International Scientific Journal

Starting from the Navier-Stokes and the continuity equations of a viscous incompressible fluid, a statistical theory is developed for the prediction of transition and breakdown to turbulence in a laminar boundary layer exposed to small, statistically stationary axisymmetric disturbances. The transport equations for the statistical properties of the disturbances are closed using the two-point correlation technique and invariant theory. By considering the local equilibrium to exist between production and viscous dissipation, which forces the energy of the disturbances in the boundary layer to be lower than that of the free stream, the transition criterion is formulated in terms of the anisotropy of the disturbances and a Reynolds number based on the intensity and the length scale of the disturbances. The transition criterion determines conditions that guarantee maintenance of the laminar flow regime in a flat plate boundary layer. It is shown that predictions of the transition onset deduced from the transition criterion yield the critical Reynolds number, which is in good agreement with the experimental data obtained under well-controlled laboratory conditions reported in the literature. For the preferred mode of the axisymmetric disturbances, for which the intensity of the disturbances in the stream wise direction is larger than in the other two directions, the analysis shows that the anisotropy increases the critical Reynolds number. Theoretical considerations yield the quantitative estimate for the minimum level of the anisotropy of the free stream required to prevent transition and breakdown to turbulence. The numerical databases for fully developed turbulent wall-bounded flows at low and moderate Reynolds numbers were utilized to demonstrate the stabilizing and destabilizing role of the anisotropy in the disturbances on the development of the transition process in wall-bounded flows. The stabilizing role of increased anisotropy in a free stream on the boundary layer development was successfully tested experimentally in a large wind tunnel by maintaining the stable laminar regime in a flat plate boundary layer up to (Rex)T 4·106.

PAPER SUBMITTED: 2006-05-30

PAPER REVISED: 2006-06-03

PAPER ACCEPTED: 2006-06-15

DOI REFERENCE: https://doi.org/10.2298/TSCI0602063J

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© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence