Acta Mechanica

, Volume 44, Issue 1–2, pp 1–48 | Cite as

Laminarescent, relaminarizing and retransitional flows

  • K. R. Sreenivasan
Review Article

Summary

This report examines in detail all accelerated turbulent boundary layers and subcritical pipe or channel flows undergoing relaminarization and possible retransition, with a view to evolving a broad picture in regard to the status of experiments in these flows, the trustworthiness or shortcomings of the data, the sources of difficulties peculiar to these flows, etc. With the hindsight so acquired, a discussion is provided of the directions in which future work would most usefully supplement the existing data.

Notation

a

pipe radius or channel half-height

cf

skin-friction coefficient

H

shape factor,δ*

K

acceleration parameter, ν(dU/dx)/U2

k

Karman constant

P

kinematic pressure

Re

Reynolds number,Uava/ν

Rθ

momentum thickness Reynolds number,Uθ/ν

T

temperature

U, V

mean velocity inx andy directions respectively

U*

friction velocity,\(\tau _{w^{1/2} }\)

u, v, w

fluctuating velocity components in thex, y andz directions respectively

x, y, z

streamwise, normal and spanwise Cartesian coordinates

Δp

\(v(dP/dx)/U_{*^3 }\)

Δτ

\(v(\partial \tau /\partial y)/U_{*^3 }\)

δ

boundary layer thickness,U(δ)/U=0.995

δ*

displacement thickness,\(\int\limits_{ - \infty }^\infty {(1 - U/U_\infty ) dy}\)

θ

momentum thickness,\(\int\limits_{ - \infty }^\infty {(U/U_\infty ) (1 - U/U_\infty ) dy}\)

Λ

pressure gradient parameter,(dP/dx) δ/τw

ν

kinematic viscosity coefficient

τ

kinematic Reynolds shear stress,\(\overline { - uv}\)

