Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T02:52:21.083Z Has data issue: false hasContentIssue false

An experimental study of reverse transition in two-dimensional channel flow

Published online by Cambridge University Press:  28 March 2006

M. A. Badri Narayanan
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Science, Bangalore, India

Abstract

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$ and $\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but $\overline{u^{\prime}v^{\prime}} $ tends to become zero at a reasonably well-defined point. During reverse transition $\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$ also decreases as the flow moves downstream and Lissajous figures taken with u’ and v’ signals confirm this trend. There is approximate similarly between $\overline{u^{\prime 2}} $ profiles if the value of $\overline{u^{\prime 2}_{\max}} $ and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of $\overline{u^{\prime 2}} $ is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

Type
Research Article
Copyright
© 1968 Cambridge University Press

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

Batchelor, G. K. 1959 The Theory of Homogeneous Turbulence. Cambridge University Press.
Corrsin, S. 1953 Interpretation of viscous terms in the turbulent energy equation J. Aero. Sci. Readers Forum, 20, 853854.Google Scholar
Holder, D. W., Gadd, G. E. & Regan, J. D. 1956 Base pressures in supersonic flow. C.P. no. 271.
Laufer, J. 1962 Decay of nonisotropic turbulent field. Mitteilungen der Angewandten Mechanik, pp. 16674. Edited by Manfred Schaefer. Gottingen.
Launder, B. E. 1964 Laminarization of the turbulent boundary layer in a severe pressure gradient. Trans. ASME (J. Appl. Mech.).Google Scholar
Moretti, P. M. & Kays, W. M. 1965 Heat transfer to a turbulent boundary layer with varying free-stream velocity and varying surface temperature—an experimental study Int. J. Heat Mass Transfer, 8, 11871202.Google Scholar
Sergienko, A. A. & Gretsov, V. K. 1959 Transition from turbulent to laminar boundary layer. Dokl. Akad. Nauk, SSSR, 746 (1959) 125.Google Scholar
Sibulkin, M. 1962 Transition from turbulent to laminar flow The Physics of Fluids, 5, 280289.Google Scholar
Sternberg, J. 1954 The transition from turbulent to laminar boundary layer. U.S. Army Bal. Res. Lab. Rept. no. 906.Google Scholar
Townsend, A. A. 1947 The measurement of double and triple correlation derivatives in isotropic turbulence Proc. Cambridge Phil. Soc. 43, 560.Google Scholar