Aerodynamic Forces on a Wing Surfing in a Two-dimensional Vortex Wake

TL;DR

The paper investigates how a downstream wing experiences aerodynamic forces when immersed in the 2-D wake of an upstream pitching plate. It combines wind-tunnel PIV measurements with fixed-wing force data to reveal that lift fluctuations align with impinging wake structures and scale with wake parameters such as the Strouhal number, reduced frequency, and reduced amplitude. Time-resolved predictions based on local flow conditions are tested against classical unsteady aerodynamics models (Wagner, Küssner, Sears), with the Wagner approach providing the best overall agreement in the time domain. The findings advance understanding of wake–wing interactions and demonstrate the potential and limits of local-flow-based unsteady theories for predicting vortex-induced lift in engineering and biological contexts.

Abstract

Inspired by the wake-surfing nature of animals, this study aims to understand the aerodynamic force variation on a wing surfing in an unsteady 2-D wake. Wind tunnel experiments were conducted using Particle Image Velocimetry (PIV) and force measurements with a fixed wing immersed in the wake of a pitching airfoil. The comparison between force and PIV measurements shows that the lift response of the surfing wing is aligned with the impingement of flow structures, and that the dependence of the cycle-averaged lift fluctuations on the upstream flapping kinematics can be scaled as a function of the reduced amplitude and reduced frequency of the flapping motion. Good collapse of the data is found, and deviations from scaling are explained in terms of the wake characteristics. The phase-resolved lift fluctuations on the vortical wake encountering can be effectively predicted using classic unsteady aerodynamics based on measured unsteady local flow conditions (instantaneous angle of attack and speed). The theoretical predictions compare well with direct force sensor measurements.

Figures (16)

• Figure 1: Experimental setup in wind tunnel. The motorized wake generator is installed upstream, with a flat plate spanning the test section pitching sinusoidally. An NACA0012 airfoil is aligned with the center of the wake and mounted to loadcell through a streamlined support. Both the surfing wing and the wake generator are included in a 300x500 streamwise field of view (FOV) of the PIV, taken by the two side-by-side PIV cameras.
• Figure 2: The parameter sets of tested cases
• Figure 3: Unsteady coefficient of lift (center) and four instantaneous vorticity distributions at $t/T = 0.11, 0.32, 0.61$ and 0.82. $\text{Re} = 42\text{k}$, $\text{St} = 0.017$, $A/c = 0.2$. At these conditions we observe a continuous vortex sheet shed from wake generator and impinging on the surfing wing.
• Figure 4: Unsteady coefficient of lift (center) and six instantaneous vorticity distributions at $t/T = 0.10, 0.18, 0.25, 0.30, 0.50$ and 0.68. At $\text{Re} = 42\text{k}$, $\text{St} = 0.052$, $A/c = 0.5$. At these conditions we observe discrete vortex shedding from the flapping wing, and impingement on the surfing wing.
• Figure 5: (a) As the flapping frequency of the wake generator increases (with a constant free-stream velocity $U_{\infty} = 4m/s$ and flapping amplitude $f_0 = 4Hz$), the lift coefficient fluctuations increase with a slight phase shift forward.The case shown in figure \ref{['fig:surferPIVHigh']} is marked by star symbol. (b) As the flapping frequency of the wake generator increases (with a fixed free-stream velocity $U_{\infty} = 4m/s$ and flapping amplitude $A/c = 0.2$), the lift fluctuations also increase with a phase shift backward.The case shown in figure \ref{['fig:surferPIVLow']} is marked by star symbol.