Equivalent Surface Roughness Research Articles

Revisiting dependences of the drag coefficient at the sea surface on wind speed and sea state

Accurate representation of wind stress is important for modelling and predictions of marine environmental conditions. The effect of sea state on wind stress is usually parameterized by relating the equivalent sea surface roughness to the wave age or wave steepness. In this study, a new parameterization is presented for the dependences of sea surface roughness on the wind speed and sea state based on observations. Analyses of observations demonstrate that the sea surface roughness is correlated with the wave age stronger than the wave steepness. As a result, the wave-dependent sea surface roughness is parameterized in terms of the wave age in the new parameterization. The new parameterization features that the sea surface roughness has different dependences on the wave age under wind-sea-dominated, mixed and swell-dominated sea states. Younger waves have larger values of the drag coefficient under wind-sea-dominated and mixed sea states but older waves have larger values under swell-dominated sea states. The drag coefficient predicted by the new parameterization is enhanced at low winds and levels off at high winds. The applicability of the new parameterization is investigated using a nested-grid wave model for the northwest Atlantic based on WAVEWATCH III. The wave model results during a winter storm in March 2014 are compared with the available measurements from buoys and satellite altimeters over the study region. Our results demonstrate that the new parameterization reduces deficiencies of three existing parameterizations of underestimating significant wave heights (SWHs) at low winds (or old waves) and overestimating SWHs at moderate and high winds (or young waves). Overall, the new parameterization performs the best in predicting SWHs during the winter storm in comparison with the existing schemes.

On a model for the prediction of asperity interactions of the coated friction pair

PurposeSurface coatings have been introduced on the contact surfaces to protect the mechanical parts for a long time. However, in terms of the optimum design of coatings, some key coating parameters are still selected by trial and error. The optimum design of coatings can be conducted by numerical experiments. This paper aims to predict the contact behavior of the coated rough surfaces accurately. One improved asperity contact model for the coated rough surfaces considering the misalignment of asperities would be developed.Design/methodology/approachIncorporating the coated asperity contact model into the improved Greenwood Tripp-based statistical approach, the proposed model can predict the elastic-plastic behaviors of the interacting coated asperities.FindingsAccording to numerical experiments, compared with the coated asperity contact model in which an equivalent rough surface against a plane is assumed, the improved asperity contact model for the coated contacts can account for the effect of permitting misalignment of two rough surfaces. The contacts having the thicker, stiffer and harder coatings result in higher asperity contact pressure and smaller real contact area fraction under the given Stribeck oil film ratio.Originality/valueIn this paper, one statistical coated asperity contact model for two rough surfaces was developed. The developed model can consider the elastic-plastic behavior of interacting coated asperities. The effects of the coating thickness and its mechanical properties on the contact behavior of the rough surfaces with coatings can be evaluated based on the developed model.

Boundary Layer Turbulence over Surface Waves in a Strongly Forced Condition: LES and Observation

AbstractThe impact of sea state on air–sea momentum flux (or wind stress) is a poorly understood component of wind–wave interactions, particularly in high wind conditions. The wind stress and mean wind profile over the ocean are influenced by the characteristics of boundary layer turbulence over surface waves, which are strongly modulated by transient airflow separation events; however, the features controlling their occurrence and intensity are not well known. A large-eddy simulation (LES) for wind over a sinusoidal wave train is employed to reproduce laboratory observations of phase-averaged airflow over waves in strongly forced conditions. The LES and observation both use a wave-following coordinate system with a decomposition of wind velocity into mean, wave-coherent, and turbulent fluctuation components. The LES results of the mean wind profile and structure of wave-induced and turbulent stress components agree reasonably well with observations. Both LES and observation show enhanced turbulent stress and mean wind shear at the height of the wave crest, signifying the impact of intermittent airflow separation events. Disparities exist particularly near the crest, suggesting that airflow separation and sheltering are affected by the nonlinearity and unsteadiness of laboratory waves. Our results also suggest that the intensity of airflow separation is most sensitive to wave steepness and the surface roughness parameterization near the crest. These results clarify how the characteristics of finite-amplitude waves can control the airflow dynamics, which may substantially influence the mean wind profile, equivalent surface roughness, and drag coefficient.

