Numerical Investigation of Hydrodynamic Forces on Obstacles in Non-Linear Viscosity Flow Fields

Abstract

Abstract This thesis is concerned with the numerical simulation techniques which allow the computation of hydrodynamic forces on obstacles of various shapes submerged in non- linear flow fields. The objective is to optimize these hydrodynamic forces to obtain practical advantages in designing shapes and structures that interact with the fluid. Since the modeling and analysis of the flows with non-linear viscosity models possess no analytical solutions, the Finite Element Method with higher-order elements will be set as a base for the simulations. In CFD, the drag and lift forces are significant quantities of interest for fluid- solid interaction problems. These forces can be computed through the line integrals over the boundary of the obstacles submerged in the flow field. The dimensionless analog of these quantities given by the coefficients of drag and lift to evaluate the quantity of resistance and lift of an object in a fluid field, such as air and water. Besides the other quantities necessary in a fluid flow system, our focus would also be on the calculation of drag and lift coefficients CD and CL. The non-linear viscosity fluid models, including Bingham fluid, Power-law fluid, and Herschel-Bulkley fluids, are considered. The governing equations are non- dimensionalized, and then the Finite Element Method is utilized to discretize the equations. The non-differentiability of the Bingham model is handled with the help of the regularization model proposed by Papanastasiou. It is observed that drag and lift values converge to a specific fixed value for each value of yield stress. It is also observed that the drag coefficient values are increasing with an increase in the yield stress. In contrast, the lift values have an inverse relationship with the yield stress, which confirms the resistance property of yield stress. viii The dependence of pressure on the viscoplastic constitutive law is confirmed. It has been observed that the behavior of pressure is strongly related to the yield property for the non-yielded regions. Thesis Supervisor: Dr. Rashid Mahmood Title: Associate Professor of Mathematics