Dimensionless Roughness Research Articles

Modeling of turbulent flows through annuli with smooth and rough walls; drag reduction and heat transfer

A model of a turbulent flow in an annular channel with rough walls is developed. An effect of roughness on hydraulic resistance of the channel is accounted for through the formal dimensionless negative velocity shift at the wall by using an empirical function linking this velocity shift to the dimensionless sandgrain wall roughness. The developed annular flow model is validated by experimental data found in literature for both smooth walls, both rough walls, smooth outer wall and rough inner wall as well as vice versa. The same flow model is applied also to a polymer solution turbulent flow in annular channel with hydraulically smooth walls. A turbulent drag reduction effect, observed in this case, is accounted for by a positive velocity shift at the wall determined for a certain drag reduction chemical from experiments in a round cross-section pipe. Also, an engineering approach for modeling heat transfer through either outer or inner wall of an annular channel with rough walls is suggested. This approach is based on the known analogy of heat transfer in a hydraulically smooth annular channel and a pipe. This analogy is extended to an annular channel with rough walls by using the developed flow model. The heat transfer model developed is validated, discussed and illustrated by calculation examples. Key attention is paid to analyzing an effect of the Reynolds number on both a Nusselt number increase and an efficiency change for different wall roughening cases.

Wind waves impact on the velocity in wave boundary layer in the condition of dynamically smooth surface

One of the factors of wind wave impact on vertical distributions in atmosphere surface layer is the flux of momentum produced by the wave-produced fluctuations. Wave surface are supposed to be a dynamically rough and effects of the molecular viscosity are neglected. In this paper impact of wave momentum fluxes with values of wind velocity which lead to dynamically smooth ocean surface is estimated. The well-known theoretical aspects and results of experimental research are applied. Dependence of dimensionless thickness of viscosity layer on dimensionless roughness of smooth surface is analyzed. The equations of motion are formed taking into account the manifestation of three factors: molecular, turbulent and wave momentum flux. The models based on these equations are described.The choice of constant coefficients that are set in calculations with this model is considered. Results of calculations and analysis of vertical profiles of wind speed and the dependence of the drag coefficient on wind velocity under various wave age.

Effect of dimensionless roughness on cascade flow separation

This study examines the impact of dimensionless roughness on flow separation structures and flow characteristics through a combination of experimental and numerical simulation methods. The findings indicate that a specific dimensionless roughness k+ exists for the fixed airfoil that minimizes cascade loss. Furthermore, increasing surface dimensionless roughness can alter the flow separation structure and effectively prevent flow separation. The numerical simulation results indicate that as dimensionless roughness increases, the impact of open separation and separation bubbles on the flow state over the blade surface is reduced or eliminated. In cases where separation occurs in the cascade, increasing dimensionless roughness results in a reduction in the boundary layer thickness and the width of the wake jet, thereby leading to a smoother outlet angle and improved efficiency. Conversely, when there is no separation, increasing dimensionless roughness leads to the accumulation of low-energy fluid at the trailing edge of the cascade. This results in an increase in the boundary layer thickness and the width of the wake loss, a larger outlet angle of the blade, and a decrease in the efficiency of the cascade. By analyzing the influence of dimensionless roughness on flow separation in cascades, engineers can quickly identify the geometric roughness height to suppress flow separation.

Heat transfer mechanism in vibrational turbulent Rayleigh–Bénard convection with rough plates

The joint effect of rectangular-type roughness and horizontal vibration on two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) is investigated by using the thermal lattice Boltzmann method (LBM) in this article. The present work focuses on the Nusselt number and plume dynamics of the convection in the range of dimensionless vibration frequency 0 ≤ ω* ≤ 1000 and the range of dimensionless roughness height 0 ≤ h* ≤ 0.05. The Rayleigh number is 108 and Prandtl number is 4.38. Our numerical results indicate that the relationship between the Nusselt number and roughness height is mostly proportional, and the relationship between the Nusselt number and the vibration frequency is exponential. It is further found that heat transfer enhances by 3.06 times under the joint effect of horizontal vibration and rectangular roughness on turbulent RBC. It provides significant physical insight into the mechanism of cooperative heat transfer enhancement.

