PDF (2 MB)
Collect
Submit Manuscript
Show Outline
Outline
Abstract
Keywords
References
Show full outline
Hide outline
Review | Open Access

Evolutionary understanding of airfoil lift

Department of Mechanical and Aerospace Engineering, Western Michigan University, Kalamazoo, MI 49008, USA
Show Author Information

Abstract

This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations, particularly focusing on the critical effect of the fluid viscosity. The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model. In particular, the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed, including Newton’s sine-squared law, Rayleigh’s lift formula, thin-airfoil theory and viscous-flow lift formula. The vortex-force theory is described to provide a solid foundation for consistent treatment of lift, form drag, Kutta condition, and downwash. The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil, and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition. The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.

References

1

McMaster J (1989) The flight of the bumblebee and related myths of entomological engineering: bees help bridge the gap between science and engineering. Am Sci 77(2): 164–169

2

McLean D (2012) Understanding aerodynamics. Wiley, New York. https://doi.org/10.1002/9781118454190

3

Eastlake CN (2002) An Aerodynamicist’s view of lift, Bernoulli, and Newton. Phys Teach 40(3): 166–173. https://doi.org/10.1119/1.1466553

4

Anderson JD (2008) Introduction to flight, 6th edn. McGraw-Hill, New York

5

Bloor D (2011) The enigma of the aerofoil: rival theories in aerodynamics, 1909–1930. The University of Chicago Press, Chicago

6

Babinsky H (2003) How do wings work? Phys Educ 38(6): 497–503. https://doi.org/10.1088/0031-9120/38/6/001

7

Weltner K (1987) A comparison of explanations of the aerodynamic lifting force. Am J Phys 55(1): 50–54. https://doi.org/10.1119/1.14960

8

Anderson JD, Eberhardt S (2001) Understanding Flight. McGraw-Hill, New York

9

Templin RJ (2000) The Spectrum of animal flight: insects to pterosaurs. Prog Aerosp Sci 36(5-6): 393–436. https://doi.org/10.1016/S0376-0421(00)00007-5

10

Liu T (2007) Time-area-averaged momentum stream tube model for flapping flight. J Aircraft 44(2): 459–466. https://doi.org/10.2514/1.23660

11

Prandtl L, Tietjen OG (1934) Fundamentals of hydro- and aeromechanics. Dover, New York

12

Milne-Thomson LM (1958) Theoretical aerodynamics. Dover, New York

13

Von Mises R (1959) Theory of Flight. Dover, New York

14
Theodorsen T, Garrick IE (1979) General potential theory of arbitrary wing sections. NACA Technical Report, NACA-TR-452
15

Glauert H (1983) The elements of aerofoil and airscrew theory, 2nd edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511574481

16
Jones RT (1979) Classical aerodynamic theory. NASA Ames Research Center Moffett Field, NASA-RP-1050
17

Sears WR (2011) Introduction to theoretical aerodynamics and hydrodynamics. AIAA Press, Washington, DC. https://doi.org/10.2514/4.867743

18

Ackrody JAD, Axcell BP, Ruban AI (2001) Early developments of modern aerodynamics. Elsevier, New York. https://doi.org/10.2514/4.475160

19

Anderson JD (1997) A history of aerodynamics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511607

20

Liu T, Wang S, He G (2017) Explicit role of viscosity in generating lift. AIAA J 55(11):3990–3994. https://doi.org/10.2514/1.J055907

21

Rayleigh L (1876) On the resistance of fluids. London Edinburgh Dublin Philosophic Magazine J Sci 2(13):430–441. https://doi.org/10.1080/14786447608639132

22

Lamb H (1945) Hydrodynamics. Dover, New York

23

Truesdell C (1954) The kinematics of vorticity. Indiana University Press, Bloomington. https://doi.org/10.1002/zamm.19570370525

24
Lanchester FW (1907) Aerodynamics. A. Constable and Company, London
25
Giacomelli R, Pistolesi E (1934) Historical sketch. In: Durand WF (ed) Aerodynamic theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-91489-8_4
26
Kutta W (1902) Lift forces in owing fluids. Aero Mitt Ⅲ
27
Jowkowski N (1906) De la chute dans I’air de Corps l_egers de Forme allong_ee, Anim_es d’un Mouvement Rotatoire. Bulletin de I’Institute Aerodynamic de Koutchino, Petersbourg
28

Liu T, Misaka T, Asai K, Obayashi S, Wu JZ (2016) Feasibility of skin-friction diagnostics based on surface pressure gradient field.Meas Sci Technol 27(12):125304. https://doi.org/10.1088/0957-0233/27/12/125304

29

Chen T, Liu T, Wang LP, Chen SY (2019) Relations between skin friction and other surface quantities in viscous flows. Phys Fluids 31:107101. https://doi.org/10.1063/1.5120454

30

Liu T (2018) Skin-friction and surface-pressure structures in near-wall flows. AIAA J 56(10):3887–3896. https://doi.org/10.2514/1.J057216

