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Incompressible flow in contracting ducts

Published online by Cambridge University Press:  04 July 2016

J. C. Gibbings
J. C. Gibbings*
Affiliation:
Department of Mechanical Engineering, University of Liverpool
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Extract

This paper describes the incompressible flow through contracting ducts as used in windtunnel circuits. The value of the velocity gradients that are critically adverse to the boundary layer development are specified and the contraction profile is derived for two-dimensional flow. Solutions to the flow through three-dimensional contractions of circular, square, and square to rectangle shape are obtained. These lead to simple rules for scaling the profile of two-dimensional flow to provide three-dimensional shapes having short lengths with the required velocity distributions. The development of both laminar and turbulent boundary layers is calculated to provide criteria for the avoidance of separation.

Type
Research Article
Information
The Aeronautical Journal , Volume 97 , Issue 967 , September 1993 , pp. 230 - 246
Copyright
Copyright © Royal Aeronautical Society 1993 

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References

1. Pankhurst, R.C. and Holder, D.W. Windtunnel technique, Pitman, London. (Corrected ed), 1965.Google Scholar
2. Bradshaw, P. and Pankhurst, R.C. The design of lowspeed wind tunnels, Prog Aeronaut Sci, 5, pp 1–69.Google Scholar
Kuchemann, D. and Sterne, L.H.G. (Eds), Pergamon, Oxford. 1964.Google Scholar
3. Batchelor, G.K. The theory of homogeneous turbulence, Cambridge Univ Press, pp 55–75, 1970.Google Scholar
4. Tulapurkara, E.G. and Ramjee, U. Effect of contraction on screen-generated turbulence, Aeronaut J, September 1980, 84, pp 290–295.Google Scholar
5. Szczeniowski, B. Contraction cone for a wind tunnel, J Aeronaut Sci, October 1943, 10, pp 311–312.Google Scholar
6. Batchelor, G.K. and Shaw, F. A Consideration of the Design of Wind Tunnel Contractions, Australian Council Aeronautics, Report ACA-4, March 1944.Google Scholar
7. Squire, H.B. and Winter, K.G. The Royal Aircraft Establishment 4 ft x 3 ft Experimental Low Turbulence Wind Tunnel, Part 1, General Flow Characteristics, Aeronautical Research Council R & M No 2690, Feb 1948, Tech Rep No 78, 2, pp 1433–1460, 1960.Google Scholar
8. Schuh, H. and Winter, K.G. The RAE 4 ft x 3 ft Experimental Low Turbulence Wind Tunnel, Part 2, Measurements of Turbulence intensity and Noise in the Working Section, Aeronautical Research Council R & M No 2905, March 1951, Tech Rep No 85, 2, pp 1389–1407, 1962.Google Scholar
9. Schuh, H. The RAE 4 ft x 3 ft Experimental Low Turbulence Wind Tunnel, Part 4, Further Turbulence Measurements, Aeronautical Research Council R & M No 3261, June 1953, Tech Rep No 89, 2, pp 1399–1447, 1964.Google Scholar
10. Thom, A. and Douglas, G.P. High speed tunnels and other research in Germany, CIOS item No 25, File No 38-47, HMSO, London, (circa 1945).Google Scholar
11. Thompson, J.S. Velocity distribution in the working section of the high speed tunnel RAE, R Aircr Est TN Aero 1471, July 1944.Google Scholar
12. Morkovin, M.V. On supersonic wind tunnels with low free-stream disturbances, ASME J Appl Mechs, September 1959, 26, pp 319–323.Google Scholar
