Showing papers in "Numerical Heat Transfer Part B-fundamentals in 2010"
TL;DR: In this article, the use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium.
Abstract: Use of the lattice Boltzmann method (LBM) has been extended to analyze radiative transport problems in an absorbing, emitting, and scattering medium. In terms of collision and streaming, the present approach of the LBM for radiative heat transfer is similar to those being used in fluid dynamics and heat transfer for the analyses of conduction and convection problems. However, to mitigate the effect of the isotropy in the polar direction, in the present LBM approach, lattices with more number of directions than those being used for the 2-D system have been employed. The LBM formulation has been validated by solving benchmark radiative equilibrium problems in 1-D and 2-D Cartesian geometry. Temperature and heat flux distributions have been obtained for a wide range of extinction coefficients. The LBM results have been compared against the results obtained from the finite-volume method (FVM). Good comparison has been obtained. The numbers of iterations and CPU times for the LBM and the FVM have also been com...
108 citations
TL;DR: Gaseous flow and heat transfer in a lid-driven cavity under nonequilibrium flow conditions is investigated using the direct simulation Monte Carlo method, from the slip to the free-molecular regime.
Abstract: Gaseous flow and heat transfer in a lid-driven cavity under nonequilibrium flow conditions is investigated using the direct simulation Monte Carlo method, from the slip to the free-molecular regime. The emphasis is on understanding thermal flow features. The impact of the lid velocity and various degrees of rarefaction on the shear stress and heat flux rates are analyzed. The role of expansion cooling and viscous dissipation on the heat transfer mechanism is investigated. Complex heat flow phenomena, such as counter-gradient heat transfer, are revealed by the simulations which the conventional Navier-Stokes-Fourier equations are not able to capture, even in the slip-flow regime.
108 citations
TL;DR: In this article, the authors present truncation error terms for flux approximations on mesh faces, needed by the finite-volume method, and their influence on solution accuracy in the search for the optimal cell type.
Abstract: This article presents truncation error terms for flux approximations on mesh faces, needed by the finite-volume method, and their influence on solution accuracy in the search for the optimal cell type. Face truncation errors are used to assemble truncation errors for different cell types such as squares, triangles, and hexagons. It is shown that squares have the smallest and triangles the largest truncation errors, for the same cell size, which is also confirmed by numerical experiments. It is also shown that polyhedral meshes consisting of hexagons are slightly less accurate than hexahedral meshes with the same cell size.
57 citations
TL;DR: In this article, a coupled lattice Boltzmann (LB) and finite-difference (FD) method is used to solve for the heat transport in a two-dimensional domain.
Abstract: A coupled lattice Boltzmann (LB)–finite-difference (FD) method is used to solve for the heat transport in a two-dimensional domain. The LB method is used to capture relevant phonon physics near a microscopic heat-generation region by solving the Boltzmann transport equation, while a finite-difference model is used to capture the thermal transport at the macroscopic level. The coupling region between the LB and FD domains, which enables multiscale modeling, is discussed. The model is evaluated versus other numerical methods as well as experimental results. In all cases, the multiscale approach yielded results that were accurate to within the experimental uncertainty.
55 citations
TL;DR: In this paper, a lattice Boltzmann (LB) simulation strategy is proposed for the incompressible transport phenomena occurring during macroscopic solidification of pure substances, where the underlying hydrodynamics are monitored by a conventional single-particle density distribution function (DF) through a kinetic equation, whereas the thermal field is obtained from another kinetic equation which is governed by a separate temperature DF.
Abstract: A lattice Boltzmann (LB) simulation strategy is proposed for the incompressible transport phenomena occurring during macroscopic solidification of pure substances. The proposed model is derived by coupling a passive scalar-based thermal LB model with the classical enthalpy–porosity technique for solid–liquid phase-transition problems. The underlying hydrodynamics are monitored by a conventional single-particle density distribution function (DF) through a kinetic equation, whereas the thermal field is obtained from another kinetic equation which is governed by a separate temperature DF. The phase-changing aspects are incorporated into the LB model by inserting appropriate source terms in the respective kinetic equations through the most formal technique following the extended Boltzmann equations along with an appropriate enthalpy updating scheme. The proposed model is validated extensively with one- and two-dimensional solidification problems for which analytical and numerical results are available in the ...
