No-slip Wall Research Articles

Buoyancy Term Evolution in the Multi Relaxation Time Model of Lattice Boltzmann Method with Variable Thermal Conductivity Using a Modified Set of Boundary Conditions

During the last few years, a number of numerical boundary condition schemes have been used to study various aspects of the no-slip wall condition using the lattice Boltzmann method. In this paper, a modified boundary condition method is employed to simulate the no-slip wall condition in the presence of the body force term near the wall. These conditions are based on the idea of the bounce-back of the non-equilibrium distribution. The error associated with the modified model is smaller than those of other boundary condition models available in the literature. Additionally, various schemes to simulate body forces have been studied. Based on the numerical results, the model demonstrating minimum error has been reported. Finally, it has been shown that the present model is capable of simulating the effect of high nonlinearity in the heat transfer equation in the presence of a variable thermal conductivity. This has been accomplished by employing a multi relaxation time scheme to model a Rayleigh-Benard natural convection current in a 2-D domain with high Rayleigh numbers. Previous studies reported that the onset of oscillation occurs at Ra≈30,000 and Pr=6.0. By the modified boundary condition method which is used in this study, the oscillation is removed until at least Ra≈ 45,000 and Pr=6.0. The results show that applying scheme 3 for the current boundary condition yields the least amount of error compared to the semi-empirical correlation. The Rayleigh-Benard convection problem has been revisited in the presence of a variable thermal conductivity and the simulation results remain stable for flows with a large variation of thermal conductivity ( = 0.7) and Rayleigh numbers up to 1,000,000 and Pr=0.7.

Viscoplastic flow development in a channel with slip along one wall

The flow development of a Herschel–Bulkley fluid in a horizontal channel is considered assuming that slip occurs only on the upper wall due to slip heterogeneities. Hence, the velocity profile is allowed to be asymmetric as was the case in recent experiments on softy glassy suspensions [13]. A power-law slip equation is employed, which generalizes the Navier-slip law. The one-dimensional fully-developed solutions are derived and the different flow regimes are identified. The two-dimensional development flow is solved numerically using finite elements along with the Papanastasiou regularization for the constitutive equation. Due to the asymmetry and the viscoplastic character of the flow, the classical definition of the development length is not applicable. The global and upper-wall development lengths are thus considered and the combined effects of slip and the Bingham number are investigated. Numerical results are presented for two values of the power-law exponent, i.e. n = 1 (Bingham plastic) and n = 1/2 (Herchel–Bulkley fluid). It is demonstrated that the global development length increases with the Bingham number and that flow development is slower near the no-slip wall. The global development length increases with slip exhibiting two plateaus and an intermediate rapid increase zone and doubles in the limit of infinite slip.

Dissipative particle dynamics study of phase separation in binary fluid mixtures in periodic and confined domains.

We investigate the phase separation behavior of binary mixtures in two-dimensional periodic and confined domains using dissipative particle dynamics. Two canonical problems of fluid mechanics are considered for the confined domains: square cavity with no-slip walls and lid-driven cavity with one driven wall. The dynamics is studied for both weakly and strongly separating mixtures and different area fractions. The phase separation process is analyzed using the structure factor and the total interface length. The dynamics of phase separation in the square cavity and lid-driven cavity are observed to be significantly slower when compared to the dynamics in the periodic domain. The presence of the no-slip walls and the inertial effects significantly influences the separation dynamics. Finally, we show that the growth exponent for the strongly separating case is invariant to changes in the inter-species repulsion parameter.

Onset of convection induced by centrifugal buoyancy in a rotating cavity

Flows induced by centrifugal buoyancy occur in rotating systems in which the centrifugal force is large when compared to other body forces and are of interest for geophysicists and also in engineering problems involving rapid rotation and unstable temperature gradients. In this numerical study we analyse the onset of centrifugal buoyancy in a rotating cylindrical cavity bounded by two plane, insulated disks, adopting a geometrical configuration relevant to fundamental studies of buoyancy-induced flows occurring in gas turbine’s internal air systems. Using linear stability analysis, we obtain critical values of the centrifugal Rayleigh number $Ra$ and corresponding critical azimuthal wavenumbers for the onset of convection for different radius ratios. Using direct numerical simulation, we integrate the solutions starting from a motionless state to which small sinusoidal perturbations are added, and show that nonlinear triadic interactions occur before energy saturation takes place. At the lowest Rayleigh number considered, the final state is a limit-cycle oscillation affected by the presence of the disks, having a spectrum dominated by a certain mode and its harmonics. We show that, for this case, the limit-cycle oscillations only develop when no-slip end walls are present. For the largest $Ra$ considered chaotic motion occurs, but the critical wavenumber obtained from the linear analysis eventually becomes the most energetic even in the turbulent regime.