13. Tsien, H-S On the design of the contraction cone for a wind tunnel, J Aeronaut Sci, February 1943, 10, pp 68–70.Google Scholar
14. Waters, M.H.L. PhD Thesis, University of London, 1951.Google Scholar
15. Gibbings, J.C. The combination of a contraction with a supersonic nozzle for a wind tunnel, ingenieur - Archiv, 1966, 35, (4), pp 269–275.Google Scholar
16. Cox, R.M. and Freestone, M.M. Design of Ventilated Walls with Special Emphasis on the Aspect of Noise Generation, Agard Report No 602, pp 6.1-6.7, April 1973.Google Scholar
17. Lukasiewicz, J. Effects of boundary layer and geometry on characteristics of perforated walls for transonic wind tunnels, Aerospace Eng, 1961, 20, (4), 1961.Google Scholar
18. Lighthill, M.J. A New Method of Two-Dimensional Aerodynamic Design, Aeronaut Res Council, R & M, No 2112, April 1945, and. Tech Report 1945,1, pp 105-157, 1955.Google Scholar
19. Moretti, G. The calculation of converging channels, Aeronautica, Argentine Comm inf C10, 29 November 1954, Argentina, Trans. TIL, London, TIL/T4612, April 1956.Google Scholar
20. Goldstein, S. Notes of the Design of Converging Channels, Aeronaut Research Council, R & M No 2643, (March 1945), and Tech Report (1945), 1, pp 245–258, 1955.Google Scholar
21. Gibbings, J.C. and Dixon, J.R. Two-dimensional contracting duct flow, Q J Mech App Maths, 1957, 10, (1), pp 24–41.Google Scholar
22. Jordinson, R. Design of wind tunnel contractions, Aircr Eng, October 1961, 33, (392), pp 294–297.Google Scholar
23. Whitehead, L.G., Wu, L.Y. and Waters, M.H.L. Contracting ducts of finite length, Aeronaut Q, February 1951, 2, pp 254–271.Google Scholar
24. Gibbings, J.C. PhD Thesis, University of London, 1951.Google Scholar
25. Morel, T. Comprehensive design of axisymmetric wind tunnel contractions, J Fluid Eng, June 1975, 97, (2), pp 225–233.Google Scholar
26. Stratford, B.S. The prediction of separation of the turbulent boundary layer, J Fluid Mech, 1959, 5, pp 1–16.Google Scholar
27. Bell, J.H. and Mehta, R.D. Boundary layer predictions for small low speed contractions, A1AA J, March 1989, 27, (3), pp 372–374.Google Scholar
28. Mehta, R.D. and Bradshaw, P. Design rules for small low speed wind tunnels, Aeronaut J, November 1979, 83, pp 443–449.Google Scholar
29. Cheers, F. Note on Wind Tunnel Contractions, Aeronaut Res Council, R & M No 2137, March 1945, Tech Report 1945, IV, pp 2957–2963, 1955.Google Scholar
30. Libby, P.A. and Reiss, H.R. The design of two-dimensional contraction sections, Q Appl Maths, 1951, 9, pp 95–98, 1951.Google Scholar
31. Gibbings, J.C. The throat profile for contracting ducts containing incompressible, irrotational flows, int J Mech Sci, 1969, 11, pp 293–301.Google Scholar
32. Gibbings, J.C. Flow in contracting ducts, AIAA J, January 1964, 2, (l), pp 191–192.Google Scholar
33. Bradshaw, P. and Pankhurst, R.C. The Design of Lowspeed Wind Tunnels, NPL Aero Rep 1039, ARC24041, AC853, Revised 4 June 1963, and 21 September 1962.Google Scholar
34. Gibbings, J.C. The choice of a hodograph boundary for contracting ducts, Aeronaut J, June 1964, 68, (642), pp 420–422.Google Scholar
35. Gibbings, J.C. The effective length of two-dimensional contracting ducts, Aeronaut J, June 1966, 70, (660), p 676.Google Scholar
