Rough-wall Turbulent Flow Research Articles

Impact of spanwise effective slope upon rough-wall turbulent channel flow

Whereas streamwise effective slope ( $ES_{x}$ ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( $ES_{y}$ ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of $ES_{y}$ is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height $k^{+}\approx 65.8$ (where $k$ is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified $ES_{y}$ for three different values of $ES_{x}$ . All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying $ES_{y}$ , since roughness amplitude, skewness and $ES_{x}$ can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that $ES_{y}$ can strongly affect the roughness drag penalty – particularly for low- $ES_{x}$ surfaces. A secondary observation is that particular low- $ES_{y}$ surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.

Contributions to pressure drag in rough-wall turbulent flows: Insights from force partitioning

The Force Partitioning Method is employed to decompose the hydrodynamic drag in rough-wall turbulent channel flows. The contributions of vortex and strain dominated regions on the pressure drag are quantified using an auxiliary surface-dependent potential field $\ensuremath{\phi}$. Different sources of drag are identified, and their relative importance quantified. The \ensuremath{\mathit{Q}}-induced force (where \ensuremath{\mathit{Q}} is the second invariant of the velocity gradient tensor) is responsible for about 50% of the rough-wall drag, and is mainly generated by the strain-dominated (\ensuremath{\mathit{Q}} 0) regions before each roughness element. The equivalent sand-grain height ${k}_{s}$ is also characterized using $\ensuremath{\phi}\ensuremath{-}$dependent norms.

A review on turbulent flow over rough surfaces: Fundamentals and theories

• Townsend hypothesis can explain large-scale motions near rough and smooth walls. • Is unable to describe all roughness regimes and does not scale d-type roughness. • Wall similarity hypothesis faces both supporting and conflicting evidence. • Roughness function can be scaled with height and effective slope of roughness. • Available models do not point to agreed conclusions or trends for all roughness types, Surface roughness can significantly influence the fluid dynamics and heat transfer in convective flows by inducing perturbations in the velocity profile which affect surface drag, turbulent mixing and heat transfer. While surface roughness can often negatively affect the performance of systems, it can also lead to performance improvements, such as in convective flows where roughness elements have been shown to enhance heat transfer. Turbulent flows over rough surfaces have been studied for about a century leading to significant developments in this field. Direct Numerical Simulation (DNS) has made significant contributions to the knowledge of turbulent flows over rough surfaces as well as evaluation of the developed theories. Moreover, the turbulent closures model has seen wide use for simulation of rough-wall turbulent flows in practical applications where DNS is hindered by its complexity and computational resources. Despite a significant number of experimental and CFD studies and the latest advances in this field, a recent review was not available. Therefore, this review surveys the past and recent experimental and numerical studies to address the fundamentals and theories related to the structure of turbulent flows over rough walls. This study chiefly investigates the structure of mean flow profile over rough surfaces, and its correlation with smooth wall mean flow profile. This review study can contribute to prospective experimental and CFD work, and for characterising rough-wall turbulent flows and heat transfer in different academic and engineering applications such as aerodynamics, hydraulics, meteorology, and manufacturing. The review concludes that despite significant progress, the structure of turbulent flow is still not fully understood. This is mainly due to a lack of systematic studies on the structure of turbulent flow and also due to the variety of roughness which influence the dynamics of the flow in the roughness sublayers. The current roughness scale (sand-grain roughness height) fails to completely characterise roughness in many cases. Therefore, there is a need for a universal roughness scale that can describe every type of roughness and be used in any rough-flow regimes, including fully rough and transitionally rough regimes.

