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Travelling Panels Interacting with External Flow

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This chapter is devoted to the analysis of the travelling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account somehow. The light weight of the material leads to the inertial contribution of the surrounding air to the acceleration of the material becoming significant. In the small displacement regime, the geometry of the vibrating panel is approximately flat, and hence flow separation is unlikely. We will use the model of potential flow for the fluid. The approach described in this chapter allows for an efficient semi-analytical solution, where the fluid flow is solved analytically in terms of the panel displacement function, and then strongly coupled into the partial differential equation describing the panel displacement. The panel displacement, accounting also for the fluid–structure interaction, can then be solved numerically from a single integrodifferential equation. In the first section of this chapter, we will set up and solve the problem of axial potential flow obstructed by the travelling panel. In the second section, we will use the results to solve the fluid–structure interaction problem, and give so me numerical examples.