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arXiv2013

Dynamics of electrochemical flows 3 Closure models

The electrolyte (comprising of solute ions and solvents) flow-through the porous media is frequently encountered in nature or in many engineering applications, such as the electrochemical systems, manufacturing of composites, oil production, geothermal engineering, nuclear thermal disposal, soil pollution. Our previous work derived the interfacial interaction terms between the solid and the fluid, which can be used to investigate the details of transports of mass, heat, electric flied, potential, or momentum in the process of the electrochemical flows-through porous electrode. In this work, we establish the closure models for these interfacial interaction terms to close the governing equations from mathematical algebra. The interfacial interaction terms regard to the electric field, potential and electric force are firstly revealed. Our new theory provides a new approach to describe the electrochemical flows-through porous media.

physics.flu-dyn↗

arXiv2013

Solute transport predicts scaling of surface reaction rates in porous media: Applications to silicate weathering

We apply our theory of conservative solute transport, based on concepts from percolation theory, directly and without modification to reactive solute transport. This theory has previously been shown to predict the observed range of dispersivity values for conservative solute transport over ten orders of magnitude of length scale. We now show that the temporal dependence derived for the solute velocity accurately predicts the time-dependence for the weathering of silicate minerals over nine orders of magnitude of time scale, while its predicted length dependence agrees with data obtained for reaction rates over five orders of magnitude of length scale. In both cases, it is possible to unify lab and field results. Thus, net reaction rates appear to be limited by solute transport velocities. We suggest the possible relevance of our results to landscape evolution of the earth's terrestrial surface.

physics.flu-dyn↗

arXiv2013

Simulation of Temperature Distribution In a Rectangular Cavity using Finite Element Method

This paper presents the study and implementation of finite element method to find the temperature distribution in a rectangular cavity which contains a fluid substance. The fluid motion is driven by a sudden temperature difference applied to two opposite side walls of the cavity. The remaining walls were considered adiabatic. Fluid properties were assumed incompressible. The problem has been approached by two-dimensional transient conduction which applied on the heated sidewall and one-dimensional steady state convection-diffusion equation which applied inside the cavity. The parameters which investigated are time and velocity. These parameters were computed together with boundary conditions which result in temperature distribution in the cavity. The implementation of finite element method was resulted in algebraic equation which is in vector and matrix form. Therefore, MATLAB programs used to solve this algebraic equation. The final temperature distribution results were presented in contour map within the region.

physics.flu-dyn↗

arXiv2013

Stochastic moving particle semi-implicit for inviscid fluid wave simulation

The present paper introduces stochastic velocity as improvement for moving particle semi-implicit (MPS) method. This improvement is to overcome energy loss caused by numerical dissipation in the basic MPS that brings about rapid decay of waves. Stochastic velocity is added in the explicit step of the basic MPS method. MPS with stochastic improvement is compared with the basic method in the case of linear water waves, in particular dam break problem and standing wave in a rectangular tank. Surface detection and curve fitting are used to analyze the parameters of wave on the standing wave case. The surface detection and curved fitting was efficient to determine parameters of the wave and it was found that the stochastic improvement made the waves survived longer than in the basis method.

physics.flu-dyn↗

arXiv2013

3D Simulation of Dam-break effect on a Solid Wall using Smoothed Particle Hydrodynamics

Dam is built for water supply, water flow or flooding control and electricity energy storage, but in other hand, dam is one of the most dangerous natural disaster in many countries including in Indonesia. The impact of dam break in neighbour area and is huge and many flooding in remote area, as happen in Dam Situ Gintung in Tangerang (close to Jakarta) in 2009. Smoothed Particle Hydrodynamics (SPH), is one of numerical method based on Lagrangian grid which is ap- plied in astrophysical simulation may be used to solve the simulation on dam break effect. The development of SPH methods become alternative methods to solving Navier Stokes equation, which is main key in fluid dynamic simulation. In this paper, SPH is developed for supporting solid par- ticles in use for 3D dam break effect (3D-DBE) simulation. Solid particle have been treated same as fluid particles with additional calculation for converting gained position became translation and rotation of solid object in a whole body. With this capability, the result of 3D-DBE simulation has been varies and interesting. The goals of this simulation is for analyse fluid and solid particle interaction by using two different scenario. The first scenario relation between height of fluid to a solid wall barrier and second scenario, is to study relation between solid wall and its collapse time by dam break. The results show sliding distance of a solid wall is depend on a fluid height, and relation between fluid heght and wall dimension will be discussed too in this paper.

physics.flu-dyn↗

arXiv2013

Use of the Basset coefficient in the calculation of the velocity of a spheroid slowing down in a viscous incompressible fluid after a sudden impulse

