Adverse Pressure Gradient Research Articles

Experimental and numerical investigation of bow wave and wake flows around towed surface-piercing cylinders

An investigation was conducted to study the flow characteristics around towed surface-piercing cylinders and understand the mechanisms behind the bow wave and wake region formation. The experiments took place in a towing tank using three different cylinder models, covering a range of Froude numbers based on cylinder diameter from 0.28 to 1.73. Three-cylinder models are considered M1 is circular, M2 is semicircular ellipse and M3 is elliptical. Numerical simulations were performed using the OpenFOAM framework, considering turbulence effects through the unsteady Reynolds-Averaged Navier Stokes equations with the Shear Stress Transport k-ω turbulence model. The numerical results matched well with the experimental data. The bow wave's general features were similar across all cylinder models, with the height increasing as the Froude number rose. Froude numbers between 0.28 and 0.58 displayed a smooth surge surface, transitioning to a rough surface with roll-up initiation between 0.87 and 1.15. At Froude numbers 1.44 to 1.73, a fountain-like bow wave formed. Models M1 and M2 had the same average bow wave height, approximately 15% higher than that of Model M3. The depression depth or air ventilation at the trailing edge of the cylinders increased with the Froude number. Model M1 exhibited a greater depression depth than Models M2 and M3 at Froude number 1.15, and this difference further increased at Froude number 1.73 due to high vorticity and adverse pressure gradient generated by Model M1. Vortex coherent structures visualization revealed that at a low Froude number of 0.58, only the Karman vortex at the trailing edge was observed. At Froude number 1.15, the deep wake region maintained predominantly two-dimensional vortex structures, while the free surface displayed pronounced three-dimensional vortex structures. Model M1 had a drag coefficient approximately 40% higher than Model M3. These findings are valuable for engineering applications, particularly in the design of submarine masts.

Hydrodynamics of a Remora-inspired autonomous underwater vehicle approaching and docking to a benchmark submarine

Autonomous underwater vehicles (AUVs) are applied in a variety of industries to increase the efficiency and safety of maritime operations. Traditional docking and recovery techniques for AUVs, however, can be inefficient. Therefore, the development of a dynamic underwater recovery mechanism for AUVs is now needed.Recent research has investigated the symbiotic relationship between the remora fish and the shark from a hydrodynamic perspective. Numerical simulations have demonstrated that by exploiting the boundary layer and adverse pressure gradient regions around the shark, the resistance experienced by remora fish can be significantly reduced. Inspired by this, an AUV was designed, and numerical simulations were conducted to investigate the impact of various attachment locations. Moreover, simulations were performed to investigate the hydrodynamic characteristics of the AUV during the docking process, specifically when it enters the boundary layer of the submarine and approaches it. The boundary layer flow, which influences the AUV's resistance, can also provide a force that attract the AUV towards the submarine.This research identifies an optimal attachment location and investigates the effects on the AUV when two underwater vehicles of significantly different sizes are in close proximity. It supports further study to develop a dynamic underwater docking operation.

Improved prediction of turbomachinery flows using Reynolds stress model with [formula omitted] transition model

Transition is a prominent flow phenomenon in turbomachinery, especially at low and moderate Reynolds numbers. The turbomachinery internal flow often encounters complex vortex structures, typically accompanied by strong turbulence anisotropy and non–equilibrium. Conventional Reynolds–averaged Navier–Stokes (RANS) modeling with linear eddy–viscosity models (LEVMs) may fail short in capturing certain complex flow features. The Reynolds stress model (RSM) based on a higher turbulence closure level has more potential to reasonably consider turbulence anisotropy and non–equilibrium for such complex flows within turbomachinery than the LEVMs. However, the current RSM lacks an effective representation of transition phenomena. This paper presents an improved prediction of turbomachinery flows using RSM with transition modeling. The transition effects are incorporated into the RSM (SSG/LRR–ω model) via Menter's γ transport equation. The blending of the SSG/LRR–ω model with the γ transition model (SSG/LRR–ω–γ model) is firstly validated based on the T3 series flat plate cases with zero pressure gradient (T3A, T3B, T3A–) and variable pressure gradients (T3C1–C5). Comparisons with experiments show that the SSG/LRR–ω–γ model predicts corner separation flows with transition more accurately, although there is still room for further improvement. Then, the performance of the SSG/LRR–ω–γ model is assessed in a linear highly loaded prescribed velocity distribution (PVD) cascade and a NACA65 K48 compressor cascade. Comparisons with experiments indicate that, in both compressor cascades, the SSG/LRR–ω–γ model can predict more accurately corner flows with boundary layer transition on suction surfaces than the SSG/LRR–ω and SST model. Nevertheless, it still exhibits a tendency to overestimate the size of corner separation, especially in cases characterized by strong adverse pressure gradients. Comparisons of skin friction and velocity profiles predicted by the SSG/LRR–ω model with and without transition modeling illustrate the rationale behind the improved prediction. Further improvement of the SSG/LRR–ω–γ model for predicting turbomachinery corner flows should be conducted in future.

