Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.     

DNS of viscoelastic turbulent channel flow with rectangular orifice at low Reynolds number

Direct numerical simulations of turbulent viscoelastic-fluid flow in a channel with a rectangular orifice were performed to investigate the influence of viscoelasticity on turbulence statistics and turbulent structures downstream of the orifice. The geometry considered is periodic rectangular orifices with 1:2 expansion. The constitutive equation follows the Giesekus model, valid for polymer (or surfactant) solutions, which are generally capable of reducing the turbulent frictional drag in a smooth channel. The friction Reynolds number and the Weissenberg number were set to 100 and 20-30, respectively. A drag reduction of about 20% was achieved in the viscoelastic flows. The onset Reynolds number for the transition from a symmetric to an asymmetric state was found to be shifted to higher values than that for the Newtonian flow. In the viscoelastic flow, the turbulent kinetic energy was decreased and fewer turbulent eddies were observed, as the Kelvin-Helmholtz vortices were quickly damped. Away from the orifice, quasi-streamwise vortices in the viscoelastic flow were sustained for a longer period, accompanied by energy exchange from elastic energy of the viscoelastic fluid to kinetic energy.     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

A Reynolds stress model for turbulent flow of homogeneous polymer solutions

Using a priori analyses of direct numerical simulation (DNS) data, a Reynolds stress model (RSM) is developed to account for the influence of polymer additives on turbulent flow over a wide range of flow conditions. The Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model is utilized to evaluate the polymer contribution to the stress tensor. Thirteen DNS data sets are used to analyze the budgets of elastic stress–velocity gradient correlations as well as Reynolds stress and dissipation transport. Closures are developed in the framework of the RSM model for all the required unknown and non-linear terms. The polymer stresses, velocity profiles, turbulent flow statistics and the percentage of friction drag reduction predicted by the RSM model are in good agreement with present and those obtained from independent DNS data over a wide range of rheological and flow parameters.     

Polymer Induced Drag Reduction in a Turbulent Pipe Flow Subjected to a Coriolis Force

The skin friction factor f in a turbulent wall-bounded flow can be greatly reduced by using polymer solutions. In this paper we discuss experimental results on the effect of the Coriolis force on turbulent drag reduction. To study this, a horizontal smooth-walled pipe with internal diameter 25?mm is placed on a horizontal table rotating about its vertical axis. The rotation is made non-dimensional with friction velocity and pipe diameter, to form the Rotation number Ro. For a range of bulk Rotation number (Ro _b ) between 0 and 0.6 for two different Reynolds numbers (Re _b = 15 & 30 × 10³), the pressure drop is measured, from which the average friction factor f is obtained. Additionally the effect of four different polymer concentrations has been investigated. The single-phase results show that the friction factor increases monotonic but gradual with Rotation. With polymer additives a drag reduction is found that increases with concentration, but which is not affected by the rotation.     

Turbulent Drag Reduction by Uniform Blowing Over a Two-dimensional Roughness

Direct numerical simulation (DNS) of turbulent channel flow over a two-dimensional irregular rough wall with uniform blowing (UB) was performed. The main objective is to investigate the drag reduction effectiveness of UB on a rough-wall turbulent boundary layer toward its practical application. The DNS was performed under a constant flow rate at the bulk Reynolds number values of 5600 and 14000, which correspond to the friction Reynolds numbers of about 180 and 400 in the smooth-wall case, respectively. Based upon the decomposition of drag into the friction and pressure contributions, the present flow is considered to belong to the transitionally-rough regime. Unlike recent experimental results, it turns out that the drag reduction effect of UB on the present two-dimensional rough wall is similar to that for a smooth wall. The friction drag is reduced similarly to the smooth-wall case by the displacement of the mean velocity profile. Besides, the pressure drag, which does not exist in the smooth-wall case, is also reduced; namely, UB makes the rough wall aerodynamically smoother. Examination of turbulence statistics suggests that the effects of roughness and UB are relatively independent to each other in the outer layer, which suggests that Stevenson’s formula can be modified so as to account for the roughness effect by simply adding the roughness function term.     

