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A BOUNDARY ELEMENT FORMULATION USING THE simple METHOD

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1993年第7期16卷 549-579页

作者： GRIGOREV, MM Department of Mechanical Engineering Chemical Technology Institute of Kazan K. Marx Street 68 Kazan 420015 Russia

A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well-known simple algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding.32 However, the new method demands a much larger computer storage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two-dimensional domain are found analytically. To preserve the stability in the iteration process, under-relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re - 1 and Re = 100 and the flow in a plane channel with sudden symmetric expansion at Re = 46.6.

关键词： BOUNDARY INTEGRAL EQUATION BOUNDARY ELEMENT METHOD simple algorithm 2-DIMENSIONAL LAMINAR FLOW

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CONVECTIVE HEAT-TRANSFER IN A CURVED ANNULAR-SECTOR DUCT

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1993年第3期7卷 441-446页

作者： YANG, G EBADIAN, MA Florida International Univ. Miami

A numerical analysis of heat transfer behavior in a curved annular-sector duct is presented in this article. A uniform axial heat flux and constant peripheral wall temperature boundary condition are applied in this study. The effects of three major parameters on the heat transfer process (the axial pressure gradient, the dimensionless radius ratio, and the dimensionless curvature) are systematically studied. The results indicate that completely different temperature distribution patterns are evident among the segmented duct in different locations relative to the symmetrical centerline. The Nusselt number significantly increases as the pressure gradient increases. Furthermore, an increase of the dimensionless curvature will also enhance heat transfer because of a strong secondary now. Finally, the results indicate that heat transfer is improved dramatically as the duct radius ratio decreases, especially when the duct radius ratio is smaller than 0.6.

关键词： Forced Convection Heat transfer Temperature Distribution Wall Temperature Heat Flux Numerical Analysis Vortices Flow Patterns Dean Number Thermal Boundary Layer simple algorithm

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Turbulent natural convection flow and heat transfer in an inclined square enclosure

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KSME Journal 1992年第1期6卷 16-23页

作者： Park, Man-Heung Lee, Jae-Heon System Eng Research Dept Korea Power Engineering Company Inc. Seoul Yeoung Dong South Korea Department of Mechanical Engineering Hanyang University Seoul 133-791 South Korea

Numerical analysis was performed for the two-dimensional turbulent natural convection in an inclined enclosure. The enclosure has two walls which one is heated and the other cooled, and has the other two walls of the linear temperature distributions. The inclined angle is equal to zero when the wall of linear temperature was horizontal and increases counter-clockwise. The mean continuity, mean momentum and mean energy equations have been obtained by using the conventional time-averaging procesure. The turbulent model has been applied a k-ε two equation model of turbulence similar to the one proposed by the Launder and Spalding. Numerical results were studied for a series of inclined angle, ranging from 0° to 60° and for a Grashof number range of 6×10⁶∼10⁸. The average heat transfer rate on hot wall is shown maximum value at 30° regardless of Grashof number taken here. When Gr≥5×10⁷ and θ≥45°, the flow region of whole enclosure became a significant turbulence. © 1992 The Korean Society of Mechanical Engineers (KSME).

关键词： Enclosure k-ε Model simple algorithm Tubulent Natural Convection

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2ND-ORDER UPWIND AND CENTRAL DIFFERENCE-SCHEMES FOR RECIRCULATING FLOW COMPUTATION

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AIAA JOURNAL 1992年第4期30卷 923-932页

作者： SHYY, W THAKUR, S WRIGHT, J University of Florida Gainesville Florida 32611

Two-dimensional driven cavity flows with the Reynolds number ranging from 10(2) to 3.2 x 10(3) are used to assess the performance of second-order upwind and central difference schemes for the convection terms. Three different implementations of the second-order upwind scheme are designed and tested in the context of the simple algorithm, with the grid size varying from 21 x 21 to 161 x 161 uniformly spaced nodes. Converged solutions are obtained for all Reynolds numbers. Although these different implementations of the second-order upwind scheme have the same formal order of accuracy, significant differences in numerical accuracy are observed. It is demonstrated that better performance can be obtained for the second-order upwind scheme if the discretization is cast in accordance with the finite volume formulation. Although both the second-order upwind and central difference schemes exhibit no oscillations in the solution, the upwind scheme is more accurate. In assessing and comparing the performance of these schemes, the distribution of cell Reynolds number is discussed and its impact on numerical accuracy illustrated.

