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The lift on an aerofoil in grid-generated turbulence

Published online by Cambridge University Press:  14 April 2015

Shaopeng Li ,
Mingshui Li  and
Haili Liao
Shaopeng Li
Affiliation:
Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, PR China
Mingshui Li*
Affiliation:
Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, PR China Key Laboratory for Wind Engineering of Sichuan Province, Chengdu 610031, PR China
Haili Liao
Affiliation:
Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu 610031, PR China Key Laboratory for Wind Engineering of Sichuan Province, Chengdu 610031, PR China
*
†Email address for correspondence: lms\_rcwe@126.com
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Abstract

The three-dimensional effects of turbulence cannot be neglected when the spanwise wavelength of the incident turbulence is not effectively infinite with respect to the chord, which may invalidate the strip assumption. Based on three-dimensional theory, a general approach, expressed in terms of a two-dimensional Fourier transform of the correlation of the buffeting force, is proposed to identify the two-wavenumber spectrum and aerodynamic admittance of the lift force on an aerofoil. It is essential that the approach presented can be validated in wind tunnel experiments. The coherence of the lift force on an aerofoil in grid-generated turbulence is obtained by simultaneous measurements of unsteady surface pressures around several chordwise strips on a stiff sectional model, which controls the accuracy of results. For the purpose of the Fourier transform, three empirical coherence models of the lift force are presented to fit the experimental results. Compared with the linearized theory, the two-wavenumber aerodynamic admittance can describe well the pressure distribution and the pattern of energy transition in an isotropic turbulence field. Thus, the failure mechanism of the traditional strip assumption can be demonstrated explicitly. In addition, the results obtained also validate the theory proposed by Graham (Aeronaut. Q., vol. 21, 1970, pp. 182–198; Aeronaut. Q., vol. 22, 1971, pp. 83–100). The present approach can be extended to study the three-dimensionality of the buffeting force on line-like structures with arbitrary cross-configurations, such as long-span bridges and high-rise buildings.

JFM classification

Aerodynamics: Aerodynamics Turbulent Flows: Isotropic turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , pp. 16 - 35
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Copyright
© 2015 Cambridge University Press 