Dissipation of coherent structures in confined two-dimensional turbulence

Since the seminal article “Inertial ranges in two-dimensional turbulence” by Kraichnan in 1967, our understanding of the dynamics and transport properties of two-dimensional turbulence is largely built on the assumption of homogeneity and isotropy of statistically steady or decaying turbulence. In the last two decades, more attention has been paid to the presence of lateral walls, either with stress-free or no-slip boundary conditions, and also considering a variety of geometries such as square, rectangular, or circular domains. The impact of confining boundaries on the dynamics of two-dimensional turbulence is important. This is in sharp contrast with three-dimensional turbulence, where homogeneity and isotropy are locally restored due to the cascade process in the inertial range. The impact of confining boundaries is therefore limited in three-dimensional turbulence. The presence of an inverse energy cascade in two-dimensional turbulence, however, will continuously generate large-scale energy-containing eddies, and their vigorous interaction with, in particular, no-slip walls generates large amounts of vorticity and contributes significantly to the dissipation of kinetic energy of the flow. The dissipation is even strongly enhanced compared with the unbounded case. In this review, we will focus on one of the elementary structures observed in two-dimensional turbulent flows: the dipolar vortex. With its self-induced velocity, it propagates easily through the domain and is hence likely to interact with domain boundaries. Standard vortex generation mechanisms allow to create well-defined dipoles and to investigate the collision of such structures with rigid domain boundaries in detail. Relevant aspects of the collision process concern the dynamics and stability of the generated boundary layers, the vorticity, and vorticity gradients contained in these boundary layers, and the dissipation of kinetic energy when dipoles collide with walls. Some of these aspects will be discussed in this review. Moreover, we are interested in the Reynolds-number dependence of these processes, including exploration of the vanishing viscosity limit.

Wall-Modeled Large-Eddy Simulation of a High Reynolds Number Separating and Reattaching Flow

The performance of two wall models based on Reynolds-averaged Navier–Stokes is compared in large-eddy simulation of a high Reynolds number separating and reattaching flow over the NASA wall-mounted hump. Wall modeling significantly improves flow prediction on a coarse grid where the large-eddy simulation with the no-slip wall boundary condition fails. Low-order statistics from the wall-modeled large-eddy simulation are in good agreement with the experiment. Wall-pressure fluctuations from the resolved-scale solution are in good agreement with the experiment, whereas wall shear-stress fluctuations modeled entirely through the wall models appear to be significantly underpredicted. Although the two wall models produce comparable results in the upstream attached flow region, the nonequilibrium wall model outperforms the equilibrium wall model in the separation bubble and recovery region where the key assumptions in the equilibrium model are shown to be invalid.

Physical Effects of Variable Thermophysical Fluid Properties on Flow and Thermal Development in Micro-Channel

ABSTRACTMicro-scale cooling is an efficient and effective cooling technique to achieve the goal of higher heat removal capabilities. The present research focuses to find the physical effects of fluid property variations on flow and thermal development in micro-channel. The effects of temperature-dependent density, viscosity, and thermal conductivity variations on single-phase laminar forced convection are numerically investigated. The problem is especially simulated for hydrodynamically and thermally developing water flow in micro-channel with no-slip, no-temperature jump, and constant wall heat flux boundary conditions. It is observed that the density variation induces radially inward flow due to continuity, which sharpens the axial velocity profile and decreases Nusselt number compared to constant property solution. The axial velocity profile significantly alters due to viscosity variation. This alteration varies along the micro-flow and it induces radially flow due to flow continuity. The reducing rate of Nusselt number for viscosity variation is substantially lower than constant property solution due to a significant flattening effect of the axial velocity profile, which augments the Nusselt number. Thermal-conductivity variation across the flow induces radial conduction, which enhances convection compared to constant property solution. Additionally, the effects of thermophysical fluid property variations on static gauge pressure drop are also investigated.