48 citations
TL;DR: In this paper, a new slip model is proposed for slip flows and an analytical approach is developed for collisionless steady-state heat conduction inside a fully diffuse enclosure for non-continuum gas phase conduction encountered in micro/nano devices.
Abstract: This article presents a comprehensive study of various modeling techniques for noncontinuum gas-phase heat conduction encountered in micro/nano devices over a broad range of Knudsen number. A new slip model is proposed for slip flows and an analytical approach is developed for collisionless steady-state heat conduction inside a fully diffuse enclosure. Excellent agreements with direct simulation Monte Carlo (DSMC) simulations have been achieved for both of them. For problems in the transition regime and/or with partially thermal accommodated walls, the DSMC method is employed. Some noncontinuum phenomena such as the steady gas flows induced by the nonuniform temperature field are observed.
43 citations
TL;DR: In this paper, separate 3D models of thermomechanical behavior of the solidifying shell, turbulent fluid flow in the liquid pool, and thermal distortion of the mold are combined to create an...
Abstract: Separate three-dimensional (3-D) models of thermomechanical behavior of the solidifying shell, turbulent fluid flow in the liquid pool, and thermal distortion of the mold are combined to create an ...
40 citations
TL;DR: In this paper, the modified Levenberg-Marquardt method is used for simultaneous estimation of decomposition kinetic coefficients and temperature-dependent thermophysical properties of charring ablators with a moving boundary over a wide temperature range.
Abstract: The modified Levenberg-Marquardt method is used for simultaneous estimation of decomposition kinetic coefficients and temperature-dependent thermophysical properties of charring ablators with a moving boundary over a wide temperature range. No prior information is used for the functional forms of the unknown thermal conductivity and specific heat. The procedure used differs from the traditional one in that it does not require prescribed time-dependent surface heat flux, recession rate, and pyrolysis gas mass flow rate. These time-dependent quantities may recover during an iterative procedure. The measured temperatures are simulated numerically by the Charring material ablation code, which accounts for unsteady ablation. The method can determine unknown parameters in an efficient manner with reasonable accuracy, without exact advance knowledge about the net surface heat flux, surface recession, and gas flux through the material.
39 citations
TL;DR: In this article, the fully matrix-inversion-free artificial compressibility (AC), characteristic based split (CBS) algorithm is used to produce a stable and accurate solution for high Rayleigh number natural convection in rectangular cavities.
Abstract: The fully matrix-inversion-free artificial compressibility (AC), characteristic based split (CBS) algorithm is used to produce a stable and accurate solution for high Rayleigh number natural convection in rectangular cavities Two benchmark problems are solved using the AC-CBS scheme: the classical differentially heated (DH) cavity, and a cavity subject to temperature boundary conditions on its sides, which is proposed here as a new benchmark For the DH cavity problem, the dependence of the solution on the computational grid is highlighted, and it is shown how the horizontal velocity is more sensitive than the other calculated quantities For the newly proposed benchmark, the numerical results are compared to experimental data that has recently appeared in the open literature
38 citations
TL;DR: In this article, an analytic expression called a reconstruction operator is proposed for the exchange from velocity of finite-type methods to the singleparticle distribution function of the lattice Boltzmann method (LBM).
Abstract: An analytic expression called a reconstruction operator is proposed for the exchange from velocity of finite-type methods to the single-particle distribution function of the lattice Boltzmann method (LBM). The combined finite-volume method and lattice Boltzmann method (called the CFVLBM) is adopted to solve three flow cases, backward-facing flow, flow around a circular cylinder, and lid-driven cavity flow. The results predicted by the CFVLBM agree with the available numerical solutions very well. It is shown that the vorticity contour distribution is a more appropriate parameter to ensure good smoothness and consistency at the coupling interface. At the same time, CPU time used by the CFVLBM(II), with more than one outer iteration before interface information exchange, is much less than that of the CFVLBM(I), where interface information exchanges are executed after each outer iteration.
36 citations
TL;DR: In this paper, the meshless local Petrov-Galerkin (MLPG) method is used to solve nonlinear steady and transient heat conduction problems, and the essential boundary condition is enforced by the method of direct interpolation.
