Equivalent Sand-grain Roughness Height Research Articles

Surface roughness effects on transonic aircraft performance: Experimental/numerical comparisons

This work highlights the necessity of taking into account surface roughness when conducting experimental tests, and when using numerical simulations to precisely calculate the turbulent lift and drag of wind-tunnel models or real aircraft in transonic conditions. The present article is a continuation of “Turbulent drag induced by low surface roughness at transonic speeds: Experimental/numerical comparisons,” Physics of Fluids, Vol. 32, 045108 (2020) by Hue and Molton. The outcomes of this former study, which was focused on flat plate samples, are here applied to a three-dimensional aircraft configuration: the Common Research Model used as a reference in the recent international Drag Prediction Workshops. Experimental campaigns have been performed in the largest ONERA wind tunnels S1MA and S2MA involving models with average surface roughness heights Ra close to 0.5 micrometers, wingspans up to 3.5 meters, Mach and Reynolds numbers up to 0.95 and 5 million respectively. Reynolds-averaged Navier–Stokes computations based on the wind-tunnel tests have then been carried out, using the equivalent sand-grain roughness height approach as well as a Musker-type correlation to determine relevant ks values. The results of both the experimental and numerical campaigns have demonstrated that the aerodynamic coefficients of the aircraft can be significantly affected by the surface roughness, even with roughness Reynolds numbers ks+ potentially below the usual threshold values sometimes considered in engineering applications (i.e. in the order of 3.5 to 5). In particular, the surface roughness effects on lift and drag have been studied using far-field analyses to evaluate the responses of friction, viscous pressure, wave and lift-induced drag components. Finally, the numerical studies have been extended to the full-scale geometry in flight conditions in order to assess the roughness effects and potential gains in realistic aircraft operating conditions.

Roughness effects on compressible turbulent boundary layers under different Mach numbers and wall temperature conditions

Compressible turbulent boundary layers over a zero-pressure gradient flat plate with three-dimensional sinusoidal roughness are simulated by direct numerical simulation. The roughness effects on surface drag, velocity transformation, and turbulence fluctuation characteristics are analyzed in a wide range of Mach numbers (Ma∞ = 2.25–7.25) and different ratios of wall-to-recovery temperature (Tw/Taw = 0.43 and 0.84) conditions. It is found that the roughness significantly amplifies the surface drag coefficient due to the extra pressure drag induced by roughness, and the relative increase in surface drag induced by the roughness rises by 31.1% when Ma∞ changes from 2.25 to 7.25. Current compressible velocity transformations cannot make the logarithmic region of velocity profiles independent of Tw/Taw conditions for rough cases due to the strong wall heat transfer effect below roughness peak. Therefore, a new velocity transformation (Uρt+) is proposed to make the logarithmic region of Uρt+ profiles and roughness induced a downward shift of Uρt+ profiles (ΔUρt+) in a logarithmic region independent of Ma∞ and Tw/Taw conditions. Further numerical experiments validate that, in hypersonic boundary layers, the relation between ΔUρt+ and equivalent sand-grain roughness height Reynolds number still satisfies the roughness function proposed earlier for incompressible flows. Moreover, roughness significantly changes the distribution of mean turbulent kinetic energy (TKE) in compressible turbulent boundary layers: TKE is suppressed at the bottom of roughness, while reaching its maximum at the roughness peak, which is 50%–60% larger than that in smooth case. Finally, the expansion/compression wave patterns induced by roughness alter the turbulence fluctuations in outer layer.