Acoustic multipole sources for the regularized lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit.

In this paper, a variant of the acoustic multipole source (AMS) method is proposed within the framework of the lattice Boltzmann method. A quadrupole term is directly included in the stress system (equilibrium momentum flux), and the dependency of the quadrupole source in the inviscid limit upon the fortuitous discretization error reported in the works of E. M. Viggen [Phys. Rev. E 87, 023306 (2013)PLEEE81539-375510.1103/PhysRevE.87.023306] is removed. The regularized lattice Boltzmann (RLB) method with this variant AMS method is presented for the 2D and 3D acoustic problems in the inviscid limit, and without loss of generality, the D3Q19 model is considered in this work. To assess the accuracy and the advantage of the RLB scheme with this AMS for acoustic point sources, the numerical investigations and comparisons with the multiple-relaxation-time (MRT) models and the analytical solutions are performed on the 2D and 3D acoustic multipole point sources in the inviscid limit, including monopoles, x dipoles, and xx quadrupoles. From the present results, the good precision of this AMS method is validated, and the RLB scheme exhibits some superconvergence properties for the monopole sources compared with the MRT models, and both the RLB and MRT models have the same accuracy for the simulations of acoustic dipole and quadrupole sources. To further validate the capability of the RLB scheme with AMS, another basic acoustic problem, the acoustic scattering from a solid cylinder presented at the Second Computational Aeroacoustics Workshop on Benchmark Problems, is numerically considered. The directivity pattern of the acoustic field is computed at r=7.5; the present results agree well with the exact solutions. Also, the effects of slip and no-slip wall treatments within the regularized boundary condition on this pure acoustic scattering problem are tested, and compared with the exact solution, the slip wall treatment can present a better result. All simulations demonstrate that the RLB scheme with the AMS method is capable of accurately simulating 2D and 3D acoustic generation, propagation, and scattering at zero viscosity.

Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear

Induction of flow is commonly used to control the migration of a microswimmer in a confined system such as a microchannel. The motion of a swimmer, in general, is governed by nonlinear equations due to non-trivial hydrodynamic interactions between the flow and the swimmer near a wall. This paper derives analytical expressions for the equations of motion governing a circular treadmilling swimmer in simple shear near a no-slip wall by combining the reciprocal theorem for Stokes flow with an exact solution for the dragging problem of a cylinder near a wall. We demonstrate that the reduced dynamical system possesses a Hamiltonian structure, which we use to show that the swimmer cannot migrate stably at a constant distance from a wall but only exhibit periodic oscillatory motion along the wall, or to escape from it. A treadmilling swimmer with the lowest two treadmilling modes is investigated in detail by means of a bifurcation analysis of the reduced dynamical system. It is found that the swimming direction of oscillatory motion is clarified by the sign of the Hamiltonian in the absence of flow, and that the induction of the flow suppresses upstream migration but aligns swimmer orientations in downstream migration. These results could inform strategies for the transport and control of micro-organisms and micromachines.

Brownian motion as a new probe of wettability.

Understanding wettability is crucial for optimizing oil recovery, semiconductor manufacturing, pharmaceutical industry, and electrowetting. In this letter, we study the effects of wettability on Brownian motion. We consider the cases of a sphere in an unbounded fluid medium, as well as a sphere placed in the vicinity of a plane wall. For the first case, we show the effects of wettability on the statistical properties of the particles' motion, such as velocity autocorrelation, velocity, and thermal force power spectra over a large range of time scales. We also propose a new method to measure wettability based on the particles' Brownian motion. In addition, we compare the boundary effects on Brownian motion imposed by both no-slip and perfect-slip flat walls. We emphasize the surprising boundary effects on Brownian motion imposed by a perfect-slip wall in the parallel direction, such as a higher particle mobility parallel to a perfect flat wall compared to that in the absence of the wall, as well as compared to a particle near a no-slip flat wall.

Brownian dynamics of confined suspensions of active microrollers.

