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.

Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.

Biochemical Conversions of Lignocellulosic Biomass for Sustainable Fuel-Ethanol Production in the Upper Midwest

Biofuels are an increasingly important component of worldwide energy supply. This research aims to understand the pathways and impacts of biofuels production, and to improve these processes to make them more efficient. In Chapter 2, a life cycle assessment (LCA) is presented for cellulosic ethanol production from five potential feedstocks of regional importance to the upper Midwest - hybrid poplar, hybrid willow, switchgrass, diverse prairie grasses, and logging residues - according to the requirements of Renewable Fuel Standard (RFS). Direct land use change emissions are included for the conversion of abandoned agricultural land to feedstock production, and computer models of the conversion process are used in order to determine the effect of varying biomass composition on overall life cycle impacts. All scenarios analyzed here result in greater than 60% reduction in greenhouse gas emissions relative to petroleum gasoline. Land use change effects were found to contribute significantly to the overall emissions for the first 20 years after plantation establishment. Chapter 3 is an investigation of the effects of biomass mixtures on overall sugar recovery from the combined processes of dilute acid pretreatment and enzymatic hydrolysis. Biomass mixtures studied were aspen, a hardwood species well suited to biochemical processing; balsam, a high-lignin softwood species, and switchgrass, an herbaceous energy crop with high ash content. A matrix of three different dilute acid pretreatment severities and three different enzyme loading levels was used to characterize interactions between pretreatment and enzymatic hydrolysis. Maximum glucose yield for any species was 70% oftheoretical for switchgrass, and maximum xylose yield was 99.7% of theoretical for aspen. Supplemental β-glucosidase increased glucose yield from enzymatic hydrolysis by an average of 15%, and total sugar recoveries for mixtures could be predicted to within 4% by linear interpolation of the pure species results. Chapter 4 is an evaluation of the potential for producing Trichoderma reesei cellulose hydrolases in the Kluyveromyces lactis yeast expression system. The exoglucanases Cel6A and Cel7A, and the endoglucanase Cel7B were inserted separately into the K. lactis and the enzymes were analyzed for activity on various substrates. Recombinant Cel7B was found to be active on carboxymethyl cellulose and Avicel powdered cellulose substrates. Recombinant Cel6A was also found to be active on Avicel. Recombinant Cel7A was produced, but no enzymatic activity was detected on any substrate. Chapter 5 presents a new method for enzyme improvement studies using enzyme co-expression and yeast growth rate measurements as a potential high-throughput expression and screening system in K. lactis yeast. Two different K. lactis strains were evaluated for their usefulness in growth screening studies, one wild-type strain and one strain which has had the main galactose metabolic pathway disabled. Sequential transformation and co-expression of the exoglucanase Cel6A and endoglucanase Cel7B was performed, and improved hydrolysis rates on Avicel were detectable in the cell culture supernatant. Future work should focus on hydrolysis of natural substrates, developing the growth screening method, and utilizing the K. lactis expression system for directed evolution of enzymes.