Quantification of Mesoscale Deformation-Induced Surface Roughness in α-Titanium

The phenomenon of mesoscale deformation-induced surface roughening in titanium polycrystals is examined experimentally and numerically. The evolution of the surface morphology under uniaxial tension is analyzed in terms of the standard and ad hoc roughness parameters and the fractal dimension. The statistical estimates are compared to the grain-scale stress-strain fields in order to reveal an interrelation between the in-plane plastic strains and out-of-plane surface displacements. A strong correlation with a determination coefficient of 0.99 is revealed between the dimensionless roughness parameter Rd and the corresponding in-plane plastic strain. The standard roughness parameters Ra and RRMS are shown to correlate linearly with the in-plane strains, but only for moderate tensile deformation, which is due to filtering out low-frequency components in the surface profiles. The fractal dimension DF changes with the subsection strains in a sawtooth fashion, with an abrupt drop in the neck region. The descent portions of the DF dependences are supposedly related to the appearance of low-frequency components in the structure of the surface profiles.

CFD analysis of Fe transfer on roughened wall caused by turbulent lead-bismuth eutectic flow

Structural material compatibility with lead bismuth eutectic is one of the main challenges for design and operation of the LBE-cooled nuclear systems. To better understand the mechanisms of stainless steel corrosion behavior in LBE flow, the iron mass transfer phenomenon on roughened walls under various LBE pipe flow conditions are numerically investigated in this study. CFD simulations are performed, by applying a low Reynolds number k-ε model, in a range of Reynolds number from 5 × 103 to 105. Meanwhile, various pipe wall roughness conditions are considered, which are simulated by crests with different depths and periodic lengths. Effects of roughness dimensions and Reynolds numbers on the near-wall mass transfer rate are investigated. Results showed that higher flow velocities and shorter crest length led to higher mass transfer coefficient. On the basis of the results, the mass transfer coefficients are proposed both for smooth wall and roughened walls. The mass transfer enhanced by wall roughness is characterized by the ratio of rough-to-smooth mass transfer coefficient, and this ratio is demonstrated by a regression equation, in which dimensionless roughness number, Reynolds number and geometrical ratio of the roughness are included. Moreover, it is found that the ratio of rough-to-smooth mass transfer coefficient is relatively more dependent on Reynolds number.

Wettability of Metal Surfaces Affected by Paint Layer Covering.

The aim of the work was to quantify the surface wettability of metallic (Fe, Al, Cu, brass) surfaces covered with sprayed paints. Wettability was determined using the contact angle hysteresis approach, where dynamic contact angles (advancing ΘA and receding ΘR) were identified with the inclined plate method. The equilibrium, ΘY, contact angle hysteresis, CAH = ΘA − ΘR, film pressure, Π, surface free energy, γSV, works of adhesion, WA, and spreading, WS, were considered. Hydrophobic water/solid interactions were exhibited for the treated surfaces with the dispersive term contribution to γSV equal to (0.66–0.69). The registered 3D surface roughness profiles allowed the surface roughness and surface heterogeneity effect on wettability to be discussed. The clean metallic surfaces turned out to be of a hydrophilic nature (ΘY < 90°) with high γSV, heterogeneous, and rough with a large CAH. The surface covering demonstrated the parameters’ evolution, ΘA↑, ΘR↑, γSV↓, WA↓, and WS↓, corresponding to the surface hydrophobization and exhibiting base substratum-specific signatures. The dimensionless roughness fluctuation coefficient, η, was linearly correlated to CAH. The CAH methodology based on the three measurable quantities, ΘA, ΘR, and liquid surface tension, γLV, can be a useful tool in surface-mediated process studies, such as lubrication, liquid coating, and thermoflow.

