Volumetric measurement and vorticity dynamics of leading-edge vortex formation on a revolving wing

Abstract

Abstract

Leading-edge vortex (LEV) is a hallmark of insect flight that forms and remains stably attached on high angle-of-attack (AoA), low aspect ratio (AR) wings undergoing revolving or flapping motion. Despite the efforts on explaining the stability of LEV when it reaches steady state in revolving wings, its formation process remains largely underexplored. Here, we investigate the LEV formation on a revolving wing (AoA = 45°, AR = 4 and Re = 1500), starting with a constant acceleration in the first chord (c) length of travel and then rotating at a constant velocity. The ‘Shake-the-box’ (STB) Lagrangian particle tracking velocimetry (PTV) system together with a volumetric patching process were performed to reconstruct the entire time-resolved flow field. Results show that LEV reaches steady state after approximately 4c of travel, within which its formation can be separated into three stages. In the first stage, a conical LEV structure begins to form with a tangential downstream convection of (negative) radial shear vorticity. In the second stage, the radial vorticity within the LEV is further convected downwards by the developed downwash, which limits its growth, whereas vorticity stretching increases the LEV strength. In the third stage, vorticity tilting and spanwise convection reduce the LEV strength at its rear end next to the trailing edge and, therefore, preventing it from growing. Our results suggest that insect wings with AR ~ 4, Re ~ 103 and flapping amplitude between 2c and 4c may barely or even not reach the steady state of LEV, indicating an indispensable role of transient LEV dynamics in understanding insect flight.

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Notes

  1. 1.

    The threshold of Q criteria to calculate the integral is chosen after a sensitivity study. No significant variation of the volume-averaged LEV circulation is observed if Q is further increased (Fig. 4c).

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Acknowledgements

This research was supported by National Science Foundation (NSF CMMI 1554429), Army Research Office DURIP Grant (No. W911NF-16-1-0272), National Natural Science Foundation of China (NSFC, Grant No. 11672022), China Scholarship Council (joint Ph.D. program for Long Chen) and the Academic Excellence Foundation of BUAA for Ph.D. Students. We thank Dr. Steve Anderson at LaVision Inc. for his assistance with the ‘Shake-The-Box’ system, and Shih-Jung Hsu for the design of robotic wing mechanism.

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Correspondence to Bo Cheng.

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Chen, L., Wu, J. & Cheng, B. Volumetric measurement and vorticity dynamics of leading-edge vortex formation on a revolving wing. Exp Fluids 60, 12 (2019). https://doi.org/10.1007/s00348-018-2657-2

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