Modeling of turbulent precipitation: A transported population balance‐PDF method

Veroli, Giovanni Y. Di; Rigopoulos, Stelios

doi:10.1002/aic.12064

Cited by 29 publications

(17 citation statements)

References 54 publications

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“…Here, the semi-discrete system consists of scalar transport equations for so-called discrete number densities. Since these transport equations are formally identical to those of the reactive scalars which characterize the fluid phase, the PBE can be naturally incorporated into models for the laminar or turbulent carrier flow [8,9,34,35].…”

Section: Introductionmentioning

confidence: 99%

An explicit adaptive grid approach for the numerical solution of the population balance equation

Sewerin

Rigopoulos

2017

Chemical Engineering Science

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Section: Introductionmentioning

confidence: 99%

An explicit adaptive grid approach for the numerical solution of the population balance equation

Sewerin

Rigopoulos

2017

Chemical Engineering Science

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“…Campos and Lage [9] pointed out that, strictly, DPBs are not function approximation methods and that the particle size distribution hence converges slower than its moments as the number of bins is increased. This is at variance with direct discretization approaches such as finite volume [72] or finite element methods [12,13]. Here, however, both the particle property distribution and all of its moments are affected by a discretization error [63].…”

Section: Introductionmentioning

confidence: 82%

“…The main advantage of the so-called PBE-PDF method is that it allows for the prediction of the particle property distribution and is able to accommodate any fluid or particle phase kinetics without approximation. This was first demonstrated by Di Veroli and Rigopoulos [11,12,13] who considered the RANS turbulence model and validated PBE-PDF predictions for a finite element discretization of the particle size distribution in two experimental test cases. Additionally, they were able to show that a numerical solution of the joint scalar-discrete number density pdf transport equation is computationally viable and can be achieved in reasonable computing times by using a Lagrangian stochastic particle solver [53].…”

Section: Introductionmentioning

confidence: 99%

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An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

Sewerin

Rigopoulos

2017

Physics of Fluids

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Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact.In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported PDF approach for fluid phase scalars by the particle number density and obtain a modelled evolution equation for the filtered probability density function (PDF) associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost.As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model, but also indicates the computational efficiency of the numerical solution scheme.

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“…The main advantages of the transported PBE-PDF method are that: a) it resolves the closure problem of precipitation and, more generally, of turbulent reactive flows with particles formation, b) it allows for kinetics of arbitrary complexity (such as size-dependent growth and aggregation) to be incorporated without the need for approximations, and c) it directly computes the entire particle size distribution. On the other hand the approach involves the transport of a larger number of scalars, but application to turbulent precipitation [45] has reported reasonable times in multi-core desktop PCs. The approach would be prove useful in cases where the timescales associated with transport, mixing, and particle formation are of similar orders of magnitude, thereby not permitting simplifications of the problem based on timescale separation (such as the neglect of fluctuations or conserved scalar approaches).…”

Section: The Closure Problem For Particle Formationmentioning

confidence: 99%

Population balance modelling of polydispersed particles in reactive flows

Rigopoulos

2010

Progress in Energy and Combustion Science

133

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Polydispersed particles in reactive flows is a wide subject area encompassing a range of dispersed flows with particles, droplets or bubbles that are created, transported and possibly interact within a reactive flow environment -typical examples include soot formation, aerosols, precipitation and spray combustion. One way to treat such problems is to employ as a starting point the Newtonian equations of motion written in a Lagrangian framework for each individual particle and either solve them directly or derive probabilistic equations for the particle positions (in the case of turbulent flow). Another way is inherently statistical and begins by postulating a distribution of particles over the distributed properties, as well as space and time, the transport equation for this distribution being the core of this approach. This transport equation, usually referred to as population balance equation (PBE) or general dynamic equation (GDE), was initially developed and investigated mainly in the context of spatially homogeneous systems. In the recent years, a growth of research activity has seen this approach being applied to a variety of flow problems such as sooting flames and turbulent precipitation, but significant issues regarding its appropriate coupling with CFD pertain, especially in the case of turbulent flow. The objective of this review is to examine this body of research from a unified perspective, the potential and limits of the PBE approach to flow problems, its links with Lagrangian and multifluid approaches and the numerical methods employed for its solution. Particular emphasis is given to turbulent flows, where the extension of the PBE approach is met with challenging issues. Finally, applications including reactive precipitation, soot formation, nanoparticle synthesis, sprays, bubbles and coal burning are being reviewed from the PBE perspective. It is shown that popualtion balance methods have been applied to these fields in varying degrees of detail, and future prospects are discussed.

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Modeling of turbulent precipitation: A transported population balance‐PDF method

Cited by 29 publications

References 54 publications

An explicit adaptive grid approach for the numerical solution of the population balance equation

An explicit adaptive grid approach for the numerical solution of the population balance equation

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

Population balance modelling of polydispersed particles in reactive flows

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