Mixing, reaction, and precipitation: Interaction by exchange with mean micromixing models

Tavare, Narayan S.

doi:10.1002/aic.690411204

Cited by 23 publications

(13 citation statements)

References 32 publications

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“…The Lagrangian solver tracks the vaporous cavities: The trajectory equation, the momentum balance, and the bubble dynamic, typically the Rayleigh-Plesset equation [Eq. (32)] or one of its modified forms (e.g., Ref. 25), are solved for individual bubbles.…”

Section: Lagrangian-eulerian Formulationmentioning

confidence: 99%

“…(6), term 1 represents the change of rate and convection of the pdf; term 2 is the source term of the pdf; term 3 accounts for the turbulent transport of the pdf; and term 4 represents the micromixing in the composition space using the interaction by exchange with the mean model. 32 Note that the dimensions of this equation include time, space, and sample space, yielding 1 + 3 + N φ independent variables. Note the analogy with the Boltzmann equation where gas molecule velocity is introduced as an independent variable.…”

Section: Probability Density Function Approachmentioning

confidence: 99%

“…(10) represents the micromixing of the vapor mass fraction in the composition space using the interaction by exchange with the mean model. 32 Note that the dimensions of this equation include time, space, and sample space, yielding 1 + 3 + 1 = 5 independent variables.…”

Section: B Vapor Mass Fraction Fdfmentioning

confidence: 99%

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Stochastic-field cavitation model

2013

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Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

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Section: Lagrangian-eulerian Formulationmentioning

confidence: 99%

Section: Probability Density Function Approachmentioning

confidence: 99%

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Stochastic-field cavitation model

2013

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“…Previous work in this area has used empirical micro-or macro-mixing models [1,2] which do not in general reflect the details of the mixing and precipitation processes inside the vessel.…”

Section: Introductionmentioning

confidence: 99%

Simulation of reactive precipitation processes using the network-of-zones model

ZareNezhad

2007

Korean J. Chem. Eng.

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A 2-D network-of-zones model is extended and applied to a reactive precipitation process in batch mode. The simulations are performed for a network of size 2×(10×10) for an elementary reaction through the solution of 1400 ODEs. The complicated interactions between mixing efficacy and the system kinetics are systematically investigated. When the stirrer speed is very slow, the crystal size distribution (CSD) of the product in the precipitator is determined by the intensity of mixing. Conversely, at higher stirrer speed, the CSD is controlled by the system kinetics. More effective mixing leads to an increase in the number of crystals, a reduction of the average size and a narrower crystal size distribution. The extended network-of-zones model presented in this work can be used conveniently for integrating computational fluid dynamics and reactive precipitation processes.

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“…Tavare (1995) has already reported a significant impact on the MSMPR precipitator performance by feed conditions i.e. premixed and un-premixed feeds.…”

Section: Introductionmentioning

confidence: 99%