Experimental and theoretical investigation of drag loads on side-by-side flexible blades in a uniform current

TL;DR

This paper combines experimental and theoretical methods to analyze how side-by-side flexible blades experience drag and become unstable in steady currents, revealing key parameters that influence drag and flutter onset.

Contribution

It introduces a comprehensive analysis of drag and flutter in side-by-side flexible blades, including new models for predicting drag reduction and stability thresholds.

Findings

Drag coefficient decreases with increasing Ca/B ratio in static regime.

Increasing B, β, or λ stabilizes the system and delays flutter.

Analytical and numerical models effectively predict drag reduction and flutter onset.

Abstract

This study investigates the hydrodynamic drag force on side-by-side flexible blades in a uniform steady current through experimental and theoretical approaches. Four different blade mimics were arranged in side-by-side bunches and tested in a circulating water tunnel. The experiments cover a static regime and a dynamic instability regime known as flutter. We examine four non-dimensional parameters to assess their effects on the bulk drag coefficient $C_{D,\mathrm{bulk}}$ and the onset of flutter: the drag-to-stiffness ratio $\mathrm{Ca}$, the buoyancy-to-stiffness ratio $\mathrm{B}$, the mass ratio of fluid inertia to total system inertia $\beta$, and the slenderness parameter $\lambda$, which represents the ratio of the resistive drag to the reactive force. The results show that $C_{D,\mathrm{bulk}}$ decreases in the static regime starting at $\mathrm{Ca}/B > \textit{O}(1)$ and settles to an almost constant value in the flutter regime at high $\mathrm{Ca}$. In the static regime, $\mathrm{B}$ is the primary influencing factor. Increasing $\beta$, $\mathrm{B}$, or $\lambda$ stabilizes the system and delays the onset of flutter. By introducing an equivalent thickness and bending stiffness for a bunch of blades, we utilize well-established analytical and numerical models for individual blades to predict the drag reduction of side-by-side blade assemblies. The analytical model accurately predicts drag reduction in the static regime, while the numerical model effectively predicts both the onset of flutter and drag reduction across both regimes with appropriate cross-flow hydrodynamic coefficients. Meanwhile, we investigate the reactive force terms to unveil their impact on the system stability and drag reduction, demonstrating its superiority over the traditional Morison's equation for highly compliant blades in cross-flow scenarios.