A FENE-P k–ε turbulence model for low and intermediate regimes of polymer-induced drag reduction

A new low-Reynolds-number k–ε turbulence model is developed for flows of viscoelastic fluids described by the finitely extensible nonlinear elastic rheological constitutive equation with Peterlin approximation (FENE-P model). The model is validated against direct numerical simulations in the low and intermediate drag reduction (DR) regimes (DR up to 50%). The results obtained represent an improvement over the low DR model of Pinho et al. (2008) [A low Reynolds number k–ε turbulence model for FENE-P viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, 154, 89–108]. In extending the range of application to higher values of drag reduction, three main improvements were incorporated: a modified eddy viscosity closure, the inclusion of direct viscoelastic contributions into the transport equations for turbulent kinetic energy (k) and its dissipation rate, and a new closure for the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors (NLT_ij). The NLT_ij appears in the Reynolds-averaged evolution equation for the conformation tensor (RACE), which is required to calculate the average polymer stress, and in the viscoelastic stress work in the transport equation of k. It is shown that the predictions of mean velocity, turbulent kinetic energy, its rate of dissipation by the Newtonian solvent, conformation tensor and polymer and Reynolds shear stresses are improved compared to those obtained from the earlier model.     

Towards a Direct Numerical Simulation of a Simplified Pressurized Thermal Shock

The aim of this research work is to perform high quality direct numerical simulations (DNS) of a simplified single phase pressurized thermal shock (PTS) scenario with and without buoyancy effects. In that context, the objectives of this paper are (i) to present the road towards the DNS of a PTS design without buoyancy effects and (ii) to demonstrate that the code NEK5000 is adequate for true DNS analyses. This DNS of the PTS design will serve as a reference to validate low order CFD approaches. The higher order spectral element code NEK5000 is selected to perform the high quality DNS computations. The capabilities of this code, in order to perform the DNS for PTS like geometries, have been extensively assessed for a well-known turbulent channel flow configuration with Re_τ =?180 (turbulent Reynolds number based on the wall friction velocity). Different numerical parameters of NEK5000 have been thoroughly tested and their influence has been studied to obtain high quality turbulence statistics. This assessment of NEK5000 is further extended for the application of highly skewed hexahedral (non-orthogonal) meshes in a turbulent channel flow. The obtained results have shown that NEK5000 is capable of producing high quality DNS solution for a PTS like complex flow configuration for skewed elements (meshes) up to 60 degrees. Finally, this tested numerical framework is adopted to perform the targeted DNS computations of the simplified PTS design.     

Surfactant systems for drag reduction: Physico-chemical properties and rheological behaviour

The first part of the work presents an overview of the physical chemistry of surfactants which in aqueous solutions reduce the frictional loss in turbulent pipe flow. It is shown that these surfactants form rodlike micelles above a characteristic concentraionc _t. The experimental evidence for rodlike micelles are reviewed and the prerequisites that the surfactant system must fulfill in order to form rodlike micelles are given. It is demonstrated by electrical conductivity measurements that the critical concentration for the formation of spherical micelles shows little temperature dependence, whereasc _t increases very rapidly with temperature. The length of the rodlike micelles, as determined by electric birefringence, decreases with rising temperature and increases with rising surfactant concentration. The dynamic processes in these micellar systems at rest and the influence of additives such as electrolytes and short chain alcohols are discussed.In the second part, the rheological behaviour of these surfactant solutions under laminar and turbulent flow conditions are investigated. Viscosity measurements in laminar pipe and Couette flow show the build-up of a shear induced viscoelastic state, SIS, from normal Newtonian fluid flow. A complete alignment of the rodlike micelles in the flow direction in the SIS was verified by flow birefringence. In turbulent pipe flow, drag reduction occurs in these surfactant systems as soon as rodlike micelles are present in the solution. The extent and type of drag reduction, i.e. the shape of the friction factor versus Reynolds number curve, depends directly on the size, number and surface charge of the rodlike micelles. The friction factor curve of each surfactant investigated changes in the same characteristic way as a function of temperature. For each surfactant, independent of concentration, an upper absolute temperature limit,T _L, for drag reduction exists which is caused by the micellar dynamics.T _L is influenced by the hydrophobic chain length and the counter-ion of the surfactant system. A first attempt is made to explain the drag reduction of surfactants by combining the results of these rheological measurements with the physico-chemical properties of the micellar systems.     

