PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,

The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to an hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasised. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.Comment: 23 pages, 10 figure

Large Eddy Simulation of Particle Agglomeration with Shear Breakup in Turbulent Channel Flow

A systematic technique is developed for studying particle dynamics as induced by a turbulent liquid flow, in which transport, agglomeration, and breakup are considered. An Eulerian description of the carrier phase obtained using large eddy simulation is adopted and fully coupled to a Lagrangian definition of the particle phase using a pointwise discrete particle simulation. An efficient hard-sphere interaction model with deterministic collision detection enhanced with an energy-balance agglomeration model was implemented in an existing computational fluid dynamic code for turbulent multiphase flow. The breakup model adopted allows instantaneous breakup to occur once the transmitted hydrodynamic stress within an agglomerate exceeds a critical value, characterised by a fractal dimension and the size of the agglomerate. The results from the developed technique support the conclusion that the local turbulence kinetic energy, its dissipation rate, and the agglomerate fractal dimension control the kinetics of the agglomeration and de-agglomeration processes, and as well as defining with time the morphology of the particles and their resultant transport. Overall, the results are credible and consistent with the expected physical behavior and with known theories

Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: Simulation by coupling Eulerian, Lagrangian and 3D random walks models

[EN] Two phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the carrier fluid that are seen by the bubbles due to turbulence fluctuations. Also we have included in the model the deformation that suffers the bubble when it touches the wall and it is compressed by the forces that pushes it toward the wall, provoking that the bubble rebound like a ball.The authors of this paper are indebted to the National Plan of I+D by the support of the coordinated projects REMOD-ERN ENE2010-21368-C02-01/CON and ENE2010-21368-C02-02/CON to perform the experiments.Muñoz-Cobo, JL.; Chiva, S.; Ali Abdelaziz Essa, M.; Mendez, S. (2012). Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: Simulation by coupling Eulerian, Lagrangian and 3D random walks models. Archives of Thermodynamics. 33(1):3-39. https://doi.org/10.2478/v10173-012-0001-4S33933

Mapping Genetic Diversity of Cherimoya (Annona cherimola Mill.): Application of Spatial Analysis for Conservation and Use of Plant Genetic Resources

There is a growing call for inventories that evaluate geographic patterns in diversity of plant genetic resources maintained on farm and in species' natural populations in order to enhance their use and conservation. Such evaluations are relevant for useful tropical and subtropical tree species, as many of these species are still undomesticated, or in incipient stages of domestication and local populations can offer yet-unknown traits of high value to further domestication. For many outcrossing species, such as most trees, inbreeding depression can be an issue, and genetic diversity is important to sustain local production. Diversity is also crucial for species to adapt to environmental changes. This paper explores the possibilities of incorporating molecular marker data into Geographic Information Systems (GIS) to allow visualization and better understanding of spatial patterns of genetic diversity as a key input to optimize conservation and use of plant genetic resources, based on a case study of cherimoya (Annona cherimola Mill.), a Neotropical fruit tree species. We present spatial analyses to (1) improve the understanding of spatial distribution of genetic diversity of cherimoya natural stands and cultivated trees in Ecuador, Bolivia and Peru based on microsatellite molecular markers (SSRs); and (2) formulate optimal conservation strategies by revealing priority areas for in situ conservation, and identifying existing diversity gaps in ex situ collections. We found high levels of allelic richness, locally common alleles and expected heterozygosity in cherimoya's putative centre of origin, southern Ecuador and northern Peru, whereas levels of diversity in southern Peru and especially in Bolivia were significantly lower. The application of GIS on a large microsatellite dataset allows a more detailed prioritization of areas for in situ conservation and targeted collection across the Andean distribution range of cherimoya than previous studies could do, i.e. at province and department level in Ecuador and Peru, respectively

Computation of plane turbulent flow using Probability Density Function method

Application of the PFD method to turbulence modelling is surveyed. Important parts of the algorithm and of variance reduction techniques used therein are described. The computation results for a free-shear flow (mixing layer) and a wall-bounded flow in simple geometry (channel flow) are reported and perspectives for further development of the method are suggested.Omówiono zastosowanie metody funkcji gęstości prawdopodobieństwa (PDF) do modelowania turbulencji, wraz z przykładami własnych obliczeń dla swobodnego przepływu ścinającego (strefa mieszania) i przepływu w prostej geometrii w obecności ścianek (kanał płaski). Wyszczególniono elementy algorytmu metody oraz sposoby redukcji szumu statystycznego uzyskiwanego rozwiązania. Omówiono perspektywy dalszego rozwoju metody PFD

On general-purpose turbulence models in CFD

The computational fluid dynamics (CFD) tools for various flow problems have become widespread nowadays, yet their use still needs attention and care. In particular, turbulence models are often a crucial part of flow computations undertaken with various software packages, either commercial, open-source or in-house. In the paper, an overview of available model categories is provided, together with some discussion of their advantages or drawbacks with respect to flow cases of interest

Wprowadzenie równania kinetycznego dla cząstek w turbulentnym przepływie dwufazowym

An alternative way to obtain the kinetic equation for dispersed particles in turbulent flows is presented. The method uses some tools developed within the theory of the stochastic differential equations. They are presented first in an outline, including the cumulant expansion of linear stochastic equations as well as the approach to non-linear equations. Then, the general method is applied to the equation of motion of small particles in turbulent flows. The governing kinetic equation for particles is derived; it involves the correlations of the fluctuating fluid velocity along the particle trajectories.W pracy przedstawiono alternatywny sposób wyprowadzenia równania kinetycznego dla cząstek w turbulentnym przepływie dwufazowym. Wykorzystano metody rozwinięte w ramach teorii stochastycznych równań różniczkowych. Przedstawiono je w zarysie, łącznie z rozwinięciem liniowych i nieliniowych równań stochastycznych w szereg półniezmienników (kumulantów). Następnie, to ogólne podejście zastosowano do równania ruchu małych cząstek w przepływie turbulentnym i wyprowadzono odpowiadające mu równanie kinetyczne. Zawiera ono korelacje fluktuacji prędkości płynu wzdłuż trajektorii cząstek