Rough Boundary Conditions Research Articles

Quantitative coarse graining of laminar fluid flow penetration in rough boundaries

The interaction between a fluid and a wall is described with a certain boundary condition for the fluid velocity at the wall. To understand how fluids behave near a rough wall in a completely laminar flow regime, the fluid velocity at every point on the rough surface may be provided. This approach requires detailed knowledge of, and likely depends strongly on the roughness. Another approach of modelling the boundary conditions of a rough wall is to coarse grain and extract a penetration depth over which on average the fluid penetrates into the roughness. In this work, we examine the impact of well-defined patterned surfaces on the fluid flow behaviour. We considered two extreme cases: one with horizontal ridges and another with vertical ridges on the wall and an intermediate case with ridges at an angle on the wall. We show that for a broad range of periodic roughness patterns and relative flow velocities, a universal penetration depth function can be obtained. We obtain these results with experiments and complementary numerical simulations. We evaluate how this penetration depth depends on the various roughness parameters such as ridge depth, ridge spacing and ridge angle. Our results present a novel approach to investigating wall roughness boundary conditions by considering the penetration depth δ that captures the spatially averaged behaviour of the decaying velocity profile between the asperities. We find that this penetration depth δ can be rescaled into a simple exponential master curve δ = δ∞(1 − e−kD/S) for horizontal ridges with varying depth D and spacing S. A similar variation of δ with D and S is observed for vertical ridges, but with a smaller magnitude δ∞, while for ridges at an angle, the penetration depth lies between the two extreme cases.

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.

A Study of a Thermally-Vigorous Rayleigh-Bénard Convection in a Hybrid Nanofluid Using Non-Classical Boundary Condition

A linear stability analysis of a thermally-vigorous Rayleigh-Bénard convection in a mono and a hybrid nanofluid is carried out using the single-phase model. We make use of non-classical boundary condition on velocity (rough boundary condition) and temperature (third-type boundary condition) instead of a specific boundary condition (free-free isothermal, rigid-rigid isothermal, etc.) which is traditionally considered. The thermophysical properties are calculated using phenomenological laws and mixture theory. A unique and novel combination of a single-term Galerkin technique and the Maclaurin series expansion is used to solve the boundary-eigen-value problem obtained in the problem. The critical value of the wave number and the Rayleigh number that are calculated using the procedure are quite accurate up to 5 and 3 decimal places respectively. A comparative study on the instability in two types of nanofluids is carried out so as to infer which type of nanofluid suits best for thermally vigorous systems. This paper aims to provide a theoretical basis to ease the selection process pertaining to the making of a choice from different types of nanofluids. To validate the study sixteen limiting cases have been obtained. To visualize the flow behavior physically, streamlines have been plotted.

Thermal instability analysis in magneto-hybrid nanofluid layer between rough surfaces with variable gravity and space-dependent heat source

The onset of thermal instability with hybrid nanoparticles Al2O3–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters ([Formula: see text]), Darcy number (Da), gravity variation function ([Formula: see text]), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number [Formula: see text] which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ([Formula: see text]) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and [Formula: see text] (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Thermorheological effect on Rayleigh–Bénard magnetoconvection in a biviscous Bingham fluid with rough boundary condition on velocity and Robin boundary condition on temperature

AbstractThe thermorheological effect on the onset of Rayleigh–Bénard convection in a biviscous Bingham fluid in the presence of a horizontal magnetic field is investigated considering rough boundary conditions on velocity and Robin boundary conditions on temperature. The viscosity of the electrically conducting fluid is assumed to be sensitive to temperature variation. Linear and global nonlinear stability analyses are performed using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. A general interpretation is made from the results to show the effects of the magnetic field and the variable viscosity on the system's stability. The biviscous Bingham parameter and the Chandrasekhar number are shown to have a delay in the onset of convection, while the effect of temperature sensitivity is to advance the onset. It is found that the results of linear and global nonlinear stability are not in agreement, so the region of subcritical instability exists. Also, the results obtained for Rayleigh–Bénard convection agree pretty well with those of Platten and Legros and Siddheshwar et al. for the limiting cases.

Comparison of turbulent inflow conditions for neutral stratified atmospheric boundary layer flow

In the present work, measurements of the atmospheric boundary layer (ABL) flow, reproduced in a boundary layer wind tunnel, and large eddy simulation (LES) of the full scale ABL are presented for two ground roughness lengths. In the numerical part the ABL is simulated by utilizing the cyclic boundary conditions in downstream direction and artificial turbulence specified at the inlet. Five synthetic turbulence generation techniques are used with reviewing two input methods for the Reynolds stress. Convergence of mean velocity and second order moments is discussed for various horizontal and vertical grid refinement as well as for different roughness and wall boundary conditions of the ground. The transition of mean velocity, second order moments, stream-wise velocity spectrum and longitudinal turbulent length scale in downstream direction is analyzed. The applicability of the synthetic turbulence condition was confirmed for the LES of ABL simulations. In this way, the inflow domain length for simulations can significantly be reduced.