Suffixes

free-stream values

w

wall values

av

section average values

Superscript

+

variables normalized by U* and ν

rms values

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Back, L. H., Seban, R. A.: Flow and heat transfer in a turbulent boundary layer with large acceleration parameter. Proc. Heat Transfer Fluid Mech. Inst. (Libby, Olfe, Van Atta, eds.), p. 410. 1967.Google Scholar
  2. [2]
    Back, L. H., Massier, P. F., Gier, H. L.: Convective heat transfer in a convergent-divergent nozzle. Int. J. Heat Mass Transfer7, 549 (1964).Google Scholar
  3. [3]
    Badri Narayanan, M. A.: An experimental study of reverse transition in two-dimensional channel flow. J. Fluid Mech.31, 609 (1968).Google Scholar
  4. [4]
    Badri Narayanan, M. A., Ramjee, V.: On the criteria for reverse transition in a two-dimensional boundary layer flow. J. Fluid Mech.35, 225 (1969).Google Scholar
  5. [5]
    Bardi Narayanan, M. A., Rajagopalan, S., Narasimha, R.: Some experimental investigations on the fine structure of turbulence. Rep. No. 74FM 15. Dept. Aero. Eng., Ind. Inst. Sci., Bangalore (1974).Google Scholar
  6. [6]
    Batchelor, G. K., Proundman, I.: The effect of rapid distortion of a fluid in turbulent motion. Quart. J. Mech. Appl. Math.7, 83 (1954).Google Scholar
  7. [7]
    Blackwelder, R. F., Kovasznay, L. S. G.: Large scale motion of a turbulent boundary layer during relaminarization. J. Fluid Mech.53, 61 (1972).Google Scholar
  8. [8]
    Brinich, P. F., Neumann, H. E.: Some effects of acceleration on the turbulent boundary layer. AIAA J.8, 987 (1970).Google Scholar
  9. [9]
    Brown, G. L.: Theory and application of heated films for skin-friction measurement. Proc. Heat Tr. Fluid Mech. Inst. (Libby, Olfe, Van Atta, eds.), p. 361. 1967.Google Scholar
  10. [10]
    Coles, D.: The turbulent boundary layer in a compressible fluid. RAND Rep. No. R-403-PR (1962).Google Scholar
  11. [11]
    Fiedler, H., Head, M. R.: Intermittency measurements in the turbulent boundary layer. J. Fluid Mech.25, 719 (1966).Google Scholar
  12. [12]
    Herring, H. J., Norbury, N. F.: Some experiments on equilibrium turbulent boundary layers in favourable pressure gradient. J. Fluid Mech.27, 541 (1967).Google Scholar
  13. [13]
    Jones, W. P., Launder, B. E.: Some properties of sink-flow turbulent boundary layers. J. Fluid Mech.56, 337 (1972).Google Scholar
  14. [14]
    Julien, H. L., Kays, W. M., Moffatt, R. J.: The turbulent boundary layer on a porous plate: Experimental study of the effects of a favourable pressure gradient. Stanford University, Thermosci. Dvn. Rep. HMT-4 (1969).Google Scholar
  15. [15]
    Kader, B. A., Yaglom, A. M.: Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients. J. Fluid Mech.89, 305 (1978).Google Scholar
  16. [16]
    Kim, H. T., Kline, S. J., Reynolds, W. C.: The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech.40, 133 (1971).Google Scholar
  17. [17]
    Kline, S. J., Reynolds, W. C., Schraub, F. A., Runstadler, P. W.: The structure of turbulent boundary layers. J. Fluid Mech.30, 741 (1967).Google Scholar
  18. [18]
    Laufer, J.: Decay of non-isotropic turbulent field. In: Miszellen der angewandten Mechanik, Festschrift Walter Tollmien. Berlin: Akademie-Verlag 1962.Google Scholar
  19. [19]
    Launder, B. E.: Laminarization of the turbulent boundary layer by acceleration. Rep. No. 77. Gas Turbine Lab., Massachusetts Institute of Technology, Cambridge (1964).Google Scholar
  20. [20]
    Launder, B. E., Jones, W. P.: Sink flow turbulent boundary layers. J. Fluid Mech.38, 817 (1969).Google Scholar
  21. [21]
    Launder, B. E., Stinchcombe, H. S.: Non-normal similar turbulent boundary layers. Imp. Coll. Note TWF/TN 21. Dept. Mech. Eng. (1967).Google Scholar
  22. [22]
    Liepmann, H. W., Skinner, G. T.: Shearing-stress measurements by use of a heated element. NACA TN 3268 (1954).Google Scholar
  23. [23]
    Loyd, R. J., Moffat, R. J., Kays, W. M.: The turbulent boundary layer on a porous plate: An experimental study of the fluid dynamics with strong favourable pressure gradients and blowing. Stanford University, Thermosci. Dvn. Rep. HMT-13 (1970).Google Scholar
  24. [24]
