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.

Analysis of a Non-Traditional Micro Tube Hydroforming Process

As the demand for miniature products and components continues to increase, the need for manufacturing processes to provide these products and components has also increased. To meet this need, successful macroscale processes are being scaled down and applied at the microscale. Unfortunately, many challenges have been experienced when directly scaling down macro processes. Initially, frictional effects were believed to be the largest challenge encountered. However, in recent studies it has been found that the greatest challenge encountered has been with size effects. Size effect is a broad term that largely refers to the thickness of the material being formed and how this thickness directly affects the product dimensions and manufacturability. At the microscale, the thickness becomes critical due to the reduced number of grains. When surface contact between the forming tools and the material blanks occur at the macroscale, there is enough material (hundreds of layers of material grains) across the blank thickness to compensate for material flow and the effect of grain orientation. At the microscale, there may be under 10 grains across the blank thickness. With a decreased amount of grains across the thickness, the influence of the grain size, shape and orientation is significant. Any material defects (either natural occurring or ones that occur as a result of the material preparation) have a significant role in altering the forming potential. To date, various micro metal forming and micro materials testing equipment setups have been constructed at the Michigan Tech lab. Initially, the research focus was to create a micro deep drawing setup to potentially build micro sensor encapsulation housings. The research focus shifted to micro metal materials testing equipment setups. These include the construction and testing of the following setups: a micro mechanical bulge test, a micro sheet tension test (testing micro tensile bars), a micro strain analysis (with the use of optical lithography and chemical etching) and a micro sheet hydroforming bulge test. Recently, the focus has shifted to study a micro tube hydroforming process. The intent is to target fuel cells, medical, and sensor encapsulation applications. While the tube hydroforming process is widely understood at the macroscale, the microscale process also offers some significant challenges in terms of size effects. Current work is being conducted in applying direct current to enhance micro tube hydroforming formability. Initially, adding direct current to various metal forming operations has shown some phenomenal results. The focus of current research is to determine the validity of this process.