Numerical study of flexible flapping wings.

摘要

In this study, we apply a strong-coupling approach to simulate highly flexible flapping wings interacting with surrounding fluid flows for both two-dimensional configurations and three-dimensional configurations. In this approach, the elastic body and its interaction with the fluid are implemented as body/surface force terms. In this way, the fluid and solid can be solved by a combined and modified form of typical Navier-Stokes equations in a global Eulerian framework. To control the flapping motion of the wings, direct-forcing type of Immersed Boundary (IB) method is implemented into the above approach to provide the "skeleton" of the wings. Prescribed flapping motion is defined on the "skeleton" , and the rest of the wing moves passively through elasticity and fluid-structure interaction (FSI).;First, the approach is applied on some benchmark cases for validation purpose. There are four cases: 1) two-dimensional stationary rigid cylinder; 2) three-dimensional stationary rigid sphere; 3) three-dimensional pitching panel; and 4) viscoelastic particle in a free shear layer. The first two cases are classical two-dimensional and three-dimensional benchmarks for incompressible flow passing objects, the third case represents problems with a moving boundary in prescribed motion; and the last case is to test the performance for strong fluid-structure interaction involving a flexible body. For all cases, our new algorithm performs well in a comparison to other literatures.;This new algorithm is then used to study the propulsion characteristics of a flexible two-dimensional NACA0012 airfoil, which is under active plunging defined by control cells and corresponding passive pitching motion. The propulsion of airfoils with different elastic moduli and at different flapping frequencies and amplitudes are studied. With different input parameters, various wake structures can be observed. As a result, the coupled plunging-pitching motion can be either drag-producing or thrust-producing. Finally, passive pitching angle &thetas; and nominal angle of attack α for flexible wings are defined to characterize the flapping motion. It is found that &thetas; needs to be greater than 0.262 and α needs to be greater than 0.295 to generate thrust instead of drag for the flapping motion within current parametric matrix.;The last step towards the study of flapping wings is to extend the code to three-dimensional cases. The algorithm and the corresponding computer code has been first extended to a three-dimensional serial version then to a parallel HPC version for beowulf clusters. With the high-efficiency of the parallel code, we were able to run the following four cases with acceptable computational time. There are three test cases: rectangular plates in heaving motion, a rectangular wing in root-flapping motion, and a triangular wing in root-flapping motion. The last case is a curved wing in root-flapping motion which is studied in more details. The curved wing case uses the wing shape from a toy MAV and matches approximately the motion, angle of attack, and other control parameters with the MAV performing "in live" and in experiments of a collaborative effort. The numerical study focuses on the vortex structures, the force, and the relation to control parameters (e.g. angle of attack).;With the data available from a collaborative experimental work, we are able to further benchmark our simulation algorithm and computer code. At the end of the dissertation, we show the comparison of numerical data with experimental data for two cases: 1) two-dimensional flexible airfoil heaving in a oil tank; 2) three-dimensional curved wing flapping in a wind tunnel. The cases show good match for characteristics both qualitatively and quantitatively.