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The Transonic Flow Past Two-Dimensional Aerofoils

Published online by Cambridge University Press:  04 July 2016

D. W. Holder
D. W. Holder*
Affiliation:
University of Oxford
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Extract

It is both an honour and a responsibility to deliver a lecture commemorating the names of two scientists who have made unique contributions to fluid dynamics, and whose names perhaps above all others will remain immortal in our subject. The range of topics that would be suitable for such a lecture is very wide, because there is scarcely a branch of fluid dynamics in which the work of Reynolds and Prandtl does not continue to play a significant part. In a lecture of current interest there is, therefore, no problem of relating the subject matter to the names to be commemorated; the influence of Reynolds and Prandtl remains as strong as when they were alive, and many of the problems that engaged their attention are even today only partially solved. The lecturer must, therefore, use other considerations for guidance in the selection of his subject from the limited range on which he is qualified to speak, for few could hope to work over the wide field covered by Reynolds and Prandtl. He must if possible select a, topic in which major contributions have originated from Germany and the United Kingdom, on which research is actively in progress in both countries, and for which progress has relied on the combination of theoretical and experimental work to provide acceptable simplifying assumptions that characterised many of the investigations of Reynolds and Prandtl.

Type
The Second Reynolds-Prandtl Lecture
Information
The Aeronautical Journal , Volume 68 , Issue 644 , August 1964 , pp. 501 - 516
Copyright
Copyright © Royal Aeronautical Society 1964

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References

1.Pearcey, H. H.The Aerodynamic Design of Section Shapes for Swept Wings. Advances in Aeronautical Sciences, Vol. 3, p. 277. Pergamon Press, 1962.CrossRefGoogle Scholar
2.Pearcey, H. H.Some Aspects of the Physical Nature of Transonic Flows Past Aerofoils and Wings. Proc. Symposium Transsonicum Aachen. Springer-Verlag, 1962.Google Scholar
3.Lock, R. C. and Rogers, E. W. E.Aerodynamic Design of Swept Wings and Bodies for Transonic Speeds. Advances in Aeronautical Sciences, Vol. 3, p. 253. Pergamon, 1962.Google Scholar
4.Lock, R. C.The Aerodynamic Design of Swept Winged Aircraft at Transonic and Supersonic Speeds. Journal of the Royal Aeronautical Society, Vol. 67, June 1963.Google Scholar
5.Bagley, J. A.The Aerodynamic Design of Swept Wings. Progress in Aeronautical Sciences, Vol. 2. Pergamon Press.Google Scholar
6.Janzen, O.Beitrag zu einer Theorie der stationaeren Stroemung Kompressibler Fluessigkeiten. Phys. Z., Vol. 14, p. 639, 1913.Google Scholar
7.Rayleigh, Lord. On the Flow of a Compressible Fluid Past an Obstacle. Phil. Mag., Vol. 32, p. 1, 1916.CrossRefGoogle Scholar
8.Prandtl, L.Ueber Stroemungen, deren Geschwindigkeitenmit der Schallgeschwindigkeit vergleichbarsind. J. Aero. Res. Inst., Univ. of Tokyo, No. 6, p. 14, 1930.Google Scholar
9.Glauert, H. The Effect of Compressibility on the Lift of an Aerofoil. A.R.C. R. & M. 1135, 1927.Google Scholar
10.Stanton, T. E. A High-Speed Wind Channel for Tests on Aerofoils. A.R.C. R. & M. 1130, 1928.Google Scholar
11.See, e.g. Goethert, B. Profilmessungen im Hochgeschwindig keitskanal 2.7 m.D. F.B. 1490, 1941.Google Scholar
12.See, e.g. Stack, J. and Von Doenhoff, A. E. Tests of 16 Related Aerofoils at High Speeds. NACA Report 492, 1934.Google Scholar
13.Lock, C. N. H.Problems of High-Speed Flight as Affected by Compressibility. Journal of the Royal Aeronautical Society, Vol. 42, p. 93, 1938.Google Scholar
14.See, e.g. Holder, D. W. The High-Speed Laboratory of the Aerodynamics Division, N.P.L. A.R.C. R. & M. 2560, 1946.Google Scholar
