Roughness Reynolds Number Research Articles

An Integral Solution for Skin Friction in Turbulent Flow Over Aerodynamically Rough Surfaces With an Arbitrary Pressure Gradient

The combined law of the wall and wake, with the inclusion of the “roughness depression function” for the inner law in the “Log” region, is used as the inner coordinates' velocity profile in the integral form of the x momentum equation to solve for the local skin friction coefficient. The “equivalent sand grain roughness” concept is employed in the roughness depression function in the solution. Calculations are started at the beginning of roughness on a surface, as opposed to starting them using the measured experimental values at the first data point, when making comparisons of predictions with data sets. The dependence of the velocity wake strength on both pressure gradient and momentum thickness Reynolds number are taken into account. Comparisons of the prediction with experimental skin friction data, from the literature, have been made for some adverse, zero, and favorable (accelerating flows) pressure gradients. Predictions of the shape factor, roughness Reynolds number, and momentum thickness Reynolds number and comparisons with data are also made for some cases. In addition, some comparisons with the predictions of earlier investigators have also been made.

Parameterization of Boundary-Layer Transition Induced by Isolated Roughness Elements

The laminar-to-turbulent transition of boundary layers induced by isolated three-dimensional roughness elements is analyzed by mining a direct numerical simulation database, which covers the variation of many physical parameters, including Mach and Reynolds numbers, and obstacle shape and size. It is found that the transition process is approximately controlled by a Reynolds number based on the momentum deficit past the obstacle, which is proportional to the classical roughness Reynolds number and which approximately incorporates the effects of the roughness element shape. The analysis of the perturbation energy past the obstacle shows that the varicose mode of instability is always dominant in the close proximity of the obstacle, and it promotes transition in supercritical flow cases. On the other hand, the sinuous mode appears to dominate the evolution of marginally subcritical cases, which feature quasi-steady momentum streaks.

The effects of habitat complexity and hydraulic conditions on the establishment of benthic stream macroalgae

Summary Habitat complexity is thought to play an important role in various ecological communities, but its role under variable natural conditions is not well understood, particularly in lotic habitats where the complexity of the substratum influences the diversity and abundance of the benthic community. We investigated the effects of the habitat complexity of the substratum, as represented by fractal structure, on the establishment of stream macroalgae. We also analysed the influence of hydraulic conditions associated with variations in the fractal dimension of the substratum. We hypothesised that habitats with higher surface complexity would have higher macroalgal abundance and that hydraulic conditions would affect macroalgal establishment differently on surfaces of differing complexity. We designed a field experiment to elucidate the role of habitat complexity (represented by the fractal dimension and density of roughness elements) and consequent hydraulic conditions (assessed by the Reynolds number and drag forces) on algal growth. Sterile artificial substrata with five levels of complexity were placed in four unshaded streams. After 60 days of complete submergence, the substrata were removed from the streams, and the per cent cover of macroalgae was measured. We used a principal components analysis (PCA) to reduce the dimensionality and collinearity among our variables (fractal dimension, density of roughness elements, Reynolds number and drag force) and summarise them adequately. Axis 1 (PC1) values were used in a linear model to assess the relationship between the variables and macroalgal cover. PC1 explained 82.2% of the variability in substratum complexity and hydraulic condition. The fractal dimension and density of the roughness elements were negatively related with PC1, whereas the Reynolds number and drag force were related positively. Hydraulic conditions differed among each level of complexity, with the Reynolds number and drag force decreasing with increasing complexity. Macroalgal cover increased on surfaces with lower turbulence and drag force, indicating that less aggressive conditions are suitable for macroalgal colonisation. Additionally, the establishment of macroalgae was greatest on the leading edge of flat‐top ridges, where the water velocity slows and the current changes direction. Habitat complexity and hydraulic conditions play an important role in the establishment of macroalgae in streams and could explain their naturally patchy distribution.

A study of the atmospheric surface layer and roughness lengths on the high‐altitude tropical Zongo glacier, Bolivia

