Modelling vortex formation in an unbaffled stirred tank reactors

Agitating liquids in unbaffled stirred tank leads to the formation of a vortex in the region of the impeller shaft when operating in the turbulent flow regime. A numerical model is presented here that captures such a vortex. The volume of fluid model, a multiphase flow model was employed in conjunction with a multiple reference frame model and the shear stress turbulence model. The dimensions of the tank considered here, were 0.585 m for the liquid depth and tank diameter with a 0.2925 m diameter impeller at a height of 0.2925 m. The impeller considered was an eight-bladed paddle type agitator that was rotating with an angular velocity of 7.54 rad s (72 rpm) giving a Reynolds number of 10 and Froude number of 0.043. Preliminary results of a second investigation into the effect of liquid phase properties on the vortex formed are also presented. © 2006 Elsevier B.V. All rights reserved.

Vortex shedding from a row of square bars

Interactions of wakes in a flow past a row of square bars, which is placed across a uniform flow, are investigated by numerical simulations and experiments on the tassumption that the flow is two-dimensional and incompressible. At small Reynolds numbers the flow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric flow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the flow is obtained.

Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

2000 Mathematics Subject Classification: 47A10, 47A13.

A note on the propagation of quantized vortex rings through a quantum turbulence tangle:energy transport or energy dissipation?

We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high-resolution numerical simulations, we examine the validity of simple estimates for the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipation

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Vortex-density fluctuations, energy spectra, and vortical regions in superfluid turbulence

Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Kockázattal kiegészített Taylor-szabályok becslése Magyarországra = Estimation of risk-augmented Taylor rules for Hungary

Cikkünkben a magyar monetáris politikát vizsgáljuk olyan szempontból, hogy kamatdöntései meghozatalakor figyelembe vette-e az országkockázatot, és ha igen, hogyan. A kérdés megválaszolásához a monetáris politika elemzésének leggyakoribb eszközét használjuk: az ország monetáris politikáját leíró Taylor-szabályokat becslünk. A becslést több kockázati mérőszámmal is elvégeztük több, különféle Taylor-szabályt használva. Az érzékenységvizsgálatban az inflációhoz és a kibocsátási réshez is alkalmaztunk más, az alapspecifikációban szereplőtől eltérő mérőszámokat. Eredményeink szerint a Magyar Nemzeti Bank kamatdöntései jól leírhatók egy rugalmas, inflációs célkövető rezsimmel: a Taylor-szabályban szignifikáns szerepe van az inflációs céltól való eltérésének és - a szabályok egy része esetén - a kibocsátási résnek. Emellett a döntéshozók figyelembe vették az országkockázatot is, annak növekedésére a kamat emelésével válaszoltak. Az országkockázat Taylor-szabályba történő beillesztése a megfelelő kockázati mérőszám kiválasztása esetén jelentős mértékben képes javítani a Taylor-szabály illeszkedését. _____ The paper investigates the degree to which Hungarian monetary policy has considered country risk in its decisions and if so, how. The answer was sought through the commonest method of analysing a countrys monetary policy: Taylor rules for describing it. The estimation of the rule was prepared using several risk indicators and applying various types of Taylor rules. As a sensitivity analysis, other indicators of inflation and output gap were employed than in the base rule. This showed that the interest-rate decisions of the National Bank of Hungary can be well described by a flexible inflation targeting regime: in the Taylor rules, deviation of inflation from its target has a significant role and the output gap is also significant in one part of the rules. The decision-makers also considered country risk and responded to an increase in it by raising interest rates. Insertion of country risk into the Taylor rule could improve the models fit to an important degree when choosing an appropriate risk measure.

„A gyári üzemnek évszázados fejlődésből leszűrt breviáriuma” A magyar vezetés- és szervezéstudományi gondolkodás kezdetei: Vitasorozat a Taylor-rendszerről 1912-ben

Magyarország társadalmi és gazdasági változásai kapcsán gyakran merül fel a kérdés, hogy egyes új fejlemények vajon a nemzetközi folyamatok hatására bontakoztak-e ki, és ha igen, azokkal egyidejűleg vagy bizonyos idővel később került-e sor rájuk? Egyidejűség vagy fáziskésés? Külföldi minták szolgai másolása vagy hazai viszonyokra történő alkalmazása, esetleg egy speciális „harmadik út” megfogalmazása volt-e jellemző az időszerűvé vált problémákra adott „magyar válaszra”?

Rapid responses of vegetation to hydrological changes in Taylor Slough, Everglades National Park, Florida, USA

We analyzed the dynamics of freshwater marsh vegetation of Taylor Slough in eastern Everglades National Park for the 1979 to 2003 period, focusing on cover of individual plant species and on cover and composition of marsh communities in areas potentially influenced by a canal pump station (‘‘S332’’) and its successor station (‘‘S332D’’). Vegetation change analysis incorporated the hydrologic record at these sites for three intervals: pre-S332 (1961–1980), S332 (1980–1999), post-S332 (1999–2002). During S332 and post-S332 intervals, water level in Taylor Slough was affected by operations of S332 and S332D. To relate vegetation change to plot-level hydrological conditions in Taylor Slough, we developed a weighted averaging regression and calibration model (WA) using data from the marl prairies of Everglades National Park and Big Cypress National Preserve. We examined vegetation pattern along five transects. Transects 1–3 were established in 1979 south of the water delivery structures, and were influenced by their operations. Transects 4 and 5 were established in 1997, the latter west of these structures and possibly under their influence. Transect 4 was established in the northern drainage basin of Taylor Slough, beyond the likely zones of influence of S332 and S332D. The composition of all three southern transects changed similarly after 1979. Where muhly grass (Muhlenbergia capillaris var. filipes) was once dominant, sawgrass (Cladium jamaicense), replaced it, while where sawgrass initially predominated, hydric species such as spikerush (Eleocharis cellulosa Torr.) overtook it. Most of the changes in species dominance in Transects 1–3 occurred after 1992, were mostly in place by 1995–1996, and continued through 1999, indicating how rapidly vegetation in seasonal Everglades marshes can respond to hydrological modifications. During the post-S332 period, these long-term trends began reversing. In the two northern transects, total cover and dominance of both muhly grass and sawgrass increased from 1997 to 2003. Thus, during the 1990’s, vegetation composition south of S332 became more like that of long hydroperiod marshes, but afterward it partially returned to its 1979 condition, i.e., a community characteristic of less prolonged flooding. In contrast, the vegetation change along the two northern transects since 1997 showed little relationship to hydrologic status.

View of the TS/Ph-2 autosampler site from road, Taylor Slough

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

Snake at TS/Ph-1b, Taylor Slough

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

Xavier Zapata (FIU graduate student) collecting a groundwater sample, Taylor Slough

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.