Photogrammetry based characterization of hydro-mechanical properties of a rock fracture

Hydro-mechanical properties of a single fracture are governed by several parameters such as contact area, roughness, tortuosity, aperture, channeling, matedness, sample sizes, normal stress, flow regime, and flow boundary conditions. In this study, photogrammetry with numerical modeling and laboratory measurements were used to investigate the influences of roughness, normal stress, aperture, water pressure, and different flow boundary conditions on fluid flow in an artificial granite fracture. A Finnish Kuru grey granite block was mechanically split, and a 250 mm × 250 mm × 100 mm slab pair sample with a tensile crack in the middle was extracted. A photogrammetry-based method was used to reconstruct a 3D model of the fracture geometry. The resulting model was numerically simulated with COMSOL using the Navier-Stokes equations. Fluid flow experiments were computed with the Forchheimer equation. Comparison between the numerical modeling results and the analytical solution confirms that the 3D roughness geometry has a crucial role in defining the transmissivity, especially for nonlinear flow. On the other hand, normal stress increases fracture closure and increases contact areas, decreasing the hydraulic aperture and changing the flow paths. The presented method can be used in the contactless estimation of fluid flow properties of rock joints.

Micropolar fluid flow in a thick domain with multiscale oscillating roughness and friction boundary conditions

We consider an unsteady micropolar fluid flow in a two-dimensional domain Ωε. The velocity field is assumed to satisfy a fluid-solid friction interface condition on a part of the boundary while the micro-rotation field satisfies non-homogeneous Dirichlet boundary conditions. The problem is thus described by a non-linear coupled variational parabolic system for the fluid velocity vϵ, the pressure pϵ and the angular micro-rotation field Zϵ. The thickness and the roughness of the fluid domain are described by multiple separated scales of periodic oscillations, i.e. Ωε={(z1,z2):0<z1<L,0<z2<εmhε(z1)} with hε(z1)=h(z1,z1ε,z1ε2,⋯,z1εm), 0<ε<<1, and m≥2. Existence, uniqueness and uniform estimates of the solution (vϵ,pϵ,Zϵ) are stated. Then we study the asymptotic behaviour of the flow as ε tends to zero by using the multiple scale convergence method for reiterated homogenization. The assumption m≥2 raises several technical difficulties in the limit process and leads to non-standard divergence free conditions for the limit velocity. We derive the limit problem which is totally decoupled for the limit velocity and pressure (v0,p0) on the one hand and the limit micro-rotation field Z0 on the other hand. More precisely (v0,p0) is solution of a variational elliptic inequality and Z0 solves an elliptic partial differential equation, where the time variable appears as a parameter. Moreover we prove that v0,p0 and Z0 are uniquely determined by auxiliary well-posed problems.

Using Image Analysis Technique to Study the Effect of Boundary and Environment Conditions on Soil Cracking Mechanism

In geotechnical engineering, there is a significant potential of using image analysis technique to study cracking soils by quantifying the characteristics of the crack network. In the current work, the image analysis process was used to obtain comprehensive information about the cracking mechanism and shrinkage during drying. Artificial soil samples investigated in the lab via desiccation tests under different boundary and environment conditions. Soil specimens with smooth and rough bottom contact surfaces were allowed to desiccate under opened and closed environments with specific pressure and temperature conditions. Digital photos were regularly taken during the tests then processed with image j software to characterize the crack patterns. The investigated effects were expressed in terms of crack intensity factor, CIF, and total crack intensity factor, (CIF)tot. The friction of the bottom contact surface, the environment, and the exposition to a saturated salt solution affect cracks formation and affect the cracking mechanism and shrinkage during drying. Smooth and rough boundaries showed significant differences at the end. For rough bottom contact surface, the difference between the values of suction under the opened environment and the closed one may have a small or insignificant effect on (CIF)tot, also the pattern of the cracks did not differ that much. CIF increases with an increase in the friction of the bottom contact surface. Also, samples dried under the open environment exhibit higher CIF and (CIF)tot than those under a closed environment. However, (CIF)tot decreases with an increase in the friction of the bottom surface. For the rough boundary condition under the open environment, the samples exposed to a salt solution had lower CIF and (CIF)tot in comparison with the other one not exposed. Since the orthogonal intersections are more dominant than others, it could be observed that the tensile stresses have a significant effect on desiccation cracks under the investigated conditions.

The heat equation with rough boundary conditions and holomorphic functional calculus

In this paper we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded H∞-calculus on weighted Lp-spaces for power weights which fall outside the classical class of Ap-weights. Furthermore, we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity. In particular, we obtain a new maximal regularity result for the heat equation with rough inhomogeneous boundary data.

