Abstract
We determine the time dependence of pressure and shear stress distributions on the surface of a pitching and deforming hydrofoil from measurements of the three dimensional flow field. Period-averaged stress maps are obtained both in the presence and absence of steady flow around the foil. The velocity vector field is determined via volumetric three-component particle tracking velocimetry and subsequently inserted into the Navier-Stokes equation to calculate the total hydrodynamic stress tensor. In addition, we also present a careful error analysis of such measurements, showing that local evaluations of stress distributions are possible. The consistency of the force time-dependence is verified using a control volume analysis. The flapping foil used in the experiments is designed to allow comparison with a small trapezoidal fish fin, in terms of the scaling laws that govern the oscillatory flow regime. As a complementary approach, unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the flexible hydrofoil from its deflection and the results are compared to the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field.
Highlights
The evaluation of hydrodynamic forces on the surface of submerged and deforming foils constitutes a key element in understanding how synthetic and animal fins interact with the surrounding fluid to achieve their appropriate functions of propulsion and maneuvering
Countless studies have resorted to particle imaging or particle tracking velocimetry (PIV and PTV) to investigate the flow topology and hydrodynamic forces of bio-inspired or authentic fish fins [25,26,27,28,29,30,31,32,33,34,35,36,37]
In the present study of a prototypical fin-like foil, we performed three-dimensional hydrodynamic stress calculations based on a pressure gradient multi-path integration scheme, which we applied to a time series of volumetric PTV measurements of an unsteady vortical flow
Summary
The evaluation of hydrodynamic forces on the surface of submerged and deforming foils constitutes a key element in understanding how synthetic and animal fins interact with the surrounding fluid to achieve their appropriate functions of propulsion and maneuvering. An experimental workflow is proposed here to measure local distributions of hydrodynamic pressure and viscous stress over the surfaces of a flexible artificial fin, starting from the volumetric acquisition of 3D flow velocimetry data. This methodology broadens the possibility of studying in detail the propulsion and force regulating mechanisms in fish or biomimetic systems [18]. Countless studies have resorted to particle imaging or particle tracking velocimetry (PIV and PTV) to investigate the flow topology and hydrodynamic forces of bio-inspired or authentic fish fins [25,26,27,28,29,30,31,32,33,34,35,36,37]. Euler-Bernoulli beam theory has been employed to describe the fluid-structure interactions of fins and hydrofoils, addressing
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