A moment methodology for coagulation and breakage problems: Part 3—generalized daughter distribution functions

Diemer, R. Bertrum; Olson, J.H.

doi:10.1016/s0009-2509(02)00366-4

Cited by 109 publications

(103 citation statements)

References 16 publications

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“…This work has been recently reviewed by Frenklach [70]. Diemer and Olson [48], [46], [47], also presented a moment method and investigated the reconstruction of the distribution from the moments. Their studies were focussed on steady-state population balance formulations with coagulation and breakage.…”

Section: Moment-based Methodsmentioning

confidence: 99%

Population balance modelling of polydispersed particles in reactive flows

Rigopoulos

2010

Progress in Energy and Combustion Science

135

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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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Section: Moment-based Methodsmentioning

confidence: 99%

Population balance modelling of polydispersed particles in reactive flows

Rigopoulos

2010

Progress in Energy and Combustion Science

135

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“…This can be expressed in terms of the functionb i (k) , which for k = 0 represents the number of particles formed by a fragmentation event, and for k = 3 represents the volume of the original particle. An extensive discussion of the problems related to the fragment distribution function (or daughter distribution) can be found in [43], where a generalized daughter distribution function is proposed. The fragment distribution functions used in this work are reported in Table 3.…”

Section: Application Of Qmommentioning

confidence: 99%

“…Comparison between the QMOM prediction and the "exact" numerical solution is made in terms of the total particle number density (m 0 ) and the mean particle size (d 43 = m 4 /m 3 ). The QMOM performance has been studied with two nodes (tracking the first four moments, QMOM2), three nodes (tracking the first six moments, QMOM3), and four nodes (tracking the first eight moments, QMOM4) in the ten cases reported in Table 4.…”

Section: Effect Of the Number Of Nodes On The Global Error Functionmentioning

confidence: 99%

“…Marchisio et al / Journal of Colloid and Interface Science 258 (2003) [322][323][324][325][326][327][328][329][330][331][332][333][334]. Total particle number density (m 0 ) and mean crystal size evolution (d 43 ) obtained with the rigorous solution (line) and the QMOM3 approximation (circles) for case 3. In case 3, the QMOM performance is tested for the hydrodynamic aggregation kernel and exponential fragmentation kernel. Note that the breakage distribution function is again the one for symmetric fragments.…”

Section: Qmom3 Performancementioning

confidence: 99%

“…14. Total particle number density (m 0 ) and mean crystal size evolution (d 43 ) obtained with the rigorous solution (line) and the QMOM3 approximation (circles) for case 10. predicted whereas for intermediate times some substantial differences were found (see Fig. 14).…”

Section: Qmom3 Performancementioning

confidence: 99%

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