Showing papers in "Numerical Heat Transfer Part B-fundamentals in 1994"
TL;DR: In this paper, a new normalized variable and space formulation (NVSF) methodology is developed to derive connective schemes for uniformly or nearly uniformly discretized spaces, where spatial parameters are introduced so as to extend the applicability of the NVF methodology to nonuniformly discretised domains.
Abstract: The normalized variable formulation (NVF) methodology of Leonard [1] provides the proper framework for the development and analysis of high-resolution convection-diffusion schemes, which combine the accuracy of higher-order schemes with the stability and boundedness of the first-order upwind scheme. However, in its current form the NVF methodology helps in deriving connective schemes for uniformly or nearly uniformly discretized spaces. To remove this shortcoming, a new, normalized variable and space formulation (NVSF) methodology is developed. In the newly developed technique, spatial parameters are introduced so as to extend the applicability of the NVF methodology to nonuniformly discretized domains. Furthermore, the required conditions for accuracy and boundedness of connective schemes on nonuniform grids are also derived. Several schemes formulated using NVF are generalized to nonuniform grids using the suggested method. Both formulations are tested on nonuniform grids by solving two problem...
159 citations
TL;DR: In this paper, a blocked-off region procedure was proposed to model radiative transfer in irregular geometries using a Cartesian coordinates finite-volume method (FVM) for straight-edged, inclined and curved boundaries.
Abstract: This article presents a blocked-off-region procedure to model radiative transfer in irregular geometries using a Cartesian coordinates finite-volume method (FVM). Straight-edged, inclined and curved boundaries can be treated. It is capable of handling participating or transparent media enclosed by black or reflecting walls. With this procedure, irregular geometries can be specified through the problem specification portion of the program. Four test problems are used to show that the procedure is capable of reproducing available results for inclined and curved walls, transparent, nonscattering, and anisotropically scattering media.
118 citations
TL;DR: In this article, a co-located equal-order control-volume-based finite-element method (CVFEW) is presented for two-and three-dimensional, incompressible, viscous fluid flow.
Abstract: A co-located equal-order control-volume-based finite-element method (CVFEW) for two- and three-dimensional, incompressible, viscous fluid flow is presented. The method works directly with the primitive variables. Triangular elements and polygonal control volumes, and tetrahedral elements and polyhedral control volumes are used to discretize the calculation domains in two- and three-dimensional problems, respectively. Two available flow-oriented upwind schemes (FLO and FLOS) and a novel mass-weighted skew upwind scheme (MAW) are investigated. In each dement, the velocity components in the mass flux terms are interpolated by special functions that prevent the generation of spurious pressure oscillations. The discretized equations are solved using an iterative sequential variable adjustment algorithm. Verification of the proposed CVFEM is presented in a companion article.
99 citations
TL;DR: In this paper, a new temperature-transforming model for binary solid-liquid phase-change problems is proposed, which is based on the separation of the coupled effects of temperature and concentration on the latent heat evolution in the energy equation.
Abstract: The objective of this work is to develop a new temperature-transforming model for the treatment of binary solid-liquid phase-change problems. The essential feature of the proposed model is the separation of the coupled effects of temperature and concentration on the latent heat evolution in the energy equation. That is, the latent heat evolution due to temperature variation is accounted for by the definition of an effective heat coefficient, while latent heat evolution owing to the concentration variation is accounted for by a source term. The main advantages of this model include direct treatment of the coupling relations among temperature, concentration, and liquid fraction, and the improvement of numerical stability by the definition of the effective heat coefficient.
49 citations
TL;DR: In this article, a numerical model employing co-located variables is developed for the solution of all speed flows, considering the extra coupling between pressure and density, and results are obtained for selected test cases, including incompressible as well as supersonic flows.
Abstract: The use of the segregated finite-volume method requires special procedures for handling the pressure-velocity coupling. It is a normal practice to employ staggered grids to promote the adequate coupling between pressure and velocity. However, this alternative becomes unfeasible for three-dimensional problems, especially if boundary-fitted grids are employed. In this work a numerical model employing co-located variables is developed. The model uses nonorthogonal boundary-fitted meshes and is therefore suitable for the solution of all speed flows, considering the extra coupling between pressure and density. Results are obtained for selected test cases, including incompressible as well as supersonic flows, which are compared with experimental ones.
