Yundi Jiang Jari Kolehmainen Yile Gu Yannis Kevrekidis Ali Ozel amp Sankaran Sundaresan Princeton University NJ 2018 NETL Workshop on Multiphase Flow Science 1 ID: 805252
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Slide1
Machine Learning Based Filtered Drag Force ModelYundi Jiang, Jari Kolehmainen, Yile Gu Yannis Kevrekidis , Ali Ozel & Sankaran SundaresanPrinceton University, NJ 2018 NETL Workshop on Multiphase Flow Science
1
Funded
by ExxonMobil
Slide2Gas–particle flows in fluidized bedsInherently unstable with multiscale structuresWeight of particle is principally balanced by the drag forceAccurate estimation of the drag force is essential for reliable prediction of flow behaviorBackground 2 Frank Schaffer, NETL
Slide3Fine-grid simulations1Euler-Euler ApproachContinuum averaged equations of motion for the fluid and solid phasesCoarse-grid simulationsFiltered Euler-Euler ApproachMulti-scale structures in gas-particle Flow1. Igci, Y., Andrews, A. T., Sundaresan
, S., Pannala, S. and O'Brien, T. (2008), Filtered two-fluid models for fluidized gas-particle suspensions. AIChE
J., 54:
1431–1448
3
Slide4Particle phase momentum balance in
Filtered Two-fluid
model
Multi-scale structures in
gas-particle
Flow
4
Upon filtering
=
Particle phase
momentum balance in
Two-fluid model
Slide55Sub-grid scale terms:Sub-grid scale contribution to drag force
Meso
-
scale stress:
S
ub-grid scale contribution to gas-phase stress:
Sub-grid scale contribution to
solid-phase stress (Kinetic Theory):
Multi-scale structures in gas-particle Flow
- unresolved
structures in filtered models
- need
to be modeled to account for
meso
-scale
inhomogeneities
most significant
5
.
Parmentier
, J.-F.,
Simonin
, O. and
Delsart
, O
.,
(2012),
AIChE
J., 58: 1084–1098
6
.
Ozel
,
A.,
Fede
,
P.,
Simonin
,
O., (
2013)
Int. J
Multiph
.
Flow,
55:43-63 0301 -93222.
7
.
Ozel
, A. et al., (2017)
Physics of Fluid
(2017) 29: 103308.
Slide6Prior studies from our group Drag correction
Modeling filtered drag force
6
3
.
Igci
, Y.,
Sundaresan
, S.,
(
2011)
Ind. Eng. Chem.
Res.
50
(23
): 13190-13201
4
. Milioli,C., Milioli, F.E., Holloway, W., Kapil, A., Sundaresan, S., (2013). AIChE J. 59..
Slide7: Microscopic drag coefficient evaluated with filtered variables
: Drift velocity
Modeling filtered drag force
7
Toulouse group approach
5,6
and also our current
approach
7
Takes into account
inhomogeneities
inside filtering volume
Difference between filtered gas velocity and gas velocity seen by the particles
Not available in coarse simulations - need to be modeled
5
.
Parmentier
, J.-F., Simonin, O. and Delsart, O., (2012), AIChE J., 58: 1084–10986. Ozel, A.,Fede, P., Simonin, O., (2013) Int. J Multiph. Flow, 55:43-63 0301 -93222.7. Ozel, A. et al., (2017) Physics of Fluid (2017) 29: 103308.
Slide8Drag correction needs drift velocityChallenge: drift velocity is NOT available in a filtered model simulation. It needs to be estimated5-7Scale similarity approach Good a priori resultPearson correlation coefficient : 0.8 for with
( for smaller filter size)
Good agreement between fine and coarse simulation results
Approach
in the current study
Derive a transport equation for drift velocity
Analyze the transport equation to identify key quantities
Use data mining approach to obtain closure model
Drift velocity for drag force correction
8
7.
Ozel
, A. et al., (2017) Physics of Fluid (2017) 29: 103308.
