Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-04T18:36:57.976Z Has data issue: false hasContentIssue false

Theoretical modelling of three-dimensional vortex flows in aerodynamics

Published online by Cambridge University Press:  04 July 2016

J. H. B. Smith*
Affiliation:
Aerodynamics Department, Royal Aircraft Establishment, Farnborough

Summary

A unified account is presented of the various inviscid models used to represent three-dimensional vortex flows in aerodynamics; essentially those relying on vortex sheets and linevortices. Recent developments in extending the scope, accuracy, and stability of these models are described. An evaluation of their relative strengths and weaknesses suggests that the different models all have continuing roles to play. It is claimed that vortex modelling has come of age, in the sense that we can now learn about the real world from the behaviour of models, after decades of trying to make the models conform with reality.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1984 

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

1. Mangler, K. W. and Smith, J. H. B. A theory of the flow past a slender delta wing with leading-edge separation. Proc Roy Soc Lond A, 1959, 251,200217; also Report Aero 2593,1957.Google Scholar
2. Johnson, F. T., Lu, P., Tinoco, E. N. and Epton, M. A. An improved panel method for the solution of three-dimensional vortex flows: Vol 1 —Theory document. NASA CR-3278 1980.Google Scholar
3. Rehbach, C. Numerical investigation of leading-edge vortex for low aspect ratio thin wings, 1976, AIAA J, 14,253255.Google Scholar
4. Nangia, R. K. and Hancock, G. J. A theoretical investigation for delta wings with leading-edge separation at low speeds. ARC CP 1086, 1968.Google Scholar
5. Sacks, A. H., Lundberg, R. E. and Hanson, C. W. A theoretical investigation of the aerodynamics of slender wingbody combinations exhibiting leading-edge separation. NASA CR-719, 1967.Google Scholar
6. Brown, C. E. and Michael, W. H. Effect of leading-edge separation on the lift of a delta wing. J Aero Sci, 1954, 21,690694 and 706.Google Scholar
7. Hoeijmakers, H. W. M. Computational vortex flow aerodynamics. In AGARD FDP Symposium Aerodynamics of vortical type flow in three dimensions. AGARD-CP-342,1983.Google Scholar
8. Smith, J. H. B. Achievements and problems in modelling highlyswept flow separations. In Numerical methods in aeronautical fluid dynamics (ed. Roe, P. L.), Academic Press, 1982.Google Scholar
9. Clark, R. W. Non-conical flow past slender wings with leadingedge vortex sheets. ARC R&M 3814,1976.Google Scholar
10. Jones, I. P. Leading-edge separation from a slender rolling wing-body combination. RAE Technical Report 80039,1980.Google Scholar
11. Tinoco, E. N., Lu, P. and Johnson, F. T. An improved panel method for the solution of three-dimensional vortex flows: Vol 2 — Users’ guide. NASA CR-3279,1980.Google Scholar
12. Smith, J. H. B. In Three-dimensional and unsteady separation at high Reynolds numbers, AGARD-LS-94,1978.Google Scholar
13. Legendre, R. Écoulement au viosinage de lapointe avant d'une aile à forte flèche aux incidences moyennes. Rech Aero, Nos 30, 31 and 35,1953.Google Scholar
14. Bryson, A. E. Symmetrical vortex formation on circular cylinders and cones. J Appl Mech (ASME), 1959,26,643648.Google Scholar
15. Matoi, T. K., Covert, E. E. and Widnall, S. E. A threedimensional lifting-surface theory with leading-edge vortices. US Office of Naval Research ONR-CR-215-230-2,1975.Google Scholar
16. Hall, M. G. A theory for the core of a leading-edge vortex. J Fluid Mech, 1961,11,209228.Google Scholar