45 citations
TL;DR: In this paper, a method for solving the primitive-variable equations of motion for viscous, incompressible, free-surface flows is presented, where the control volume corners are moved by applying a natural closure of the mass and momentum equations along the surface.
Abstract: A method is presented for solving the primitive-variable equations of motion for viscous, incompressible, free-surface flows. The computational mesh defines quadrilaterals that are used as the control volumes in a finite-volume method in which the mesh moves to adapt to the free surface. Dependent variables are co-located at the center of each volume. The strength of the present method results from the innovative way in which the control volume corners, which define the surface location, are moved by applying a „natural“ closure of the mass and momentum equations along the surface. This avoids the need for a separate kinematic condition while ensuing that the kinematic condition is exactly satisfied. The results of several test problems are provided, including sloshing in a tank, propagation of a solitary wave, and filling of tanks.
39 citations
TL;DR: The study demonstrates that the multigrid method is robust and rapidly convergent, resulting in improvement in CPU requirements by a factor of approximately S to 15 compared to the sequential signal-grid SIMPLER procedure.
Abstract: A coupled-point solution procedure employing a multilevel correction strategy is developed and test results are presented in this article. The method is based on the principle of deriving the coarse-grid discretization equations from the fine-grid discretization equations. The adaptive scheme is applied to the sample problems of laminar flow in lid-driven square and cubic cavities and flow over a backward-facing step. The study demonstrates that the multigrid method is robust and rapidly convergent, resulting in improvement in CPU requirements by a factor of approximately S to 15 compared to the sequential signal-grid SIMPLER procedure. The performance of procedure improves, in comparison to the SIMPLER, as the number of grid points increases.
37 citations
TL;DR: The generalized zonal method (GZM) as discussed by the authors is a generalization of the conventional CZM for the analysis of radiative heat transfer in absorbing, emitting, and anisutropically scattering media and is shown to be applicable both for media with arbitrary scattering phase function and general nondiffuse reflecting surfaces.
Abstract: The generalized zonal method ( GZM) for the analysis of radiative heat transfer in absorbing, emitting, and anisutropically scattering media is developed and implemented. It is shown to be applicable both for media with arbitrary scattering phase function and general nondiffuse reflecting surfaces. Mathematically, the GZM is a generalization of the conventional zonal method ( CZM). In addition to the exchange factors utilized by the CZM, the GZM introduces scattering and reflecting exchange factors. These factors characterize the scattering properties of the medium and the reflectivities of the bounding surfaces. Expressions for the scattering and reflecting exchange factors are shown; their numerical and analytical properties are identified. To illustrate the implementation of the GZM, cubic enclosures in radiative equilibrium are analyzed. Based on numerical data, the effect of anisotropic scattering on three-dimensional radiative heat transfer is assessed.
36 citations
TL;DR: In this paper, a dynamic programming methodology for the solution of the two-dimensional inverse Stefan design problem is presented, aimed particularly at the calculation of the boundary heat flux in a body that solidifies with a desired freezing-front motion.
Abstract: This article presents a dynamic programming methodology for the solution of the two-dimensional inverse Stefan design problem (ISDP). It is aimed particularly at the calculation of the boundary heat flux in a body that solidifies with a desired freezing-front motion. Such problems are of particular technological significance considering that the freezing-front motion is related directly to the quality of castings.
34 citations
TL;DR: In this article, two low-Reynolds-number k-σ turbulence models have been used to predict turbulent natural convection within a differentially heated enclosure for the purpose of assessing their relative merits.
Abstract: Two available low-Reynolds-number k-σ turbulence models have been used to predict turbulent natural convection within a differentially heated enclosure for the purpose of assessing their relative merits. In one model, fixed numerical values are employed for the model coefficients; in the other model, the coefficients vary with the value of the local turbulence Reynolds number. The numerical results from both models are compared to published experimental data. In general, the variable coefficient model predicts lower turbulence levels than the fixed coefficient model. Both models predict measured velocity profiles adequately, but overall, the predictions of the variable coefficient model are superior. The average Nusselt numbers are predicted more accurately by the variable coefficient model than by the fixed coefficient model.
32 citations
TL;DR: In this paper, the model and numerical scheme developed in Part I were first verified with upward freezing experiments of an NH4Cl-H2O solution on a cold isothermal surface.
