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Magneto-convection in an anisotropic porous cavity due to nonuniform heat flux at bottom wall

NUMERICAL HEAT TRANSFER PART A-APPLICATIONS 2023年第1期84卷 1-15页

作者： Chandra, Harish Bera, P. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttarakhand India

In the present article, a comprehensive numerical investigation of the magneto-convection in an electrically conducting isotropic, and hydro-dynamically as well as a thermally anisotropic porous cavity, is presented. The motion of the flow is due to the applied nonuniform heat flux on the bottom wall of the cavity and the insulation of other walls. The non-Darcy model has been adopted that includes Darcy and Brinkman terms in the momentum equations. The coupled governing equations are solved numerically by using the finite volume method (FVM). The impact of periodicity parameter (N), Hartmann number (Ha), and anisotropy parameters (K*, phi, and k*) on the dynamics of flow as well as heat transfer rate have been investigated. From rigorous numerical experiments, it has been found that the structure of streamlines is unicellular except for the inner kernel in some situations. In general, the profile of local heat transfer rate possesses (N - 1) points of singularity for sinusoidal heat flux with periodicity parameter (N), and the profile of local Nusselt number is not symmetric for even values of N. The heat transfer rate is highly affected by a relatively large value of thermal conductivity ratio (k*) as well as Ha, and the absolute difference between the maximum and minimum temperature of the system increases as a function of k* as well as Ha, whereas the strength of flow decreases gradually with increasing Ha.

关键词： Anisotropic porous medium magneto-convection non-Darcy model nonuniform heating simpler algorithm

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Oscillations of physical pendulum with a cavity of elliptic shape filled with viscous liquid

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THERMOPHYSICS AND AEROMECHANICS 2015年第3期22卷 339-344页

作者： Botalov, A. Yu. RAS SB Tyumen Branch Khristianovich Inst Theoret & Appl Mech Tyumen Russia Tyumen State Univ Tyumen Russia

The plane oscillations of the elliptic cavity filled with a viscous incompressible liquid have been investigated numerically. Characteristic decay time depending on the values of system parameters has been determined, the values of parameters at which this time is minimum have been found. Flow patterns of liquid in the cavity are presented.

关键词： cavity with liquid plane oscillations simpler algorithm

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A thermal non-equilibrium approach on double-diffusive natural convection in a square porous-medium cavity

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2014年 78卷 1080-1094页

作者： Bera, P. Pippal, Sarita Sharma, Abhishek K. Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India

In this manuscript the influence of local thermal non-equilibrium state on double-diffusive natural convection in a square cavity filled with fluid-saturated porous medium has been addressed numerically. The two dimensional steady state flow is induced due to maintenance of constant temperature and concentration on the vertical walls and insulation of both horizontal walls of the cavity. Non-Darcy (Darcy-Brinkman-Forchheimer) model has been taken and the complete governing equations are solved by standard simpler algorithm. A comparative study of the effect of the presence of Brinkman term in the momentum equation showed that results under the Darcy model are very close to those for the non-Darcy Brinkman model for relatively low permeable medium (e.g., in this study Da = 10(-4)). From our experiments it has been found that the impact of Lewis number (Le) on the average heat transfer rate of fluid (Nu(f)) and solid (Nu(s)) as well as on the thermal distribution of fluid and solid is not straightforward. It depends on the buoyancy ratio (N) and the value of inter-phase heat transfer coefficient (H). However, Le increases the average mass transfer rate (Sh). Also, for each Le there exist a point in the domain of N where Nu(f) is minimum. Similar points also exist for Nu(s) and Sh. In general, these points are different and depend on the LTNE state parameters, except at Le = 1. For any relatively large value of H, when almost thermal equilibrium state is achieved, the point at which Nu(f) and Nu(s) are minimum is same due to similar thermal distribution of fluid and solid. Also, it has been found that, for the buoyancy aided flow (N > 0), the increase in H up to a threshold value (H-0) decreases Sh as well as Nu(f) but increases Nu(s). The H-0 is found to be a decreasing function of the porosity scaled thermal conductivity ratio (gamma) of fluid and solid phases. Overall, the impact of LTNE state on the heat transfer rate and thermal distribution is significant but it

关键词： Thermal non-equilibrium Double diffusive convection Non-Darcy Brinkman-Forchheimer model simpler algorithm

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A finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2013年第Jan.1期253卷 146-159页

作者： Xue, S. -C. Barton, G. W. Univ Sydney Sch Chem & Biomol Engn Sydney NSW 2006 Australia

This paper describes a finite volume method for simulating transport processes governed by convection-diffusion type equations. The formulation is based on a cell-centred, unstructured grid. With an edge-based data structure, discretisation is independent of control volume (or cell) shape. By using a surface vector decomposition at the midpoint of the interface between cells, along with a deferred-correction approach, any cross-diffusion due to grid skewness can be readily accounted for when discretising the diffusive flux. For modelling fluid flow processes, a collocated arrangement of variables is employed so that a single coefficient matrix applies for the momentum equations of each velocity component. To avoid 'checkerboard oscillation' (arising from pressure-velocity decoupling) occurring under the collocated variable arrangement when a pressure-based solution algorithm is employed, a novel pseudo-flux interpolation method is proposed for unstructured grids, ensuring that the solution is both under-relaxation factor and time-step (for transient calculation) independent. The methodology can be formulated within a framework whereby either a coupled or a decoupled solution algorithm can be employed. The features and advantages of the method are demonstrated by solution of the Navier-Stokes equations for two benchmark flow problems. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Convective and diffusive fluxes Finite volume formulation Multi-dimensional flow simpler algorithm Unstructured grid

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Implementation of boundary conditions and global mass conservation in pressure-based finite volume method on unstructured grids for fluid flow and heat transfer simulations

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2012年第19-20期55卷 5233-5243页

作者： Xue, S. -C. Barton, G. W. Univ Sydney Sch Chem & Biomol Engn Sydney NSW 2006 Australia

Proper boundary condition implementation can be critical for efficient, accurate numerical simulations when a pressure-based finite volume methodology is used to solve fluid flow and heat transfer problems, especially when an unstructured mesh is used for domain discretization. This paper systematically addresses the relationships between the flow boundary conditions for the discretized momentum equations and the corresponding conditions for the (Poisson type) pressure-linked equation in the context of a cell-centred finite volume formulation employing unstructured grids and a collocated variable arrangement. Special attention is paid to the treatment of the outflow boundary where flow conditions are either known to be fully developed (if a long enough channel is used) or unknown prior to solution (if a truncated channel is used). In the latter case, due to the singularity of the coefficient matrix of the pressure-linked equation, no pressure or pressure corrector solution can exist without explicitly enforcing global mass conservation (GMC) during each iteration. After evaluating published methods designed to ensure GMC, two new methods are proposed to correct for global mass imbalance. The validity of the overall methodology is demonstrated by solving the evolving flow between two parallel plates and the laminar flow over a backward-facing step on progressively truncated domains. In the latter case, our methodology is shown to handle situations where the outflow boundary passes through a recirculation zone. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Multi-dimensional fluid flow Finite volume formulation Flow boundary conditions Open flow boundaries Pressure-linked equation simpler algorithm

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Numerical prediction of natural convection in vented cavities using restricted domain approach

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2009年第3-4期52卷 724-734页

作者： Lal, S. Anil Reji, C. Coll Engn Dept Mech Engn Thiruvananthapuram 16 Kerala India