Evaluation of surface topography of SiCp/Al composite in grinding

As the main processing technique of SiCp/Al composite, grinding directly affects usability performance. However, cavity defects usually occur during the SiCp/Al grinding process. In this study, the surface micro-topography of SiCp/Al composite in grinding was observed by means of SEM, and the chemical ingredients over the cavity defect surface were analyzed by energy dispersive spectrometry. The surface topography was reconstructed with bilinear interpolation algorithm by a point cloud, and the contour map including cavity defects was obtained. Based on the contour map including cavity defects, a new relationship curve between the projection area ratio and contour height was proposed. A novel comprehensive evaluation system was established and included four aspects, namely the profile height and surface roughness of the entire topography, profile height, and equivalent surface roughness of the cavity defect. The optimized algorithm was proposed with the objective function of maximum grinding efficiency and constraints of profile height and surface roughness. The optimized grinding process parameters were obtained and verification experiments were carried out. The results demonstrated that the predicted results were consistent with the experimental results, and the comprehensive evaluation system including cavity defects can reflect the surface topography intuitively. The comprehensive evaluation system for the surface topography including cavity defects in grinding provides guidance for the usability performance of SiCp/Al composite.

Melt‐Compounded Keratin‐TPU Self‐Assembled Composite Film as Bioinspired e‐Skin

AbstractInspired by the keratin–elastin composition of human skin, here an artificial skin (alias electronic (e)‐skin) is developed through solvent‐free extrusion based melt mixing of thermoplastic polyurethane (TPU) with the biowaste human hair keratin. Self‐assembled composite film of TPU and keratin (i.e., PUK) shows leg skin equivalent coefficient of friction value of 0.26 ± 0.05, cheek skin equivalent average surface roughness (Ra) of 0.047 ± 0.07 µm, cytoskeletal keratin intermediate filament network like rheological behavior, porous morphology, and skin like positive triboelectric property, when the keratin content is 10 wt%. H‐bonded self‐assembled network and lubricating behavior of cysteine‐rich keratin provide such tribological and rheological behaviors of the PUK. Single electrode triboelectric nanogenerator (STENG) made of PUK containing 10 wt% keratin (i.e., 10% PUK) not only shows clear discrimination between the touch feeling sensations of bare, and glove protected human finger, by producing output voltage of ≈1 and ≈16 V cm−2, respectively, but it also can discriminate the tactile sensations of different objects viz., aluminum foil, cotton glove, wood, polyimide, and poly(tetrafluoroethylene) by producing different output voltages, resembling that the PUK composite film is well fitted for e‐skin applications.

Effects of Surface Roughness and Bend Geometry on Mass Transfer in an S-Shaped Back to Back Bend at Reynolds Number of 200,000

Experiments were performed to investigate the local development of roughness and its effect on mass transfer in an S-shaped bend at Reynolds number of 200,000. The tests were performed over four consecutive time periods using a 203-mm-diameter test section with a dissolving gypsum lining to water in a closed flow loop at a Schmidt number of 1200. The surface roughness and the mass transfer over the test periods were measured using X-ray computed tomography (CT) scans of the surface. Two regions of high mass transfer are found: along the intrados of the first and second bends. The surface roughness in these two regions, characterized by the height-to-spacing ratio, grows more rapidly than in the upstream pipe. There is an increase in the mass transfer with time, which corresponds well with the local increase in the height-to-spacing ratio of the roughness. The two regions of high mass transfer enhancement in the bend can be attributed to both a roughness effect and a flow effect due to the bend geometry. The geometry effect was determined by normalizing the local mass transfer with that in a straight pipe with equivalent surface roughness. The mass transfer enhancement due to the geometry effect was found to be relatively constant for the two high mass transfer regions, with a value of approximately 1.5.

A Comparative Study on Equivalent Modeling of Rough Surfaces Contact

Greenwood and Tripp (GT model) have proposed that the contact analysis of two rough surfaces (two-rough-surface contact model) could be considered as an equivalent rough surface in contact with a rigid flat (single-rough-surface contact model). In this paper, by virtue of finite element method, the normal contact analysis was performed with two-rough-surface contact model and its equivalent single-rough-surface contact model, and it was verified that the resultant normal contact forces are in good agreement with each other for these two models, meanwhile the equivalent stress is a little bit lower for two-rough-surface model due to shoulder-to-shoulder contact. In contrast, the sliding contact analysis was also performed with these two models, respectively, and the results show a great disparity with each other in all contact parameters due to the strong plowing effects in two-rough-surface model. Therefore, this equivalence approach proposed by Greenwood and Tripp is only valid for normal contact of rough surfaces and not valid for sliding contact.

The Analysis of Three-Body Contact Temperature under the Different Third Particle Size, Density, and Value of Friction.