Abstract: The meshless local Petrov-Galerkin (MLPG) method is an effective meshless method to solve partial differential equations. In this article, the MLPG method is used to solve nonlinear steady and transient heat conduction problems. The essential boundary condition is enforced by the method of direct interpolation. The moving least-squares (MLS) method is used for interpolation. Thermal conductivity of the material is assumed to be dependent on the temperature. An iterative procedure based on the predictor-corrector method is used. Time integration is performed using the θ method. Results are compared with the available exact solution and the solution by the finite-element method, and is found to be in good agreement.
TL;DR: This work was to develop the FFD by improving its speed and accuracy by modifying the time-splitting method and by proposing a correction function for mass conservation.
Abstract: Indoor environment design and air management in buildings requires fast simulation of air distribution. A fast fluid dynamics (FFD) model seems very promising. This work was to develop the FFD by improving its speed and accuracy. Enhancement of computing speed can be realized by modifying the time-splitting method. Improvements in accuracy were achieved by replacing the finite-difference scheme by the finite-volume method and by proposing a correction function for mass conservation. Using the new FFD model for several indoor air flows, the results show significant reduction in computing time and great improvements on accuracy.
TL;DR: In this paper, a level set-based topological shape optimization method considering design-dependent convection boundaries is developed for steady-state heat conduction problems, which minimizes the thermal compliance of systems by varying the implicit boundary, satisfying the constraint of allowable material volume.
Abstract: A level set–based topological shape optimization method considering design-dependent convection boundaries is developed for steady-state heat conduction problems. We embed the level set function obtained from a Hamilton-Jacobi type of equation into a fixed initial domain to implicitly represent thermal boundaries. The effects of the implicit convection boundary obtained from topological shape variations are represented by numerical Dirac delta and Heaviside functions. The method minimizes the thermal compliance of systems by varying the implicit boundary, satisfying the constraint of allowable material volume. During design optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is derived from an optimality condition.
TL;DR: In this paper, an implementation of the unstructured polygonal meshes is adopted by connecting each center point of the Unstructured triangular meshes rather than joining the centroids of the triangular elements to the midpoints of the corresponding sides to form a polygon.
Abstract: Radiative heat transfer in a complex axisymmetric enclosure with participating medium is investigated by using the finite-volume method (FVM). In particular, an implementation of the unstructured polygonal meshes is adopted by connecting each center point of the unstructured triangular meshes rather than joining the centroids of the triangular elements to the midpoints of the corresponding sides to form a polygonal element. Also, typical considerations regarding application of the present polygonal mesh system to axisymmetric radiation are discussed. After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, the final discretization equation is introduced with the conventional finite-volume approach by using the directional weights. For validation and comparison, three test examples with complex axisymmetric geometries have been accomplished. The present study shows that not only is the method flexible in treating radiative problems wi...
TL;DR: In this paper, a numerical method for solving three-dimensional, unsteady, incompressible flows with immersed moving solids of arbitrary geometric complexity is developed for solving the Navier-Stokes equations.
Abstract: A numerical method is developed for solving three-dimensional, unsteady, incompressible flows with immersed moving solids of arbitrary geometric complexity. A co-located (nonstaggered) pressure-based finite-volume method is employed to solve the Navier-Stokes equations for the flow region, and the solid region is represented by material points with known position and velocity. The influence of the body on the flow is accounted for by reconstructing implicitly the velocity on the immersed boundary faces b-tween fluid and solid. Canonical test cases and mesh convergence tests are carried out. A validation test for the vibration of microcantilevers shows good agreement between computed and measured damping factor values.
TL;DR: In this article, a finite-volume formulation commonly employed in the well-known SIMPLE family algorithms is used to discretize the lattice Boltzmann equations on a cell-centered, non-uniform grid.