Shear-induced modulation on thermal convection over rough plates

External modulation on thermal convection has been studied extensively to achieve the control of flow structures and heat-transfer efficiency. In this paper, we carry out direct numerical simulations on Rayleigh–Bénard convection accounting for both the modulation of wall shear and roughness over the Rayleigh number range $1.0 \times 10^6 \le Ra \le 1.0 \times 10^8$ , the wall shear Reynolds number range $0 \le Re_w \le 5000$ , the aspect-ratio range $2 \le \varGamma \le 4{\rm \pi}$ , and the dimensionless roughness height range $0 \le h \le 0.2$ at fixed Prandtl number $Pr = 1$ . Under the combined actions of wall shear and roughness, with increasing $Re_w$ , the heat flux is initially enhanced in the buoyancy-dominant regime, then has an abrupt transition near the critical shear Reynolds number $Re_{w,cr}$ , and finally enters the purely diffusion regime dominated by shear. Based on the crossover of the kinetic energy production between the buoyancy-dominant and shear-dominant regimes, a physical model is proposed to predict the transitional scaling behaviour between $Re_{w,cr}$ and $Ra$ , i.e. $Re_{w,cr} \sim Ra^{9/14}$ , which agrees well with our numerical results. The reason for the observed heat-transport enhancement in the buoyancy-dominant regime is further explained by the fact that the moving rough plates introduce an external shear to strengthen the large-scale circulation (LSC) in the vertical direction and serve as a conveyor belt to increase the chances of the interaction between the LSC and secondary flows within cavities, which triggers more thermal plumes, efficiently transports the trapped hot (cold) fluids outside cavities.

Thermohydrodynamic lubrication analysis of misaligned journal bearing considering surface roughness and couple stress

The modified average Reynolds equation for friction pairs with arbitrary three-dimensional rough surfaces lubricated by couple stress fluid is derived by the average flow method. And the performance parameters under the effect of couple stress, surface roughness, journal misalignment, and thermal effect are obtained with the finite difference numerical method. The surface roughness factor plays an important role even though the nominal eccentricity ratio is small. With the increase of the nominal eccentricity ratio, the greater values of the couple stress parameter, the greater values of performance parameters except for the dimensionless maximum oil film temperature and the dimensionless friction power. With the increase of the degree of misalignment, the greater values of the couple stress parameter, the greater the dimensionless maximum average film pressure, the dimensionless load capacity, and the dimensionless misalignment moment. As the value of the couple stress parameter is increased, the greater values of the dimensionless surface roughness, the greater values of the performance parameters except for the dimensionless side leakage. This research can widely use in various forms of friction pairs such as thrust bearings, sliding bearings, piston ring-cylinder liners.

A Correlation between Deformation-Induced Surface Roughness and In-Plane Plastic Strain in an Aluminum Alloy at the Mesoscale

Experimental and numerical studies on deformation-induced surface roughening in a commercial purity aluminum alloy are presented and discussed. Mesoscale surface profiles evolving in the experimental and numerical specimens in the course of tension are processed to reveal a correlation between roughness characteristics and in-plane plastic strains at the mesoscale. A dimensionless parameter calculated as a ratio of the rough profile length to the profile evaluation length has been used for quantitative estimations of the mesoscale roughness patterns. The dimensionless roughness parameter is shown to depend exponentially on the in-plane plastic strains at the mesoscale. The results support an early assumption that in-plane plastic strains accumulated in a loaded material can be evaluated from the estimations of mesoscale surface roughness.

