The Immersed Boundary Projection Method and Its Application to Simulation and Control of Flows Around Low-Aspect-Ratio Wings

Citation

Taira, Kunihiko (Sam) (2008) The Immersed Boundary Projection Method and Its Application to Simulation and Control of Flows Around Low-Aspect-Ratio Wings. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VSDD-P465. https://resolver.caltech.edu/CaltechETD:etd-05232008-124342

Abstract

First, we present a new formulation of the immersed boundary method that is algebraically identical to the traditional fractional step algorithm. This method, called the immersed boundary projection method, allows for the simulations of incompressible flows over arbitrarily shaped bodies under motion and/or deformation in both two and three dimensions. The no-slip condition along the immersed boundary is enforced simultaneously with the incompressibility constraint through a single projection. The boundary force is determined implicitly without any constitutive relations for the rigid body formulation, which in turn allows the use of high CFL numbers in our simulations compared to past methods.

Next, the above immersed boundary projection method is used to analyze three-dimensional separated flows around low-aspect-ratio flat-plate wings. A number of simulations highlighting the unsteady nature of the separated flows are performed for Re = 300 and 500 with various aspect ratios, angles of attack, and planform geometries. The aspect ratio and angle of attack are found to have a large influence on the stability of the wake profile and the force experienced by the low-aspect-ratio wing. At early times, following an impulsive start, topologies of the wake vortices are found to be the same across different aspect ratios and angles of attack. Behind low-aspect-ratio rectangular plates, leading-edge vortices form and eventually separate as hairpin vortices following the start-up. This phenomenon is found to be similar to dynamic stall observed behind pitching plates. The detached structure would then interact with the tip vortices, reducing the downward velocity induced by the tip vortices acting upon the leading-edge vortex. At large time, depending on the aspect ratio and angles of attack, the wakes reach one of the three states: (i) a steady state, (ii) a periodic unsteady state, or (iii) an aperiodic unsteady state. We have observed that the tip effects in three-dimensional flows can stabilize the flow and also exhibit nonlinear interaction with the shedding vortices.

At last, we apply steady blowing to separated flows behind the low-aspect-ratio rectangular wings. The objective of the flow control is to enhance lift at post-stall angles of attack by changing the dynamics of the wake vortices. This controller strengthens the tip vortices by engulfing the trailing-edge vortex sheet to increase the downward thrust and the downward induced velocity onto the leading-edge vortices. The tip vortices that are traditionally considered as an aerodynamic nuisance, have been used favorably to increase lift in post-stall flows for the considered low-aspect-ratio wings.

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