AbstractThe atmospheric surface layer of high‐altitude tropical glaciers is inadequately understood, particularly concerning turbulent fluxes. Measurements have shown that sublimation reduces melt energy in the dry season, but the errors are large when a katabatic wind maximum occurs at a low height. This study analyzed wind and temperature vertical profiles measured by a 6 m mast in the ablation area of the tropical Zongo glacier (16°S, 5060 m above sea level) in the dry seasons of 2005 and 2007. Surface roughness lengths for momentum and temperature were derived from least squares fits of hourly wind and temperature profile data. Measurement errors were explored, focusing on the poorly defined reference level for sensor heights. A katabatic wind maximum at heights between 2 and 3 m was regularly observed during low wind speed and strong inversion conditions, or about ~50%of the time, greatly reducing the surface layer depth. The glacier surface, experiencing melting conditions in the early afternoon and strong cooling at night, remained relatively smooth with z0 ~ 1 mm and zT ~ 0.1 mm. Sensible heat flux measured at ~1 m was not very sensitive to the zero reference level due to two opposite effects: when measurement heights increase, profile‐derived roughness lengths increase but temperature and wind gradients decrease. The relation between zT/z0 and the roughness Reynolds number Re* roughly agrees with the surface renewal model. However, this is mostly due to self‐correlation because of the shared variable z0 in zT/z0 and Re*, which prevents a sound experimental validation of the model.

Development of a Numerical Based Correlation for Performance Losses due to Surface Roughness in Axial Turbines

AbstractIn the present work, a recently developed in-house 2D CFD code is used to study the effect of gas turbine stator blade roughness on various performance parameters of a two-dimensional blade cascade. The 2D CFD model is based on a high resolution flux difference splitting scheme of Roe (1981). The Reynolds Averaged Navier-Stokes (RANS) equations are closed using the zero-equation turbulence model of Baldwin-Lomax (1978) and two-equation Shear Stress Transport (SST) turbulence model. For the smooth blade, results are compared with experimental data to validate the model. Finally, a correlation between roughness Reynolds number and loss coefficient for both turbulence models is presented and tested for three other roughness heights. The results of 2D turbine blade cascades can be used for one-dimensional models such as mean line analysis or quasi-three-dimensional models e.g. streamline curvature method.

Numerical simulations of sink-flow boundary layers over rough surfaces

Turbulent sink flows over smooth or rough walls with sand-grain roughness are studied using large-eddy and direct numerical simulations. Mild and strong levels of acceleration are applied, yielding a wide range of Reynolds number (Reθ = 372 − 2748) and cases close to the reverse-transitional state. Flow acceleration and roughness are shown to exert opposite effects on boundary-layer integral parameters, on the Reynolds stresses, budgets of turbulent kinetic energy, and properties of turbulent structures in the vicinity of the rough surface; statistics exhibit similarity when plotted using inner scaling for cases with the same roughness Reynolds number, k+. Acceleration leads to a decrease of k+, while roughness increases it. For cases with higher k+, the low-speed streaks become destabilized, and turbulent structures near the wall are distributed more uniformly in the wall-parallel plane; they are less extended in the streamwise direction, but more densely packed. Higher k+ also causes decorrelation of the outer-layer hairpin packets with the near-wall structures, probably due to the direct impact of random roughness elements on the hairpin legs. Wall-similarity applies for the fully turbulent cases, in which the outer-layer turbulent statistics are affected by acceleration only. It is shown that being in the hydraulically smooth regime is a necessary condition for reverse-transition, supporting the idea that relaminarization starts from the inner region, where roughness effects dominate.

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer. Part 1: The Boundary-Layer Simulation

Measurements have been made in both a neutral and a stable boundary layer as part of an investigation of the wakes of wind turbines in an offshore environment, in the EnFlo stratified flow wind tunnel. The working section is long enough for the flow to have become very nearly invariant with streamwise distance. In order to be systematic, the flow profile generators of Irwin-type spires and surface roughness were the same for both neutral and stable conditions. Achieving the required profiles by adjusting the flow generators, even for neutral flow, is a highly iterative art, and the present results indicate that it will be no less iterative for a stable flow (as well as there being more conditions to meet), so this was not attempted in the present investigation. The stable-case flow conformed in most respects to Monin–Obukhov similarity in the surface layer. A linear temperature profile was applied at the working section inlet, resulting in a near-linear profile in the developed flow above the boundary layer and ‘strong’ imposed stability, while the condition at the surface was ‘weak’. Aerodynamic roughness length (mean velocity) was not affected by stability even though the roughness Reynolds number \({<}1\), while the thermal roughness length was much smaller, as is to be expected. The neutral case was Reynolds-number independent, and by inference, the stable case was also Reynolds-number independent.

Numerical Simulation of Aerodynamic Performance of Film Cooling on a Flat Plate with Surface Roughness

This study is aimed at researching surface roughness effect on the performance of blades in terms of aerodynamics. Numerical simulation on a rough flat plate with a row of 35°round film holes under different roughness heights, Reynolds numbers and blowing ratios is conducted to see how they affect film cooling on a flat plate. In terms of aerodynamics, the increase of surface roughness height, Reynolds number and blow ratio will result in the increase of skin friction coefficient. Besides, roughness has combined effects with Reynolds number and blowing ratio So the effect of surface roughness on blades performance is too big to ignore.

