On the solution of population balance equations by discretization—III. Nucleation, growth and aggregation of particles

Kumar, Sanjeev; Ramkrishna, Doraiswami

doi:10.1016/s0009-2509(97)00307-2

Cited by 333 publications

(276 citation statements)

References 12 publications

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“…(3)) describing the evolution of PSD is solved in PrecipiCalc with the characteristic methods [16], and an adaptive discretization framework to provide accurate and efficient computation. To provide efficiency, the thermodynamics/diffusivity quantities are not calculated at every timestep, and are done only when the departure of current temperature and matrix composition exceeds certain limits from the state where expansion is performed.…”

Section: Numerical Schemesmentioning

confidence: 99%

Computer Simulations for the Prediction of Microstructure/Property Variation in Aeroturbine Disks

Jou¹,

Voorhees²,

Olson³

2004

Superalloys 2004 (Tenth International Symposium)

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In support of a new methodology of accelerated development and qualification of new materials, the PrecipiCalc TM software has been developed as an efficient, high-fidelity 3D multiphase precipitation simulator grounded in computational thermodynamics and multicomponent diffusional nucleation and growth models incorporating interfacial dissipations. With extensive validation under a major federally sponsored program, the software has been successfully applied to the accurate and rapid simulation of multiscale (from nm to µm), multimodal γ microstructure development in IN100 Ni-based aeroturbine disk alloys under complex commercial heattreatment processing. Integration of PrecipiCalc with FEM heat transfer simulation and a strength model has demonstrated accurate prediction of property variation for accelerated process optimization and probabilistic modeling of design minimum properties.

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Section: Numerical Schemesmentioning

confidence: 99%

Computer Simulations for the Prediction of Microstructure/Property Variation in Aeroturbine Disks

Jou¹,

Voorhees²,

Olson³

2004

Superalloys 2004 (Tenth International Symposium)

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show abstract

“…The kernels for aggregation, breakage, and nucleation, due to their complexity, are often described by semi-empirical models [107,108]. More recently the combination of molecular modelling with detailed experiments for the development of crystal nucleation mechanisms from molecular level has attracted much attention [15].…”

Section: Multi-dimensional and Morphological Population Balance Modelsmentioning

confidence: 99%

“…Therefore, various numerical algorithms have been developed for solving PB equations such as method of moment [114][115][116][117], method of characteristics [108,[118][119][120][121], Monte Carlo techniques [122,123], and discretization methods including finite element technique [119,124,125], cell average methods [107], hierarchical solution strategy based on multilevel discretization [126], method of classes [82,95], fixed and moving pivot method [127,128], and finite difference/volume methods [90,119,[129][130][131]. Table 1 summarises these numerical solution methods with the further reviews below.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

“…The main weakness of the method of moments is the moment closure conditions are violated for more complex systems. The method of characteristics [108,118] aims to solve the PB equations by finding curves in the L-t plane that reduce the equation to an ODE. While the method is highly efficient when the physics are simple, the approach does not generalize to complex physics.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

“…In the method of finite difference/volume discretisation, the PB equation is approximated by a finite difference scheme [90,127,[129][130][131]. Numerous discretisation methods for the PB equations with different orders of accuracy have been investigated and applied to various particulate systems (see for example [82,90,108,[129][130][131]). An alternative approach, high resolution finite volume method, was proposed [90,129,132] to provide high accuracy while avoiding the numerical diffusion (that is, smearing) and numerical dispersion (that is, nonphysical oscillations) associated with other finite difference and finite volume methods.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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Evaluation of the Chain Length Distribution in Free-Radical Polymerization, 1. Bulk Polymerization

Butté

Storti

Morbidelli³

2002

Macromol. Theory Simul.

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On the solution of population balance equations by discretization—III. Nucleation, growth and aggregation of particles

Cited by 333 publications

References 12 publications

Computer Simulations for the Prediction of Microstructure/Property Variation in Aeroturbine Disks

Computer Simulations for the Prediction of Microstructure/Property Variation in Aeroturbine Disks

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Evaluation of the Chain Length Distribution in Free-Radical Polymerization, 1. Bulk Polymerization

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