Coherence of unsteady wake of periodically plunging airfoil

Abstract

We present an experimental investigation of the flow structure in the near wake of a NACA0012 airfoil plunging sinusoidally at a chord Reynolds number of Re = 20 000 and for a wide range of reduced frequency k and Strouhal number based on peak-to-peak amplitude St. Estimated mean thrust coefficients using the mean and fluctuating velocity fields confirm the St2 dependence as well as a significant effect of the reduced frequency for k ≤ 1. Generally, time-averaged flow quantities are better correlated with St than k in the range tested (k ≤ 3.14 and St ≤ 0.24). Analysis of the streamwise flow and cross-flow in the near wake using two-point cross-correlations and proper orthogonal decomposition reveals that the unsteady characteristics are even better correlated with St than the mean flow quantities. The percentage energy of the fundamental wake modes of the streamwise flow and the flapping mode of the cross-flow increases with increasing St, but at different rates in the drag-producing and thrust-producing wakes. There are similarities to the wake synchronisation behind oscillating bodies. The spanwise-averaged cross-correlation coefficient in the measurement domain grows linearly for small St (in drag-producing wakes), and is nearly constant at a high value for larger St (in thrust-producing wakes). Results show that the Strouhal number is the most important parameter that determines the degree of two-dimensionality of the wake, and suggest that spanwise vortices are quasi-two-dimensional for St ≥ 0.05 and x/c ≤ 4. The implications for experimental gust generators using oscillating airfoils are discussed.

Interaction of quasi-two-dimensional vortical gusts with airfoils, unswept and swept wings

“…The cross-flow velocity is fairly independent of the spanwise distance, confirming its nearly two-dimensional structure. This is consistent with the findings of Turhan et al (2022). Their data for the same chord Reynolds number and in the same downstream region suggest that the spanwise vortices are nearly two-dimensional for the normalized maximum plunge velocity V pmax /U ∞ ≥ 0.15.…”

“…The latter dissipates quickly and cannot be captured downstream of the trailing-edge. In addition, we made sure that the acceleration part of the plunge motion is sufficiently rapid, which ensures high coherence and two-dimensionality of the vortices (Turhan et al 2022). The slow deceleration of the airfoil ensures that the opposite sign of vorticity shed does not roll up.…”

“…This is highly relevant to the present study in which two-dimensional vortices interact with airfoils and wings. Recently, Turhan et al (2022) investigated the spanwise coherence and correlation length scale of the incident unsteady wakes shed from a periodically plunging upstream airfoil at a Reynolds number based on the chord length of Re = 20,000. It was concluded that the Strouhal number is the most important parameter that determines the degree of two-dimensionality of the wake.…”

“…Using the findings of Turhan et al (2022), it can be assumed that spanwise vortices are quasi-two-dimensional for V pmax /U ∞ ≥ 0.15 and x/c ≤ 4 at Re = 20,000. Turhan et al (2022) furthermore discussed the implications for experimental gust generators using oscillating airfoils. In the present experiments, we were able to produce nearly-two-dimensional single vortices.…”

Post-stall flow control with upstream flags

“…This implies that the excitation of the flow over the downstream wing will not be perfectly synchronized in the spanwise direction. There is an improvement of the two-dimensionality of the wake for oscillating bluff bodies (Bearman 1984) and plunging airfoils (Turhan et al 2022). Thus, we may expect that the wakes of oscillating flags may have improved coherence.…”