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Numerical Methods For The Simulation Of A Coalescence-driven Droplet Size Distribution

R. Bordás, V. John, E. Schmeyer, D. Thévenin
Published 2013 · Mathematics

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The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.
This paper references
10.1515/zpch-1918-9209
Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen
M. Smoluchowski (1918)
10.1038/1811298a0
Cloud Physics
J. Atkinson (1958)
10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS
J. Smagorinsky (1963)
10.1016/0009-2509(64)85047-8
Some problems in particle technology: A statistical mechanical formulation
H. M. Hulburt (1964)
Otto von Guericke
F. Krafft (1978)
10.1016/0021-9991(79)90051-2
Fully multidimensional flux-corrected transport algorithms for fluids
S. Zalesak (1979)
Fully multi-dimensional flux corrected transport algorithms for fluid flow
S. T. Zalesak (1979)
10.1175/1520-0469(1980)037<2486:ADMMWA>2.0.CO;2
A Detailed Microphysical Model Within a Two-Dimensional Dynamic Framework: Model Description and Preliminary Results
W. Hall (1980)
10.1038/284088b0
Microphysics of Clouds and Precipitation
H. Pruppacher (1980)
10.1016/0045-7825(83)90122-6
The group finite element formulation
C. Fletcher (1983)
10.1016/0021-9991(89)90222-2
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu (1989)
10.1007/978-3-0348-8629-1_3
Scalar Conservation Laws
R. LeVeque (1992)
10.1002/CITE.330671125
Crystallization Technology Handbook. A. MERSMANN (HRSG.) MARCEL DEKKER Inc., New York, 1995. 691 S., zahlr. Abb. und Tab., geb., $ 195,00
H.-P. Wirges (1995)
10.1080/02786829708965471
Description of Aerosol Dynamics by the Quadrature Method of Moments
R. Mcgraw (1997)
Population Balances: Theory and Applications to Particulate Systems in Engineering
D. Ramkrishna (2000)
10.1002/FLD.195
Higher‐order finite element discretizations in a benchmark problem for incompressible flows
V. John (2001)
10.1201/9780203908280
Crystallization Technology Handbook
A. Mersmann (2001)
10.1177/095441000121500302
Incompressible flow and the finite element method
J. Szmelter (2001)
10.1016/b978-0-7506-7012-8.x5000-9
Handbook of Industrial Crystallization
A. Myerson (2002)
10.1016/B978-075067012-8/50006-9
Analysis and measurement of crystallization utilizing the population balance
K. Berglund (2002)
10.1002/FLD.377
Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier–Stokes equations
V. John (2002)
10.1146/ANNUREV.FLUID.35.101101.161125
PARTICLE-TURBULENCE INTERACTIONS IN ATMOSPHERIC CLOUDS
R. Shaw (2003)
10.1137/1.9780898718003
Iterative methods for sparse linear systems
Y. Saad (2003)
Iterative Methods for Sparse Linear Systems
Y. Saad (2003)
10.1007/S00791-003-0120-1
MooNMD – a program package based on mapped finite element methods
V. John (2004)
Flux-corrected transport : principles, algorithms, and applications
D. Kuzʹmin (2005)
10.1137/030601533
A Finite Element Variational Multiscale Method for the Navier-Stokes Equations
V. John (2005)
10.1016/J.JAEROSCI.2004.07.009
Solution of population balance equations using the direct quadrature method of moments
D. Marchisio (2005)
10.1007/3-540-27206-2_6
Algebraic Flux Correction I. Scalar Conservation Laws
D. Kuzmin (2005)
Algebraic flux correction I
D. Kuzmin (2005)
10.1016/J.CMA.2005.10.006
A two-level variational multiscale method for convection-dominated convection-diffusion equations
V. John (2006)
10.1007/s00607-006-0174-2
On the Efficient Evaluation of Coalescence Integrals in Population Balance Models
W. Hackbusch (2006)
10.1175/2007JAS2406.1
Growth of Cloud Droplets by Turbulent Collision–Coalescence
Y. Xue (2006)
10.1016/J.CES.2007.02.041
Techniques for the reconstruction of a distribution from a finite number of its moments
V. John (2007)
10.1016/j.jcp.2006.11.016
A hybrid approach for simulating turbulent collisions of hydrodynamically-interacting particles
Orlando Ayala (2007)
10.1002/FLD.1461
Simulations of the turbulent channel flow at Reτ = 180 with projection-based finite element variational multiscale methods
V. John (2007)
10.1007/s00211-007-0077-y
Approximation of coalescence integrals in population balance models with local mass conservation
W. Hackbusch (2007)
10.1093/IMANUM/DRN047
Convolution of hp-functions on locally refined grids - extended version
W. Hackbusch (2007)
10.1007/s10444-005-9010-z
Finite element error analysis of a variational multiscale method for the Navier-Stokes equations
V. John (2008)
10.1002/FLD.1712
Variants of projection-based finite element variational multiscale methods for the simulation of turbulent flows
V. John (2008)
10.1007/978-3-642-00605-0_13
Finite element methods for time-dependent convection – diffusion – reaction equations with small diffusion
V. John (2008)
10.1021/CG070161F
L-Glutamic Acid Precipitation : Agglomeration Effects
C. Lindenberg (2008)
10.1016/J.CMA.2008.08.016
On Finite Element Methods for 3D Time-Dependent Convection-Diffusion-Reaction Equations with Small Diffusion
V. John (2008)
10.1175/2007JAS2358.1
Collisions of Cloud Droplets in a Turbulent Flow. Part V: Application of Detailed Tables of Turbulent Collision Rate Enhancement to Simulation of Droplet Spectra Evolution
M. Pinsky (2008)
10.1016/J.CES.2008.05.004
Simulations of Population Balance Systems with One Internal Coordinate using Finite Element Methods
V. John (2009)
10.1002/ASL.210
The role of air turbulence in warm rain initiation
L. Wang (2009)
10.1016/j.jcp.2008.12.011
Explicit and implicit FEM-FCT algorithms with flux linearization
D. Kuzmin (2009)
10.1016/j.jcp.2009.09.025
A variational multiscale method for turbulent flow simulation with adaptive large scale space
V. John (2010)
10.1016/J.CMA.2010.02.015
Analysis of a variational multiscale method for Large-Eddy simulation and its application to homogeneous isotropic turbulence
L. Röhe (2010)
10.1002/NME.2830
On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems
V. John (2010)
10.1016/j.cam.2009.06.005
Finite element LES and VMS methods on tetrahedral meshes
V. John (2010)
10.1016/J.CMA.2009.01.010
Numerical Studies of Finite Element Variational Multiscale Methods for Turbulent Flow Simulations
V. John (2010)
10.1016/J.CES.2010.01.007
Reconstruction of a distribution from a finite number of moments with an adaptive spline-based algorithm
L. D. Souza (2010)
10.1063/1.3609275
Droplet collisions and interaction with the turbulent flow within a two-phase wind tunnel
R. Bordás (2011)
10.1002/FLD.2656
A numerical method for the simulation of an aggregation‐driven population balance system
W. Hackbusch (2012)
10.1016/J.ATMOSRES.2011.11.008
Simulation of pure sedimentation of raindrops using quadrature method of moments
A. Mukhopadhyay (2012)
10.1016/J.COMPFLUID.2012.05.003
Measurement and simulation of a droplet population in a turbulent flow field
R. Bordás (2012)
10.1007/978-94-007-4038-9_6
Algebraic Flux Correction II
D. Kuzmin (2012)
10.1016/j.jcp.2011.10.025
On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations
V. John (2012)



