Cylindrical Vortex Research Articles

Measurement of air–water oxygen transfer of cylindrical vortex flow regulators at a recirculating system

Hydrodynamic flow regulators are used for diversion and/or limiting excess discharge in wastewater and stormwater systems as a replacement for traditional flow throttling devices. They are highly efficient, reliable and free from common disadvantages of traditional devices. Recent research of the authors indicated that atomization of a liquid by vortex flow regulators accelerates oxygenation and prevents the putrefaction process in wastewater and storm water collection systems. The study presents experimental results of the oxygen transfer measurements for basic designs of cylindrical hydrodynamic flow regulators in a closed-circuit experimental setup at the semi-commercial scale. The oxygen mass transfer coefficient, standard oxygen transfer rate and standard aeration efficiency were determined for the range of tested configurations by the clean water test.

Modeling of the influence of cavitation on petroleum hydrocarbon cracking

It is shown that axial, radial, and peripheral velocities of feed material in centrifugal vortex chamber pronouncedly differ in magnitude. The full velocity is high and attains 43 m/sec on the vortex surface. It is concluded that the cavitation region must be on the vortex surface itself, where indeed cracking of hydrocarbons intensifies. The parameters of the cavitaiton region are determined from the static liquid pressure at all points of the cavitation apparatus. The distribution of static pressure of the liquid in the centrifugal vortex chamber has a complicated pattern: the cavitation region represents a hollow truncated cone, inside which occurs a cylindrical steam vortex. Formation of a turbulent layer expands the cavitation region, the shape and size of which are calculated from the parameters of a real centrifugal chamber.

Oscillations of the flow parameters in the vicinity of a cylindrical vortex

In the modern literature, the oscillations of flow parameters have been investigated insufficiently; their connection with the fundamental solution of the Navier-Stokes equations has not been shown. Some types of vortical structures in a 2D steady incompressible flow were analyzed in [2]. Below, a nonlinear system of the Navier-Stokes equations was used for calculation of unsteady gas flow in the vicinity of a cylindrical vortex. The problem is set within the domain z ≥ 0 and the flow is shown to be oscillatory; the oscillations of pressure, density, and temperature were investigated. The distinctive feature of this computation method is that no finite-difference schemes are used. The method can be used on the condition that the gas is considered as a perfect one (cp/cv = γ = const).

The Numerical Investigation on Vortex Flow Behavior Using FLOW-3D

In this paper a numerical investigation is given for a Rankine type vortex flow inside the cylindrical vortex chamber using FLOW-3D. The FLOW-3D is a general purpose computational fluid dynamics (CFD) package. The fluid motion is described with non-linear, transient, second-order differential equations. Additionally the free surface also exists in many simulations carried out with FLOW-3D because flow parameters and materials properties, such as density, velocity and pressure experience a discontinuity at it. After analysis of the vortex by mentioned details, the finding of time-averaged velocity components, turbulent components, turbulence dissipation, in the 2D briefed sections of chamber were depicted. It was found that there are different flow patterns like clockwise/anticlockwise vortices and some sink points combined with each other in different time intervals, decaying and generating along the time. Also the turbulence intensity and dissipations around the boundary conditions of chamber like central flushing discharge are higher than the flow body. It was also found that this CFD package was not able to simulate thoroughly the central air core of chamber after filling of chamber. This analysis is validated by comparison with previous experimental data that was measured in vortex settling basin.

Discharge coefficient for bottom orifice of vortex chamber

This research presents investigations on the discharge coefficient of a circular orifice located at the apex of an inverted conical hopper attached to the bottom of a cylindrical vortex chamber. A circular jet inflow tangentially enters the vortex chamber at the top periphery of the conical hopper. Different sizes of orifices and inflow jet discharges were applied in the experiments to investigate the variation of the discharge coefficient. The effect of overflow at the upper outlet on the discharge coefficient was also investigated. Based on the test data, empirical relations for the discharge coefficient are proposed. It is found that in the presence of tangential jet inflow, the discharge coefficient is considerably smaller than that without tangential jet inflow and the presence of overflow significantly reduces it.

Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates

We discuss stabilization strategies for finite-difference approximations of the compressible Euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables. Our approach rather relies on a skew-symmetric-like splitting of the convective derivatives, that guarantees preservation of kinetic energy in the semi-discrete, low-Mach-number limit. A locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers. The validity of the approach is tested for benchmark flow cases, including the propagation of a cylindrical vortex, and the head-on collision of two vortex dipoles. The tests support high accuracy and superior stability over conventional central discretization of the convective derivatives. The potential use for DNS/LES of turbulent compressible flows in complex geometries is discussed.

The vortex filament model and velocity structure functions of well-developed hydrodynamical turbulence

We present a further elaboration of a vortex filament theory which was developed in our previous papers. A representative example of a cylindrical vortex filament is considered in detail. It is shown that contraction and stretching of a filament provide an energy flux from larger to smaller scales. A connection between velocity scaling exponents and moments of vorticity is clarified. Lagrangian and Eulerian transversal scaling exponents are derived based on the concept of vortex filament evolution. Arguments hypothesizing that Lagrangian scaling exponents tend to a constant for n→∞ and an upper constraint for are presented.

The Instability of High Speed Jets

This paper provides a review of the stability characteristics of high speed jets. These characteristics not only play a role in the transition of jet flows to turbulence, in the traditional sense of hydrodynamic stability theory, but also are key to understanding the behavior of large scale turbulent structures in the jet. They are also an important component in understanding the noise radiation by high speed jets. The paper begins with the development of the linear stability equations and then reviews the classes of instability waves in a jet, modeled as a cylindrical vortex sheet. Finite shear layer thickness effects are then discussed. This includes a review of numerical methods for the solution of the stability equations. The effects of jet Mach number and temperature are then presented. Additional topics considered include, the effects of mean flow divergence, the effect of Reynolds number, and the effect of the jet's geometry. Finally, the nature of absolute instabilities in jet flows is described, both from an analytical viewpoint as well as applications.

On long-wave sound scattering by a Rankine vortex: Non-resonant and resonant cases

The well-known two-dimensional problem of sound scattering by a Rankine vortex at small Mach number M is considered. Despite its long history, the solutions obtained by many authors still are not free from serious objections. The common approach to the problem consists in the transformation of governing equations to the d’Alembert equation with right-hand part. It was recently shown [I.V. Belyaev, V.F. Kopiev, On the problem formulation of sound scattering by cylindrical vortex, Acoustical Physics 54(5) (2008) 603–614] that due to the slow decay of the mean velocity field at infinity the convective equation with nonuniform coefficients instead of the d’Alembert equation should be considered, and the incident wave should be excited by a point source placed at a large but finite distance from the vortex instead of specifying an incident plane wave (which is not a solution of the governing equations).

Influence of design parameters on throttling efficiency of cylindrical and conical vortex valves

Selected hydraulic test results of cylindrical and conical vortex valves in a pilot-plant scale are presented to discuss the effects of the geometric parameters and the spatial orientation of a vortex chamber. Tests performed include the effects of the inlet and outlet diameters, swirl radius, chamber height, and diameter on the hydraulic characteristics. A novel, universal variable K, describing the geometry of vortex valves and grouping their geometrical parameters, is introduced. This constant K increases the quantitative accuracy of the relationship between the discharge coefficient and the geometrical parameters. A test methodology for hydrodynamic vortex regulators has been developed and was applied to environmental engineering, based on dimensional analysis. This research presents the empirical equations enabling to predict the discharge coefficient according to the geometrical parameters of the devices. The investigated relationships allow for a rational parameter selection for hydrodynamic vortex regulators.

Vortices of mesoscopic rings in an external magnetic field: Phenomenological Ginzburg-Landau theory

Vortex states in mesoscopic superconducting rings are investigated by the phenomenological Ginzburg-Landau theory in the presence of an externally applied magnetic field. We obtain the cylindrical symmetric giant vortex states (GVS) by solving an eigenvalue problem and minimizing the system free energy. Ground state transitions between GVS and multivortex states are found as system dimensions and magnetic field vary. Metastability and negative flux jump associated with quantum size effect and proximity effect are revealed. Also, We find that the superconducting state and the normal state can alternately appear with external field increasing.