Abstract: The model and numerical scheme developed in Part I were first verified with upward freezing experiments of an NH4Cl-H2O solution on a cold isothermal surface. Then, two-dimensional convection problems with different buoyancy terms in binary solid-liquid phase-change systems were studied. Finally, the model was used to simulate the solidification of an aqueous ammonium chloride solution in a rectangular cavity. The comparison of the results obtained from the present studies with the experimental and numerical results from the literature revealed a good agreement.
TL;DR: In this paper, an IR-CAT-based method is proposed for the detection of irregular-shaped subsurface cavities within irregular shape bodies by using an anchored grid pattern (AGP).
Abstract: An algorithm is presented for the high-resolution detection of irregular-shaped subsurface cavities within irregular-shaped bodies by the IR-CAT method. The theoretical basis of the algorithm is rooted in the solution of an inverse geometric steady-state heat conduction problem. A Cauchy boundary condition is prescribed at the exposed surface, and the inverse geometric heat conduction problem is formulated by specifying the thermal condition at the inner cavities walls, whose unknown geometries are to be detected. The location of the inner cavities is initially estimated, and the domain boundaries are discretized. Linear boundary elements are used in conjunction with cubic splines for high resolution of the cavity walls. An anchored grid pattern (AGP) is established to constrain the cubic spline knots that control the inner cavity geometry to evolve along the AGP at each iterative step. A residual is defined measuring the difference between imposed and computed boundary conditions. A Newton-Raphs...
TL;DR: In this paper, a detailed comparison of two finite-volume calculation methods for incompressible flows in complex geometries, one with a staggered grid arrangement and the other with a non-staggered grid arrangement, is presented.
Abstract: This article presents a detailed comparison of two finite-volume calculation methods for incompressible flows in complex geometries, one with a staggered grid arrangement and the other with a nonstaggered grid arrangement. The relative performance of the two schemes is examined through applications to test problems. Several numerical experiments are performed, changing the numerical grids and the flow nonlinearity. The results of these numerical experiments show that the staggered grid-based method generally reaches the grid-independent solutions earlier. However, both schemes result in nearly the same converged solutions when the numerical grids are properly refined.
TL;DR: In this article, a comparative study of two finite-volume calculation methods for incompressible flows on nonorthogonal grids with different grid arrangements is presented, and the computed results are compared with the analytic solution and the experimental data available in the literature.
Abstract: A comparative study of two finite-volume calculation methods for incompressible flows on nonorthogonal grids with different grid arrangements is presented. One of the methods is based on the conventional staggered grid arrangement, and the other method is based on the nonstaggered grid arrangement of Rhie and Chow. The existing schemes have been slightly modified to employ the same dependent variables in the momentum equations and the same pressure and velocity coupling technique, in order to compare effectively the relative performances of the two schemes. Both schemes are applied to test problems, and the computed results are compared with the analytic solution and the experimental data available in the literature.
TL;DR: In this paper, a two-dimensional hyperbolic heat conduction (HHC) problem with temperature-dependent thermal properties is investigated numerically, which involves the hybrid application of the Laplace transform and control-volume methods.
Abstract: Two-dimensional hyperbolic heat conduction (HHC) problems with temperature-dependent thermal properties are investigated numerically. The present numerical method involves the hybrid application of the Laplace transform and control-volume methods. The Laplace transform technique is used to remove time-dependent terms, and then the transformed equation is discretized in the space domain by the control-volume formulation. Nonlinear terms induced by temperature-dependent thermal properties are linearized by using the Taylor's series approximation. In general, the numerical solution of the HHC problem has the phenomenon of the jump discontinuity in the vicinity of the thermal wave front. This phenomenon easily causes numerical oscillations in this region. In order to suppress these numerical oscillations, the selection of shape functions is an important task in the present study. The bi-hyperbolic shape function is introduced in the present control-volume formulation. Three examples involving a problem with a...
TL;DR: In this article, a new adaptive finite element procedure for the solution of transient heat conduction problems is described, which is capable of accounting for the effect of the boundary conditions on the discretization error.
