Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T23:56:33.427Z Has data issue: false hasContentIssue false

An unsteady aerodynamic model for three-dimensional wing based on augmented lifting-line method

Published online by Cambridge University Press:  25 April 2022

X. Li*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an, China
Z. Zhou
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an, China
J.H. Guo
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi’an, China
*
*Corresponding author. Email: lixu24@outlook.com

Abstract

A fast numerical method for unsteady aerodynamic calculation of 3D wing is established, which is suitable for the preliminary design. Based on the lifting-line method, the aerodynamic data of the 2D aerofoil obtained by the unsteady CFD simulation is used as the model input to solve the aerodynamic force of the 3D wing. Compared with the traditional steady lifting-line method, the augmented method adopts the unsteady Kutta-Jouowski (K-J) theorem to calculate the circulation and improve the accuracy of the method through the circulation correction. The pitching motion of 3D wing at different aspect ratio and reduction frequencies are studied. The results show that the aerodynamic forces obtained by the augmented lifting-line method have good agreement with the 3D unsteady CFD calculations. Compared with 3D CFD calculation, the calculation efficiency of the improved method is increased by more than 12 times. The improved method has extensive applicability and can be used to estimate the unsteady aerodynamic forces of 3D single or multiple wing configurations.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Katz, J. and Plotkin, A. Low Speed Aerodynamics. Cambridge England, UK: Cambridge University Press, 2001, pp 347384.CrossRefGoogle Scholar
Joseph, C. and Mohan, R. A parallel, object-oriented framework for unsteady free-wake analysis of multi-rotor/wing systems. Comput. Fluids, 2021, 215, pp 104788. doi:10.1016/j.compfliud.2020.104788.CrossRefGoogle Scholar
Lucia, D.J., Beran, P.S. and Silva, W.A. Reduced-order modelling: new approaches for computational physics. Prog. Aerosp. Sci. 2004, 40, pp 51117.CrossRefGoogle Scholar
Kou, J.Q. and Zhang, W.W. Data-driven modeling for unsteady aerodynamics and aeroelasticity. Prog. Aerosp. Sci., 2021, 125, pp 100725. doi:10.1016/j.paerosci.2021.100725.CrossRefGoogle Scholar
Brunton, S.L., Noack, B.R. and Koumoutsakos, P. Machine learning for fluid mechanics. Annu. Rev. Fluid Mech., 2020, 52, pp 477508.CrossRefGoogle Scholar
Bourgault-Cote, S., Ghasemi, S., Mosahebi, A. and Laurendeau, E. Extension of a two-dimensional Navier–stokes solver for infinite swept flow. AIAA J., 2017, 55, (2), pp 662667.CrossRefGoogle Scholar
Prandtl, L. Tragflugel Theorie [Aerofoil Theory]. Nachrichten von der Gesellschaft derWisseschaften zu Gottingen. Vols. Geschaeftliche Mitteilungen, Klasse [News from the Society of Sciences in Gottinggen, business messages class], 1918, Gottingen, Germany, pp 451477.Google Scholar
Phillips, W.F. and Snyder, D.O. Modern adaptation of Prandtl’s classic lifting-line theory. J. Aircr., 2000, 37, (4), pp 662670.CrossRefGoogle Scholar
Phillips, W.F. Lifting-line analysis for twisted wings and washout-optimized wings, J. Aircr., 2012, 41, (1), pp 128136.CrossRefGoogle Scholar
Fluck, M. and Crawford, C. A lifting line model to investigate the influence of tip feathers on wing performance. Bioinspir. Biomim., 2014, 9, (4), pp 046017. doi:10.1088/1748-3182/9/4/046017.CrossRefGoogle ScholarPubMed
Vernengo, G., Bonfiglio, L. and Brizzolara, S. Supercavitating three-dimensional hydrofoil analysis by viscous lifting-line approach. AIAA J., 2017, 55, (12), pp 41274141.CrossRefGoogle Scholar
Van Dam, C.P. The aerodynamic design of multi-element high-lift systems for transport airplanes. Prog. Aerosp. Sci., 2002, 38, (2), pp 101144.CrossRefGoogle Scholar
Gallay, S. and Laurendeau, E. Preliminary-design aerodynamic model for complex configurations using lifting-line coupling algorithm. J. Aircr., 2016, 53, (4), pp 11451159.CrossRefGoogle Scholar
Anderson, J.D., Corda, S. and Van Wie, D.M. Numerical lifting line theory applied to drooped leading-edge wings below and above stall. J. Aircr., 1980, 17, (12), pp 898904.CrossRefGoogle Scholar
