In this thesis, two numerical modeling methods are used to investigate the thermal conductivity of the polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL). First, an analytical model is used to study the through-plane thermal conductivity from representative physical GDL models informed by microscale computed tomography imaging of four commercially available GDL materials. The effect of the heterogeneity of the through-plane porosity of the GDL and polytetrafluoroethylene (PTFE) treatment is studied and it is noted that the high porosity surface transition regions have a dominating effect over the addition of PTFE in impacting the overall thermal conductivity. Next, the lattice Boltzmann method (LBM) is employed to study both the in-plane and through-plane thermal conductivity of stochastic numerically generated GDL modeling domains. The effect of GDL compression, binder content, PTFE treatment, addition of a microporous layer (MPL), heterogeneous porosity distributions, and water saturation on the thermal conductivity are investigated.

A VOF based multiphase Lattice Boltzmann method that explicitly prescribes kinematic boundary conditions at the interface is developed. The advantage of the method is the direct control over the surface tension value. The details of the numerical method are presented. The Saffman instability, Taylor instability, and flow of deformable suspensions in a channel are used as example-problems to demonstrate the accuracy of the method. The method allows for relatively large viscosity and density ratios.

In this thesis, we develop and test a fundamentally new linear-discontinuous least-squares (LDLS) method for spatial discretization of the one-dimensional (1-D) discrete-ordinates (SN) equations. This new scheme is based upon a least-squares method with a discontinuous trial space. We implement our new method, as well as the lineardiscontinuous Galerkin (LDG) method and the lumped linear-discontinuous Galerkin (LLDG) method. The implementation is in FORTRAN. We run a series of numerical tests to study the robustness, L2 accuracy, and the thick diffusion limit performance of the new LDLS method. By robustness we mean the resistance to negativities and rapid damping of oscillations. Computational results indicate that the LDLS method yields a uniform second-order error. It is more robust than the LDG method and more accurate than the LLDG method. However, it fails to preserve the thick diffusion limit. Consequently, it is viable for neutronics but not for radiative transfer since radiative transfer problems can be highly diffusive.

Magnetohydrodynamic (MHD) investigations of decaying isotropic turbulence and rectangular jets (RJ) are carried out. A novel MHD lattice Boltzmann scheme that combines multiple relaxation time (MRT) parameters for the velocity field with a single relaxation time (SRT) parameter for the Maxwell’s stress tensor is developed for this study. In the MHD homogeneous turbulence studies, the kinetic/magnetic energy and enstrophy decays, kinetic enstrophy evolution, and vorticity alignment with the strain-rate tensor are evaluated to assess the key physical MHD turbulence mechanisms. The magnetic and kinetic energies interact and exchange through the influence of the Lorentz force work. An initial random fluctuating magnetic field increases the vortex stretching and forward cascade mechanisms. A strong uniform mean magnetic field increases the anisotropy of the turbulent flow field and causes inverse cascading. In the RJ studies, an investigation into the MHD effects on velocity, instability, and the axis-switching phenomena is performed at various magnetic field strengths and Magnetic Reynolds Numbers. The magnetic field is found to decelerate the jet core, inhibit instability, and prevent axis-switching. The key physical mechanisms are: (i) the exchange of energy between kinetic and magnetic modes and (ii) the magnetic field effect on the vorticity evolution. From these studies, it is found that magnetic field influences momentum, vorticity, and energy evolution and the degree of modification depends on the field strength. This interaction changes vortex evolution, and alters turbulence processes and rectangular jet flow characteristics. Overall, this study provides more insight into the physics of MHD flows, which suggests possible applications of MHD Flow Control.

¡@¡@¡@¡@¡@¡@¡@­^¡@¤å¡@ºK¡@­n¡@¡@¡@¡@¡@¡@¡@ Heat transfer of a molten splat to a thin layer rapidly solidified on a cold substrate and the heat transfer coefficient at the bottom surface of a splat is extensively and self-consistently investigated. Rapid freezing in the splat is governed by a nonequilibrium kinetics at the solidification front in contrast to the melting in the substrate simulated by the traditional phase change problem. Solving one-dimensional unsteady heat conduction equations and accounting for distinct properties between phases and splat and substrate, the results show the effects of dimensionless parameters such as the dimensionless kinetic coefficient, stefan number, latent heat ratio, initial, equilibrium melting, and nucleation temperature, and conductivity, density, and specific heat ratios between solid and liquid and splat and substrate on unsteady temperature fields and freezing and melting rates in the splat and substrate and on unsteady variation of Biot number are presented. The unsteady variation of the heat coefficient or Biot number can be divided by five regimes: liquid splat-solid substrate, liquid splat-liquid substrate, solid splat-solid substrate, solid splat-liquid substrate, and the nucleation of the splat. Appropriate choices of dimensionless parameters to control the time for freezing and melting of the splat and substrate and an understanding and estimation of the heat coefficient at the bottom surface of the splat therefore are presented. The velocity distribution function and transport variables of the positive ions and electrons in the collisionless presheath and sheath of a plasma near a wall partially reflecting ions and electrons are determined from a kinetic analysis. Since velocities of the ions and electrons near the wall are highly non-Maxwell-Boltzmann distributions, accurate predictions of transport variables such as density, fluid velocity, mean pressure, fluidlike viscous stress and conduction require kinetic analysis. The result find that dimensionless transport variables of ions and electrons in the presheath and sheath can be exactly expressed in terms of transcendental functions determined by dimensionless independent parameters of ions and electrons reflectivities of the wall, ion-to-electron mass ratio, charge number and electron-to-ion temperature ratio at the presheath edge. The effects of the parameters on transport variables at the wall are also obtained. The computed transport variables in the presheath and sheath show agreement with available theoretical data for a completely absorbing wall.