Elliptical instability of a vortex tube and drift current induced by it

We revisit, with some extension to the nonlinear regime, the Moore–Saffman–Tsai–Widnall instability, which is the three-dimensional instability of a straight vortex tube elliptically strained by a pure shear flow. A circular cylindrical vortex tube supports neutrally stable three-dimensional waves called Kelvin waves. A pure shear breaks the circular symmetry, causing a parametric resonance between two Kelvin waves whose azimuthal wavenumbers are separated by two. The eigenvalues and functions are written out in full in terms of the Bessel and the modified Bessel functions, and so is the growth rate. That this instability has a link with the elliptical instability in the short-wave limit is established in this study. This result is studied in the light of Krein's theory for Hamiltonian spectra. We develop a Lagrangian (particle) formulation that makes feasible an efficient calculation of iso-vortical disturbances up to second order in amplitude and thereby facilitates calculation of the energy of Kelvin waves. It is found that a Kelvin wave induces a drift current along the vortex tube.

Vortex flows in open cylindrical-section cavities

Flow within a large-aspect-ratio cylindrical vortex cell has been explored experimentally. The flow was driven by a shear layer above an opening in the cylinder circumference. Reynolds numbers, based on the length of the opening and the velocity just outside it, exceed 50,000. It is shown that the expected solid body rotation within the cell, with a constant velocity gradient across most of the core, is qualitatively present, but is significantly distorted by three-dimensional effects. Nonetheless, turbulence levels within the core are very low, only rising to levels similar to those in regular turbulent shear flows within the driving mixing layer itself and the cell-wall boundary layers.

Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

On the statement of the problem of sound scattering by a cylindrical vortex

The well-known problem of sound wave scattering by a Rankine vortex is investigated. Although the problem has been studied for years, none of the solutions reported in the literature can be considered completely correct. It is demonstrated that the main difficulty consists in the absence of a mathematically well-posed statement of the problem for a plane wave (which is used in most of the approaches) because of the slow decrease in the mean flow velocity at infinity. This gives rise to multiple solutions, including those singular on a line behind the vortex, and each of them claims to be correct. It is shown that, in spite of the decrease in the mean flow velocity, the problem does not possess any remote region at infinity, tending to which it is possible to preset the plane wave condition for the incident field. Therefore, for the external field, the remote point source condition is proposed. This approach makes it possible to state a mathematically well-posed problem, to reveal the origin of the aforementioned ambiguity, and to compare previous approaches used for solving the problem under consideration.

Mathematical simulation of the formation of heat tornadoes

A numerical simulation of convective swirling jets arising as a result of the rotation of a heated disk in an initially immovable medium has been carried out. It is shown that in the case where a jet is swirled moderately, the flow is relaminarized and the intensity of the heat and mass transfer in the convective jet decreases, which leads to an increase in the buoyancy force and, consequently, an increase in the velocity of the flow. The air mass in the form of a cylindrical column-shaped vortex rises above the disk to a large height and, in doing so, retains its individuality.

Sound radiation from annular jet ducts with impedance walls

An analytical model for sound radiation from a semi‐infinite annular duct with cylindrical infinite centre section and carrying a jet issuing into an uniform mean flow is presented. The interior of the outer wall of the duct is allowed to have an acoustic impedance. This is an extension to a recent model where only rigid walls were considered. The unstable cylindrical vortex layer attached to the edge of the duct, between the jet and the uniform mean flow, is considered. The geometry considered aims to model a turbofan exhaust, where sound generated at the inlet propagates along the annular duct and refracts through the bypass jet before radiating into the far field. In this paper the effect of the acoustic impedance of the duct outer wall on the radiated acoustic field is studied.

Vortices in a wave travelling over dry ground

Experimental investigations revealed that large cylindrical vortices are formed near the bottom in a head wave traveling over dry ground (“water wall” during a dam break). The vortices rise to the water surface and are thrown into the air perpendicularly to the wave slope. The vortices entrain and transport bottom ground.

Green’s model of cylindrical vortex decay

Modeling vortex decay is essential for estimating the risk that during landing an aircraft will hit the wake vortex from a preceding aircraft. The relevance of this problem has increased due to the growing traffic in airports and the development of vortex forecasting systems. Green’s model, one of the models describing the decay of point vortices, is generalized in this article to cylindrical vortices.

Vortex structures in mesoscopic superconducting spheres

Vortex states in mesoscopic superconducting spheres are investigated within the framework of the phenomenological Ginzburg-Landau theory in the presence of an externally applied magnetic field. We treat the linearized first Ginzburg-Landau equation as an eigenvalue problem and find the cylindrical symmetric giant vortex states. Taking linear combinations of solutions of the linearized equation and minimizing the free energy, we obtain the stable multivortex and giant vortex states.