Reliability assessment of cylindrical joints with tensioned roll band of the rolling mill

The work addresses to the problem of ensuring the operability of a composite roll made in the form of a cylindrical joint with the tension of a carbide band and a steel axis. When considering the wear processes, all the characteristics related to the surface microgeometry are combined by a dimensionless complex roughness parameter, which, along with the roughness class, includes the features of the surface treatment technology. To determine the contact pressure associated with the tension, the Lame formula for calculating thick-walled cylinders is used. When a hard-alloy bandage is placed on a steel roll with the tension between the contacting surfaces, a plastic unsaturated or saturated contact is performed, for which a method for calculating the tension values shall be proposed. Formulas are given for determining the maximum permissible torque that does not cause a change in the strength of the joint with tension under conditions of plastic saturated and unsaturated contact. In order to test the strength of the connection elements with tension, the theory of the greatest tangential stresses is applied for two dangerous points located on the inner surfaces of the covered and the covering parts: a formula is obtained for determining the maximum permissible calculated value of tension from the strength condition of the covered part. An example of fitting with the tension of a band made of hard alloy VK8 on a working roll made of improved steel 45 with a diameter of d = 100 mm is considered. The band is installed using a press with an H7/p6 fit to transmit a torque of M = 5 kNm. The minimum tension value is obtained from the condition of fixing the contact surfaces without their relative slippage, and the maximum tension value is obtained from the condition of the strength of the steel axis. As a result of the calculations, it was found that the minimum tolerance for this attachment does not provide the transmission of the specified torque since its value is less than the minimum allowable tension. Therefore, to ensure reliable operation of the connection with tension, it is recommended to use the H7/s6 fit, which provides the transmission of the specified torque without the strength of the connection elements.

A series approximation to the Kirchhoff integral for Gaussian and exponential roughness covariance functions.

The Kirchhoff integral is a fundamental integral in scattering theory, appearing in both the Kirchhoff approximation and the small slope approximation. In this work, a functional Taylor series approximation to the Kirchhoff integral is presented, under the condition that the roughness covariance function follows either an exponential or Gaussian form-in both the one-dimensional and two-dimensional cases. Previous approximations to the Kirchhoff integral [Gragg, Wurmser, and Gauss (2001) J. Acoust. Soc. Am. 110(6), 2878-2901; Drumheller and Gragg (2001) J. Acoust. Soc. Am. 110(5), 2270-2275] assumed that the outer scale of the roughness was very large compared to the wavelength, whereas the proposed method can treat arbitrary outer scales. Assuming an infinite outer scale implies that the root mean square (rms) roughness is infinite. The proposed method can efficiently treat surfaces with finite outer scale and therefore finite rms height. This series is shown to converge independently of roughness or acoustic parameters and converges to within roundoff error with a reasonable number of terms for a wide variety of dimensionless roughness parameters. The series converges quickly when the dimensionless rms height is small and slowly when it is large.

Process maps and optimal processing windows based on three-dimensional morphological characteristics in laser directed energy deposition of Ni-based alloy

Constructing processing window to fabricate defect-free components with high forming quality and desired performance has been crucial in directed energy deposition. Due to its complexity as a mass and energy time-dependent system, it is still a key problem to be solved for laser powder-fed additive manufacturing to choose opportune processing parameters. In this paper, single scan track experiments were conducted under various combinations of processing parameters including laser power, scanning speed and powder feeding rate. Scan tracks had been thoroughly investigated through three-dimensional information including surface, longitudinal section and transverse section, which were correlated to each other in showing track morphological characteristics in directed energy deposition. Surface ripples, resembling fish scale in welding and chevron in selective laser melting, were found in directed energy deposition under low powder feeding rate and high linear energy density. Furthermore, several quantitative indexes, which were dimensionless mean roughness and ripples’ interval in surface, dimensional roughness in longitudinal section and dilution rate in transverse section, were used to evaluate the forming quality. These quantitative indexes were found to be closely related to the defects in additive manufacturing, and forming quality and accuracy of additive-manufactured components. Relationship between proposed indexes and processing parameters was studied and the mechanism behind it was also discussed. Five states which were no fusion, lack of fusion, optimum, rough surface and undesired dilution rate were distinguished based on the proposed quantitative indexes. Finally, a processing window based on these indexes was proposed for the laser powder-fed additive manufacturing for Inconel alloys. It is found that powder feeding rate affects the distribution of the five states and laser power, scanning speed affect the range of the five states.