15.See, e.g. Thompson, J. S. and Mair, W. A. The RAE High-Speed Tunnel and a Review of the Work Accomplished in 1942-45. A.R.C. R. & M. 2222, 1946.Google Scholar
16.See, e.g. Shaw, R. A. Changes in Control Characteristics with Changes in Flow Pattern at High Subsonic Speeds. A.R.C. R. & M. 2436, 1948.Google Scholar
17.Ackeret, J., Feldmann, F. and Rott, N.Untersuchungen an Verdichtungsstoeben und Grenzschichten in Schnell bewegten Gasen. Mitt. Inst. Aerodyn., No. 10. E.T.H. Zurich, 1946.Google Scholar
18.Liepmann, H. W.The Interaction between Boundary Layer and Shock Waves in Transonic Flow. Journal of the Aeronautical Sciences, Vol. 13, p. 623, 1946.Google Scholar
19.Holder, D. W., Pearcey, H. H. and Gadd, G. E. The Interaction Between Shock Waves and Boundary Layers. A.R.C. C.P. 180, 1954.Google Scholar
20.See, e.g. Gray, W. E. A Chemical Method for Indicating Transition in the Boundary Layer. A.R.C. 8034, 1944.Google Scholar
21.Goethert, B. Widerstandsanstieg bei Profilen im Bereichhoher Unterschallgeswindigkeiten. U.M. 1167, 1944.Google Scholar
22.Holder, D. W. Transition Indication in the N.P.L. 20 inX 8 in High-Speed Tunnel. A.R.C. R. & M. 2079, 1945.Google Scholar
23.Holder, D. W. and Gadd, G. E. The Interaction Between Shock Waves and Boundary Layers. Proc. N.P.L. Symposium on Boundary Layers, 1955.Google Scholar
24.Pearcey, H. H. and Holder, D. W. Examples of the Effects of Shock-induced Boundary Layer Separation in Transonic Flight. A.R.C. 16,446, 1954.Google Scholar
25.Millikan, C. B. High-Speed Testing in the Southern California Co-Operative Wind Tunnel. Proc. 1st Anglo-American Aeronautical Conference, London, 1947, p. 137, R.Ae.S., 1948.Google Scholar
26.Weaver, W.A Method of Wind Tunnel Testing Through the Transonic Range. Journal of the Aeronautical Sciences, Vol. 15, p. 28, 1948.CrossRefGoogle Scholar
27.Lock, C. N. H. and Beavan, J. A. Tunnel Interference at Compressibility Speeds Using the Flexible Walls of the Rectangular High-Speed Tunnel. A.R.C. R. & M. 2005, 1944.Google Scholar
28.Habel, L. W. and Henderson, J. H. Preliminary Investigation of Aerofoil Characteristics in the Langley Annular Transonic Tunnel. NACA RM L50E18, 1950.Google Scholar
29.Wright, R. H. and Ward, V. G. NACA Transonic Wind-Tunnel Test Sections. NACA RM L8J06, 1948.Google Scholar
30.Holder, D. W., North, R. J. and Chinneck, A. Experiments with Slotted and Perforated Walls in a Two-dimensional High-Speed Tunnel. A.R.C. R. & M. 2955, 1951.Google Scholar
31.Von Karman, Th.Compressibility Effects in Aerodynamics. Journal of the Aeronautical Sciences, Vol. 8, p. 337, 1941.Google Scholar
32.Temple, G. and Yarwood, T. The Approximate Solution of the Hodograph Equation for Compressible Flow. RAE Report SME 3201, 1942.Google Scholar
33.Weber, J. The Calculation of the Pressure Distribution over the Surface of Two-dimensional and Swept Wings with Symmetrical Aerofoil Sections. A.R.C. R. & M. 2918. See also A.R.C. 17927, 1955.Google Scholar
34.Riegels, F. W.Aerofoil Sections. Butterworths, 1961.Google Scholar
35.Spreiter, J. R. and Alksne, A. Thin Aerofoil Theory based on an Approximate Solution of the Transonic Flow Equation. NACA Report 1359.Google Scholar
36.Woods, L. C. The Application of the Polygon Method to the Calculation of the Compressible Subsonic Flow Round Two-Dimensional Profiles. A.R.C. C.P. 115, 1952.Google Scholar
37.Spence, D. A.Prediction of the Characteristics of Two-Dimensional Aerofoils. Journal of the Aeronautical Sciences, Vol. 21, p. 577, 1954.Google Scholar
38.Nieuwland, G. Y. Enige opmerkingen over theorie en experiment in het transsone gebied. N.L.R. Report T57, 1962.Google Scholar
39.Von Karman, Th.Similarity Law of Transonic Flow. J. Math. Phys., Vol. 26, p. 182, 1947.Google Scholar
40.Guderley, G. and Yoshihara, H.The Flow over a Wedge Profile at Mach Number 1. Journal of the Aeronautical Sciences, Vol. 17, p. 723, 1950.Google Scholar
