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1.
Edmondo Bassano 《国际流体数值方法杂志》2003,41(7):765-788
In the present paper the thermo‐solutal‐capillary migration of a dissolving liquid drop, composed by a binary mixture having a miscibility gap, injected in a closed cavity with differentially heated end walls, is studied. The main goal of the analysis is to clarify if and how the drop migration is affected by the dissolution process. The numerical code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases. A thermodynamic constraint fixes the concentration jump between the interface sides. This jump, together with that of the concentration normal derivatives, in turn defines the entity of the dissolution cross‐flow through the interface and the interface velocity relative to the fluid. Since the jump singularity of normal derivatives cannot be easily mollified, while retaining the necessary accuracy, a scheme for the species equation is elaborated that allows sharp jumps and has subcell resolution. Steady migration speeds are determined after the start‐up phase for different radii and temperature differences. The results will be used for the preparation of a sounding rocket space experiment. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
2.
The motion of deformable drops in pipes and channels is studied using a level set approach in order to capture the interface of two fluids. The interface is described as the zero level set of a smooth function, which is defined to be the signed normal distance from the interface. In order to solve the Navier–Stokes equations, a second‐order projection method is used. The dimensionless parameters of the problem are the relative size of the drop to the size of the pipe or channel cross‐section, the ratio of the drop viscosity to the viscosity of the suspending fluid and the relative magnitude of viscous forces to the surface tension forces. The shape of the drop, the velocity field and the additional pressure loss due to the presence of the drop, varying systematically with the above‐mentioned dimensionless parameters, are computed. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
3.
In this paper, we present a macroscopic numerical model that is capable of capturing the interaction between the double‐diffusive convective field and a localized fluid flow on account of solutal undercooling during non‐equilibrium solidification of binary alloys. The model is essentially based on a fixed‐grid enthalpy based control volume approach. In the present model, microscopic features pertaining to non‐equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition‐coefficient. The effective partition‐coefficient is numerically modelled by means of a number of macroscopically observable parameters related to the solidifying domain. This feature has made the present treatment different from micro‐macro modelling of alloy solidification, which involves certain parameters that may not be macroscopically resolvable. Numerical simulations are performed for the case of two‐dimensional transient solidification of Pb–Sn alloys (both hypoeutectic and hypereutectic) in a rectangular cavity, employing the present model. The simulation results are also compared with the corresponding experimental results quoted in the literature, and the agreement is excellent. From the results, it can be concluded that non‐equilibrium effects on account of solutal undercooling result in a more enhanced macrosegregation. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
4.
毛管上升现象与许多行业密切相关,系统地对此现象进行研究具有重大意义。与传统理论研究方法不同,本文使用N-S方程耦合水平集方法模拟毛管气液上升行为。通过与简化条件的解析解对比,验证了模拟方法的可靠性。此外,详细地研究了毛管振荡现象,并分析了影响毛管振荡行为的主要因素。结果表明,水平集方法能够精确地表征毛管振荡现象,与数值解相比具有更高的精度。毛管长度的增加能够减弱液柱振荡,主要归结于非湿相气体的粘滞力作用;湿相密度和湿相粘度同样对毛管振荡现象影响显著。湿相密度越大,惯性力越大,促进了毛管振荡;而湿相粘度变大,会增大粘滞力作用,因此减弱了毛管振荡现象。毛管振荡是由多种影响因素共同控制的,流体的惯性力是造成毛管振荡的主要原因,而粘滞力是减弱毛管振荡行为的主要因素,使液柱振荡逐渐衰减,并稳定至平衡高度。 相似文献
5.
Numerical study has been performed to investigate the effects of cavity shape on flow and heat transfer characteristics of the lid‐driven cavity flows. Dependence of flow and thermal behaviour on the aspect ratio of the cavities is also evaluated. Three types of the cross‐sectional shape, namely, circular, triangular, and rectangular, and four aspect ratios, 0.133, 0.207, 0.288, and 0.5, are taken into account to construct twelve possible combinations; however, attention is focused on the small‐aspect‐ratio situations. Value of the Reynolds number considered in this study is varied between 100 and 1800. For the cases considered in this study a major clockwise vortex driven by the moving lid prevailing in the cavity is always observed. When the Reynolds number is fixed, the rectangular cavity produces strongest lid‐driven flow, and the triangular cavity weakest. For the cases at small aspect ratio and low Reynolds number, the streamlines appear symmetric fore‐and‐aft with respect to the central line at x/L = 0.5. Data for the local and average Nusselt numbers are also provided. For rectangular cavities, it is observed that case 1/5R produces the highest average Nusselt number at any Reynolds number. Among the twelve possible geometric cases considered herein, the highest and lowest average Nusselt numbers are found with cases 1/6T and 1/2C, respectively. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
6.