Turbulent boundary-layer structure of flows over freshwater biofilms

The structure of the turbulent boundary-layer for flows over freshwater biofilms dominated by the diatom Tabellaria flocculosa was investigated. Biofilms were grown on large test plates under flow conditions in an Australian hydropower canal for periods up to 12 months. Velocity-profile measurements were obtained using LDV in a recirculating water tunnel for biofouled, smooth and artificially sandgrain roughened surfaces over a momentum thickness Reynolds number range of 3,000–8,000. Significant increases in skin friction coefficient of up to 160 % were measured over smooth-wall values. The effective roughnesses of the biofilms, ks, were significantly higher than their physical roughness measured using novel photogrammetry techniques and consisted of the physical roughness and a component due to the vibration of the biofilm mat. The biofilms displayed a k-type roughness function, and a logarithmic relationship was found between the roughness function and roughness Reynolds number based on the maximum peak-to-valley height of the biofilm, Rt. The structure of the boundary layer adhered to Townsend’s wall-similarity hypothesis even though the scale separation between the effective roughness height and the boundary-layer thickness was small. The biofouled velocity-defect profiles collapsed with smooth and sandgrain profiles in the outer region of the boundary layer. The Reynolds stresses and quadrant analysis also collapsed in the outer region of the boundary layer.

Parametric Analysis of Turbulent Wall Jet in Still Air Over a Transitional Rough, With Asymptotes of Fully Rough and Fully Smooth Wall Jets

The novel scalings for streamwise variations of the flow in a turbulent wall jet over a fully smooth, transitional, and fully rough surfaces have been analyzed. The universal scaling for arbitrary wall roughness is considered in terms of the roughness friction Reynolds number (that arises from the stream wise variations of roughness in the flow direction) and roughness Reynolds number at the nozzle jet exit. The transitional rough wall jet functional forms have been proposed, whose numerical constants power law index and prefactor are estimated from best fit to the data for several variables, like, maximum wall jet velocity, boundary layer thickness at maxima of wall jet velocity, the jet half width, the friction factor and momentum integral, which are supported by the experimental data. The data shows that the two asymptotes of fully rough and fully smooth surfaces are co-linear with transitional rough surface, predicting same constants for any variable of flow for full smooth, fully rough and transitional rough surfaces. There is no universality of scalings in terms of traditional variables as different expressions are needed for each stage of the transitional roughness. The experimental data provides very good support to our universal relations.

A wave roughness Reynolds number parameterization of the sea spray source flux

AbstractParameterizations of the sea spray aerosol source flux are derived as functions of wave roughness Reynolds numbers, RHa and RHw, for particles with radii between 0.176 and 6.61 µm at 80% relative humidity. These source functions account for up to twice the variance in the observations than does wind speed alone. This is the first such direct demonstration of the impact of wave state on the variability of sea spray aerosol production. Global European Centre for Medium‐Range Weather Forecasts operational mode fields are used to drive the parameterizations. The source flux from the RH parameterizations varies from approximately 0.1 to 3 (RHa) and 5 (RHw) times that from a wind speed parameterization, derived from the same measurements, where the wave state is substantially underdeveloped or overdeveloped, respectively, compared to the equilibrium wave state at the local wind speed.

Numerical Investigation of Passive Separation Control for an Airfoil at Low-Reynolds-Number Conditions

Two different passive flow control strategies were investigated for a modified NACA airfoil at a chord-based Reynolds number of and an angle of attack of . For these conditions, the laminar boundary layer separates from the suction side, resulting in a loss of lift and a drag increase. Distributed roughness elements with roughness Reynolds numbers of and 446 that were mounted near the leading edge and scalloped leading edges with serration amplitudes of 5 and 0.5% of the chord were considered. The large roughness elements and the scalloped leading edge reduce the flow separation and enhance performance. The flow physics are, however, different. For , the roughness elements result in high-frequency shedding. The shedding results in an accelerated transition of the separated boundary layer. For the scalloped leading edge with 5% serration amplitude, laminar separation bubbles are situated in the leading-edge troughs. The turbulent wedges that originate from these bubbles coalesce near midchord. For a serration amplitude of 0.5%, the separation line is deformed in the spanwise direction in a manner that is reminiscent of stall cells.

