Rough-wall Flows Research Articles

Transport of particles in a turbulent rough-wall pipe flow

Abstract

Direct Numerical Simulations of Turbulent Flow Over Various Riblet Shapes in Minimal-Span Channels

Riblets reduce skin-friction drag until their viscous-scaled size becomes large enough for turbulence to approach the wall, leading to the breakdown of drag-reduction. In order to investigate inertial-flow mechanisms that are responsible for the breakdown, we employ the minimal-span channel concept for cost-efficient direct numerical simulation (DNS) of rough-wall flows (MacDonald et al. in J Fluid Mech 816: 5–42, 2017). This allows us to investigate six different riblet shapes and various viscous-scaled sizes for a total of 21 configurations. We verify that the small numerical domains capture all relevant physics by varying the box size and by comparing to reference data from full-span channel flow. Specifically, we find that, close to the wall in the spectral region occupied by drag-increasing Kelvin–Helmholtz rollers (Garcia-Mayoral and Jimenez in J Fluid Mech 678: 317–347, 2011), the energy-difference relative to smooth-wall flow is not affected by the narrow domain, even though these structures have large spanwise extents. This allows us to evaluate the influence of the Kelvin–Helmholtz instability by comparing fluctuations of wall-normal and streamwise velocity, pressure and a passive scalar over riblets of different shapes and viscous-scaled sizes to those over a smooth wall. We observe that triangular riblets with a tip angle $$\alpha =30^{\circ }$$ and blades appear to support the instability, whereas triangular riblets with $$\alpha =60^{\circ }$$ – $$90^{\circ }$$ and trapezoidal riblets with $$\alpha =30^{\circ }$$ show little to no evidence of Kelvin–Helmholtz rollers.

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.

Effects of the roughness height in turbulent boundary layers over rod- and cuboid-roughened walls

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over two-dimensional (2D) rod-roughened walls and three-dimensional (3D) cuboid-roughened walls are conducted to investigate the effects of the roughness height on the flow characteristics in the outer layer. The rod elements are periodically aligned along the downstream direction with a pitch of px/θin = 12, and the cuboid elements are periodically staggered with a pitch of px/θin = 12 and pz/θin = 3, where px and pz are correspondingly the streamwise and spanwise pitches of the roughness and θin is the momentum thickness at the inlet. The first surface roughness is placed 80θin downstream from the inlet, leading to a step change from a smooth to rough surface. The rod and cuboid roughness height (k) is varied in the range of 0.1 ≤ k/θin ≤ 1.8 (13 ≤ δ/k ≤ 285), respectively (δ is the boundary layer thickness), and the Reynolds number based on the momentum thickness (θ) is varied in the range of Reθ = 300 ~ 1400. For each case, the self-preservation form of the velocity-defect and the turbulent Reynolds stresses is achieved along the downstream direction. As the roughness height increases, the roughness function (ΔU+) extracted from the mean velocity profiles increases, although the velocity-defect profiles for the rough-wall cases show good agreement with the profile from the smooth-wall case. The magnitude of the Reynolds stresses in the outer layer increases with an increase of k/δ. The outer layer similarity between the flows over the rough and smooth-walls is found when δ/k ≥ 250 and 100 for the 2D rod and 3D cuboid, respectively. The continuous increase of the Reynolds stresses in the outer layer with an increase of k/δ is explained by a large population of very long structures over the rough-wall flows. Because the characteristic width of the structures increases continuously with an increase of k/δ for the rod and cuboid roughness, a wide width of the structures leads to frequent spanwise merging between adjacent structures. The active spanwise merging events with an increase of k/δ increase the streamwise coherence of the structures with the appearance of significant meandering.

A direct comparison of pulsatile and non-pulsatile rough-wall turbulent pipe flow

Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al. , J. Fluid Mech. , vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

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).

