Interaction of fluids and thin structures: Simulation and applications

This dissertation includes the discussion and implementation of the numerical algorithms for treatment of the fluid-solid interface and the fluid-fluid interface, and it also covers three independent applications of the current method. Chapter 1 provides the overall motivation for a numerical method capable of simulating the interaction between fluids and thin structures. The background of the three applications are briefly described. Chapter 2 provides the descriptions of the numerical methods. The Navier-Stokes equations are numerically solved on a fixed Cartesian grid. The sharp and diffuse immersed-boundary methods are combined in one program to separately treat the fluid-solid interface and the fluid-fluid interface. The level-set function is introduced with the mass conservation and stability issues addressed. Numerical validation cases are provided. Chapter 3 describes the application of the current method to the fluid-structure interaction of flapping wings. A two-dimensional model is developed to model the hovering flight of insects. The effect of wing deformation and the role of the wing inertia are addressed by varying the mass ratio and structural flexibility of the wing. The implication of the findings on insect flight is discussed. Chapter 4 describes the application of the current method to the fluid-structure interaction of an array of elastic sheets placed in a free stream. The parameter regime for the system resonance is studied, and the mechanism of the resonance is examined in detail. Chapter 5 describes the application of the current method to the drops going through an asymmetric microfluidic channel that has bumps on one side. The parameters that lead to the asymmetric flow pattern inside the drops are investigated for the purpose of mixing enhancement. Chapter 6 provides a summary of the dissertation. Overall conclusions and contributions are presented, and future work based on the current results is suggested.