We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev, and P. Chaikin, Nat. Phys. (2016), preprint arXiv:1609.08673. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost but is more accurate than the widely used Euler-Maruyama scheme, and use a random finite difference to capture the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. We generate the Brownian increments using a Krylov method and show that for particles confined to remain in the vicinity of a no-slip wall by gravity or active flows, the number of iterations is independent of the number of particles. Our numerical experiments with active rollers show that the thermal fluctuations set the characteristic height of the colloids above the wall, both in the initial condition and the subsequent evolution dominated by active flows. The characteristic height in turn controls the time scale and wavelength for the development of the fingering instability.

Parametric study on smoothed particle hydrodynamics for accurate determination of drag coefficient for a circular cylinder

Simulations of two-dimensional (2D) flow past a circular cylinder with the smoothed particle hydrodynamics (SPH) method were conducted in order to accurately determine the drag coefficient. The fluid was modeled as a viscous liquid with weak compressibility. Boundary conditions, such as a no-slip solid wall, inflow and outflow, and periodic boundaries, were employed to resemble the physical problem. A sensitivity analysis, which has been rarely addressed in previous studies, was conducted on several SPH parameters. Hence, the effects of distinct parameters, such as the kernel choices and the domain dimensions, were investigated with the goal of obtaining highly accurate results. A range of Reynolds numbers (1–500) was simulated, and the results were compared with existing experimental data. It was observed that the domain dimensions and the resolution of SPH particles, in comparison to the obstacle size, affected the obtained drag coefficient significantly. Other parameters, such as the background pressure, influenced the transient condition, but did not influence the steady state at which the drag coefficient was determined.

SPH-[formula omitted] simulation of 2D turbulence driven by a moving cylinder

The aim of this paper is to describe how effectively a turbulence model for the particle method SPH (Monaghan 2011 denoted by SPH-ϵ) simulates 2D turbulence driven by a moving cylinder inside a square box with no-slip walls. The model makes few assumptions, conserves linear and angular momentum, satisfies a discrete version of Kelvin’s circulation theorem and is computationally efficient. Furthermore, the results from the model for decaying two dimensional turbulence are in good agreement with the experimental and computational results. The SPH turbulence model is based on a Lagrangian similar to that used for the Lagrangian averaged Navier–Stokes (LANS) turbulence model, but with a different smoothed velocity. The smoothed velocity preserves the shape of the spectrum of the unsmoothed velocity for short length scales, but reduces its magnitude by an amount which depends on a parameter ϵ, where 0≤ϵ≤1. When ϵ=0, there is no smoothing, and when ϵ=1 the smoothing is a maximum. We compare calculations with resolution given by the Reynolds length ℓR and those using SPH-ϵ with ϵ=0.8, and a coarser resolution 2ℓR. The second and fourth order velocity correlation functions, the energy spectrum and the mixing calculated using SPH-ϵ and the coarse resolution 2ℓR, are in good agreement with those using the resolution ℓR, but requires 8 times less work to integrate to the same time. The mixing induced by the turbulence is in good agreement with high resolution calculations.

Dynamics of a flexible helical filament rotating in a viscous fluid near a rigid boundary

The effects of a no-slip wall on flagellar propulsion are investigated by experiments with macroscopic-scale model flagella and simulations based on algorithms from computer graphics. A nearby wall shifts the threshold for buckling of the flexible flagellum and increases the propulsive force.

Effect of Magnetic Field on Natural Convection and Entropy Generation in Al2O3/Water Nanofluid-Filled Enclosure With Twin Protruding Heat Sources

In this paper, the effect of magnetic field on natural convection of Al2O3/water nanofluid in an enclosure containing twin protruding heat sources placed on top and bottom walls arranged in-line and staggered manner is presented. For this purpose, coupled equations governing fluid flow and heat transfer are solved in Cartesian framework using streamline upwind/Petrov–Galerkin (SUPG) finite element method. Numerical computations are performed to predict the fluid flow, heat transfer, and entropy generation for a wide range of Hartmann number (0.0 ≤ Ha ≤ 100.0), Rayleigh number (103≤Ra≤106), and nanoparticle volume fraction (0.0≤ϕ≤0.1). The simulated results indicate that, for both in-line and staggered arrangement, the entropy generation due to heat transfer is significant along isothermal surfaces, whereas entropy generation due to fluid friction is higher at no-slip walls and along the regions of contact between adjacent recirculation cells. For both in-line and staggered arrangement, increase in global total entropy generation and average Nusselt number along top and bottom heat sources is obtained with decreasing Ha and increasing Ra. Furthermore, for both in-line and staggered arrangement, variation in global total entropy generation and average Nusselt number along top and bottom heat sources with increasing nanoparticle volume fraction, depend on both Ha and Ra.