41.Spreiter, J. R. and Alksne, A. Theoretical Prediction of Pressure Distributions on Non-Lifting Aerofoils at High Subsonic Speeds. NACA Report 1217, 1955.Google Scholar
42.Oswatitsch, K.Die Geschwindigkeitsverteilung bei lakalen Uberschallgebieten an Flachen Profilen. Z.A.M.M., Vol. 30, 1950. See also A New Law of Similarity for Profiles Valid in the Transonic Region. A.R.C. 10,807,1947.Google Scholar
43.Gullstrand, T. R. Flow Over Symmetrical Aerofoils With out Incidence in the Lower Transonic Range. K.T.H. Aero T.N. 20.Google Scholar
44.Sinnott, C. S. On the Prediction of Mixed Subsonic/Supersonic Pressure Distributions over Aerofoils, Part III. A.R.C. 20461, 1958.Google Scholar
45.Nikolskii, A. A. and Tagenov, G. I. Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown. NACA T.M. 1213, 1949.Google Scholar
46.Busemann, A.The Drag Problem at High Subsonic Speeds. Journal of the Aeronautical Sciences, Vol. 16, p. 337, 1949.Google Scholar
47.Shapiro, A. H.The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. II, pp. 896 and 889. The Ronald Press, 1954.Google Scholar
48.Liepmann, H. W., Ashkenas, H. and Cole, J. D. Experiments in Transonic Flow. Wright Field Technical Report 5667, 1950.Google Scholar
49.See, e.g. Holder, D. W. Note on the Wakes behind Bodies Moving at High Mach Number. A.R.C. 14720, 1952. See also A High-Speed Camera for Recording Shock-Wave Oscillations. A.R.C. R. & M. 2901, 1949.Google Scholar
50.Nieuwland, G. Y. The Computation by Lighthill’s Method of Transonic Flow Potential Flow around a Family of Quasi-elliptical Aerofoils. N.L.R. Report to be issued shortly.Google Scholar
51.Lock, C. N. H. and Holder, D. W.Proceedings 1st Anglo-American Aeronautical Conference, London, 1947, p. 220. Royal Aeronautical Society, 1948.Google Scholar
52.Rogers, E. W. E. Observations on a Thin Cambered Aerofoil beyond the Critical Mach Number. A.R.C. R. & M. 2432, 1950.Google Scholar
53.Pearcey, H. H. Some Effects of Shock-induced Separation of Turbulent Boundary Layers in Transonic Flow Past Aerofoils. A.R.C. R. & M. 3108, 1955. See also Proc. N.P.L. Symposium on Boundary Layers, 1955.Google Scholar
54.Holder, D. W. The Interaction Between Shock Waves and Boundary Layers. Proc. 5th Anqlo-American Aeronautical Conference Los Angeles, 1955. I.A.S. 1956.Google Scholar
55.Pearcey, H. H. A Method for the Prediction of the Onset of Buffeting and other Separation Effects from Wind Tunnel Tests on Rigid Models. A.R.C. 20631, AGARD Rep. 223, 1958.Google Scholar
56.Pearcey, H. H. and Holder, D. W. Simple Methods for the Prediction of Wing Buffeting Resulting from Bubble Type Separation. A.R.C. 23,884, 1962.Google Scholar
57.Farren, W. S. The Aerodynamic Art, 44th Wilbur Wright Lecture. Journal Royal Aeronautical Society, July 1956.CrossRefGoogle Scholar
58.Holder, D. W. and Pearcey, H. H.A Method for Providing Warning of the Onset of Buffeting, Stalling and Other Undesirable Effects of Flow Separation. Journal of the Royal Aeronautical Society, Vol. 62, p. 674, 1958.Google Scholar
59.Pearcey, H. H. and Pankhurst, R. C. Survey of Progress in N.P.L. High-Speed Tunnel Tests of Spoilers on an Aero foil with 025c. Hap. Unpublished N.P.L. Report, 1952.Google Scholar
60.Pearcey, H. H. and Stuart, C. M. Methods of Boundary-Layer Control for Postponing and Alleviating Buffeting and Other Effects of Shock-induced Separation. I.A.S. S.M.F. Fund Paper FF-22, 1959.Google Scholar
61.Pearcey, H. H.Shock-induced Separation and its Prevention by Design and Boundary Layer Control. Contribution to Boundary Layer and Flow Control. Pergamon Press, 1960.Google Scholar
62.Haines, A. B., Holder, D. W. and Pearcey, H. H. Scale Effects at High Subsonic and Transonic Speeds and Methods For Fixing Boundary Layer Transition in Model Experiments. A.R.C. R. & M. 3012, 1954.Google Scholar
