On the Criterion for the Determination Transition Onset and Breakdown to Turbulence in Wall-Bounded Flows

[+] Author and Article Information
J. Jovanović, M. Pashtrapanska

Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058, Germany

J. Fluids Eng 126(4), 626-633 (Sep 10, 2004) (8 pages) doi:10.1115/1.1779663 History: Received March 12, 2003; Revised March 02, 2004; Online September 10, 2004
Copyright © 2004 by ASME
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Anisotropy-invariant mapping of the disturbances generated by small, two-dimensional roughness element in a initially laminar flat plate boundary layer from Fischer, Jovanović and Durst 7: (a) specially designed two-component laser-Doppler system for near-wall measurements; (b) schematic of flat plate arrangement in the wind tunnel with layout of two different beam configurations which allowed measurements of all components of the “apparent” stresses of the disturbances; (c) traces of the joint variations of invariants IIa and IIIa across the anisotropy invariant map confirm the two-component nature of the disturbances
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Intermittency (Υ) measurements of the transition process from laminar to turbulent states at the channel centerline from Fischer 8: (a) channel flow test section; (b) transition due to the natural disturbances is accompanied by large hysteresis in the experimental data; (c) transition due to the two-component disturbances implies that for such disturbances the critical Reynolds number may be found by extrapolation data of a fully developed turbulent flow if the transition criterion is known
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Anisotropy invariant map and the asymptotic forms for the unknown correlations involved in the equations for the “apparent” stresses
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Anisotropy invariant mapping of turbulence in a channel flow. Data, which correspond to low Reynolds numbers, show the trend as Re→(Re)crit towards the theoretical solution valid for small, neutrally stable, statistically stationary, axisymmetric disturbances (Jovanović, Hillerbrand and Pashtrapanska 29). The shading indicates the area occupied by the stable disturbances: for such disturbances a laminar regime in the boundary layer will persist up to very high Reynolds numbers.
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Turbulent dissipation rate at the wall normalized with the wall shear velocity and the kinematic viscosity of the flow medium versus the anisotropy of turbulence IIa at the wall. A best-line fit through the numerical data extrapolates fairly well the expected trend ε→0 as the one-component limit (IIa=2/3) is approached.
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Cross plot of Rλ versus Reτ1/2 for fully developed turbulent pipe and channel flows at low Reynolds numbers
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Cross plot of Rλ versus Reτ1/2 for turbulent boundary layer at low Reynolds numbers




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