Abstract
Molecular dynamics simulations with a purely repulsive Lennard-Jones potential and a normal damping force is used to simulate the granular flow in the annular region between two differentially-rotating cylinders, called the Taylor-Couette flow. The flow transition from the azimuthally-invariant Circular Couette flow (CCF) to the Taylor-vortex flow (TVF) is studied by increasing the rotation rate (ωi) of the inner cylinder, with the outer cylinder being kept stationary. Multiplicity of states, highlighting the hysteretic nature of the “CCF ↔ TVF” transition, is observed over a wide range of rotation rates. The onset of Taylor vortices is quantified in terms of the maximum radial velocity and the net circulation per vortex.
Highlights
Molecular dynamics simulations with a purely repulsive Lennard-Jones potential and a normal damping force is used to simulate the granular flow in the annular region between two differentially-rotating cylinders, called the Taylor-Couette flow
The flow between two concentric, independently rotating cylinders, called the Taylor-Couette flow (TCF), has attracted considerable attention since the foundational work of Couette [1] and Mallock [2] which was followed up by Taylor’s seminal linear stability analysis [3] on incompressible TCF, confirming the genesis of Taylor vortices beyond a minimum rotation speed of the inner cylinder
This geometry should, intuitively, admit Taylor vortices that break the mid-plane axial symmetry close to the critical point. This is followed by discussions regarding a relatively tall TC-cell with Γ = 10 where simulations are carried out to further explore the bifurcation scenario and the multiplicity of states in a dense granular gas undergoing TCF
Summary
The open source LAMMPS MD code[14], compiled on a mixed CPU-GPU architecture, with modifications to model the Taylor-Couette flow with the ‘reflecting’ endwall conditions [13] is employed for the simulations. Where r is the distance between two particle centres, σ is the effective diameter of the particles and is the depth of the potential well – the cutoff distance, rc = 21/6σ, results in a purely ‘repulsive’ potential known as the Weeks-Chandler-Andersen (WCA) potential. A damping force of the form, Fd = −mγnvn implements a velocity-dependent normal restitution force as a function of mass of the particle (m), the normal component of the relative velocity (vn) and the damping coefficient (γn).
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