Квантовый транспорт в полупроводниковом нанослое с учетом поверхностного рассеяния носителей заряда

The problem of the conductivity of a thin conductive nanolayer is solved taking into account the quantum theory of transport processes. The layer thickness can be comparable to or less than the de Broglie wavelength of charge carriers. The constant-energy surface has the form of an ellipsoid of revolution with the main axis parallel to the layer plane. Analytical expressions are obtained for the conductivity tensor components as a function of dimensionless thickness, chemical potential, ellipticity parameter, and surface roughness parameters. The conductivity analysis for the limiting cases of a degenerate and non-degenerate electron gas are conducted. The results are compared with known experimental data for a silicon layer.

Comparative Study on the Machine Learning and Regression-Based Approaches to Predict the Hydraulic Jump Sequent Depth Ratio

The hydraulic jump phenomenon plays a significant role in dissipating the energy of the upstream current in either natural or artificial waterways. River’s bed roughness is defined as a key parameter that affects the characteristics of the hydraulic jump. In this study, a non-linear regression algorithm was developed to predict the sequent depth ratio of hydraulic jumps over a smooth and rough bed surface using the experimental hydraulic data extracted from the previous studies. Four popular machine learning techniques, known as adaptive network-based fuzzy inference system (ANFIS), ANFIS-Particle Swarm Optimization (ANFIS-PSO), bayesian model averaging (BMA), least absolute shrinkage and selection operator (LASSO), are applied to check the accuracy of the proposed algorithm. The dimensional analysis and Gamma Test model are used to select the effective parameters on the hydraulic jump. In this study, four major parameters named the roughness height (ks), hydraulic radius (R), velocity and Froude number at the upstream of the hydraulic jump control volume were selected as more effective parameters. To compare the performance of the models in prediction of both sequent hydraulic depths, the coefficient of determination, root mean square error (RMSE), mean error, Mean Absolute Error and Nash–Sutcliffe efficiency (NSE) were calculated in both training and testing subsets. It is shown that the proposed model, along with two other non-linear methods, ANFIS and ANFIS-PSO, predicted the hydraulic jump sequent depth ratio more accurately compared to the linear regression techniques, BMA and LASSO. However, the statistical measures show an acceptable accuracy for the linear regression techniques. The results show that the proposed model increases the correlation between observed and predicted values up to 0.987 and decreases the RMSE to 0.324. Simultaneously, the last two linear techniques have RMSE, correlation coefficient 0.333 and 0.98, respectively. Finally, a new non-linear formula addressing the hydraulic jump sequent depth ratio over smooth and rough beds have been proposed. A comparison between the resulted formula of the present study with the previous studies proves the accuracy of the developed equation. Moreover, a dimensionless primary roughness coefficient is presented as a non-linear function of the roughness height (ks) and hydraulic radius (R) parameters.

Turbulent universality and the drift velocity at the interface between two homogeneous fluids

The drift velocity U0 at the interface between two homogeneous turbulent fluids of arbitrary relative densities in differential mean motion is considered. It is shown that an analytical expression for U0 follows from the classical scaling for these flows when the scaling is supplemented by standard turbulent universality and symmetry assumptions. This predicted U0 is the weighted mean of the free-stream velocities in each fluid, where the weighting factors are the square roots of the densities of the two fluids, normalized by their sum. For fluids of nearly equal densities, this weighted mean reduces to the simple mean of the free-stream velocities. For fluids of two widely differing densities, such as air overlying water, the result gives U0 ≈ αV∞, where α ≪ 1 is the square root of the ratio of the fluid densities, V∞ is the free-stream velocity of the overlying fluid, and the denser fluid is assumed nearly stationary. Comparisons with two classical laboratory experiments for fluids in these two limits and with previous numerical simulations of flow near a gas–liquid interface provide specific illustrations of the result. Solutions of a classical analytical model formulated to reproduce the air–water laboratory flow reveal compensating departures from the universality prediction, of order 15% in α, including a correction that is logarithmic in the ratio of dimensionless air and water roughness lengths. Solutions reproducing the numerical simulations illustrate that the logarithmic correction can arise from asymmetry in the dimensionless laminar viscous sublayers.