This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
7.
S. Maleki M. Tahani 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2012,92(8):652-667
Non‐linear bending analysis of moderately thick laminated plates and cylindrical panels with various thermo‐mechanical loadings and boundary conditions is presented using generalized differential quadrature (GDQ) method together with the Newton‐Raphson iterative scheme. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported and free boundary conditions are considered. Assuming the effects of shear deformation and initial curvature, based on the first‐order shear deformation theory (FSDT) and von Kármán‐type of geometric non‐linearity, the governing system of equations is obtained. This system includes thirteen non‐linear partial differential equations (PDEs) in terms of unknown displacements, rotations, forces and moments. The solution domain, governing equations and related boundary conditions are then discretized based on the GDQ technique. It is observed that the method provides reasonably accurate results with relatively small number of grid points. Comparisons of the predictions with results of finite element analyses show very good agreement. More results for panels with particular boundary conditions are presented for future references. 相似文献
8.
The standard level set (LS) method can capture the interface smoothly and gives accurate normal vectors but suffers from an excessive amount of mass gain/loss. The conservative LS method exhibits excellent mass conservation properties, but the result is usually contaminated by inaccurate interface normal vectors. To address this problem, the improved conservative LS method is proposed to capture the interface smoothly with excellent mass conservation properties. The improvement of the method lies in that the surface normal is computed from a signed distance function, which is also advected and reinitialized in the flow fields, instead of using the Heaviside function. The proposed method is implemented by implicit two‐step Taylor–Galerkin approximation within the finite element context. The approach is validated with the well‐known benchmark problems and is found out to be highly reliable and accurate. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
We present an overset grid method for solution of the integro‐differential vorticity–velocity formulation of the Navier–Stokes equations for two‐dimensional, incompressible flow. The method uses a body‐fitted inner grid, on which vorticity is evolved semi‐implicitly, and a Cartesian outer grid with explicit vorticity evolution. The Biot–Savart integral is solved using an adaptive, optimized multipole acceleration method. The Biot–Savart integration is performed over all inner grid cells, over all ‘active cells’ of the outer grid that lie entirely outside of the inner grid, and over sub‐elements of a set of ‘overhanging’ cells of the outer grid that overlap part of the inner grid. A novel method is developed using a level‐set distance function to rapidly and easily partition the overhanging grid cells, which is essential for the Biot–Savart integration in order to avoid double‐counting vorticity in the overhanging region. A similar decomposition into outer, inner and overhanging cells is used in solving for pressure using a boundary‐element formulation, which requires evaluation of an integral over the vorticity field using a method similar to that used for the Biot–Savart integral. The new overset grid method is applied to flow past stationary and moving bodies in two dimensions and found to agree well with prior experimental and numerical results. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
10.
In the past, when either the perturbation‐type method or direct‐simulation approach was used to analyse capillary jets, the governing equations, which are parabolic in time and elliptic in space, were simplified or linearized. In the present study, the convective derivative term and a full, nonlinear form of the capillary pressure term are retained in the governing equations to investigate nonlinear effects on the break‐up of capillary jets. In this work, the TVD (i.e. total variation diminishing) scheme with flux‐vector splitting is applied to obtain the solutions of the system of nonlinear equations in a matrix form. Numerical results show that the present nonlinear model predicts longer jet break‐up lengths and slower growth rates for capillary jets than the previous linear model does. Comparing with other measurements from past literatures, the nonlinear results are consistent with the experimental data and appear more accurate than the linear analysis. In the past, the classic perturbation‐type analyses assumed constant growth rates for the fundamental and all harmonic components. By contrast, the present model is able to capture the local features of growth rates, which are not spatially and temporally constant. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
11.
The difference between a presumed distribution of flamelet position and a numerically simulated distribution of distance function (a signed distance to flamelet) is investigated. It is shown that even if the distribution of flamelet position is symmetrical and close to Gaussian, the distribution of distance function away from the mean flame position is skewed towards the mean position and the mean of the distance function is also different from the distance to the mean position. The difference depends on the distance to the mean flame and the flame wrinkling amplitude. An extension method for the variance of the distance function and an upwind scheme for solving the re‐initialization equation are presented. A numerical simulation of a premixed turbulent flame is compared to experimental data. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
12.
