Time-average flows in closed cavity subject to swing oscillations D.V. Lyubimov a , T.P. Lyubimova b, * a Perm State University, Bukireva Street, 15, 614990 Perm, Russia b Institute of Continuous Media Mechanics UB RAS, Computational Fluid Dynamics Laboratory, Koroleva Street, 1, 614013 Perm, Russia Received 3 November 2004; received in revised form 18 May 2005; accepted 20 May 2005 Abstract The paper deals with the investigation of time-average flows in a closed cavity subjected to high frequency swing oscillations. Analysis is based on the governing equations and effective boundary conditions for thermal vibrational convection under non-uni- form vibrations obtained by averaging method. Vibrational flows induced by volumetric and boundary-layer-type mechanisms are studied for zero gravity conditions, at different values of oscillation arm length. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Thermal vibrational convection; Schlichting flow; Swing vibrations; Pulsational and average flows; Zero gravity 1. Introduction It is known that translational vibrations of a con- tainer with rigid walls, completely filled with a uniform fluid cannot induce average flow in this fluid. Indeed, in this case, inertial forces are the gradient of a potential, and the effect of vibration reduces to the renormaliza- tion of the pressure. In the case of non-translational vibrations, inertial forces are not potential and the fluid cannot remain quiescent relative to the container walls. At high vibration frequencies, the pulsational velocity field in the interior of the container is described by the equations of inviscid fluid motion and is potential. Such a flow does not satisfy no-slip boundary conditions at a solid wall. Indeed, the total flow may be considered as the sum of the potential flow and a viscous flow that is manifested in the form of a dynamical skin-layer near the cavity walls. Here the no-slip conditions for the total velocity are satisfied. The problem of the boundary layer near the rigid walls can be solved by conventional boundary layer techniques. This solution is then matched with the interior solution. As was shown by Schlichting (1955), the value of the asymptotic boundary layer solution for the average velocity at the outer bor- der of the skin-layer is not equal to zero. That is, at this boundary the tangential component of velocity does not vanish, but has a finite value. This value is taken as an effective boundary condition for the tangential compo- nent of average velocity on the rigid wall. It follows from the above discussion that in this case the Stokes boundary layer arises near rigid walls. The average vor- ticity generated in the skin-layer diffuses into the fluid interior and there generates time-average flow. In space-flight conditions vibrations with non-zero angular component are very important. Time-average flows in a closed fluid-filled cavity subject to non-transla- tional vibrations have been studied experimentally and theoretically in a number of papers. The average velocity in the near-wall areas was calculated for the case of swing oscillations of a cylinder with an elliptic and triangular cross-sections by Povitskii and Lyubin (1972). Experi- ments and numerical simulations by Ivanova et al. (1995) have considered average flows in an isothermal fluid-filled cylinder of square cross-section subject to high-frequency torsional oscillations about the cylinder 0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.05.093 * Corresponding author. Tel.: +73422396208; fax: +73422371611. E-mail address: lyubimovat@mail.ru (T.P. Lyubimova). www.elsevier.com/locate/asr Advances in Space Research 36 (2005) 75–79