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Natural Convection (natural + convection)
Selected AbstractsNatural Convection in Heat Generating Oval Porous Enclosures: A Non-Darcian ModelTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2003Subrat Das Abstract This paper presents a series of numerical simulations dealing with the problem of natural convection flows and associated heat transfer in an enclosure filled with a fluid-saturated porous medium. The analysis is based on the finite element technique and incorporates the Brinkman-extended Darcy model for an oval enclosure. The numerical results obtained for a modified Rayleigh number, Ra, Darcy number, Da, offset, E, and eccentricity, e, are presented and discussed. The numerical predictions for a square enclosure compared well with published data. It is found that any increase in Da or Ra results in a higher fluid velocity that is responsible for shifting the core of the flow. Moreover, at higher ovality (E = 0.5), asymmetric flow is observed even at the lower range of Rayleigh number (Ra , 20), which may be attributed to the effect of curved isothermal wall. On présente dans cet article une série de simulations numériques des écoulements avec convection naturelle et du transfert de chaleur associé, dans une enceinte remplie d'un milieu poreux saturé en fluide. L'analyse repose sur la technique des éléments finis et fait appel à un modèle généralisé de Darcy-Brinkman pour une enceinte de forme ovale. Les résultats numériques obtenus pour le nombre de Rayleigh modifié, Ra, le nombre de Darcy, Da, le décentrement, E, et l'eccentricité, e, sont présentés et analysés. Les prédictions numériques pour une enceinte carrée se comparent bien aux données publiées. On trouve que toute augmentation de Da ou Ra entraîne une plus grande vitesse de fluide qui est responsable du déplacement du c,ur de l'écoulement. En outre, à une plus grande ovalité (E = 0,5), un écoulement asymétrique est observé même dans la gamme inférieure de nombre de Rayleigh (Ra" 20), ce qui peut être l'effet de la paroi isotherme courbée. [source] A numerical study of natural convection in a vertical cylinder bundleHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2003Yuji Isahai Abstract Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary-fitted coordinate system. Numerical calculations for center-to-center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 108. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nui are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330,341, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10095 [source] Natural convection of a water-fine particle suspension in a rectangular cell heated and cooled from opposing vertical walls: The effect of distribution of particle sizeHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2001Masashi Okada Abstract A water-fine particle suspension with a uniform initial temperature and concentration in a rectangular cell was heated from a vertical wall and cooled from the opposing vertical wall. The dispersed particles had a distribution in size. In this natural convection, many layers separated by almost-horizontal sharp interfaces were observed. In the beginning many layers appear, and each interface of the layers falls gradually with a constant velocity, and finally all layers vanish. To clarify this phenomenon, concentrations and mean diameters of the particles in each layer and temperature distributions were measured. Moreover, natural convection of the other suspension with particles which had a narrow size distribution was also investigated. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 636,647, 2001 [source] Introducing natural-convective chilling to food engineering undergraduate freshmen: Case studied assisted by CFD simulation and field visualizationCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2009J. A. Rabi Abstract A computational fluid dynamics (CFD)-assisted didactic activity has been applied to Food Engineering freshmen aiming at introducing basic concepts of process modeling and simulation towards the food industry. Evoking natural convection, a relatively simple case study was proposed involving two initially room temperature porous samples (identified as two fruits) that were placed inside a refrigeration chamber. Three different configurations were suggested for placing such warmer samples so that students were asked to order them with respect to their chilling capability, that is, to their ability to chill samples as fast as possible. Freshmen's written answers were collected before CFD was used to simulate and visualize each distinct chilling scenario. Accordingly, a finite-volume FORTRAN simulator for transport phenomena in domains fully or partially filled up with porous matrix was used to help compare each chilling performance. Among all possible combinations, answer distribution is presented and discussed in the light of freshmen's scholar background as well as based on the way natural convection concepts were introduced. © 2008 Wiley Periodicals, Inc. Comput Appl Eng Educ 17: 34,43, 2009; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae20161 [source] Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growthCRYSTAL RESEARCH AND TECHNOLOGY, Issue 8 2009F. Mokhtari Abstract In order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Recent developments in modelling of liquid phase electroepitaxy under applied magnetic fieldCRYSTAL RESEARCH AND TECHNOLOGY, Issue 4-5 2005S. Dost Abstract Growth of single crystals under magnetic field is of interest for suppressing the adverse effect of natural convection and for better mixing in the liquid solution, which are the favorable conditions for prolonged growth and high quality crystals. In this short review article, recent developments in the modelling of electroepitaxy under magnetic field are presented. An application is given for the liquid phase electroepitaxial growth of GaAs bulk single crystals under a static magnetic field. Experimental results, that have shown that the growth rate under an applied static magnetic field is proportional to the applied magnetic field, and increases with the field intensity level, are predicted from the present model. The model also predicts growth interface shapes accurately. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] New Stack Design of Micro-tubular SOFCs for Portable Power SourcesFUEL CELLS, Issue 6 2008T. Suzuki Abstract Micro-tubular solid oxide fuel cells (SOFCs) have high thermal stability and higher volumetric power density, which are considered to be ideal features for portable power sources and auxiliary power units for automobile. Here, we report a new stack design using anode supported micro-tubular SOFCs with 2,mm diameter using Gd doped CeO2 (GDC) electrolyte, NiO-GDC anode and (La, Sr)(Co, Fe)O3 (LSCF)-GDC cathode. The new stack consists of three bundles with five tubular cells, sealing layers and interconnects and fuel manifolds. The performance of the stack whose volume is 1,cm3 was shown to be 2.8,V OCV and maximum power output of 1.5,W at 500,°C, applying air only by natural convection. The results also showed strong dependence of the fuel flow rates on the stack performance, which was correlated to the gas diffusion limitation. [source] Solidification of binary aqueous solution cooled from aboveHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 1 2010Shigeo Kimura Abstract Freezing and melting phenomena are important in many different fields, including crystal growth, casting, metallurgy, geophysics, and oceanography. Solidification of a multi-component solution is the one often observed in nature. In order to investigate basic features of the freezing processes of binary systems, we conducted a series of laboratory experiments in a rectangular box cooled from above using aqueous NaNO3 solution. During the freezing, the solid phase always grows into many needle-like crystals called the mushy layer. We measured the growth of the mushy layer thickness, the solid fraction, the temperature, and the concentration distributions. The average solid fraction is found to increase with time in the mushy layer. This causes a slow descent of the released solute in the mushy layer and its eventual fall into the liquid region below because of gravity. We propose a one-dimensional model to explain the horizontally-averaged mushy layer growth. In the model, the estimate of a heat flux at the mushy-liquid interface due to natural convection is found essential for a correct prediction. The proposed theory predicts well the growth of the mushy-layer and the average solid fraction, once the convective heat flux is properly given. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20278 [source] Fluid flow and heat transfer of natural convection around array of vertical heated platesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 2 2009Kenzo Kitamura Abstract Natural convective flows around an array of vertical heated plates were investigated experimentally. Main concerns were directed to the influences of plate numbers on the heat transfer characteristics of the plates. Both surfaces of the test plates were heated with constant and equal heat fluxes and their local heat transfer coefficients were measured. The results showed that the coefficients of the surfaces of the array facing outward became higher than those facing inward. The flow fields around the bottom of the plate array were visualized with smoke. The result showed that the ambient flow is directed from the sides to the center of the array and enters the parallel channel obliquely. These flows cause the above difference in the coefficients. While the difference gradually diminished in between the plates placed in the central section of the array, their coefficients asymptotically approach those of the analytical correlation that assumed a uniform velocity at the channel inlet. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20232 [source] Heat transfer of combined forced and natural convection from horizontal cylinder to airHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2007Kenzo Kitamura Abstract Experimental investigations have been carried out for combined convective flows of air induced around uniformly heated, horizontal cylinders. Three cases of aiding, opposing, and cross flows were examined. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers of Red=50 to 900 and Rad*=5×104 to 3×106. The flow fields around the cylinders were visualized with smoke. The results showed that separation points gradually shift from those of the forced convection to the top edge of the cylinder with increasing wall heat fluxes. The local heat transfer coefficients of the cylinders were also measured. Although the local coefficients show complex variations with the forced flow velocities and the wall heat fluxes, the overall coefficients become higher than those estimated from pure forced and natural convections throughout the cases of aiding, opposing, and cross flows. Moreover, it was confirmed that the overall Nusselt numbers as well as the separation points can be predicted with the non-dimensional parameter (Grd*/NudRed2). © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 474,488, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20180 [source] Experimental study on heat transfer enhancement on natural convection in a vertical plate by using longitudinal vortex generators arranged in rowsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2006JingAn Long Abstract Longitudinal vortices are capable of producing beneficial effects in heat transfer enhancement. Experiments in natural convection heat transfer enhancement were done on a vertical flat heating plate using delta-winglet longitudinal vortex generators (LVGs) arranged in rows. In an experimental range of Rayleigh number, the height and width of the winglet of the longitudinal vortex generator (LVG), the array form of the longitudinal vortex generators on the heat transfer performance were experimentally investigated, and the best height of the winglet of the longitudinal vortex generator was obtained. The results showed the change of the array form of the longitudinal vortex generators could affect the heat transfer effect. Finally by arranging some longitudinal vortex generator arrays with the appropriate interval, the whole heat transfer effect of the interval could reach a prime value. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 351,358, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20119 [source] A numerical study of natural convection in a vertical cylinder bundleHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2003Yuji Isahai Abstract Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary-fitted coordinate system. Numerical calculations for center-to-center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 108. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nui are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330,341, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10095 [source] Fluid flow and heat transfer of natural convection at a slightly inclined, upward-facing, heated plateHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2002Fumiyoshi Kimura Abstract Natural convective flows over upward-facing, inclined plates were investigated experimentally, with an emphasis on the role of opposing flows that appear over the plates inclined slightly from the horizontal line. The flow fields over the plates and the surface temperatures of the heated plates were visualized with both dye and a liquid-crystal thermometry. The results showed that both the descending and ascending flows appeared over the plates when the inclination angles of the plates were less than 15°. The two flows collided with each other at a certain distance from the plate edge, and then detached from the plate to become a thermal plume. It was found that the above distance was determined solely by the inclination angles and was independent of sizes and heat fluxes of the plates. The local heat transfer coefficients of the plates were also measured. The results showed that the heat transfer from the plate was enhanced by the occurrence of the descending flows. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 362,375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10036 [source] Natural convection of a water-fine particle suspension in a rectangular cell heated and cooled from opposing vertical walls: The effect of distribution of particle sizeHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2001Masashi Okada Abstract A water-fine particle suspension with a uniform initial temperature and concentration in a rectangular cell was heated from a vertical wall and cooled from the opposing vertical wall. The dispersed particles had a distribution in size. In this natural convection, many layers separated by almost-horizontal sharp interfaces were observed. In the beginning many layers appear, and each interface of the layers falls gradually with a constant velocity, and finally all layers vanish. To clarify this phenomenon, concentrations and mean diameters of the particles in each layer and temperature distributions were measured. Moreover, natural convection of the other suspension with particles which had a narrow size distribution was also investigated. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 636,647, 2001 [source] Fluid flow and heat transfer in the transition process of natural convection over an inclined plateHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2001Katsuo Komori Abstract The present study deals with fluid flow and heat transfer in the transition process of natural convection over an inclined plate. In order to examine the mechanism of the transition process, experiments on the flow and heat transfer were performed for various plate inclination angles in the range of 20 to 75°. The wall temperature and fluid flow fields were visualized using a liquid crystal sheet and fluorescent paint, respectively. The visualization confirmed that separation of a boundary layer flow took place, and the onset point of streaks appeared over the plate wall when the modified Rayleigh number exceeded a characteristic value for each inclination angle. The local Nusselt number in the transition range was proportional to the one-third power of the local modified Rayleigh number. By introducing a nondimensional parameter, a new correlation between visualizations of the flow and temperature fields and heat transfer was proposed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 648,659, 2001 [source] Natural convection heat transfer along a vertical flat plate with a projection in the turbulent regionHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2001Katsuo Komori Abstract In the present study, the heat transfer coefficients occurring with a projection in the turbulent region of a vertical flat plate were measured experimentally for various projection heights in the range of 0 to 20 mm. The wall temperature and fluid flow fields were also visualized using a liquid crystal sheet and nylon 12 powder, respectively. The average and local Nusselt numbers reach 1.07 to 1.22 and 1.2 to 1.7 times those for pure turbulent natural convection, respectively. The maximum enhancement rates of heat transfer are attained at a position of 2.3 to 3.3 times the projection height from the upper projection surface toward the downstream, and these positions are in good agreement with those of the reattachment of the fluid flow and with centers of dark red regions in the liquid crystal. On the other hand, the heat transfer coefficients in the just upstream and downstream regions of the projection are small compared with those for no projection. By introducing the nondimensional parameter R, the present experimental results are rearranged quantitatively and effectively. © 2001 Scripta Technica, Heat Trans Asian Res, 30(3): 222,233, 2001 [source] Extension of weakly compressible approximations to incompressible thermal flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Mofdi