New dynamic two-layer model for predicting depth-averaged velocity in open channel flows with rigid submerged canopies of different densities

The depth-averaged velocity is the commonly used engineering quantity in natural rivers, and it needs to be predicted in advance, especially in flood seasons. A model that can provide a unified physical foundation for open channel flows with different canopy densities remains lacking despite ongoing researches. Here, we use the concept of the auxiliary bed to describe the influence of momentum exchange on rigid canopy elements with varying density and submergence. The auxiliary bed divides the vegetated flow into a basal layer and a suspension layer to predict average velocity in each layer separately. In the basal layer, the velocity profile is assumed to be uniform. In the suspension layer, a parameter called “penetration depth” is applied to present the variations in velocity distribution. We also apply a data-driven method, called genetic programming (GP), to derive Chezy-like predictors for average velocity in the suspension layer. Compared to the hydraulic resistance equation for rough-wall flows, the new formulae calculated by the weighted combination method show sound physical meanings. In addition, comparison with other models shows that the new dynamic two-layer model achieves high accuracy in flow rate estimation, especially for vegetated flow with sparse canopies.

Turbulence structures over realistic and synthetic wall roughness in open channel flow at Reτ = 1000

ABSTRACTTurbulence structures in flow over three types of wall roughness: sand-grain, cube roughness and a realistic, multi-scale turbine-blade roughness, are compared to structures observed in flow over a smooth wall in open channel flow at , using direct numerical simulations. Two-point velocity correlations, length scales, inclination angles, and velocity spectra are analysed, and the applicability of Townsend's outer layer similarity hypothesis [Townsend. The structure of turbulent shear flow. Cambridge: Cambridge University Press; 1976] to these parameters was examined. Results from linear stochastic estimation suggest that, near the wall, the quasi-streamwise vortices observed in smooth-wall flow are present in the large-scale recessed regions of multi-scale roughness, whereas they are replaced by a pair of ‘head-up, head-down’ horseshoe structures in sandgrain and cube roughness, similar to those observed by Talapatra and Katz [Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV. J Fluid Mech. 2012;711:161–170]. The configuration of conditional eddies near the wall suggests that the kinematical process of vortices differ for each kind of rough surface. Eddies over multiscale roughness are conjectured to obey a growth mechanism similar to those over smooth walls, while around the cube roughness the head-down horse-shoe vortices of Talapatra and Katz [Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV. J Fluid Mech. 2012;711:161–170] may undergo solid-body rotation on top of a cube roughness on account of the strong shear layer, shortening the longitudinal extent of near-wall structure and promoting turbulence production during this process. These results illustrate the sensitivity of turbulence structure to the roughness texture, particularly within the roughness sublayer.

Single-point structure tensors in turbulent channel flows with smooth and wavy walls

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and nonequilibrium behaviors of turbulence under arbitrary mean deformation or frame rotation. A more complete single-point characterization of the flow can be obtained using the structure dimensionality, circulicity, and inhomogeneity tensors. These tensors are one-point correlations of local stream vector gradients and carry nonlocal information regarding the structure of the flow field. We explore the potential of these tensors to improve understanding of complex turbulent flows using direct numerical simulation of flows in channels with a smooth wall and a two-dimensional sinusoidal wavy wall. To enforce no-slip and no-penetration conditions at wavy-wall boundaries, an immersed boundary method for the stream vector Poisson equation was adopted within the framework of Stylianou, Pecnik, and Kassinos, “A general framework for computing the turbulence structure tensors,” Comput. Fluids 106, 54–66 (2015). The results show that the effects of wall waviness on the inclination and aspect ratio of the two-point velocity correlation near the wall are reproduced qualitatively by their corresponding single-point tensor representations. In the outer layer, good quantitative agreement is achieved for both parameters. Additional observations on the structural changes of turbulence due to wall waviness and their relevance to turbulence modeling with surface roughness are discussed. The findings of this investigation suggest that single-point structure tensors can be appended to the modeling basis for inhomogeneous flows with geometrically complex boundaries, such as rough-wall flows, to develop improved turbulence models.

