Drag coefficient prediction for non-spherical particles in dense gas–solid two-phase flow using artificial neural network

Abstract Artificial neural network (ANN) was adopted to predict and analyze the relationship of drag coefficient, Reynolds number, and sphericity for non-spherical particles in dense gas–solid two-phase flow. We first employed Back Propagation Neural Network (BPNN) and Radial Basis Function Neural Network (RBFNN) to predict drag coefficients based on experimental results (Pettyjohn, 1948; Yow et al., 2005). Comparisons between simulation and experimental results indicate that RBFNN efficiently predicts the drag coefficients with as high precision as BPNN. Furthermore, we made predictions and analyses of drag coefficients under different sphericities employing Radial basis function neural network. Results reveal that artificial neural network is applicable in predicting and investigating drag coefficient in gas–solid non-spherical particulate systems. Based on the predicted results of drag coefficients, we conducted a curve fitting of drag coefficient, Reynolds number, and particle sphericity, obtaining a correlation on drag coefficient. Incorporating the drag coefficient correlation with Syamlal-O'Brien and Gidaspow-blend model, simulation on gas–solid two-phase flow by Eulerian–Eulerian model was carried out from fixed beds to bubbling fluidized beds. Simulation pressure drop are compared with experimental results obtaining a good agreement with each other, which indicates that the drag force of non-spherical particles in a gas–solid system could be predicted reasonably by an artificial neural network method. This work provides a reference for predicting drag coefficients of particles with complex shape in gas–solid two-phase system.

[1]  J. Padding,et al.  Nonspherical particles in a pseudo‐2D fluidized bed: Experimental study , 2018, AIChE journal. American Institute of Chemical Engineers.

[2]  C. Bonadonna,et al.  Dedicated vertical wind tunnel for the study of sedimentation of non-spherical particles. , 2013, The Review of scientific instruments.

[3]  Jam Hans Kuipers,et al.  Direct numerical simulation of fluid flow accompanied by coupled mass and heat transfer in dense fluid-particle systems , 2014 .

[4]  Daniel Graupe,et al.  Principles of Artificial Neural Networks , 2018, Advanced Series in Circuits and Systems.

[5]  Efstathios E. Michaelides,et al.  Drag coefficients of irregularly shaped particles , 2004 .

[6]  T. Heindel,et al.  Bed height and material density effects on fluidized bed hydrodynamics , 2011 .

[7]  F. Dioguardi,et al.  A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results , 2015 .

[8]  C. Bonadonna,et al.  On the drag of freely falling non-spherical particles , 2016, 1810.08787.

[9]  Jam Hans Kuipers,et al.  Review of direct numerical simulation of fluid–particle mass, momentum and heat transfer in dense gas–solid flows , 2014 .

[10]  Junwu Wang,et al.  Eulerian–Eulerian simulation of irregular particles in dense gas–solid fluidized beds , 2015 .

[11]  Subana Shanmuganathan,et al.  Artificial Neural Network Modelling , 2016 .

[12]  S. Das,et al.  Non-spherical solid-non-Newtonian liquid fluidization and ANN modelling: Minimum fluidization velocity , 2018 .

[13]  Ivan Nunes da Silva,et al.  Artificial Neural Networks , 2017 .

[14]  Fariborz Taghipour,et al.  CFD Modeling of the Hydrodynamics and Reaction Kinetics of FCC Fluidized-Bed Reactors , 2005 .

[15]  M. Zastawny,et al.  Derivation of drag and lift force and torque coefficients for non-spherical particles in flows , 2012 .

[16]  J. F. Richardson,et al.  The sedimentation of a suspension of uniform spheres under conditions of viscous flow , 1954 .

[17]  S. Ergun Fluid flow through packed columns , 1952 .

[18]  Raymond Lau,et al.  Modeling the change in particle size distribution in a gas-solid fluidized bed due to particle attrition using a hybrid artificial neural network-genetic algorithm approach , 2016 .

[19]  D. Gidaspow,et al.  Hydrodynamics of binary fluidization in a riser : CFD simulation using two granular temperatures , 2003 .

[20]  C. Wen Mechanics of Fluidization , 1966 .

[21]  Y. Chen,et al.  A drag force correlation for approximately cubic particles constructed from identical spheres , 2015 .

[22]  A. Yu,et al.  Micromechanical analysis of flow behaviour of fine ellipsoids in gas fluidization , 2017 .

[23]  N. K. Sinha,et al.  Drag on non-spherical particles: an evaluation of available methods , 1999 .

[24]  Kin Keung Lai,et al.  Foreign-Exchange-Rate Forecasting with Artificial Neural Networks , 2007 .

[25]  G. Lu,et al.  Discrete element models for non-spherical particle systems: From theoretical developments to applications , 2015 .

[26]  Lasse Rosendahl,et al.  On the motion of non-spherical particles at high Reynolds number , 2010 .

[27]  Sze-Foo Chien,et al.  Settling Velocity of Irregularly Shaped Particles , 1994 .

[28]  Gary H. Ganser,et al.  A rational approach to drag prediction of spherical and nonspherical particles , 1993 .

[29]  O. Levenspiel,et al.  Drag coefficient and terminal velocity of spherical and nonspherical particles , 1989 .

[30]  Andreas Hölzer,et al.  Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles , 2009 .

[31]  P. Jalali,et al.  Characterization method of average gas–solid drag for regular and irregular particle groups , 2014 .

[32]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[33]  Dimitri Gidaspow,et al.  Fluidization in Two-Dimensional Beds with a Jet. 2. Hydrodynamic Modeling , 1983 .

[34]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[35]  J. Bellan,et al.  Modeling and simulation of bubbling fluidized beds containing particle mixtures , 2000 .

[36]  D. Gidaspow Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions , 1994 .

[37]  J. Kuipers,et al.  A New Drag Correlation from Fully Resolved Simulations of Flow Past Monodisperse Static Arrays of Spheres , 2015 .

[38]  Václav Veselý,et al.  Influence of Particle Shape on the Drag Coefficient for Isometric Particles , 1994 .

[39]  Jam Hans Kuipers,et al.  Two-fluid modeling of three-dimensional cylindrical gas–solid fluidized beds using the kinetic theory of granular flow , 2013 .

[40]  P. Cleary,et al.  The influence of particle shape on flow modes in pneumatic conveying , 2011 .

[41]  P. Cleary,et al.  Dynamics of gas–solid fluidised beds with non-spherical particle geometry , 2010 .

[42]  K. Vollmari,et al.  Experimental and numerical study of fluidization and pressure drop of spherical and non-spherical particles in a model scale fluidized bed , 2016 .

[43]  Agba D. Salman,et al.  Drag correlations for particles of regular shape , 2005 .

[44]  Prabhata K. Swamee,et al.  Closure of discussion on Drag coefficient and fall velocity of nonspherical particles , 1991 .

[45]  F. Taghipour,et al.  Experimental and computational study of gas¿solid fluidized bed hydrodynamics , 2005 .

[46]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[47]  K. Vollmari,et al.  Flow-regime transitions in fluidized beds of non-spherical particles , 2016 .

[48]  Xianzhi Song,et al.  A new model for predicting drag coefficient and settling velocity of spherical and non-spherical particle in Newtonian fluid , 2017 .