Direct numerical simulation of turbulent flow in pipes with realistic large roughness at the wall

We carry out direct numerical simulation (DNS) of turbulent flow in rough pipes. Two types of irregular roughness are investigated, namely a grit-blasted and a graphite surface. A wide range of Reynolds numbers is tested, from the laminar up to the fully rough regime, attempting to replicate Nikuradse's pioneering study. Despite the large relative roughness, outer-layer similarity is achieved at high Reynolds number as hypothesised by Townsend, with deviations from the smooth wall case of 4 % for the grit-blasted surface and 13 % for the graphite surface. This makes it possible to define a roughness function and the equivalent sand-grain roughness. The results are compared with those obtained in plane channels, with small differences pointing to the residual influence of the duct cross-sectional shape in the presence of relatively large roughness. The computed friction factors behave similar to those Nikuradse's chart, with differences in terms of the friction factor in the laminar region and of the critical Reynolds number, which are partly absorbed by using the hydraulic radius as reference length scale. The distributions of the velocity fluctuations intensities point to a isotropisation of turbulence in the near-wall region resulting from the roughness, with influence of the roughness geometry. Comparison of the computed equivalent sand-grain roughness height suggest that existing correlations suffer from poor predictive power, at least for surfaces with large relative roughness.

Assessment of aerodynamic roughness parameters of turbulent boundary layers over barnacle-covered surfaces

Full-scale drag penalty predictions of flows over rough walls require surface roughness characterisation from laboratory experiments or numerical simulations. In either approach, it is necessary to determine the so-called equivalent sand-grain roughness height (k_s). There are several steps involved in determining this aerodynamic roughness lengthscale, but its procedure typically includes a combination of measurement of wall-shear stress (tau _w) using direct or indirect methods as well as analysis of velocity profiles. Indirect methods usually rely on assumptions made about flow and its scaling including the validity of universal outer-layer similarity. However, the implications of the underlying assumptions involved in full-scale drag prediction are unclear. In this work, we carry out wind tunnel measurements over a realistic rough surface (from a fouled ship-hull) to evaluate the impact of different methods with an emphasis on using the outer-layer similarity hypothesis for full-scale drag predictions. Wall-shear stress is measured using an in-house floating-element drag balance (DB), and velocity profiles are obtained using particle image velocimetry (PIV), allowing the evaluation of k_s, and the associated wake parameters through several methods. The aerodynamic roughness parameters hence obtained are used for full-scale drag penalty calculations. It is observed that the predicted drag penalty can vary by over 15% among the different methods highlighting the care that should be taken when employing such methods.

Modeling the Surface Pressure Spectrum on Rough Walls in Pressure Gradients

Abstract Models for surface pressure spectra beneath rough wall boundary layers are assessed, with particular emphasis on prediction from steady, Reynolds-averaged Navier–Stokes (RANS) data. RANS roughness boundary conditions are shown to have qualitatively good trends between roughness function and roughness Reynolds number, but model-to-model discrepancies remain and the universality of an equivalent sandgrain roughness height for turbulence models is doubtful. Existing empirical models for the surface pressure spectrum show good agreement in some spectral regions and a newly proposed model shows good matching across the spectrum in a variety of pressure gradient conditions. Adjustments are made to existing TNO analytical models to incorporate rough wall effects, including changes to the velocity spectrum model and the inclusion of a wall-shift, shown to be independent of local Reynolds number, pressure gradient, or turbulence model. The mathematical character of the rough wall spectrum has been revealed, but challenges remain to implement both flow and spectral modeling without a priori knowledge of the flow.

Surface roughness effects on film-cooling effectiveness in a fan-shaped cooling hole

Large eddy simulations (LES) were carried out to investigate the influence of surface roughness, which was applied to the inner walls of a cooling hole, on cooling performance and flow structures. The cooling hole was a 30-degree inclined, baseline 7-7-7 fan-shaped hole relative to a turbulent flat plate boundary layer of the mainstream. Numerical simulations were performed at two different blowing ratios (M=1.5 and 3.0) and at a constant density ratio (DR=1.5) for various configurations of surface roughness. In order to numerically consider the effects of surface roughness, the equivalent sand-grain roughness model was utilized. Different correlations between the equivalent sand-grain roughness height and arithmetic average roughness height were numerically tested to find an accurate correlation compared to the measurements. The time-averaged numerical results were validated by experiments looking at the velocity and thermal fields for the smooth and rough cooling holes. Results revealed that increasing the surface roughness applied to the cooling hole, increases the thickness of the boundary layers within the hole, especially at the higher blowing ratio. This leads to a higher jet core flow at the cooling hole exit and lower cooling effectiveness at the flat plate surface compared with a smooth cooling hole. The minimum area-averaged film-cooling performance showed a 58% reduction compared to a smooth hole in the case of the highest blowing ratio (M=3.0) and the largest surface roughness height. In addition, the time-space evaluation of the velocity fluctuations showed greater flow unsteadiness and increased wavy patterns within the cooling hole in the case of rough holes.