Particle-fluid flow and transport within rough fractures

Proppant injection is an important part of a hydraulic fracturing programs in which fluid-particle slurry is injected into rock fractures. Injected particles are lodged between fracture surfaces during wall close-in thereby propping open the fracture, improving connectivity and production. This paper investigates behaviour of proppant particles within artificially generated rock fractures, providing insight into transport behavioural differences caused by realistic surface roughness. Better understanding of proppant behaviour within more realistic rough fracture conditions provides greater understanding of proppant transport as compared to past works where smooth walled fracture configurations were utilized. A clearer understanding is important in providing more accurate evaluation of realistic proppant flow and distribution and improving injection design. In this study a roughened surface, analogues to actual rock fracture surface, is artificially generated based on a rock surface’s fractal dimension and asperity height standard deviation. Computational representation of the rock surfaces and flow domain is generated. Resolved Discrete Element Method coupled with computational fluid dynamics (DEM-CFD) is implemented in this study to evaluate proppant particle transport behaviour within the fractures. This work highlights importance of considering fracture surface roughness in evaluating proppant flow and transport and more generally the impact of rough boundary conditions of particle-fluid systems.

Sensitivity Analysis of Input Data in Surface Water Quality Models

Abstract The article is focused on analysis of input data impact on outputs of water quality models. The authors examined the impact of roughness coefficient, both boundary and initial conditions setup on changes of outputs generated by HEC-RAS model. Simulation results have shown a various response rate of input data on simulated results. The strong impact shows roughness coefficient setup that through the value of longitudinal dispersion coefficient affects pollution transport process. Changes in boundary conditions have had less influence on outputs. Relatively strong impact shows the setup of initial state of pollution concentration along the reach mainly for the case of low gradient rivers.

Evaluation of the impact of channel geometry and rough elements arrangement in hydraulic jump energy dissipation via SVM

Abstract Rough bed channels are one of the appurtenances used to dissipate the extra energy of the flow through hydraulic jump. The aim of this paper is to assess the effects of channel geometry and rough boundary conditions (i.e., rectangular, trapezoidal, and expanding channels with different rough elements) in predicting the hydraulic jump energy dissipation using support vector machine (SVM) as a meta-model approach. Using different experimental data series, different models were developed with and without considering dimensional analysis. The results approved capability of the SVM model in predicting the relative energy dissipation. It was found that the developed models for expanding channel with central sill performed more successfully and, for this case, superior performance was obtained for the model with parameters Fr1 and h1/B. Considering the rectangular and trapezoidal channels, the model with parameters Fr1, (h2−h1)/h1, W/Z led to better predictions. It was observed that between two types of strip and staggered rough elements, strip type led to more accurate results. The obtained results showed that the developed models for the case of simulation based on dimensional analysis yielded better predictions. The sensitivity analysis results showed that Froude number had the most significant impact on the modeling.

Rough boundary effect in thermal transport: A Lorentz gas model

A Lorentz gas model with rough periodic boundary conditions is proposed to investigate the boundary effect on thermal transport of noninteracting particles. The normal thermal transport is confirmed as the linear temperature gradient, and length independent thermal conductivity is obtained. We demonstrate that the thermal conductivity indeed decreases as the degree of roughness increases, which is consistent with previous works. Furthermore, we find that the thermal conductivity is oscillating with the degree of the boundary roughness. This interesting phenomenon is related to the successful transport probability of particles, which results from the interference between transporting particles and the periodic boundary conditions.

The onset of nanofluid natural convection inside a porous layer with rough boundaries

Smooth boundaries guarantee the infinitely stable flow when the linear stability analysis is implemented. Hence, the study on rough boundaries is essential when the laminar-turbulent transition is being considered. Because of the importance of rough boundaries, the present paper concentrates on the analysis of the onset of nanofluid natural convection (Rayleigh-Bénard convection) in a porous layer between two rough solid walls. The nanofluid surrounded between these surfaces contains the influence of both Brownian motion and thermodiffusion (thermophoresis). The non-negligible roughness boundary conditions are modeled according to the Saffman interface condition. For this purpose, the roughness is analogized as a shallow saturated fluid porous media. The simulation is performed under the isothermal condition and the zero nanoparticle flux condition for both surfaces. Then the governing equations are transported to an eigenvalue problem, and they are solved by a numerical method. The results prove that boundaries roughness and porosity parameters have a stabilizing influence on the onset of convective heat transfer while nanoparticle-concentration Rayleigh number, thermophoresis parameter, modified nanoparticle-density increment, and Lewis number have the destabilizing effects on the onset of Rayleigh-Bénard convection. For example, by increasing the roughness parameter from zero (i.e., stress-free boundary condition) to 100 (i.e., rigid solid walls with no-sleep condition), the critical convection Rayleigh number and the critical wave number increase around 145% and 41%, respectively.

Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid

The lubrication theory is mostly concerned with the behaviour of a lubricant flowing through a narrow gap. Motivated by the experimental findings from the tribology literature, we take the lubricant to be a micropolar fluid and study its behaviour in a thin domain with rough boundary. Instead of considering (commonly used) simple zero boundary conditions, we impose physically relevant (nonzero) boundary conditions for the microrotation and perform the asymptotic analysis of the corresponding 3D boundary value problem. We formally derive a simplified mathematical model acknowledging the roughness-induced effects and the effects of the nonzero boundary conditions on the macroscopic flow. Using the obtained asymptotic model, we study numerically the influence of the roughness on the performance of a linear slider bearing. The numerical results clearly indicate that the use of the rough surfaces may contribute to enhance the mechanical performance of such device.

Numerical investigation on the suitability of a fourth-order nonlinear k-ω model for secondary current of second type in open-channels

ABSTRACTThis study evaluated a typical nonlinear fourth-order k-ω model and the associated roughness boundary condition for their suitability for simulating secondary current of the second kind in open-channels induced by roughness non-uniformity. Three test cases were simulated: square duct flow, open-channel flow with uniformly roughened bed and smooth side walls, and open-channel flow over roughness patches. The nonlinear model and the roughness boundary condition performed relatively well for the first two cases where the corner effect was dominant. For the third case, with alternate roughness patches, strong pressure gradient was generated at the edge between adjacent patches and the secondary current was greatly over-predicted. Two remedial options were tested: increasing the roughness height for smooth walls to a reasonable value and smoothing the roughness transition with a hyperbolic tangent function. We found the first option works better and the second only marginally improves the results.

Sparse operator compression of higher-order elliptic operators with rough coefficients

We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary conditions. The operator compression is achieved by using localized basis functions, which are energy minimizing functions on local patches. On a regular mesh with mesh size h, the localized basis functions have supports of diameter O(hlog (1/h)) and give optimal compression rate of the solution operator. We show that by using localized basis functions with supports of diameter O(hlog (1/h)), our method achieves the optimal compression rate of the solution operator. From the perspective of the generalized finite element method to solve elliptic equations, the localized basis functions have the optimal convergence rate O(h^k) for a (2k)th-order elliptic problem in the energy norm. From the perspective of the sparse PCA, our results show that a large set of Matérn covariance functions can be approximated by a rank-n operator with a localized basis and with the optimal accuracy.

Lateral boundary effects in centrifuge foundation tests

Large deformation finite-element analyses were conducted to explore the effect of the container lateral boundary in centrifuge tests where a large offshore foundation is tested. A spudcan foundation, typically used to support jack-up drilling rigs, was penetrated into uniform clay, uniform sand and sand overlying clay stratigraphies under rough and smooth lateral boundary conditions. The effect that the proximity of the container lateral boundary has on the measured load–penetration response is quantified. The boundary impact varies with the soil profile and boundary roughness, and for sand-only or sand-over-clay conditions the required separation between the foundation and the container boundary is far greater than in clay-only conditions. In most cases, during large penetration of the spudcan foundation, the largest influence from the lateral boundary was on peak resistance, and diminished during the subsequent deeper penetration. For practical use, a centrifuge container design chart is proposed to check whether the dimensions are adequate for the foundation and model size to be used in an experiment. It is shown that the results from many earlier studies could have been potentially influenced by container boundary effects.

Detached-eddy and large-eddy simulations of wind effects on a high-rise structure

Abstract In this study, detached-eddy simulations (DES) and large-eddy simulations (LES) of wind effect on a high-rise structure with elliptical shape are performed. The aim of this study is to examine the accuracy of the numerical simulations for wind flow around a complex high-rise structure and investigate the effects of surface roughness on the wind loading. In order to reproduce appropriate inflow turbulence, the improved recycling method combined with the weighted amplitude wave superposition (WAWS) method is used to generate the inflow turbulence in the streamwise direction. Also, to study the surface roughness effects on the wind loading, the rough wall boundary conditions are adopted in the DES models. Typical results including the mean and fluctuating pressure coefficients, force spectra, Reynolds stresses and wind-induced top-floor response are obtained and compared with the corresponding wind tunnel experimental data. Through the cross-comparisons, the numerical results by the DES and LES models are found to be comparable with the experimental results. Additionally, the surface roughness effects on the wind loading is well reproduced with the DES models, such as the slow pressure recovery in the separation regions and the increased mean drag force coefficients. It is demonstrated through the validations that the DES and LES models and the numerical treatments adopted in this study can provide reasonably good results.