CFD MODELING OF VORTEX AFTERBURNING OF BIOMASS GASIFICATION PRODUCTS IN A FLUIDIZED BED FURNACE

CFD modeling of the afterburning of biomass gasification products in a fluidized bed furnace with a vortex supply of secondary air has been carried out. The effect of secondary air heating on the ecological characteristics of flue gases has been determined. Modeling has shown that gasification products swirl in the primary chamber with the formation of a central vortex, which obeys the law of solid-body rotation. An increase in the temperature of the secondary air leads to an increase in its tangential velocity and, as a consequence, to an increase in centrifugal mass forces. Calculations have shown that with an increase in the secondary air temperature, the maximum of the kinetic energy of turbulence shifts to the periphery and increases in absolute value. This results in more efficient mixing of the central (producer gas) and peripheral (secondary air) streams. As a result, this leads to a more complete combustion. The influence of secondary air heating on the ecological characteristics of the furnace has been determined. As a result of air heating from 30° C to 300° C, the concentration of carbon monoxide decreases by more than 1.5 times. The concentration of nitrogen oxides practically does not change and amounts to 3.5 mg /nm3.

Different Faces of Confinement

In this review, we provide a short outlook of some of the current most popular pictures and promising approaches to non-perturbative physics and confinement in gauge theories. A qualitative and by no means exhaustive discussion presented here covers such key topics as the phases of QCD matter, the order parameters for confinement, the central vortex and monopole pictures of the QCD vacuum structure, fundamental properties of the string tension, confinement realisations in gauge-Higgs and Yang–Mills theories, magnetic order/disorder phase transition, among others.

Modeling the stability of polygonal patterns of vortices at the poles of Jupiter as revealed by the Juno spacecraft

From its pole-to-pole orbit, the Juno spacecraft discovered arrays of cyclonic vortices in polygonal patterns around the poles of Jupiter. In the north, there are eight vortices around a central vortex, and in the south there are five. The patterns and the individual vortices that define them have been stable since August 2016. The azimuthal velocity profile vs. radius has been measured, but vertical structure is unknown. Here, we ask, what repulsive mechanism prevents the vortices from merging, given that cyclones drift poleward in atmospheres of rotating planets like Earth? What atmospheric properties distinguish Jupiter from Saturn, which has only one cyclone at each pole? We model the vortices using the shallow water equations, which describe a single layer of fluid that moves horizontally and has a free surface that moves up and down in response to fluid convergence and divergence. We find that the stability of the pattern depends mostly on shielding—an anticyclonic ring around each cyclone, but also on the depth. Too little shielding and small depth lead to merging and loss of the polygonal pattern. Too much shielding causes the cyclonic and anticyclonic parts of the vortices to fly apart. The stable polygons exist in between. Why Jupiter’s vortices occupy this middle range is unknown. The budget—how the vortices appear and disappear—is also unknown, since no changes, except for an intruder that visited the south pole briefly, have occurred at either pole since Juno arrived at Jupiter in 2016.

A vortex ring on a sphere: the case of total vorticity equal to zero

The stability of a ring of vortices has attracted the interest of researchers for over a century. Recent beautiful observations of polygonal configurations of vortices present in the atmospheres of Jupiter and Saturn, and of polygonal jets in the Earth's atmosphere, have revived the interest in the subject. In the observed cases, the vortex ring is in the presence of a central vortex. We present analytical and numerical results about the linear, spectral and Lyapunov stability of a ring in the presence of polar vortices. Motivated by both atmospheric observations we considered the special case of total vorticity equal to zero. Such a case has also the very nice property of being universal , i.e. not depending on a choice of gauge. We considered the two cases of fixed and non-fixed polar vortices. A ring in the northern (respectively, southern) hemisphere is stabilized by the presence of a northern (respectively, southern) polar vortex of suitable strength, in agreement with what is observed numerically and atmospherically. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

The stability and nonlinear evolution of quasi-geostrophic toroidal vortices

We investigate the linear stability and nonlinear evolution of a three-dimensional toroidal vortex of uniform potential vorticity under the quasi-geostrophic approximation. The torus can undergo a primary instability leading to the formation of a circular array of vortices, whose radius is approximately the same as the major radius of the torus. This occurs for azimuthal instability mode numbers $m\geqslant 3$, on sufficiently thin tori. The number of vortices corresponds to the azimuthal mode number of the most unstable mode growing on the torus. This value of $m$ depends on the ratio of the torus’ major radius to its minor radius, with thin tori favouring high mode $m$ values. The resulting array is stable when $m=4$ and $m=5$ and unstable when $m=3$ and $m\geqslant 6$. When $m=3$ the array has barely formed before it collapses towards its centre with the ejection of filamentary debris. When $m=6$ the vortices exhibit oscillatory staggering, and when $m\geqslant 7$ they exhibit irregular staggering followed by substantial vortex migration, e.g. of one vortex to the centre when $m=7$. We also investigate the effect of an additional vortex located at the centre of the torus. This vortex alters the stability properties of the torus as well as the stability properties of the circular vortex array formed from the primary toroidal instability. We show that a like-signed central vortex may stabilise a circular $m$-vortex array with $m\geqslant 6$.

