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Abstract
The ultra-low Reynolds number flow over airfoils is considered from the perspective of boundary vorticity dynamics in this paper. The dynamic balance between the streamwise pressure gradient and vorticity creation rate at the wall is highlighted by the boundary vorticity flux. It is a localized feature with a high peak generally indicating impending boundary layer separation. Two interesting features of ultra-low Reynolds number flows are considered. Firstly, the higher values of lift coefficient with decreasing Reynolds number is seen to be due to delayed boundary layer separation. The peak in boundary vorticity flux clearly predicts the separation event. Secondly, the lift enhancement achieved by certain optimal airfoils due to a vortex trapped in the airfoil cavity is considered. An interesting double-peak in boundary vorticity flux seen for the optimal airfoil enhances the lift. An alternative interpretation of the lift enhancement is also provided by examining the Lamb vector-field.
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References
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- Rashmi, N. and Sivapragasam, M., "Lift Enhancement by Trapped Vortex at Ultra-Low Reynolds Numbers", to be submitted, 2020.
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References
Glauert, H., "The Elements of Aerofoil and Airscrew Theory", Second Edition, Cambridge University Press, Cambridge, 1947.
Pranesh, C., Sivapragasam, M. and Deshpande, M. D., "Aerodynamic Characteristics of Flow Past NACA 0008 Airfoil at Very Low Reynolds Numbers", Journal of Aerospace Sciences and Technologies, Vol.66, No.4, pp.247-266, 2014.
Dheepak, A., Sivapragasam, M. and Deshpande, M. D., "Airfoil Optimisation at a Very Low Reynolds Number", Proceedings of the 17th Annual CFD Symposium, Bangalore, 2015.
Ukken, M. G. and Sivapragasam, M., "Aerodynamic Shape Optimization of Airfoils at Ultra-Low Reynolds Numbers", Sadhana, Vol.44, Article ID 130, 2019.
Varsha, N., Deshpande, M. D. and Sivapragasam, M., "Airfoil Optimisation at Ultra-Low Reynolds Number", Journal of Aerospace Sciences and Technologies, Vol.71, No.3, pp.347-353, 2019.
Rashmi, N. and Sivapragasam, M., "Lift Enhancement by Trapped Vortex at Ultra-Low Reynolds Numbers", to be submitted, 2020.
Kunz, P. J. and Kroo, I. M., "Analysis, Design, and Testing of Airfoils for Use at Ultra-Low Reynolds Numbers", in "Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications", Edited by T. J. Mueller, Vol.195, Progress in Aeronautics and Astronautics, AIAA, Reston, VA, 2001.
Srinath, D. N. and Mittal, S., "Optimal Airfoil Shapes for Low Reynolds Number Flows", International Journal Numer. Meth. Fluids, Vol.61, pp.355-381, 2009.
Mateescu, D. and Abdo, M., "Analysis of Flows Past Airfoils at very Low Reynolds Numbers", Proceedings of IMechE, Part G: Journal of Aerospace Engineering, Vol.224, pp.757-775, 2010.
Suryanarayana, G. K., Naveen, K. M. and Mudkavi, V. Y., "Mimicking the Mechanism of Lift Generation in Dragonflies", Journal of Aerospace Sciences and Technologies, Vol.70, No.1, pp.42-46, 2018.
Lighthill, M. J., "Introduction: Boundary Layer Theory", in "Laminar Boundary Layers", Edited by L. Rosenhead, Clarendon Press, Oxford, 1963.
Wu, J. C., "Theory for Aerodynamic Force and Moment in Viscous Flows", AIAA Journal, Vol.19, No.4, pp.432-441, 1980.
Wu, J. Z., Ma, H. Y. and Zhou, M. D., "Vorticity and Vorticity Dynamics", Springer, Berlin, 2006.
Schlichting, H. and Gersten, K., "Boundary-Layer Theory", Ninth Edition, Springer, Berlin, 2017.
Ansari, M. I., Siddique, M. H., Samad, A. and Anwer, S. F., "On the Optimal Morphology and Performance of a Modeled Dragonfly Airfoil in Gliding Mode", Phys. Fluids, Vol.31, Iss.5, Article ID. 051904, 2019.