Parameter extension simulation of turbulent flows

The use of parameter extension simulation (PES) as a mathematical method for simulating turbulent flows is proposed in this study. It is defined as the calculation of a turbulent flow with the help of a reference solution. A typical PES calculation includes three steps, as follows: setting up an asymptotic relationship between the exact solution of the Navier–Stokes equations and the reference solution for the initial parameter values, calculating the reference solution and the necessary asymptotic coefficients, and extending the reference solution to the parameter values to produce the exact solution. The method of controlled eddy simulation (CES) has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special case of large eddy simulation (LES), in which a weighting coefficient and an artificial force distribution are used to damp part of the turbulent motions. The distribution of artificial force is modeled with the help of eddy viscosity. The reference-weighting coefficient can be determined empirically or in a convergence study. To demonstrate potential uses, the proposed PES method is used to simulate four types of turbulent flows. The flows are decaying homogeneous and isotropic turbulence, smooth-wall channel flows, rough-wall channel flows, and compressor-blade cascade flows. The numerical results show that the PES solution is more accurate than a Reynolds-average Navier–Stokes simulation solution. Unlike a traditional LES method, which uses the Smagorinsky, k-equation-transport, or WALE subgrid model, the PES requires a lower mesh resolution. These characteristics make it a potential method for simulating the engineering of turbulent flows with complex geometry and a high Reynolds number.

Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness

The influence of surface anisotropy upon the near-wall region of a rough-wall turbulent channel flow is investigated using direct numerical simulation (DNS). A set of nine irregular rough surfaces with fixed mean peak-to-valley height, near-Gaussian height distributions and specified streamwise and spanwise correlation lengths were synthesised using a surface generation algorithm. By defining the surface anisotropy ratio (SAR) as the ratio of the streamwise and spanwise correlation lengths of the surface, we demonstrate that surfaces with a strong spanwise anisotropy (SAR < 1) can induce an over 200% increase in the roughness function ΔU+, compared to their streamwise anisotropic (SAR > 1) equivalent. Furthermore, we find that the relationship between the roughness function ΔU+ and the SAR parameter approximately follows an exponentially decaying function. The statistical response of the near-wall flow is studied using a “double-averaging” methodology in order to distinguish form-induced “dispersive” stresses from their turbulent counterparts. Outer-layer similarity is recovered for the mean velocity defect profile as well as the Reynolds stresses. The dispersive stresses all attain their maxima within the roughness canopy. Only the streamwise dispersive stress reaches levels that are comparable to the equivalent Reynolds stress, with surfaces of high SAR attaining the highest levels of streamwise dispersive stress. The Reynolds stress anisotropy also shows distinct differences between cases with strong streamwise anisotropy that stay close to an axisymmetric, rod-like state for all wall-normal locations, compared to cases with spanwise anisotropy where an axisymmetric, disk-like state of the Reynolds stress anisotropy tensor is observed around the roughness mean plane. Overall, the results from this study underline that the drag penalty incurred by a rough surface is strongly influenced by the surface topography and highlight its impact upon the mean momentum deficit in the outer flow as well as the Reynolds and dispersive stresses within the roughness layer.

Characteristics of the pressure fluctuations generated in turbulent boundary layers over rough surfaces

Experiments were carried out in high Reynolds number turbulent boundary layers over rough surfaces of diverse geometries. Roughness configurations varied in element height, distribution (random versus ordered), shape and spacing. Rough surfaces comprising of two superposed element geometries were also tested. All flows were free of transitional effects with upwards of 40 000 and ratios above 73. The wall-pressure spectrum and turbulent velocity profiles revealed that the roughness element spacing has the greatest impact on the turbulent structures in the boundary layer. The high-frequency scaling on shear friction velocity, , (Meyers et al.J. Fluid Mech., vol. 768, 2015, pp. 261–293) was validated and was shown to be the viscous contribution to the overall surface drag. An empirical formula for the pressure drag on roughness elements was developed to reflect the finding that the pressure drag is a function of only two variables: sparseness ratio and roughness Reynolds number . Results also suggest that the viscous contribution to drag approaches a constant non-zero value at high Reynolds numbers, and ‘fully rough-wall flow’ may occur at higher than previously thought.