Dimensionless Model of Frost Roughness on Cold Flat Plate Under Forced Convection

Laboratory experiments were conducted to generate empirical dimensionless correlations for estimating surface roughness of frost formed on a cold flat plate under forced convection. Environmental variables, including wall temperature , air velocity , relative humidity , and air temperature , were considered when generating the correlations. The test conditions were chosen to simulate the environmental conditions experienced by cold-soaked fuel frost formation on the upper surface of airplane wings. Experimental conditions included wall temperatures from to , freestream temperatures from 8 to , relative humidities from 60 to 91%, and air velocities from 0.5 to . The root-mean-square height, skewness, and equivalent sand-grain roughness height of frost were correlated as functions of the Reynolds number, absolute humidity, and dimensionless temperatures. The comparison between the correlation of frost equivalent sand-grain roughness height in this study and a previous model revealed the importance of test surface geometry on frost roughness formation.

The effect of cleaning and repainting on the ship drag penalty

Although the hull of a recently dry-docked large ship is expected to be relatively smooth, surface scanning and experimentation reveal that it can exhibit an “orange-peel” roughness pattern with an equivalent sand-grain roughness height = 0. 101 mm. Using the known value and integral boundary layer evolution, a recently cleaned and coated full-scale ship was predicted to experience a significant increase in the average coefficient of friction and total hydrodynamic resistance during operation. Here the report also discusses two recently reported empirical estimations that can estimate ks directly from measured surface topographical parameters, by-passing the need for experiments on replicated surfaces. The empirical estimations are found to have an accuracy of 4.5 − 5 percentage points in

A novel indicator for ship hull and propeller performance: Examples from two shipping segments

Ship hulls and propellers suffer from both mechanical defects and marine growth, which increase surface roughness and thus lead to significant power/speed penalties. A recent standard, ISO 19030:2016, aimed at establishing a transparent and accurate method to compare a vessel's performance to itself over time. However, the standard performance value, percentage speed difference Vdiff, is both vessel-specific and sensitive to operation point, most importantly vessel speed. The current paper thus proposes a new performance indicator, based on the concept of equivalent sand-grain roughness height ks, which would enable comparisons between vessels, increased accuracy for comparison of a vessel to itself over time, and calculation of penalties under operating conditions differing from past data (e.g. slow steaming). Sand-grain height ks is determined iteratively, through modelling roughness penalties on propulsive power (Granville's similarity law scaling), comparing modelled and measured penalties, and stopping the iterative process at a given tolerance on power penalty. This new performance indicator is applied to onboard-collected data from a Panamax tanker and two Roll-on/Roll-off sister vessels, yielding qualitative agreement with hull condition reported from diving inspections. Comparative advantages and limitations of ks are discussed in relation to the ISO 19030 performance value.

Skin Friction Measurements of Systematically-Varied Roughness: Probing the Role of Roughness Amplitude and Skewness

Skin-friction, roughness functions and predictive correlations are presented for random roughness that has a Gaussian power spectral density distribution of surface elevations. The root-mean-square (rms) roughness height and the skewness of the probability density function are parametrically varied to investigate the role of these parameters in generating the friction at the wall. Results are presented for all roughness regimes, from hydraulically-smooth to fully-rough. Negative skewness (pits) had a much smaller influence on drag than positive skewness (peaks). Predictive engineering correlations for the equivalent sandgrain roughness height indicate that the rms roughess height and skewness are important scaling parameters. However, the scaling does not appear to be universal as different correlations are needed for surface roughness with positive, negative and zero skewness. Most surfaces collapse to a single roughness function in the transitionally-rough regime similar to the one developed by Nikuradase (1933) for uniform sand-grain roughness. The exceptions are the wavy surface (low effective slope) and the surface with high positive skewness.

