Abstract
The concept vortex force in aerodynamics is systematically examined based on a new steady vortex-force theory (Wu et al., Vorticity and vortex dynamics, Springer, 2006) which expresses the aerodynamic force (and moment) by the volume and boundary integrals of the Lamb vector. In this paper, the underlying physics of this theory is explored, including the general role of the Lamb vector in nonlinear aerodynamics, its initial formation, and its relevance to the total-pressure non-uniformity. As a typical example, the theory is applied to the flow over a slender delta wing at a large angle of attack. The highly localized flow structures with high Lamb-vector peaks are identified in terms of their net contribution to various constituents of the total aerodynamic force. This vortex-force diagnosis sheds new light on the flow control and configuration optimization.
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Prandtl, L., Tragflügeltheorie, I.: Mitteilungen, Nachrichten Ges. Wiss. Göttingen, Math-Phys. Kl. 151–177 (Also: Gesammelte Abhandlungen, vol. 1, pp. 322–345) (1918)
Kármán, T., von Burgers, J.M.: General aerodynamic theory, perfect fluids. Aerodynamic Theory. Durand ed. vol. II, Stanford (1934)
Lighthill M.J. (1962). Physical intergretation of the mathematical theory of wave generation by wing. J. Fluid Mech. 14: 385–398
Saffman P.G. (1992). Vortex Dynamics. Cambridge University Press, Cambridge
Wu J.Z., Ma H.Y. and Zhou M.D. (2006). Vorticity and Vortex Dynamics. Springer, Heidelberg
Wu J.C. (2005). Elements of Vorticity Aerodynamics. Tsinghua University Press, Beijing
Wu J.Z., Zhou Y., Lu X.Y. and Fan M. (1999). Turbulent force as a diffusive field with vortical sources. Phys. Fluids 11: 627–635
Lighthill M.J. (1986). An Informal Introduction to Theoretical Fluid Mechanics. Clarendon Press, Oxford
Wu, J.M., Ondrusek, B., Wu, J.Z.: Exact force diagnostics of vehicles based on wake-plane data. AIAA 96-0559 (1996)
Lee M. and Ho C.M. (1990). Lift force of delta wings. Appl. Mech. Rev. 43(9): 209–221
Wu J.Z., Lu X.Y. and Zhuang L.X. (2006). Integral force acting on a body due to local flow structures. J. Fluid Mech. 576: 265–286
Wu, J.Z., Wu, J.M.: Vortical sourses of aerodynamics force and moment. SAE 89-2346 (1989)
Wu, J.Z., Roach, R.L., Lo, C.F., Zhu, F.L.: Aerodynamic diagnosis and design based on boundary vorticity dynamics. AIAA 99-3103 (1999)
Luo, Y.B.: Boundary vorticity dynamics, derivative-moment theory and their application in flow diagnosis and control (in Chinese). Master dissertation, Peking University, Beijing (2004)
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The project supported partly by the National Natural Science Foundation of China (10572005).
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Yang, Y.T., Zhang, R.K., An, Y.R. et al. Steady vortex force theory and slender-wing flow diagnosis. Acta Mech. Sin. 23, 609–619 (2007). https://doi.org/10.1007/s10409-007-0107-0
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DOI: https://doi.org/10.1007/s10409-007-0107-0