDE, including the pressure and deflection angle of flow behind the shock wave and rarefaction wave. Most of the errors between the numerical and theoretical results are less than 10%.

Shear-induced permeability evolution of natural fractures in granite: Implications for stimulation of EGS reservoirs

Permeability evolution of natural fractures during shearing is one of the critical issues in enhanced geothermal system (EGS). In this study, we conducted a series of numerical simulations of shear-flow tests under different normal stresses to investigate the permeability evolution and shear behavior of natural fractures during shearing. All numerical simulations in this study are executed based on a coupled hydro-mechanical pore network model (PNM) for fluid flow within the discrete element method (DEM). The numerical model uses a 33 mm × 25 mm fracture surface profile extracted from X-ray computed tomography scanning data of joints in a rock core retrieved from a 4.2-km-deep well at the Pohang EGS site. The results demonstrate a positive correlation between fracture permeability and shear displacement when the normal stress is relatively high. The central aspect of permeability evolution lies in the variation of local aperture distribution along the pathway: an increase in the variance of fracture aperture distribution leads to an increase in fracture permeability. Permeability evolution of fractures is significantly affected by normal stress, fracture roughness, and relative flow direction. Larger fracture roughness facilitates the formation of high-permeability pathways. Higher local normal stress often corresponds to lower local permeability. Moreover, high normal stress amplifies the effect of fracture roughness on permeability evolution. These findings enhance our comprehensive understanding of hydraulic-mechanical coupling effects during EGS stimulation.

Experiments on flow velocity profiles in mountain river channels

ABSTRACT Research on the vertical profiles of flow velocity in mountainous river channels is limited, particularly in scenarios where complex bed geometries are absent. Due to the coarse roughness and seepage flow on streambeds composed of gravel, the conventional formulae for flow velocity profiles derived from fluvial river channels do not apply to mountainous river channels. Based on flume experiments with a bed packed with natural gravel and a slope ranging from 0.006 to 0.16, we derived a theoretical formula for flow velocity profiles. This new formula integrates the influence of the subsurface flow and velocity reduction near the water surface, demonstrating a strong alignment with measurements. Our findings indicate that for shallow water flow over rough bed surfaces, the turbulence intensity diminishes along the vertical direction in the near-bed region while remaining relatively constant in the upper water body. Contrary to conventional theories which attribute the increase in flow resistance and the decrease in sediment transport rates in mountainous river channels to form drag, our study emphasizes that the subsurface flow plays a significant role in the overall flow resistance of mountainous river channels and should not be overlooked.

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 < \theta < 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 < {w_s}/{u_\ast } < 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 < St < 3.5 and dp/η > 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

Deformation of vegetated channel bed under ice-covered flow conditions

A common feature of cold regions is the presence of ice cover on water surface. In the presence of vegetation in the channel bed which is normally leafless in winter, interaction between river ice and vegetated channel bed becomes very complex. In the present study, the impacts of ice cover and submerged leafless vegetation on channel bed deformation and flow resistance have been investigated based on 144 experiments conducted in a large-scale outdoor flume. The independent variables associated with the maximum scour depth around vegetation elements have been assessed and equations have been developed. Results indicate that the most important variable affecting the maximum scour depth around vegetation under ice-covered flow conditions is the ratio of the ice cover roughness to the bed roughness (ni/nb). However, under open channel flow conditions, the flow Froude number is the most important variable influencing the maximum scour depth. The methods based on the law of the wall provide reliable Manning's coefficient for both smooth and rough ice covers in the presence of submerged vegetation in the channel bed. As the vegetation density increases, the size of scour holes becomes smaller. With the increase in vegetation density, the median grain size of the armour layer in scour holes decreases correspondingly. When vegetation elements are placed in a staggered configuration, the median grain size of the armour layer in scour holes is less than that of squared configuration of vegetation elements. Regardless of the roughness of ice cover on water surface and the grain size of sediment in the bed, the maximum depth of scour holes always occurs at the upstream front face of each vegetation element. Under the rough ice-covered flow condition, the maximum depth of scour holes is more than that under the smooth ice-covered and open flow conditions.

Bed Shear Stress and Near‐Bed Flow Through Sparse Arrays of Rigid Emergent Vegetation

AbstractVegetation is an essential component of natural rivers and has significant effects on flow and morphodynamic processes. Although progress has been made in characterizing flow resistance in vegetated flows, the impact of vegetation on bed shear stress, a key driver of sediment transport, still needs better characterization and understanding. This research, explores bed shear stress and near‐bed flow characteristics in sparse arrays of rigid emergent cylinders mimicking vegetation over a rough bed. For this purpose, a novel adaptation of a shear plate was used to measure bed shear stress at the canopy scale. These measurements were analyzed in relation to spatially averaged near‐bed flow quantities for different array densities. The results show that, for a constant water depth, the investigated cylinder canopy enhances the ratio between bed shear stress and bulk flow velocity (i.e., Darcy‐Weisbach bed friction factor) compared to unobstructed open‐channel flows, and that this ratio increases with array density. Moreover, higher near‐bed velocities were observed for higher array densities. On the other hand, no influence of the cylinder array on near‐bed values of turbulent kinetic energy and turbulent stresses was observed. Finally, it is shown that the thickness of the near‐bed layer is a suitable parameter to scale the ratio between bed shear stress and bulk flow velocity in vegetated rough bed flows.

