(336c) Multiphase Particle-in-Cell Coupled Population Balance Equation Method for Multiscale Computational Fluid Dynamics

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0cm;mso-para-margin-bottom:1.0gd;mso-para-margin-left:0cm;text-align:center;
line-height:150%">The Multiphase Particle-in-Cell coupled
Population Balance Equation (MPPIC) Method for CFD of Processes with
Micro-Sized Particulates

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0cm;mso-para-margin-bottom:1.0gd;mso-para-margin-left:0cm;text-align:center;
line-height:150%">Shin Hyuk
Kim^¢Ó, Richard
D. Braatz^¢Ô, and Jay H. Lee^¢Ó*

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0cm;mso-para-margin-bottom:1.0gd;mso-para-margin-left:0cm;text-align:center;
line-height:150%">^¢ÓDepartment of Chemical and
Biomolecular Engineering, Korea Advanced Institute of Science and Technology,
291 Daehak-Ro, Yuseong-Gu, Daejeon, 34141, Republic of Korea

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0cm;mso-para-margin-bottom:1.0gd;mso-para-margin-left:0cm;text-align:center;
line-height:150%">^¢Ô Massachusetts Institute of
Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

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0cm;mso-para-margin-bottom:1.0gd;mso-para-margin-left:0cm;text-align:center;
text-indent:5.0pt;mso-char-indent-count:.5;line-height:150%">(jayhlee@kaist.ac.kr^¢Ó*, braatz@mit.edu)

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mso-char-indent-count:.5;line-height:150%"> " arial>Many chemical processes, e.g., crystallizers, fluidized bed
reactors and polymerization reactors, involve micro-sized particulates.  The multiphase particulate flow exhibit complex
patterns that are not seen from gas and liquid fluids. In order to facilitate
the simulation of the multiphase particulate flow in the computational fluid
dynamics (CFD) setting, there exist several CFD solvers, which can be
categorized into the Euler-Eulerian and Euler-Lagrangian methods. The
Euler-Eulerian expresses the flows of all phases using the continuum governing
equations, but modeling the flow of particles of different types and sizes
greatly complicates the continuum formulation because it requires a separate
model for each type and size. The population balance equation (PBE) is one way
to reflect the particle size distribution in the Euler-Eulerian setting.
However, solving both the PBE and fluid dynamics simultaneously is costly because
it is expressed as a partial differential equation involving a total of five
variables: time, 3-dimensional space, and particle distribution. The
Euler-Lagrangian uses the Lagrangian description for the particulate phase and
the Euler description for the continuum phase. Using this approach, the
particles can have different sizes, shapes, densities, and velocities. However,
when the volume fraction of particles in the system is higher than 5%, the
frequency of particle collisions is unrealistically increased and accuracy is
drastically lowered¹. Also, expressing chemical reactions or mass transfer for
all the particles represented by the Lagrangian method and simulating particle
size changes at the micro-scale can require unrealistically high computational
cost.

12.0pt;margin-left:0cm;mso-para-margin-top:1.0gd;mso-para-margin-right:0cm;
mso-para-margin-bottom:1.0gd;mso-para-margin-left:0cm;line-height:150%">To overcome the limitations
of the conventional CFD solvers for such chemical engineering problems, this work
proposes the multiphase particle-in-cell (MPPIC) model² coupled the population
balance equation, which we refer to as MPPIC-PBE. Specifically, the current
state-of-the art involves the consideration of PBE within the Lagrangian frame
in an effort to combine with the particle distribution function used in MPPIC
in a practical manner. This allows for the preservation of mass and energy
between Eulerian and Lagrangian frames. The PBE in this procedure is directly
linked to each of the discrete parcels and retains all the original information
while maintaining the homogeneity. This characteristic makes the calculation of
the particle size distribution more efficient than in the PBE approach in the Euler-Eulerian
framework. For validation, a crystallizer³ is simulated by both the newly
developed method and the conventional method. The simulation result
demonstrates that the developed approach is more efficient and potentially more
accurate than the conventional method.

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lang=EN-US> style='mso-spacerun:yes'> ADDIN EN.REFLIST field-separator'> " mso-no-proof:yes>1. 1">       O'Rourke PJ. Collective drop effects on vaporizing liquid
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margin-left:36.0pt;margin-bottom:.0001pt;text-indent:-36.0pt;line-height:normal">2. " mso-no-proof:yes>       Andrews
MJ, O'Rourke PJ. The multiphase particle-in-cell (MP-PIC) method for dense
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normal">3. " mso-no-proof:yes>       da
Rosa CA, Braatz RD. Multiscale Modeling and Simulation of Macromixing,
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