The role of geometry in rough wall turbulent mass transfer

We report on RANS simulations of high Schmidt number turbulent mass transfer due to a first-order reaction on the surface of a d-type rough wall. We find that for low reaction coefficients, the additional surface area of the rough wall causes an increased mass transfer in comparison with a smooth wall. However, when the reaction coefficient is high, the mass transfer becomes lower than for a smooth wall. A detailed analysis shows that the mass transport in the cavity is dominated by diffusion which becomes the limiting factor at high reaction coefficients. A conceptual model, which is in good agreement with the simulations, highlights that the influence of geometry roughness is not confined to the roughness Reynolds number for molecular-diffusion-dominated cavities.

Transition Experiments on Blunt Cones with Distributed Roughness in Hypersonic Flight

Blunt cones with smooth nosetips and roughened frusta were flown in the NASA Ames Research Center hypersonic ballistic range at a Mach number of 10 through quiescent air environments. Global surface temperature distributions were optically measured and analyzed to determine transition onset and progression over the roughened frusta. Real-gas Navier–Stokes calculations of model flowfields, including laminar boundary-layer development in these flowfields, were conducted to predict values of key dimensionless parameters used to correlate transition on such configurations in hypersonic flow. It was found that nose bluntness has a major influence on roughness-induced transition onset and progression. For small-bluntness cones, pretest computations showed that values of the roughness Reynolds number increased with increasing distance from the beginning of the roughness elements. Transition onset was first observed on the roughened frusta near the cone base, and the transition front progressed forward with increasing freestream pressure at a constant value of the critical roughness Reynolds number. Conversely, for large-bluntness cones, pretest computations showed that values of the roughness Reynolds number decreased with increasing distance from the beginning of the roughness. Transition onset was again observed near the cone base, but forward progression of the transition front with increasing freestream pressure occurred at ever-increasing values of the roughness Reynolds number, a response characteristic of breakdown to turbulence downstream of a “trip ring” or “trip array.”

Large-eddy simulation of passive scalar dispersion in an urban-like canopy

AbstractResults from large-eddy simulations of short-range dispersion of a passive scalar from a point source release in an urban-like canopy are presented. The computational domain is that of a variable height array of buildings immersed in a pressure-driven, turbulent flow with a roughness Reynolds number ${\mathit{Re}}_{\tau } = 433$. A comparative study of several cases shows the changes in plume behaviour for different mean flow directions and source locations. The analysis of the results focuses on utilizing the high-fidelity datasets to examine the three-dimensional flow field and scalar plume structure. The detailed solution of the flow and scalar fields within the canopy allows for a direct assessment of the impact of local features of the building array geometry. The staggered, skewed and aligned arrangements of the buildings with respect to the oncoming flow were shown to affect plume development. Additional post-processing quantified this development through parameters fundamental to reduced-order Gaussian dispersion models. The parameters include measures of concentration decay with distance from the source as well as plume trajectory and spread. The horizontal plume trajectory and width were found to be more sensitive to source location variations, and hence local geometric features, than vertical plume parameters.

Influence of geometrical parameters and forced convective heat transfer in transversely corrugated circular tubes

A numerical investigation is performed to study the effects of different geometrical parameters on the thermal and flow fields through transversely corrugated circular tubes with Reynolds number ranging from 5000 to 60,000 and heat flux of 50W/cm2. The optimization through nineteen transversely corrugated (roughened) tubes having 10mm inner diameter was studied by changing the dimensions of roughness such as relative roughness height (e/d) in the range of 0.025–0.1, relative roughness pitch (p/d) in the range of 0.5–1.5 and relative roughness width (w/d) in the range of 0.05–0.2. For water as a working fluid, heat transfer can be increased with optimal roughness dimensions and maximum performance evaluation criterion (PEC). The results show that the corrugated tube performance was greatly influenced by the geometrical parameters. The Nusselt number increased as the roughness height, width and Reynolds number increased and with the decrease of roughness pitch. The highest Nusselt number was obtained with e/d=0.1, while the efficient flow (max. PEC) was achieved with e/d=0.025 for p/d=0.5 and w/d=0.2. For the rib-roughened tubes, the influence of Reynolds number on the friction factor is quite weak while it is increased with the increase of roughness height compared with the smooth tube.