Effect of the shaft on the aerodynamic performance of urban vertical axis wind turbines

The central shaft is an inseparable part of a vertical axis wind turbine (VAWT). For small turbines such as those typically used in urban environments, the shaft could operate in the subcritical regime, resulting in large drag and considerable aerodynamic power loss. The current study aims to (i) quantify the turbine power loss due to the presence of the shaft for different shaft-to-turbine diameter ratios δ from 0 to 16%, (ii) investigate the impact of different operational and geometrical parameters on the quantified power loss and (iii) evaluate the impact of the addition of surface roughness on turbine performance improvement. Unsteady Reynolds-averaged Navier-Stokes (URANS) calculations are performed on a high-resolution computational grid. The evaluation is based on validation with wind-tunnel measurements. The results show that the power loss increases asymptotically with increasing δ due to the higher width and length of the shaft wake as the blades pass through a larger region with lower velocity in the downwind area. A maximum power loss of 5.5% compared to the hypothetical case without shaft is observed for δ=16%. The addition of surface roughness is shown to be an effective approach to shift the flow over the shaft into the critical regime, reducing the shaft drag and wake width as a result of a delay in separation. For an optimal dimensionless equivalent sand-grain roughness height of 0.08, the turbine power coefficient at δ=4% improves by 1.7%, which is equivalent to a 69% recovery of the corresponding turbine power loss. The results are found to be virtually independent of the shaft-to-turbine rotational speed ratio.

Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces

ABSTRACTRough 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.

Numerical simulation of roughness effects on the flow past a circular cylinder

In the present work large eddy simulations of the flow past a rough cylinder are performed at a Reynolds number of Re = 4.2 × 105 and an equivalent sand-grain surface roughness height ks = 0.02D. In order to determine the effects of the surface roughness on the boundary layer transition and as a consequence on the wake topology, results are compared to those of the smooth cylinder. It is shown that surface roughness triggers the transition to turbulence in the boundary layer, thus leading to an early separation caused by the increased drag and momentum deficit. Thus, the drag coefficient increases up to CD ≈ 1.122 (if compared to the smooth cylinder it should be about CD ≈ 0.3 — 0.5). The wake topology also changes and resembles more the subcritical wake observed for the smooth cylinder at lower Reynolds numbers than the expected critical wake at this Reynolds number.

An assessment of the ship drag penalty arising from light calcareous tubeworm fouling

A test coupon coated with light calcareous tubeworm fouling was scanned, scaled and reproduced for wind-tunnel testing to determine the equivalent sand grain roughness ks. It was found that this surface had a ks = 0.325 mm, substantially less than the previously reported values for light calcareous fouling. This result was used to predict the drag on a fouled full scale ship. To achieve this, a modified method for predicting the total drag of a spatially developing turbulent boundary layer (TBL), such as that on the hull of a ship, is presented. The method numerically integrates the skin friction over the length of the boundary layer, assuming an analytical form for the mean velocity profile of the TBL. The velocity profile contains the roughness (fouling) information, such that the prediction requires only an input of ks, the free-stream velocity (ship speed), the kinematic viscosity and the length of the boundary layer (the hull length). Using the equivalent sandgrain roughness height determined from experiments, a FFG-7 Oliver Perry class frigate is predicted to experience a 23% increase in total resistance at cruise, if its hull is coated in light calcareous tubeworm fouling. A similarly fouled very large crude carrier would experience a 34% increase in total resistance at cruise.

