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Songze Chen - One of the best experts on this subject based on the ideXlab platform.
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an implicit kinetic scheme for multiscale heat transfer problem accounting for phonon dispersion and polarization
International Journal of Heat and Mass Transfer, 2019Co-Authors: Chuang Zhang, Zhaoli Guo, Songze ChenAbstract:Abstract An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport Equation (BTE) based on the non-gray model with the consideration of phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has to be solved efficiently for varied phonon frequencies and branches. The proposed kinetic scheme is composed of a microscopic iteration and a Macroscopic iteration. The microscopic iteration is capable of automatically adapting with varied phonon mean free path of each phonon frequency and branch by solving the phonon BTE. The energy transfer of all phonons is gathered together by the microscopic iteration to evaluate the heat flux. The temperature field is predicted by a Macroscopic heat transfer Equation according to the heat flux, and the equilibrium state in the phonon BTE is also updated. The combination of the phonon BTE solver and the Macroscopic Equation makes the present method very efficient in a wide range of length scales. Three numerical tests, including the cross-plane, in-plane and nano-porous heat transfer in silicon, demonstrate that the present scheme can handle the phonon dispersion and polarization correctly and predict the multiscale heat transfer phenomena efficiently. Furthermore, the proposed method can be tens of times faster than the typical implicit DOM while keeps the same amount of the memory requirements as Fourier solvers for multiscale heat transfer problems.
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unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon boltzmann transport Equation
Physical Review E, 2017Co-Authors: Chuang Zhang, Zhaoli Guo, Songze ChenAbstract:An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport Equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a Macroscopic Equation to accelerate the convergence in the diffusive regime. The Macroscopic Equation can be taken as a moment Equation for phonon BTE. The heat flux in the Macroscopic Equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the Macroscopic Equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the Macroscopic Equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic Equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
Zhaoli Guo - One of the best experts on this subject based on the ideXlab platform.
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an implicit kinetic scheme for multiscale heat transfer problem accounting for phonon dispersion and polarization
International Journal of Heat and Mass Transfer, 2019Co-Authors: Chuang Zhang, Zhaoli Guo, Songze ChenAbstract:Abstract An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport Equation (BTE) based on the non-gray model with the consideration of phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has to be solved efficiently for varied phonon frequencies and branches. The proposed kinetic scheme is composed of a microscopic iteration and a Macroscopic iteration. The microscopic iteration is capable of automatically adapting with varied phonon mean free path of each phonon frequency and branch by solving the phonon BTE. The energy transfer of all phonons is gathered together by the microscopic iteration to evaluate the heat flux. The temperature field is predicted by a Macroscopic heat transfer Equation according to the heat flux, and the equilibrium state in the phonon BTE is also updated. The combination of the phonon BTE solver and the Macroscopic Equation makes the present method very efficient in a wide range of length scales. Three numerical tests, including the cross-plane, in-plane and nano-porous heat transfer in silicon, demonstrate that the present scheme can handle the phonon dispersion and polarization correctly and predict the multiscale heat transfer phenomena efficiently. Furthermore, the proposed method can be tens of times faster than the typical implicit DOM while keeps the same amount of the memory requirements as Fourier solvers for multiscale heat transfer problems.
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unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon boltzmann transport Equation
Physical Review E, 2017Co-Authors: Chuang Zhang, Zhaoli Guo, Songze ChenAbstract:An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport Equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a Macroscopic Equation to accelerate the convergence in the diffusive regime. The Macroscopic Equation can be taken as a moment Equation for phonon BTE. The heat flux in the Macroscopic Equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the Macroscopic Equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the Macroscopic Equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic Equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
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volume averaged Macroscopic Equation for fluid flow in moving porous media
International Journal of Heat and Mass Transfer, 2015Co-Authors: Lianping Wang, Liang Wang, Zhaoli GuoAbstract:Abstract Darcy’s law and the Brinkman Equation are two main models used for creeping fluid flows inside moving permeable particles. For these two models, the time derivative and the nonlinear convective terms of fluid velocity are neglected in the momentum Equation. In this paper, a new momentum Equation including these two terms are rigorously derived from the pore-scale microscopic Equations by the volume-averaging method. It is shown that Darcy’s law and the Brinkman Equation can be reduced from the derived Equation under creeping flow conditions. Using the lattice Boltzmann Equation (LBE) method, the Macroscopic Equations are solved for the problem of a porous circular cylinder moving along the centerline of a channel. Galilean invariance of the Equations are investigated both with the intrinsic phase averaged velocity and the phase averaged velocity. The results demonstrate that the commonly used phase averaged velocity cannot be considered, while the intrinsic phase averaged velocity should be chosen for porous particulate systems. In addition, the Poiseuille flow in a porous channel is simulated using the LBE method with the improved Equations, and good agreements are obtained when compared with the finite-difference solutions.
Krishna M. Pillai - One of the best experts on this subject based on the ideXlab platform.