Wickenheiser, A.M. and Garcia, E. Extended nonlinear lifting-line method for aerodynamic modeling of reconfigurable aircraft. J. Aircr., 2011, 48, (5), pp 18121817.CrossRefGoogle Scholar
Smyth, A.S.M., Young, A.M. and Mare, L.D. Effect of three-dimensional geometry on harmonic gust–airfoil interaction. AIAA J., 2021, 59, (2), pp 737750.CrossRefGoogle Scholar
Sugar-Gabor, O. A general numerical unsteady non-linear lifting line model for engineering aerodynamics studies. Aeronaut. J., 2018, 122, (1254), pp 11991228.CrossRefGoogle Scholar
Sugar-Gabor, O. and Koreanschi, A. Fast and accurate quasi-3D aerodynamic methods for aircraft conceptual design studies. Aeronaut. J., 2021, 125, (1286), pp 593617.CrossRefGoogle Scholar
Parenteau, M., Plante, F. and Laurendeau, E. Unsteady coupling algorithm for lifting-line methods. 50th AIAA Aerospace Sciences Meeting, 9–13, January 2017, 2017, Grapevine Texas, USA. doi:10.2514/6.2017-0951.CrossRefGoogle Scholar
Kharlamov, D., Da Ronch, A., Drofelnik, J. and Walker, S. Fast aerodynamic calculations based on a generalized unsteady coupling algorithm. AIAA J., 2021, 59, (8), pp 29162934.Google Scholar
Sclavounos, P.D. An unsteady lifting-line theory. J. Eng. Math., 1987, 21, (3), pp 201226.CrossRefGoogle Scholar
Bird, H.J.A. and Ramesh, K. Theoretical and computational studies of a rectangular finite wing oscillating in pitch and heave. Proceedings of the 6th, European Conference on Computational Mechanics (ECCM 6) and the 7th. European Conference on Computational Fluid Dynamics (ECFD 7), 11–15, June 2018, 2018, Glasgow, UK. http://eprints.gla.ac.uk/164669/ Google Scholar
Bird, H.J.A., Otomo, S., Ramesh, K.K. and Viola, I.M. A geometrically non-linear time-domain unsteady lifting-line theory. AIAA Scitech Forum, 7–11, January 2019, 2019, San Diego, California, USA. doi:10.2514/6.2019-1377.CrossRefGoogle Scholar
Bird, H.J.A. and Ramesh, K. Unsteady lifting-line theory and the influence of wake vorticity on aerodynamic loads. Theor. Comput. Fluid Dyn., 2021, 35, (5), pp 609631.CrossRefGoogle Scholar
Bird, H.J.A., Ramesh, K., Ōtomo, S. and Viola, I.M. Usefulness of inviscid linear unsteady lifting-line theory for viscous large-amplitude problems. AIAA J., 2021, articles in advance.CrossRefGoogle Scholar
Boutet, J. and Dimitriadis, G. Unsteady lifting line theory using the Wagner function. 55th AIAA Aerospace Sciences Meeting, 9–13, January 2017, 2017, Grapevine Texas, USA. doi:10.2514/6.2017-0493.CrossRefGoogle Scholar
Boutet, J. and Dimitriadis, G. Unsteady lifting line theory using the Wagner function for the aerodynamic and aeroelastic modeling of 3D wings. Aerospace, 2018, 5, (3), pp 92. doi:10.3390/aerospace5030092.CrossRefGoogle Scholar
Izraelevitz, J.S., Zhu, Q. and Triantafyllou, M.S. State-space adaptation of unsteady lifting line theory: twisting/flapping wings of finite Span. AIAA J., 2017, 55, (4), pp 12791294.CrossRefGoogle Scholar
Ahmadi, A.R. and Widnall, S.E. Unsteady lifting-line theory as a singular perturbation problem. J. Fluid Mech., 1985, 153, pp 5981.CrossRefGoogle Scholar
Branlard, E. Wind Turbine Aerodynamics and Vorticity-Based Methods: Fundamentals and Recent Applications. Berlin: Springer, 2017, pp 227243.CrossRefGoogle Scholar
Halfman, R.L. Experimental aerodynamic derivatives of a sinusoidally oscillating airfoil in two-dimensional flow, 1952, NACA Report-1108.Google Scholar
Piziali, R.A. 2-D and 3-D Oscillating Wing Aerodynamics for a Range of Angle of Attack Including Stall, 1994, NASA Report-4632.Google Scholar
Yu, H.T. and Bernal, L.P. Effects of pivot location and reduced pitch rate on pitching rectangular flat plates. AIAA J., 2016, 55, (3), pp 702718.CrossRefGoogle Scholar
Hosseini, N., Tadjfar, M. and Abba, A. Configuration optimization of two tandem airfoils at low reynolds numbers. Appl. Math. Modell., 2022, 102, pp 828846.CrossRefGoogle Scholar
Li, K., Kou, J.Q. and Zhang, W.W. Unsteady aerodynamic reduced-order modeling based on machine learning across multiple airfoils, Aerosp. Sci. Technol., 2021, 119, pp 107173. doi:10.1016/j.ast.2021.107173.CrossRefGoogle Scholar