Simulations of population balance systems with one internal coordinate using finite element methods

John, Volker; Mitkova, Teodora; Roland, Michael; Sundmacher, Kai; Tobiska, Lutz; Voigt, Andreas

doi:10.1016/j.ces.2008.05.004

Cited by 60 publications

(45 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The remedy consists in the application of a stabilized discretization. Two approaches for stabilizing the reaction-and convection-dominated equations describing the chemical reaction were already studied in [16]. The first approach was the streamline-upwind Petrov-Galerkin (SUPG) method from [8].…”

Section: The Equations For the Chemical Reactionmentioning

confidence: 99%

“…The simulation of such equations has been studied meanwhile separately in [17,18]. In these studies, much better methods than the standard schemes used in [16] could be identified, see Section 3.2 for details. We will use one of these better methods in the numerical studies presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…The modeling assumptions are such that on the one hand some properties of the actual process are simplified. On the other hand, the arising coupled system of equations is still so complex that severe difficulties in the simulations, using some standard numerical methods, have been reported in [16]. For completeness of presentation, the modeling assumptions are repeated here:…”

Section: Introductionmentioning

confidence: 99%

“…Functionals of the distribution of particles, in particular at the outlet of the chemical device, are of primary interest in applications. There are only initial attempts to simulate the population balance system describing a precipitation process [5,16,19,20,30]. The present paper will study the example from [16].…”

Section: Introductionmentioning

confidence: 99%

“…A main difficulty of the simulations presented in [16] was the solution of the equations describing the chemical reaction. The simulation of such equations has been studied meanwhile separately in [17,18].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

John

Roland

2010

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Population balance systems are models for processes in nature and industry which lead to a coupled system of equations (Navier-Stokes equations, transport equations, . . .) where the equations are defined in domains with different dimensions. This paper will study the impact of using different schemes for solving the three-dimensional equation of a precipitation process in a two-dimensional flow domain. The numerical schemes for the three-dimensional equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs. It turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results. For a highly time-dependent flow field, the evolution of the median of the volume fraction differs considerably between first order and higher order schemes.

show abstract

Section: The Equations For the Chemical Reactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

John

Roland

2010

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

A numerical method for the simulation of an aggregation‐driven population balance system

Hackbusch

John

Khachatryan

et al. 2011

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

SUMMARY A population balance system that models the synthesis of urea is studied in this paper. The equations for the flow field, the mass and the energy balances are given in a three‐dimensional domain, while the equation for the particle size distribution is given in a four‐dimensional domain. This problem is convection‐dominated and aggregation‐driven. Both features require the application of appropriate numerical methods. This paper presents a numerical approach for simulating the population balance system, which is based on finite element schemes, a finite difference method and a modern method to evaluate convolutIon integrals that appear in the aggregation term. Two experiments are considered and the numerical results are compared with experimental data. Unknown parameters in the aggregation kernel have to be calibrated. For appropriately chosen parameters, good agreements are achieved of the experimental data and the numerical results computed with the proposed method. A detailed study of the computational results reveals the influence of different parts of the aggregation kernel. Copyright © 2011 John Wiley & Sons, Ltd.

show abstract

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Aland

Boden

Hahn³

et al. 2013

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYA pressure‐driven flow of elongated bullet‐shaped bubbles in a narrow channel is known as Taylor flow or bubble‐train flow. This process is of relevance in various applications of chemical engineering. In this paper, we describe a typical simplified experimental setting, with surface tension, density and viscosity as prescribed input parameters. We compare a sharp‐interface model based on a moving grid aligned with the bubble boundary (ALE coordinates) and a diffuse‐interface model where the bubble shape is implicitly given by a phase‐field function. Four independent implementations based on the two modeling approaches are introduced and described briefly. Besides the simulation of the bubble shapes, we compare some resulting quantities such as pressure difference and film widths within the implementations and to existing analytical and experimental results. The simulations were conducted in 2D and 3D (rotationally symmetric). Good accordance of the results indicate the applicability and the usability of all approaches. Differences between the models and their implementations are visible but in no contradiction to theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

Simulations of population balance systems with one internal coordinate using finite element methods

Cited by 60 publications

References 20 publications

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

A numerical method for the simulation of an aggregation‐driven population balance system

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Contact Info

Product

Resources

About