Three-dimensional quasi-geostrophic vortex equilibria with -fold symmetry

We investigate arrays of $m$ three-dimensional, unit-Burger-number, quasi-geostrophic vortices in mutual equilibrium whose centroids lie on a horizontal circular ring; or$m+1$ vortices where the additional vortex lies on the vertical ‘central’ axis passing through the centre of the array. We first analyse the linear stability of circular point vortex arrays. Three distinct categories of vortex arrays are considered. In the first category, the $m$ identical point vortices are equally spaced on a circular ring and no vortex is located on the vertical central axis. In the other two categories, a ‘central’ vortex is added. The latter two categories differ by the sign of the central vortex. We next turn our attention to finite-volume vortices for the same three categories. The vortices consist of finite volumes of uniform potential vorticity, and the equilibrium vortex arrays have an (imposed) $m$-fold symmetry. For simplicity, all vortices have the same volume and the same potential vorticity, in absolute value. For such finite-volume vortex arrays, we determine families of equilibria which are spanned by the ratio of a distance separating the vortices and the array centre to the vortices’ mean radius. We determine numerically the shape of the equilibria for $m=2$ up to $m=7$, for each three categories, and we address their linear stability. For the $m$-vortex circular arrays, all configurations with $m\geqslant 6$ are unstable. Point vortex arrays are linearly stable for $m<6$. Finite-volume vortices may, however, be sensitive to instabilities deforming the vortices for $m<6$ if the ratio of the distance separating the vortices to their mean radius is smaller than a threshold depending on $m$. Adding a vortex on the central axis modifies the overall stability properties of the vortex arrays. For $m=2$, a central vortex tends to destabilise the vortex array unless the central vortex has opposite sign and is intense. For $m>2$, the unstable regime can be obtained if the strength of the central vortex is larger in magnitude than a threshold depending on the number of vortices. This is true whether the central vortex has the same sign as or the opposite sign to the peripheral vortices. A moderate-strength like-signed central vortex tends, however, to stabilise the vortex array when located near the plane containing the array. On the contrary, most of the vortex arrays with an opposite-signed central vortex are unstable.

Pressure Fluctuation Mitigation in a Francis Turbine With Water Injection: Computational Study

Computational fluid dynamics simulations were performed on Francis turbine using Reynolds-averaged Navier-Stokes (RANS) with k-ω SST turbulence model. Simulations were conducted at the turbine’s best efficiency point with a Reynolds number of 2.01 × 107. Water injection was admitted from the runner cone in the stream-wise direction. The aim of this process was to investigate the influence of water injection on the turbine performance and the pressure pulsation. The water injection did not affect the nominal value of the turbine’s power generation. Straight vortex rope was observed at the centerline of the draft tube. Moreover, helix-shaped vortex ropes were obtained near the draft tube surface. The water injection expands the central vortex rope, but it did not suppress or disrupt the helix-shaped peripheral vortex rope near the draft tube surface. The pressure fluctuation became less regular after the water injection, but the fluctuation level remained similar.

Transitions and oscillatory regimes in two-layer geostrophic hetons and tripoles

We investigate numerically the transitions and oscillatory regimes in two-layer quasigeostrophic hetons and tripoles composed of patches of uniform potential vorticity (PV). The contour-surgery algorithms are employed, in which either some symmetries are preserved, or asymmetric evolution of the vortex structures is allowed, induced by generally asymmetric numerical noise. The fluid layers are assumed equally thick. First, the evolution of hetons is considered. A heton, a steadily translating pair of vortices residing in different layers, is antisymmetric in the sense that the two PV patches are opposite in sign and symmetric in shape about the axis of translation. A feebly stable heton, when exposed to weak antisymmetric perturbations, responds by developing an oscillation, which culminates in a transition to a new, substantially robust oscillating heton. The results obtained reinforce our earlier findings regarding the modon-to-modon transition (Kizner et al., J. Fluid Mech., vol. 468, 2002, pp. 239–270; Kizner, Phys. Fluids, vol. 18 (5), 2006, 056601; Kizner, UTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (ed. Borisov et al.), IUTAM Bookseries, vol. 6, 2008, pp. 125–133. Springer) and clarify the transition mechanism. Asymmetric perturbations might cause a heton-to-tripole transition. Next we consider the transitions and oscillations in carousel tripoles exposed to weak, generally asymmetric perturbations. A carousel tripole is a steadily rotating centrally symmetric ensemble of three PV patches, with the central vortex being located in one layer and the two remaining, satellite vortices in the other layer. Depending on the tripoles’ size, hence also on the shape of the satellite vortices, three different types of transition are revealed, the transition to a ringed (shielded) monopole being one of them. Whereas the transition of a ringed monopole into a tripole is a known phenomenon, the reverse transition in baroclinic flows is detected for the first time.