Showing papers in "Numerical Heat Transfer Part B-fundamentals in 2001"
TL;DR: In this article, a high-accuracy discrete singular convolution (DSC) approach is proposed for the numerical simulation of coupled convective heat transfer problems, where the problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures.
Abstract: This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.
311 citations
TL;DR: In this paper, an extended lattice Boltzmann (LB) equation was developed for the simulation of the phase change problem governed by the heat conduction equation incorporated with enthalpy formation.
Abstract: An extended lattice Boltzmann (LB) equation was developed for the simulation of the phase-change problem governed by the heat conduction equation incorporated with enthalpy formation. Mathematical consistency between the proposed extended LB equation and the governing equation was accomplished by the Chapman-Enskog expansion. Illustrative examples include one-dimensional half-space melting and solidification as well as two-dimensional solidification in a corner. Phase change at a single temperature and with a mushy zone are both demonstrated. Two types of boundary condition, prescribed temperature and prescribed heat flux, are considered in the illustrative examples. Different thermal diffusivities in the separated phases/zones are accomplished through varying the relaxation times in the LB equation. All numerical results obtained by the present scheme agree very well with previous analytical or numerical results in the literature.
255 citations
TL;DR: A numerical procedure for the calculation of buoyancy-driven flows using the finite-volume approach is presented in this article, which is based on an extension of the operator-splitting procedure PISO of Issa [1] to the specific case in which the coupling between velocity/pressure and temperature is important, as is the case in problems involving free-convection flows.
Abstract: A numerical procedure for the calculation of buoyancy-driven flows using the finite-volume approach is presented. It is based on an extension of the operator-splitting procedure PISO of Issa [1] to the specific case in which the coupling between velocity/pressure and temperature is important, as is the case in problems involving free-convection flows. A comparison of the proposed procedure with a standard iterative method shows improvement both in terms of computing speed (a factor of 2.1 to 4.1) and robustness.
112 citations
TL;DR: In this article, an unstructured FVM for radiative heat transfer in a complex two-dimensional enclosure with obstacles with participating medium is derived using the unstructural grid system.
Abstract: The radiative heat transfer in a complex two-dimensional enclosure with obstacles with participating medium is very important in practical engineering applications. In order to deal with this problem, in this study the enite-volume method (FVM) for radiation has been derived using the unstructured grid system. A general discretization equation was formulated by introducing the directional weight and the step scheme for spatial differencing. For its comparison and validation, two test cases, an equilateral triangular enclosure and a square enclosure with bafe e, were chosen. Then, more complex and practical cases, such as a semicircular enclosure with cylinder hole, a square enclosure withe nned internal cylinder, anda furnacewithembeddedcoolingpipes, were investigated. All the results obtained by the unstructured FVM agreed very well with the exact solutions as well as the results obtained by the zone method. Furthermore, the wiggling behavior occurring in the blocked-off FVM was not produced by the unstructured FVM. Three types of manipulation of control angle overlap were also examined here. It was found that the solutions depended on the type of manipulation of control angle overlap, especially when the number of control angles was small. Usually, both the pixelation method and exact treatment introduced here yielded better solutions than the bold approximation.
81 citations
TL;DR: In this paper, a numerical method for computing the motion of bubbles undergoing liquid?vapor phase change is presented based on a level set technique for capturing the phase interface, which is modified to include the effect of phase change at the interface as well as to achieve mass conservation during the whole calculation procedure.
Abstract: A numerical method for computing the motion of bubbles undergoing liquid?vapor phase change is presented. The method is based on a level set technique for capturing the phase interface, which is modified to include the effect of phase change at the interface as well as to achieve mass conservation during the whole calculation procedure. The modified level set method is applied for numerical simulation of bubble rise and growth in a stationary liquid. The numerical results are found to compare well with the data reported in the literature and the analytical solutions.
70 citations
TL;DR: In this paper, the radiation element method is formulated to solve transient radiative transfer with light radiation propagation effect in scattering, absorbing, and emitting media with inhomogeneous property, and the sensitivity of the method against element size, ray emission number, and time increment size is examined.
Abstract: In this study the radiation element method is formulated to solve transient radiative transfer with light radiation propagation effect in scattering, absorbing, and emitting media with inhomogeneous property. The accuracy of the method is verified by good agreement between the present calculations and Monte Carlo simulations. The sensitivity of the method against element size, ray emission number, and time increment size is examined. The transient effect of radiation propagation is essential in short-pulse laser radiation transport when the input pulse width is not considerably larger than the system radiation propagation time. The transient characteristics of radiative transfer are investigated in the media subject to collimated laser irradiation and/or diffuse irradiation withtemporal Gaussian and/or square profiles. The inhomogeneous profile of extinction coefficient of the medium affects strongly the transient radiative flux divergence inside the medium.