Turbulence Intensity Scaling: A Fugue

We study streamwise turbulence intensity definitions using smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. Scaling of turbulence intensity with the bulk (and friction) Reynolds number is provided for the definitions. The turbulence intensity scales with the friction factor for both smooth- and rough-wall pipe flow. Turbulence intensity definitions providing the best description of the measurements are identified. A procedure to calculate the turbulence intensity based on the bulk Reynolds number (and the sand-grain roughness for rough-wall pipe flow) is outlined.

Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows

A theoretically based relationship for the Darcy–Weisbach friction factor $f$ for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.

Modelling smooth- and transitionally rough-wall turbulent channel flow by leveraging inner–outer interactions and principal component analysis

Direct numerical simulations (DNS) of turbulent channel flow over rough surfaces, formed from hexagonally packed arrays of hemispheres on both walls, were performed at friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=200$, $400$ and $600$. The inner normalized roughness height $k^{+}=20$ was maintained for all Reynolds numbers, meaning all flows were classified as transitionally rough. The spacing between hemispheres was varied within $d/k=2$–$4$. The statistical properties of the rough-wall flows were contrasted against a complementary smooth-wall DNS at $Re_{\unicode[STIX]{x1D70F}}=400$ and literature data at $Re_{\unicode[STIX]{x1D70F}}=2003$ revealing strong modifications of the near-wall turbulence, although the outer-layer structure was found to be qualitatively consistent with smooth-wall flow. Amplitude modulation (AM) analysis was used to explore the degree of interaction between the flow in the roughness sublayer and that of the outer layer utilizing all velocity components. This analysis revealed stronger modulation effects, compared to smooth-wall flow, on the near-wall small-scale fluctuations by the larger-scale structures residing in the outer layer irrespective of roughness arrangement and Reynolds number. A predictive inner–outer model based on these interactions, and exploiting principal component analysis (PCA), was developed to predict the statistics of higher-order moments of all velocity fluctuations, thus addressing modelling of anisotropic effects introduced by roughness. The results show excellent agreement between the predicted near-wall statistics up to fourth-order moments compared to the original statistics from the DNS, which highlights the utility of the PCA-enhanced AM model in generating physics-based predictions in both smooth- and rough-wall turbulence.

Roughness effects in turbulent forced convection

We conducted direct numerical simulations of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal-span channel is used to circumvent the high cost of simulating high-Reynolds-number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, $k^{+}$, is increased, the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$, increases in the transitionally rough regime before tending towards the fully rough asymptote of $\unicode[STIX]{x1D705}_{m}^{-1}\log (k^{+})+C$, where $C$ is a constant that depends on the particular roughness geometry and $\unicode[STIX]{x1D705}_{m}\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $Re_{b}$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}^{+}$, appears to tend towards a constant value, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $Re_{b}$ in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat-transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness $k_{s}/k$ and the temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, $z_{0m}/z_{0h}$, being linearly proportional to the inner-normalised momentum roughness length, $z_{0m}^{+}$, where the constant of proportionality is related to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress are observed. Instantaneous visualisations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.

Recent advances in the numerical simulation of rough-wall boundary layers

Turbulent flows over rough surfaces are ubiquitous in nature and in man-made devices. They present many unique aspects, as roughness alters the turbulence structure and the momentum and energy transfer mechanisms. Numerical simulations that resolve the roughness sublayer are computationally demanding: for an accurate calculation of a flow in realistic conditions, such as the flow in a hydraulic turbine, or over terrain, the roughness should be much smaller than the boundary-layer thickness, and the Reynolds number should be high enough to achieve the fully rough regime. While simulations that relaxed these constraints have highlighted new physical phenomena, more advanced numerical techniques and increased computational power make it possible to perform simulations of rough-wall flows in more realistic conditions. This paper reviews some recent work carried out at the Turbulence Simulation and Modelling Laboratory at Queen's University, highlighting the unique information that can be obtained from numerical simulations.

