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A general numerical unsteady non-linear lifting line model for engineering aerodynamics studies

Published online by Cambridge University Press:  06 June 2018

O. Sugar-Gabor*
Affiliation:
Aeronautical and Mechanical Engineering, School of Computing, Science and Engineering, University of Salford, Salford, UK

Abstract

The lifting-line theory is widely used for obtaining aerodynamic performance results in various engineering fields, from aircraft conceptual design to wind-power generation. Many different models were proposed, each tailored for a specific purpose, thus having a rather narrow applicability range. This paper presents a general lifting-line model capable of accurately analysing a wide range of engineering problems involving lifting surfaces, both steady-state and unsteady cases. It can be used for lifting surface with sweep, dihedral, twisting and winglets and includes features such as non-linear viscous corrections, unsteady and quasi-steady force calculation, stable wake relaxation through fictitious time marching and wake stretching and dissipation. Possible applications include wing design for low-speed aircraft and unmanned aerial vehicles, the study of high-frequency avian flapping flight or wind-turbine blade design and analysis. Several validation studies are performed, both steady-state and unsteady, the method showing good agreement with experimental data or numerical results obtained with more computationally expensive methods.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2018 

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References

REFERENCES

1.Prandtl, L. Tragflugel Theorie, Nachrichten von der Gesellschaft der Wisseschaften zu Gottingen. Vols. Geschaeftliche Mitteilungen, Klasse, 1918, Gottingen, Germany, pp 451477.Google Scholar
2.Glauert, H. The Elements of Aerofoil and Airscrew Theory, 1927, Cambridge University Press, Cambridge, UK.Google Scholar
3.Tani, I. A simple method of calculating the induced velocity of a monoplane wing, Report no. 111, vols. IX, 3, Tokyo Imperial University, 1934, Tokyo, Japan.Google Scholar
4.Multhopp, E. Die Berechnung der Auftriebsverteilung von Tragflugein, Luftfahrtforschung Bd. 15, vol. 4, 1938, pp 153169.Google Scholar
5.Weissinger, J. The lift distribution of swept back wings, NACA Technical Note No. 1120, 1947, Langley Field, Virginia, US.Google Scholar
6.Sivells, J. and Neely, R. Method for calculating wing characteristics by lifting line theory using nonlinear section lift data, NACA Technical Note No. 1269, 1947, Langley Field, Virginia, US.Google Scholar
7.Mccormick, B. An iterative non-linear lifting line model for wings with unsymmetrical stall, SAE Technical Paper 091020, 1989, Proceedings of the General Aviation Aircraft Meeting and Exposition, Wichita, Kansas, United States, 11–13 April 1989.Google Scholar
8.Anderson, J., Corda, S. and Van Wie, D. Numerical lifting line theory applied to drooped leading edge wings below and above stall, J Aircr, 1980, 17, (12), pp 898904.Google Scholar
9.Katz, J. and Plotkin, A. Low-Speed Aerodynamics: From Wing Theory to Panel Methods, 2001, Cambridge University Press, Cambridge, UK.Google Scholar
10.Phillips, W.F. and Snyder, D.O. Modern adaptation of Prandtl's classic lifting-line theory, J Aircr, 2000, 37, (4), pp 662670.Google Scholar
11.Spall, R.E., Phillips, W.F. and Pincock, B.B. Numerical analysis of multiple, Thin-sail geometries based on Prandtl's lifting-line theory, Computers and Fluids, 2013, 82, pp 2937.Google Scholar
