Ylo Rudi

A model for the formation of “optimal” vortex rings taking into account viscosity

The evolution of a viscous vortex ring from thin to thick-cored form is considered using an improved asymptotic solution, which is obtained after impressing a spatially uniform drift on the first-order solution of the Navier–Stokes equations. The obtained class of rings can be considered as the viscous analog solution to the Norbury vortices and classified in terms of the ratio of their initial outer radius to the core radius. The model agrees with the reported theoretical and experimental results referring to the post-formation and the formation stages. By using the matching procedure suggested earlier and the obtained properties of the viscous vortex ring, it is found that when the length-to-diameter aspect ratio L∕D reaches the limiting value 4.0 (“formation number”), the appropriate values of the normalized energy and circulation become around 0.3 and 2.0, respectively. An approach that enables to predict the “formation number” is proposed.

Reynolds-number effect on vortex ring evolution in a viscous fluid

It is known that the cross section of the vortex ring core takes an approximately elliptical shape with increasing Reynolds number. In order to model this feature, the functional form of a vortex ring solution of the Stokes equations is modified so as to be able to model higher Reynolds number rings. The model introduces two nondimensional parameters that govern the shape of the vortex core:λ ⩾ 1 and β ⩾ 1. Based on this modification, new expressions for the translation velocity, energy, circulation, and streamfunction are derived for a wide range of section ellipticity that are specific to such vortices. To validate the model, the data adapted from the numerical study of vortex ring at Reynolds number Re = 1400 performed by Danaila and Helie [Phys. Fluids 20, 073602 (2008)], is used. In this case, the appropriate values of λ and β are calculated by equating the normalized energy Ed and circulation Γd of the theoretical vortex to the corresponding values obtained from the numerical data. The model provide...

RSTM Numerical Simulation of Channel Particulate Flow with Rough Wall

Turbulent gas-solid particles flows in channels have numerous engineering applications ranging from pneumatic conveying systems to coal gasifiers, chemical reactor design and are one of the most thoroughly investigated subject in the area of the particulate flows. These flows are very complex and influenced by various physical phenomena, such as particle-turbulence and particle-particle interactions, deposition, gravitational and viscous drag forces, particle rotation and lift forces etc.

Reynolds-number effect on vortex ring evolution

An analytical model describing a vortex ring for low Reynolds numbers (Re) proposed previously by Kaplanski and Rudi [Phys. Fluids,17, 087101 (2005)], is extended to a vortex rings for higher Reynolds numbers. The experimental results show that the vortex ring core takes the oblate ellipsoidal shape with increasing Re. In order to model this feature, we suggest an expression for the vorticity distribution, which corrects the linearized solution of the Navier‐Stokes equation, with two disposable nondimensional parameters λ and β governing the shape of the vortex core, and derive the new expressions for the streamfuction, circulation, energy and translation velocity on the basis of it. The appropriate values of λ and β are calculated by equating the nondimensional energy Ed and circulation Гd of the theoretical vortex to the corresponding values obtained from the experimental or numerical vortex ring. To validate the model, the data adapted from the numerical study of a vortex ring at Re = 1400 performed by...