A wind tunnel study of adverse pressure gradient impact on wind turbine wake dynamics

Wind tunnel experiments were conducted to investigate the impact of an adverse streamwise pressure gradient on the wake dynamics of a small-scale horizontal-axis wind turbine. The study used high-frequency constant temperature hotwire anemometry to measure wake velocities up to 7 rotor diameters (dT) downstream. Two cases were studied: zero pressure gradient (ZPG) and adverse pressure gradient (APG). Experimental conditions included a Reynolds number based on the rotor diameter of Re≈6.7×104 and an inflow velocity of 7 m/s. The results show significant differences between the ZPG and APG cases as the wake progresses downstream. The APG case exhibits a higher maximum velocity deficit in the far wake and a more distorted, oval-shaped wake than the ZPG case. Turbulence intensity trends also differ, with a decreasing trend in the ZPG case and an increasing trend in the APG case. Energy spectra analysis at specific wake locations offers insights into flow structure development. In both cases, small-scale (high-frequency) energy decreases as the wake advances, while large-scale (low-frequency) energy increases. Specifically, the adverse pressure gradient attenuates certain large-scale flow structures λx/dT∈[0.05,0.2], corresponding to f∈[20,100]Hz near the rotor tip height and narrows downstream. Additionally, in the APG case, energy increases in the lower half of the wake for flow structures ranging from λx/dT∈[0.04,0.5], or f∈[10,100]Hz near the rotor, narrowing further downstream. The results suggest that an adverse pressure gradient enhances turbulence and hinders velocity recovery toward freestream conditions in the wake of a wind turbine.

Generalisation of the Penalised Wall Function Method for the Simulation of Turbulent flows With Unfavourable Pressure Gradients

The penalized wall function method for simulation of compressible near-wall turbulent flow regions in the numerical modeling of viscous compressible flows is developed. The method is formulated as a differential condition to match the outer and the wall function solutions and is based on a generalized characteristic-based volume penalization method to transfer shear stress from the outer region of the boundary layer to the wall. The method is modified to extend its applicability to turbulent flows with adverse pressure gradient, when separation and reattachment zones are formed, as well as to use computational meshes with coarser near-wall resolution. These advantages are demonstrated for two test problems, namely, the flow over a flat plate with zero and adverse pressure gradients.

Mechanism of width effects on cavity-induced transitions at hypersonic speed using direct numerical simulation

Cavities on the surfaces of hypersonic vehicles cannot be avoided easily. Moreover, they can trigger boundary layer transition under certain conditions. However, little progress has been reported on boundary layer transitions induced by a three-dimensional (3-D) shallow cavity. In this study, transitions induced by six 3-D shallow cavities with the same length–depth ratios of 20 and different widths of 0.25, 0.5, 0.75, 1.0, and 1.5 times the baseline width (W), as well as infinite width, were investigated. A direct numerical simulation was conducted using the Roe scheme with 4th-order minimum dispersion and controllable dissipation, and weighted essentially non-oscillatory reconstruction, based on our in-house code: Unsteady NavIer–STokes equations solver. Cavity width was observed to have non-monotonic influences on transition. Both the 0.25 and 1.0 W cavities could induce transition constantly. Moreover, flow was maintained as laminar past the 1.5 W and InfW cavities. For the 0.5 and 0.75 W cavities, intermittent transition was observed with different intermittency factors. The intermittent transition phenomenon was determined to be caused by the periodic increase and decrease in the adverse pressure gradient (APG) in the front part of cavity. Notably, the recirculation with a synchronic size change was the origin of the APG oscillation.