An alternative floating element design for skin-friction measurement of turbulent wall flows

Indirect methods to estimate surface shear stress are commonly used to characterise rough-wall boundary-layer flows. The uncertainty is typically large and often insufficient to carry out quantitative analysis, especially for surface roughness where established scaling and similarity laws may not hold. It is, thus, preferable to rely instead on independent measurement techniques to accurately measure skin friction. The floating element was one of the first to be introduced, and still is the most popular for its features. Although its fundamental principle has remained unchanged, different arrangements have been suggested to overcome its inherent limitations. In this paper, we review some of these designs and further present an alternative that is able to correct for extraneous loads into the drag measurement. Its architecture is based on the parallel-shift linkage, and it features custom-built force transducers and a data acquisition system designed to achieve high signal-to-noise ratios. The smooth-wall boundary-layer flow is used as a benchmark to assess the accuracy of this balance. Values of skin-friction coefficient show an agreement with hot-wire anemometry to within 2% for Re_{theta } = 4times 10^3 up to 10^4. A rough surface of staggered distributed cubes with large relative height, delta /hsimeq 10, is also investigated. Results indicate the flow reaches the fully rough regime, at the measurement location, for the entire range of Reynolds number. Furthermore, the values of skin friction agree with existing estimations from alternative methods.Graphical abstractDrawings of the floating-element (FE) balance and skin-friction measurements for a smooth-wall boundary layer. On top: slice along the X-Y plane and top view (left) next to their corresponding pictures (right). Colors highlight distinctsubsystems, namely, the floating frame for drag measurement (yellow), the pitching moment mechanism (red) and the acquisitionsystem (blue). Bottom left: smooth-wall setup and calibration system. The FE is flush mounted with the wind tunnel floor and thepulley is attached to a linear traverse which allows setting its position at different wall-normal locations. During calibration, a lid isremoved to make way for the pulley to move into the test section. A wire is then strung over to suspend the weights. Bottom right: Skin friction over a smooth wall. The inset indicates the relative discrepancy between the FE values (blue) and those inferred fromhot-wire anemometry of the boundary-layer profile (red).

Statistical discussions on skin frictional drag of turbulence over randomly distributed semi-spheres

The influence of dynamical effects of rough wall turbulence, namely velocity dispersion, drag force and turbulence, on rough wall skin friction coefficient is statistically discussed by performing direct numerical simulation of rough-walled open channel flows and analyzing spatial and Reynolds (double) averaged equations. Numerical calculations are conducted by the D3Q27 multiple-relaxation-time lattice Boltzmann method (MRT-LBM). For the rough surfaces, randomly distributed semi-spheres are considered. Analyzing an integrated double averaged momentum equation, a main contributor to the skin friction coefficient is found to be the turbulence contribution and a second contributor is the drag contribution, and the drag contribution particularly increases with increasing the equivalent roughness. Although the streamwise mean velocity dispersion is significantly induced by the acceleration/deceleration of the streamwise velocity due to the roughness elements, the wall-normal mean velocity dispersion is not significant. Consequently, the off-diagonal component of the dispersive covariant term is far smaller than the Reynolds shear stress and the velocity dispersion thus hardly contributes to an increase in the skin friction coefficient.

The effect of surface roughness on rotor-stator cavity flows

We are concerned with the CFD simulation of annular rotor-stator cavities using the general purpose second-order finite volume method (FVM) solver OpenFOAM® and Large Eddy Simulation (LES) methods. Simulations of cavities with smooth surfaces are conducted at various Reynolds numbers, and the properties of the mean turbulent flows are validated against experimental and numerical data available in the literature. Comparisons show that second-order accurate FVM approaches can produce high-fidelity simulations of rotor-stator cavities to an acceptable accuracy and are therefore a viable alternative to the computationally intensive high-order methods. Our validated second-order FVM model is then combined with the parametric force approach of Busse and Sandham [“Parametric forcing approach to rough-wall turbulent channel flow,” J. Fluid Mech. 712, 169–202 (2012)] to simulate cavities with a rough rotor surface. Detailed flow visualisations suggest that roughness-induced disturbances propagate in the downstream direction of the rotor flow toward the outer wall of the cavity. The outer wall subsequently provides a passage to transport said roughness effects from the rough rotor layer to the smooth stator layer. We demonstrate that rotor-stator cavity flows are sensitive to even small roughness levels on the rotor surface alone.