关键词： simple algorithm Reynolds Numbers Convection Finite Volume Formulation Velocity Profiles Finite Difference Approximation Convection Diffusion Equation Taylor Series Mass Flux Three Dimensional Turbulent Flow

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Numerical Solution of Convection-Diffusion Problems in Irregular Domains Mapped onto a Circle

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1991年第1期5卷 103-109页

作者： Asaba, Makoto Asako, Yutaka Nakamura, Hiroshi Faghri, Mohammad Tokyo Metropolitan Univ Dept Mech Engn Tokyo 158 Japan Univ Rhode Isl Dept Mech Engn & Appl Mech Kingston RI 02881 USA

A coordinate transformation methodology has been developed for convection-diffusion problems with an arbitrary solution domain. An algebraic coordinate transformation is used that maps the solution domain onto a circle. The transformed conservation equations are discretized by a control-volume finite difference technique. Sample computations are performed for fully developed flow and heat transfer in a polygonal duct, and for natural convection in a square cavity, to validate the present methodology. The numerical results obtained compared reasonably well, even in the extreme case of a rectangular domain mapped onto a circle.

关键词： Natural Convection Thermal Boundary Condition Friction Factor Thermal Diffusivity Kinematic Viscosity Thermal Conductivity Diffusion Coefficient Conservation Equations Geometric Functions simple algorithm

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CALCULATION OF TURBULENCE-DRIVEN SECONDARY MOTION IN DUCTS WITH ARBITRARY CROSS-SECTION

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AIAA JOURNAL 1991年第4期29卷 531-537页

作者： DEMUREN, AO NASA LEWIS RES CTR INST COMPUTAT MECH PROP CLEVELAND OH 44135 USA

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered in the present study. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. The importance of the secondary Reynolds shear stress is stressed, but there are no reliable experimental data for this component. Model predictions are compared to experimental data for developed flow in a triangular duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with measured data.

关键词： Turbulence Stress Distribution Logarithmic Law of the Wall Continuity Equation Velocity Profiles Kinetic Energy Turbulence Models Turbulent Flow simple algorithm Aspect Ratio

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NUMERICAL MODELING OF A RADIO-FREQUENCY PLASMA IN ARGON

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AIAA JOURNAL 1989年第12期27卷 1779-1784页

作者： RHODES, R KEEFER, D University of Tennessee Space Institute Tullahoma Tennessee

An axisymmetric, two-dimensional mathematical model of a radio frequency gas heater is described and compared with experimental data. The model includes mass, axial momentum, radial momentum, and energy conservation equations along with Maxwell's equation for the circumferential component of the electric vector potential. Buoyancy along the heater axis and radial Lorentz forces are included in the momentum equations. Ohmic heating and radiation losses are included in the energy equation. The radiation loss terms are divided into an optically thin component that leaves the gas directly and an optically thick component that is modeled as a conduction term. Results from the model agree reasonably well with data obtained from a laboratory-scale gas heater using a bluff body to stabilize the plasma. Calculated results at increased mass flow and pressure are shown to indicate the model’s capability in designing larger scale heaters. © 1989 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Numerical Modeling Magnetic Induction Mass Flow Thermal Diffusivity Viscosity Thermal Conductivity Electric Potential Temperature Fields simple algorithm Power Supplies

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Natural convection of a variable property gas in asymmetrically heated square cavities

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Journal of Thermophysics and Heat Transfer 1989年第1期3卷 85-87页

作者： Farouk, Bakhtier Fusegi, Toru Department of Mechanical Engineering Drexel University PhiladelphiaPA United States

