×

On unsteady two-phase fluid flow due to eccentric rotation of a disk. (English) Zbl 1130.76321

Summary: We examine the unsteady flow of a two-phase fluid generated by the nontorsional oscillations of a disk when the disk and the fluid at infinity rotate noncoaxially with the same angular velocity. The solutions are obtained for both the fluid and the particle velocities in closed form. It is found that the solutions remain valid for all values of the frequency of oscillations of the disk including the resonant frequency, which is equal to the angular velocity of rotation. But, in absence of particles, only in the case of resonance no oscillatory solution is possible, which is similar to that of solid-body rotation as pointed out by Thornley (1968). It is also shown that, unlike the case of single-disk configuration, no unique solution exists in a double-disk configuration, a result which is the reverse to that of solid-body rotation. Finally, the results are presented graphically to determine the quantitative response of the particle on the flow.

MSC:

76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76T99 Multiphase and multicomponent flows
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI EuDML