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Symmetry-breaking bifurcations and hysteresis in compressible Taylor–Couette flow of a dense gas: a molecular dynamics study

Published online by Cambridge University Press:  08 September 2020

Nandu Gopan Open the ORCID record for Nandu Gopan [Opens in a new window]  and
Meheboob Alam Open the ORCID record for Meheboob Alam [Opens in a new window]
Nandu Gopan
Affiliation:
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore560064, India Amrita Vishwa Vidyapeetham, Amritanagar P.O., Coimbatore641112, India
Meheboob Alam*
Affiliation:
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore560064, India
*
†Email address for correspondence: meheboob@jncasr.ac.in
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Abstract

Molecular dynamics simulations with a repulsive Lennard-Jones potential are employed to understand the bifurcation scenario and the resulting patterns in compressible Taylor–Couette flow of a dense gas, with the inner cylinder rotating ($\omega _i>0$) and the outer one at rest ($\omega _o=0$). The steady-state flow patterns are presented in terms of a phase diagram in the ($\omega _i,\varGamma$) plane, where $\varGamma =h/\delta$ is the aspect ratio, $h$ is the height of the cylinders and $\delta =R_o-R_i$ is the gap between the outer and inner cylinders, and the underlying bifurcation scenario is analysed as a function of $\omega _i$ for different $\varGamma$. Considerable density stratification is found along both radial and axial directions in the Taylor-vortex regime of a dense gas, which makes the present system fundamentally different from its incompressible analogue. In the circular Couette flow regime, the stratifications remain small and the predicted critical Reynolds number for the onset of Taylor vortices matches well with that of its incompressible counterpart. The emergence of asymmetric Taylor vortices at $\varGamma >1$ is found to occur via saddle-node bifurcations, resulting in hysteresis loops in the bifurcation diagrams that are characterized in terms of the net circulation or the maximum radial velocity or the axial density contrast as order parameters. For $\varGamma \leq 1$ with reflecting axial boundary conditions, the primary bifurcation yields a single-vortex state which is connected to a two-roll branch via saddle-node bifurcations; however, changing to stationary (no-slip) endwalls yields a new state, which consists of two large symmetric vortices near the inner cylinder coexisting with an irregular pattern near the stationary outer cylinder. It is shown that the endwall conditions and the fluid compressibility play crucial roles on the genesis of asymmetric and stratified vortices and the related multiplicity of states in the Taylor-vortex regime of a dense gas.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Rarefied Gas Flow: Molecular dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A18
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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