TOWARD AN INVARIANT-THRESHOLD TURBULENT-NON-TURBULENT DETECTOR FUNCTION IN VANE CASCADE TRANSITIONAL BOUNDARY LAYERS

Abstract

This paper investigates the variations on the threshold values used for turbulent-nonturbulent discrimination in transitional boundary layers on the suction surface of a vane under varying levels of inflow turbulence intensities. The invariant-threshold here refers to a potential characteristic of a detector function if a single threshold value can be effectively used to distinguish turbulent and nonturbulent states at any stage of flow development or wall-normal distance. The analysis is based on velocity time series extracted at constant <i>d/δ</i> wall-normal distances obtained by wall-resolved large eddy simulations (LES), with the detector function being the sum of the time derivatives of the spanwise and wall-normal velocity signals, normalized by the boundary layer edge velocity. The detector function's probability density function (PDF) minima is chosen as the turbulent-nonturbulent discrimination threshold. The variations of the selected threshold value are examined at different stages of transition to turbulence and wall-normal distances. Findings suggest that a single threshold value is sufficient for turbulent-nonturbulent discrimination at <i>d/δ</i> > 0.2, throughout the depth of the flow, and for both levels of inflow turbulence intensities considered in this study. Although the appropriate threshold decreases closer to the wall for <i>d/δ</i> < 0.2, it remains invariant across different streamwise positions.