    Moretti, P. H., Kays, W. M.: Heat transfer in turbulent boundary layer with varying free stream velocity and varying surface temperature- an experimental study. Int. J. Heat Mass Transfer8, 1187 (1965).Google Scholar
  25. [25]
    Narasimha, R., Sreenivasan, K. R.: Relaminarization in highly accelerated turbulent boundary layers. J. Fluid. Mech.61, 417 (1973).Google Scholar
  26. [26]
    Narasimha, R., Sreenivasan, K. R.: Relaminarization of fluid flows. Adv. Appl. Mech.19, 221 (1979).Google Scholar
  27. [27]
    Narasimha, R., Viswanath, P. R.: Reverse transition at an expansion corner in supersonic flows. AIAA J.13, 693 (1975).Google Scholar
  28. [28]
    Nash-Webber, J. L.: Wall shear-stress and laminarization in accelerated turbulent compressible boundary layers. Rep. No. 94, Gas Turbine Lab. Massachusetts Institute of Technology, Cambridge (1968).Google Scholar
  29. [29]
    Okamoto, T., Misu, I.: Reverse transition of turbulent boundary layer on plane wall of two-dimensional contraction. Trans. Jpn. Soc. Aerosp. Sci.20, 1 (1977).Google Scholar
  30. [30]
    Patel, V. C.: Calibration of the preston tube and limitations on its use in pressure gradients. J. Fluid Mech.23, 185 (1965).Google Scholar
  31. [31]
    Patel, V. C., Head, M. R.: Reversion of turbulent to laminar flow. J. Fluid Mech.34, 371 (1968).Google Scholar
  32. [32]
    Patel, V. C., Head, M. R.: Some observations on skin-friction and velocity profiles in fully developed pipe and channel flows. J. Fluid Mech.38, 181 (1969).Google Scholar
  33. [33]
    Preston, J. H.: The minimum Reynolds number for a turbulent boundary layer and the selection of a transition device. J. Fluid Mech.3, 373 (1958).Google Scholar
  34. [34]
    Ramjee, V.: Reverse transition in a two-dimensional boundary layer flow. Ph. D. Thesis, Dept. Aero. Eng., Ind. Inst. Sci., Bangalore (1968).Google Scholar
  35. [35]
    Rosenhead, L. (ed.): Laminar boundary layers. London-New York: Oxford University Press 1963.Google Scholar
  36. [36]
    Rubesin, M. W., Okuno, A. F., Mateer, G. G., Brosh, A.: A hot-wire surface gauge for skin-friction and separation measurements. NASA TMX62, 465 (1975).Google Scholar
  37. [37]
    Schraub, F. A., Kline, S. J.: A study of the structure of the turbulent boundary layer with and without longitudinal pressure gradients. Rep. No. MD-12. Thermosci. Div., Stanfod University, Stanford, California (1965).Google Scholar
  38. [38]
    Sergienko, A. A., Gretsov, K. V.: Transition from turbulent to laminar boundary layer. Dokl. Akad. Nauk. SSSR 125 (RAE Translation No. 827) (1959).Google Scholar
  39. [39]
    Sibulkin, M.: Transition from turbulent to laminar flow. Phys. Fluids5, 280 (1962).Google Scholar
  40. [40]
    Simpson, R. L., Shackleton, C. R.: Laminarescent turbulent boundary layers: Experiments on nozzle flows. Proj. SQUID Tech. Rep. No. SMU-2-PU (1977).Google Scholar
  41. [41]
    Simpson, R. L., Wallace, D. B.: Laminarescent turbulent boundary layers: Experiments on sink flows. Proj. SQUID Tech. Rep. No. SMU-1-PU (1975).Google Scholar
  42. [42]
    Spence, D. A., Brown, G. L.: Heat transfer to a quadratic shear profile. J. Fluid Mech.33, 753 (1968).Google Scholar
  43. [43]
    Sreenivasan, K. R.: Notes on the experimental data on reverting boundary layers. Rep. No. 72 FM2. Dept. Aero. Eng., Ind. Inst. Sci. Bangalore (1972).Google Scholar
  44. [44]
    Sreenivasan, K. R., Narasimha, R.: Rapid distortion of shear flows. Aero Soc. India, Silver Jubille Tech. Conf., Paper 2/3 (1974).Google Scholar
  45. [45]
    Sreenivasan, K. R., Narasimha, R.: Rapid distortion of axisymmetric turbulence. J. Fluid Mech.84, 497 (1978).Google Scholar
  46. [46]
    Sternberg, J.: The transition from a turbulent to a laminar boundary layer. Rep. No. 906. Ballistic Res. Lab., Aberdeen (1954).Google Scholar
  47. [47]
    Thwaites, B.: Approximate calculation of the laminar boundary layers. Aero. Quart.1, 245 (1949).Google Scholar
  48. [48]
    Townsend, A. A.: The structure of turbulent shear flow. London-New York: Cambridge University Press 1956.Google Scholar
  49. [49]
    Van Driest, E. R.: On turbulent flow near a wall. J. Aero. Sci.23, 1007 (1956).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • K. R. Sreenivasan
    • 1
  1. 1.Applied MechanicsYale UniversityNew HavenUSA

Personalised recommendations