倾斜吹吸控制下湍流边界层减阻的直接数值模拟

雷诺切应力是壁湍流高摩擦阻力的重要来源, 有理论认为可以通过壁面生成负雷诺应力(数值上为正)的方式来削弱湍流流场中雷诺应力的分布, 以此获得流动减阻. 而通过对雷诺平均运动方程的法向二次积分, 可以发现壁面生成正雷诺应力(数值上为负)对壁面摩擦阻力系数才有负贡献. 文中在湍流边界层流动的控制区域下边界设置一系列倾斜狭缝, 利用该装置通过周期性吹吸的方法产生壁面生成正(负)雷诺应力, 并采用直接数值模拟方法考察和验证上文提到的减阻理论. 文中采用的湍流边界层流动模型, 其流动雷诺数(基于外流速度及动量损失厚度)从300 发展到860. 文中通过多组数值模拟算例, 考察了射流强度和频率对壁面摩擦阻力系数的影响, 并对比了壁面生成正或负雷诺应力对流动的影响. 研究表明, 壁面生成正雷诺应力控制的减阻率能达到3.26, 而壁面生成负雷诺应力控制的减阻效果较壁面生成正雷诺应力控制的要差; 壁面生成的正雷诺应力对壁面摩擦阻力有负贡献, 而壁面生成的负雷诺应力对壁面摩擦阻力有正贡献; 通过考察控制的收支比, 发现控制方案不能获得能量净收益.      

Direct drag measurements in a turbulent flat-plate boundary layer with turbulence manipulators

The effect of turbulence manipulators on the turbulent boundary layer above a flat plate has been investigated. These turbulence manipulators are often referred to as Large Eddy Break Up (LEBU) devices. The basic idea is that thin blades or airfoils are inserted into the turbulent flow in order to reduce the fluctuating vertical velocity component v above the flat plate. In this way, the turbulent momentum transfer and with it the wall shear stress downstream of the manipulator should be decreased. In our experiments, for comparison, a merely drag-producing wire also was inserted into the boundary layer.In particular, the trade-off between the drag of the turbulence manipulator and the drag reduction due to the shear-stress reduction on the flat plate downstream of the manipulator has been considered. The measurements were carried out with very accurate force balances for both the manipulator drag and the shear stress on the flat plate. As it turns out, no net drag reduction is found for a fairly large set of configurations. A single thin blade as a manipulator performed best, i.e., it was closest to break-even. However, a further improvement is unlikely, because the device drag of the thin blade elements used here has already been reduced to only that due to laminar skin friction, and is thus the minimum possible drag. Airfoils performed slightly worse, because their device drag was higher. A purely drag-producing wire device performed disastrously. The wire device, which consisted of a wire with another thin wire wound around it to suppress coherent vortex shedding and vibration, was designed to have (and did have) the same drag as the airfoil manipulator with which it was compared. The comparison showed that airfoil and blade manipulators recovered 75–90% of their device drag through a shear-stress reduction downstream, whereas the wire device recovered only about 25–30% of its device drag.Conventional LEBU manipulators with airfoils or thin blades produce between 0.25% and 1% net drag increase, whereas the wire device (with equal device drag) produces as much as 4% net drag increase. These data are valid for the specific plate length of our experiments, which was long enough in downstream extent to realize the full effect of the LEBU manipulators. Turbulence manipulators do indeed decrease the turbulent momentum exchange in the boundary layer by rectifying the turbulent fluctuations. This generates a significant shear-stress reduction downstream, which is much more than just the effect of the wake of the manipulator. However, the device drag of the manipulator cannot be reduced without simultaneously reducing the skin friction reduction. Thus, the manipulator's device drag exceeds, or at best cancels, the drag reduction achieved by the shear-stress reduction downstream. A critical survey of previous investigations shows that the suggestion that turbulence manipulators may produce net drag reduction is also not supported by the available previous drag force measurements. The issue had been stirred up by less conclusive measurements based on local velocity data, i.e., data collected using the so-called momentum balance technique.List of symbols b lateral breadth of test plate - c chord length of turbulence manipulator - d diameter of wire manipulator - e distance of the elastic center from the leading edge of the manipulator airfoil - h height of manipulator above test plate - q dynamic pressure of the potential flow above the test plate - s spacing of turbulence manipulator elements - t thickness of turbulence manipulator elements - u,v,w fluctuating velocities in downstream, platenormal, and lateral directions - x distance from the leading edge of the test plate in the downstream direction - x ₀ location of the trailing edge of the first manipulator - z distance from test plate center in the lateral direction - C _D drag coefficient - C _L lift coefficient - D _m drag of manipulated plate including device drag and shear stress, calculated from manipulator location to downstream location - D ₀ drag of unmanipulated plate boundary layer, consisting of the shear stress calculated from manipulator location to downstream location - F drag force - F ₀ total skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream of manipulator, measured without turbulence manipulator - F _LEBU device drag force of the LEBU, i.e., the turbulence manipulator - F _m total drag force of manipulated plate, consisting of - F _LEBU and skin friction force, measured over a distance from 0.4 m upstream of manipulator to 6.35 m downstream - F _cf skin friction force as measured by the floating element balance, manipulated case - F _cfo skin friction force, as measured by the floating element balance, unmanipulated case - F _cf skin friction saving, defined as F _cf = F _cf – F _cfo - F _cf cumulative skin friction savings, i.e., the sum of the skin friction savings F _cf , added up from the location of the manipulator to the downstream location , as shown in Fig. 11. In Fig. 13 the cumulative skin friction savings are summarized up to their asymptotic value, reached at 200 - Re _c Reynolds number of the manipulator elements, calculated with the chord length c and the local velocity in the boundary layer - Re ₀ Reynolds number at the location x ₀ of the manipulator, calculated with the momentum thickness of the boundary layer and the mean flow velocity U - U mean flow velocity in the potential regime of the wind tunnel test section - angle of attack of the manipulator airfoils - ₀ boundary layer thickness at the location x ₀ of the manipulator - dimensionless distance from the manipulator in the downstream direction, defined as - density of the air - ₀ local skin friction shear stress, unmanipulated case - _{0 Average} skin friction shear stress, average value over the lateral span (b = 2 m) of the test plate, unmanipulated case - _m local skin friction shear stress, manipulated case - momentum thickness of the undisturbed turbulent boundary layer at the location x ₀ The authors would like to thank Prof. H. H. Fernholz for his scientific and administrative support. The hardware for the experiments was designed and built by C. Daase, W. Hage and R. Makris. Funding for the project was provided by the Deutsche Forschungsgemeinschaft and is gratefully acknowledged.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG

We report an adaptive viscoelastic stress splitting (AVSS) scheme, which was found to be extremely robust in the numerical simulation of viscoelastic flow involving steep stress boundary layers. The scheme is different from the elastic viscous split stress (EVSS) in that the local Newtonian component is allowed to depend adaptively on the magnitude of the local elastic stress. Two decoupled versions of the scheme were implemented for the Upper Convected Maxwell (UCM) model: the streamline integration (AVSS/SI), and the streamline upwind Petrov-Galerkin (AVSS/SUPG) methods of integrating the stress. The implementations were benchmarked against the known analytic Poiseuille solution, and no upper limiting Weissenberg number was found (the computation was stopped at Weissenberg number of O(10⁴)). The flow past a sphere in a tube was solved next, giving convergent results up to a Weissenberg number of 3.2 with the AVSS/SI and 1.55 with the AVSS/SUPG (both were decoupled schemes; without the adaptive scheme, the limiting Weissenberg number for the decoupled streamline integration method was about 0.3). These results show that the decoupled AVSS is more stable than the corresponding EVSS, and the SI is more robust than SUPG in solving the constitutive equation of hyperbolic type. In addition, we found a very long stress wake behind the sphere, and a weak vortex in the rear stagnation region at a Weissenberg number above W_i of about 1.6, which does not seem to increase in size or strength with increasing W_i.     

One Equation Model for Turbulent Channel Flow with Second Order Viscoelastic Corrections