68 citations
TL;DR: In this paper, a high-order velocity-slip boundary condition is validated for gas microflows, by comparing predictions of the new model against the first-order slip condition and the direct-simulation Monte Carlo (DSMC) results.
Abstract: A recently developed high-order velocity-slip boundary condition is validated for gas microflows, by comparing predictions of the new model against the first-order slip condition and the direct-simulation Monte Carlo (DSMC) results. Numerical solutions of gas flow through microchannels and backward-facing step geometry are presented. The backward-facing step geometry is a suitable testbed for studying gas microflows subject to strong adverse pressure gradients and separation. The new slip boundary condition, based on obtaining the slip information one mean free path away from the surface, results in good agreement with the DSMC for both attached and separated flows.
68 citations
TL;DR: In this paper, an artificial compressibility method characterized by the pressure-based algorithm is developed on a nonorthogonal collocated grid for incompressible fluid flow problems, using a cell-centered finite-volume approximation.
Abstract: An artificial compressibility method characterized by the pressure-based algorithm is developed on a nonorthogonal collocated grid for incompressible fluid flow problems, using a cell-centered finite-volume approximation. Unlike the traditional pseudo-compressibility concept, the continuity constraint is perturbed by the material derivative of pressure, the physical relevance of which is to invoke matrix preconditionings. The approach provokes density perturbations, assisting the transformation between primitive and conservative variables. To account for the flow directionality in the upwinding, a rotational matrix is introduced to evaluate the convective flux. A rational means of reducing excessive numerical dissipation inherent in the pressurevelocity coupling is contrived which has the expedience of greater flexibility and increased accuracy in a way similar to the MUSCL approach. Numerical experiments in reference to a few laminar flows demonstrate that the overall artifacts expedite enhanced robustn...
61 citations
TL;DR: In this article, a new method was proposed to accelerate the convergence rate for the SIM PLER algorithm by artiucially changing the underrelaxation term to match the dependent variable to be solved.
Abstract: A new method is proposed to accelerate the convergence rate for the SIM PLER algorithm by artiucially changing the underrelaxation term to match the dependent variable to be solved Based on this idea, a new pressure-correction equation is derived, and the modiued algorithm is named M SIM PLER Five numerical experiments show that the M SIM PLER algorithm can appreciably enhance the convergence rate for cases of low and moderate underrelaxation factors with good robustness
48 citations
TL;DR: In this article, a finite-difference-based Boltzmann model for compressible Euler equations is presented. But the model is restricted to a single particle, and the particle can possess both kinetic and thermal energies.
Abstract: A finite-difference-based lattice Boltzmann model, employing the 2-D, 9-velocity square (D2Q9) lattice for the compressible Euler equations, is presented. The model is constructed by allowing the particles to possess both kinetic and thermal energies. Such a lattice structure can represent both incompressible and compressible flow regimes. In the numerical treatment, to attain desirable accuracy, the total-variation-diminishing (TVD) scheme is adopted with either the minmod function or a second-order corrector as the flux limiter. The model can treat shock/expansion waves as well as contact discontinuity. Both one- and two-dimensional test cases are computed, and the results are compared with the exact as well as other reported numerical solutions, demonstrating that there is consistency between macroscopic and kinetic computations for the compressible flow.
47 citations
TL;DR: In this paper, the location and strength identification of multiple point heat sources in transient heat conduction has been studied, and the identification procedure is based on a boundary integral formulation using space and time Green functions.
Abstract: This article deals with an inverse problem, which consists of the location and strength identification of multiple-point heat sources in transient heat conduction. The identification procedure is based on a boundary integral formulation using space and time Green functions. The discretized problem is nonlinear if the location of the point heat sources is unknown. In order to reduce the sensitivity of the solution to errors, we use the future time step procedure associated to a Tikhonov regularization procedure. The proposed numerical approach is applied to numerical two- and three-dimensional examples.
TL;DR: In this paper, an iterative global method to perform analysis of heat exchangers is proposed, called SEWTLE, which provides flexibility to any flow arrangement or geometry, consideration of multiple streams, local evaluation of properties, friction factor, and heat transfer coefficient.
