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  • Numerical Study of Liquid Metal Flow in a Rectangular Duct under the Influence of a Heterogeneous Magnetic Field
  • Abstract We simulated numerically the laminar flow in the geometry and the magnetic field of the experimental channel used in [Andreev, Kolesnikov, and Thess (2006)]. This provides detailed information about the electric potential distribution for the laminar regime (numerical simulation) and in the turbulent regime as well (experiment). As follows from comparison of simulated and experimental results, the flow under the magnet is determined by the interaction parameter N = Ha2 / Re representing the ratio between magnetic force, determined by the Hartmann number Ha, and inertial force, determined by the Reynolds number Re. We compared two variants: (i)(Re,N)=(2000,18.6) (experiment), (400,20.25)…
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  • An arbitrary Lagrangian-Eulerian (ALE) method for interfacial flows with insoluble surfactants
  • Abstract An arbitrary Lagrangian-Eulerian (ALE) method for interfacial flows with insoluble surfactants is presented. The interface is captured using a coupled level set and volume of fluid method, which takes advantage of the strengths of both the level set method and the volume of fluid method. By directly tracking the surfactant mass, the method conserves surfactant mass, and prevents surfactant from diffusing off the interface. Interfacial area is also tracked. To accurately approximate the interfacial area, the fluid interface is reconstructed using piece-wise parabolas. The surfactant concentration, which determines the local surface tension through an equation of state, is then computed…
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  • Adaptive 3D finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage
  • Abstract An adaptive phase field model for the solidification of binary alloys in three space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid. Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh tetrahedrons having high aspect ratio whenever needed. Numerical results show that our method is effective and allows to perform…
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  • Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations
  • Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid velocity in a standard projection…
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  • Improvements for calculating two-phase bubble and drop motion using an adaptive sharp interface method.
  • Abstract In this paper, we describe new techniques for numerically approximating two-phase flows. Specifically, we present new techniques for treating the viscosity and surface tension terms that appear in the Navier-Stokes equations for incompressible two-phase flow. Our resulting numerical method has the property that results computed using our two-phase algorithm approach the corresponding "one-phase'' algorithm in the limit of zero gas density/viscosity; i.e. the two-phase results approach the one-phase free-boundary results in the limit that the gas is assumed to become a uniform pressure void. By grid convergence checks and comparison with previous experimental data, we shall demonstrate the advantages of…
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  • Surface Phase Separation and Flow in a Simple Model of Multicomponent Drops and Vesicles
  • Abstract We introduce and investigate numerically a thermodynamically consistent simple model of a drop or vesicle in which the interfacial surface contains multiple constitutive components (e.g. amphiphilic molecules). The model describes the nonlinear coupling among the flow, drop/vesicle morphology and the evolution of the surface phases. We consider a highly simplified version of the Helfrich model for fluid-like vesicle membranes in which we neglect the effects of bending forces and spontaneous curvature but keep the effects of inhomogeneous surface tension forces. Thus, this model may also describe liquid drops. To solve the highly nonlinear, coupled system a new numerical method is…
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  • Computational Fluid Dynamics Modeling of the Effect Of Rotation During Reaming into the Intramedullary Canal of a Long Bone
  • Abstract The penetration of the reamer into the medullary cavity can be compared to a piston entering a cylinder filled with viscous fluid. When the flutes of the reamer are clogged with bone debris, fat and marrow, the piston effect is magnified and larger pressures are usually obtained. This paper considers a reamer with clogged flutes and investigates whether the rotation speed of the reamer has a significant influence on the pressure within the intramedullary cavity. The effect of reamer rotation speed on the pressure distribution within the bone is investigated numerically by solving the full three-dimensional Navier-Stokes equations together with…
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  • A High Resolution Pressure-Based Method for Compressible Fluid Flow
  • Abstract A pressure-based Euler scheme, based on a collocated grid arrangement is described. The newly developed algorithm has two new prominent features: (i) the use of normalized variables to bound the convective fluxes and (ii) the use of a high-resolution scheme in calculating interface density values to enhance the shock-capturing property of the algorithm. The algorithm is first tested for flows at different Mach numbers ranging from subsonic to supersonic on a bump in a channel geometry; then the results are compared with the corresponding ones obtained without the bounded scheme in the correction step. The output is also compared with…
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  • Numerical Study of Low Frequency G-jitter Effect on Thermal Diffusion
  • Abstract Convection has a major impact on diffusion in fluid mixtures either on the Earth or in the microgravity condition. G-jitters, as the primary source that induces the vibrational convection in space laboratories, should be studied thoroughly in order to improve the diffusion-dominated fluid science experiments. In this paper we consider the effect of g-jitters on thermal diffusion. The mixture water-isopropanol (90:10 wt%) bounded in a cubic cell is simulated with a lateral heating and various vibration conditions. The fluid flow, concentration and temperature distributions are thoroughly analyzed for different g-jitter scenarios. It is shown that the overall effect of vibrations…
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  • Thermal Communication between Two Vertical Systems of Free and Forced Convection via Heat Conduction across a Separating Wall
  • Abstract This work deals with the problem of thermal interaction between two fluid media at two different bulk temperatures and separated by a vertical plate. The problem is analyzed by taking into account the heat conduction across the separating plate. The flow configuration considered is one in which the two vertical boundary layers of free and forced convection developed on plate sides are in parallel flow. The dimensionless parameters governing the thermal interaction mechanisms are analytically deduced. The obtained results are presented in graphs to demonstrate the heat transfer characteristics of investigated phenomenon. The work reports a means to estimate the…
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