7. Eulerian Flow-Oscillator Models

We apply the Eulerian formulations of the last chapter to derive a general variational formulation of a flow-oscillator modeling framework. A brief review of the application of variational principles to fluid–structure interactions is given. A summary is provided of Jourdain’s principle for fluid systems. Boundary conditions are discussed, in particular the no-slip condition and its interpretations. The control volume is expanded upon. Fluid–structure interaction is then modeled in two ways: (i) as a single governing equation of motion for a translating cylinder and for an inverted pendulum, and (ii) as coupled equations of motion utilizing the concept of a wake oscillator. For the wake oscillator, the no-slip condition is further examined and implemented. Experimental data is used to derive a more specific reduced-order model that can be compared with some of the models found in the literature: McIver, Benaroya and Wei, and Hartlen and Currie. A primary conclusion is that the derived framework is an excellent basis for the development of flow-oscillator models, where assumptions are explicitly identified.