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A NUMERICAL STUDY OF THE PLANAR CONTRACTION FLOW OF A VISCOELASTIC FLUID USING THE simpler algorithm

JOURNAL OF NON-NEWTONIAN FLUID MECHANICS 1991年第1期39卷 89-106页

作者： YOO, JY NA, Y Department of Mechanical Engineering College of Engineering Seoul National University Seoul 151-742 Korea

A finite volume technique has been introduced in an attempt to simulate the planar 4:1 contraction flow of the Oldroyd B fluid on a non-uniform staggered grid system, which incorporates the simpler algorithm in discretizing the momentum equations and the deferred correction method in discretizing the constitutive equations. For some combinations of viscoelastic parameters, the size and shape of the corner vortex growth are shown to be in good qualitative agreement with those observed experimentally by others for constant viscosity viscoelastic fluids. In general, however, they seem to be sensitive to the ratio of retardation time to relaxation time.

关键词： EFFECT OF INERTIA NONUNIFORM GRID SYSTEM OLDROYD-B FLUID PLANAR 4-1 CONTRACTION FLOW 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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A semi-Lagrangian finite volume method for Newtonian contraction flows

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2001年第6期22卷 2152-2177页

作者： Phillips, TN Williams, AJ Univ Wales Dept Math Aberystwyth SY23 3BZ Dyfed Wales

A new finite volume method for solving the incompressible Navier Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to ow through a constricted channel, and results are obtained for Reynolds umbers, based on half the ow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 ( 1980), pp. 393-414] and the asymptotic theory of Smith.

关键词： semi-Lagrangian approach Navier Stokes finite volume method contraction geometry staggered mesh simpler algorithm

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EVALUATION OF A COUPLED SOLUTION APPROACH FOR FLUID-FLOW CALCULATIONS IN BODY-FITTED COORDINATES

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1990年第1期11卷 1-20页

作者： KARKI, KC MONGIA, HC Allison Gas Turbine Division General Motors Corporation Indianapolis IN 46206-0420 U.S.A.

AbstractAn investigation has been conducted to study the performance of a coupled solution approach for solving the fluid flow equations in body‐fitted co‐ordinates using a covariant velocity formulation. The set of discrete equations is solved using a sparse matrix variant of LU decomposition. A series of test problems have been considered to study the effects of Reynolds number, mesh skewness and grid size on the convergence rate. The coupled solution approach has been compared with a state‐of‐the‐art sequential approach. The results indicate that the coupled technique is faster by a factor of about two for reasonable grids. For severely non‐orthogonal grids the performance of the coupled solution approach deteriorates c

关键词： Curvilinear co‐ordinates Coupled solution Viscous flows simpler algorithm

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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 simulation of heat transfer at an array of co-planar slat-like surfaces oriented normal to a forced convection flow

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INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS IN TECHNOLOGY 2000年第6期13卷 285-294页

作者： Li, ZY Hung, TC Tao, WQ Xian Jiao Tong Univ Sch Energy & Power Engn Xian 710049 Shaanxi Peoples R China

Numerical study of the per-slat heat transfer coefficient was made for an array of co-planar slat-like surfaces which face upstream into an oncoming airflow. The flow washes over the slats as it passes into slot-like gaps between the slats. The computations were performed for several different slat-slot configurations characterized by the ratio of the slot-slat width to the slat width (P/W), the Reynolds number varied from 500 to 7000, and the range of Prandtl number was 0.7-10. Based on the simpler algorithm and the central difference scheme (CDS), parametric studies on the effects of the Reynolds number, P/ Wand the Prandtl number were performed. Numerical results agree well with the test results for mass transfer(Se = 2.5). From the numerical results, a general heat transfer correlation was obtained which covers the following range of parameters: 500 less than or equal to Re less than or equal to 7000. 1.25 less than or equal to P/W less than or equal to 5, 0.7 less than or equal to Pr less than or equal to 10.

关键词： numerical study heat transfer simpler algorithm central difference scheme

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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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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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Properties predictions of different mixed-gas induction plasmas by pulse modulated approach

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THIN SOLID FILMS 2001年第2期386卷 165-172页

作者： Paul, KC Sakuta, T Univ Toronto Power Grp Toronto ON M5S 3G4 Canada Kanazawa Univ Dept Elect & Comp Engn Kanazawa Ishikawa 9208667 Japan

Introduction of pulsing phenomenon in thermal plasmas has been anticipated as an outstanding feature to promote industrial applications of thermal plasma technology. Numerical models are found to be effective in giving ideas on fundamental plasma properties. Here, a two-dimensional and time-dependent model was solved to predict plasma properties for a 70-mm inner diameter torch. Calculations were carried out for a wide variety of gas combinations: argon, argon-N-2, argon-O-2, argon-air, argon-He, argon-H-2, argon-CO2, and argon-SF6, for step-current modulation and comparative results are presented. The coil current levels for step modulations corresponded to 45- and 35-kW steady-state plasmas. Applying corresponding current transition for all considered plasmas, the time-dependent profiles for plasma power, temperature, velocity, Lorentz force and Joule heating were determined. Comparing the plasma temperatures at mid-coil (z = 151.5 mm) and r = 18 mm for step-down pulsation, it was found that the temperature difference between the two steady-state magnitudes, corresponding to current levels, was the maximum for Ar-SF6 plasma (114 K) and the minimum for Ar plasma (65 K). The response times, determined from the temporal temperature profiles at mid-coil and r = is mm for step-down current pulsation, were the lowest at 4.9 ms for Ar-SF6, the highest at 42.7 ms for Ar-H-2, and between 31 and 35 ms for other ICPs. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： local thermodynamic equilibrium (LTE) response time shimmer current level simpler algorithm

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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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