Features of laminar separation bubble subjected to varying adverse pressure gradients

This article describes the spatial development of a laminar separation bubble (LSB), its transition, and eventual breakdown under the influence of adverse pressure gradients (APGs) similar to those experienced by low-pressure turbine blades. The investigation combines a comprehensive experimental approach with a well-resolved large eddy simulation (LES). The streamwise pressure gradients were varied by manipulating the upper wall within the test section. The Reynolds number (Re), based on the plate length and inlet velocity, was 0.2 × 106 with a freestream turbulence intensity of 1.02%. The particle image velocimetry (PIV) and hotwire data were used to illustrate the vortex dynamics, growth of perturbations, and intermittency. The onset and end of transition progressively shift upstream, resulting in a reduction of the laminar shear layer length and bubble length with increasing APG. Interestingly, the flow features exhibit self-similarity in velocity profiles and the growth rate of velocity fluctuations when normalized against the bubble length. The formation of two-dimensional Kelvin–Helmholtz (K–H) rolls is apparent in the beginning, resulting in the selective amplification of frequency and exponential growth of fluctuations. Linear stability theory explains the most amplified frequency and phase speed of convective vortices, apart from the growth of disturbances. Analysis of LES data reveals intricate inviscid–viscous interactions that trigger shear layer breakdown. In brief, evolving perturbations within the braid region of vortices in the latter half interact with the advecting K–H rolls, culminating in the breakdown and the onset of turbulent flow downstream.

Generalization of the Penalized Wall Function Method for Modeling of Turbulent Flows with Adverse Pressure Gradient

Generalization of the Penalized Wall Function Method for Modeling of Turbulent Flows with Adverse Pressure Gradient

Hybrid suction/blowing actuator to control flow separation on the ramp and energy cost analysis

The flow separation control on an adverse-pressure-gradient ramp model is studied using various flow control strategies. Using a steady turbulent flow, the effects of utilizing an active hybrid control (suction and blowing) on the separation bubble behind a ramp are investigated numerically. A parametric analysis is conducted in which the actuators' pitch angle, diameter, and streamwise position are varied. The results are compared to determine the most effective method for compensating adverse pressure gradients and managing the separated flows on a ramp model. The best results for the blowing scenario correspond to a blowing actuator with a dimensionless distance of Lx/L1=−1/70 from the top of the ramp, a dimensionless diameter of d/L1=1/70, and a dimensionless angle of θ/θ0=2/6. The actuator is found to be able to wipe out the separation zone entirely at a velocity ratio of 3. The best results for the suction approach belong to a suction actuator with Lx/L1=1+1/70 from the top of the ramp, d/L1=3/70, and θ/θ0=−4/6. The modeling shows that the actuator removes the separation zone at a lower velocity ratio, namely, at 1.5. Nonetheless, a recirculation zone forms behind the suction point. Using a combined system, with a velocity ratio of 0.5 for a diameter of 3 and 2 for a diameter of 1, eliminates the separation zones on the ramp and after the suction actuator while lowering energy consumption. The blowing actuator consumed 3.2 times as much power as the combined actuator, whereas the suction actuator consumed 1.2 times as much power. Therefore, analyzing the present results as a prerequisite makes it possible to reduce flow separation and its adverse effects in more practical environments such as airfoils with an optimal cost.

Turbulent kinetic energy redistribution in a gravity current interacting with an emergent cylinder

Gravity currents are flows driven by density gradients between two or more contacting fluids and play a key role in nature and industrial environments via global ocean circulations, climate variability and the distribution of airborne pollutants. In the present work, we study, experimentally, the changes induced by an emergent vertical PVC cylinder on the mean and turbulent flow fields of an unsteady bottom-generated lock release gravity current. Tests were carried out, with and without the cylinder, in refractive index matching conditions and instantaneous velocities were acquired with a Particle Image Velocimetry system. The mean velocity field, Reynolds stresses and terms of turbulent kinetic energy (TKE) budget for the currents head were presented and discussed. The results show that the adverse pressure gradient generated by the cylinder induces a uniform deceleration of the current head. Hence, there are no appreciable differences on the spatial distribution of the mean velocities in the current head, compared to the undisturbed current. On the other hand, the changes on the turbulent flow field are remarkable. The total diffusion of TKE decays in the inner part of the head while becoming stronger at the interface between the two fluids, as the current approaches the cylinder. This is associated to an increase of the diffusion term due to pressure fluctuations, that acts against diffusion due to velocity fluctuations and contributes to disrupt the transport of TKE from the interface between the fluids and the inner part of the current. As a result, in the presence of an obstacle, Reynolds stresses are suppressed in the inner part of the current head and enhanced at the interface.