Abstract: A new adaptive finite element procedure for the solution of transient heat conduction problems is described. The proposed technique is capable of accounting for the effect of the boundary conditions on the discretization error, which is usually significant in boundary-value problems and is neglected by other researchers. A new adaptive strategy for transient problems considering the error behavior is also presented. The technique can be applied to both linear and nonlinear problems. Several heat conduction problems are used to evaluate the performance of the method. Results obtained show significant improvements when compared with the conventional finite element approach.
TL;DR: In this paper, a diagonal enhancement technique has been devised that improves the stability for both problems while substantially broadening the range of relaxation factors allowable by the iterative algorithm, and an illustration of how nonlinear thermal conductivities can destabilize a line iterative procedure, with the usefulness of the diagonal enhancement method demonstrated.
Abstract: Iterative characteristics of convective-diffusive equations can be substantially different from the results obtained from analyzing diffusive equations. This study investigates the convergence characteristics of both a single-phase convective-diffusive equation and a conjugate heat transfer problem represented by a combined pair of convective-diffusive and purely diffusive equations. A diagonal enhancement technique has been devised that improves the stability for both problems while substantially broadening the range of relaxation factors allowable by the iterative algorithm. An illustration is also presented on how nonlinear thermal conductivities can destabilize a line iterative procedure, with the usefulness of the diagonal enhancement method demonstrated. Furthermore, poor convergence rates can arise from constant heat flux boundary conditions if the ratio of thermal conductivities between the solid and fluid is greater than 0(l). In such cases a method employing nonuniform grid spacing is s...
TL;DR: In this paper, the integral transform method is employed in conjunction with second-order-accurate explicit finite-differences schemes, to handle accurately a class of parabolic-hyperbolic problems that appear in connection with transient forced convection inside ducts.
Abstract: The integral transform method is employed in conjunction -with second-order-accurate explicit finite-differences schemes, to handle accurately a class of parabolic-hyperbolic problems that appear in connection with transient forced convection inside ducts. The integral transformation process eliminates the independent variables in which the diffusion phenomena predominate. A system of coupled hyperbolic equations then results, involving time and the space coordinates in which convection is dominant, which is solved numerically through a modified upwind second-order finite-difference scheme. Stability and convergence characteristics of the proposed mixed approach are also examined. Typical applications in two- and three-dimensional geometries are considered, for both slug and laminar flow situations.
TL;DR: In this paper, a parametrical sensitivity study on the stochastic separated flow model which adopts the Lagrangian framework with the Monte Carlo method to track the drops in turbulent flow field is performed.
Abstract: A parametrical sensitivity study on the stochastic separated flow model which adopts the Lagrangian framework with the Monte Carlo method to track the drops in turbulent flow field is performed. It is found that an approximate 10-μm uniform width of each discrete size interval can adequately represent the spectral effects of drop size distribution in the investigated hollow-cone spray. The number of computational drops required for the statistically stationary solution is greatly dependent on the interval range of PDF domain employed. For the case using the interval range of PDF domain bounded within it is shown that the use of no less than 1000 computational drops for each representative size can yield nearly invariant solution.
TL;DR: In this paper, a new treatment method for nonorthogonal terms in the pressure-correction equation was proposed to enlarge the ranges of relaxation factors for convergence that are independent of the grid skewness and thus to ease the difficulty in determining the relaxation factors.
Abstract: This article proposes a new treatment method for nonorthogonal terms in the pressure-correction equation in order to enlarge the ranges of relaxation factors for convergence that are independent of the grid skewness and thus to ease the difficulty in determining the relaxation factors. The proposed method has been tested against four typical nonorthogonal two-dimensional cavity flows on a nonstaggered grid system. The results show that this method yields converged solution in wide ranges of relaxation factors, [alpha][sub u] and [alpha][sub p], which is nearly independent of the grid skewness. In addition, since only seven nodes are required to define the coefficient matrix of the pressure-correction equation for three-dimensional flows, the proposed method makes computations of three-dimensional flows quite practical.
TL;DR: In this article, a finite-element method was developed that combines the segregated velocity-pressure equal-order formulation of the Navier-Stokes equation originated from the SIMPLE algorithm and the streamline upwind Petrov-Galerkin weighted residual method.
Abstract: A finite-element method has been developed that combines the segregated velocity-pressure equal-order formulation of the Navier-Stokes equation originated from the SIMPLE algorithm and the streamline upwind Petrov-Galerkin weighted residual method. To verify the proposed finite-element method, driven cavity flow and backward-facing step flow have been considered. The present results are compared with existing experimental results using laser Doppler velocimetry and numerical results using the finite-difference method and the velocity-pressure integrated, mixed-order interpolation method. It has been shown that the present method gives accurate results with less memory and execution time than the conventional finite-element method.
TL;DR: In this article, the controlled variation scheme (CVS) was proposed to suppress spurious oscillations that commonly occur in convection-dominated viscous flows, by injecting a nonlinear numerical diffusion, similar to the original TVD schemes, into the central difference scheme.
Abstract: The formalism of the total variation diminishing (TVD) schemes is utilized to design a convection scheme for incompressible recirculating flows. The scheme has been named the controlled variation scheme (CVS). Even though the CVS does not possess the TVD property for sequential solution algorithms, due to the appearance of source terms, the concept of controlled variation fluxes can be effective in suppressing spurious oscillations that commonly occur in convection-dominated viscous flows, by injecting a nonlinear numerical diffusion, similar to the original TVD schemes, into the central difference scheme. This is demonstrated by using the one-dimensional linear convection-diffusion equation with and without a source term as model problems. The formulation and an efficient implementation of the CVS in a sequential pressure-based solver for incompressible steady-state Navier-Stokes equations is presented in this work. The applications of the CVS for two-dimensional laminar and turbulent flows is presented ...
TL;DR: In this paper, an iterative SIMPLEC-type segregated solution technique (HPTAM-Revised) was used to solve the pressure-velocity coupling and reduce the linearization errors of the kinetic theory relationship and equations of state.
Abstract: Simulating the transient operation of fully thawed heat pipes involves solving a highly nonlinear homogeneous two-phase flow problem, which necessitates the development of a stable and efficient numerical technique. In this work, various segregated numerical techniques are implemented, and their accuracy and computation time requirement are examined using experimental data of a water heat pipe. Best results are obtained using an iterative SIMPLEC-type segregated solution technique (HPTAM-Revised), which includes two internal iterative steps to resolve the pressure-velocity coupling and reduce the linearization errors of the kinetic theory relationship and equations of state. While all solution techniques examined performed the same in terms of accuracy, the HPTAM-Revised is 90 times faster than the basic noniterative SIMPLE-type approach in terms of CPU time. Also, using the iterative SIS solver, instead of the banded Gauss-elimination solver, for the discretized energy and momentum equations resulted in ...
TL;DR: In this article, a pressure-based multiblock computational method was developed for solving the incompressible Navier-Stokes equations in general curvilinear grid systems.
Abstract: A pressure-based multiblock computational method is developed for solving the incompressible Navier-Stokes equations in general curvilinear grid systems. A conservative interface scheme is devised with desirable accuracy to handle the information transfer between blocks. The scheme is based on the semiimplicit-type flow solver with the staggered grid. Issues concerning discontinuous grids, global mass conservation, viscous term treatment, and boundary conditions at the grid interface are addressed. The method is tested for two flow problems, a curved channel flow and a bifurcated channel flow. The calculations demonstrate that, besides maintaining desirable solution characteristics across discontinuous grid interfaces, the present multiblock algorithm can achieve convergence rates comparable to that of the single-block algorithm, yielding an improved computational capability for treating complex flow problems.
TL;DR: In this article, a hybrid method that uses both approaches, isothermal approximation and direct integration, is presented, which leads to a faster method that is easy to introduce into a finite-element code.
Abstract: This study deals with the finite-element modeling of radiation coupled with diffusion heat transfer. In many engineering problems, radiation occurs at the field boundary, where transfer is purely conductive. Traditional resolutions of such problems use the lumped radiosity method by delimiting the field into isothermal surfaces. This isothermal assumption implies the use of very refined meshes. An alternative simple method suppresses this isothermal restriction by integrating the Fredholm integral form directly. This method is slower but more accurate. In this work we present a hybrid method that uses both approaches, isothermal approximation and direct integration. This leads to a faster method that is easy to introduce into a finite-element code.
TL;DR: In this paper, natural convection induced by combined heat and mass transfer in an enclosure filled with two layers of anisotropic porous media saturated with a two-component fluid is investigated by means of numerical experiments, Darcy's law together with the energy and specie equations are solved by a domain decomposition and a pseudo-spectral method using Chebyshev polynomials as the basis functions.