A modified second order viscoelastic constitutive equation is used to derive a k–l type turbulence closure to qualitatively assess the effects of elastic stresses on fully-developed channel flow. Specifically, the second order correction to the Newtonian constitutive equation gives rise to a new term in the momentum equation involving the time-averaged elastic shear stress and in the turbulent kinetic energy transport equation quantifying the interaction between the fluctuating elastic stress and rate of strain tensors, denoted by P _w , for which a closure is developed and tested. This closure is based on arguments of isotropic turbulence and equilibrium in boundary layer flows and a priori P _w could be either positive or negative. When P _w is positive, it acts to reduce the production of turbulent kinetic energy and the turbulence model predictions qualitatively agree with direct numerical simulation (DNS) results obtained for more realistic viscoelastic fluid models with memory which exhibit drag reduction. In contrast, P _w  < 0 leads to a drag increase and numerical breakdown of the model occurs at very low values of the Deborah number, which signifies the ratio of elastic to viscous stresses. Limitations of the turbulence model primarily stem from the inadequacy of the k–l formulation rather than from the closure for P _w . An alternative closure for P _w , mimicking the viscoelastic stress work predicted by DNS using the Finitely Extensible Nonlinear Elastic-Peterlin fluid model, which is mostly characterized by P _w  > 0 but has also a small region of negative P _w in the buffer layer, was also successfully tested. This second model for P _w leads to predictions of drag reduction, in spite of the enhancement of turbulence production very close to the wall, but the equilibrium conditions in the inertial sub-layer were not strictly maintained.     

Bulk flow parameters in turbulent wall boundary layers near separation

Experiments were conducted in a turbulent boundary layer near separation along a flat plate. The pressure gradient in flow direction was varied such that three significant boundary layer configurations could be maintained. The flow in the test section thus had simultaneously a region of favourable pressure gradient, a region of strong adverse pressure gradient with boundary layer separation and a region of reattached boundary layer. Specially designed fine probes facilitated the measurements of skin friction and velocity distribution very close to the wall. Bulk flow parameters such as skin friction coefficient C _f, Reynold's number Re_δ2 and shape factors H and G, which are significant characteristics of wall boundary layers were evaluated. The dependence of these parameters on the Reynolds number and along the test section was explored and the values were compared with other empirical and analytical formulae known in the literature.     

Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer

A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of R e _θ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for \(\lambda _{z}^{+} > 1000\) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.     

Flow and heat transfer characteristics of drag reducing surfactant solution in a helically coiled pipe

The reduction characteristic of turbulent drag and heat transfer of drag reduction surfactant solution flowing in a helically coiled pipe were experimentally investigated. The drag reduction surfactant used in the present study was the amine oxide type nonionic surfactant of oleyldihydroxyethylamineoxide (ODEAO, C₂₂H₄₅NO₃=371). The zwitterion surfactant of cetyldimethylaminoaciticacidbetaine (CDMB, C₂₀H₄₁NO₂=327) was added by 10% to the ODEAO solution in order to avoid the chemical degradation of ODEAO by ionic impurities in a test tape water. The experiments of flow drag and heat transfer reduction were carried out in the helically coiled pipe of coil to pipe diameter ratio of 37.5 and the helically coiled pipe length to pipe diameter of 1180.5 (pipe diameter of 14.4 mm) at various concentrations, temperatures and flow velocities of the ODEAO surfactant solution. The ODEAO solution showed a non-Newtonian behavior at high concentration of the ODEAO. From the experimental results, it was observed that the friction factor of the ODEAO surfactant solution flowing through the coiled pipe was decreased to a great extent in comparison with water as a Newtonian fluid in the turbulent flow region. Heat transfer measurements for water and the ODEAO solution were performed in both laminar and turbulent flow regions under the uniform heat flux boundary condition. The heat transfer coefficients for the ODEAO solution flow were the same as water flow in the laminar region. On the other hand, heat transfer reduction of the ODEAO solution flow was remarkedly reduced as compared with that of the water flow in the turbulent flow region.     

VLES Modeling of Flow Over Walls with Variably-shaped Roughness by Reference to Complementary DNS

Turbulent flow over variably-shaped rough walls, characterized by either a regular or a random arrangement of axisymmetric roughness elements in an open channel flow configuration, is investigated computationally within a VLES (Very Large Eddy Simulation) framework by utilizing a volumetric forcing-based roughness model. The prime objective of the present work is to assess the roughness model’s capability to predict mean velocities and turbulent intensities in conjunction with this recently formulated hybrid LES/RANS (Reynolds-Averaged Navier-Stokes) model. The friction velocity-based Reynolds number is in the range Re_τ =?460 ? 500. A non-dimensional drag function accounting for the shape of the roughness elements is introduced and evaluated based on the results of complementary direct numerical simulations (DNS). The dynamics of the residual motion of the presently adopted VLES methodology is described by an appropriately modified elliptic-relaxation-based ζ ? f (\(\zeta =\overline {v^{2}}/k\)) RANS model.