The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.
In this paper, an unstructured Chimera mesh method is used to compute incompressible flow around a rotating body. To implement the pressure correction algorithm on unstructured overlapping sub-grids, a novel interpolation scheme for pressure correction is proposed. This indirect interpolation scheme can ensure a tight coupling of pressure between sub-domains. A moving-mesh finite volume approach is used to treat the rotating sub-domain and the governing equations are formulated in an inertial reference frame. Since the mesh that surrounds the rotating body undergoes only solid body rotation and the background mesh remains stationary, no mesh deformation is encountered in the computation. As a benefit from the utilization of an inertial frame, tensorial transformation for velocity is not needed. Three numerical simulations are successfully performed. They include flow over a fixed circular cylinder, flow over a rotating circular cylinder and flow over a rotating elliptic cylinder. These numerical examples demonstrate the capability of the current scheme in handling moving boundaries. The numerical results are in good agreement with experimental and computational data in literature.
C o m p u t a t i o n of Flow over a R o t a t i n g B o d y on U n s t r u c t u r e d C h i m e r a M e s hX. Zhang*, G. W. He, S. Z. Ni LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, ChinaEmail: zhangx@lnm.imech, ac.cn Abstract Flow around moving boundary is ubiquitous in engineering applications. To increse the efficienly of the algorithm to handle moving boundaries is still a major challenge in Computational Fluid Dynamics (CFD). The Chimera grid method is one type of method to handle moving boundaries. A concept of domain de-composition has been proposed in this paper. In this method, sub-domains are meshed independently and governing equations are also solved separately on them. The Chimera grid method was originally used only on structured (curvilinear) meshes. However, in a problem which involves both moving boundary and complex geometry, the number of sub-domains required in a traditional (structured) Chimera method becomes fairly large. Thus the time required in the interior boundary locating, link-building and data exchanging also increases. The use of unstructured Chimera grid can reduce the time consumption significantly by the reduction of domain(block) number. Generally speaking, unstructured Chimera grid method has not been developed. In this paper, a wellknown pressure correction scheme-SIMPLEC is modified and implemented on unstructured Chimera mesh. A new interpolation scheme regarding the pressure correction is proposed to prevent the possible decoupling of pressure. A moving-mesh finite volume approach is implemented in an inertial reference frame. This approach is then used to compute incompressible flow around a rotating circular and elliptic cylinder. These numerical examples demonstrate the capability of the proposed scheme in handling moving boundaries. The numerical results are in good agreement with other experimental and computational data in literature. The method proposed in this paper can be efficiently applied to more challenge cases such as free-falling objects or heavy particles in fluid. Mech Eng, 1995; 125:235-55 3. Zhang X. Computation of viscous incompressible flow using pressure correction method on unstructured Chimera grid. Int J Comput Fluid Dynamics, 2007; (In Press).
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