No-slip Velocity Boundary Conditions Research Articles

Long time dynamics of nonequilibrium electroconvection

The Nernst-Planck-Stokes (NPS) system models electroconvection of ions in a fluid. We consider the system, for two oppositely charged ionic species, on three dimensional bounded domains with Dirichlet boundary conditions for the ionic concentrations (modelling ion selectivity), Dirichlet boundary conditions for the electrical potential (modelling an applied potential), and no-slip boundary conditions for the fluid velocity. In this paper, we obtain quantitative bounds on solutions of the NPS system in the long time limit, which we use to prove (1) the existence of a compact global attractor with finite fractal (box-counting) dimension and (2) space-time averaged electroneutrality ρ ≈ 0 \rho \approx 0 in the singular limit of Debye length going to zero, ϵ → 0 \epsilon \to 0 .

Axisymmetric motion of a solid particle embedded in a Brinkman micropolar fluid in the presence of a plane wall

The axisymmetric motion of a solid spherical particle embedded in a hydrogel medium in the presence of a planar wall surface is investigated semi-analytically. The hydrogel medium is modeled as a porous medium saturated with a microstructure fluid of micropolar type. The no-slip velocity and no-slip spin boundary conditions are considered at both the particle surface and the plane wall surface. The sixth-order differential equation describing the stream function of the micropolar fluid flow through the voids of the porous medium is constructed under the assumption of low Reynolds numbers. The general solution of the equation satisfied by the stream function in the porous region is obtained from the superposition of basic solutions in both cylindrical and spherical coordinates. To satisfy first the boundary condition at the planar surface, we apply the Fourier–Bessel transforms and then at the surface of the particle by a boundary collocation technique. The collocation scheme for the normalized drag force acting on the particle is calculated with good convergence for various values of the relevant parameter. Our results are in good agreement with the available data in the literature. The findings of the present investigation demonstrate that the presence of the planar surface, micropolarity, and permeability parameters has significant effects on the drag force. This study is motivated by its potential application on micro- and ultra-filtration.

Finite element simulations of inclined magnetic field and mixed convection in an enclosure with periodically heated walls in the presence of an obstacle

The current manifestation is utilized to explicate the inspiration of combined convection flows in a cavity with a square cylinder placed at the center of the cavity having coordinates (0.5, 0.5). To be more specific, right- and left-sided vertical walls are kept cold, and the lower wall is to be heated in uniform and non-uniform manners, while the upper horizontal wall is moved with a constant velocity ULid and is thermally adiabatic. The obstacle is treated as cold as well as thermally adiabatic, and the no-slip velocity boundary conditions are specified at its surface. For the purpose of computing the velocity profile and temperature, a space including the quadratic polynomials (P2) is chosen; however, the pressure has been approximated using a linear ( P1 ) finite element space of functions. The Newton technique is used to perform the computations needed to solve the discrete systems of non-linear algebraic equations. The non-linear iterations are terminated at residual below 10–6, whereas the inner core linear solver is based on Gaussian elimination with special reordering of unknowns. To show the consistency of the implemented numerical technique, the parametric study is designed based on the most relevant non-dimensional parameters, namely, the Grashof number Gr ranging from 102 to 105, the Hartmann number Ha changing from 0 to 50, and the Reynolds number Re varying from 10 to 200. Computations in the forms of velocity streamlines and isotherm contour profiles are adorned. In addition, the production of temperature disparities is associated with an increase in Nuavg as Re increases. In contrast, a diminishing aptitude in kinetic energy is observed due to the creation of Lorentz forces.

Numerical analysis of Carreau fluid flow over a vertical porous microchannel with entropy generation

This study investigates novel aspects of entropy generation in fully developed heat transport of Carreau fluid in a porous vertical microchannel. Consequences of thermal radiation and viscous heating are included in the thermal energy equation. The no-slip velocity and convective heating temperature boundary conditions are also considered. Darcy–Forchheimer model model is also considered. The system is solved using the bvp4c approach to solve a dimensional less two-point boundary value problem derived from the governing equations. The effect of effective factors on the Bejan number, entropy generation rate, temperature, and velocity are depicted in graphs. According to our analysis, increasing values of the Weissenberg number reduce entropy generation on the left and right sides of the channel, whereas the Bejan number improves on both sides of the channel and is highest in the middle. The fluid transport in a microchannel is enhanced by the pressure gradient. Because of the boundary conditions of convection heating at the microchannel walls, entropy production is at its maximum. Furthermore, the magnitude of the Bejan number is lessened due to a stronger viscous heating mechanism, whereas entropy production gets larger. The results were compared to those previously reported in the literature as a limiting case of the problem, and they were found to be in excellent agreement.