Verification and validation for large eddy simulation of the turbulent flow around an underwater entity

The objective is to analyze the errors and uncertainty in the simulation results of the complex, unsteady turbulent flow and vortices. The implicitly filtered large eddy simulation (LES) with the boundary data immersion method is used to investigate the transient turbulent flow around a fully appended underwater entity model (SUBOFF) proposed by Groves et al. [Geometric Characteristics of DARPA Suboff Models: (DTRC Model Nos. 5470 and 5471) (David Taylor Research Center, 1989)] with emphasis on verification and validation. As for the verification, the five-equation method is used to assess the LES error, including the modeling error and numerical error in the transient flow. They offset each other, leading to a small total error. As for the validation, it has been achieved in the most area when the experimental result is located at the band of ysim ± UV (ysim is the simulation result, and UV is the validation uncertainty). There is a strong relationship between the validation uncertainty and the complex vortex interaction. The validation uncertainty becomes significant, which means less accuracy of the simulation result, within the tip flow region, adverse pressure gradient region, tip vortex interacting with the boundary layer region and shear layer region. Most all of these regions occur behind the appendage and at the shape changing position of the SUBOFF.

Observations and modeling of tidally generated high-frequency velocity fluctuations downstream of a channel constriction

Abstract. We investigate data from an acoustic Doppler current profiler deployed in a constricted ocean channel showing a tidally dominated flow with intermittent velocity extrema during outflow from the constriction but not during inflow. A 2D numerical ocean model forced by tides is used to examine the spatial flow structure and underlying dynamical processes. We find that flow-separation eddies generated near the tightest constriction point form a dipole pair which propagates downstream and drives the observed intermittent flow variability. The eddies, which are generated by an along-channel adverse pressure gradient, spin up for some time near the constriction until they develop local low pressures in their centers that are strong enough to modify the background along-channel pressure gradient significantly. When the dipole has propagated some distance away from the constriction, the conditions for flow separation are recovered, and new eddies are formed.

Dynamic separation on an accelerating prolate spheroid

Time-varying flow separation on an accelerating prolate spheroid has been studied at various angles of incidence. Instantaneous pressure and scanning stereoscopic particle image velocimetry were used to shed light on the evolution of cross-flow structures for the Reynolds number ( $Re$ ) range of $1.0\times 10^6\leq Re \leq 1.5\times 10^6$ . The movement of separation lines is examined for various model accelerations to investigate on the interplay between acceleration and flow separation. The results demonstrate that for axial accelerations, the streamwise pressure distribution in the rear part of the prolate spheroid switches from an adverse to a favourable pressure gradient. At the same time, the circumferential adverse pressure gradient present during steady motion vanishes during said accelerations. In contrast, both streamwise and circumferential adverse pressure gradients strengthen when the model is axially decelerated. These dynamic pressure distributions influence the location of the separation line, which in turn moves closer to the model meridian during accelerations while moving outwards during decelerations. The streamwise vorticity distribution and the streamwise circulation both show how the separation-line position impacts the vortex formation. A high-vorticity region near the model surface is established during acceleration. In contrast, a decelerating model leads to transport of high-vorticity fluid into the outer area of the cross-flow separation. We further assess the memory effects following the near-impulsive velocity changes. The cross-flow retains the memory of moving separation lines shortly after the acceleration. However, the separation recovers quickly to a steady state.

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layer with Spatially Varying Pressure Gradients

Wall-modeled large-eddy simulations of turbulent boundary layers subjected to spatially varying streamwise pressure gradients are conducted to assess the predictive performance of three wall models: ordinary differential equation equilibrium, integral nonequilibrium, and partial differential equation (PDE) nonequilibrium models. The test case is based on experiments conducted by Volino (Journal of Fluid Mechanics, Vol. 897, Aug. 2020, p. A2), where the flow is subjected successively to zero pressure gradient (ZPG), favorable pressure gradient (FPG), recovery ZPG, and adverse pressure gradient (APG) regions. Skin friction is overpredicted in FPG by all the wall models. For equilibrium and integral models, this overprediction is attributed to the strong deviation of mean velocity profiles within FPG from the log law, used explicitly in the equilibrium and implicitly in the integral model. The overprediction is more pronounced for the PDE model, which is attributed to dynamic correction of wall-model eddy viscosity for resolved stresses and a lack of correction for pressure gradient. Potential remedies to mitigate this problem are proposed. Grid refinement improves wall-stress predictions in both FPG and APG but only affects the outer profiles in APG, revealing that accurate wall-flux modeling is more critical for APG. Anisotropic grid analysis shows streamwise grid refinement to be more crucial than spanwise for the convergence of skin-friction, outer velocity, and Reynolds stress profiles.

