Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Water transport in complex, non-wetting porous layers with applications to water management in low temperature fuel cells

An experimental setup was designed to visualize water percolation inside the porous transport layer, PTL, of proton exchange membrane, PEM, fuel cells and identify the relevant characterization parameters. In parallel with the observation of the water movement, the injection pressure (pressure required to transport water through the PTL) was measured. A new scaling for the drainage in porous media has been proposed based on the ratio between the input and the dissipated energies during percolation. A proportional dependency was obtained between the energy ratio and a non-dimensional time and this relationship is not dependent on the flow regime; stable displacement or capillary fingering. Experimental results show that for different PTL samples (from different manufacturers) the proportionality is different. The identification of this proportionality allows a unique characterization of PTLs with respect to water transport. This scaling has relevance in porous media flows ranging far beyond fuel cells. In parallel with the experimental analysis, a two-dimensional numerical model was developed in order to simulate the phenomena observed in the experiments. The stochastic nature of the pore size distribution, the role of the PTL wettability and morphology properties on the water transport were analyzed. The effect of a second porous layer placed between the porous transport layer and the catalyst layer called microporous layer, MPL, was also studied. It was found that the presence of the MPL significantly reduced the water content on the PTL by enhancing fingering formation. Moreover, the presence of small defects (cracks) within the MPL was shown to enhance water management. Finally, a corroboration of the numerical simulation was carried out. A threedimensional version of the network model was developed mimicking the experimental conditions. The morphology and wettability of the PTL are tuned to the experiment data by using the new energy scaling of drainage in porous media. Once the fit between numerical and experimental data is obtained, the computational PTL structure can be used in different types of simulations where the conditions are representative of the fuel cell operating conditions.

MAGNETO-PHOTONIC CRYSTALS FOR OPTICAL SENSING APPLICATIONS

Among the optical structures investigated for optical sensing purpose, a significant amount of research has been conducted on photonic crystal based sensors. A particular advantage of photonic crystal based sensors is that they show superior sensitivity for ultra-small volume sensing. In this study we investigate polarization changes in response to the changes in the cover index of magneto-optic active photonic band gap structures. One-dimensional photonic-band gap structures fabricated on iron garnet materials yield large polarization rotations at the band gap edges. The enhanced polarization effects serve as an excellent tool for chemical sensing showing high degree of sensitivity for photonic crystal cover refractive index changes. The one dimensional waveguide photonic crystals are fabricated on single-layer bismuth-substituted rare earth iron garnet films ((Bi, Y, Lu)3(Fe, Ga)5O12 ) grown by liquid phase epitaxy on gadolinium gallium garnet substrates. Band gaps have been observed where Bragg scattering conditions links forward-going fundamental waveguide modes to backscattered high-order waveguide modes. Large near-band-edge polarization rotations which increase progressively with backscattered-mode order have been experimentally demonstrated for multiple samples with different composition, film thickness and fabrication parameters. Experimental findings are supported by theoretical analysis of Bloch modes polarization states showing that large near stop-band edge rotations are induced by the magneto-photonic crystal. Theoretical and experimental analysis conducted on polarization rotation sensitivity to waveguide photonic crystal cover refractive index changes shows a monotonic enhancement of the rotation with cover index. The sensor is further developed for selective chemical sensing by employing Polypyrrole as the photonic crystal cover layer. Polypyrrole is one of the extensively studied conducting polymers for selective analyte detection. Successful detection of aqueous ammonia and methanol has been achieved with Polypyrrole deposited magneto-photonic crystals.