An Analytical Approach to Estimate the Effect of Surface Roughness on Particle Rebound

Atmospheric air is always contaminated by liquid or solid particles of different size, concentration and chemical composition. This leads to performance degradation during the operation of stationary or flying gas turbines. Erosion and the deposition of particles along the flow path are of particular importance. Multiple numerical studies investigated the influences of these phenomena. However, the basic challenge of modelling the particle wall interaction and its data spread with sufficient accuracy remains. In this work a model that estimates the statistical spread of rebound data due to target surface roughness through analytical considerations is presented. The model predicts the local impact angle of an individual particle by evaluating how deep a particle can theoretically penetrate the target surface with respect to its size. Based on roughness profiles which have been found to be characteristic for performance deterioration in compressor application a sensitivity study is conducted. A dimensionless roughness parameter Φ_R was found that characterizes the effect of target surface roughness on rebound spread data. The spread model is connected with a quasi-physical model, to evaluate the effect of surface roughness for a particle’s individual rebound behaviour. The synthesized data is discussed by taking into account measurement data reported in literature.

Numerical study of the texture effect on deformation-induced surface roughening in titanium polycrystals

The influence of a texture on the mesoscale deformation-induced surface roughening in titanium polycrystals is studied using direct microstructure-based simulations. Relying on the experimental data for commercial purity titanium, equiaxed grain conglomerates are generated by the method of step-by-step packing. The grain constitutive behavior is described in terms of crystal plasticity, with the grain orientations being assigned randomly or representing a basal texture. The micro- and mesoscale roughness evolution in the model polycrystals under uniaxial tension is calculated using ABAQUS/Explicit. In order to quantify mesoscale roughening, a dimensionless roughness parameter is calculated for a set of experimental and numerical roughness profiles evolving in the course of tension. The mesoscale roughness parameter is shown to grow nonlinearly with the plastic strain of the evaluated mesoscale regions. Particularly, it begins increasing rapidly in the region of neck formation well before necking becomes macroscopically evident. The basal texture is shown to significantly affect the plastic strain localization and roughness patterns. The mesoscale roughness, strongly pronounced in the untextured polycrystal, is mostly suppressed in the presence of texture. A set of in-plane shear bands are formed in the textured polycrystal at an angle of 45° to the tensile axis much like those observed experimentally.

Thermal turbulent lubrication analysis of rough surface journal bearing with journal misalignment

Abstract The generalized turbulent lubrication equation for isotropic rough surface bearings is presented by integrating the Hashimoto turbulent lubrication model and the Patir-Cheng laminar flow lubrication model. The finite difference method is used to solve the generalized turbulent lubrication equation and energy equation. And the variations for turbulent lubrication performance of journal bearing with the nominal eccentricity ratio and nominal average Reynolds number are obtained under the influence of surface roughness and journal misalignment. As the dimensionless surface roughness height of the bearing and the journal increases or the degree of misalignment increases, the dimensionless maximum film pressure, dimensionless load capacity and dimensionless misalignment moment of the bearing increases. The research of journal misalignment, thermal effect, and surface roughness is needed.

Nano-mechanical Characterization of SLM-Fabricated Ti6Al4V Alloy: Etching and Precision

In this research, we are reporting that the nanoindentation results vary between etched and unetched SLM-fabricated titanium alloy (Ti6Al4V) in spite of the same microhardness values. The dimensionless roughness parameter α, as a metric for the sensitivity of nano-hardness values on the surface roughness, is used to highlight whether etching plays any role. Although the value of α for both samples is below the recommended maximum value, the effect of etching is still significant. The hypothesis for a 19% increase in nano-hardness of etched samples is also discussed in this paper. Furthermore, the maximum proposed value of α (α < 0.05) appeared to be invalid for SLM-fabricated titanium and a lower value of α may need to be proposed as a critical value.