Sensitivity Analysis of an Unsteady Flow Around a Pitching Airfoil

Various ways to control the loads and thus the output of the wind turbine by pitching the blades and by controlling the rotational speed already exist. However, adverse pressure gradient leading to flow separation at the trailing edge, with relatively high angles of attack (AOA) due to blade-pitching motion, largely affects the airfoil aerodynamic performance. This work presents the results of a numerical study of the unsteady flow around a pitching FFA-W3-301 airfoil at a Reynolds 1.6 × 106 using OpenFOAM®, as obtained by first performing 2D Unsteady Reynolds-Averaged Navier- Stokes (URANS) simulations whereby the flow characteristics are simulated by the shear stress transport (SST) k − ω model and Spalart-Allmaras (SA). The influence of various parameters on the numerical results is investigated, namely y+, computational grid resolution, dynamic mesh technique, time step and turbulence model. Integral aerodynamic forces and detailed flow patterns are compared with experimental measurements presented in the literature. A range of angles of attack, including early stalls, are examined. For best-performing parameters, an adequate refinement close to the wall was imperative in order to match experiments, especially during the upstroke motion of the airfoil, while for the downstroke phase, some differences still appeared. The agreement was greatly improved by using a 2.5D hybrid RANS-LES approach with enhanced delayed-Detached Eddy Simulation (DES) capabilities.

A POD-mode-augmented wall model and its applications to flows at non-equilibrium conditions

Insights gained from modal analysis are invoked for predictive large-eddy simulation (LES) wall modelling. Specifically, we augment the law of the wall (LoW) by an additional mode based on a one-dimensional proper orthogonal decomposition (POD) applied to a two-dimensional turbulent channel. The constructed wall model contains two modes, i.e. the LoW-based mode and the POD-based mode, and the model matches with the LES at two, instead of one, off-wall locations. To show that the proposed model captures non-equilibrium effects, we perform a priori and a posteriori tests in the context of both equilibrium and non-equilibrium flows. The a priori tests show that the proposed wall model captures extreme wall-shear stress events better than the equilibrium wall model. The model also captures non-equilibrium effects due to adverse pressure gradients. The a posteriori tests show that the wall model captures the rapid decrease and the initial decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients, respectively, both of which are missed by currently available wall models. These results show promise in applying modal analysis for turbulence wall modelling. In particular, the results show that employing multiple modes helps in the modelling of non-equilibrium flows.

A Numerical Study on the Influence of Transverse Grooves on the Aerodynamic Performance of Micro Air Vehicles Airfoils

Micro Air Vehicles (MAVs) airfoils usually operate at low Reynolds number conditions, where viscous drag will consume a large amount of propulsion power. Due to the small dimensions, many drag reduction methods have failed, resulting in limited current research. To develop an effective method of reducing viscous drag, transverse grooves were placed on the surface of MAVs airfoils in this study, and a numerical investigation was implemented to uncover the corresponding flow control law as well as the mechanism. Research has shown that transverse grooves have an impact on the drag and lift of airfoils. For drag, properly sized transverse grooves have the effect of reducing drag, but under high adverse pressure gradients or when the continuous arrangement of grooves is excessive, the optimal drag reduction effect achieved by the grooves is weakened, and even the drag increases due to the significant increase in pressure difference. In severe cases, it may also cause strong flow separation, which is not conducive to MAV flight. For lift, the boundary vortex in the groove has the ability to reduce the static pressure near the groove. However, high adverse pressure gradients or too many grooves will thicken the boundary layer and increase the blockage effect, resulting in a large static pressure on the grooved side of the airfoil (with an increase in drag). From the perspective of circulation, the static pressure changes on the suction and pressure surfaces have opposite effects on lift. Considering the comprehensive aerodynamic performance of the airfoil, we designed a high lift-to-drag ratio airfoil with grooves, which increased the lift-to-drag ratio by 33.747% compared to the smooth airfoil. Based on the conclusions, we proposed preliminary design criteria for grooved airfoils, providing guidance for subsequent research and applications.

