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A flow-visualization study of transition in plane Poiseuille flow

Published online by Cambridge University Press:  20 April 2006

Dale R. Carlson ,
Sheila E. Widnall  and
Martin F. Peeters
Dale R. Carlson
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Sheila E. Widnall
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Martin F. Peeters
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Flow visualization of artificially triggered transition in plane Poiseuille flow in a water channel by means of 10–20 μm diameter tihnium-dioxide-coated mica particles revealed some striking features of turbulent spots. Strong oblique waves were observed both at the front of the arrowhead-shaped spot as well as trailing from the rear tips. Both natural and artificially triggered transition were observed to occur for Reynolds numbers slightly greater than 1000, above which the flow became fully turbulent. The front of the spot moves with a convection speed of about two-thirds of the centreline velocity, while the rear portion moves at about $\frac{1}{3}U_{\rm cl}$. The spot expands into the flow with a spreading half-angle of about 8°. After growing to a size of some 36 times h (the channel depth) at a downstream distance x/h of about 130, the spot began to split into two spots, accompanied by strong wave activity. The spot(s) was followed visually downstream of its origin a distance x/h of about 300. These results indicate that wave propagation and breakdown play a crucial role in transition to turbulence in Poiseuille flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 487 - 505
Copyright
© 1982 Cambridge University Press

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References

A.S.M.E. 1960 Symp. on Flow Visualization. A.S.M.E.
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Cantwell, B. J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457–515.Google Scholar
Cantwell, B., Coles, D. & Dimotakis, P. 1978 Structure and entrainment in the plane of symmetry of a turbulent spot. J. Fluid Mech. 87, 641–672.Google Scholar
Elder, J. W. 1960 An experimental investigation of turbulent spots and breakdown to turbulence. J. Fluid Mech. 9, 235–246.Google Scholar
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer – Part I. J. Aero. Sci. 18, 490–498.Google Scholar
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1979 A visual study of the growth and entrainment of turbulent spots. In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 297–310. Springer.
Grosch, C. E. & Salwen, H. 1978 The continuous spectrum of the Orr–Sommerfeld equation. Part 1. The spectrum and the eigenifunctions. J. Fluid Mech. 87, 33–54.Google Scholar
Gustavsson, L. H. 1978 On the evolution of disturbances in boundary layer flows. Tech. Rep. TRITA-MEK-78-02, Dept of Mechanics, KTH, Stockholm.Google Scholar
Gustavsson, L. H. 1979 Initial-value problem for boundary layer flows. Phys. Fluids 22, 1602–1605.Google Scholar
Gustavsson, L. H. 1981 Resonant growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 112, 253–264.Google Scholar
Gustavsson, L. H. & Hultgren, L. 1980 A resonance mechanism in plane Couette flow. J. Fluid Mech. 98, 149–159.Google Scholar
Kao, T. W. & Park, C. 1970 Experimental investigations of the stability of channel flows. Part 1. Flow of a single liquid in a rectangular channel. J. Fluid Mech. 43, 145–164.Google Scholar
Karnitz, M. A., Potter, M. C. & Smith, M. C. 1974 An experimental investigation of transition of a plane Poiseuille flow. Trans. A.S.M.E. I, J. Fluids Engng 96, 384–388.Google Scholar
Kline, S. J. 1978 The role of visualization in the study of the structure of the turbulent boundary layer. In Proc. Lehigh Workshop on Coherent Structures of Turbulent Boundary Layers, pp. 1–26.
Lix, C. C. 1945a On the stability of two-dimensional parallel flows. Part I. General theory. Q. Appl. Math. 3, 117–142.Google Scholar
Lin, C. C. 1945b On the stability of two-dimensional parallel flows. Part II. Stability in an inviscid fluid. Q. Appl. Math. 3, 218–234.Google Scholar
Lin, C. C. 1945c On the stability of two-dimensional parallel flows. Part III. Stability in a viscous fluid. Q. Appl. Math. 30, 277–301.Google Scholar
Mack, L. M. 1967 A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73, 497–520.Google Scholar
Matsui, T. 1979 Visualization of turbulent spots in the boundary layer along a flat plate in a water flow. In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 288–296. Springer.
Mitchner, M. 1954 Propagation of turbulence from an instantaneous point disturbance. J. Aero. Sci. 21, 350–351.Google Scholar
Narayanan, M. A. B. & Narayana, T. 1967 Some studies on transition from laminar to turbulent flow in a two-dimensional channel. Z. angew. Math. Mech. 18, 642–650.Google Scholar
Nishioka, M., Iida, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731–751.Google Scholar
Nishioka, M., Asai, M. & Iida, S. 1980 Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. R. E. Mayer). Academic.
Orszag, S. A. 1971 Accurate solutions of the Orr–Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.Google Scholar
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille flow and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Orszag, S. A. & Patera, A. T. 1980 Suberitical transition to turbulence in plane channel flows. Phys. Rev. Lett. 45, 989–993.Google Scholar
Patel, V. C. & Head, M. R. 1969 Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J. Fluid Mech. 38, 181–201.Google Scholar
Rubin, Y., Wygnanski, I. & Haritonidis, J. H. 1979 Further observations on transition in a pipe. In Laminar–Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 288–296. Springer.
Schlichting, H. 1968 Boundary Layer Theory, 6th edn, p. 177. McGraw-Hill.
Schubauer, G. B. & Klebanoff, P. S. 1956 Contributions on the mechanics of boundary layer transition. NACA Rep. no. 128.Google Scholar
Schubauer, G. B. & Skramstad, H. K. 1948 Laminar boundary layer oscillations on a flat plate. NACA Rep. no. 909.Google Scholar
Sherlin, G. C. 1960 Behavior of isolated disturbances superimposed on laminar flow in a rectangular pipe. J. Res. Nat. Bur. Stand. 64A, 281–289.Google Scholar
Stuart, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. J. Fluid Mech. 9, 353–370.Google Scholar
Thomas, L. H. 1952 The stability of plane Poiseuille flow. Phys. Rev. 86, 812–813.Google Scholar
Wygnanski, I., Haritonidis, J. H. & Kaplan, R. E. 1979 On a Tollmien–Schlichting wave packet produced by a turbulent spot. J. Fluid Mech. 92, 505–528.Google Scholar
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 On a turbulent ‘spot’ in a laminar boundary layer. J. Fluid Mech. 78, 785–819.Google Scholar
Zilberman, M., Wygnanski, I. & Kaplan, R. E. 1977 Transitional boundary layer spot in a fully turbulent environment. Phys. Fluids 20, 258–271.Google Scholar