Speaker
Description
The distinct sound of a string instrument depends on harmonic attenuation. While past studies have mostly focused on high-frequency thermoelastic damping, we investigate here low-frequency dissipation in a real (viscous) fluid. Todo so, we solve the incompressible Navier-Stokes equations using Basilisk, a finite volume solver capable of handling adaptive octree meshes around moving bodies with immersed boundaries. Assuming a long coherence length, we model the string as a 2D oscillating cylinder. Accordingly, flow regimes are characterized via the Reynolds (Re) and Keulegan-Carpenter (KC) numbers. We first obtain reference time-resolved data via prescribed cylinder motion. The Valette & Cuesta model, partially based on the potential flow theory, reveals limited validity within the (Re, KC) space. We propose Morison’s equation as an improvement: a semi-empirical, physically consistent model that extends the predictions validity by extracting parameters from the simulation data. Finally, a two-way coupled simulation dynamically injects the computed drag forces at each time step, demonstrating Basilisk’s ability to capture the coupling between variable oscillation amplitude and viscosity. This last method, although computationally heavier, provides a versatile method valid for any Re, KC, paving the way for comparison with experiments described in a companion paper.