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.

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.

AN INVESTIGATION OF VARIABLE VALVE TIMING EFFECTS ON HCCI ENGINE PERFORMANCE

The Homogeneous Charge Compression Ignition (HCCI) engine is a promising combustion concept for reducing NOx and particulate matter (PM) emissions and providing a high thermal efficiency in internal combustion engines. This concept though has limitations in the areas of combustion control and achieving stable combustion at high loads. For HCCI to be a viable option for on-road vehicles, further understanding of its combustion phenomenon and its control are essential. Thus, this thesis has a focus on both the experimental setup of an HCCI engine at Michigan Technological University (MTU) and also developing a physical numerical simulation model called the Sequential Model for Residual Affected HCCI (SMRH) to investigate performance of HCCI engines. The primary focus is on understanding the effects of intake and exhaust valve timings on HCCI combustion. For the experimental studies, this thesis provided the contributions for development of HCCI setup at MTU. In particular, this thesis made contributions in the areas of measurement of valve profiles, measurement of piston to valve contact clearance for procuring new pistons for further studies of high geometric compression ratio HCCI engines. It also consists of developing and testing a supercharging station and the setup of an electrical air heater to extend the HCCI operating region. The HCCI engine setup is based on a GM 2.0 L LHU Gen 1 engine which is a direct injected engine with variable valve timing (VVT) capabilities. For the simulation studies, a computationally efficient modeling platform has been developed and validated against experimental data from a single cylinder HCCI engine. In-cylinder pressure trace, combustion phasing (CA10, CA50, BD) and performance metrics IMEP, thermal efficiency, and CO emission are found to be in good agreement with experimental data for different operating conditions. Effects of phasing intake and exhaust valves are analyzed using SMRH. In addition, a novel index called Fuel Efficiency and Emissions (FEE) index is defined and is used to determine the optimal valve timings for engine operation through the use of FEE contour maps.