This paper is referenced by
10.1007/978-3-030-45168-4_14
Numerical Methods for Coupled Population Balance Systems Applied to the Dynamical Simulation of Crystallization Processes
Robin Ahrens (2020)
10.1007/978-3-030-45168-4
Dynamic Flowsheet Simulation of Solids Processes
Stefan Heinrich Editor (2020)
10.1016/J.COMPCHEMENG.2019.01.012
Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach
C. Bartsch (2019)
10.1002/aic.16810
Time‐dependent density functional study for nanodroplet coalescence
Yapeng Niu (2019)
10.1155/2018/1579431
The Asymptotic Behavior of Particle Size Distribution Undergoing Brownian Coagulation Based on the Spline-Based Method and TEMOM Model
Q. He (2018)
10.1007/S40324-018-0160-6
A unified analysis of algebraic flux correction schemes for convection–diffusion equations
G. Barrenechea (2018)
10.1016/j.camwa.2016.12.020
ParMooN - A modernized program package based on mapped finite elements
Ulrich Wilbrandt (2017)
10.1016/J.CES.2017.03.062
Simulating separation of a multiphase liquid-liquid system in a horizontal settler by CFD
A. Misra (2017)
10.1137/15M1018216
Analysis of Algebraic Flux Correction Schemes
G. Barrenechea (2016)
10.1016/j.compchemeng.2015.09.008
Reconstruction of a distribution from a finite number of its moments: A comparative study in the case of depolymerization process
Noureddine Lebaz (2016)
10.1016/j.compchemeng.2015.01.010
A comparative study of a direct discretization and an operator-splitting solver for population balance systems
Felix Anker (2015)
10.1007/S11831-015-9161-0
A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows
N. Ahmed (2015)
10.1021/CG501092K
Coupled Computational Fluid Dynamics–Discrete Element Method Simulations of a Pilot-Scale Batch Crystallizer
B. A. Ali (2015)
Modélisation de l’hydrolyse enzymatique de substrats lignocellulosiques par bilan de population
Noureddine Lebaz (2015)
10.1016/J.CES.2013.11.029
Direct discretizations of bi-variate population balance systems with finite difference schemes of different order
V. John (2014)
10.1127/0941-2948/2014/0570
Numerical simulations and measurements of a droplet size distribution in a turbulent vortex street
E. Schmeyer (2014)
Numerische Verfahren zur Simulation von Mehrphasenströmungen mittels Populationsbilanzen
E. Schmeyer (2014)
Aggregation Dynamics: Numerical Approximations, Inverse Problems, and Generalized Sensitivity
Dustin D. Keck (2014)
10.15407/FZ60.04.030
[The changes of processes of free radical oxidation of lipids and proteins, antioxidant defence in rats with hypofunction of the thyroid gland in conditions of iodine and copper deficiency].
Voronych-Semchenko Nm (2014)
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