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MPPIC model implementation in
MFIX: frictional solid-stress model
Rahul Garg1,2
1: National Energy Technology Laboratory
2: URS Corp.
Collaborators
J. Dietiker, WVURC
P. Gopalakrishnan, VPISU
D. Huckaby, DOE
J. Carney, DOE
T. Li, URS
J. Musser, WVU
M. Shahnam, DOE
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Current simulation types in MFIX
Two-Fluid Method
(Volume/Ensemble
averaging)
Quadrature methods
(discretized distribution
function)
EE simulations
Fluid Solid
EL simulations
Fluid Solid
Discrete-element method
(MFIX-DEM)
Multiphase-Particle-In-Cell
method (MPPIC), DPM,
dense-phase-DPM, etc.
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Discrete Element Method (DEM)
Collision between real particles
AdvantagesCollisions directly resolvedTool for model validation
DisadvantagesImpractical for large-scale problems Not ideal for distributed memory parallelization
RemedyUse parcels/notional particles
i
j
Spring
Slider
Normal Force
i
j
Spring
Dashpot
Slider
Tangential Force
i
j
Spring
Slider
Normal Force
i
j
Spring
Dashpot
Slider
Tangential Force
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MPPIC model
Dilute
Dense/device-scale
AdvantageTrade off between accuracy and computational cost
DisadvantageInter-particle collision modeling
Real particles Parcels/notional particles
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MPPIC: current state-of-the-art
MPPIC model is a useful tool for quick turnaround
simulations of engineering applications (2006
roadmap)
Several commercial implementations (Barracuda by
CPFD, Dense-phase-DPM by ANSYS)
Hard to ascertain and further develop sub-models
(such as collision, friction, etc.)
Lack of an open-source implementation that can be
used for model development/enhancement, and
independent verification and validation (V&V)
Objective of this study: Implement MPPIC like model
in open-source MFIX code to probe its accuracy and
speed
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MPPIC model details
Carrier Phase: averaged Navier-Stokes equation
Dispersed Phase
Acoll is the collision operator used to model collisions in the kinetic and frictional regimes.
Robust implementation of frictional regime Acoll is critical to stability of MPPIC model
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Particle trajectory evolution
How is Acoll applied ?
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Acoll implementation (frictional regime)
is like a coloring function used to indicate the close-packed regions. is non-zero inside and at the interfaces of close-packed regions. It only indicates the direction of the correction due to close-packing.
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Acoll implementation
Case 1
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Acoll implementation
Case 1 Case 2
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Acoll implementation
Case 1 Case 2 Case 3
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Case 4Case 1 Case 2 Case 3
Acoll implementation
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Case 4Case 1 Case 2 Case 3
Acoll implementation
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Comparison with existing literature
Snider, D. M., An incompressible 3-D MP-PIC model for dense particle flows, JCP (2001)
No inter-particle collision term so far
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Isotropic inter-particle stress (Harris and Crighton)
Decides the direction of solid-stress correction velocity
Matters mostly near close-packing, otherwise statistical noise!
Comparison with existing literature
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Comparison with existing literature
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Case 1 Case 2 Case 3 Case 4
Explanation of limiters
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Case 1 Case 2 Case 3 Case 4
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Snider, D. M., An incompressible 3-D MP-PIC model for dense particle flows, JCP (2001)
Implementation comparison
Existing Literature MFIX
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Sample Problem 1: Sedimentation
Properties
Solids: Dp = 0.4 cm, ρp = 2 g/cm3
Initial solid volume fraction: 0.3 – 0.4
5 parcels per cell (2 particles per parcel)
Gas: Air at standard conditions
en,wall = 0.8, et,wall = 1.0
en = 0.6 (frictional Acoll )
box dimension = (20x200x0.4) cm3 ≡ (20x100x1) cells
DT = 1.E-02 – 1.E-04 sec
Drag model: Wen & Yu / Ergun
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(Dt max=0.001)DEM
MFIX-PIC
Case 1
Stable simulation with rebound captured at the top
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(Dt max=0.001)DEM
MFIX-PIC
Case 1
Stable simulation with rebound captured at the top
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Effect of DT
DT max = 0.01
Over packing in the wall cells normal to gravity
not so much of a problem where there is a counter flow
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Sample Problem 2: bubbling bed
Properties
Solids: Dp = 0.1 cm, ρp = 2.5 g/cm3
Initial solid volume fraction: 0.4 up to 20 cm
5 parcels per cell
Gas: Air at standard conditions
Fluidization velocity = 80 cm/s
en,wall = 0.8, et,wall = 1.0
en = 0.8
box dimension = (10x50x2) cm3 ≡ (20x100x4) cells
DTmax = 1.E-03
Drag model: Wen &Yu / Ergun
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DEM MFIX-PIC Small bubbles compared to DEM
Case 1B
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Conclusions/Observations
MPPIC model implemented in open-source MFIX
code
A new limiter based on physical arguments
formulated for solid-stress model
The method is very sensitive to interpolation and/or
sequence of particle trajectory equation integration
Further work and independent V&V needed to
establish physics-based rules for a robust solid-
stress model
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Extension to complex geometries
MFIX is based on structured grid
Complex geometries are represented
in EE solver by cut-cell technique
MPPIC implementation will use same
cut cell technique to avoid staircase
steps
Staircase steps Cut cells
EE simulation of NETL CFB (Challenge problem)J. Dietiker, Cartesian Grid User Guide, https://mfix.netl.doe.gov
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Extension to complex geometries
Future work: extension to two-way coupling
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Acknowledgments
This technical effort was performed in support of the National Energy
Technology Laboratory’s ongoing research in advanced numerical simulation
of multiphase flow under the RES contract DE-FE0004000.
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Thanks