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Special Section: Computational Fluid Mechanics and Fluid–Structure Interaction

Space-Time Computational Techniques for the Aerodynamics of Flapping Wings

[+] Author and Article Information
Kenji Takizawa

Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study,  Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan

Bradley Henicke, Anthony Puntel, Timothy Spielman

Department of Mechanical Engineering,  Rice University, MS 321, 6100 Main Street, Houston, TX 77005

Tayfun E. Tezduyar

Department of Mechanical Engineering,  Rice University, MS 321, 6100 Main Street, Houston, TX 77005tezduyar@rice.edu

J. Appl. Mech 79(1), 010903 (Dec 13, 2011) (10 pages) doi:10.1115/1.4005073 History: Received April 14, 2011; Revised May 20, 2011; Published December 13, 2011; Online December 13, 2011

We present the special space-time computational techniques we have introduced recently for computation of flow problems with moving and deforming solid surfaces. The techniques have been designed in the context of the deforming-spatial-domain/stabilized space-time formulation, which was developed by the Team for Advanced Flow Simulation and Modeling for computation of flow problems with moving boundaries and interfaces. The special space-time techniques are based on using, in the space-time flow computations, non-uniform rational B-splines (NURBS) basis functions for the temporal representation of the motion and deformation of the solid surfaces and also for the motion and deformation of the volume meshes computed. This provides a better temporal representation of the solid surfaces and a more effective way of handling the volume-mesh motion. We apply these techniques to computation of the aerodynamics of flapping wings, specifically locust wings, where the prescribed motion and deformation of the wings are based on digital data extracted from the videos of the locust in a wind tunnel. We report results from the preliminary computations.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Data represented with NURBS. The data and control variables (top). The basis functions corresponding to each control variables (bottom).

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Figure 2

The data represented with basis functions after the knot insertion. The data and control variables (top). The basis functions corresponding to each control variables (bottom).

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Figure 3

The data and control variables (top). The basis functions that we simply form for a given interval for the space-time computation (bottom). To integrate over the interval, in the NURBS representation of the data we need to search for the corresponding element and parametric coordinate for the time t(ϑg) of each quadrature point ϑg, and interpolate the value from the data.

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Figure 4

NURBS representation for a time-varying spatial position vector. The circles are the spatial position vector at each sampling time. The squares are the temporal-control points and the smooth curve is represented by them.

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Figure 5

A circular arc represented by quadratic NURBS

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Figure 6

SSDM. Complex shape is shaded. Circles are tracked points. SS is represented by squares (control points).

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Figure 7

Remeshing and trimming NURBS. A set of un-remeshed meshes (top). A set of remeshed meshes (middle). Common basis functions (bottom).

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Figure 8

Remeshing with knot insertion. For the set of un-remeshed meshes, there are p newly-defined basis functions and the corresponding control points are marked “New.” We carry out the mesh moving computations for those meshes.

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Figure 9

Mesh representation for the starting condition

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Figure 10

Forewing (FW) and hindwing (HW) surfaces represented by NURBS and the control points

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Figure 11

Wing and body surface meshes with triangular elements

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Figure 12

Volume mesh shown for the full computational domain (top), cylindral-refinement region (middle), and refinement region near the wing surface (bottom)

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Figure 13

Deformed SS and associated control points along with the projected HW NURBS surface

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Figure 14

FW control mesh and corresponding surface at three temporal-control points

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Figure 15

The volume mesh obtained by the automatic mesh generator (top) and after being moved to the first temporal-control point of that patch (bottom)

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Figure 16

FW and HW tip position in time with the shaded regions showing the extrapolation region (gray) and section used for results visualization (green). Dashed, vertical lines indicate the points in the cycle used in Figs. 1, 1, and 1.

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Figure 17

Streamlines colored by velocity at the time indicated by the vertical, white dashed line in Fig. 1

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Figure 18

Voriticty at eight points during the flapping cycle (left to right, top to bottom) indicated by the vertical lines in Fig. 1

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Figure 19

Surface pressures at eight points during the flapping cycle (left to right, top to bottom) indicated by the vertical lines in Fig. 1

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