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Continuation and stability of rotating waves in the magnetized spherical Couette system: secondary transitions and multistability.

ABSTRACT: Rotating waves (RW) bifurcating from the axisymmetric basic magnetized spherical Couette (MSC) flow are computed by means of Newton-Krylov continuation techniques for periodic orbits. In addition, their stability is analysed in the framework of Floquet theory. The inner sphere rotates while the outer is kept at rest and the fluid is subjected to an axial magnetic field. For a moderate Reynolds number Re?=?103 (measuring inner rotation), the effect of increasing the magnetic field strength (measured by the Hartmann number Ha) is addressed in the range Ha?(0,?80) corresponding to the working conditions of the HEDGEHOG experiment at Helmholtz-Zentrum Dresden-Rossendorf. The study reveals several regions of multistability of waves with azimuthal wavenumber m?=?2,?3,?4, and several transitions to quasi-periodic flows, i.e modulated rotating waves. These nonlinear flows can be classified as the three different instabilities of the radial jet, the return flow and the shear layer, as found in the previous studies. These two flows are continuously linked, and part of the same branch, as the magnetic forcing is increased. Midway between the two instabilities, at a certain critical Ha, the non-axisymmetric component of the flow is maximum.

SUBMITTER: Garcia F

PROVIDER: S-EPMC6304025 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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Continuation and stability of rotating waves in the magnetized spherical Couette system: secondary transitions and multistability.

Garcia Ferran F Stefani Frank F

Proceedings. Mathematical, physical, and engineering sciences 20181212 2220

Rotating waves (RW) bifurcating from the axisymmetric basic magnetized spherical Couette (MSC) flow are computed by means of Newton-Krylov continuation techniques for periodic orbits. In addition, their stability is analysed in the framework of Floquet theory. The inner sphere rotates while the outer is kept at rest and the fluid is subjected to an axial magnetic field. For a moderate Reynolds number <i>Re</i> = 10<sup>3</sup> (measuring inner rotation), the effect of increasing the magnetic fie ...[more]

PMID: 30602925

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Project description:Viscoelastic fluid is an advanced fluid which exhibits both elastic and viscous properties. Whereas rotation of viscoelastic fluid is a very complex phenomenon and has an immense amount of applications in engineering and product making industries. Due to various applications in real life researchers are working to understand the rheology of viscoelastic fluids. Viscoelastic dusty fluids are used in gas cooling systems. In nuclear reactors, dusty fluids are used to lower the temperature of the system. Such fluids are also used in centrifugal separators, which separate solid particles from the liquid state, etc. Therefore, in the present study, viscoelastic dusty fluid is analyzed. More precisely free convective Couette flow under the influence of the transversely applied uniform magnetic field in a rotating frame is considered. The subject fluid is driven by the sine oscillations of the upper plate along with the effect of free convection. Due to rotation, the fluid and dust particles have complex velocities which is the sum of primary velocity and secondary velocity. The flow regime is modeled in terms of partial differential equations. To non-dimensionalize the system of governing equations, dimensionless variables have been derived through Buckingham-Pi theorem. The system of partial differential equations is solved through assumed periodic solutions (Poincare-Light Hill Technique). The expressions for skin friction (shear stresses at [Formula: see text]) and Nusselt number (the rate of heat transfer) are also calculated. Moreover, parametric influence on Nusselt number, and velocity profile of the fluid and the dust particles, is discussed. It is observed that increase in rotation parameter η causes retardation in the velocity of dust particles and the fluid. This is due to the fact that the increase in η enhances the Coriolis forces that are in fact inertial forces, causing a retardation in the velocity of the fluid phase and the dust phase.

Dataset Information

Continuation and stability of rotating waves in the magnetized spherical Couette system: secondary transitions and multistability.

Publications

Continuation and stability of rotating waves in the magnetized spherical Couette system: secondary transitions and multistability.

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