The motion of a spheroid in a viscous incompressible fluid after a sudden small impulse in the direction of the symmetry axis is studied on the basis of the linearized Navier-Stokes equations. The time-dependence of the spheroid velocity follows by a Fourier transform from the frequency- dependence of the impedance involving friction coefficient, body mass, and added fluid mass. A term proportional to the square root of frequency in the asymptotic high frequency expansion of the impedance, with a Basset coefficient, describes the initial decay in time from the initial value determined by the effective mass. It is shown from numerical evidence based on the exact multipole expansion of the solution for the flow field in terms of spheroidal wavefunctions that the knowledge of the Basset coefficient is insufficient for a reliable estimate of the deviations from a simple two-pole approximation to the complete behavior in time. The two-pole approximation can be calculated from the effective mass and the steady state friction coefficient.

physics.flu-dyn↗

arXiv2013

Three-Dimensional Smoothed Particle Hydrodynamics Simulation for Liquid Droplet with Surface Tension

We provide a basic method of Smoothed Particle Hydrodynamics (SPH) to simulate liquid droplet with surface tension in three dimensions. Liquid droplet is a simple case for surface tension modeling. Surface tension works only on fluid surface. In SPH method, we simply apply the surface tension on the boundary particles of liquid. The particle on the 3D boundary was detected dynamically using Free-Surface Detection algorithm. The normal vector and curvature of the boundary surface were calculated simultaneously with 3D boundary surface reconstruction using Moving Least-Squares (MLS) method. Before the reconstruction, the coordinate system was transformed into a local coordinate system. Afterwards, the surface tension force which depends on curvature of the surface, was calculated and applied on the boundary particles of the droplet. We present the simulation result of droplet motion with gravity force. By using the basic method of SPH for fluid modeling, and a combination of 3D Free-Surface Detection algorithm with MLS method, we can simulate droplet phenomena with expected result.

physics.flu-dyn↗

arXiv2013

Fundamental solutions of MHD Stokes flow

A simple analytical solution is obtained for the MHD stokeslet in a homogeneous magnetic field. This solution represents the flow past a small particle and can also be interpreted as the flow sufficiently far away from a body of finite size. Fundamental solutions are found in terms of velocity, pressure and scalar potential distributions for the flows due to either a concentrated force or a current source. The former consists of two basic solutions for the force parallel and transverse to the magnetic field, respectively. All fundamental solutions have the characteristic length scale of the Hartmann boundary layer and two parabolic wakes developing along the magnetic field.

physics.flu-dyn↗

arXiv2013

Three-Dimensional Smoothed Particle Hydrodynamics Method for Simulating Free Surface Flows

In this paper, we applied an improved Smoothing Particle Hydrodynamics (SPH) method by using gradient kernel renormalization in three-dimensional cases. The purpose of gradient kernel renormalization is to improve the accuracy of numerical simulation by improving gradient kernel approximation. This method is implemented for simulating free surface flows, in particular dam break case with rigid ball structures and the propagation of waves towards a slope in a rectangular tank.

physics.flu-dyn↗

arXiv2013

Three-Dimensional Smoothed Particle Hydrodynamics Simulation for Liquid Metal Solidification Process

The solidification behavior of liquid metal in a container under rapid cooling process is one of the major concerns to be analyzed. In order to analyze its fundamental behavior, a three- dimensional (3D) fluid dynamics simulation was developed using a particle-based method, known as the smoothed particle hydrodynamics (SPH) method. Governing equations that determine the fluid motion and heat transfer involving phase change process are solved by discretizing their gradient and Laplacian term with the moving particles and calculating the interaction with its neighboring particles. The results demonstrate that the SPH mehod can successfully reproduce the behavior and defect prediction of liquid metal solidification process.

physics.flu-dyn↗

arXiv2013

Simple free-surface detection in two and three-dimensional SPH solver

A simple free-surface particle detection method for two and three-dimensional SPH simulation has been implemented. The method uses sphere representation for the SPH particle. The fluid domain is covered by overlapping spheres. A sphere whose surface is not fully covered considered as boundary. To test particle boundary status, we used a sum of normalized relative position vectors from neighbouring particles to the test particle. By checking the existence of un- covered sphere surface by this vector sum, boundary status of the test particle can be determined. This boundary detection method can be easily embedded in the SPH solver algorithm.

physics.flu-dyn↗

arXiv2013

Limits to the power density of very large wind farms

A simple analysis is presented concerning an upper limit of the power density (power per unit land area) of a very large wind farm located at the bottom of a fully developed boundary layer. The analysis suggests that the limit of the power density is about 0.38 times $τ_{w0}U_{F0}$, where $τ_{w0}$ is the natural shear stress on the ground (that is observed before constructing the wind farm) and $U_{F0}$ is the natural or undisturbed wind speed averaged across the height of the farm to be constructed. Importantly, this implies that the maximum extractable power from such a very large wind farm will not be proportional to the cubic of the wind speed at the farm height, or even the farm height itself, but be proportional to $U_{F0}$.

