Investigating chaotic wake dynamics past a flapping airfoil and the role of vortex interactions behind the chaotic transition

Abstract

The present study investigates the complex vortex interactions in two-dimensional flow-field behind a symmetric NACA0012 airfoil undergoing a prescribed periodic pitching-plunging motion in low Reynolds number regime. The flow-field transitions from periodic to chaotic through a quasi-periodic route as the plunge amplitude is gradually increased. This study unravels the role of the complex interactions that take place among the main vortex structures in making the unsteady flow-field transition from periodicity to chaos. The leading-edge separation plays a key role in providing the very first trigger for aperiodicity. Subsequent mechanisms like shredding, merging, splitting, and collision of vortices in the near-field that propagate and sustain the disturbance have also been followed and presented. These fundamental mechanisms are seen to give rise to spontaneous and irregular formation of new vortex couples at arbitrary locations, which are the primary agencies for sustaining chaos in the flow-field. The interactions have been studied for each dynamical state to understand the course of transition in the flow-field. The qualitative changes observed in the flow-field are manifestation of changes in the underlying dynamical system. The overall dynamics are established in the present study by means of robust quantitative measures derived from classical and non-classical tools from the dynamical system theory. As the present analysis involves a high fidelity multi-unknown system, non-classical dynamical tools such as recurrence-based time series methods are seen to be very efficient. Moreover, their application is novel in the context of pitch-plunge flapping flight.

Active lift inversion process of heaving wing in uniform flow by temporal change of wing kinematics

“…The wake direction (deflection angle) is constant or time dependent [23,27,29]. Similar asymmetric vortex patterns have been reported for a simple flapping wing [31][32][33][34], a wing with both heaving and flapping motion [30,[35][36][37], and even for a wing model that can move according to the generated thrust [38][39][40][41].…”

“…4(c)). A chaotic flow generation due to LEV-TEV interaction was analyzed in the case of the pitching and heaving wing with larger Reynolds number (1,000) [37] 2. Vortex dynamics in wake deflection The details of the asymmetric vortex pattern also depend on the initial phase φ; two cases, φ = π/2 and φ = π, were compared.…”

“…Reynolds number [37] . On the other hand, in the case of φ = π/2, the vortex structure is horizontal rather than deflected ( Fig.…”

Dynamic interlinking between near- and far-field wakes behind a pitching–heaving airfoil

“…2008, 2010). Also, very recently, Bose & Sarkar (2018) considered a pitching–heaving case and observed a quasi-periodic transition to chaos in the near-field patterns. Each dynamical state and the transitions were established using robust measures from dynamical systems theories.…”

Modeling the interplay between the shear layer and leading edge suction during dynamic stall

“…The response of the flow to unsteady changes in angle of attack is non-linear and depends on many parameters such as the airfoil profile, inflow Reynolds number, motion kinematics. If the angle of attack is increased fast enough to an angle above the static stall limit, flow will separate from the leading edge [23][24][25][26][27][28][29] . It thus seems natural to search for the Modelling the interplay between the shear layer and leading edge suction indication of massive dynamic flow separation near the leading edge.…”