Due to increasing demands for faster and faster manufacturing of new complex materials, such as casting of particulate composites, the determination of pumping pressures needed for particle-laden fluids through channels is critical. In particular, the increase in viscosity as a function of the particle volume fraction can lead to system malfunction, due to an inability to deliver necessary pressures to pump the more viscous fluid through the system. This paper studies the pressure gradient needed to maintain a given flow rate, explicitly as a function of the volume fraction of particles present in the fluid. It is also crucial to control voids in the casted products, which can be traced to air-entrainment, spurious internal reactions, dewetting, etc., which can be traced to high Reynolds numbers. Accordingly, an expression for the resulting Reynolds number as a function of the particle volume fraction and flow rate is also developed. Numerical examples are provided to illustrate the practical use of the derived relations to characterize the necessary pumping pressures for process-driven, particle-laden fluid flows.
Issue Section:
Research Papers
Keywords:
Materials processing
References
1.
Wei
, C.
, and Dong
, J.
, 2014
, “Development and Modeling of Melt Electrohydrodynamic-Jet Printing of Phase-Change Inks for High-Resolution Additive Manufacturing
,” ASME J. Manuf. Sci. Eng.
, 136
(6
), p. 061010
.10.1115/1.40284832.
Onate
, E.
, Idelsohn
, S. R.
, Celigueta
, M. A.
, and Rossi
, R.
, 2008
, “Advances in the Particle Finite Element Method for the Analysis of Fluid-Multibody Interaction and Bed Erosion in Free Surface Flows
,” Comput. Methods Appl. Mech. Eng.
, 197
(19–20
), pp. 1777
–1800
.10.1016/j.cma.2007.06.0053.
Onate
, E.
, Celigueta
, M. A.
, Idelsohn
, S. R.
, Salazar
, F.
, and Suárez
, B.
, 2011
, “Possibilities of the Particle Finite Element Method for Fluid-Soil-Structure Interaction Problems
,” Comput. Mech.
, 48
(3
), pp. 307
–318
.10.1007/s00466-011-0617-24.
Rojek
, J.
, Labra
, C.
, Su
, O.
, and Onate
, E.
, 2012
, “Comparative Study of Different Discrete Element Models and Evaluation of Equivalent Micromechanical Parameters
,” Int. J. Solids Struct.
, 49
(13
), pp. 1497
–1517
.10.1016/j.ijsolstr.2012.02.0325.
Carbonell
, J. M.
, Onate
, E.
, and Suarez
, B.
, 2010
, “Modeling of Ground Excavation With the Particle Finite Element Method
,” J. Eng. Mech., ASCE
, 136
(4
), pp. 455
–463
.10.1061/(ASCE)EM.1943-7889.00000866.
Labra
, C.
, and Onate
, E.
, 2009
, “High-Density Sphere Packing for Discrete Element Method Simulations
,” Commun. Numer. Methods Eng.
, 25
(7
), pp. 837
–849
.10.1002/cnm.11937.
Leonardi
, A.
, Wittel
, F. K.
, Mendoza
, M.
, and Herrmann
, H. J.
, 2014
, “Coupled DEM-LBM Method for the Free-Surface Simulation of Heterogeneous Suspensions
,” Comput. Part. Mech.
, 1
(1
), pp. 3
–13
.10.1007/s40571-014-0001-z8.
Cante
, J.
, Davalos
, C.
, Hernandez
, J. A.
, Oliver
, J.
, Jonsen
, P.
, Gustafsson
, G.
, and Haggblad
, H. A.
, 2014
, “PFEM-Based Modeling of Industrial Granular Flows
,” Comput. Part. Mech.
, 1
(1
), pp. 47
–70
.10.1007/s40571-014-0004-99.
Rojek
, J.
, 2014
, “Discrete Element Thermomechanical Modeling of Rock Cutting With Valuation of Tool Wear
,” Comput. Part. Mech.
, 1
(1
), pp. 71
–84
.10.1007/s40571-014-0008-510.
Onate
, E.
, Celigueta
, M. A.
, Latorre
, S.
, Casas
, G.
, Rossi
, R.
, and Rojek
, J.
, 2014
, “Lagrangian Analysis of Multiscale Particulate Flows With the Particle Finite Element Method
,” Comput. Part. Mech.
, 1
(1
), pp. 85
–102
.10.1007/s40571-014-0012-911.
Bolintineanu
, D. S.
, Grest
, G. S.
, Lechman
, J. B.
, Pierce
, F.
, Plimpton
, S J.
, and Schunk
, P. R.
, 2014
, “Particle Dynamics Modeling Methods for Colloid Suspensions
,” Comput. Part. Mech.
, 1
(3
), pp. 321
–356
.10.1007/s40571-014-0007-612.
Avci
, B.
, and Wriggers
, P.
, 2012
, “A DEM-FEM Coupling Approach for the Direct Numerical Simulation of 3D particulate Flows
,” ASME J. Appl. Mech.
, 79
(1
), p. 010901
.10.1115/1.400509313.
Zohdi
, T. I.
, 2007
, “Computation of Strongly Coupled Multifield Interaction in Particle-Fluid Systems
,” Comput. Methods Appl. Mech. Eng.
, 196
(37
), pp. 3927
–3950
.10.1016/j.cma.2006.10.04014.
Zohdi
, T. I.
, 2014
, “Embedded Electromagnetically Sensitive Particle Motion in Functionalized Fluids
,” Comput. Part. Mech.
, 1
(1
), pp. 27
–45
.10.1007/s40571-014-0013-815.
Zohdi
, T. I.
, and Wriggers
, P.