El-Amrani Abstract Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831,847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge,Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Stabilized finite element formulation of buoyancy driven incompressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2002S. Aliabadi Abstract Streamline-upwind/Petrov,Galerkin finite element method is developed for buoyancy-driven incom-pressible flows with heat and mass transfer. The stabilized finite element formulations are implemented in parallel using message passing interface libraries. To measure the accuracy of the method, we solve a 2D numerical example of natural convection flows at moderate to high Rayleigh numbers. The 3D applications include the dispersion of smoke from a chimney and within a stadium. Copyright © 2002 John Wiley & Sons, Ltd. [source] Fast single domain,subdomain BEM algorithm for 3D incompressible fluid flow and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009Jure Ravnik Abstract In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity,vorticity formulation of the incompressible Navier,Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Copyright © 2008 John Wiley & Sons, Ltd. [source] A visual incompressible magneto-hydrodynamics solver with radiation, mass, and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Necdet AslanArticle first published online: 8 JAN 200 Abstract A visual two-dimensional (2D) nonlinear magneto-hydrodynamics (MHD) code that is able to solve steady state or transient charged or neutral convection problems under the radiation, mass, and heat transfer effects is presented. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by similar relaxation schemes in the form of pseudo-iterations between the real time levels. The numerical method utilizes a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm developed here utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta (RK) algorithm. It is possible for the user to choose different normalizations (natural, forced, Boussinesq, Prandtl, double-diffusive and radiation convection) automatically. The code is visual and runs interactively with the user. The graphics algorithms work multithreaded and allow the user to follow certain flow features (color graphs, vector graphs, one-dimensional profiles) during runs, see (Comput. Fluids 2007; 36:961,973) for details. With the code presented here nonlinear steady or time-dependent evolution of heated and stratified neutral and charged liquids, convection of mixture of neutral and charged gases, double-diffusive and salinity natural convection flows with internal heat generation/absorption and radiative heat transfer flows can be investigated. In addition, the numerical method (combining concentration, radiation, heat transfer, and MHD effects) takes the advantage of local time stepping and employs simplified residual jacobian matrix to increase pseudo-convergence rate. This code is currently being improved to simulate three-dimensional problems with parallel processing. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical solutions of liquid metal flows by incompressible magneto-hydrodynamics with heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Kenan, entürk Abstract A two-dimensional incompressible magneto-hydrodynamic code is presented in order to solve the steady state or transient magnetized or neutral convection problems with the effect of heat transfer. The code utilizes a numerical matrix distribution scheme that runs on structured or unstructured triangular meshes and employs a dual time-stepping technique with multi-stage Runge,Kutta algorithm. The code can be used to simulate the natural convection with internal heat generation and absorption and nonlinear time-dependent evolution of heated and magnetized liquid metals exposed to external fields. Copyright © 2008 John Wiley & Sons, Ltd. [source] A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuliINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008N. Mai-Duy Abstract This paper reports a radial basis function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of higher-order derivatives. The method is applied to simulate thermally driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleigh number solutions are achieved and they are in good agreement with previously published numerical data. Copyright © 2007 John Wiley & Sons, Ltd. [source] Volumetric methods for evaluating energy loss and heat transfer in cavity flows,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2007Stuart Norris Abstract Methods have been developed for calculating irreversible energy losses and rates of heat transfer from computational fluid dynamics solutions using volume integrations of energy dissipation or entropy production functions. These methods contrast with the more usual approach of performing first law energy balances over the boundaries of a flow domain. Advantages of the volumetric approach are that the estimates involve the whole flow domain and are hence based on more information than would otherwise be used, and that the energy dissipation or entropy production functions allow for detailed assessment of the mechanisms and regions of energy loss or entropy production. Volume integrations are applied to the calculation of viscous losses in a lid-driven cavity flow, and to the viscous losses and heat transfer due to natural convection in a side-heated cavity. In the convection problem comparison with the entropy increase across a stationary heat conducting layer leads to a novel volume integral expression for the Nusselt number. The predictions using this method compare well with traditional surface integrals and benchmark results. Copyright © 2007 John Wiley & Sons, Ltd. [source] A control volume finite-element method for numerical simulating incompressible fluid flows without pressure correctionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007Ahmed Omri Abstract This paper presents a numerical model