Evolution of Lagrangian coherent structures in a cylinder-wake disturbed flat plate boundary layer

Abstract

Evolution of Lagrangian coherent structures (LCS) in a flat plate boundary layer transition induced by the wake of a circular cylinder is investigated. Both hydrogen bubble visualization and particle image velocimetry (PIV) techniques are used. It is found that downstream of the cylinder, the disturbance in the boundary layer experiences a fast growth followed by a slow decay in the transition. Lagrangian coherent structures are revealed by qualitative hydrogen bubble visualizations and quantitative finite-time Lyapunov exponents (FTLE) fields derived from the PIV data. The evolution of the LCS is considered from the very beginning of the transition up to when the boundary layer becomes fully developed turbulent flow. The mean convection velocity and average inclination angle of the LCS are first extracted from the FTLE fields. The streamwise length of the low-speed streaks seems to increase, while their spanwise distance decreases in the boundary layer transition. Proper orthogonal decomposition (POD) of the PIV data shows that low-speed streaks associated with the hairpin vortices and hairpin packets are the dominant coherent structures close to the wall in the transitional and turbulent boundary layer. The POD modes also reveal a variety of scales in the turbulent boundary layer. Moreover, it is found that large-scale coherent structures can modulate the amplitude of the small-scale ones.

Effect of excitation frequency on flow characteristics around a square cylinder with a synthetic jet positioned at front surface

“…According to previous studies (Shadden, Dabiri & Marsden 2006; Haller 2015; Huang & Green 2015; He et al. 2016; Krishna et al. 2018), the calculation of FTLE is based on the fluid particle trajectories which can be derived from the velocity field.…”

“…Now FTLE is a convenient method to identify the structure boundary with the ridges corresponding to the Lagrangian coherent structures (LCS) (Haller 2002;Huang & Green 2015;Krishna, Green & Mulleners 2018). According to previous studies (Shadden, Dabiri & Marsden 2006;Haller 2015;Huang & Green 2015;He et al 2016;Krishna et al 2018), the calculation of FTLE is based on the fluid particle trajectories which can be derived from the velocity field. If Φ(x 0 , t 0 , t 1 ) is defined as the flow map for fluid particles from the location at the initial time t 0 to the location after a time interval t 1 , the FTLE can be calculated from…”

“…Since ε(t P ) is really small, the item containing ε(t P ) is negligible. The maximum absolute uncertainty of x p is 0.1 pixel according to He et al (2016) and Raffel et al (2018). With the highest sampling rate of 150 Hz and current image magnifications mentioned in § 2.2, the absolute uncertainties of velocity ε(U) computed based on (2.6) are less than 0.9 mm s −1 and 1.8 mm s −1 for the upstream and downstream flow fields, respectively.…”

“…The maximum absolute uncertainty of is 0.1 pixel according to He et al. (2016) and Raffel et al. (2018).…”

Wake-induced transition in the low-Reynolds-number flow over a multi-element airfoil

“…Subsequently, He et al. (2016) further tracked the Lagrangian coherent structures throughout the transition process. At the intermediate stage of transition, the deformed secondary vortices had the same spanwise wavelength as that of the mode-A instability of the cylinder wake (Williamson 1996).…”