UC Irvine

This Dissertation investigates the three-dimensional nature of dynamic stall and introduces a new variational formulation for vortex dynamics, both contributing to a deeper understanding of aerodynamic phenomena. The first part of the research involves numerical simulation of the flow around a harmonically pitching NACA 0012 airfoil using Unsteady-Reynolds-Averaged Navier–Stokes (URANS) and Detached Eddy Simulation (DES) solvers, including Delayed-DES (DDES) and Improved-DDES (IDDES). Both two- and three-dimensional simulations are conducted, with results compared against experimental measurements. It is found that three-dimensional simulations, particularly those using DES solvers, outperform two-dimensional ones in capturing the different stages of dynamic stall and predicting the lift dynamics. The IDDES simulations, which are inherently three-dimensional, accurately model the cascaded amalgamation of vortices forming the dynamic stall vortex, supporting the hypothesis that dynamic stall is intrinsically a three-dimensional phenomenon. Since the complex flow in dynamic stall is mainly related to vortex-vortex interactions, richer models of vortex dynamics are needed to develop a reduced-order model for dynamic stall in the future. For this goal, the second part of the study introduces a new variational formulation for vortex dynamics based on the principle of least action. Unlike the traditional Kirchhoff-Routh (KR) function, which describes vortex dynamics through first-order differential equations of motion derived from the Biot-Savart law, this new formulation results in second-order differential equations that define vortex accelerations. This leads to more complex dynamics, such as unique patterns formed by equal-strength, counter-rotating vortices with different initial velocities. Moreover, the new model can incorporate arbitrary external body forces; when an electrodynamic force is considered, it reveals rich, counter-intuitive behaviors that cannot be captured by the KR formulation.