31

Chen T, Liu T, Dong ZQ, Wang LP, Chen SY (2021) Near-wall flow structures and related surface quantities in wall-bounded turbulence. Phys Fluids 33:065116. https://doi.org/10.1063/5.0051649

32

Schlichting H (1979) Boundary-layer theory, 7th edn. McGraw-Hill, New York. https://doi.org/10.1115/1.324061

33
Okamoto M (2006) An experimental study on aerodynamic characteristics of steady and unsteady airfoils at low Reynolds number. Dissertation, University of Tokyo, Tokyo
34

Wu JZ, Ma HY, Zhou MD (2006) Vorticity and vortex dynamics. Springer, Berlin. https://doi.org/10.1007/978-3-540-29028-5

35

Marongiu C, Tognaccini R, Ueno M (2013) Lift and lift-induced drag computation by Lamb vector integration. AIAA J 51(6):1420–1430. https://doi.org/10.2514/1.J052104

36

Noca F, Shiels D, Jeon D (1999) A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J Fluids Structures 13(5):551–578. https://doi.org/10.1006/jfls.1999.0219

37

Wang S, He G, Zhang X, Liu T (2015) Evaluation of lift formulas applied to low Reynolds number flows. AIAA J 53(1):161–175. https://doi.org/10.2514/1.J053042

38

Wu JZ, Liu LQ, Liu T (2018) Fundamental theories of aerodynamic force in viscous and compressible complex flows. Prog Aerosp Sci 99:27–63. https://doi.org/10.1016/j.paerosci.2018.04.002

39

Prandtl L (1918) Tragflügeltheorie. Ⅰ. Mitteilung. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Math Phys 1918:451–477

40
Von Kármán T, Burgers JM (1935) General aerodynamic theory — perfect fluids. In: Durand WF (ed) Aerodynamic theory, vol Ⅱ. Dover, New York, pp 1–24
41

Saffman PG (1992) Vortex dynamics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511624063

42

Bryant LW, Williams DH, Taylor GI (1926) An investigation of the flow of air around an aerofoil of infinite span. Phil Trans Royal Soc A 225:626–635. https://doi.org/10.1098/rsta.1926.0005

43

Taylor GI (1926) Note on the connection between the lift in an airfoil in a wind and the circulation round it. Phil Trans Royal Soc A 225:238–245

44

Sears WR (1956) Some recent developments in airfoil theory. J Aero Sci 23(5):490–499. https://doi.org/10.2514/8.3588

45

Sears WR (1976) Unsteady motion of airfoil with boundary-layer separation. AIAA J 14(2):216–220. https://doi.org/10.2514/3.7072

46

Liu T, Wang S, Zhang X, He G (2015) Unsteady thin airfoil theory revisited: application of a simple lift formula. AIAA J 53(6):1493–1502. https://doi.org/10.2514/1.J053439

47

Von Kárman T, Sears WR (1938) Airfoil theory for non-uniform motion. J Aeronautic Sci 10(10):379–390. https://doi.org/10.2514/8.674

48

Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511800955

49
Lighthill MJ (1963) Introduction of Boundary Layer Theory. In: Rosenhead L (ed) Laminar boundary layers. Oxford University Press, Oxford, pp 46–113
50
Lighthill MJ (1995) Fluid Mechanics. In: Brown LM, Pais A, Pippard B (eds) Twentieth Century Physics, Vol. Ⅱ, Chap. 10, pp 795–912. Inst Phys Publishing & AIP Press, Melville, NY
51

Zhu JY, Liu TS, Liu LQ, Zou SF, Wu JZ (2015) Causal mechanism in airfoil-circulation formation. Phys Fluids 27(12):123601. https://doi.org/10.1063/1.4937348

52
Liu T, Schulte M (2007) Flight testing education at Western Michigan University. 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2007–0700, 08–11 January 2007, Reno. https://doi.org/10.2514/6.2007-700
53

Liu T, Liou W, Schulte M (2009) Aeroship: a hybrid flight platform. J Aircraft 46(2):667–674. https://doi.org/10.2514/1.39950

54
Germann KP (1997) Flight test evaluation of a differential global positioning system sensor in runway performance testing. MS Thesis, Mississippi State University, Jackson
55

Hunt JCR, Abell CJ, Peterka JA, Woo H (1978) Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization. J Fluid Mech 86(1):179–200. https://doi.org/10.1017/S0022112078001068

56

Tobak M, Peake DJ (1982) Topology of three-dimensional separation flows. Annu Rev Fluid Mech 14(1):61–85. https://doi.org/10.1146/annurev.fl.14.010182.000425

Advances in Aerodynamics
Pages 37-37
Cite this article:
Liu T. Evolutionary understanding of airfoil lift. Advances in Aerodynamics, 2021, 3(1): 37. https://doi.org/10.1186/s42774-021-00089-4
Metrics & Citations  
Article History
Copyright
Rights and Permissions
Return