36. Milne-Thomson, L.M. Theoretical hydrodynamics, 2nd Ed, Para 8.61, Macmillan, 1949.Google Scholar
37. Morel, T. Design of two-dimensional wind tunnel contractions, J Fluids Eng, 1977, 99, pp 371–378.Google Scholar
38. Lin, T.C. Ducts for accelerated flow, Proc 2nd US National Congress App Mech, ASME, pp 629-635, 1954.Google Scholar
39. Downie, J.H., Jordinson, R. and Barnes, F.H. On the design of three-dimensional wind tunnel contractions, Aeronaut.J, 1984, 88, pp 287–295.Google Scholar
40. Hartree, D.R. Numerical analysis, Oxford, p 110, 2nd Ed, 1958.Google Scholar
41. Katsikadelis, J.T. and Armenakas, A.E. Numerical evaluation of line integrals with a logarithmic singularity, AIAA .J, July 1985, 23, (7), pp 1135–1137.Google Scholar
42. Mikhail, M.N. Optimum design of wind tunnel contractions. AIAA J, May 1979, 17, (5), pp 471–477.Google Scholar
43. Southwell, R.V. Relaxation Methods in Theoretical Physics, Clarendon Press, Oxford, 1946.Google Scholar
44. Thwaites, B. On the Design of Wind Tunnel Contractions, Aeronaut Res Council, R & M No 2278, 1946.Google Scholar
45. Smith, R.H. and Wang, C.T. Contracting cones giving uniform throat speeds, J Aeronaut Sci, October 1944, 11, pp 356.Google Scholar
46. Tulapurkara, E.G. Studies on Thwaite's method for wind tunnel contraction, Aeronaut J, June 1980, 84, pp 167–169.Google Scholar
47. Cohen, M.J. and Ritchie, N.J.B. Lowspeed three-dimensional contraction design, Aeronaut J, April 1962, 66, (616), pp 231–236.Google Scholar
48. Bloomer, M.T. Notes on the mathematical design of nozzles and wind tunnel contractions, Aeronaut Q, 1957, 8, pp 279–290.Google Scholar
49. Fox, L. and Southwell, R.V. On the flow of a gas through a nozzle with velocities exceeding the speed of sound, Proc R Soc A, 1944, 183, pp 38–54.Google Scholar
50. Mehta, R.D. The aerodynamic design of blower tunnels with wide-angle diffusers, Prog Aerospa Sci, 1977, 18, pp 59–120.Google Scholar
51. Jordinson, R. and Rodger, J.G. On an approximation to the flow through axisymmetric contracting ducts, Aeronaut Q, February 1981, 32, pp 72–81.Google Scholar
52. Crosby, N. Numerical and experimental investigations of three-dimensional turbomachine flows, PhD Thesis, University of Newcastle upon Tyne, 1982.Google Scholar
53. Titchmarsh, E.C. The theory of functions, Oxford University Press, London, p 83, 1932.Google Scholar
54. Von Karman, T. and Levi-Civita, T. Hydro und Aerodynamik, Springer, Berlin, p 248, 1924.Google Scholar
55. Liddle, S.G. and Archer, R.D. incompressible flow in conical contraction using the method of integral relations. J Hydronaut, January 1971, 5, (l),pp 25–30.Google Scholar
56. Hoerner, S. Tests on the wind tunnel at the Technical High School, Brunswick, Luftfahrtforschung, January 1937, 14, (1), p 36, British RTP Translation No 520.Google Scholar
57. Watmuff, J.H. Design of a new contraction for the ARL Low Speed Wind Tunnel (U), Aeronaut Res Labs (Melbourne), Aeronaut Rep ARL-Aero-R-171, August 1986.Google Scholar
58. Karlsson, R.I. An Experimental investigation of Boundary Layer Development on a Wind Tunnel Wall After Contraction, Euromech 72, University of Salford, 30 September 1976, Chalmers Univ Tech inst Report No 760325, Gothenburg, March 1976.Google Scholar