Passive scalar roughness lengths for atmospheric boundary layer flow over complex, fractal topographies

When modeling atmospheric boundary layer flow over rough landscapes, surface fluxes of flow quantities (momentum, temperature, etc.) can be described with equilibrium logarithmic law expressions, all of which require specification of a roughness length that is, physically, the elevation at which the flow quantity equals its surface value. In high Reynolds number flows, such as the atmospheric boundary layer, inertial forces associated with turbulent eddy motions are responsible for surface momentum fluxes (form, or pressure drag). Surface scalar fluxes, on the other hand, occur exclusively via diffusion in the immediate vicinity of the topography—the interfacial region—before being advected by turbulent eddy motions into the bulk of the flow. Owing to this difference in surface transfer mechanism, the passive scalar roughness length, $$z_{0S}$$ , is known to be less than the momentum roughness length, $$z_0$$ . In this work, classical relations are used to specify $$z_{0S}$$ during large-eddy simulation of atmospheric boundary layer flow over aerodynamically rough, synthetic, fractal topographies which exhibit power-law height energy spectrum, $$E_h (k) \sim k^{\beta _s}$$ , where $$\beta _s$$ is a (predefined) spectral exponent. These topographies are convenient since they resemble natural landscapes and $$\beta _s$$ can be varied to change the topography’s aerodynamic roughness (the study considers a suite of topographies with $$-2.4 \le \beta _s \le -1.2$$ , where $$-2.4$$ and $$-1.2$$ are the “most smooth” and “most rough” cases, respectively, corresponding with roughness Reynolds number, $$Re_0 \approx 10$$ and $$300$$ ). It is often assumed that $$z_{0S}/z_{0} \approx 10^{-1}$$ for all $$Re_0$$ . But results from this work show that the roughness length ratio, $$z_{0S}/z_{0}$$ , depends strongly on $$Re_0$$ , ranging between $$10^{-3}$$ and $$10^{-1}$$ .

The Flow Dynamics in Near-Wall Turbulence for the Boundary Layer over a Rough Surface with Two-Dimensional Square Ribs

LDV (Laser Doppler Velocimetry) measurement has been made near a rough surface to clarify the effect of momentum transports to pressure distribution acting on a roughness element. The measurements were performed for an equilibrium boundary layer developing over the rough surface that the roughness height is proportional to a streamwise distance. The momentum thickness and roughness Reynolds numbers are 6000 and 150, respectively. The accuracy of the mean velocities and turbulence in LDV measurement was checked by a momentum balance method and the estimated value was compared with the local skin friction coefficient measured by a direct measurement. Near the rough surface except for a cavity region, it was confirmed analytically and experimentally that the averaged shear stress profile given as a sum of apparent shear stress due to waviness of mean streamlines, Reynolds shear stress and viscous stress per a roughness pitch length is approximately equal to the wall shear stress. In the cavity region, the averaged shear stress profile can be expressed as a function of an integral of the mean pressure difference on downstream and upstream sidewalls of the cavity, and takes positive value except for the bottom region. In the present rough surface, the gradient of spatially-averaged Reynolds shear stress with respect to height will mainly contribute to the mean pressure difference on sidewalls in the cavity.

Transition Experiments on Slightly Blunted Cones with Distributed Roughness in Hypersonic Flight

‡Slightly blunted cones with smooth tips and roughened frusta were flown in the NASA Ames hypersonic ballistic range through quiescent air environments. Global surface intensity (temperature) distributions were optically measured and analyzed to determine transition onset and progression over the roughened surface. Real-gas Navier-Stokes calculations of model flowfields, including laminar boundary layer development in these flowfields, were conducted to predict key dimensionless parameters used to correlate transition on such configurations in hypersonic flow. For distributed roughness elements totally immersed within the laminar boundary layer, the critical roughness Reynolds number correlating approach was found to well model transition onset and progression over the roughened conic frusta. The critical value of the roughness Reynolds number for transition was found to be 269  20%, in agreement with the critical value of 250  20% determined in earlier experiments for transition on rough, blunt bodies in hypersonic free flight.

Nusselt number and friction factor correlations for solar air heater duct having protrusions as roughness elements on absorber plate

An experimental investigation has been carried out to study the effect of heat transfer and friction characteristics of turbulent flow of air passing through rectangular duct which is roughened by circular protrusions arranged in angular arc fashion. The roughened wall is uniformly heated while other three walls are kept insulated. The thermal and friction characteristics are governed by duct aspect ratio (W/H), hydraulic diameter (D), relative roughness pitch (P/e), relative roughness height (e/D), arc angle (α) and Reynolds number (Re). Experiments encompassed that the Reynolds number ranges from 3600 to 18,100, P/e ranges from 12 to 24, e/D ranges from 0.015 to 0.03 and arc angle of protrusions arrangement ranges from 45° to 75°. The maximum enhancement in heat transfer and friction factor is 2.89 and 2.93 times as compared with smooth duct. These experimental results have been used to develop correlations for Nusselt number and friction factor.