Heat transfer analysis for EMHD peristalsis of ionic-nanofluids via curved channel with Joule dissipation and Hall effects.

The objective of this research is to study the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel. A two-phase model of a nanofluid, Maxwell's model of thermal conductivity [1], and no-slip velocity and thermal boundary conditions have been used in this study. Hall effects, Joule heating (due to magnetic and electric fields), and viscous heating aspects are under consideration. Governing equations for the present flow configuration have been modeled and simplified by enforcing the lubrication scheme. Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation). Resulting expressions are solved numerically through the NDSolve command in Mathematica and plotted in order to understand the effects of different dimensionless parameters on the temperature, stress, heat transmission rate, and fluid's velocity. Graphical results demonstrated that the thermal transmission rate is augmented by increasing the Hartmann number, Brinkman number, and Debye-Huckel parameter while decreases for zeta potential ratio, Joule dissipation parameter, and electro-osmotic velocity. A decrease in axial velocity is noted near the lower wall for higher values of [Formula: see text].

Flow dynamics of a time-dependent non-Newtonian and non-isothermal fluid between coaxial squeezing disks

The goal of this research is to investigate the behaviours of porosity and squeezing phenomena in the presence of time-dependent heat flow that affect the flow rate and improve the system’s heating/cooling mechanism, reduce non-Newtonian fluid turbulence and scale-up flow tracers. Squeezing discs in the presence of no-slip velocity and convective surface boundary conditions induces a laminar, unstable and incompressible non-Newtonian fluid. The convective form of the momentum, concentration and energy equations are modelled for smooth discs to evaluate and offer an analytical and numerical examination of the flow for heat and mass transfer, which are further transformed to a highly non-linear system of ordinary differential equation using similarity transformations. In the case of smooth disks, the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The comparison of HAM solutions with numerical solver programme BVP4 c proves the validity and correctness of HAM results. It is found that increasing or bypassing the Hartman number reduces the capillary region, making the Lorentz force effect more visible for small values of non-Newtonian parameter. The concentration rate at the bottom disc rises rapidly as the thermal diffusivity rises. In addition, because the rate of outflow from the flow domain increases, the suction/injection parameter lowers the radial velocity. Additionally, as the non-Newtonian parameter is increased, skin friction and heat/mass flux rise. In the suction/injection situation, all physical characteristics have the opposite effect on flow field profiles.

Numerical simulation of Electrokinetically Driven Peristaltic Pumping of Silver-Water Nanofluids in an asymmetric microchannel

This article intends to focus on the theoretical and numerical investigation of the peristaltic pumping of water-based silver nanofluid in the presence of electroosmotic forces. The investigation is carried out in an asymmetric microchannel subject to the influence of mixed convection and viscous dissipation. No-slip boundary conditions for velocity, temperature, and nanoparticle volume fraction are imposed on channel walls. The lubrication approach is utilized to simplify the normalized constitutive equations. The distribution of electric potential in the electric double layer is characterized by Poisson-Boltzmann ionic distribution which is further linearized by Debye-Hückel approximation. Nanofluid properties are predicted by a combination of the Buongiorno two-phase mixture model and homogeneous flow model. Additionally, the effective thermal conductivity and dynamic viscosity of silver-water nanofluid are characterized by the Corcione model. Silver nanoparticles of 20nm diameter are utilized in this suspension. The transformed set of nonlinear and coupled equations is numerically executed for axial velocity, temperature, and nanoparticle volume fraction by employing the mathematical software Maple 17. Pumping and trapping phenomena are also investigated. A comparison between the thermal conductivity of nanofluid predicted by the Corcione model and the Maxwell model is further presented. The influence of various flow parameters is outlined through graphical results. It has been observed that the thermal conductivity of silver-water nanofluid enhances with increasing nanoparticle volume fraction and temperature but decreases for larger sized nanoparticles. Moreover, the heat transfer rate rises significantly when smaller silver nanoparticles are suspended in water. Furthermore, the temperature of nanofluid is directly related to the Debye length parameter and the Helmholtz- Smoluchowski velocity parameter.

