Wavy Swing Deformable Body Unsteady Viscous Flow Around A Numerical Study

Numerical analysis is carried out to investigate the viscous flow around a flexible body by solving two-dimensional incompressible Navier-Stokes equations. The lateral motion of the flexible body is in the form of a traveling wave, which is similar to the backbone undulation of swimming animals. In the present study, we use the undulatory flexible body as a simplified model to deal with the relevant mechanisms of swimming animals.The two-dimensional Navier-Stokes equations are numerically solved using Space-time FEM/Galerkin Least Squares method. In space-time formulations, finite element method is employed for both temporal and spatial discretization, which proves to be effective for solving moving boundary problems. The resultant nonlinear algebraic equations via space-time finite element discretization of Navier-Stokes equations are iteratively solved using Newton-Raphson method. At each iterative substep, the linear equations are solved using iterative GMRES solver. "Pseudo Elastic Body" mesh moving technique is employed to treat moving grid nodes. A code solver is developed and verified to be reliable based on extensive validations.Three typical problems are studied in this dissertation. We have obtained the following results and conclusions:(1) Viscous flow around a traveling wavy plate. The influences of some typical parameters, including the phase speed, amplitude and relative wavelength, on the flow structures and force characteristics are analyzed. As the phase speed c increases, the form drag due to the pressure distribution decreases, even to be negative and act as a thrust as c exceeds a critical value. The friction drag increases somewhat as c increases. The total drag, i.e. summation of form drag and friction drag, decreases monotonically as c increases and becomes negative when c exceeds a threshold value, which means the waving plate is propelled by thrust. The total power consumption reaches its minimum value around c = 1.2. As c increases, the size of the vortices shed from the plate decreases, the lateral width of vortices array decreases. When the amplitude of the waving plate increases, the drag force decreases, but the total power consumption increases. Thus, there exists an optimal amplitude, at which the plate is propelled at an appropriate expense. The relative wavelength has a significant effect on the lateral force. As the relative wavelength increases, the lateral force decreases remarkably. Compared with uniform amplitude distribution, when the amplitude increases gradually from head to tail, the plate is propelled at relatively smaller power consumption, and the propulsion efficiency is increased.(2) Viscous flow around traveling wavy foils arranged side-by-side. Viscous flow around a single traveling wavy foil and an array of foils arranged side by side are analyzed. For the viscous flow around a traveling wavy foil, the effect of phase speed on the flow structure and force characteristics is similar to that of a traveling wavy plate. Viscous flows around traveling wavy foils are investigated for two typical cases: the neighboring foils undulate laterally inphase and antiphase. The effect of lateral distance between neighboring foils on the flow structures and force characteristics are examined. In the inphase cases, as the lateral distance increases, the drag force and total power consumption decrease, and three typical vortex structures are found.