Abstract: A finite-volume formulation commonly employed in the well-known SIMPLE family algorithms is used to discretize the lattice Boltzmann equations on a cell-centered, non-uniform grid. The convection terms are treated by a higher-order bounded scheme to ensure accuracy and stability of solutions, especially in the simulation of turbulent flows. The source terms are linearized by a conventional method, and the resulting algebraic equations are solved by a strongly implicit procedure. A method is also presented to link the lattice Boltzmann equations and the macroscopic turbulence modeling equations in the frame of the finite-volume formulation. The method is applied to two different laminar flows and a turbulent flow. The predicted solutions are compared with the experimental data, benchmark solutions, and solutions by the conventional finite-volume method. The results of these numerical experiments for laminar flows show that the present formulation of the lattice Boltzmann method is slightly more diffusive t...
TL;DR: In this article, a numerical approach is presented for analysis of bubble growth and departure from a microcavity during nucleate boiling, where the level set formulation for tracking the phase interfaces is modified to include the effect of phase change on the liquid-vapor interface and to treat the no-slip and contact angle conditions on the immersed (or irregularly shaped) solid surface of the micro cavity.
Abstract: A numerical approach is presented for analysis of bubble growth and departure from a microcavity during nucleate boiling. The level-set formulation for tracking the phase interfaces is modified to include the effect of phase change on the liquid–vapor interface and to treat the no-slip and contact angle conditions on the immersed (or irregularly shaped) solid surface of the microcavity. Also, the formulation is coupled with a simple and efficient model for predicting the evaporative heat flux from the liquid microlayer on an immersed solid surface. The effects of cavity size and geometry on the bubble growth and departure in nucleate boiling are investigated.
TL;DR: In this article, the authors compared the film cooling effectiveness of a two-dimensional gas turbine endwall with an adiabatic wall condition using five common turbulence models: the RNG k-e model, the realizable k e model, standard k-ω model, SST k -ω model and the RSM model.
Abstract: The film cooling effectiveness of a two-dimensional gas turbine endwall is compared for the cases of conjugate heat transfer and an adiabatic wall condition using five common turbulence models. The turbulence models employed in this study are: the RNG k–e model, the realizable k–e model, the standard k–ω model, the SST k–ω model, and the RSM model. The computed flow field and surface temperature profiles along with the film effectiveness for one and two cooling slots at different injection angles are presented. The results show the strong effect of conjugate heat transfer on the film effectiveness compared to the adiabatic case and also compared to the effectiveness values obtained from analytically solvable models.
TL;DR: In this paper, an efficient method has been developed to incorporate the effects of heat transfer in a liquid pool into models of heat conduction with solidification, which has been added into the commercial package Abaqus as a user-defined subroutine (UMATHT).
Abstract: An efficient new method has been developed to incorporate the effects of heat transfer in a liquid pool into models of heat conduction with solidification. The procedure has been added into the commercial package Abaqus [1] as a user-defined subroutine (UMATHT). Computational results of fluid flow and heat transfer in a liquid domain can be characterized by the heat flux crossing the boundary representing the solidification front, or liquidus temperature. This “superheat flux” can be incorporated into an uncoupled transient simulation of heat transfer phenomena in the mushy and solid regions by enhancing latent heat. The new method has been validated and compared to semianalytical solutions and two other numerical methods on simple test problems: two-dimensional, steady-state ledge formation in cryolite in aluminum extraction cells, and shell thinning in continuous casting of steel. Its real power, however, is for multiphysics simulations involving complex phenomena, such as solidification stress analysis...
TL;DR: In this paper, a new formulation is proposed for the calculation of stress components at control-volume faces, within the context of cell-centered finite-volume methods which have the stress tensor as one of the main dependent variables.
Abstract: In this study, a new formulation is proposed for the calculation of stress components at control-volume faces, within the context of cell-centered finite-volume methods which have the stress tensor as one of the main dependent variables. Test case results from calculations with viscoelastic fluids flowing through a T-junction demonstrate the merits of the method. Previous formulations for stress interpolation yielded results that would depend on the time-step value employed, even when calculating steady-state problems. We have removed this inconsistency by devising an improved method that gives results independent of the time step and that in addition is more robust, with a wider range of allowable Deborah numbers. A FENE-CR constitutive model is used to replicate the known viscoelastic nature of blood, and results are given for varying fluid elasticities, at values of Reynolds number and extraction ratio typical of hemodynamic applications.
TL;DR: In this paper, a pseudospectral multidomain method is proposed for the solution of the two-dimensional incompressible Navier-Stokes equations and energy equation.