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Governing Equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows
Composites Part A: Applied Science and Manufacturing, 2002Co-Authors: Krishna M. PillaiAbstract:Abstract Correct modeling of resin flow in liquid composite molding (LCM) processes is important for accurate simulation of the mold-filling process. Recent experiments indicate that the physics of resin flow in woven (also stitched or braided) fiber mats is very different from the flow in random fiber mats. The dual length-scale porous media created by the former leads to the formation of a sink term in the Equation of continuity; such an Equation in combination with the Darcy's law successfully replicate the drooping inlet pressure history, and the region of partial saturation behind the flow-front, for the woven mats. In this paper, the mathematically rigorous volume averaging method is adapted to derive the averaged form of mass and momentum balance Equations for unsaturated flow in LCM. The two phases used in the volume averaging method are the dense bundle of fibers called tows, and the surrounding gap present in the woven fiber mats. Averaging the mass balance Equation yields a Macroscopic Equation of continuity which is similar to the conventional continuity Equation for a single-phase flow except for a negative sink term on the right-hand side of the Equation. This sink term is due to the delayed impregnation of fiber tows and is equal to the rate of liquid absorbed per unit volume. Similar averaging of the momentum balance Equation is accomplished for the dual-scale porous medium. During the averaging process, the dynamic interaction of the gap flow with the tow walls is lumped together as the drag force. A representation theorem and dimensional analysis are used to replace this drag force with a linear function of an average of the relative velocity of the gap fluid with respect to the tow matrix for both the isotropic and anisotropic media. Averaging of the shear stress term of the Navier–Stokes Equation gives rise to a new quantity named the interfacial kinetic effects tensor which includes the effects of liquid absorption by the tows, and the presence of slip velocity on their surface. Though the gradient of the tensor contributes a finite force in the final momentum balance Equation, a scaling analysis leads to its rejection in the fibrous dual-scale porous medium if the permeability of flow through the gaps is small. For such a porous medium, the momentum Equation reduces to the Darcy's law for single-phase flow.
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a model for unsaturated flow in woven fiber preforms during mold filling in resin transfer molding
Journal of Composite Materials, 1998Co-Authors: Krishna M. Pillai, Suresh G. AdvaniAbstract:In this paper, the unsaturated flow encountered in the woven or stitched fiber mats used in RTM is studied for the case of constant rate injection into a 1-D mold. Such fiber mats are characterized as a dual scale porous medium and a two-layer model, based on the difference in the length scales of the intra-tow and inter-tow spaces, is proposed. The mass balance is derived from first principles for an idealized representation of such type of porous media and incorporation of a sink term in the Macroscopic Equation of continuity is established. First a simple sink function, the constant sink, is studied and the downwardly drooping profile of the injection pressure, reported in previous experiments, is shown to be a natural consequence of the absorption of resin by the tows. Next an On/Off type constant sink function is proposed; critical parameters of unsaturated flows such as pore volume ratio and sink strength are introduced. Then the two-layer model with rectangular cross section is extended to two othe...
Chuang Zhang - One of the best experts on this subject based on the ideXlab platform.
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an implicit kinetic scheme for multiscale heat transfer problem accounting for phonon dispersion and polarization
International Journal of Heat and Mass Transfer, 2019Co-Authors: Chuang Zhang, Zhaoli Guo, Songze ChenAbstract:Abstract An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport Equation (BTE) based on the non-gray model with the consideration of phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has to be solved efficiently for varied phonon frequencies and branches. The proposed kinetic scheme is composed of a microscopic iteration and a Macroscopic iteration. The microscopic iteration is capable of automatically adapting with varied phonon mean free path of each phonon frequency and branch by solving the phonon BTE. The energy transfer of all phonons is gathered together by the microscopic iteration to evaluate the heat flux. The temperature field is predicted by a Macroscopic heat transfer Equation according to the heat flux, and the equilibrium state in the phonon BTE is also updated. The combination of the phonon BTE solver and the Macroscopic Equation makes the present method very efficient in a wide range of length scales. Three numerical tests, including the cross-plane, in-plane and nano-porous heat transfer in silicon, demonstrate that the present scheme can handle the phonon dispersion and polarization correctly and predict the multiscale heat transfer phenomena efficiently. Furthermore, the proposed method can be tens of times faster than the typical implicit DOM while keeps the same amount of the memory requirements as Fourier solvers for multiscale heat transfer problems.
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unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon boltzmann transport Equation
Physical Review E, 2017Co-Authors: Chuang Zhang, Zhaoli Guo, Songze ChenAbstract:An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport Equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a Macroscopic Equation to accelerate the convergence in the diffusive regime. The Macroscopic Equation can be taken as a moment Equation for phonon BTE. The heat flux in the Macroscopic Equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the Macroscopic Equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the Macroscopic Equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic Equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
Stephen Whitaker - One of the best experts on this subject based on the ideXlab platform.
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convection dispersion and interfacial transport of contaminants homogeneous porous media
Advances in Water Resources, 1994Co-Authors: Michel Quintard, Stephen WhitakerAbstract:The assumption of local mass equilibrium for describing the transport of a contaminant in an aquifer containing a trapped non-aqueous-phase liquid has been under investigation for the past decade. Laboratory and field studies have shown that this assumption fails under certain circumstances, and heuristic Macroscopic models have been introduced to describe the dispersion process when the assumption of local mass equilibrium is removed from the analysis. In this paper, a Macroscopic model is developed for homogeneous porous media using the method of local volume averaging. The resulting Macroscopic Equation involves a dispersion tensor that is influenced by the mass transfer process, additional convective transport terms, and a linear form for the interfacial mass flux. Two local closure problems are provided that allow one to compute the effective transport coefficients so that theory and experiment can be compared in the absence of adjustable parameters. Numerical methods are used to solve the two local closure problems, and preliminary results are presented for two-dimensional, spatially periodic models of porous media.