17. Brown, S. N. The compressible inviscid leading-edge vortex. J Fluid Mech, 1965,22,1732.Google Scholar
18. Mangler, K. W. and Weber, J. The flow field near the centre of a rolled-lip vortex sheet. J Fluid Mech, 1967,30,177196.Google Scholar
19. Moore, D. W. and Saffman, P. G. The motion of a vortex filament with axial flow. Phil Trans Roy SocLondA, 1972,272, 403429.Google Scholar
20. Hoeijmakers, H. W. M. and Vaatstra, W. A higher-order panel method for the computation of the flow about slender delta wings with leading-edge vortex separation. NLR MP 81053U, 1981.Google Scholar
21. Verhaagen, N. G. and Van Der Snoek, L. An experimental investigation into the entrainment into a leading-edge vortex. Delft Univ of Techn Report LR-332,1981.Google Scholar
22. Moore, D. W. A numerical study of the roll-up of a finite vortex sheet. J Fluid Mech, 1974,63,225235.Google Scholar
23. Fink, P. T. and Soh, W. K. A new approach to roll-up calculations of vortex sheets. Proc Roy Soc Lond A, 1978, 362, 195209.Google Scholar
24. Peace, A. J. A multi-vortex model of leading-edge vortex flows. Int J of Numercial Methods in Fluids, 1983,3,543565.Google Scholar
25. Fiddes, S. P. A theory of the separated flow past a slender elliptic cone at incidence. Paper 30 in Computation of viscousinviscid interactions, AGARD CP 291.1980.Google Scholar
26. Smith, J. H. B. Behaviour of a vortex sheet separating from a smooth surface. RAE Technical Report 77058. 1977.Google Scholar
27. Smith, F. T. Three-dimensional viscous and inviscid separation of a vortex sheet from a smooth non-slender body. RAE Technical Report 78095. 1978.Google Scholar
28. Fiddes, S. P. and Smith, J. H. B. Calculations of asymmetric separated flow past circular cones at large angles of incidence. Paper 14 in Missile aerodynamics, AGARD CP 336,1982.Google Scholar
29. Sychev, V. V. On laminar separation. Izv Ak Nauk Mekh Zh Gaza, 1972, No 3, 4759; Trans in Fluid Dynamics, Plenum, March 1974,407-417.Google Scholar
30. Smith, F. T. The laminar separation of an incompressible fluid streaming past a smooth surface. Proc Roy Soc Lond A, 1977, 356, 443463.Google Scholar
31. Rainbird, W. J.,Crabble, R. S. and Jurewicz, L. S. A watertunnel investigation of flow separation about circular cones at incidence. NRC (Canada) Aeron Rep LR 385,1963.Google Scholar
32. Rainbird, W. J. The external flow field about yawed circular cones. Paper 19 in AGARD CP 30.1968.Google Scholar
33. Nangia, R. K. A study of slender conical thick wings and bodies with variation of flow separation point. Bristol Univ, Dept of Aero Eng, Grant No AFOSR-77-3243. 1978.Google Scholar
34. Moore, K. Line-vortex models of separated flow past a circular cone at incidence. RAE Technical Memorandum Aero 1917. 1981.Google Scholar
35. Hoeijmakers, H. W. M. and Vaatstra, W. A higher-order panel method applied to vortex sheet roll up. AIAA Paper 82-0096. 1982.Google Scholar
36. Hoeijmakers, H. W.M. and Vaatstra, W. On the vortex flow over delta and double-delta wings. AIAA Paper 82-0949.1982.Google Scholar
37. Moore, D. W. The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc Roy Soc Lond A, 1979,365,105119.Google Scholar
38. Butterworth, P. J. Flow measurements in the wake of a wing fitted with a leading-edge root extension (strake). RAE Technical Report 79120. 1979.Google Scholar
39. Smith, J. H. B. Improved calculations of leading-edge separation from slender, thin, delta wings. Proc Roy Soc Lond A, 1968,306, 6790; RAE Technical Report 66070. 1966.Google Scholar
40. Dyer, D. E., Fiddes, S. P. and Smith, J. H. B. Asymmetric vortex formation from cones at incidence — a simple inviscid model. Aeronautical Quarterly, November 1982, 33, 293312; also RAE Technical Report 81130. 1981.Google Scholar