Recently, many studies have investigated the friction, wear, and temperature characteristics of the interface between two relative movements. Such analyses often set the coefficient of friction as a fixed value and are analyzed in cases of two-body contact; however, the interface is often a three-body contact and the coefficient of friction varies depending on the operating conditions. This is a significant error in the analysis of contact characteristics, therefore, in this study, the actual interface and the change of the coefficient of friction were analyzed based on three-body micro-contact theory where the contact temperature was also analyzed and the difference between the generally assumed values were compared. The results showed that under three-body contact, the coefficient of total friction increased with an increase in particle size; and at a different particle size and area density of particles, the surface contact temperature increased with the plasticity index and load increases, and the particle contact temperature increased with the increasing particle size. The surface temperature rise was mainly affected by the ratio of the average temperature between surface 1 and surface 2 to the multiplication between the 100th root of the area density of particles and the square root of the equivalent surface roughness (Ts1s2_ave*/ηa0.01σ0.5) and the ratio of the 10th root of the mean particle diameter to the 100th root of the equivalent surface roughness (xa0.1/σ0.001). Particle temperature was mainly affected by the ratio of the 10th root of the mean particle diameter to the 100th root of the equivalent surface roughness (xa0.1/σ0.001) and the area density of particles ηa. Our study indicated that when the contact of surface with surface and the contact of the particles with the surface, the resulting heat balance was assigned to the particles and the surface in a three-body contact situation. Under this contact behavior, it could avoid a too high a rise in micro-contact temperature to achieve the material failure temperature.

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.

Elasto-plastic contact of rough surfaces: a mixed-lubrication model for the textured surface analysis

An improved asperity contact model for two rough surfaces with misalignment is presented in this study. The contact model is statistical and can account for the elasto-plastic behavior of interacting asperities. By combining the improved asperity contact model and the average flow Reynolds equation together, a mixed-lubrication model is developed to understand the effect of surface texturing. By comparing with the results of the purely elastic asperity contact model, it is found that the improved asperity contact model can predict the contact force and actual contact area more accurately, particularly under high load conditions. Moreover, comparing with the elasto-plastic model with an equivalent rough surface against a plane, the improved contact model can consider the effect of permitting misalignment of two rough surfaces. This is beneficial for analyzing the performance of the textured piston ring/liner system, especially when asperities contact and wear happen.

Wave Boundary Layer Turbulence over Surface Waves in a Strongly Forced Condition

AbstractAccurate predictions of the sea state–dependent air–sea momentum flux require a thorough understanding of the wave boundary layer turbulence over surface waves. A set of momentum and energy equations is derived to formulate and analyze wave boundary layer turbulence. The equations are written in wave-following coordinates, and all variables are decomposed into horizontal mean, wave fluctuation, and turbulent fluctuation. The formulation defines the wave-induced stress as a sum of the wave fluctuation stress (because of the fluctuating velocity components) and a pressure stress (pressure acting on a tilted surface). The formulations can be constructed with different choices of mapping. Next, a large-eddy simulation result for wind over a sinusoidal wave train under a strongly forced condition is analyzed using the proposed formulation. The result clarifies how surface waves increase the effective roughness length and the drag coefficient. Specifically, the enhanced wave-induced stress close to the water surface reduces the turbulent stress (satisfying the momentum budget). The reduced turbulent stress is correlated with the reduced viscous dissipation rate of the turbulent kinetic energy. The latter is balanced by the reduced mean wind shear (satisfying the energy budget), which causes the equivalent surface roughness to increase. Interestingly, there is a small region farther above where the turbulent stress, dissipation rate, and mean wind shear are all enhanced. The observed strong correlation between the turbulent stress and the dissipation rate suggests that existing turbulence closure models that parameterize the latter based on the former are reasonably accurate.

STRIBECK AND TRACTION CURVES FOR ELLIPTICAL CONTACTS: ISOTHERMAL FRICTION MODEL

This paper deals with the prediction of the Stribeck and traction curves, by proposing a mixed lubrication model for highly loaded elliptical contacts. The model represents an extension on the mixed lubrication model of Gelinck and Schipper and comprehends both the asperity component or the so called boundary lubrication component (BL) and the elastohydrodynamic component (EHL). The asperity component is calculated from a fully deterministic contact perspective, where an equivalent rough surface is in contact with a smooth and rigid surface. In EHL regime, the film thickness is calculated according to Nijenbanning et al. and the separation for the asperity component is derived from Johnson, with a small adaptation, which was possible due to the deterministic contact model approach. In this way, the separation is calculated from the volume conservation theory of Johnson and even if this can be negative, the film thickness remains above zero permitting the calculation of highly loaded contacts. For the traction curve calculation, an elastic-plastic approximation for BL micro-contacts as proposed by Gelinck and Schipper for line contacts is used.

