Steady Flows in an Oscillating Spheroidal Cavity with Elastic Wall

Vibrational Heat Transfer Intensification in an Annulus with a Deformable Boundary

“…is regular flow pattern closely resembles to those observed in isothermal oscillating droplets or containers with elastic boundary [8][9][10][11] and should be related to the steady flows due to the boundary oscillations.…”

“…Second, the low-frequency limit, ω ∼ 1: this means that viscous force is important to the oscillating flow in the entire container volume. As shown in [10,11], with an increase in ω, the steady-flow structure transforms. In the high-frequency limit, outside the boundary layers, a flow exists, whose velocity in the direction tangential to the boundary is as follows [22]:…”

“…e latter is independent of the dimensionless frequency. In the lowfrequency limit, as shown theoretically in [11], the parameter that determines the magnitude of the dimensionless velocity of the steady flows is Re p ω � b 2 Ω 2 h 2 /] 2 , where h is the characteristic size of the container. Both limiting cases are confirmed experimentally in containers with deformable oscillating boundaries [10,11].…”

“…For this reason, despite all experiments conducted at the constant vibration frequency, the dimensionless frequency varies in the range ω � 30 − 80. According to [10,11], where cylindrical and spherical containers with oscillating boundaries were considered, in this range, the dependence on ω was weak. us, one may assume that, for the presently studied system, the main parameter that controls the steady streaming is indeed Re p .…”

“…eoretical studies [8,9] demonstrate that steady flows in an oscillating droplet have the shape of toroidal vortices and lead to the interface renewal by tangential time-average flows. Recent experiments [10,11] on fluid oscillations in cylindrical and spherical containers with elastic boundaries demonstrate that similar steady flows can be modelled in relatively large containers.…”