physics.flu-dyn↗

arXiv2013

Analytical Approximation for 2-D Nonlinear Periodic Deep Water Waves

A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for a set of parameter values that correspond to heights slightly smaller than the critical. The wave shapes are shown to be analytic. The method presented in quite general and does not assume smallness of wave height or steepness and can be readily extended to other interfacial problems involving Laplace's equation.

physics.flu-dyn↗

arXiv2013

Lattice Boltzmann simulation of the surface growth effects for the infiltration of molten Si in carbon preforms

The infiltration of molten silicon into carbon preforms is a widespread technique employed in the industry in order to enhance the thermal and mechanical properties of the final ceramic products. A proper understanding of this phenomenon is quite challenging since it stems from the reciprocal action and reaction between fluid flow, the transition to wetting, mass transport, precipitation, surface growth as well as heat transfer. As a result, the exhaustive modeling of such problem is an involved task. Lattice Boltzmann simulations in 2D for capillary infiltration are carried out in the isothermal regime taking into account surface reaction and subsequent surface growth. Precisely, for a single capillary in the linear Washburn regime, special attention is paid to the retardation for the infiltration process induced by the thickening of the surface behind the contact line of the invading front. Interestingly, it turns out that the process of surface growth leading to pore closure marginally depends on the infiltration velocity. We conclude that porous matrices with straight and wide pathways represent the optimal case for impregnation. Our analysis includes also a comparison between the radii characterizing the infiltration process (i.e., minimum, hydraulic, average and effective radii).

cond-mat.soft↗

arXiv2013

Why asymmetric interparticle interaction can result in convergent heat conductivity

We show that the asymmetric inter-particle interactions may induce rapid decay of heat current autocorrelation in one-dimensional momentum conserving lattices. When the asymmetry degree and the temperature are appropriate, the decay is sufficient rapid for resulting a convergence conductivity practically. To understand the underlying mechanism, we further studied the relaxation behavior of the hydrodynamic modes. It is shown that for lattice with symmetric potential, the heat mode relaxs in the superdiffusive manner, while in the case of asymmetric potential, the heat mode may relax in the normal manner.

cond-mat.stat-mech↗

arXiv2013

Averaging and spectral properties for the 2D advection-diffusion equation in the semi-classical limit for vanishing diffusivity

We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable Hamiltonians that satisfy conditions conducive to applying the averaging principle. Transformation to action-angle coordinates permits averaging in time and angle, leading to an underlying eigenvalue equation that allows for separation of the angle and action coordinates. The result is a one-dimensional second-order equation involving an anti-symmetric imaginary potential. For radial flows on a disk or an annulus, we rigorously apply existing complex-plane WKBJ methods to study the spectral properties in the semi-classical limit for vanishing diffusivity. In this limit, the spectrum is found to be a complicated set consisting of lines related to Stokes graphs. Eigenvalues in the neighborhood of these graphs exhibit nonlinear scaling with respect to diffusivity leading to convection-enhanced rates of dissipation (relaxation, mixing) for initial data which are mean-free in the angle coordinate. These branches coexist with a diffusive branch of eigenvalues that scale linearly with diffusivity and contain the principal eigenvalue (no dissipation enhancement).

physics.flu-dyn↗

arXiv2013

A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure

In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential / capillary potential formulation of the two-phase flow system. After discretizing in time with diagonally implicit Runge-Kutta schemes the resulting systems of nonlinear algebraic equations are solved with Newton's method and the arising systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. The new scheme is investigated for various test problems from the literature and is also compared to a cell-centered finite volume scheme in terms of accuracy and time to solution. We find that the method is accurate, robust and efficient. In particular no post-processing of the DG velocity field is necessary in contrast to results reported by several authors for decoupled schemes. Moreover, the solver scales well in parallel and three-dimensional problems with up to nearly 100 million degrees of freedom per time step have been computed on 1000 processors.

physics.flu-dyn↗

arXiv2013

Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluid flows

In this article, we present a detailed asymptotic analysis of the lattice Boltzmann method with two different collision mechanisms of BGK-type on the D2Q9-lattice for generalized Newtonian fluids. Unlike that based on the Chapman-Enskog expansion leading to the compressible Navier-Stokes equations, our analysis gives the incompressible ones directly and exposes certain important features of the lattice Boltzmann solutions. Moreover, our analysis provides a theoretical basis for using the iteration to compute the rate-of-strain tensor, which makes sense specially for generalized Newtonian fluids. As a by-product, a seemingly new structural condition on the generalized Newtonian fluids is singled out. This condition reads as "the magnitude of the stress tensor increases with increasing the shear rate". We verify this condition for all the existing constitutive relations which are known to us. In addition, it it straightforward to extend our analysis to MRT models or to three-dimensional lattices.

physics.flu-dyn↗