The present study reports the numerical simulation of natural convection heat transfer from an open square cavity with two side vents provided symmetrically on the side walls. The top wall which is maintained at a constant temperature (T-w), is the heat source for the cavity and the side walls are adiabatic. A restricted domain approach that predicts the regions of inflow, outflow and velocity distributions is employed. The applicability of two types of pressure boundary conditions at entry and exit regions are studied and compared. Non-linear coupled partial differential equations governing natural convection are solved on a structured non-uniform staggered grid using a second-order accurate upwind least square scheme for discretising the convection terms, central difference scheme for diffusion terms and simpler algorithm for pressure-velocity decoupling. An in-house code is developed and is validated with the results of three classical natural convection problems. Simulations have been carried out for a wide range of thermal parameter, Rayleigh numbers (10(4) <= Ra <= 10(8)), orientation of the cavity about horizontal (0 <= delta <= 180) and geometrical parameter, vent ratio (0.05 <= D/L <= 0.25). The numerical simulation predicts the dimensionless mass flow rate through the cavity and variation of local Nusselt number over the hot wall. A correlation for average Nusselt number is developed in terms of Rayleigh number and angle of tilt of the cavity for D/L >= 0.1. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Natural convection Vented cavities Restricted domain approach simpler algorithm Upwind least square scheme

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Performance analysis of IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2009年第10期61卷 1132-1160页

作者： Sun, Dong-Liang Qu, Zhi-Guo He, Ya-Ling Tao, Wen-Quan Xi An Jiao Tong Univ Sch Energy & Power Engn Xian 710049 Shaanxi Peoples R China

Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the Coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (simpler, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9-52.7% over simpler algorithm, by 45.3-73.4% over SIMPLEC algorithm and by 10.7-53.1% over PISO algorithm. Copyright (C) 2009 John Wiley & Sons, Ltd. C,

关键词： segregated algorithm IDEAL algorithm simpler algorithm SIMPLEC algorithm PISO algorithm three-dimensional cases

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Numerical investigation of heat transfer and fluid flow characteristics inside a wavy channel

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HEAT AND MASS TRANSFER 2007年第7期43卷 603-611页

作者： Xie, Gong-Nan Wang, Qiu-Wang Zeng, Min Luo, Lai-Qin Xian Jiaotong Univ State Key Lab Multiphase Flow Power Engn Xian 710049 Peoples R China

The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on simpler algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop.

关键词： heat transfer flow friction wavy channel simpler algorithm

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Development of a new simulation method of mold filling and solidification based on the simpler algorithm

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ISIJ INTERNATIONAL 2003年第8期43卷 1206-1212页

作者： Mok, J Hong, CP Lee, J Innovat Res Inc Plymouth MN USA Yonsei Univ Ctr Comp Aided Mat Proc Dept Met Engn Seoul 120749 South Korea Yonsei Univ Dept Mech Engn Seoul 120749 South Korea

A new combined method is to be introduced and applied to the mold filling and solidification process. In the present method, the simpler algorithm was adopted to solve the momentum and energy equations. The VOF (Volume of Fluid) method was also adopted to track the free surfaces in the filling process and the Equivalent Specific Heat Method to solve the phase change heat transfer problem in the solidification process. The staggered grid system was used to prevent the false velocity field and the non-uniform control volumes were used to improve the efficiency of calculation. The standard DAFA (donor and acceptor flux approximation) method was adopted in the VOF method. In order to verify the new combined method, the numerical results were compared with the experimental results of mold filling and other simulation methods. It is concluded that the new method can be used as an effective simulation method for the simulation of mold filling and solidification in the casting processes.

关键词： combined algorithm mold filling solidification simpler algorithm VOF method Equivalent Specific Heat method numerical simulation normal stress condition tangential stress condition resistance circuit

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PERTURBATIONAL FINITE VOLUME METHOD FOR THE SOLUTION OF 2-D NAVIER-STOKES EQUATIONS ON UNSTRUCTURED AND STRUCTURED COLOCATED MESHES

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Applied Mathematics and Mechanics(English Edition) 2005年第2期26卷 242-251页

作者：高智代民果李桂波柏威 Institute of Mechanics Chinese Academy of Sciences Beijing 100080 P.R. China

Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.

关键词： colocated grid structured grid unstructured grid perturbation finite volume method incompressible fluid NS equations SIMPLEC algorithm MSIMPLEC algorithm simpler algorithm

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