Thesis (Ph. D.)--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 64-65).

Thesis (M.S.)--University of Delaware, 2009. / Principal faculty advisor: Xiaoming Li, Dept. of Electrical & Computer Engineering. Includes bibliographical references.

A new method has been developed to incorporate particles with internal structure into the framework of the Variance Reduction method [17] for solving the discrete velocity Boltzmann Equation. Internal structure in the present context refers to physical phenomena like rotation and vibration of molecules consisting of two or more atoms. A gas in equilibrium has all modes of internal energy at the same temperature as the translational temperature. If the gas is in a non-equilibrium state, translational temperature and internal temperatures tend to proceed towards an equilibrium state during equilibration, but they all do so at different relaxation rates. In this thesis, rotational energy of a distribution of molecules is modeled as a single value at a point in a discrete velocity space; this represents the average rotational energy of molecules at that specific velocity. Inelastic collisions are the sole mechanism of translational and rotational energy exchange, and are governed by a modified Landau-Teller equation. The method is tested for heat bath simulations, or homogeneous relaxations, and one dimensional shock problems. Homogeneous relaxations demonstrate that the rotational and translational temperatures equilibrate to the correct final temperature, which can be predicted by conservation of energy. Moreover, the rates of relaxation agree with the direct simulation Monte Carlo (DSMC) method with internal energy for the same input parameters. Using a fourth order method for convecting mass along with its corresponding internal energy, a one dimensional Mach 1.71 normal shock is simulated. Once the translational and rotational temperatures equilibrate downstream, the temperature, density and velocity, predicted by the Rankine-Hugoniot conditions, are obtained to within an error of 0.5%. The result is compared to a normal shock with the same upstream flow properties generated by the DSMC method. Internal vibrational energy and a method to use Larsen Borgnakke statistical sampling for inelastic collisions is formulated in this text and prepared in the code, but remains to be tested. / text

In this work, the lattice Boltzmann method (LBM) was validated for direct numerical simulation (DNS) of wall-bounded turbulent flows. The LBM is a discrete-particle-based method that numerically solves the Boltzmann equation as opposed to conventional DNS methods that are based on the Navier-Stokes (NS) equations. The advantages of the LBM are its simple implementation, its ability to handle complex geometries, and its scalability on modern high-performance computers. An LBM code was developed and used to simulate fully-developed turbulent channel flow. In order to validate the results, the turbulence statistics were compared to those calculated from a conventional NS-based finite difference (FD) simulation. In the present study, special care was taken to make sure the computational domains for LBM and FD simulations were the same. Similar validation studies in the literature have used LBM simulations with smaller computational domains in order to reduce the computational cost. However, reducing the size of the computational domain affects the turbulence statistics and confounds the results of the validation. The turbulence statistics calculated from the LBM and FD simulations were found to agree qualitatively; however, there were several significant deviations, particularly in the variance profiles. The largest discrepancy was in the variance of the pressure fluctuations, which differed by approximately 7%. Given that both the LBM and FD simulations resolved the full range of turbulent scales and no models were used, this error was deemed to be significant. The cause of the discrepancy in the pressure variance was found to be the compressibility of the LBM. The LBM allows the density to vary, while the FD method does not since it solves the incompressible form of the NS equations. The effect of the compressibility could be reduced by lowering the Mach number, but this would come at the cost of significantly increasing the computational cost. Therefore, the conclusion of this work is that, while the LBM is capable of producing accurate solutions for incompressible turbulent flows, it is significantly more expensive than conventional methods for simple wall-bounded turbulent flows. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2011-09-15 23:24:09.968

Proefschrift Universiteit van Amsterdam. / Met lit.opg. en samenvatting in het Nederlands.