UCLA

Unsteady fluid dynamics at low to moderate Reynolds number, i.e. O(10²)∼ O(10⁴), has drawn increasing attention during the past decades as a result of the growing interest in the biological and bio-inspired locomotion like the flying and swimming of different creatures. In this work, several numerical methods, including low-order modeling and high-fidelity simulations, are developed and explored, which target to explore and understand the moving capabilities observed in nature as well as provide general guidances for the future development of similar agile air/underwater vehicles.

In the first part of the work, a low-order point vortex model for the two-dimenional unsteady aerodynamics of a flat plate wing section is developed. The flow field is described by several point vortices, which can be divided into two categories. A variable-strength vortex is referred to the one just released from either leading or trailing edges of the sharp edge and the strength of each is determined by enforcing the Kutta condition at the edges. The vortex is moved into the second category when its strength reaches its extremum and is frozen. The motion of the fixed-strength vortices is easy to find according to the potential flow theory, while the motion of the vortices with variable-strength requires special evolution equations. Two ways are considered in our work. In the first approach, the Brown-Michael equation is used in order to ensure that no spurious force is generated by the branch cut associated with each vortex. In the second approach, a new evolution equation for a vortex by equating the rate of change of its impulse with that of an equivalent surrogate vortex with identical properties but constant strength. The results of the new model, when applied to a pitching or perching plate, agree better with experiments and high-fidelity simulations than the Brown-Michael model, using fewer than ten degrees of freedom. The model performance is also assessed on the impulsive start of a flat plate at various angles of attack.

In the second part of the work, a strong coupling algorithm is presented for simulating the dynamic interactions between incompressible viscous flows and rigid-body systems in both two- and three-dimensional problems. The incompressible flow is solved by the vorticity-based immersed boundary projection method, and dynamical equations for arbitrary rigid-body systems are also developed. The resulting partitioned system of equations is solved with a simple, physically-motivated relaxation scheme, based on an identification of virtual inertia from the fluid. Several two- and three-dimensional numerical examples are conducted to validate and demonstrate the method, including a falling cylinder, flapping of flexible wings, self-excited oscillations of a system of linked plates in a free stream, passive pivoting of a finite aspect ratio plate in a free stream and gravity and self-propelled motion of a flexible flapping tail. The results from the current method are compared with previous experimental and numerical results and good agreements are achieved.