This paper presents a contribution to level‐set reinitialization in the context of discontinuous Galerkin finite element methods. We focus on high‐order polynomials for the discretization and level set geometries, which are comparable to the element size. In contrast to hyperbolic and geometric reinitialization techniques, our method relies on solving a nonlinear elliptic PDE iteratively. We critically compare two different variants of the algorithm experimentally in numerical studies. The results demonstrate that the method is stable for nontrivial test cases and shows high‐order accuracy. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
13.
A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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This paper presents a coupled finite volume inner doubly iterative efficient algorithm for linked equations (IDEAL) with level set method to simulate the incompressible gas–liquid two‐phase flows with moving interfaces on unstructured triangular grid. The finite volume IDEAL method on a collocated grid is employed to solve the incompressible two‐phase Navier–Stokes equations, and the level set method is used to capture the moving interfaces. For the sake of mass conservation, an effective second‐order accurate finite volume scheme is developed to solve the level set equation on triangular grid, which can be implemented much easier than the classical high‐order level set solvers. In this scheme, the value of level set function on the boundary of control volume is approximated using a linear combination of a high‐order Larangian interpolation and a second‐order upwind interpolation. By the rotating slotted disk and stretching and shrinking of a circular fluid element benchmark cases, the mass conservation and accuracy of the new scheme is verified. Then the coupled method is applied to two‐phase flows, including a 2D bubble rising problem and a 2D dam breaking problem. The computational results agree well with those reported in literatures and experimental data. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
17.
An unsteady Navier–Stokes solver for incompressible fluid is coupled with a level set approach to describe free surface motions. The two‐phase flow of air and water is approximated by the flow of a single fluid whose properties, such as density and viscosity, change across the interface. The free surface location is captured as the zero level of a distance function convected by the flow field. To validate the numerical procedure, two classical two‐dimensional free surface problems in hydrodynamics, namely the oscillating flow in a tank and the waves generated by the flow over a bottom bump, are studied in non‐breaking conditions, and the results are compared with those obtained with other numerical approaches. To check the capability of the method in dealing with complex free surface configurations, the breaking regime produced by the flow over a high bump is analyzed. The analysis covers the successive stages of the breaking phenomenon: the steep wave evolution, the falling jet, the splash‐up and the air entrainment. In all phases, numerical results qualitatively agree with the experimental observations. Finally, to investigate a flow in which viscous effects are relevant, the numerical scheme is applied to study the wavy flow past a submerged hydrofoil. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
18.
The single‐phase level set method for unsteady viscous free surface flows is presented. In contrast to the standard level set method for incompressible flows, the single‐phase level set method is concerned with the solution of the flow field in the water (or the denser) phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions. A reinitialization procedure has been developed for non‐orthogonal grids with large aspect ratios. A convective extension is used to obtain the velocities at previous time steps for the grid points in air, which allows a good estimation of the total derivatives. The method was applied to three unsteady tests: a plane progressive wave, sloshing in a two‐dimensional tank, and the wave diffraction problem for a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level set method works, as long as the stress on the second phase can be specified (or neglected) and no bubbles appear in the flow during the computation. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
19.
A mass‐conserving Level‐Set method to model bubbly flows is presented. The method can handle high density‐ratio flows with complex interface topologies, such as flows with simultaneous occurrence of bubbles and droplets. Aspects taken into account are: a sharp front (density changes abruptly), arbitrarily shaped interfaces, surface tension, buoyancy and coalescence of droplets/bubbles. Attention is paid to mass‐conservation and integrity of the interface. The proposed computational method is a Level‐Set method, where a Volume‐of‐Fluid function is used to conserve mass when the interface is advected. The aim of the method is to combine the advantages of the Level‐Set and Volume‐of‐Fluid methods without the disadvantages. The flow is computed with a pressure correction method with the Marker‐and‐Cell scheme. Interface conditions are satisfied by means of the continuous surface force methodology and the jump in the density field is maintained similar to the ghost fluid method for incompressible flows. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
20.
‘Fluid buckling’ is a phenomenon characterized mainly by the existence of fluid toroidal oscillations during flow. It appears when a high viscosity fluid flows vertically against a flat surface and may occur in industrial applications, as in injection molding of a propergol in complex‐shaped cavities. These coiling or folding oscillations appear during the mold filling stage, leading to air entrapment. To understand and to model this free surface flow problem, a convected level set method is proposed. First, a sinus filter is applied to the distance function to get a smooth truncation far from the interface. Second, the reinitialization is embedded in the transport equation model, avoiding it as a separate step during calculation. In order to validate the method, numerical results are presented on classical interface capturing benchmarks. Finally, results are shown on two‐dimensional and three‐dimensional viscous jet buckling problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献