Abstract: A pseudospectral multidomain method is proposed for the solution of the two-dimensional incompressible Navier-Stokes equations and energy equation. The governing equations are spatially discretized by the Chebyshev pseudospectral method. Within each subdomain, the algebraic system is solved by a semi-implicit pseudotime method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly marched by the matrix diagonalization method. An interface/boundary-value updating algorithm is proposed to obtain the interfaces and boundaries values to satisfy both the boundary conditions and interface transmission conditions. Since the solution of the interior collocation point values and the updating of interface/boundary values are carried out independently, the multidomain method is easy to implement with an existing single-domain solver. The pseudospectral multidomain method is validated by three benchmark heat transfer problems: natural convect...
TL;DR: In this paper, the use of Bayesian inference in the estimation of spatially variable thermal conductivity for one-dimensional heat conduction in heterogeneous media, such as particle-filled composites and other two-phase dispersed systems, by employing a Markov chain Monte Carlo (MCMC) method, through the implementation of the Metropolis-Hastings algorithm.
Abstract: This work illustrates the use of Bayesian inference in the estimation of spatially variable thermal conductivity for one-dimensional heat conduction in heterogeneous media, such as particle-filled composites and other two-phase dispersed systems, by employing a Markov chain Monte Carlo (MCMC) method, through the implementation of the Metropolis-Hastings algorithm. The direct problem solution is obtained analytically via integral transforms, and the related eigenvalue problem is solved by the generalized integral transform technique (GITT), offering a fast, precise, and robust solution for the transient temperature field, which are desirable features for the implementation of the inverse analysis. Instead of seeking the function estimation in the form of a sequence of local values for the thermal conductivity, an alternative approach is proposed here, which is based on the eigenfunction expansion of the thermal conductivity itself. Then, the unknown parameters become the corresponding series coefficients. ...
TL;DR: In this paper, numerical calculations of the unsteady, Reynolds-averaged Navier-Stokes (URANS) equations were performed to simulate isothermal single-phase flow in the geometry of a pulverized-solids burner, with double air intake and swirl, at large Reynolds numbers.
Abstract: We perform numerical calculations of the unsteady, Reynolds-averaged Navier-Stokes (URANS) equations to simulate isothermal single-phase flow in the geometry of a pulverized-solids burner, with double air intake and swirl, at large Reynolds numbers. Two simulations are run with different turbulence closures, viz., the standard k–ϵ and Reynolds stresses models. Computations are validated concerning grid density and placement of boundaries. Results describe an almost periodic flow that exhibits very convincing time-dependent, coherent structures. We analyze it, as well as the differences arising from the nature of the turbulence model, which is an important issue given the cost involved.
TL;DR: In this article, the authors investigated the performance of modification techniques for resolving the singularity at the final time in the gradient method for the inverse heat conduction problem and selected four representative methods based on the literature and analyzed for the same case.
Abstract: This work investigates overall performance of the modification techniques for resolving the singularity at the final time in the gradient method for the inverse heat conduction problem. Four representative methods are selected based on the literature and analyzed for the same case. They are the regularization term method, the differential equation method, the gradient integration method, and the sequential gradient method. All four methods are reproduced and tested for the same test case. Based on the test results, a two-step method that can both alleviate the systematic bias and at the same time resolve the singularity is proposed.
TL;DR: In this article, a ghost cell method was developed to solve the incompressible flows over immersed bodies with heat transfer, and a two-point stencil was used to build the flow reconstruction models for both Dirichlet and Neumann boundary conditions on the immersed surface.
Abstract: A simple, stable, and accurate ghost cell method is developed to solve the incompressible flows over immersed bodies with heat transfer. A two-point stencil is used to build the flow reconstruction models for both Dirichlet and Neumann boundary conditions on the immersed surface. Tests show that the current scheme is second-order-accurate in all error norms for both types of boundary condition, with the only exception that under Neumann condition the order of the maximum norm of temperature error is 1.44. Various forced- and natural-convection problems for cylinders immersed in open field or in a cavity are computed and compared with published data.
TL;DR: In this paper, a finite-volume model is used to analyze alternate melting and solidification, which is the fundamental operational mode of latent thermal energy storage (LTES) systems.
