The Kinematics of Lagrangian Flow Separation in External Aerodynamics

TL;DR

This paper investigates the initial and long-term kinematic processes of flow separation in external aerodynamics using Lagrangian methods, linking wall events to flow structures and employing high-order numerical derivatives for analysis.

Contribution

It introduces a novel approach to identify the spiking point in flow separation through high-order derivatives of wall-normal velocity from direct numerical simulations.

Findings

Wall signature of upwelling fluid can be computed from curvature and derivatives.

Short-term kinematics correlate with boundary layer scaling lengths.

Robust identification of the spiking point despite boundary profile oscillations.

Abstract

Kinematic aspects of flow separation in external aerodynamics are investigated in the Lagrangian frame. Specifically, the initial motion of upwelling fluid material from the wall is related to the long-term attracting manifolds in the flow field. While the short-time kinematics are governed by the formation of a material spike upstream of the zero-skin-friction point and ejection of particles in direction of the asymptotic separation line, the trajectories of the fluid tracers are guided by attracting ridges in the finite-time Lyapunov exponents once they leave the vicinity of the wall. The wall signature of this initial fluid upwelling event, the so-called \textit{spiking point} [Serra, M., Vetel, J., Haller, G., "Exact theory of material spike formation in flow separation", \textit{J. Fluid Mech.}, Vol. 845, 2018], is computed from the curvature of advected material lines and, for the first time, from high-order numerical derivatives of the wall-normal velocity obtained from direct numerical simulations of a circular cylinder and a cambered NACA 65(1)-412 airfoil. As the spline-based boundary parametrization of the airfoil profile induces oscillations, the principle spiking point can be recovered robustly through appropriate filtering. The short-term kinematics correlate strongly with the scaling lengths in the boundary layer.