Hydrodynamic stress maps on the surface of a flexible fin-like foil

TL;DR

This study maps the time-dependent pressure and shear stresses on a flexible hydrofoil using volumetric velocimetry and Navier-Stokes calculations, validating results with beam theory and control volume analysis.

Contribution

It introduces a method to accurately measure and analyze hydrodynamic stress distributions on a deforming hydrofoil, combining experimental measurements with theoretical validation.

Findings

Stress maps are obtained with validated accuracy.

Flow and stress distributions are consistent with theoretical models.

Method enables detailed analysis of unsteady hydrodynamic forces.

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 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. Unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the deflecting hydrofoil from its deflection and thereby validate the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field. The consistency of the force time-dependence is verified using a control volume analysis.