Data-driven prediction of the equivalent sand-grain height in rough-wall turbulent flows

Abstract

A DNS/URANS approach for simulating rough-wall turbulent flows

A novel hybrid method combining direct numerical simulation (DNS) and the Reynolds-averaged Navier Stokes (RANS), denoted as a stress-blended method (SBM), has been developed. The SBM is targeted at simulating turbulent flows over arbitrary rough surfaces in which computational savings can be achieved by making the DNS domain as small as possible. Within the SBM framework, a RANS model is enforced above the roughness layer to prevent the momentum build-up which arises in simulations where the computational domain is too small to represent the largest eddies. The SBM is validated for turbulent channel flow, both for smooth wall turbulence and using a parametric forcing approach to mimic roughness effects, with a computational cost that scales linearly with Reτ. The method is then applied to selected subsets of a scanned grit-blasted surface. For the same subset, the roughness function is found to be within 1% of available DNS. Comparisons of small and large subsets showed differences of over a factor of two in equivalent sand grain roughness, indicating the importance of choosing representative surface samples. Simulations in the fully rough regime are carried out using one to two orders of magnitude fewer points than in a typical DNS. Since no assumptions on the roughness properties or the flow structure (such as outer layer similarity) are made, we expect the SBM to be applicable to non-equilibrium turbulent boundary layer flows.

Large-eddy simulation and modelling of Taylor–Couette flow

Wall-resolved large-eddy simulations (LES) of the incompressible Navier–Stokes equations together with empirical modelling for turbulent Taylor–Couette (TC) flow are presented. LES were performed with the inner cylinder rotating at angular velocity Ω_i and the outer cylinder stationary. With R_i, R_₀ the inner and outer radii respectively, the radius ratio is η = 0.909 . The subgrid-scale stresses are represented using the stretched-vortex subgrid-scale model while the flow is resolved close to the wall. LES is implemented in the range Re_i = 10⁵-10⁶ where Re_i = Ω_iR_id/v and d = R₀-R_i is the cylinder gap. It is shown that the LES can capture the salient features of the flow, including the quantitative behaviour of spanwise Taylor rolls, the log variation in the inner-cylinder mean-velocity profile and the angular momentum redistribution due to the presence of Taylor rolls. A simple empirical model is developed for the turbulent, TC flow for both a stationary outer cylinder and also for co-rotating cylinders. This consists of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. Model results include the Nusselt number Nu (torque required to maintain the flow) and measures of the wall-layer thickness as functions of both the Taylor number Ta and η. These are compared with results from measurement, direct numerical simulation and the LES. A model extension to rough-wall turbulent flow is described. This shows an asymptotic, fully rough-wall state where the torque is independent of Re_i/Ta, and where Nu ~ Ta^(1/2).

The minimal-span channel for rough-wall turbulent flows

Roughness predominantly alters the near-wall region of turbulent flow while the outer layer remains similar with respect to the wall shear stress. This makes it a prime candidate for the minimal-span channel, which only captures the near-wall flow by restricting the spanwise channel width to be of the order of a few hundred viscous units. Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418–431) showed that a minimal-span channel can accurately characterise the hydraulic behaviour of roughness. Following this, we aim to investigate the fundamental dynamics of the minimal-span channel framework with an eye towards further improving performance. The streamwise domain length of the channel is investigated with the minimum length found to be three times the spanwise width or 1000 viscous units, whichever is longer. The outer layer of the minimal channel is inherently unphysical and as such alterations to it can be performed so long as the near-wall flow, which is the same as in a full-span channel, remains unchanged. Firstly, a half-height (open) channel with slip wall is shown to reproduce the near-wall behaviour seen in a standard channel, but with half the number of grid points. Next, a forcing model is introduced into the outer layer of a half-height channel. This reduces the high streamwise velocity associated with the minimal channel and allows for a larger computational time step. Finally, an investigation is conducted to see if varying the roughness Reynolds number with time is a feasible method for obtaining the full hydraulic behaviour of a rough surface. Currently, multiple steady simulations at fixed roughness Reynolds numbers are needed to obtain this behaviour. The results indicate that the non-dimensional pressure gradient parameter must be kept below 0.03–0.07 to ensure that pressure gradient effects do not lead to an inaccurate roughness function. An empirical costing argument is developed to determine the cost in terms of CPU hours of minimal-span channel simulations a priori. This argument involves counting the number of eddy lifespans in the channel, which is then related to the statistical uncertainty of the streamwise velocity. For a given statistical uncertainty in the roughness function, this can then be used to determine the simulation run time. Following this, a finite-volume code with a body-fitted grid is used to determine the roughness function for square-based pyramids using the above insights. Comparisons to experimental studies for the same roughness geometry are made and good agreement is observed.

