Free Vortex Formation Research Articles

Mathematical simulation of the near-bottom section of an ascending twisting flow

The available results of laboratory experiments on the formation of free vortices and controlling of their behavior are compared with the results of mathematical simulation of corresponding flows. This is accomplished by constructing solutions for a set of gas dynamics equations. The comparison is performed for a specific scheme of origination and functioning of free ascending twisting flows. In particular, it is shown that the experimental results confirm the proposed scheme of the origination and initial twisting of ascending vortex flows and validate the reason of their stable functioning with the help of the method intended for controlling generated vortices using vertical grids which was implemented in the experiments. The fact of origination of an ascending flow twisting and its directing is mathematically substantiated using the solution to a specific initially edge problem for a set of gas dynamics equations. A stationary flow whose parameters are close to gas-dynamic parameters of free vortices reproduced in the experiments is calculated.

Free-vortex formation and topological phase transitions of two-dimensional spin systems.

A numerical method to study defect-mediated phase transitions is proposed, which combines a standard Monte Carlo technique with a particular type of boundary conditions. The method is applied to the two-dimensional XY (plane rotator) model as well as to the two-dimensional SO(3) Heisenberg model which models a triangular-lattice Heisenberg antiferromagnet. Our results give a direct numerical support for the occurrence of a topological transition in these systems driven by the vortex binding-unbinding.

Free-vortex formation of the plane rotator model

Free-vortex contribution to the Kosterlitz-Thouless (KT) transition of the two-dimensional plane rotator model is studied by Monte Carlo simulations. We calculate the excess free energy due to a free vortex using a particular boundary condition which introduces a free vortex into the system. The formation of free vortices is suppressed at low temperatures, while it is enhanced at high temperatures, consistent with the vortex pair binding-unbinding mechanism of the KT theory.

Vortex‐Settling Basin Design Considerations

The vortex‐settling basin (VSB) is a fluidic device that uses only the vortices of the flow to remove sediment. This is an economical, efficient, and water‐conserving alternative to the other available sediment‐extraction devices. This paper presents guidelines for designing and modeling VSBs. It shows that the circular basin should have diameter equal to five times (as compared with six times stipulated in American practice) the bed width of inlet canal. The distinctive features of the proposed design are formation of free vortex in the outer region and flow in the basin traversing a relatively longer path before reaching the overflow weir. Extraction of sediment smaller than 0.5 mm is optimized when a diaphragm and a deflector are incorporated in the inlet canal and basin, respectively. Diameter of the flushing pipe and the flushing discharge to be adopted for the extraction of different sediment fractions are specified. Formulas suggested for prediction of trapping efficiency are simpler and more relia...