Development Of Immersed Boundary Method And Its Applications

Moving boundary problems occur extensively in nature and engineering applications. Typical examples are insect flight and flow control of circular cylinders. Due to the amazing flight skills of insects, the study on the flapping motions of foils has aroused great interest. Although there have been a number of experimental and numerical investigations about the influence of different motion parameters of a flapping foil on its flight performance, very few studies have been focused on the influence of the asymmetry in flapping stroke. In fact, the asymmetry in flapping stoke is a common feature in real insect flight. In this work, a numerical investigation on the dynamic performance of a flapping foil with asymmetric motion is carried out by using a velocity correction-based immersed boundary method(IBM) for incompressible flows. The effect of downstroke ratio, time duration to perform rotation and phase difference between the rotation and the translation on a flapping foil is analyzed. Besides, this method is also applied to investigate the flow control of a circular cylinder by using a flexible filament. The cylinder is either fixed or elastically mounted, and the filament is attached to the base of the cylinder. Its leading end is fixed and its trailing end is free to flap. The effects of the filament on the flow control of the cylinder are systematically examined by varying the bending coefficient and length of the filament. It is found that the fluctuation of lift force and vortex shedding of a fixed cylinder and the vortex-induced vibration of an elastically mounted cylinder can be suppressed efficiently.Moreover, a boundary condition-enforced immersed boundary method for simulating compressible viscous flows is also proposed in this work. It is developed from the implicit velocity correction-based IBM for incompressible flows. However, the IBM for incompressible flows cannot be directly applied to simulate compressible flows. This is because the immersed boundary has a great effect on velocity, temperature, density and pressure fields in compressible flows, but the IBM for incompressible flows has no mechanism to correct the density and pressure fields. To overcome this difficulty, in this work, the momentum field is firstly corrected by converting the no-slip velocity condition to the momentum condition. After that, from the continuity equation, the density correction can be made from the momentum correction. Then, the corrected velocity field can be given from the corrected momentum field and corrected density. Similar to the correction of momentum field, the temperature field can be corrected from the given temperature condition. Finally, the pressure can be obtained from the equation of state by using the corrected density and temperature. In this way, all the flow variables are corrected and the given physical boundary conditions are accurately implemented. To validate the proposed method, the flows over a stationary cylinder and one or two airfoils at different Mach and Reynolds numbers are simulated. Compared to the results in the literature, good agreement is achieved.