59. Hussain, A.K.M.F. and Ramjee, V. Effects of an axisymmetric contraction shape on incompressible turbulent flow, J Fluids Eng, March 1976, 98, (l), pp 58–69.Google Scholar
60. Ramjee, V. and Hussain, A.K.M.F. influence of the axisymmetric contraction ratio on free-stream turbulence, J Fluids Eng, September 1976, 98, (3), pp 506–515.Google Scholar
61. Back, L.H., Cuffel, R.F. and Massier, P.F. Laminarization of a turbulent boundary layer in nozzle flow, AIAA J, 1969, 7, pp 730–733.Google Scholar
62. Chmielewski, G.E. Boundary layer considerations in the design of aerodynamic contractions, J Aircr, August 1974, 11, (8), pp 435–438.Google Scholar
63. Hall, D.J. and Gibbings, J.C. influence of stream turbulence and pressure gradient upon boundary layer transition, J Mech Eng Sci, 1972, 14, (2), pp 134–146.Google Scholar
64. Heskestad, G. Discussion of T. Morel (Ref. 25), J Fluids Eng, March 1976, 98, (2), pp 131–132.Google Scholar
65. Bradshaw, P. The effect of windtunnel screens on nominally two-dimensional boundary layers, J Fluid Mechs, 1965, 22, pp 679–687.Google Scholar
66. Mehta, R.D. Turbulent boundary layer perturbed by a screen, AIAA J, September 1985, 23, (9), pp 1335–1342.Google Scholar
67. Launder, B.E. Laminarization of the Turbulent Boundary Layer by Acceleration, Report 77, Gas Turbine Lab, Massachusetts Inst Tech, 1964.Google Scholar
68. Beckwith, I.E. Development of a high Reynolds number quiet tunnel for transition research, AIAA J, 1975, 13, pp 300–306.Google Scholar
69. Harvey, W.D., Stainback, P.C., Anders, J.B. and Cary, A.M. Nozzle wall boundary layer transition and fee stream disturbances at Mach 5, AIAA.J, March 1975, 13, (3), pp 307–314.Google Scholar
70. Bearman, P.W. in Momentum transfer in boundary layers, McGraw Hill, Cebeci, T. and Bradshaw, P. (Eds) pp 321–322, 1977.Google Scholar
71. Riley, S., Johnson, M.W. and Gibbings, J.C. Boundary layer transition on strongly concave surfaces, ASME Proc Gas Turbine Conf, Toronto, June 1989.Google Scholar
72. Mokhtari, S. and Bradshaw, P. Longitudinal vortices in wind tunnel wall boundary layers, Aeronaut J, June/July 1983, 87, (866), pp 233–236.Google Scholar
73. Sproston, J.L. The hodograph method of aerofoil and cascade design for incompressible flow, Part 3, The effect of the boundary layer on the flow past a surface singularity, Aeronaut Res Council, Rep No 34481, FM 4403, April 1973.Google Scholar
74. Smith, F.T. Boundary layer flow near a discontinuity in wall conditions, J inst Maths Applies, 1974, 13, pp 127–145.Google Scholar
75. Gibbings, J.C. and Yousif, A.H. The Separating Flow of a Boundary Layer, Part 4, The Transitional Layer, Dept Mech Eng, Report No TF/3/88, University of Liverpool, 1988.Google Scholar
76. Gibbings, J.C. and Yousif, A.H. The Separating Flow of a Boundary Layer, Part 1; The Laminar Layer, Dept Mech Eng, Report No FM/121/88, University of Liverpool, 1988.Google Scholar
77. Gibbings, J.C. and Yousif, A.H. The Separating Flow of a Boundary Layer, Part 2, The Turbulent Layer, Dept Mech Eng, Report No TF/l/88, University of Liverpool, 1988.Google Scholar
78. Stratford, B.S. Flow in the Laminar Boundary Layer Near Separation, Aeronaut Res Council, R & M 3002, November 1954, Tech Report 1954, pp 151-177, 1962.Google Scholar
79. White, F.M. Viscous Fluid Flow, McGraw Hill, New York, 1974.Google Scholar