12.Phillips, W.F. and Hunsaker, D.F. Lifting-line predictions for induced drag and lift in ground effect, J Aircr, 2013, 50, (4), pp 12261233.Google Scholar
13.Phillips, W.F. Lifting-line analysis for twisted wings and washout-optimized wings, J Aircr, 2004, 41, (1), pp 128136.Google Scholar
14.Phillips, W.F. and Alley, N.R. Predicting maximum lift coefficient for twisted wings using lifting-line theory, J Aircr, 2007, 44, (3), pp 898910.Google Scholar
15.Piszkin, S.T. and Levinsky, E.S. Nonlinear lifting line theory for predicting stalling instabilities on wings of moderate aspect ratio, General Dynamics Convair Division, Report No. CASD-NSC-76-001, 1976, San Diego, California, US.Google Scholar
16.Gallay, S. and Laurendeau, E. Nonlinear generalized lifting-line coupling algorithms for pre/post-stall flows, AIAA J, 2015, 53, (7), pp 17841792.Google Scholar
17.Gallay, S. and Laurendeau, E. Preliminary-design aerodynamic model for complex configurations using lifting-line coupling algorithm, J Aircr, 2016, 53, (4), pp 11451159.Google Scholar
18.Phlips, P.J., East, R.A. and Pratt, N.H. An unsteady lifting line theory of flapping wings with application to the forward flight of birds, J Fluid Mechanics, 1981, 112, pp 97125.Google Scholar
19.James, E.C. Lifting-line theory for an unsteady wing as a singular perturbation problem, J Fluid Mechanics, 1975, 70, pp 753771.Google Scholar
20.Ahmadi, A.R. and Widnall, S.E. Unsteady lifting-line theory as a singular perturbation problem, J Fluid Mechanics, 1985, 153, pp 5981.Google Scholar
21.Sclavounos, P.D. An unsteady lifting line theory, J Engineering Mathematics, 1987, 21, (3), pp 201226.Google Scholar
22.Guermond, J.L. and Sellier, A. A unified unsteady lifting-line theory, J Fluid Mechanics, 1991, 229, pp 427451.Google Scholar
23.Cline, S. and Crawford, C. Comparison of potential flow wake models for horizontal-axis wind turbine rotors, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 4–7 January 2010, Orlando, Florida, US.Google Scholar
24.McWilliam, M.K. and Crawford, C. Finite element based Lagrangian vortex dynamics model for wind turbine aerodynamics, Journal of Physics: Conference Series 524, paper 012127, 2014.Google Scholar
25.Fluck, M. Accelerating Unsteady Wind Turbine Aerodynamics: A Stochastic Lagrangian Vortex Model, PhD Candidacy Proposal, University of Victoria, 2014, Victoria, British Columbia, Canada.Google Scholar
26.Van Garrel, A. Development of a wind turbine aerodynamics simulation module, Tech. Rep. ECN-C-03-079, 2003, The Hague, Netherlands.Google Scholar
27.Le Bouar, G., Costes, M., Leroy-Chesneau, A. and Devinant, P. Numerical simulations of unsteady aerodynamics of helicopter rotor in manoeuvering flight conditions, Aerospace Science and Technology, 2004, 8, pp 1125.Google Scholar
28.Marten, D., Lennie, M., Pechlivanoglou, G., Nayeri, C.N. and Paschereit, C.O. Implementation, optimization, and validation of a nonlinear lifting line-free vortex wake module within the wind turbine simulation code QBLADE, J Engineering for Gas Turbines and Power, 2016, 138, (7).Google Scholar
29.Fluck, M. and Crawford, C. Fast analysis of unsteady wing aerodynamics via stochastic models, AIAA J, 2017, 55, (3), pp 719728.Google Scholar
30.Saffman, P. Vortex Dynamics, 1992, Cambridge University Press, Cambridge, UK.Google Scholar
31.Drela, M. Integrated simulation model for preliminary aerodynamic, structural and control-law design of aircraft, AIAA Paper 99–1394, Proceedings of the 40th AIAA SDM Conference, St. Louis, Missouri, United States, 12–15 April 1999.Google Scholar
32.Fritz, T.E. and Long, L.N. Object-oriented unsteady vortex lattice method for flapping flight, J Aircr, 2004, 41, (6), pp 12751290.Google Scholar
