Vortex precession and exchange in a Bose-Einstein condensate

Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.

Numerical study on the flow characteristics in swirl meter

The swirl meter (vortex precession flow meter) popularly used in natural gas industry is a kind of velocity flow meter with high turndown ratio and well performance in low flow measurement and other known advantages. In order to further understand the flow pattern of swirl meter to further improve its performance, computational fluid dynamics simulations are used to simulate the flow and predict the coefficient for swirl meter at different flow rates. Using renormalization group k–ε turbulent model and SIMPLEC algorithm, numerical simulations have been performed through commercial codes Fluent, and meter coefficients are also obtained experimentally to validate the numerical results. The simulated velocity and pressure in swirl meter are analyzed in detail, which are time-averaged distributions during a time period based on the transient numerical simulation. It is found that centerline pressure is lowest at the outlet of the swirler and rises gradually along the axial direction. While near-wall pressure presents an opposite variation tendency, it is significantly low at the end of throat due to strong influence of vortex precession. Centerline velocity increases as the flow approaches throat and reaches its maximum at center region of throat, and then it decreases and keeps relatively stable at downstream of divergent section. Both time-averaged pressure and axial velocity distributions are axisymmetric, and pressure variation is small on the cross section at the end of throat, although vortex precession is strong.

Numerical simulations for swirlmeter on flow fields and metrological performance

Measurements of flow rates of fluids are important in industrial applications. Swirlmeters (vortex precession meters) are widely used in the natural gas industry because of their advantage in having a large measurement range and strong output signal. In this study, using air as a working medium, computational fluid dynamics (CFD) simulations of a swirlmeter were conducted using the Reynolds-averaged Navier–Stokes (RANS) and renormalization group (RNG) k–ε turbulence models. The internal flow characteristics and the influence of the tube structure (geometric parameter of flow passage) on metrological performance were studied, with a particular focus on the meter factor. Calibration experiments were performed to validate the CFD predictions; the results show good agreement with those from simulations. From the streamline distributions, a clear vortex precession is found in the throat region. At the end of throat, the pressure fluctuation reached a maximum accompanied by the largest shift in the vortex core from the centreline. There exists a large reverse flow zone in the vortex core region in the convergent section. To mitigate the influence of reverse flow on vortex precession, a suitable length of throat is required. For a larger convergent angle, the fluid undergoes higher acceleration leading to an increase in velocity that produces more intensive pressure fluctuations. The minor diameter of the throat also produces a higher velocity and larger meter factor. Compared with both divergent angle and throat length, the convergent angle and throat diameter play a more important role in determining precession frequency.