Abstract: An in-depth analysis has been carried out on the discretization of a heat exchanger, the discretization of the governing equations, and the solution strategy for the resulting system of equations. An iterative global method to perform analysis of heat exchangers is proposed, called SEWTLE. This method provides flexibility to any flow arrangement or geometry, consideration of multiple streams, local evaluation of properties, friction factor, and heat transfer coefficient, and is characterized by good accuracy, high robustness, and fast computation time. In addition, three different numerical schemes for the discretization of the fluid and wall conservation equations at the cell level have been studied, and their advantages and disadvantages fully discussed.
TL;DR: In this paper, the effect of buoyancy on the production and dissipation of turbulent kinetic energy is investigated in variants of the popular k-means and k-mixture.
Abstract: The effect of buoyancy on the production and dissipation of turbulent kinetic energy is investigated in variants of the popular k
TL;DR: In this article, the authors examined numerically whether deviation from one of the assumptions may enhance the stability of the discretized scheme and proposed three new bounded high-resolution schemes, SBECBC1, 2, and 3, for two advection problems and one diffusion-convection problem.
Abstract: Existing methods for analyzing the stability of a discretized scheme for convection-diffusion terms are usually based on five assumptions, i.e., one-dimensional, linear, first kind of boundary condition, source term free, and uniform grid system. In this article we examine numerically whether deviation from one of the assumptions may enhance the stability of the discretized scheme. The second part of the article is devoted to the criterion of convective boundedness. It is shown that the convective boundedness criterion (CBC) proposed by Gaskell and Lau is only a sufficient condition. Another region in the normalized variable diagram is proposed within which any scheme defined is convectively bounded. Three new bounded high-resolution schemes defined in this region, SBECBC1, 2, and 3, are proposed, and numerical experiments for two advection problems and one diffusion-convection problem demonstrate the high-resolution ability of the SBECBCs for a sharp change in scalar profile.
TL;DR: In this paper, different flux approximations are compared to identify which approximation is the most accurate, independent of the mesh structure, and the accuracy of the classical two-node approximation can be improved significantly by using a local gradient reconstruction to capture the crossdiffusion term of the flux at the control volume face.
Abstract: Finite-volume methods (FVMs) are now a popular choice among practitioners in scientific computation and engineering. This article focuses on generalized FVMs that can be implemented on any mesh structure. The accuracy of FVMs is primarily influenced by the numerical approximation of the flux term at the control-volume face. Here, different flux approximations are compared to identify which approximation is the most accurate, independent of the mesh structure. The accuracy of the classical two-node approximation can be improved significantly by using a local gradient reconstruction to capture the crossdiffusion term of the flux at the control-volume face. A simple two-dimensional isotropic diffusion equation for which an analytical solution is available is chosen for benchmarking purposes.
TL;DR: The regular lattice-based lattice Boltzmann method is still computationally expensive for obtaining steady-state solutions on single-node computers in comparison with the more advanced conventional Navier-Stokes solvers.
Abstract: In this article, a systematic investigation of the lattice Boltzmann method is reported by calculating both two-dimensional and three-dimensional steady-state incompressible flows. Accuracy is determined following a standard estimation procedure, while efficiency is evaluated by comparing with an advanced finite-volume Navier-Stokes solver. The objective of the article is to provide a brief review of the lattice Boltzmann method, to report the accuracy and efficiency of the method, and to identify possible future research directions. Overall, it is found that the accuracy of the lattice Boltzmann method is between first and second order, depending on the boundary conditions used. The regular lattice-based lattice Boltzmann method is still computationally expensive for obtaining steady-state solutions on single-node computers in comparison with the more advanced conventional Navier-Stokes solvers.
TL;DR: In this article, a block implicit procedure (BID) is introduced which utilizes a simple incomplete decomposition of the matrix resulting from the discretization of the momentum and mass conservation equations for incompressible fluid flow problems.
Abstract: A new block implicit procedure (BID) is introduced which utilizes a simple incomplete decomposition of the matrix resulting from the discretization of the momentum and mass conservation equations for incompressible fluid flow problems. In contrast to the conventional methods, the new method is not of the segregated type, and does not require an explicit equation for pressure. The complete, coupled block system is solved in its primitive form. In this way, mass and momentum conservation are satisfied simultaneously at all grid points, while pressure is calculated implicitly. Only a couple of overall iterations are required for the treatment of the nonlinearities of the problem. Tests show that the new procedure converges fast for any E value (in an E-factor formulation), and therefore virtually the E-factor formulation is not necessary.