Inelastic non-Newtonian flow over heterogeneously slippery surfaces

In this study, we investigated inelastic non-Newtonian fluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bubbles. The results reveal that for shear-thinning fluids wall slip can be increased significantly, provided that the system is operated in the shear-thinning regime. For a 0.2 wt% xanthan gum solution with a power-law index of n=0.4, the numerical results indicate that wall slip can be enhanced 3.2 times when compared to a Newtonian liquid. This enhancement factor was also predicted from a theoretical analysis, which gave an expression for the maximum slip length that can be attained over flat, heterogeneously slippery surfaces. Although this equation was derived for a no-slip/no-shear unit length that is much larger than the typical size of the system, we found that it can also be used to predict the enhancement in the regime where the slip length is proportional to the size of the no-shear region or the bubble width. The results could be coupled to the hydrodynamic development or entrance length of the system, as maximum wall slip is only reached when the fluid flow can fully adapt to the no-slip and no-shear conditions at the wall.

Lattice-Boltzmann simulations of microswimmer-tracer interactions

Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf etal., J. Chem. Phys. 144, 134106 (2016)JCPSA60021-960610.1063/1.4944962] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.

Sheltering the perturbed vortical layer of electroconvection under shear flow

Sheltering of a perturbed vortical layer by a shear flow is a common method to control turbulence and transport in plasma physics. Despite the desire to exploit this phenomenon in wider engineering applications, shear sheltering has rarely been observed in general non-ionized fluids. In this study, we visualize this shear sheltering in a generic neutral-fluid situation in electromembrane desalination: electroconvection (EC) under the Hagen–Poiseuille flow initiated by ion concentration polarization. Our work is the first demonstration of shear sheltering in electrochemical systems. Experiment, numerical simulation and scaling analysis accurately capture the effect by pinpointing the threshold for shear suppression. Determined by balancing the velocity fluctuation (with EC vortices) and the flow shear (with no-slip walls), the threshold for shear suppression is scaled as the EC height. Stable EC with coherent unidirectional vortices occurs under the threshold height, whereas chaotic EC occurs beyond this height as the EC-induced vortical perturbation overwhelms the flow shear. Attractors in a time-delay phase space illustrate this sequence of steady–periodic (stable EC)–chaotic transitions precisely. Going one step further, the shear sheltering effect is decoupled from the shear-independent mechanism of vortex suppression, i.e. vortex sweeping by the mean flow. In the frequency domain, this shear-independent effect is negligible for stable EC (when shear sheltering dominates), whereas it can reduce the level of chaotic fluctuations of chaotic EC (when shear sheltering weakens). Lastly, taken together, we describe the EC-induced convective ion transport by the new scaling law for the electric Nusselt number as a function of the electric Rayleigh number and the Reynolds number. This work not only expands the scientific understanding of EC and the shear sheltering effect, but also affects a broad range of electrochemical applications, including desalination, energy harvesting and sensors.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule.For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations.The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

Discontinuous Galerkin Method for the Study of Active Gurney Flaps

A discontinuous Galerkin method is proposed for the solution of the Reynolds-averaged Navier–Stokes equations, for turbulent flows in two dimensions. The numerical model is applied to the solution of unsteady flows associated to an actively controlled Gurney flap located in proximity of the trailing edge of an airfoil, with oscillations up to 20 Hz. The motion of the Gurney flap is simulated through no-slip viscous wall conditions applied to the interfaces between neighboring elements that coincide with the position of the flap at a given time instant. Several configurations of deployment motions are considered under different freestream conditions to demonstrate the capability of the solver to predict accurately unsteady nonlinear problems at high Reynolds numbers. The numerical calculations are compared with experimental data in the case of the NACA 0012 airfoil.