Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces

Rough surfaces are usually characterised by a single equivalent sand-grain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles show a good collapse. Profile peaks of the turbulent kinetic energy also vary depending on the surface. We then consider which surface properties are important and how new properties can be incorporated into an empirical model, the accuracy of which can then be tested. Optimised models with several roughness parameters are systematically developed for the roughness function and profile peak turbulent kinetic energy. In determining the roughness function, besides the known parameters of solidity (or frontal area ratio) and skewness, it is shown that the streamwise correlation length and the root-mean-square roughness height are also significant. The peak turbulent kinetic energy is determined by the skewness and root-mean-square roughness height, along with the mean forward-facing surface angle and spanwise effective slope. The results suggest feasibility of relating rough-wall flow properties (throughout the range from hydrodynamically smooth to fully rough) to surface parameters

Direct numerical simulation of turbulent flow over a rough surface based on a surface scan

Typical engineering rough surfaces show only limited resemblance to the artificially constructed rough surfaces that have been the basis of most previous fundamental research on turbulent flow over rough walls. In this article flow past an irregular rough surface is investigated, based on a scan of a rough graphite surface that serves as a typical example for an irregular rough surface found in engineering applications. The scanned map of surface height versus lateral coordinates is filtered in Fourier space to remove features on very small scales and to create a smoothly varying periodic representation of the surface. The surface is used as a no-slip boundary in direct numerical simulations of turbulent channel flow. For the resolution of the irregular boundary an iterative embedded boundary method is employed. The effects of the surface filtering on the turbulent flow are investigated by studying a series of surfaces with decreasing level of filtering. Mean flow, Reynolds stress and dispersive stress profiles show good agreement once a sufficiently large number of Fourier modes are retained. However, significant differences are observed if only the largest surface features are resolved. Strongly filtered surfaces give rise to a higher mean-flow velocity and to a higher variation of the streamwise velocity in the roughness layer compared with weakly filtered surfaces. In contrast, for the weakly filtered surfaces the mean flow is reversed over most of the lower part of the roughness sublayer and higher levels of dispersive shear stress are found

A modified Parametric Forcing Approach for modelling of roughness

Surface roughness in turbulent channel flow is effectively modelled using a modified version of the Parametric Forcing Approach introduced by Busse and Sandham (2012). In this modified approach, the model functions are determined based on the surface geometry and two model constants, whose value can be fine tuned. In addition to a quadratic forcing term, accounting for the effect of form drag due to roughness, a linear forcing term, analogous to the Darcy term in the context of porous media, is employed in order to represent the viscous drag. Comparison of the results with full-geometry resolved Direct Numerical Simulation (DNS) data for the case of dense roughness (frontal solidity ≅0.4) shows a satisfactory prediction of mean velocity profile, and hence the friction factor, by the model. The model is found to be able to reproduce the trends of friction factor with morphological properties of surface such as skewness of the surface height probability density function and coefficient of variation of the peak heights

Reynolds number dependence of Reynolds and dispersive stresses in turbulent channel flow past irregular near-Gaussian roughness

Data to accompany associated publication

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

Angle of attack dependence of flow past cactus-inspired cylinders with a low number of ribs

The aerodynamic coefficients and the Strouhal number of cylinders with three and four ribs, inspired by succulents Euphorbia trigona and Euphorbia Abyssinica are investigated using 2D Unsteady Reynolds-Averaged Navier-Stokes simulations at Reynolds number 20,000. Both configurations show a significant dependence of the studied characteristics on the angle of attack. The obtained results are compared to the smooth circular cylinder, previous results for cylinders with 24 ribs based on the Saguaro cactus, and cylinders with triangular and square cross-sections. Relative to the circular cylinder, the mean drag coefficient is lowered only for the four-rib case at high angles of attack. However, at some angular positions, the ability to reduce unsteady force fluctuations exceeds Saguaro-inspired cylinders. For both shapes studied, the Strouhal number at most angles of attack is lower compared to both the circular cylinder and cylinders with 24 ribs at the same Reynolds number. The minimum values of the aerodynamic coefficients for both configurations are related to the angular orientation. For the four-rib case a critical angle of αcr ≈ 40◦ is observed, at which the mean drag coefficient and the fluctuating lift coefficient attain their minima. The mean lift coefficient reaches at this angle its maximum value before a sudden drop for higher angles of attack. Therefore, for cactus-shaped cylinders with four ribs high angles of attack give the optimum orientation relative to prevailing winds

Influence of Spatial Distribution of Roughness Elements on Turbulent Flow Past a Biofouled Surface

No abstract available

The inverse cascade of magnetic helicity in magnetohydrodynamic turbulence

The nonlinear dynamics of magnetic helicity, $H^M$, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of $H^M$ is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. \textbf{77} 321 (1976)]. By revisiting this theory a universal dynamical balance relation is found that includes effects of kinetic helicity, as well as kinetic and magnetic energy on the inverse cascade of $H^M$ and explains the above-mentioned discrepancy. Considering the result in the context of mean-field dynamo theory suggests a nonlinear modification of the $\alpha$-dynamo effect important in the context of magnetic field excitation in turbulent plasmas.Comment: Minor corrections and improvements mad

Reynolds number dependence of Reynolds and dispersive stresses in turbulent channel flow past irregular near-Gaussian roughness

Direct numerical simulations of fully-developed turbulent channel flow with irregular rough walls have been performed at four friction Reynolds numbers, namely, 180, 240, 360 and 540, yielding data in both the transitionally- and fully-rough regime. The same roughness topography, which was synthesised with an irregular, isotropic and near-Gaussian height distribution, is used in each simulation. Particular attention is directed towards the wall-normal variation of flow statistics in the near-roughness region and the fluid-occupied region beneath the crests, i.e. within the roughness canopy itself. The goal of this study is twofold. (i) Provide a detailed account of first- and second-order double-averaged velocity statistics (including profiles of mean velocity, dispersive stresses, Reynolds stresses, shear stress gradients and an analysis of the mean force balance) with the overall aim of understanding the relative importance of “form-induced” and “turbulence-induced” quantities as a function of the friction Reynolds number. (ii) Investigate the possibility of predicting the levels of streamwise dispersive stress using a phenomenological closure model. Such an approach has been applied successfully in the context of idealised vegetation canopies (Moltchanov & Shavit, 2013, Water Resour. Res., vol. 49, pp. 8222-8233) and is extended here, for the first time, to an irregular rough surface. Overall, the results reveal that strong levels of dispersive stress occur beneath the roughness crests and, for the highest friction Reynolds number considered in this study, show that the magnitude (and gradient) of these “form-induced” stresses exceed their Reynolds stress counterparts. In addition, this study emphasises that the dominant source of spatial heterogeneity within the irregular roughness canopy are “wake-occupied” regions and that a suitable parameterisation of the wake-occupied area is required to obtain an accurate prediction of streamwise dispersive stress