Rough-wall Channel Flow Research Articles

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.

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.

Bypass transition mechanism in a rough wall channel flow

Implementation of a bypass laminar-to-turbulent transition is explored. We show that our method, by bypassing linear exponential growth, can induce high mixing capacity localized turbulence in a laminar channel flow at low $R\phantom{\rule{0}{0ex}}e$. An on-demand mixing enhancement in laminar channel flow is proposed.

Turbulent flow in rough wall channels: Validation of RANS models

Two kinds of a generic roughness on plane channel walls have been investigated by standard RANS turbulence models. The objective was to accurately predict mean flow quantities for steady incompressible flows through rough wall channels. Seven turbulence models have been used in a special validation procedure based on direct numerical simulation (DNS) results for several values of the roughness spacing and the Reynolds number (which here are the free parameters). In addition to single RANS solutions also a parameter expansion method (PEM) is examined with respect to its capability to accurately predict rough wall channel flows for an extended range of parameters, i.e. for various roughness heights and Reynolds numbers. Those methods that could be validated were then used to predict results for parameters beyond the validation range. Their accuracy can be assessed by comparison with reasonably extended DNS results. The final conclusion is that RANS solutions only with certain turbulence models and over some parameter ranges can be used to predict turbulent channel flows influenced by wall roughness.

Structure of a turbulent flow through plane channels with smooth and rough walls: An analysis based on high resolution DNS results

Two different DNS-approaches (direct numerical simulation of turbulent flow, i.e. without turbulence modeling) are used to determine the detailed structure of turbulent flow through channels with smooth and rough walls. They are a finite volume method (FVM) with grid refinement toward the walls and a Lattice Boltzmann method (LBM) with a uniform grid. With the LBM-approach high resolutions with up to 300million grid points are possible. Compared to the FVM-approach with less grid points and grid refinement toward the wall much higher resolutions away from the walls occur in the LBM solutions. Due to these high resolutions hairpin vortices can be clearly identified for these flows. They are known to be important building blocks in boundary layers. In channel flows, however, their dense existence has only been detected by experimental studies, whereas numerically it still has not been clearly visualized, especially in rough wall channel flows. Our LBM results show that hairpin vortices and their organizations in large scale and very large scale motions (LSM, VLSM) prevail in both smooth wall and rough wall channel flows. The similarity of the vortical structures in the outer layers over smooth walls and over the present k-type rough walls supports Townsend’s wall similarity hypothesis.

Numerical simulation of fully-developed compressible flows over wavy surfaces

Rough surfaces are common on high-speed vehicles, for example on heat shields, but compressibility is not usually taken into account in the flow modelling other than through the mean density. In the present study, supersonic fully-developed turbulent rough wall channel flows are simulated using direct numerical simulation to investigate whether strong compressibility effects significantly alter the mean flow and turbulence properties across the channel. The simulations were run for three different Mach numbers M=0.3, 1.5 and 3.0 over a range of wall amplitude-to-wavelength ratios from 0.01 to 0.08, corresponding to transitionally and fully rough cases respectively. The velocity deficit values are found to decrease with increasing Mach number. It is also found that at Mach 3.0 significant differences occur in the mean flow and turbulence statistics throughout the channel and not just in a roughness sublayer. These differences are found to be due to the presence of strong shock waves created by the peaks of the roughness elements.

Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow

AbstractThis paper focuses on turbulence structure in a fully developed rough-wall channel flow and its role in subgrid-scale (SGS) energy transfer. Our previous work has shown that eddies of scale comparable to the roughness elements are generated near the wall, and are lifted up rapidly by large-scale coherent structures to flood the flow field well above the roughness sublayer. Utilizing high-resolution and time-resolved particle-image-velocimetry datasets obtained in an optically index-matched facility, we decompose the turbulence into large (${\gt }\lambda $), intermediate ($3\text{{\ndash}} 6k$), roughness ($1\text{{\ndash}} 3k$) and small (${\lt }k$) scales, where $k$ and $\lambda (\lambda / k= 6. 8)$ are roughness height and wavelength, respectively. With decreasing distance from the wall, there is a marked increase in the ‘non-local’ SGS energy flux directly from large to small scales and in the fraction of turbulence dissipated by roughness-scale eddies. Conditional averaging is used to show that a small fraction of the flow volume (e.g. 5 %), which contains the most intense SGS energy transfer events, is responsible for a substantial fraction (50 %) of the energy flux from resolved to subgrid scales. In streamwise wall-normal ($x\text{{\ndash}} y$) planes, the averaged flow structure conditioned on high SGS energy flux exhibits a large inclined shear layer containing negative vorticity, bounded by an ejection below and a sweep above. Near the wall the sweep is dominant, while in the outer layer the ejection is stronger. The peaks of SGS flux and kinetic energy within the inclined layer are spatially displaced from the region of high resolved turbulent kinetic energy. Accordingly, some of the highest correlations occur between spatially displaced resolved velocity gradients and SGS stresses. In wall-parallel $x\text{{\ndash}} z$ planes, the conditional flow field exhibits two pairs of counter-rotating vortices that induce a contracting flow at the peak of SGS flux. Instantaneous realizations in the roughness sublayer show the presence of the counter-rotating vortex pairs at the intersection of two vortex trains, each containing multiple $\lambda $-spaced vortices of the same sign. In the outer layer, the SGS flux peaks within isolated vortex trains that retain the roughness signature, and the distinct pattern of two counter-rotating vortex pairs disappears. To explain the planar signatures, we propose a flow consisting of U-shaped quasi-streamwise vortices that develop as spanwise vorticity is stretched in regions of high streamwise velocity between roughness elements. Flow induced by adjacent legs of the U-shaped structures causes powerful ejections, which lift these vortices away from the wall. As a sweep is transported downstream, its interaction with the roughness generates a series of such events, leading to the formation of inclined vortex trains.

Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV

AbstractMicroscopic holographic PIV performed in an optically index-matched facility resolves the three-dimensional flow in the inner part of a turbulent channel flow over a rough wall at Reynolds number ${\mathit{Re}}_{\tau } = 3520$. The roughness consists of uniformly distributed pyramids with normalized height of ${ k}_{s}^{+ } = 1. 5{k}^{+ } = 97$. Distributions of mean flow and Reynolds stresses agree with two-dimensional PIV data except very close to the wall (${\lt }0. 7k$) owing to the higher resolution of holography. Instantaneous realizations reveal that the roughness sublayer is flooded by low-lying spanwise and groove-parallel vortical structures, as well as quasi-streamwise vortices, some quite powerful, that rise at sharp angles. Conditional sampling and linear stochastic estimation (LSE) reveal that the prevalent flow phenomenon in the roughness sublayer consists of interacting U-shaped vortices, conjectured in Hong et al. (J. Fluid Mech., 2012, doi:10.1017/jfm.2012.403). Their low-lying base with primarily spanwise vorticity is located above the pyramid ridgeline, and their inclined quasi-streamwise legs extend between ridgelines. These structures form as spanwise vorticity rolls up in a low-speed region above the pyramid’s forward face, and is stretched axially by the higher-speed flow between ridgelines. Ejection induced by interactions among legs of vortices generated by neighbouring pyramids appears to be the mechanism that lifts the quasi-streamwise vortex legs and aligns them preferentially at angles of $54\textdegree \text{{\ndash}} 63\textdegree $ to the streamwise direction.

Large eddy simulation of smooth-wall, transitional and fully rough-wall channel flow

Large eddy simulation (LES) is reported for both smooth and rough-wall channel flows at resolutions for which the roughness is subgrid. The stretched vortex, subgrid-scale model is combined with an existing wall-model that calculates the local friction velocity dynamically while providing a Dirichlet-like slip velocity at a slightly raised wall. This wall model is presently extended to include the effects of subgrid wall roughness by the incorporation of the Hama's roughness function \documentclass[12pt]{minimal}\begin{document}$\Delta U^+(k_{s\infty }^+)$\end{document}ΔU+(ks∞+) that depends on some geometric roughness height ks∞ scaled in inner variables. Presently Colebrook's empirical roughness function is used but the model can utilize any given function of an arbitrary number of inner-scaled, roughness length parameters. This approach requires no change to the interior LES and can handle both smooth and rough walls. The LES is applied to fully turbulent, smooth, and rough-wall channel flow in both the transitional and fully rough regimes. Both roughness and Reynolds number effects are captured for Reynolds numbers Reb based on the bulk flow speed in the range 104–1010 with the equivalent Reτ, based on the wall-drag velocity uτ varying from 650 to 108. Results include a Moody-like diagram for the friction factor f = f(Reb, ε), ε = ks∞/δ, mean velocity profiles, and turbulence statistics. In the fully rough regime, at sufficiently large Reb, the mean velocity profiles show collapse in outer variables onto a roughness modified, universal, velocity-deficit profile. Outer-flow stream-wise turbulence intensities scale well with uτ for both smooth and rough-wall flow, showing a log-like profile. The infinite Reynolds number limits of both smooth and rough-wall flows are explored. An assumption that, for smooth-wall flow, the turbulence intensities scaled on uτ are bounded above by the sum of a logarithmic profile plus a finite function across the whole channel suggests that the infinite Reb limit is inviscid slip flow without turbulence. The asymptote, however, is extremely slow. Turbulent rough-wall flow that conforms to the Hama model shows a finite limit containing turbulence intensities that scale on the friction factor for any small but finite roughness.