TL;DR: A novel a-posteriori error estimate for the finite-volume method (FVM) measuring the absolute magnitude of the discretization error is presented and is shown to perform considerably better than the traditional Taylor series error estimates.
Abstract: In this article, a novel a-posteriori error estimate for the finite-volume method (FVM) measuring the absolute magnitude of the discretization error is presented. The residual error estimate is based on the cell residual, similar to the popular error estimates in the finite-element community. An appropriate normalization of the local residual creates the error estimate with the same dimensionality as the variable of interest, making it practical for engineering use. The error estimate is tested on a series of test cases and is shown to perform considerably better than the traditional Taylor series error estimates.
TL;DR: In this paper, the authors investigated the numerical aspects of the implementation of nonlinear viscoelastic euid models in a finite volume method, and decomposition of the discretized stress equations in such a way that diagonal dominance is maximized, in order to promote numerical stability with iterative solvers.
Abstract: Numerical aspects of the implementation of nonlinear viscoelastic euid models in a enite volume method are investigated: (1) decomposition of the discretized stress equations in such a way that diagonal dominance is maximized, in order to promote numerical stability with iterative solvers; (2) imposition of boundary conditions for the stress components normal to a wall plane, and for pressure. These issues are investigated in relation to the Giesekus constitutive equation and illustrative eow examples showing the beneets of the proposed methodology are given.
TL;DR: In this paper, the precise time integration (PTI) method is introduced and then its extension to the transient heat conduction problem is presented, and the symmetry of the matrix exponential of PTI in heat convection is proved and used in subdomain integration to reduce computational expense a great deal.
Abstract: The precise time integration (PTI) method is introduced and then its extension to the transient heat conduction problem is presented. The symmetry of the matrix exponential of PTI in heat conduction is proved and used in subdomain integration to reduce computational expense a great deal. For nonlinear heat conduction, the predictor-corrector algorithm is employed to solve the nonlinear equations. Numerical examples validate the method.
TL;DR: A higher-order-accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for fluid flow problems and accuracy and robustness issues are addressed by application to several pertinent benchmark problems in Part II.
Abstract: A higher-order-accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization. New insights are presented on the elimination of the odd-even decoupling problem in the solution of the pressure Poisson equation. For consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Accuracy and robustness issues are addressed by application to several pertinent benchmark problems in Part II.
TL;DR: In this article, a finite-volume method to calculate view factors between surfaces of control volumes is presented, which does not lead to the increase in memory requirement with increasing angular grid, is used.
Abstract: This article presents a finite-volume method to calculate view factors between surfaces of control volumes. A simple approach, which does not lead to the increase in memory requirement with increasing angular grid, is used. The spatial and angular resolution errors are resolved by grid refinements. The procedure can handle straight-edged, inclined, and curved boundaries. Blockages due to internal obstructions and boundaries can also be accommodated. Five problems are examined and the exact solutions are reproduced.
TL;DR: An interface-tracking method is presented to solve two-dimensional convection-dominated melting and solidification problems in enclosures of arbitrarily geometry and is able to produce highly graded meshes that can be "online" locally adapted to react to react boundary deformation.
Abstract: An interface-tracking method is presented to solve two-dimensional convection-dominated melting and solidification problems in enclosures of arbitrarily geometry. The control-volume finite-element method (CVFEM) is applied to moving-boundary problems using an adaptive moving-grid model based on unstructured triangular grids. At every sampling instant, the liquid-solid interface is explicitly resolved by the numerical grid. A suitable chosen mesh velocity is introduced directly into the governing equations minimizing grid deformation in the vicinity of the moving interface. Additionally, the implementation of local grid adaption algorithms (refinement, coarsening, relaxation) prevents undesirable changes of mesh resolution due to the moving interfaces. Thus, even in problems involving large-scale interface motion or boundary deformation, a continuous high-quality grid can be preserved. Furthermore, the adaptive procedure is able to produce highly graded meshes that can be "online" locally adapted to react ...
TL;DR: In this paper, an adaptive front-tracking procedure is proposed to be an attractive alternative to the commonly used fixed-grid methods, and the numerical results are compared to analytical solutions, experimental data, and numerical benchmark solutions from the literature.
Abstract: In a prior article, an interface-tracking control-volume-based finite-element method (CVFEM) for moving-boundary problems has been presented [1]. In this article, the numerical method is verified by applying it to basic isothermal melting and solidification problems. Numerical results are compared to analytical solutions, experimental data, and numerical benchmark solutions from the literature. They demonstrate the capabilities of the code to reproduce known solutions even when complex flow patterns and/or interface structures are present. Thus, the proposed adaptive front-tracking procedure is supposed to be an attractive alternative to the commonly used fixed-grid methods.