, 2008
, Introduction to Computational Micromechanics
, Springer
, Berlin
10.1007/978-3-540-32360-0.16.
Hinze
, J. O.
, 1975
, Turbulence
, McGraw-Hill
, New York
.17.
Einstein
, A.
, 1906
, “A New Determination of Molecular Dimensions
,” Ann. Phys.
, 19
(4
), pp. 289
–306
.18.
Hashin
, Z.
, and Shtrikman
, S.
, 1962
, “On Some Variational Principles in Anisotropic and Nonhomogeneous Elasticity
,” J. Mech. Phys. Solids
, 10
(4
), pp. 335
–342
.10.1016/0022-5096(62)90004-219.
Hashin
, Z.
, and Shtrikman
, S.
, 1963
, “A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials
,” J. Mech. Phys. Solids
, 11
(2), pp. 127
–140
.10.1016/0022-5096(63)90060-720.
Hashin
, Z.
, 1983
, “Analysis of Composite Materials: A Survey
,” ASME J. Appl. Mech.
, 50
(3
), pp. 481
–505
.10.1115/1.316708121.
Torquato
, S.
, 2002
, Random Heterogeneous Materials: Microstructure and Macroscopic
Properties
, Springer
, New York
10.1007/978-1-4757-6355-3.22.
Hong
, Y.
, Zhou
, J. G.
, and Yao
, D.
, 2014
, “Porogen Templating Processes: An Overview
,” ASME J. Manuf. Sci. Eng.
, 136
(3
), p. 031013
.10.1115/1.402689923.
Kongsuwan
, P.
, Brandal
, G.
, and Yao
, Y. L.
, 2015
, “Laser Induced Porosity and Crystallinity Modification of a Bioactive Glass Coating on Titanium Substrates
,” ASME J. Manuf. Sci. Eng.
, 137
(3
), p. 031004
.10.1115/1.402956624.
Zohdi
, T. I.
, 2013
, “Numerical Simulation of Charged Particulate Cluster-Droplet Impact on Electrified Surfaces
,” J. Comput. Phys.
, 233
, pp. 509
–526
.10.1016/j.jcp.2012.09.01225.
Zohdi
, T. I.
, 2012
, Dynamics of Charged Particulate Systems. Modeling, Theory and Computation
, Springer
, Heidelberg
.26.
Zohdi
, T. I.
, 2004
, “A Computational Framework for Agglomeration in Thermo-Chemically Reacting Granular Flows
,” Proc. R. Soc.
, 460
(2052
), pp. 3421
–3445
.10.1098/rspa.2004.127727.
Zohdi
, T. I.
, 2005
, “A Simple Model for Shear Stress Mediated Lumen Reduction in Blood Vessels
,” Biomech. Model. Mechanobiol.
, 4
(1
), pp. 57
–61
.10.1007/s10237-004-0059-228.
Zohdi
, T. I.
, 2014
, “Mechanically-Driven Accumulation of Microscale Material at Coupled Solid-Fluid Interfaces in Biological Channels
,” Proc. R. Soc. Interface
, 11
(91
), p. 20130922
.29.
Zohdi
, T. I.
, Holzapfel
, G. A.
, and Berger
, S. A.
, 2004
, “A Phenomenological Model for Atherosclerotic Plaque Growth and Rupture
,” J. Theor. Biol.
, 227
(3
), pp. 437
–443
.10.1016/j.jtbi.2003.11.02530.
Maxwell
, J. C.
, 1867
, “On the Dynamical Theory of Gases
,” Philos. Trans. Soc. London
, 157
, pp. 49
–88
.10.1098/rstl.1867.000431.
Maxwell
, J. C.
, 1873
, A Treatise on Electricity and Magnetism
, 3rd ed., Clarendon Press
, Oxford, UK
.32.
Rayleigh
, J. W.
, 1892
, “On the Influence of Obstacles Arranged in Rectangular Order Upon Properties of a Medium
,” Philos. Mag.
32
, pp. 481
–491
.33.
Jikov
, V. V.
, Kozlov
, S. M.
, and Olenik
, O. A.
, 1994
, Homogenization of Differential Operators and Integral Functionals
, Springer
, Berlin
.34.
Mura
, T.
, 1993
, Micromechanics of Defects in Solids
, 2nd ed., Kluwer Academic Publishers
, Springer-Verlag, Berlin
.35.
Markov
, K. Z.
, 2000
, “Elementary Micromechanics of Heterogeneous Media
,” Heterogeneous Media: Micromechanics Modeling Methods and Simulations
, K. Z.
Markov
, and L.
Preziozi
, eds., Birkhauser
, Boston, MA
, pp. 1
–162
10.1007/978-1-4612-1332-1_1.36.
Ghosh
, S.
, 2011
, Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method
, CRC Press/Taylor & Francis
, Boca Raton, FL
10.1201/b10903.37.
Ghosh
, S.
, and Dimiduk
, D.
, 2011
, Computational Methods for Microstructure-Property Relations
, Springer
, New York
.38.
Abedian
, B.
, and Kachanov
, M.
, 2010
, “On the Effective Viscosity of Suspensions
,” Int. J. Eng. Sci.
, 48
(11
), pp. 962
–965
.10.1016/j.ijengsci.2010.08.01239.
Sevostianov
, I.
, and Kachanov
, M.
, 2012
, “Effective Properties of Heterogeneous Materials: Proper Application of the Non-Interaction and the “Dilute Limit” Approximations
,” Int. J. Eng. Sci.
, 58
, pp. 124
–128
.10.1016/j.ijengsci.2012.03.031
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