Turbulent flow over transitionally rough surfaces with varying roughness densities

We investigate rough-wall turbulent flows through direct numerical simulations of flow over three-dimensional transitionally rough sinusoidal surfaces. The roughness Reynolds number is fixed at $k^{+}=10$, where $k$ is the sinusoidal semi-amplitude, and the sinusoidal wavelength is varied, resulting in the roughness solidity $\unicode[STIX]{x1D6EC}$ (frontal area divided by plan area) ranging from 0.05 to 0.54. The high cost of resolving both the flow around the dense roughness elements and the bulk flow is circumvented by the use of the minimal-span channel technique, recently demonstrated by Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418–431) to accurately determine the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$. Good agreement of the second-order statistics in the near-wall roughness-affected region between minimal- and full-span rough-wall channels is observed. In the sparse regime of roughness ($\unicode[STIX]{x1D6EC}\lesssim 0.15$) the roughness function increases with increasing solidity, while in the dense regime the roughness function decreases with increasing solidity. It was found that the dense regime begins when $\unicode[STIX]{x1D6EC}\gtrsim 0.15{-}0.18$, in agreement with the literature. A model is proposed for the limit of $\unicode[STIX]{x1D6EC}\rightarrow \infty$, which is a smooth wall located at the crest of the roughness elements. This model assists with interpreting the asymptotic behaviour of the roughness, and the rough-wall data presented in this paper show that the near-wall flow is tending towards this modelled limit. The peak streamwise turbulence intensity, which is associated with the turbulent near-wall cycle, is seen to move further away from the wall with increasing solidity. In the sparse regime, increasing $\unicode[STIX]{x1D6EC}$ reduces the streamwise turbulent energy associated with the near-wall cycle, while increasing $\unicode[STIX]{x1D6EC}$ in the dense regime increases turbulent energy. An analysis of the difference of the integrated mean momentum balance between smooth- and rough-wall flows reveals that the roughness function decreases in the dense regime due to a reduction in the Reynolds shear stress. This is predominantly due to the near-wall cycle being pushed away from the roughness elements, which leads to a reduction in turbulent energy in the region previously occupied by these events.

A new second-order closure model for rough-wall turbulent flows using the Brinkman equation

A second-order turbulence closure is developed for the new rough-wall layer modeling approach using the Brinkman equation for turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. Interface stress jump conditions including the Reynolds stress components are also considered. The Reynolds-averaged Navier–Stokes equations are solved numerically above the near-wall rough layer, while a second-order turbulence closure is employed in all regions. The rough-wall second-order closure is developed by adopting an existing smooth-wall model. The computational results, including the skin friction coefficient, the log-law mean velocity, the roughness function, the Reynolds stresses, and the turbulent kinetic energy, are presented and compared with those obtained by using a previously developed two-equation turbulence closure. The results show that the new rough-wall layer modeling approach with the second-order turbulence closure model satisfactorily predicted the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress. However, the results for the Reynolds normal stresses are different from the measured data in the inner 20–60% of the boundary layer due to the interface stress jump conditions employed in the present rough-wall layer modeling approach.

A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes

AbstractIn this paper, we propose a novel explicit equation for friction factor, which is valid for both smooth and rough wall turbulent flows in pipes and channels. The form of the proposed equation is based on a new logarithmic velocity profile and the model constants are obtained by using the experimental data available in the literature. The proposed equation gives the friction factor explicitly as a function of Reynolds number and relative roughness. The results indicate that the present model gives a very good prediction of the friction factor and can reproduce the Colebrook equation and its Moody plot. Therefore, the new approximation for the friction factor provides a rational, accurate, and practically useful method over the entire range of the Moody chart in terms of Reynolds number and relative roughness.

