New volume consistent approximation for binary breakage Population Balance Equation and its convergence analysis

被引:23
作者
Singh, Mehakpreet [1 ]
Matsoukas, Themis [2 ]
Albadarin, Ahmad B. [1 ]
Walker, Gavin [1 ]
机构
[1] Univ Limerick, Bernal Inst, Dept Chem Sci, Limerick V94 T9PX, Ireland
[2] Penn State Univ, Dept Chem Engn, 8H Thomas, State Coll, PA 16802 USA
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2019年 / 53卷 / 05期
关键词
Particles; binary breakage; population balance equation; finite volume scheme; nonuniform grids; SECTIONAL METHODS; FRAGMENTATION; DISCRETIZATION; COAGULATION; SCHEME; AGGREGATION; FORMULATION; PARAMETERS; DISCRETE; KINETICS;
D O I
10.1051/m2an/2019036
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This work is focused on developing a numerical approximation based on finite volume scheme to solve a binary breakage population balance equation (PBE). The mathematical convergence analysis of the proposed scheme is discussed in detail for different grids. The proposed scheme is mathematical simple and can be implemented easily on general grids. The numerical results and findings are validated against the existing scheme over different benchmark problems. All numerical predictions demonstrate that the proposed scheme is highly accurate and efficient as compared to the existing method. Moreover, the theoretical observations concerning order of convergence are verified with the numerical order of convergence which shows second order convergence irrespective of grid chosen for discretization. The proposed scheme will be the first ever numerical approximation for a binary breakage PBE free from that the particles are concentrated on the representative of the cell.
引用
收藏
页码:1695 / 1713
页数:19
相关论文
共 34 条
  • [11] Developing ANN-Kriging hybrid model based on process parameters for prediction of mean residence time distribution in twin-screw updates wet granulation
    Ismail, Hamza Y.
    Singh, Mehakpreet
    Darwish, Shaza
    Kuhs, Manuel
    Shirazian, Saeed
    Croker, Denise M.
    Khraisheh, Majeda
    Albadarin, Ahmad B.
    Walker, Gavin M.
    [J]. POWDER TECHNOLOGY, 2019, 343 : 568 - 577
  • [12] Two-compartment modeling and dynamics of top-sprayed fluidized bed granulator
    Kaur, Gurmeet
    Singh, Mehakpreet
    Matsoukas, Themis
    Kumar, Jitendra
    De Beer, Thomas
    Nopens, Ingmar
    [J]. APPLIED MATHEMATICAL MODELLING, 2019, 68 : 267 - 280
  • [13] Improved accuracy and convergence of discretized population balance for aggregation:: The cell average technique
    Kumar, J
    Peglow, M
    Warnecke, G
    Heinrich, S
    Mörl, L
    [J]. CHEMICAL ENGINEERING SCIENCE, 2006, 61 (10) : 3327 - 3342
  • [14] Convergence analysis of sectional methods for solving breakage population balance equations-I: the fixed pivot technique
    Kumar, Jitendra
    Warnecke, Gerald
    [J]. NUMERISCHE MATHEMATIK, 2008, 111 (01) : 81 - 108
  • [15] Convergence analysis of sectional methods for solving breakage population balance equations-II: the cell average technique
    Kumar, Jitendra
    Warnecke, Gerald
    [J]. NUMERISCHE MATHEMATIK, 2008, 110 (04) : 539 - 559
  • [16] DEVELOPMENT AND CONVERGENCE ANALYSIS OF A FINITE VOLUME SCHEME FOR SOLVING BREAKAGE EQUATION
    Kumar, Jitendra
    Saha, Jitraj
    Tsotsas, Evangelos
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (04) : 1672 - 1689
  • [17] MOMENT PRESERVING FINITE VOLUME SCHEMES FOR SOLVING POPULATION BALANCE EQUATIONS INCORPORATING AGGREGATION, BREAKAGE, GROWTH AND SOURCE TERMS
    Kumar, Rajesh
    Kumar, Jitendra
    Warnecke, Gerald
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (07) : 1235 - 1273
  • [18] On the solution of population balance equations by discretization .1. A fixed pivot technique
    Kumar, S
    Ramkrishna, D
    [J]. CHEMICAL ENGINEERING SCIENCE, 1996, 51 (08) : 1311 - 1332
  • [19] Simultaneous coagulation and break-up using constant-N Monte Carlo
    Lee, K
    Matsoukas, T
    [J]. POWDER TECHNOLOGY, 2000, 110 (1-2) : 82 - 89
  • [20] Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity
    Lee, Kok Foong
    Patterson, Robert I. A.
    Wagner, Wolfgang
    Kraft, Markus
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 303 : 1 - 18