63.Holder, D. W. and Cash, R. F. Experiments with a Two-Dimensional Aerofoil Designed to be Free from Turbulent Boundary-Layer Separation at Small Angles of Incidence for all Mach Numbers. A.R.C. R. & M. 3100, 1957.Google Scholar
64.Holder, D. W. Note on the Flow Near the Tail of a Two-dimensional Aerofoil Moving at a Free-Stream Mach Number close to Unity. A.R.C. C.P. 188, 1954.Google Scholar
65.Edwards, J. B. Free-Flight Tests of Vortex Generator Configurations at Transonic Speeds. A.R.C. 24668, 1962.Google Scholar
66.Sinnott, C. S.On the Flow of a Sonic Stream Past an Aerofoil Surface. Journal of the Aerospace Sciences, Vol. 26, p. 169, 1959.Google Scholar
67.Sinnott, C. S. Estimation of the Transonic Characteristics of Aerofoils. NPL/Aero/385, 1959.Google Scholar
68.Sinnott, C. S. and Osborne, J. Review and Extension of Transonic Aerofoil Theory. A.R.C. R. & M. 3156, 1958. See also OSWATITSCH, K. The Drag Increase at High Subsonic Speeds. A.R.C. 11,246, 1947.Google Scholar
69.Randall, D. G. Transonic Flow Over Two-Dimensional Round-Nosed Aerofoils. A.R.C. 20,677, 1958.Google Scholar
70.Emmons, H. W. The Theoretical Flow of a Frictionless Adiabatic Perfect Gas Inside a Two-Dimensional Hyperbolic Nozzle. NACA TN 1003, 1946.Google Scholar
71.Oswatitsch, K. and Zierep, I. Das Problem des senkrechten Stobes an einer gekrummten Wand. AZMM v40T Sonderheft 143-144, 1960.Google Scholar
72.Gadd, G. E. and Holder, D. W.The Behaviour of Supersonic Boundary Layers in the Presence of Shock Waves. Proc. 1th Anglo-American Aeronautical Conference, New York, 1959. Institute of Aerospace Sciences, 1960.Google Scholar
73.Gadd, G. E. Interactions between Normal Shock Waves and Turbulent Boundary Layers. A.R.C. R. & M. 3262, 1961.Google Scholar
74.Rotta, J. C. Druckverteilungsmessungen an einem symmetrishchen Flugelprofil bei transsonischer Stromung im Freistrahl. Aerodynamische Versuchsanstalt, Forschungsbericht 62-01, 1962.Google Scholar
75.Betz, A. Uber die Lage des Verdichtungsstoben bei ummstromten Profilen. AVA Bericht 43/A/31, 1943.Google Scholar
76.Nitzberg, G. E. and Crandall, S. A Study of the Application of Aerofoil Section Data to the Estimation of the High-Subsonic-Speed Characteristics of Swept Wings. NACA RM A55C23, 1955.Google Scholar
77.Sinnott, C. S. and Stuart, C. M. An Analysis of the Supersonic Region in a High-Subsonic Flow Past an Aerofoil Surface. A.R.C. 21,715, 1960.Google Scholar
78.Holder, D. W., Pearcey, H. H. and NASH, J. F. Some Aerodynamic Advantages of Using Wings with Thick Trailing Edges for High-Speed Aircraft. Lecture to R.Ae.S., Feb. 1962.Google Scholar
79.Holder, D. W. and Cash, R. F. An Investigation of the Use of Thick Trailing Edges on Two-dimensional Aerofoils at Subsonic and Transonic Speeds (in preparation).Google Scholar
80.Nash, J. F. A Review of Research on Two-dimensional Base Flow. A.R.C. R. & M. 3323, 1962.Google Scholar
81.See, for example, Prandtl, L. and Tietjens, O. G. Applied Hydro and Aeromechanics, p. 132. McGraw-Hill, 1934.Google Scholar
82.Wood, C. J. An Interim Note on Two-dimensional Base Bleed. A.R.C. 24361, 1962.Google Scholar
83.Nash, I. F., Quincey, V. G. and Callinan, J. Experiments on Two-dimensional Base Flow at Subsonic and Transonic Speeds. A.R.C. 25070, 1963.Google Scholar
84.Nash, J. F. An Approximate Method for the Prediction of the Zero Lift Pressure Distribution and Drag of Symmetrical Blunt Trailing Edge Aerofoil Sections at Subsonic Speeds in the Absence of a Vortex Street. N.P.L. Report to be issued shortly.Google Scholar
85.Bratt, J. B., Raymer, N. G. and Townsend, J. E. G. Measurements of the Direct Pitching Moment Derivatives for Two-dimensional Flow at Subsonic and Supersonic Speeds. A.R.C. 20714, 1959.Google Scholar
86.Lambourne, N. C. Some Instabilities Arising from the Interaction between Shock Waves and Boundary Layers. AGARD Report 182, 1958. See also A.R.C. C.P. 473, 1958.Google Scholar
87.Iones, W. P.Research on Unsteady Flow. Journal of the Aerospace Sciences, Vol. 29, No. 3, p. 249, 1962.Google Scholar