Permeability estimation on tomographic images using curved boundary schemes in the lattice Boltzmann method

The lattice Boltzmann method (LBM) is a widely-used numerical technique for simulation of single- and two-phase flow in geometries that are obtained using tomographic imaging of natural porous media. Due to ease of implementation and numerical robustness, a vast majority of LBM-based pore-scale simulations employ the so-called bounceback scheme to enforce no-slip velocity boundary condition. Bounceback, however, requires an implicit and tight coupling between the numerical (computational) and image (voxel) grid. This coupling results in large discretization errors, since the pore-matrix interface within the 3D image is rough. This leads to overestimation of the interfacial area, and thereby inaccurate permeability predictions. The use of the bounceback scheme also causes other numerical artifacts, such as viscosity-dependent permeability results. In order to address these deficiencies, in this work, the classical marching cubes algorithm is used to reconstruct a surface mesh from the 3D voxel grid; this mesh approximates the pore-matrix surface with higher accuracy compared to the inherent stair-stepped representation. In addition, (nominally) second-order accurate curved boundary schemes are used to enforce no-slip velocity conditions at the reconstructed pore-matrix interface.The various pre-processing steps, such as surface mesh generation and voxelization, that are necessary to use curved boundary schemes are described in detail. The proposed approach of using curved surfaces and boundary schemes is tested and validated on benchmark pore geometries, including a random packing of monodisperse spheres. We conclude that compared to current methods, curved boundary schemes provide a viable option for obtaining more accurate transport properties for Digital Rock Physics-based applications.

Vertically forced stably stratified cavity flow: instabilities of the basic state

The linear stability of a stably stratified fluid-filled cavity subject to vertical oscillations is determined via Floquet analysis. Retaining the viscous and diffusion terms in the Navier–Stokes–Boussinesq equations, with no-slip velocity boundary conditions, no-flux temperature conditions on the sidewalls and constant temperatures on the top and bottom walls, we find that the instabilities are primarily subharmonic (as is typical in many parametrically forced systems), except for in a few low-forcing-frequency ranges where the instabilities are synchronous. When the viscosity is small, the Floquet modes resemble the inviscid eigenmodes of the unforced problem, except in boundary layers. We establish scaling laws quantifying how viscosity regularizes the degeneracy associated with the inviscid idealization, and how it scales the thickness and intensity of the boundary layers. The product of boundary layer thickness and intensity remains constant with decreasing viscosity, leading to a delta distribution of vorticity on the walls in the limit of zero viscosity. This is in contrast to the zero wall vorticity in the inviscid case.

Suppression of magnetorotational instability in viscous resistive magnetized Taylor–Couette flow

Magnetorotational instability (MRI) is an instability that is responsible for accretion, the phenomenon observed in astrophysical disks, for example around black holes. MRI can be modeled using the equations of MHD. A typical linear analysis in the past made use of the small Prandtl number approximation, which results in dropping one term from these equations. Previously, one of the authors (Herron) showed that the small magnetic Prandtl number approximation suppresses MRI in axisymmetric viscous resistive magnetized Taylor–Couette flow when one has no-slip velocity boundary conditions, and insulating magnetic boundary conditions. We follow up here with a proof that MRI is still suppressed with perfectly conducting magnetic boundary conditions on the cylinders.

On well-posedness of a velocity-vorticity formulation of the stationary Navier-Stokes equations with no-slip boundary conditions

We study well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations, supplemented with no-slip velocity boundary conditions, a corresponding zero-normal condition for vorticity on the boundary, along with a natural vorticity boundary condition depending on a pressure functional. In the stationary case we prove existence and uniqueness of a suitable weak solution to the system under a small data condition. The topic of the paper is driven by recent developments of vorticity based numerical methods for the Navier-Stokes equations.

A dissipative particle dynamics method for arbitrarily complex geometries

Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor–corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid–solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier–Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry – the “Brown Pacman” microfluidic device – to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles, which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration. In addition to stationary arbitrary-shape objects, the new method is particularly useful for problems involving moving and deformable boundaries, because it only uses local information of neighboring particles and satisfies the desired boundary conditions on-the-fly.

Particulate Immersed Boundary Method for complex fluid–particle interaction problems with heat transfer

In our recent work (Zhang et al., 2015), a Particulate Immersed Boundary Method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsible for the no-slip velocity and temperature boundary conditions at the particle surface, and the kinematics and trajectory of the solid particles were evaluated by the Discrete Element Method (DEM). Four case studies were implemented to demonstrate the capability of the current coupling scheme. Firstly, numerical simulation of natural convection in a two-dimensional square cavity with an isothermal concentric annulus was carried out for verification purpose. The current results were found to have good agreement with previous references. Then, sedimentation of two-and three-dimensional isothermal particles in fluid was numerically studied, respectively. The instantaneous temperature distribution in the cavity was captured. The effect of the thermal buoyancy on particle behaviors was discussed. Finally, sedimentation of three-dimensional thermosensitive particles in fluid was numerically investigated. Our results revealed that the LBM–PIBM–DEM is a promising scheme for the solution of complex fluid–particle interaction problems with heat transfer.

Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh-Bénard convection

We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($$R\sim10^9$$). These results are the basis for the later study, by the same method, of wet convection in a solar still.Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015)This paper, by I C Ramos, C B Briozzo, is licensed under the Creative Commons Attribution License 3.0.

Internally heated convection beneath a poor conductor

We consider convection in an internally heated (IH) layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we find linear and energy stability thresholds for the static state, and we construct a lower bound on the mean temperature that applies to all flows. The linear stability analysis yields a Rayleigh number above which the static state is linearly unstable ($R_{L}$), and the energy analysis yields a Rayleigh number below which it is globally stable ($R_{E}$). For various boundary conditions on the velocity, exact expressions for$R_{L}$and$R_{E}$are found using long-wavelength asymptotics. Each$R_{E}$is strictly smaller than the corresponding$R_{L}$but is within 1 %. The lower bound on the mean temperature is proven for no-slip velocity boundary conditions using the background method. The bound guarantees that the mean temperature of the fluid, relative to that of the top boundary, grows with the heating rate ($H$) no slower than$H^{2/3}$.

A second-order coupled immersed boundary-SAMR construction for chemically reacting flow over a heat-conducting Cartesian grid-conforming solid

In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid–fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed.

Computation of the flow and thermal fields in a thermoacoustic refrigerator

The hydro- and thermodynamic processes near and within two-dimensional stack plates are simulated by numerical solution of the unsteady compressible Navier–Stokes, continuity, energy equations, and the equation of state (for air as the working fluid). The stack is assumed to consist of flat plates of equal thickness. The second order mean velocity field is computed in the neighborhood of the stack plates. In the stack plate extremities the vortical mean flow is observed which is due to the abrupt change of a slip condition to a no-slip velocity boundary condition. The temperature of the stack is governed by the energy equation; therefore the entire problem is treated as a conjugate heat transfer problem. The temperature fields in the neighborhood of the solid stack plate are also observed. From the location of the heat exchangers in Fig. 1(a), it is obvious that knowledge of the flow and thermal fields at the edges of the stack plates is the key for the development of a systematic design methodology for heat exchangers in thermoacoustic devices.

Modeling permeability of 3-D nanofiber media in slip flow regime

Over the last few decades, numerous analytical and/or numerical expressions have been developed for predicting the permeability of a fibrous medium. These expressions, however, are not accurate in predicting the permeability of media made up of nanofibers. This is because the previous expressions were mostly developed for coarse fibers, where using the so-called no-slip velocity boundary condition at the fiber surface is quite justified. Removing the no-slip velocity restriction in this work, we study the effect of slip flow on the permeability of fibrous materials made up of nanofibers. This has been accomplished by generating a large series of 3-D virtual geometries that resemble the microstructure of a nanofiber (e.g., electrospun) material. Stokes flow equations are solved numerically in the void space between the nanofibers, with the slip flow boundary condition developed based on the Maxwell first order model. The influence of fiber diameter and solid volume fraction (SVF) on the media's permeability is studied, and used to establish a correction factor for the existing permeability expressions when used for nanofiber media.

A spectral solution of nonlinear mean field dynamo equations: Without inertia

In this paper we describe in detail spectral solution method for solving nonlinear mean field dynamo equations without inertial effects in a rapidly rotating spherical shell filled with electrically conducting fluid taken into account no-slip velocity boundary conditions in the core for a finitely conducting inner core and an insulating mantle. Sample results are provided for nonlinear alpha squared dynamos. The method is suitable for solving many geophysical, astrophysical and engineering problems.

A spectral solution of nonlinear mean field dynamo equations: With inertia

This paper presents a numerical solution method for the nonlinear mean field dynamo equations in a rotating fluid spherical shell. A finite amplitude field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. This equilibration process is a key aspect of the full hydrodynamic dynamo as well as mean field dynamo. Including full inertial term we present pseudo-spectral time-stepping procedure to solve the coupled nonlinear momentum equation and induction equation with no-slip velocity boundary conditions in the core for a finitely conducting inner core and an insulating mantle. The method is found suitable for solving many geophysical problems.