The influence of bacteria-based biofouling on the wall friction and velocity distribution of hydropower pipes

Algae biofouling due to freshwater diatoms has been investigated thoroughly in open channel flows. Their presence has been shown to cause a significant increase in the local skin friction coefficient, the overall drag coefficient and can produce reductions in flow capacity of up to 10%. This study extends previous work to investigate bacteria-based biofouling that forms on the inside walls of pipelines and machinery that are not exposed to direct sunlight. The effect of biofouling on a 1.5 m long internally painted pipe section of diameter 101.6 mm was investigated. The pipe section was installed in a hydropower scheme for an extended period to allow the growth of flow conditioned biofilms at an average flow velocity of U = 1.3 ms-1. The pipe section was tested over a range of Reynolds numbers under fully-developed turbulent conditions. At each flow rate the head loss of the fouled pipe was measured as well as the complete velocity profile at the downstream end of the pipe to ensure the full effect of the biofouling was captured. These results were used to evaluate the pipe friction factor and sand equivalent surface roughness. Trends in the experimentally determined values of pipe friction factor with varying Reynolds number are significantly different from those predicted by empirically-based theory. Experimental velocity profiles show significant deviations from the theoretical prediction of flow through a rough pipe, with a higher maximum velocity observed in the centre of the pipe but a lower velocity in the near wall region.

Kirchhoff Scattering From Fractal and Classical Rough Surfaces: Physical Interpretation

Scattering from both fractional Brownian motion (fBm) and classical rough surfaces under the Kirchhoff approximation is here considered. The focus is on the scattering integral analytical expression and on its physical interpretation. First, we show that, for an fBm surface, the Kirchhoff approach scattering integral is directly proportional to a symmetric alpha-stable (SαS) distribution. The interpretation of this intriguing result leads us to revisit the meaning of the Kirchhoff solution and of the geometrical optics (GO) even for a regular (classical, nonfractal) rough surface. Then, we conclude that, for both fractal and classical surfaces, the Kirchhoff scattering integral can be interpreted in terms of a sort of “intrinsic” two-scale model, and that, in the fractal case, the obtained SαS distribution can be interpreted as the probability density function (pdf) of the slopes of an equivalent rough surface whose GO scattered power density is equal to the scattered power density of the actual fBm surface.

2203 歯面研削仕上げ後に浸炭硬化した歯車の面圧強さ(OS-02 歯車の強度/OS-03 歯車の材料・熱処理・表面処理)

Because of light weight and high power of transmission, carburized and quenched gears are used as power transmission gear. Surface durability of carburized and quenched gears has been related with their tooth surface properties. The influence of abnormal carburized layer on the surface durability, however, has not been clarified. In this study, tested pinions were of two types: gear carburized and quenched after grinding, and gears carburized and quenched before grinding with two different surface roughness. In case of gears with equivalent surface roughness, the surface durability of the gear with abnormal carburized layer was longer than or almost the same as those without abnormal carburized layer. This would be because the abnormal carburized layer at the edge of tooth surface was worn during the fatigue tests.

The Effect of Determining Topography Parameters on Analyzing Elastic Contact Between Isotropic Rough Surfaces

The elastic contact between two computer generated isotropic rough surfaces is studied. First the surface topography parameters including the asperity density, mean summit radius, and standard deviation of asperity heights of the equivalent rough surface are determined using an 8-nearest neighbor summit identification scheme. Second, many cross sections of the equivalent rough surface are traced and their individual topography parameters are determined from their corresponding spectral moments. The topography parameters are also obtained from the average spectral moments of all cross sections. The asperity density is found to be the main difference between the summit identification scheme and the spectral moments method. The contact parameters such as the number of contacting asperities, real area of contact, and contact load for any given separation between the equivalent rough surface and a rigid flat are calculated by summing the contributions of all the contacting asperities using the summit identification model. These contact parameters are also obtained with the Greenwood-Williamson (GW) model using the topography parameters from each individual cross section and from the average spectral moments of all cross sections. Three different surfaces and three different sampling intervals were used to study how the method to determine topography parameters affects the resulting contact parameters. The contact parameters are found to vary significantly based on the method used to determine the topography parameters, and as a function of the autocorrelation length of the surface, as well as the sampling interval. Using a summit identification model or the GW model based on topography parameters obtained from a summit identification scheme is perhaps the most reliable approach.