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References

Bearman, P. W. 1971 An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech. 46, 177–198.Google Scholar
Bearman, P. W. 1972 Some measurements of the distortion of turbulence approaching a two-dimensional bluff body. J. Fluid Mech. 53, 451–467.CrossRefGoogle Scholar
Blake, W. K. 1986 Noncavitating lifting sections. In Mechanics of Flow-Induced Sound and Vibration (ed. Frenkiel, F. N. & Temple, G.), p. 743. Academic.Google Scholar
Bullen, H. I.1961 Gusts at low altitude in North Africa. R.A.E. Tech. Rep. 304.Google Scholar
Diederich, F. W. 1956 The dynamic response of a large airplane to continuous random atmospheric disturbances. J. Aero. Sci. 23, 917–930.Google Scholar
Dryden, H. L., Schubauer, G. N., Mock, W. C. & Skramstad, H. K.1937 Measurements of intensity and scale of wind tunnel turbulence and their relation to the critical Reynolds number of spheres. NACA Tech. Rep. 581.Google Scholar
Etkin, B. 1971 Flight in a turbulent atmosphere. In Dynamic of Atmospheric Flight (ed. Etkin, B.), pp. 547–548. John Wiley and Sons.Google Scholar
Filotas, L. T.1969a Theory of airfoil response in a gusty atmosphere. Part I – aerodynamic transfer function. Tech. Rep. UTIAS 139.Google Scholar
Filotas, L. T.1969b Theory of airfoil response in a gusty atmosphere. Part II – reponse to discrete gusts or continuous turbulence. Tech. Rep. UTIAS 141.Google Scholar
Fung, Y. C. 1969 Preliminaries. In An Introduction to the Theory of Aeroelasticity (ed. Fung, Y. C.), p. 35. Dover.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 2007 Definite integrals of special functions. In Table of Integrals, Series and Products (ed. Jeffrey, A. & Zwillinger, D.), pp. 684–732. Academic.Google Scholar
Graham, J. M. 1970 Lifting-surface theory for the problem of an arbitrary yawed sinusoidal gust incident on a thin aerofoil in incompressible flow. Aeronaut. Q. 21, 182–198.CrossRefGoogle Scholar
Graham, J. M. 1971 A lift-surface theory for the rectangular wing in non-stationary flow. Aeronaut. Q. 22, 83–100.CrossRefGoogle Scholar
Hakkinen, R. J. & Richardson, A. S.1957 Theoretical and experimental investigation of random gust loads. Part I – aerodynamic transfer function of a simple wing configuration in incompressible flow. NACA Tech. Rep. 3878.Google Scholar
Hjorth-Hansen, E., Jakobsen, A. & Strømmen, E. 1992 Wind buffeting of a rectangular box girder bridge. J. Wind Engng Ind. Aerodyn. 41–44, 1215–1226.Google Scholar
Jackson, R., Graham, J. M. & Maull, D. J. 1973 The lift on a wing in a turbulent flow. Aeronaut. Q. 24, 155–166.Google Scholar
Jakobsen, J. B. 1997 Span-wise structure of lift and overturning moment on a motionless bridge girder. J. Wind Engng Ind. Aerodyn. 69–71, 795–805.Google Scholar
von Kármán, T. 1948 Progress in the statistical theory of turbulence. Proc. Natl Acad. Sci. USA 34, 530–539.Google Scholar
Kimura, K., Fujino, Y., Nakato, S. & Tamura, H. 1997 Characteristics of buffeting forces on flat cylinders. J. Wind Engng Ind. Aerodyn. 69–71, 365–374.CrossRefGoogle Scholar
Lamson, P.1957 Measurements of lift fluctuations due to turbulence. NACA Tech. Rep. 3380.Google Scholar
Larose, G. L.1997 The dynamic action of gusty winds on long-span bridges. PhD thesis, Technical University of Denmark.Google Scholar
Larose, G. L. & Mann, J. 1998 Gust loading on streamlined bridge decks. J. Fluids Struct. 12, 511–536.CrossRefGoogle Scholar
Liepmann, H. W. 1952 On the application of statistical concepts to buffeting problem. J. Aero. Sci. 19, 793–800.CrossRefGoogle Scholar
Liepmann, H. W. 1955 Extension of the statistical approach to buffeting and gust response of wings of finite span. J. Aero. Sci. 22, 197–200.Google Scholar
Ma, C. M.2007 3-d aerodynamic admittance research of streamlined box bridge decks. PhD thesis, Southwest Jiaotong University.Google Scholar
Mugridge, B. D.1970 The generation and radiation of acoustic energy by the blades of a subsonic axial flow fan due to unsteady flow interaction. PhD thesis, University of Southampton.Google Scholar
Mugridge, B. D. 1971 Gust loading on a thin aerofoil. Aeronaut. Q. 22, 301–310.Google Scholar
Reissner, E. & Stevens, J. E.1947a Effect of finite span on the air load distributions for oscillating wings, I – aerodynamic theory of oscillating wings of finite span. NACA Tech. Rep. 1194.Google Scholar
Reissner, E. & Stevens, J. E.1947b Effect of finite span on the air load distributions for oscillating wings, II – methods of calculation and examples of application. NACA Tech. Rep. 1196.Google Scholar
Ribner, H. S. 1956 Spectral theory of buffeting and gust response: unification and extension. J. Aero. Sci. 23, 1075–1077.Google Scholar
Roberts, J. B. & Surry, D. 1973 Coherence of grid-generated turbulence. J. Engng Mech. Div. 99, 1227–1245.Google Scholar
Sankaran, R. & Jancauskas, E. D. 1993 Measurements of cross-correlation in separated flows around bluff cylinders. J. Wind Engng Ind. Aerodyn. 49, 279–288.Google Scholar
Scanlan, R. H. 1978 The action of flexible bridges under wind. I: Buffeting theory. J. Sound Vib. 60, 201–211.Google Scholar
Sears, R. W. 1941 Some aspects of non-stationary airfoil theory and its practical applications. J. Aero. Sci. 8, 104–108.Google Scholar
Taylor, J. 1965 Theoretical analysis of turbulence. In Manual on Aircraft Loads (ed. Taylor, J.), pp. 200–203. Pergamon.Google Scholar
Vickery, B. J.1965 On the flow behind a coarse grid and its use as a model of an atmospheric turbulence in studies related to wind loads on building. Tech. Rep. NPL 1143.Google Scholar