Influence of adverse pressure gradient on rough-wall turbulent flows

This paper presents an experimental investigation of adverse pressure gradient turbulent flow over two rough surfaces and a reference smooth surface. The adverse pressure gradient was produced in an asymmetric diffuser whose opening angle was 3°. The rough surfaces comprised sand grains and gravels of nominal mean diameters of 1.55 mm and 4.22 mm, respectively. The tests were conducted at an approach flow velocity of 0.5 m/s and the momentum thickness Reynolds number varied from 900 to 3000. A particle image velocimetry technique was used for the velocity measurements. Profiles of the mean velocity, turbulent intensities, Reynolds stress ratios, mixing length, eddy viscosity and the production terms were then obtained to document the effects of adverse pressure gradient (APG) on low Reynolds number rough-wall turbulent boundary layers. The results indicate that APG thickens the boundary layer and roughness sublayer. The APG and surface roughness also enhanced the production of turbulence as well as the turbulence level when compared with the smooth-wall data.

New Two-Equation Closure for Rough-Wall Turbulent Flows Using the Brinkman Equation

A new flow-physics-based modeling of surface-roughness effects is developed for the Reynolds-averaged Navier-Stokes equations numerical calculations of high-Reynolds-number turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume-averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness, and the permeability is modeled. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, and a low-Reynolds-number k-e model is employed in all regions. In this paper, we present the computational results, including the skin-friction coefficient, the log-law mean velocity, the roughness function, the turbulent kinetic energy, and the Reynolds shear stress. The results show that the new rough-wall-layer modeling approach well predicts the skin-friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress.

Rough-bed flows in geophysical, environmental, and engineering systems: Double-Averaging Approach and its applications

Rough-wall turbulent flows represent a ubiquitous feature of many natural systems and man-made structures and therefore they have attracted significant attention from mathematicians, physicists, engineers, and Earth scientists, who have extensively studied these flows for more than eighty years. However, in spite of a fairly long research history and significant progress made towards their description and understanding, accurate prediction and control of rough-wall flows are still unsolved problems and thus additional research efforts and new approaches are required. One of these approaches, the so-called Double-Averaging Methodology (DAM), is the topic of this Special Issue.

Influence of PIV interrogation area on turbulent statistics up to 4th order moments in smooth and rough wall turbulent flows

The paper presents measurements performed over a smooth surface, a transitionally rough surface generated by wire mesh and a fully rough surface that comprised transverse square ribs in a channel. The flow was seeded using fluorescent particles and the high quality vectors obtained using particle image velocimetry (PIV) technique were used to compute the mean velocity, turbulent statistics up to the fourth order moments as well as the production and dissipation terms in the transport equation for the turbulent kinetic energy. By using different interrogation areas and overlaps to process the PIV images, the interrogation area sizes in wall units varied from 2.9 to 52.4. In the first part of the paper, these interrogation areas were used to study the spatial resolution effects on the mean and higher order moments over the smooth and rough surfaces. For the second part of the paper, classical scaling and the scaling proposed by George and Castillo [W.K. George, L. Castillo, Zero-pressure-gradient turbulent boundary layer, Appl. Mech. Rev. 50 (12) (1997) 689–729] and Zagarola and Smits [M.V. Zagarola, A.J. Smits, Mean-flow scaling of turbulent pipe flow, J. Fluid Mech. 373 (1998) 33–79] were used to document the salient effects of surface roughness on the flow characteristics. The results show spatial resolution effects on some of the turbulent statistics, and it is evident that these effects are more pronounced over the rough surfaces than on the smooth surface. The smaller interrogation area sizes used in this study are adequate to reasonably evaluate all the statistics and production term but not the dissipation rate. It was observed that the power law proposed by George and Castillo [W.K. George, L. Castillo, Zero-pressure-gradient turbulent boundary layer, Appl. Mech. Rev. 50 (12) (1997) 689–729] is better than the log law for modeling low Reynolds number turbulent flows over rough surfaces. The results also support the premise that the mechanisms for turbulence production and transport close to the ribs are markedly different from those for a smooth surface.