Computation of propulsion-related flowfields using unstructured adaptive meshes

In this paper, we describe a computational fluid dynamics (CFD) technique based on unstructured triangular/tetrahedral meshes. A finite-volume scheme is used in conjunction with a multi-stage Runge-Kutta algorithm. Convergence enhancements in the form of dual time-stepping and time-derivative preconditioning are used to overcome the limitations of conventional multi-stage schemes. The method is applied to propulsion-related flows and shown to perform satisfactorily

NON-GRAY PHONON TRANSPORT USING A HYBRID BTE-FOURIER SOLVER

Non-gray phonon transport solvers based on the Boltzmann transport equation (BTE) are frequently employed to simulate sub-micron thermal transport. Typical solution procedures using sequential solution schemes encounter numerical difficulties because of the large spread in scattering rates. For frequency bands with very low Knudsen numbers, strong coupling between the directional BTEs results in slow convergence for sequential solution procedures. In this paper, we present a hybrid BTE-Fourier model which addresses this issue. By establishing a phonon group cutoff (say Kn=0.1), phonon bands with low Knudsen numbers are solved using a modified Fourier equation which includes a scattering term as well as corrections to account for boundary temperature slip. Phonon bands with high Knudsen numbers are solved using a BTE solver. Once the governing equations are solved for each phonon group, their energies are then summed to find the total lattice energy and correspondingly, the lattice temperature. An iterative procedure combining the lattice temperature determination and the solutions to the modified Fourier and BTE equations is developed. The procedure is shown to work well across a range of Knudsen numbers

SOLUTION OF THE PHONON BOLTZMANN TRANSPORT EQUATION EMPLOYING RIGOROUS IMPLEMENTATION OF PHONON CONSERVATION RULES

ABSTRACT A finite volume scheme is developed to solve the phonon Boltzmann transport equation in an energy form accounting for phonon dispersion and polarization. The physical space and the first Brillouin zone are discretized into finite volumes and the phonon BTE is integrated over them. Second-order accurate differencing schemes are used for the discretization. The scattering term employs a rigorous implementation of phonon momentum and energy conservation laws in determining the rate of normal and Umklapp processes. The method is applied to a variety of bulk silicon and silicon thin-film conduction problems and shown to perform satisfactorily

Resistance network-based thermal conductivity model for metal foams

A network model for the estimation of effective thermal conductivity of open-celled metal foams is pre-sented. A nodal network representation of three aluminum foam samples from DUOCEL – 10 ppi, 20 ppi and 40 ppi – is constructed out of X-ray microtomography data obtained by computed tomography (CT) scanning of the samples using a commercial CT scanner. Image processing and 3D skeletonization are performed with commercially available image processing software. The effective thermal conductivity is estimated through a 1D conduction model, representing individual ligaments as an effective thermal resistance using the topological information from the scan data. The effective thermal conductivity data thus obtained are compared with the Lemlich theory and other pore-based models. Further, microstruc-tural characterization of foam features – pore size, ligament thickness, ligament length and pore shapes – is performed. All the three foam samples are observed to have similar pore shapes and volumetric poros-ity, while the other features scale with the pore size. For a given porosity the computed permeability is found to scale as the square of the pore diameter, as also noted by previous researchers

Mechanism of Thermal Conductivity Reduction in Few-Layer Graphene

Using the linearized Boltzmann transport equation and perturbation theory, we analyze the reduction in the intrinsic thermal conductivity of few-layer graphene sheets accounting for all possible three-phonon scattering events. Even with weak coupling between layers, a significant reduction in the thermal conductivity of the out-of-plane acoustic modes is apparent. The main effect of this weak coupling is to open many new three-phonon scattering channels that are otherwise absent in graphene. However, reflection symmetry is only weakly broken with the addition of multiple layers, and ZA phonons still dominate thermal conductivity. We also find that reduction in thermal conductivity is mainly caused by lower contributions of the higher-order overtones of the fundamental out-of-plane acoustic mode. The results compare remarkably well over the entire temperature range with measurements of graphene and graphite

Modeling of subcontinuum thermal transport across semiconductor-gas interfaces

A physically rigorous computational algorithm is developed and applied to calculate subcontinuum thermal transport in structures containing semiconductor-gas interfaces. The solution is based on a finite volume discretization of the Boltzmann equation for gas molecules (in the gas phase) and phonons (in the semiconductor). A partial equilibrium is assumed between gas molecules and phonons at the interface of the two media, and the degree of this equilibrium is determined by the accommodation coefficients of gas molecules and phonons on either side of the interface. Energy balance is imposed to obtain a value of the interface temperature. The classic problem of temperature drop across a solid-gas interface is investigated with a simultaneous treatment of solid and gas phase properties for the first time. A range of transport regimes is studied, varying from ballistic phonon transport and free molecular flow to continuum heat transfer in both gas and solid. A reduced-order model is developed that captures the thermal resistance of the gas-solid interface. The formulation is then applied to the problem of combined gas-solid heat transfer in a two-dimensional nanoporous bed and the overall thermal resistance of the bed is characterized in terms of the governing parameters. These two examples exemplify the broad utility of the model in practical nanoscale heat transfer applications