An intermittency model for predicting roughness induced transition

An intermittency transport equation for RANS modeling, formulated in local variables, is extended for roughness-induced transition. To predict roughness effects in the fully turbulent boundary layer, published boundary conditions for k and ω are used. They depend on the equivalent sand-grain roughness height, and account for the effective displacement of wall distance origin. Similarly in our approach, wall distance in the transition model for smooth surfaces is modified by an effective origin, which depends on equivalent sand-grain roughness. Flat plate test cases are computed to show that the proposed model is able to predict transition onset in agreement with a data correlation of transition location versus roughness height, Reynolds number, and inlet turbulence intensity. Experimental data for turbine cascades are compared to the predicted results to validate the proposed model.

Estimation and prediction of the roughness function on realistic surfaces

Large-eddy simulations are carried out in turbulent open-channel flows to determine the roughness function and the equivalent sand-grain roughness height, ks, over sand-grain roughness and different types of realistic roughness replicated from hydraulic turbine blades. A range of Reynolds numbers and mean roughness heights is chosen, leading to both transitionally and fully rough regimes. The start of the fully rough regime is shown to depend on the roughness type, and ks depends strongly on the surface topography. We then examine several existing correlations that predict ks based on the information of the surface geometry. In the cases where the surface slope is an important parameter, the moments of surface height statistics do not predict the roughness function, while the existing forms of slope-based correlations perform well. The range of applicability of various correlations is shown to vary with the roughness topography, as the critical value of the effective slope, separating the waviness and roughness regimes, is shown to be higher for a realistic surface, compared to the value for the more regular types of roughness that were previously studied.

Review of Hydraulic Roughness Scales in the Fully Rough Regime

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface.

Examination of a critical roughness height for outer layer similarity

The existence of a critical roughness height for outer layer similarity between smooth and rough wall turbulent boundary layers is investigated. Results are presented for boundary layer measurements on flat plates covered with sandgrain and woven mesh with the ratio of the boundary layer thickness to roughness height (δ∕k) varying from 16 to 110 at Reθ=7.3×103–13×103. In all cases tested, the layer directly modified by the roughness (the roughness sublayer) is confined to a region <5k or <3ks from the wall (where ks is the equivalent sandgrain roughness height). In the larger roughness cases, this region of turbulence modification extends into the outer flow. However, beyond 5k or 3ks from the wall, similarity in the turbulence quantities is observed between the smooth and rough wall boundary layers. These results indicate that a critical roughness height, where the roughness begins to affect most or all of the boundary layer, does not exist. Instead, the outer flow is only gradually modified with increasing roughness height as the roughness sublayer begins to occupy an ever increasing fraction of the outer layer.

Wall boundary conditions for rough walls

The treatment of rough walls is still a considerable challenge in computational fluid dynamics. Empirical wall functions are available to bridge the flow and shear stress in the near-wall computational cells to the wall distance and roughness. The concept of equivalent sand-grain roughness has been applied. In the present paper, we present a near-wall flow model that uses the concept of equivalent sand-grain roughness height. A simple and fast numerical solution procedure is used to produce the necessary input for the wall treatment in the momentum and turbulence field transport equations. In particular, we try to make a link between real roughness geometry and the equivalent roughness height. Typical applications of the presented wall treatment are industrial applications like friction in multiphase pipelines and velocity distribution over complex terrain, in conjunction with localisation of windmills.

The Importance of the Mean Elevation in Predicting Skin Friction for Flow Over Closely Packed Surface Roughness

The discrete-element surface roughness model is used to provide insight into the importance of the mean elevation of surface roughness in predicting skin friction over rough surfaces. Comparison of experimental data and extensive computational results using the discrete-element model confirm that the appropriate surface for the imposition of the no-slip condition is the mean elevation of the surface roughness. Additionally, the use of the mean elevation in the Sigal-Danberg approach relating their parameter to the equivalent sand-grain roughness height results in replacing three different piecewise expressions with a single relation. The appropriate mean elevation for closely-packed spherical roughness is also examined.