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Uncertainty Quantification for a Flapping Airfoil with a Stochastic Velocity Deviation

Liangyu Zhao, Shuxing Yang

Abstract


From the perspective of practical engineering, an outdoor flapping wing micro aerial vehicle (FWMAV) should be capable to withstand unpredictable perturbations in the flight condition. The responses of the time average thrust coefficient and the propulsive efficiency with respect to a stochastic flight velocity deviation were numerically investigated. The deviation is assumed to obey the Gauss distribution with a mean value 0 and a specified standard deviation. The probability distributions of the flapping performances were quantified by the Non-Intrusive Polynomial Chaos method. It is observed that both of the time average thrust coefficient and the propulsive efficiency obey Gauss-like but not the exact Gauss distribution. The velocity deviation has large effect on the time average thrust coefficient and a little effect on the propulsive efficiency.

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References


McMichael, J. M., and Francis M. S., Micro air vehicles – toward a new dimension in flight, DARPA, USA, 1997.

Platzer, M. F., Jones, K. D., Young, J., and Lai, J. C. S., Flapping-wing Aerodynamics: progress and challenges, AIAA Journal, Vol.46, No.9, 2008, pp. 2136-2148.

Jones, K. D., and Platzer, M. F., Bio-Inspired design of flapping wing micro air vehicles – An engineer’s perspective, 44th AIAA Aerospace Sciences Meeting and Exhibit, 9-12 January 2006, Reno, Nevada, Paper

No. AIAA-2006-0037.

Lian Y., and Shyy W., Aerodynamics of low Reynolds number plunging airfoil in steady and gusty environments, 45th AIAA Aerospace Sciences Meeting and Exhibit, 8-11 January 2007, Reno, Nevada, Paper No. AIAA 2007-0794.

Gopalan H., and Povitsky A., A numerical study of gust suppression by flapping airfoils, 26th AIAA Applied Aerodynamics Conference, 18-21 August 2008, Honolulu, Hawaii, Paper No. AIAA 2008-6394.

Lian Y., Numerical study of a flapping airfoil in gusty environments, 27th AIAA Applied Aerodynamics Conference, 22-25 June 2009, San Antonio, Texas, Paper No. AIAA 2009-3952.

Viswanath K., and Tafti D., Effect of frontal gusts on flexible wings in forward flapping flight, 40th Fluid Dynamics Conference and Exhibit, 28 June-1 July 2010, Chicago, Illinois, Paper No. AIAA-2010-4869.

Cebeci, T., Platzer, M., Chen, H., Chang, K., Shao, J., Analysis of low-speed unsteady airfoil flows, Springer, 2005.

Young, J., Walker, S. M., Bomphrey, R. J., Taylor, G. K., and Thomas, L. R., Details of insect wing design and deformation enhance aerodynamic function and flight efficiency, Science, Vol. 325, No. 5947, 2009, pp. 1549-1552.

Kinsey T., Dumas G., Parametric study of an oscillating airfoil in a power-extraction regime, AIAA Journal, Vol. 46, No. 6, 2008, pp. 1318-1330.

Tuncer I H, Kaya M., Thrust generation caused by flapping airfoils in a biplane configuration, Journal of Aircraft, Vol. 40, No. 3, 2003, pp. 509-515.

Miao, J. M., Ho, M. H., Effect of flexure on aerodynamic propulsive efficiency of flapping flexible airfoil, Journal of Fluids and Structures, Vol. 22, 2006, pp. 401-41.

Wiener, N., The homogeneous chaos, American Journal of Mathematics, Vol. 60, No. 4, pp.897-936, 1938.

Xiu, D., and Karniadakis, E., The Wiener-Askey polynomial chaos for stochastic differential equations, Journal of Scientific Computing, Vol. 24, No. 2, pp. 619-644, 2002.

Isukapalli S., Uncertainty Analysis of Transport- Transformation Models, PhD Dissertation, the State University of New Jersey, New Braunswick, 1999.

Debusschere B, Najm H, Pebay P, Knio O, Ghanem R, and Maitre O., Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes, SIAM Journal on Scientific Computing, Vol. 26, No.2, 2004, pp.698–719.

Walters R., Towards stochastic fluid mechanics via Polynomial Chaos-invited, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 6-9 January 2003, Paper No.AIAA-2003-413.




DOI: http://dx.doi.org/10.21535%2FProICIUS.2010.v6.542

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