New discretization procedure for the agglomeration equation

Hill, Priscilla J.; Ng, Ka Ming

doi:10.1002/aic.690420313

Cited by 34 publications

(16 citation statements)

References 17 publications

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“…The method of classes, due to Marchal et al [145], treats the aggregation process as a set of chemical reactions. A number of works, such as Hill and Ng [93] have concentrated on fragmentation problems. The application of the finite element method to the PBE has its origin in the work of Gelbard and Seinfeld [80].…”

Section: Discretisation 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: Discretisation 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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“…Some can correctly predict a single property such as the total number of particles or the total particle mass (Gelbard and Seinfeld, 1980;Sastry and Gaschignard, 1981). Others can correctly predict two properties such as the total number and volume of particles simultaneously (Hounslow et al, 1988;Hounslow, 1990;Litster et al, 1995;Hill and Ng, 1996a;Kumar and Ramkrishna, 1996a,b). In particular, Hill and Ng (1996a) have developed a discretized agglomeration equation for a PSD with equal-size intervals or intervals with any geometric ratio larger than unity.…”

Section: Dissolutionmentioning

confidence: 99%

“…Others can correctly predict two properties such as the total number and volume of particles simultaneously (Hounslow et al, 1988;Hounslow, 1990;Litster et al, 1995;Hill and Ng, 1996a;Kumar and Ramkrishna, 1996a,b). In particular, Hill and Ng (1996a) have developed a discretized agglomeration equation for a PSD with equal-size intervals or intervals with any geometric ratio larger than unity. For example, for a geometric ratio 2 2 , the equation is…”

Section: Dissolutionmentioning

confidence: 99%

Simulation of solids processes accounting for particle‐size distribution

Hill

1997

AIChE Journal

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“…In most cases, one needs to resort to numerical solutions. One of the standard numerical techniques is to discretize the population balance equation using finite difference/element methods (see [4][5][6][7][8], and the references cited therein), but these methods suffer from extremely large computational requirements which cannot be accommodated by conventional computers. Sectional models offer a computationally less demanding solution by approximating the continuous size distribution by a finite number of sections within which the particle size distribution (PSD) function is assumed to be constant [9].…”

Section: Introductionmentioning

confidence: 99%

Robust Control of Particle Size Distribution in Aerosol Processes

Xiang

2010

INT J COMPUT COMMUN

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This paper deals with a comprehensive study on robust control of particle size distribution of fractal agglomerate in aerosol processes with simultaneous chemical reaction, nucleation, condensation and coagulation. Firstly, a general aerosol process is described by population balance and mass and energy balances, which describes the evolution of particle size distribution, continuous phase species and temperature of the aerosol system, respectively. A lognormal moment approximations of the population balance model is then presented. Then, the robust state feedback controller is designed for the aerosol process with some unknown uncertainties, the proposed controller is composed of an nominal control term and a robust control term so that it only ensures the stability of the closed-loop system, but also attenuates the effect of the unknown uncertainties on the system. A high-gain observer is adopted to estimate state variables required in the on-line implementation of the state feedback. Finally, the proposed robust controller is applied to an aerosol process for achieving an aerosol size distribution with desired geometric average particle diameter, the simulation results show the robustness properties of the controller with respect to parametric model uncertainty and unmodeled dynamics.

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New discretization procedure for the agglomeration equation

Cited by 34 publications

References 17 publications

Population balance modelling of polydispersed particles in reactive flows

Population balance modelling of polydispersed particles in reactive flows

Simulation of solids processes accounting for particle‐size distribution

Robust Control of Particle Size Distribution in Aerosol Processes

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