Study of the flow between the train underbody and the ballast track

The purpose of this work is to study the flow between the underbody of a high speed train and the ground, which consists of both ballast and sleepers. The flow is approximated by a turbulent Couette flow. An analytical solution of the turbulent Couette flow is proposed. Comparisons of the analytical results against wind tunnel and on track tests experiments and results of other classical models for turbulent Couette flows are made in order to validate the obtained solution. The analytical velocity profile is also compared with the corresponding one calculated with the commercial code Fluent for an idealized two-dimensional configuration. Another objective of this work is to obtain an equivalent roughness of the track made of sleepers and ballast. The results obtained enable stationary RANS simulations to be undertaken by substituting the track made of sleepers and ballast with an equivalent rough plate. This steady state analysis is not possible if the sleepers are retained. Taking into account the energy conservation, and comparing with the analytical solution, the equivalent roughness of the ballast track is obtained. The influence of the following parameters on the obtained values of the equivalent surface roughness is analyzed: height of the gap, Reynolds number and roughness of the upper wall.

Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number

The fluctuating wall pressure and its gradients in the plane of the surface were measured beneath the turbulent boundary layer that forms over the salt playa of Utah's west desert. Measurements were acquired under the condition of near-neutral thermal stability to best mimic the canonical zero-pressure-gradient boundary-layer flow. The Reynolds number (based on surface-layer thickness, δ, and the friction velocity, uτ) was estimated to be 1 × 106 ± 2 × 105. The equivalent sandgrain surface roughness was estimated to be in the range 15≤ks+≤85. Pressure measurements acquired simultaneously from an array of up to ten microphones were analysed. A compact array of four microphones was used to estimate the instantaneous streamwise and spanwise gradients of the surface pressure. Owing to the large length scales and low flow speeds, attaining accurate pressure statistics in the present flow required sensors capable of measuring unusually low frequencies. The effects of imperfect spatial and temporal resolution on the present measurements were also explored. Relative to pressure, pressure gradients exhibit an enhanced sensitivity to spatial resolution. Their accurate measurement does not, however, require fully capturing the low frequencies that are inherent and significant in the pressure itself. The present pressure spectra convincingly exhibit over three decades of approximately −1 slope. Comparisons with low-Reynolds-number data support previous predictions that the inner normalized wall pressure variance increases logarithmically with Reynolds number. The wall pressure autocorrelation exhibits its first zero-crossing at an advected length that is between one tenth and one fifth of the surface-layer thickness. Under any of the normalizations investigated, the present surface vorticity flux intensity values are difficult to reconcile with low-Reynolds-number data trends. Inner variables, however, do yield normalized flux intensity values that are of the same order of magnitude at low and high Reynolds number. Spectra reveal that even at high Reynolds number, the primary contributions to the pressure gradient intensities occur over a relatively narrow frequency range. This frequency range is shown to be consistent with the scale of the sublayer pocket motions. In accord with low-Reynolds-number data, the streamwise pressure gradient signals at high Reynolds number are also characterized by statistically significant pairings of opposing sign fluctuations.

Composite Skewness for Two Rough Surfaces in Contact

Typically, the contact of two rough bodies is transformed into an equivalent rough surface contacting a flat. Due to the mathematics involved, this was usually conducted for surfaces assumed to be Gaussian, where distribution of peaks and valleys are equal. These assumptions were acceptable when dealing with ground surfaces, which are typically Gaussian; however, other finishing techniques often result in skewed surface distributions. As such, an equation was developed numerically within, based on the Weibull distribution, to estimate the composite skewness of contacting rough bodies. The assumption of using the Weibull distribution to describe the surface variation was validated with measured data from different finishing techniques, as was the equation for composite skewness developed within. Presented at the STLE Annual Meeting in Las Vegas, Nevada, May 15-19, 2005 Review led by Alan Lebeck

Grit blasting of Ti–6Al–4V alloy: Optimization and its effect on adhesion strength of plasma-sprayed hydroxyapatite coatings

The effect of grit blasting parameters on the surface roughness of Ti–6Al–4V alloy as the substrate for plasma-sprayed hydroxyapatite (HA) coatings was examined using the factorial and Taguchi designs of experiments. In this study, two grit materials (Al2O3 and SiO2) each at two sizes, and two types of blasting systems (pressure and suction) were used. An equivalent surface roughness of 3.51 μm was obtained in three optimum conditions. The results of the Taguchi designed experiments were analyzed using signal to noise ratio. The tensile bonding strength of HA coatings deposited on the roughened substrates at the three different optimum conditions was measured by the standard adhesion test (ISO 13779-4). As the crystallinity of the coating at the interface, evaluated by the XRD analysis, reduced the bonding strength of the coatings was increased. These findings suggest that the substrate surface topography significantly influences the properties of the coating at the interface.