Recurrence Perspective of Forces Generated by Flapping Wing Under Different Frontal Inflow Conditions

Qualitative and quantitative recurrence paradigms have been frequently used to study the stability of dynamic systems. In the present work, Global Recurrence Plots (GRPs) and Windowed Recurrence Quantification Analysis (WRQA) were employed to analyse the force patterns of a flapping wing in 3D reference frame for Re = 150. The wing followed a canonical form of asymmetrica 1DoF flapping. Force patterns were numerically estimated for four different frontal inflow conditions viz. uniform inflow profile, shear inflow profile, temporally oscillating uniform inflow profile and spatiotemporally varying inflow profile. User-defined functions (UDFs) were developed to specify these frontal inflow conditions. The flapping kinematics of wing was simulated by dynamic meshing technique and UDFs. 3D unsteady Navier–Stokes equations were solved using finite volume formulation, assuming incompressible and laminar flow. Mass and momentum equations were solved in a fixed inertial reference frame by the Arbitrary Lagrangian–Eulerian (ALE) formulation. Spatial discretization was second-order upwind and temporal discretization was second-order implicit. PISO scheme was used for pressure–velocity coupling. The finite volume formulation based commercial CFD code ANSYS Fluent was used. Force patterns were qualitatively evaluated using GRPs and quantitatively by evaluating the WRQA of eight parameters viz. recurrence rate (RR), determinism (DET), laminarity (LAM), trapping time (TT), ratio (RATIO), entropy (ENTR), maximum line (Lmax) and trend (TREND). From these recurrence studies, it was observed that shear inflow condition influenced the forces and moment pattern more than the other primary inflow conditions for the chosen wing kinematics.