Klebanoff-Mode Modeling and Bypass-Transition Prediction

Abstract

A number of experiments have demonstrated that the classical Tollmien-Schlichting transitional mechanism is no longer valid inside boundary layers subjected to intense external disturbances. In such a case, perturbations in the laminar region take the form of three-dimensional streamwise-elongated structures, the Klebanoff modes, also called streaks, which may be strongly amplified, resulting in an early bypass transition. This amplification is described by the transient-growth theory. In the present paper, a semi-empirical model has been developed for the prediction of this type of bypass transition. It is based on the resolution of two parabolic linear transport equations for the longitudinal velocity and the temperature fluctuations. A transition criterion is then formed based on the ratio of streak production and dissipation. Several sets of experimental data were used for validation of the proposal model, assessing the effects of pressure gradients and of freestream turbulence properties.