Abstract: Natural convection induced by combined heat and mass transfer in an enclosure filled with two layers of anisotropic porous media saturated with a two-component fluid is investigated by means of numerical experiments, Darcy's law together with the energy and specie equations are solved by a domain decomposition and a pseudo-spectral method using Chebyshev polynomials as the basis functions. The interactions between the subdomains along the interface are decoupled by a superposition of elementary solutions. Four cases including aiding, opposing, cross diffusion with stabilizing, and destabilizing concentration fields are considered. The results show remarkable differences among the flow, temperature, and concentration fields. Depending on the orientation of the boundary conditions of the temperature and concentration fields, the overall heat transfer rates may or may not be sensitive to the Rayleigh numbers.
TL;DR: In this article, the effects of grid orthogonality and smoothness on the accuracy of finite-difference solutions of the two-dimensional Laplace, convection-diffusion and Navier-Stokes equations are studied analytically and numerically.
Abstract: The effects of grid orthogonality and smoothness on the accuracy of finite-difference solutions of the two-dimensional Laplace, convection-diffusion, and Navier-Stokes equations are studied analytically and numerically. The examples include flow past an airfoil and in a branching channel. It is concluded that orthogonality has little impact on accuracy in general, provided the angle between grid lines is not too small. Rather, accuracy is very sensitive to the clustering of points in the regions of rapid variation of the solution, and orthogonality may in fact have an adverse effect on the quality of the solution when it leads to a coarser resolution of these regions. These conclusions also extend to orthogonality at boundaries (either physical or computational), where Neumann conditions are implemented by one-sided derivatives.
TL;DR: In this paper, a strongly conservative finite-volume procedure is presented for flows in complex geometries, which is based on a complete transformation of the governing equations, and physical velocity components, rather than the traditionally used Cartesian velocity component, are used as primitive variables.
Abstract: A strongly conservative finite-volume procedure is presented for flows in complex geometries. The technique is based on a complete transformation of the governing equations, and physical velocity components, rather than the traditionally used Cartesian velocity components, are used as primitive variables. It was found that projecting the discretized vector transport equation in the direction of the covariant base vectors eliminated two substantial difficulties associated with flows in complex geometries. These difficulties stem from the presence of cross-pressure gradient terms and the need for a transformation between the different types of curvilinear velocity components in the mass conservation equation. It is shown that the present formulation ensures that the computational scheme is diagonally dominant. It was found that partially implicit treatment of nonorthogonal diffusion terms improved the convergence rate primarily for high-cell-Reynolds-number values. For nonstaggered grids, a new sol...
TL;DR: In this article, a continuum model of total mass, momentum, and energy is used to model the thermal and dynamic boundary conditions and the source terms of the energy equation for spot welding.
Abstract: Transient heat transfer, fluid flow, and phase change in spot welding are simulated using a continuum model of total mass, momentum, and energy. Emphasis is given to the numerical treatment of thermal and dynamic boundary conditions and the source terms of the energy equation. The present method for treating the boundary conditions not only can limit the solution domain within the internal control volumes for the overall discretization formulations but also makes it possible to model the free-surface mushy region using the same velocity modification method as in the internal mushy region. In an identical computational environment, the calculated temperature profile, velocity field, and weld pool shape are in excellent agreement with the general iteration method, but the computer speed is faster by 15-20% than that of the latter.
TL;DR: In this paper, a controlled variation scheme (CVS) was proposed in the context of a sequential pressure-based solver for incompressible steady-state Navier-Stokes equations.
Abstract: A controlled variation scheme (CVS) in the context of a sequential pressure-based solver for incompressible steady-state Navier-Stokes equations has been formulated in Part I of this work. In the present work, two-dimensional test cases such as laminar flows in a lid-driven cavity and over a backward-facing step as well as a turbulent flow over a backward-facing step are used to assess the performance of the CVS and the interaction of the net numerical viscosity with the grid resolution. It is demonstrated that the concept of a controlled variation scheme, with its nonlinear numerical dissipation that is dependent on the local solution gradients, holds promise in terms of computations of strongly convective flows using pressure-based algorithms.