Validation of a new method for directional dust monitoring

Abstract Fugitive dust from industrial sites is problematic to quantify and can be associated with nuisance complaints. Despite significant limitations, the British Standard 1747 Part 5 (BS 1747:5) directional dust gauge remains preferred for monitoring fugitive dust flux on site boundaries. An alternative directional dust gauge, DustScan, was developed at the University of Leeds, UK, and uses cylindrical adhesive ‘sticky pads’ to sample dust in flux. With this sampler, dust capture is measured as soiling, as opposed to mass, with the BS 1747:5 sampler. An Aerosol Test Tunnel (ATT) was developed to evaluate the performance of the DustScan sampler. Atmospheric turbulence was simulated using a coarse grid generator and maintained as rough-wall channel flow by roughness elements fixed to its floor and roof of the ATT. A polydisperse test dust was introduced upwind to form a cloud at the sampler. DustScan directional dust gauges were repeatedly exposed to aliquots of test dust at wind speeds of 2–10 m s −1 in the ATT. Dust soiling levels either side of the gauge's centreline (relative to the incident direction) were compared to demonstrate that the DustScan sampler is directionally accurate. Much lower proportions of antithetic sampling (dust catch on the downwind face of the gauge) occurred than for the BS 1747:5 sampler. The sampled particle size selection was related to the ratio of particle stop distance ( s ) to sampler diameter ( D ) ratio, s / D , showing that the particle size cut point fell with increasing wind speeds. A preliminary assessment of collection efficiency ( CE ) was made by determining dust mass after controlled ignition of selected sticky pad samples. Although dust saturation of the sticky pads can lead to sample loss over prolonged exposure periods, this loss is relatively small over the 1–2 week intervals established as appropriate for the DustScan sampler. This need for shorter sampling intervals is considered to outweigh the convenience of the longer exposure time but significantly poorer dust sampling characteristics of the BS 1747:5 sampler.

Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow

Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow forReτin the 3520–5360 range. The scales of pyramidal roughness elements satisfy the ‘well-characterized’ flow conditions, withh/k≈ 50 andk+= 60 ~ 100, wherehis half height of the channel andkis the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined toy< 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly aty<k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding tok− 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.

Direct simulations of a rough-wall channel flow

In this study, we performed simulations of turbulent flow over rectangular ribs transversely mounted on one side of a plane in a channel, with the other side being smooth. The separation between ribs is large enough to avoid forming stable vortices in the spacing, which exhibitsk-type, or sand-grain roughness. The Reynolds numberReτof our representative direct numerical simulation case is 460 based on the smooth-wall friction velocity and the channel half-width. The roughness heighthis estimated as 110 wall units based on the rough-wall friction velocity. The velocity profile and kinetic energy budget verify the presence of an equilibrium, logarithmic layer aty≳2h. In the roughness sublayer, however, a significant turbulent energy flux was observed. A high-energy region is formed by the irregular motions just above the roughness. Visualizations of vortical streaks, disrupted in all three directions in the roughness sublayer, indicate that the three-dimensional flow structure of sand-grain roughness is replicated by the two-dimensional roughness, and that this vortical structure is responsible for the high energy production. The difference in turbulence structure between smooth- and rough-wall layers can also be seen in other flow properties, such as anisotropy and turbulence length scales.

Estimation of the Drag of a Hemisphere on a Flat Plate

A model for an irregularly indented rough surface has been proposed by the authors in which tall peaks are picked up and represented by hemispheres having equal volume to corresponding peak. In practical application, drag of a hemisphere is substituted by plane shear stress on a flat plate. This simplified model surface is used to simulate flow over the original rough surface. The model requires drag of a hemisphere on a flat plate. In this work, unique drag formula which is simple and acceptably accurate in balance with the compactness of the model, is investigated by numerical simulations. The formula for a hemisphere on a flat plate is deduced on the basis of simulations by RANS, of channel flows having periodically arranged hemispheres on both plates. Obtained formula is confirmed to compare reasonably to those realized by hemispheres of different size in different ambient situation, in a rough wall channel flow, though drag largely scatters. The form is applied also to pipe flows having periodic hemispheres on the wall and is found to reproduce measured friction, satisfactorily. Although the proposed idea must be examined farther carfully and should be improved in details, promising step has been set up to make proposed model a useful method in practical application.