33.Leishman, J.G. Principles of Helicopter Aerodynamics, 2000, Cambridge University Press, Cambridge, UK.Google Scholar
34.Neely, R.H., Bollech, T.V., Westrick, G.C. and Graham, R.R. Experimental and calculated characteristics of several NACA 44-Series wings with aspect ratios of 8, 10 and 12 and taper ratios of 2.5 and 3.5, NACA Technical Note no. 1270, Langley Memorial Aeronautical Laboratory, 1947, Langley Field, Virginia, US.Google Scholar
35.Drela, M. XFOIL: An analysis and design system for low Reynolds number airfoils, Low Reynolds Number Aerodynamics, 1989, Springer, Notre Dame, Indiana, US.Google Scholar
36.Gallay, S. Private discussion with author, 2016.Google Scholar
37.Cahill, J.F. and Gottlieb, S.M. Low-speed aerodynamic characteristics of a series of swept wings having NACA 65A006 Airfoil Sections, NACA Research Memorandum L50F16, Langley Memorial Aeronautical Laboratory, 1950, Langley Field, Virginia, US.Google Scholar
38.Loftin, L.K. Theoretical and experimental data for a number of NACA 6A-series airfoil sections, NACA Technical Report no. 903, Langley Memorial Aeronautical Laboratory, 1947, Langley Field, Virginia, US.Google Scholar
39.Schneider, W.C. A comparison of the span-wise loading calculated by various methods with experimental loadings obtained on a 45 degrees sweptback wing of aspect ration 8, at a Reynolds number of 4 million, NACA Report no. 1208, Langley Memorial Aeronautical Laboratory, 1951, Langley Field, Virginia, US.Google Scholar
40.Halfman, R.L. Experimental aerodynamic derivatives of a sinusoidally oscillating airfoil in two-dimensional flow, NACA Report no. 1108, 1952, Massachusetts Inst. of Tech, Massachusetts, US.Google Scholar
42.Ho, S., Nassef, H., Pornsinsirirak, N., Tai, Y.C. and Ho, C.M. Unsteady aerodynamics and flow control for flapping wing flyers, Progress in Aerospace Sciences, 2003, 39, pp 635681.Google Scholar
42.Verstraete, M.L., Preidikman, S., Roccia, B.A. and Mook, D.T. A numerical model to study the nonlinear and unsteady aerodynamics of bioinspired morphing-wing concepts, Int J Micro Air Vehicles, 2015, 7, (3), pp 327345.Google Scholar
43.Hand, M.M., Simms, D.A., Fingersh, L.J., Jager, D.W., Cotrell, J.R., Schreck, S. and Larwood, S.M. Unsteady aerodynamics experiment phase VI: Wind tunnel test configurations and available data campaigns, Report NREL/TP-500-29955, 2001, National Renewable Energy Lab, Golden, Colorado, US.Google Scholar
44.Duque, E.P.N., Burklund, M.D. and Johnson, W. Navier-stokes and comprehensive analysis performance predictions of the NREL Phase VI Experiment, AIAA Paper AIAA-2003-0355, 2003.Google Scholar
45.Lindenburg, C. Investigation into rotor blade aerodynamics: Analysis of the stationary measurements on the UAE Phase-VI Rotor in the NASA-Ames Wind Tunnel, Report ECN-C-03-025, 2003, Energy Research Center, Sint Maartensvlotbrug, Netherlands.Google Scholar
46.Kim, H., Lee, S. and Lee, S. Numerical analysis on the aerodynamics of HAWTs using nonlinear vortex strength correction, Current Applied Physics, 2010, 10, pp 311315.Google Scholar
47.Wu, J.Z., Ma, H.Y. and Zhou, M.D. Vorticity and Vortex Dynamics, 2006, Springer-Verlag, Berlin, Germany.Google Scholar
48.Gabor, O.Ş., Koreanschi, A. and Botez, R.M. Analysis of UAS-S4 Éhecatl aerodynamic performance improvement using several configurations of a morphing wing technology, The Aeronautical J, 2016, 120, (1231), pp 13371364.Google Scholar
49.Gabor, O.Ş., Koreanschi, A. and Botez, R.M. A new non-linear vortex lattice method: Applications to wing aerodynamic optimizations, Chinese J Aeronautics, 2016, 29, (5), pp 11781195.Google Scholar