Symmetry-breaking bifurcations and hysteresis in compressible Taylor- Couette flow of a dense gas: a molecular dynamics study
N Gopan and M Alam, JOURNAL OF FLUID MECHANICS, 902, A18 (2020).
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), Gamma) plane, where G = h/d is the aspect ratio, h is the height of the cylinders and d = Ro - Ri is the gap between the outer and inner cylinders, and the underlying bifurcation scenario is analysed as a function of omega(i) for different Gamma. 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 Gamma > 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 Gamma <= 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.
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