Abstract
Abstract
Highlights
For boundary layers over Krammer-type compliant surfaces, the linear hydrodynamic instability study was performed by Carpenter & Garrad (1985, 1986) using this formulation and subsequently several studies have used the same formulation for studying flow instabilities over flexible surfaces, for example, Carpenter & Morris (1990) and Davies & Carpenter (1997)
The final form of the linear equations is evaluated on the equilibrium grid on which the base state is defined and the first-order effects of moving interfaces are captured by the modification of the interface boundary conditions
The formulation is validated for rigid-body motion FSI problems by comparing the evolution of the linear equations with the nonlinear system when both systems are perturbed with identical small-amplitude disturbances
Summary
Fluid–structure-interaction (FSI) studies span a vast and diverse range of applications – from natural phenomenon such as the fluttering of flags (Shelley & Zhang 2011), phonation (Heil & Hazel 2011), blood flow in arteries (Freund 2014), path of rising bubbles (Ern et al 2012), to the more engineering applications of aircraft stability (Dowell & Hall 2001), vortex induced vibrations (Williamson & Govardhan 2004), compliant surfaces (Riley, Gad-el Hak & Metcalfe 1988; Kumaran 2003) etc. A non-inertial reference is used by Navrose & Mittal (2016) to study the lock-in phenomenon of cylinders oscillating in cross-stream through the linear stability analysis. The standard Navier–Stokes and divergence equations are modified to account for the motion of the material points Using this formulation on moving material points, the authors have investigated several different FSI problems including ones with nonlinear structural models, elastic flutter instabilities and finite aspect ratio structures (Pfister et al 2019; Pfister & Marquet 2020). We confine the focus of the current work to FSI problems undergoing rigid-body motion and defer a more general formulation and validation to future work. The derived formulation for rigid-body linear FSI is numerically validated by comparing linear and nonlinear evolution of different cases which are started from the same base flow state, perturbed by identical small-amplitude disturbances.
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