Numerical study on the periodic control of supersonic compression corner flow using a nanosecond pulsed plasma actuator

This study investigates the effectiveness of a pulsed nanosecond dielectric barrier discharge (NSDBD) plasma actuator for flow control over a supersonic compression corner through numerical simulations. The effects of varying applied voltages, repetitive frequencies, and activated locations of the plasma actuator are examined under large-scale laminar flow separation conditions around a compression corner. The unit Reynolds number and Mach number are 7.8 × 106 m−1 and 4, respectively. The results indicate that the discharge induces a pressure rise and leads to misalignment between the pressure gradient and density gradient in the residual heat region. Because of the interaction between the supersonic freestream and the actuation-induced shock/compression flow, convection, compressibility of the fluid element, and baroclinicity of the residual heat region collectively lead to the formation of an induced spanwise vortex, which in turn enables momentum migration. The induced vortex disrupts the initial flow structures and entrains high-energy fluid from the main flow into the boundary layer, promoting momentum mixing between the main flow and the separated flow, which increases the energy of the boundary layer to resist the adverse pressure gradient. The time-averaged flow structures imply that it is possible to totally eliminate the flow separation near the supersonic compression corner. For aerodynamics on the surface, the normal force produces a pitching moment that can be potentially utilized to control the body's orientation and trajectory. Additionally, total drag on the surface can be reduced by 5 %. This suggests that choosing the most appropriate position based on its local fluid characteristics can strongly increase the control effectiveness.

Studying turbulent flows with physics-informed neural networks and sparse data

Physics-informed neural networks (PINNs) have recently become a viable modelling method for the scientific machine-learning community. The appeal of this network architecture lies in the coupling of a deep neural network (DNN) with partial differential equations (PDEs): the DNN can be considered a universal function approximator, and the physical knowledge from the embedded PDEs regularises the network during training. This regularisation improves robustness of the network and means the network only requires sparse training data in the domain. We apply PINNs with embedded Reynolds-averaged Navier–Stokes (RANS) equations to a spatially developing adverse-pressure-gradient (APG) boundary layer 1000<Reθ<3000, and also to the periodic hill problem 5600≤Reb≤37,000. We do not use a turbulence model to close the RANS equations, rather the network infers the Reynolds-stress fields during training as a means to satisfy closure. As PINNs are able to produce robust predictions with sparse training data, this paper demonstrates how PINNs can be trained with data typical of experimental campaigns. For the APG boundary layer, we seek to quantify the amount and location of data required to model a time-averaged turbulent flow with PINNs, and show that PINNs can accurately model wall shear stress and wall pressure. We demonstrate how PINNs perform when trained without information of a critical feature of the flow (such as a separation bubble), and we highlight how the cost of training the network does not increase with Reynolds number. Finally, we undertake a series of benchmarks to demonstrate how the method scales with network size and the number of residual points in the problem. This work seeks to establish the quantity and type of data required to successfully apply PINNs to time-averaged flow without a closure model, and seeks to set expectations on the prediction quality of the network when trained on an available data set.

Laminar flow in a channel bounded by porous/rough walls: Revisiting Beavers-Joseph-Saffman

The fully developed, steady, incompressible, laminar flow in a channel delimited by rough and/or permeable walls is considered. The influence of the micro-structured bounding surfaces on the channel flow behavior is mimicked by imposing high-order effective boundary conditions which stem from homogenization theory and do not contain empirical parameters. A closed-form solution of the Navier–Stokes equations is found for the flow in the channel, with conditions at each virtual boundary linking the slip velocities to shear stress and streamwise pressure gradient. The boundary condition for the longitudinal velocity coincides with a little-noticed extension of the so-called Beavers-Joseph condition, first derived by Saffman (1971); it applies to both permeable and rough surfaces, including the case of separated flow (Couette-Poiseuille motion with adverse pressure gradient). The analytical solution obtained for the velocity distribution in the channel is validated against full feature-resolving simulations of the flow for either highly ordered or random textures, highlighting the accuracy and the applicability range of the model. The Stokes-based model used to identify slip and interface permeability coefficients in the effective boundary conditions is found to be reliable and accurate up to ϵReτ≈10, with ϵ ratio of microscopic to macroscopic length scales and Reτ the shear-velocity Reynolds number. Above this threshold, the coefficients must account for advective effects: a new upscaling procedure, based on an Oseen’s approximation, is thus proposed and validated, extending considerably beyond the Stokes regime.