Numerical study of swirling flow in a cylinder with rotating top and bottom

Abstract

A numerical investigation of oscillatory instability is presented for axisymmetric swirling flow in a closed cylinder with rotating top and bottom. The critical Reynolds number and frequency of the oscillations are evaluated as function of the ratio of angular velocities of the bottom and the top ͑ = ⍀ bottom / ⍀ top ͒. Earlier linear stability analysis ͑LSA͒ using the Galerkin spectral method by Gelfgat et al. ͓Phys. Fluids, 8, 2614 ͑1996͔͒ revealed that the curve of the critical Reynolds number behaves like an "S" around = 0.54 in the co-rotation branch and around = −0.63 in the counter-rotation branch. Additional finite volume computations, however, did not show a clear S behavior. In order to check the existence of the S shape, computations are performed using an axisymmetric finite volume Navier-Stokes code at aspect ratios ͑ = H / R͒ 1.5 and 2.0. Comparisons with LSA at = 1.5 show that the S shape does exist. The S shape of the stability diagram predicted by LSA is thus confirmed by a finite-volume based Navier-Stokes solver. The additional computations at aspect ratio = 2 show that the curve of critical Reynolds number has a wider S shape in the co-rotating branch for about 0.7 whereas a sharp "beak" appears in the counter-rotating branch for approximately −0.5.

Transitional cylindrical swirling flow in presence of a flat free surface

“…At the inception of any instability breaking the axisymmetry of the flow, a three-dimensional solution of the Navier-Stokes equations is required, thereby increasing considerably the complexity of the task. The last remark justifies the observed changes in terms of numerical modeling of Lopez' group and Sørensen's group, to allow them to investigate axisymmetry breaking in the closed cylinder case [5,6,[41][42][43]. Therefore, three-dimensional flow structures have started being simulated more recently, see Gelfgat et al [44], Sotiropoulos & Ventikos [11], Sotiropoulos et al [45], Marques & Lopez [46], Blackburn & Lopez [5,6], Serre & Bontoux [47], Blackburn [48], and Lopez [49].…”

Slow Dynamics in a Turbulent von Kármán Swirling Flow

“…Here we will analyze a particular configuration, the von Kármán swirling flow, where two different propellers are rotating inside a cylindrical cavity. These flows have been studied analytically [3,4], numerically [5,6,7] and experimentally [8,9,10]. Recently it has been shown that they can present multistability and memory effects [11].…”

“…These flows have been studied analytically [3,4], numerically [5,6,7] and experimentally [8,9,10]. Recently it has been shown that they can present multistability and memory effects [11].…”

Bifurcation induced by the aspect ratio in a turbulent von Kármán swirling flow

“…Two counter-rotating propellers are used to develop turbulence in a cylindrical cavity filled with water. This model system has been largely studied numerically [3][4][5], theoretically [6,7] and experimentally [8][9][10][11]. This kind of flow is particularly used in magnetohydrodynamics (MHD) experiments.…”