41. Barsby, J. E. Separated flow past a slender delta wing at low incidence. Aeronautical Quarterly, 1973,24,120128.Google Scholar
42. Clark, R. W., Smith, J. H. B. and Thompson, C. W. Some series-expansion solutions for slender wings with leading-edge separation. ARC R&M 3785.1975.Google Scholar
43. Barsby, J. E. Flow past conically cambered slender delta wings with leading-edge separation. ARC R&M 3748. 1972.Google Scholar
44. Levinsky, E. S. and Wei, M. H. Y. Non-linear lift and pressure distribution on slender conical bodies with strakes at low speeds. NASA CR-1202,1968.Google Scholar
45. Rehbach, C. Etude numérique de nappes tourbillonnaires issues d'une ligne de décollement pres du bord d'attaque. Rech Aero, 1973, No 6,325330.*Google Scholar
46. Schroder, W. Berechnung der nichtlinearen Beiwerte von Fliigeln mit kleinem und mittlerem Seitenverhaltnis nach dem Wirbelleiterverfahren in inkompressibler Stromung. DFVLR-78-26. 1978; Trans as ESA-TT-585.Google Scholar
47. Jepps, S. A. The computation of vortex flows by panel methods. VKI Lecture Series 5, Computational Fluid Dynamics. 1978.Google Scholar
48. Belotserkovskii, S. M. and Nisht, M. I. Unsteady non-linear theory for a thin wing of arbitrary planform. Izv Ak Nauk Mekh Zh Gaza, 1974, No 4 100-108; Trans in Fluid Dynamics, 9, 583589.Google Scholar
49. Atta, E. H., Kandil, O. A., Mook, D. T. and Nayfeh, A. H. Unsteady aerodynamic loads on arbitrary wing including wingtip and leading-edge separation. AIAA Paper 77-156.1977.Google Scholar
50. Kandil, O. A., Atta, E. H. and Nayfeh, A. H., Threedimensional steady and unsteady asymmetric flow past wings of arbitrary planforms. NASA CR-145235. 1977.Google Scholar
51. Aparimov, V. A., Belotserkovskii, S. M., Nisht, M. I. and Sokolova, O. N. On the mathematical simulation in an ideal fluid of separated flow past a wing and the destruction of the vortex sheet. Dokl Ak Nauk SSSR, 1976, 227, 820823; Trans in Sov Phys Dokl, 21,4,181-183.Google Scholar
52. Rehbach, C. Calcul numérique d'ecoulement tridimensionels instationnaires avec nappes tourbilonnaires. Rech Aero, 1977, 289298.Google Scholar
53. Rehbach, C. Calcul instationnaire de nappes tourbillonnaires émises par des surfaces portantes fortement inclinées. Paper 14 in High angle of attack aerodynamics, AGARD CP 247. 1978.Google Scholar
54. Hall, M. G. A numerical method for solving the equations for a vortex core. RAE Technical Report 65106. 1965.Google Scholar
55. Rizzi, A. Numerical solution of Euler equations simulation of three-dimensional vortex flow. In AGARD FDP Symposium Aerodynamics of vortical type flow in three dimensions. AGARD-CP-342. 1983.Google Scholar
56. Lighthill, M. J. Mathematics in aeronautics. J Roy Aeron Soc, 1960, 64, 375384.Google Scholar
57. Küchemann, D. The aerodynamic design of aircraft. 1978, Pergamon, 513.Google Scholar
58. Smith, J. H. B. A review of separation in steady threedimensional flow. Paper 31 in Flow Separation, AGARD CP 168,1975.Google Scholar
59. Hunt, B. L. Asymmetric vortex forces and wakes on slender bodies. AIAA Paper 82-1336. 1982.Google Scholar
60. Keener, E. R., Chapman, G. T., Cohen, L. and Taleghani, J. T. Side-forces on forebodies at high angles of attack and Mach numbers from 0.1 to 0.7; two tangent ogives, paraboloid and cone. NASA TM X-3438. 1977.Google Scholar
61. Jones, I. P. Flow separation from yawed delta wings. Computers & Fluids, 1975,3, 155177.Google Scholar
62. Peake, D. J., Owen, F. K. and Johnson, D. A. Control of forebody vortex orientation to alleviate side-forces. AIAA Paper 80-0183. 1980. ©Copyright. Controller HMSO, London, 1983.Google Scholar