Natural convection flows of Boussinesq fluids confined in rectangular and cylindrical enclosures have been extensively investigated, and reviews of the literature are found in Ostrach1,2 and Catton.3 Although these analyses yield understanding of flows of technological importance, little research effort has been made in investigating the effects of the fluid property variation on the flow and heat transfer characteristics that may be significant when a large temperature difference is present in problems of interest. In order to study these flows, the original Navier-Stokes and energy equations (without simplification by the Boussinesq approximation) must be solved with specified relationship for the fluid property variation. The present paper studies convective flows of a variable property gas (air) in an asymmetrically heated square enclosure. The geometry of the problem is shown schematically. The cavity has a centrally located heated section on its bottom plate and a cooling element on one side wall. These partial heaters are maintained at constant temperatures with different values, whereas the remaining portions of enclosure walls are insulated. The present investigation assumes an infinitely long enclosure.

关键词： Natural Convection Boussinesq Approximation Heat Transfer Concentric Cylinders Absolute Temperature Thermal Conductivity Buoyancy Force Viscosity simple algorithm Streamlines

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EXAMINATION OF PRESSURE OSCILLATIONS ARISING IN THE COMPUTATION OF CASCADE FLOW USING A BOUNDARY-FITTED COORDINATE SYSTEM

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1988年第4期8卷 387-404页

作者： LAPWORTH, BL Turbomachinery Research Group School of Mechanical Engineering Cranfield Institute of Technology Cranfield Bedford MK430AL U.K.

AbstractThe incompressible flow through a two‐dimensional cascade is computed using the simple algorithm in a boundary‐fitted co‐ordinate system. With the standard staggered grid arrangement the numerical solution was found to allow localized pressure oscillations to persist adjacent to the periodic boundaries. These oscillations were found to be a consequence of the extended momentum control volumes which are required in this region of the cascade. Such control volumes may be removed by the use of appropriately non‐staggered velocity storage locations, which are also desirable in the boundary‐fitted system since the Cartesian velocity components are no longer related to the grid line orientations. However, this storage permits the propagation of global pressure oscillations, which were previously suppressed by the staggered grid arrangement. This paper attempts to define a solution procedure which uses non‐staggered velocity locations and is able to eliminate the consequent global pressure oscillations. To achieve this aim, two forms of pressure correction scheme were considered. The first implemented the scheme proposed by Vankaet *** was found to be inadequate in the open part of the cascade, whereas the second employed a modification of the scheme proposed by Rhie and Chow and was found to be successful in all regions of the flow. The results computed using this scheme were compared with the available experim

关键词： Boundary‐fitted co‐ordinates simple algorithm Non‐staggered grid Cascade flow

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NOTE ON A NUMERICAL-METHOD FOR SOLVING A STEADY ONE-DIMENSIONAL DIFFUSION PROBLEM

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KAGAKU KOGAKU RONBUNSHU 1988年第1期14卷 120-122页

作者： YAMADA, I HIRAOKA, S ARAGAKI, T KATO, Y Dept. of Appl. Chem. Nagoya Inst. of Tech. Nagoya 466 Japan

A numerical method is proposed for solving the steady one-dimensional diffusion problem described by Pe-1 y″-y′-f(y)=0 under the boundary conditions given by Danckwerts, y′=Pe(y-yF) at x=0 and y′=0 at x=1. In this... 详细信息

A numerical method is proposed for solving the steady one-dimensional diffusion problem described by Pe^-1 y″-y′-f(y)=0 under the boundary conditions given by Danckwerts, y′=Pe(y-y_F) at x=0 and y′=0 at x=1. In this method the central finite difference equation is used for calculating y″_j and y′_j (0≤j≤N-1), where j=0 and j=N denote x=0 and x=1, respectively. However, the feature of this method is to use the following finite difference equation, which gives the relationship between y_N-1 and y_N. [formula ommitted] This equation is derived by using y″_N-1=(Δy′_N-1+∇y′_N)/2 and y′_N-1=(Δy_N-1+∇y_N)/2 with the boundary condition y′_N=0 where the symbols Δ and ∇ show the forward and backward difference operators. The proposed method provides a stable solution at large Pe number as illustrated in numerical examples. © 1988, The Society of Chemical Engineers, Japan. All rights reserved.

关键词： Boundary Value Problem Finite Difference Method Numerical Method Peclet Number simple algorithm

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