to study the laminar flows induced in confined spaces by natural convection. A control volume finite-element method (CVFEM) with equal-order meshing is employed to discretize the governing equations in the pressure,velocity formulation. In the proposed model, unknown variables are calculated in the same grid system using different specific interpolation functions without pressure correction. To manage memory storage requirements, a data storage format is developed for generated sparse banded matrices. The performance of various Krylov techniques, including Bi-CGSTAB (Bi-Conjugate Gradient STABilized) with an incomplete LU (ILU) factorization preconditioner is verified by applying it to three well-known test problems. The results are compared to those of independent numerical or theoretical solutions in literature. The iterative computer procedure is improved by using a coupled strategy, which consists of solving simultaneously the momentum and the continuity equation transformed in a pressure equation. Results show that the strategy provides useful benefits with respect to both reduction of storage requirements and central processing unit runtime. Copyright © 2006 John Wiley & Sons, Ltd. [source] Meshfree weak,strong (MWS) form method and its application to incompressible flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2004G. R. Liu Abstract A meshfree weak,strong (MWS) form method has been proposed by the authors' group for linear solid mechanics problems based on a combined weak and strong form of governing equations. This paper formulates the MWS method for the incompressible Navier,Stokes equations that is non-linear in nature. In this method, the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries; the local Petrov,Galerkin weak form is applied only to the nodes on the natural boundaries of the problem domain. The MWS method is then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions. The simulation results are validated by comparing with those of other numerical methods as well as experimental data. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. It works perfectly well for irregular nodes using only local quadrature cells for nodes on the natural boundary, which can be generated without any difficulty. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004Alexander Yu. Abstract The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time-dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002Mark A. Christon Abstract This paper summarizes the results from a special session dedicated to understanding the fluid dynamics of the 8:1 thermally driven cavity which was held at the First MIT Conference on Computational Fluid and Solid Dynamics in June, 2001. The primary objectives for the special session were to: (1) determine the most accurate estimate of the critical Rayleigh number above which the flow is unsteady, (2) identify the correct, i.e. best time-dependent benchmark solution for the 8: 1 differentially heated cavity at particular values of the Rayleigh and Prandtl numbers, and (3) identify those methods that can reliably provide these results. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical investigation of the first instabilities in the differentially heated 8:1 cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002F. Auteri Abstract We present a new Galerkin,Legendre spectral projection solver for the simulation of natural convection in a differentially heated cavity. The projection method is applied to the study of the first non-stationary instabilities of the flow in a 8:1 cavity. Statistics of the periodic solution are reported for a Rayleigh number of 3.4×105. Moreover, we investigate the location and properties of the first Hopf bifurcation and of the three successive bifurcations. The results confirm the previous finding in the range of Rayleigh numbers investigated that the flow instabilities originate in the boundary layer on the vertical walls. A peculiar phenomenon of symmetry breaking and symmetry restoring is observed portraying the first steps of the transition to chaos for this flow. Copyright © 2002 John Wiley & Sons, Ltd. [source] A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2001E. Gadoin Abstract This paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier,Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Modelling and experimental studies on heat transfer in the convection section of a biomass boilerINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 12 2006Jukka Yrjölä Abstract This paper describes a model of heat transfer for the convection section of a biomass boiler. The predictions obtained with the model are compared to the measurement results from two boilers, a 50 kWth pellet boiler and a 4000 kWth wood chips boiler. An adequate accuracy was achieved on the wood chips boiler. As for the pellet boiler, the calculated and measured heat transfer rates differed more than expected on the basis of the inaccuracies in correlation reported in the literature. The most uncertain aspect of the model was assumed to be the correlation equation of the entrance region. Hence, the model was adjusted to improve the correlation. As a result of this, a high degree of accuracy was also obtained with the pellet boiler. The next step was to analyse the effect of design and the operating parameters on the pellet boiler. Firstly, the portion of radiation was established at 3,13 per cent, and the portion of entrance region at 39,52 per cent of the entire heat transfer rate under typical operating conditions. The effect of natural convection was small. Secondly, the heat transfer rate seemed to increase when dividing the convection section into more passes, even when the heat transfer surface area remained constant. This is because the effect of the entrance region is recurrent. Thirdly, when using smaller tube diameters the heat transfer area is more energy-efficient, even when the bulk velocity of the flow remains constant. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||||||||