Performance analysis of columnar convex-concave compound microtexture thrust bearing

PurposeThis study aims to enhance the lubrication performance of thrust bearings. The influence of columnar convex–concave compound microtexture on bearing performance is investigatedDesign/methodology/approachBased on the compound microtexture model of thrust bearings, considering surface roughness and turbulent effect, the variation of lubrication characteristics with the change in the compound microtexture parameters is studied.FindingsThe results indicate that, compared with circular microtexture, the maximum pressure of compound microtexture of thrust bearings increases by 7.42%. Optimal bearing performance is achieved when the internal microtexture depth is 0.02 mm. Turbulent flow states and surface roughness lead to a reduction in the optimal depth. The maximum pressure and load-carrying capacity of the bearing decrease as the initial angle increases, whereas the friction coefficient increases with the increase in the initial angle. The lubrication performance is best for bearings with a circumferential parallel arrangement of microtexture.Originality/valueThe novel composite microtexture with columnar convex-concave is proposed, and the computational model of thrust bearings is set. The influence of surface roughness and turbulent flow on the bearing performance should be considered for better conforming with engineering practice. The effect of microtexture depth, arrangement method and distribution position on the lubrication performance of the compound microtexture thrust bearing is investigated, which is of great significance for improving tribology, thrust bearings and surface microtexture theory.

Beyond a fixed number: Investigating uncertainty in popular evaluation metrics of ensemble flood modeling using bootstrapping analysis

AbstractEvaluation of the performance of flood models is a crucial step in the modeling process. Considering the limitations of single statistical metrics, such as uncertainty bounds, Nash Sutcliffe efficiency, Kling Gupta efficiency, and the coefficient of determination, which are widely used in the model evaluation, the inherent properties and sampling uncertainty in these metrics are demonstrated. A comprehensive evaluation is conducted using an ensemble of one‐dimensional Hydrologic Engineering Center's River Analysis System (HEC‐RAS) models, which account for the uncertainty associated with the channel roughness and upstream flow input, of six reaches located in Indiana and Texas of the United States. Specifically, the effects of different prior distributions of the uncertainty sources, multiple high‐flow scenarios, and various types of measurement errors in observations on the evaluation metrics are investigated using bootstrapping. Results show that the model performances based on the uniform and normal priors are comparable. The statistical distributions of all the evaluation metrics in this study are significantly different under different high‐flow scenarios, thus suggesting that the metrics should be treated as “random” variables due to both aleatory and epistemic uncertainties and conditioned on the specific flow periods of interest. Additionally, the white‐noise error in observations has the least impact on the metrics.

Experimental investigation on the flow boiling of R134a in a plate heat exchanger with mini-wavy corrugations

As a common component in various applications, the two-phase heat transfer of plate heat exchanger has been frequently studied. However, further investigations are still required on the flow pattern, especially for those with new plate structures brought with the emergence of new applications. This study presented an experimental investigation on the flow boiling of R134a in a plate heat exchanger with mini-wavy corrugations designed for thermal management system of electric vehicle (EV). The flow pattern transitions in the test section were captured and discussed, meanwhile the effects of vapor quality and mass flux on the variation of heat transfer coefficient (HTC) were analyzed. Based on the observation, the two-phase flow pattern developed from pulsating film flow, then rough stream flow and finally to thin stream flow with the increase of vapor quality. The flow pattern map was determined with the superficial momentum of the liquid and vapor phase refrigerant, while the empirical correlations were developed based on two-phase Weber number to predict the transitions between the flow patterns. The HTC showed an intermediate increase firstly under low vapor qualities, and rapidly decreased after reaching the peak value at the vapor quality of 0.45–0.6. In addition, the experimental data were compared with the present correlations, and a new Nu correlation was developed considering the transitions of flow patterns, showing an optimal prediction on the experimental data with the mean absolute error of 11.3%.

Direct numerical simulation of channel flow with real surface roughness using a ghost cell immersed boundary method

This paper investigates the impact of real surface roughness on channel flow using direct numerical simulation assisted by a ghost cell immersed boundary method (DNS-GCIBM). The principles and implementations of DNS-GCIBM are first introduced. Two test cases, including the two-dimensional flow around a cylinder and the three-dimensional flow in a sinusoidal roughness channel are employed to demonstrate the practicability and accuracy of the proposed approach, especially in numerical studies on the rough wall-bounded flow. Using DNS-GCIBM, channel flows under conditions of Ma = 0.3 and Reτ≈300, with both the real-world and regular roughness surfaces are studied. The results are statistically analyzed using the triple decomposition technique. The outer layer similarity in the streamwise mean velocity and Reynolds stress profiles indicate that the impact of roughness on the boundary layer primarily localizes within roughness sub-layer. In the streamwise mean velocity profile, both regular and real-world roughness surfaces induce obvious increase to the roughness function ΔU+ as roughness height Ra increases, while discrepancy of ΔU+ between the two types of roughness can be found. Furthermore, turbulence statistics are sensitive to the variations of Ra. As Ra increases, it becomes challenging to organize coherent structures near the wall, resulting in the reduction of streamwise Reynolds stress intensity. In addition, although the skin friction coefficient and ΔU+ are almost the same, the real-world roughness and the corresponding equivalent regular roughness manifest different flow structures near the wall. The real-world roughness contributes greater spatial inhomogeneity but lower turbulence intensity.

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 idealised 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 to capture the impact of turbulent secondary flows and spatial transients linking smooth and rough surface parts. 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.