Synchronous oscillations of two plates in a viscous incompressible fluid

In this paper, we investigate the synchronous oscillations of two tandem-arranged long thin plates in a viscous incompressible fluid under the action of hydrodynamic forces. The hydrodynamic action exerted on the plates by the moving fluid is studied. The flows induced by the oscillating plates are modeled based on the complete non-stationary system of Navier-Stokes equations on the assumption that the plates move as rigid bodies, and the fluid flow caused by the oscillations of the plates are two-dimensional. The resulting flow problem is solved numerically in a moving coordinate system rigidly attached to the plates. A numerical model is constructed based on the free software package OpenFOAM using the finite volume method. The hydrodynamic influence on the plates is analyzed using the Morison approximation, according to which the hydrodynamic forces are represented as the sum of the resistance and inertia forces. The changes in the drag and inertia coefficients are investigated depending on the distance between the plates at different values of the dimensionless amplitude of oscillations. The results of the study show that by varying the distance between the plates, it is possible to control the structure of the streamline modes and multiply the hydrodynamic impact on the structure. The distance value has the strongest influence on the drag force in the range of small and moderate oscillation amplitudes. By removing the plates apart from each other, it is possible to produce the effect of isolated behavior for each plate and to double the hydrodynamic resistance of the structure compared to the hydrodynamic resistance of one plate. The study showed that when the plates move closer to each other, a stagnant zone is formed in the gap, which makes it possible to reduce the resistance of the structure by a factor of three (compared to the hydrodynamic resistance of one plate).