TL;DR: A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems and it is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation.
Abstract: A higher-order-accurate numerical procedure, developed for solving incompressible Navier?Stokes equations for 2-D or 3-D fluid flow problems and presented in Part I, is validated. The procedure, which is based on low-storage Runge?Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization, is shown to eliminate the odd?even decoupling problem on regular grids, provided that compact schemes are used to approximate the Laplacian of the pressure equation. Spatial and temporal accuracy are confirmed formally through application to several pertinent benchmark problems. Stability in long-time integration is demonstrated by application to the Stuart?s mixing-layer problem.
TL;DR: In this paper, a nonlinear optimal control algorithm in determining the strength of optimal boundary heat fluxes utilizing the conjugate gradient method (CGM) of minimization is applied successfully in the present study based on the desired temperature distributions at the final time of heating.
Abstract: A nonlinear optimal control algorithm in determining the strength of optimal boundary heat fluxes utilizing the conjugate gradient method (CGM) of minimization is applied successfully in the present study based on the desired temperature distributions at the final time of heating. The thermal properties are assumed to be functions of temperature, and this makes the problem nonlinear. The accuracy of this optimal control analysis is examined by using the numerical experiments. Three different desired temperature distributions are given and the corresponding optimal control heat fluxes are to be determined. Results show that the optimal boundary heat fluxes can be obtained with any arbitrary initial guesses within a couple of seconds' CPU time on a Pentium III 600-MHz personal computer.
TL;DR: In this paper, a visibility algorithm is integrated into the self-adaptive integration technique of evaluating the entries of the radiation matrices, and the presence of shadow zones in the radiating cavities is taken into account.
Abstract: Steady-state and transient temperature fields in bodies containing concave, self-irradiating cavities are considered. Radiation and conduction equations are discretized using the boundary-element method. The technique covers nonlinear material and nonlinear boundary conditions. The presence of shadow zones in the radiating cavities is taken into account. The developed visibility algorithm is integrated into the self-adaptive integration technique of evaluating the entries of the radiation matrices. Excellent overall accuracy of this integration is achieved. Discussed problems are in two dimensions, but the technique may be extended to three dimensions. Numerical examples are included
TL;DR: In this article, a numerical method for computing unsteady, incompressible two-phase flows with open or periodic boundaries is presented, based on a level set technique for capturing the phase interface, which is combined with a second-order projection method.
Abstract: A numerical method for computing unsteady, incompressible two-phase flows with open or periodic boundaries is presented. The method is based on a level set technique for capturing the phase interface, which is combined with a second-order projection method. At the open or periodic boundaries where the normal velocity components are not prescribed, the pressure conditions are calculated iteratively so that the computed flow rate should be equal to a given flow rate. The numerical method is applied for computations of a single Taylor bubble and a train of Taylor bubbles rising in a vertical tube.
TL;DR: The use of first-order finite-difference models for the moving-interface term in the interface-following method is shown to be inaccurate for high heat transfer rates and a second-order-accurate method is presented that gives accurate results in all situations.
Abstract: The analysis of phase-change heat transfer is of interest because of the importance of phase change in many physical situations, but such analyses are difficult because of the nonlinear governing equations. The extensive use of numerical methods to analyze heat transfer problems has great potential but also some pitfalls. This article analyzes the advantages and disadvantages of the enthalpy method and several interface-following methods for modeling solid?liquid phase-change problems using the finite-difference method. Since the initiation of melting always presents numerical difficulties, this article also analyzes the effect of the initial melt region size. Finally, the use of first-order finite-difference models for the moving-interface term in the interface-following method is shown to be inaccurate for high heat transfer rates. A second-order-accurate method is presented that gives accurate results in all situations.
TL;DR: An efficient algorithm for tracing particles in large, arbitrary geometries containing nonparticipating media is presented and the method of Uniform Spatial Division (USD) is implemented.
Abstract: An efficient algorithm for tracing particles in large, arbitrary geometries containing nonparticipating media is presented. For arbitrary triangles and/or convex planar quadrilaterals, an efficient intersection algorithm is discussed in detail. Several techniques used in ray tracing to limit the number of surfaces tested are discussed and the method of Uniform Spatial Division (USD) is implemented. The ''mailbox'' technique is also discussed. The efficiency of the intersection algorithm and USD are demonstrated by timing results. For USD, speedups exceeding a factor of eighty are observed.