Abstract: A finite-volume model is used to analyze alternate melting and solidification, which is the fundamental operational mode of latent thermal energy storage (LTES) systems. The simulated cases include: (1) melting of tin with natural convection, (2) alternate melting and solidification of sodium nitrate, and (3) cyclic phase change of gallium. For each case, temporal evolution of the heat transfer rate and liquid fraction is presented. In addition, snapshots of phase interface, temperature, pressure, and liquid velocity distributions are presented. The implications of the modeling results are discussed.
TL;DR: In this article, a numerical method to solve the two-set, eight-equation, compressible, two-fluid, 2-phase flow model is developed in two dimensions as an extension of the earlier one-dimensional version.
Abstract: In this article, a numerical method to solve the two-set, eight-equation, compressible, two-fluid, two-phase flow model is developed in two dimensions as an extension of the earlier one-dimensional version. The multidimensional two-fluid model can be effectively solved by a finite-volume method in a rotated reference frame. In order to estimate the fastest wave speeds in the hyperbolic equation system for the Harten–Lax–van Leer (HLL) scheme, we first regard the liquid phase as compressible by taking the stiffened-gas equation of state. Then we derive the two-dimensional approximate Jacobian matrix and obtain the associated eight analytic eigenvalues. Using the HLL scheme, we solve a few two-phase flow problems including shape cavitation and underwater explosion, demonstrating application of the present numerical method to meaningful problems.
TL;DR: In this paper, a nonlinear minimization of the squared errors between the measured temperatures and the calculated ones is proposed to determine the geometric shape of a cavity with convective boundary condition in a heat-conducting medium.
Abstract: This article presents a system identification scheme to determine the geometric shape of a cavity with convective boundary condition in a heat-conducting medium using the measured temperatures on the surface of the object. The proposed algorithm is based on the nonlinear minimization of the squared errors between the measured temperatures and the calculated ones. In this article, a new approach based on non-boundary-fitted meshes and gradient smoothing technique is presented for the solution of the direct problem and shape sensitivity analysis. In this method, the domain boundary can be moved independently from the mesh, and the solution of the variable-domain problems can be found easily. The domain parameterization technique using cubic splines is adopted to manipulate the shape variation of the cavity. The conjugate gradient method is used as the optimization algorithm. Some numerical examples are solved to evaluate the applicability of the proposed method in the solution of inverse-geometry problems. ...
TL;DR: From the numerical results, it is clearly shown that the present formulation can provide accurate difference expressions for the steady convection-diffusion equation on unstructured grids regardless of the grid arrangement, and will serve as a kernel scheme to simulate fluid flow phenomena in complicated domains.
Abstract: A compact and accuracy discretization of incompressible Navier-Stokes equations on staggered polygonal grids is presented in this article. It is a sequel to our efforts in developing a feasible solution procedure to simulate incompressible flow problems in complicated domains. By taking advantage of the discretization procedure for the convection-diffusion equation described in our previous work, difference counterparts of the Navier-Stokes equations can be obtained on staggered polygonal grids. Additional ingredients of pressure–velocity coupling and boundary conditions for velocity gradients in the solution procedure are also described. Several test problems are solved to illustrate the feasibility of the present formulation. From the numerical results obtained, it is evident that the proposed scheme is a useful tools to simulate incompressible flow field in arbitrary domains.
TL;DR: In this paper, the authors developed a higher-order-accurate compact finite-difference scheme for solving the heat transport equations in a one-dimensional microsphere exposed to ultrashort-pulsed lasers, where the boundary is assumed to be thermally insulated.
Abstract: Ultrashort-pulsed lasers with pulse durations of the order of subpicoseconds to femtoseconds possess exclusive capabilities in limiting the undesirable spread of the thermal process zone in the heated sample. Parabolic two-step micro heat transport equations have been widely applied for thermal analysis of thin metallic films exposed to ultrashort laser pulses. In this study, we develop a higher-order-accurate compact finite-difference scheme for solving the heat transport equations in a one-dimensional microsphere exposed to ultrashort-pulsed lasers, where the boundary is assumed to be thermally insulated. The method is illustrated by two numerical examples.