Slide99Flow Configuration & Simulation ParametersFine-grid Euler-Euler simulationParticle diameter
75
Grid size (
) : 3
x 3 x 3
Particle
density [
: 1500
Restitution coefficient: 0.9
Gas density [
: 1.3
Gas viscosity [
]:
Slide10Filtering Euler-Euler resultsCollect fine-grid simulation resultsFilter all relevant quantities using a filter of chosen sizeFiltered variables:
Sub-grid scale terms
–
Budget Analysis
Additional quantities: Filtered drag, drift velocity, etc.
Fine-grid Euler-Euler simulation
10
Slide11Derivation
Sub-grid scale correlations on the right hand side: 13!
…
Transport equation for drift
v
elocity
11
Slide12Budget Analysis: Assess relative magnitudes of the terms
12
Transpor
t equation for drift
v
elocity
Potential markers for predicting
Slide13Can handle big dataGreat predictive capabilityDatasetInput: Local filtered variables (filter size
) and their gradientsOutput: axial directional drift flux:
Model:
Constitutive models with machine
l
earning
13
Neural Network
model for
predicting drift velocity
Slide1414A priori test for predicting : Pearson Correlation Coefficient for Neural Network Model: 0.99
Significant improvement from model without
Pearson correlation coefficient
for two marker
(
) scale similarity
model approach was 0.8
6
A priori Test: Neural Network Model
Probability Density
Error percent
Predicted
Real
6.
Ozel
, A.,
Fede
, P., Simonin, O., (2013) Int. J Multiph. Flow, 55:43-63 0301 -93222. is an important marker for predicting drift velocity
Slide15Grid size is 9X of the fine-grid simulation : Grid size (
) = 27 x 27 x 27
Same
flow
configuration
Coarse drag coefficient corrected by drift velocity
15
Model validated by coarse Euler-Euler simulation
A p
osteriori
Test: Coarse-grid Simulation
From a priori study:
Pearson
Correlation Coefficient =
0.99
NN Model
7.
Ozel
, A. et al., (2017)
Physics of Fluid
(2017) 29: 103308.
Slide1616Simulation SnapshotsA posteriori Test: Coarse-grid Simulation
(a)
Fine-grid (3
d
p
)
(b)
Fine-grid (3
d
p
) result mapped on coarse grid (27
d
p
)
(c)
Coarse-grid (27
d
p) with
vd corrected Wen&Yu
(d)Coarse-grid (27 dp) with Wen&Yu
Slide1717Axial Direction Solid Volume Fraction Profile A posteriori Test: Coarse-grid SimulationDimension HeightWen&Yu overpredicts
the bed height for coarse-grid simulation
Drift velocity correction effectively correct drag coefficient - bring the bed expansion closer to fine-grid results
27
3
27
Slide1818A posteriori Test: Coarse-grid Simulation(a) Wen&Yu. (b) Wen&Yu +
v
d
Particle volume fraction vs. bed elevation
Slide1919Horizontal Direction Solid flux profileA posteriori Test: Coarse-grid SimulationMean Solid flux =
, averaged over y-axis for certain horizontal layer
Z= 40% Bed
Height
Z= 80% Bed
Height
Wen&Yu
underpredicts
solid flux across the bed and
overpredicts
the bed expansion
Drift
velocity correction produces similar profile as fine-grid simulation
27
27
27
27
Dimensionless Horizontal
Position
Dimensionless Horizontal PositionDimensionless Solid FLuxDimensionless Solid FLux
Slide2020Axial Direction Drift Flux Profile Drift flux = Inside bedCoarse-grid Fine-gridTop and Bottom of bedCoarse-grid simulation results
overpredict the magnitude of drift fluxModel performance is affected by sharp gradients
–
model improvement is needed
A posteriori
Test: Coarse-grid Simulation
27
Dimensionless
Drift
FLux
Dimensionless
Height
Slide21Drift velocity is an essential marker for filtered drag coefficient correctionA transport equation for drift velocity is derived and simplified to identify proper markers for modeling drift velocityNeural Network model is developed for drift velocity based on filtered fine-grid simulation resultsNeural Network model is validated with coarse-grid simulation; Posteriori test results show agreement between coarse and filtered fine-grid simulation resultsFuture work: Explicit model form Other gas-particle systems Heat and mass transport in gas-particle flowSummary
21