Improved Modeling of Loading Kinetics in Detailed Filter ...
Transcript of Improved Modeling of Loading Kinetics in Detailed Filter ...
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Improved Modeling of Loading Kinetics in
Detailed Filter Media Simulations with
GeoDict
Jürgen Becker, Andreas Wiegmann
Math2Market GmbH, Kaiserslautern, Germany
Friedemann Hahn, Uwe Staudacher, Martin J. Lehmann
MANN+HUMMEL GMBH, Ludwigsburg, Germany
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Overview
1. Motivation - peculiar effects observed in experiments
2. Hypothetical explanations
3. Filtration simulation with GeoDict
4. Results
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The Multipass Test (ISO 4548)
Storage vessel
Contamination circuit
Testing circuit
Dilution system
Particle injection
Pump
Filter
Qp
Qinj
Pressure sensor
Pressure sensor Online particle counter 2
Online particle counter 1
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The Multipass Test (ISO 4548)
Initial efficiency Cake filtration
How to understand
what‘s going on here!?
Elapsed time [min]
Filt
er
effic
iency [
%]
100
80
60
40
20
0 0 10 20 30 40 50 60 70 80
d ~ 15 µm
d ~ 9 µm
Simulation
(GeoDict
2012R1)
Testing
Peculiarities observed in testing of depth filter media
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Filter Simulation: Efficiency
Basic idea:
1. Filter model
2. Determine flow field
3. Track particles (filtered or not?)
Randomness:
Starting positions
Brownian motion
Result:
Percentage of filtered particles
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Tracking the Particles
No interaction between particles
Flow field is not changed by a moving particle
Modeled effects:
Inertia
Brownian motion
Electrostatic attraction or repulsion
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Adhesion Model
What happens when a particle hits the filter material?
a) sticks to material (deposited)
b) bounces off
Particles always stick => Caught on first touch model
Particles always bounce off => Sieving model
Particles loose energy when bouncing => Restitution factor
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Hamaker Model
Adhesive forces:
(van-der-Waals forces between spherical particle and flat surface)
H Hamaker constant [J]
d Particle diameter
a Distance between particle and surface
Escape velocity:
1. Integrate from a0 (min distance = 4e-10) to infinity
2. Compare with kin. energy of particle
2
2
04
Hv
a r
212vdW
HdF
a
Particle sticks for smaller velocities v.
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Filter Simulation: Life Time
1. Filter Model
6. Repeat ... 5. Flow Field 4. Deposit Particles
2. Flow Field 3. Track Particles
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Improvements to FilterDict
Global time concept: particles can continue to the next batch
=> allows lingering particles
=> needed for re-entrainment
More accurate particle tracking
2012R1:
flow solver uses staggered grid but writes cell-centered result file
particle tracking uses cell-centered file
=> accuracy lost (especially at no-slip boundary)
2012R2:
flow solver uses staggered grid and writes staggered grid result file
particle tracking uses staggered grid
...
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Effect of Higher Accuracy:
MPPS Simulation Example
Structure:
Fibers with diameter 20 µm
Different porosities
Different resolutions (voxel length 1 µm – 4µm)
Simulation:
Find efficiency for all particle diameters
(caught on first touch, air filtration)
Brownian Motion: on/off
Inertia: on/off (by particle weight)
Different flow velocities
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Fixed: Porosity 90%, Resolution 2 µm
Vary: Velocity
0.00 %
10.00 %
20.00 %
30.00 %
40.00 %
50.00 %
60.00 %
70.00 %
80.00 %
90.00 %
100.00 %
0.001 µm 0.01 µm 0.1 µm 1.0 µm 10.0 µm 100.0 µm
v0.02
v0.02 Inertia + Diffusion
v0.2
v0.2 Inertia + Diffusion
Should be zero!
But: Interpolation
error!
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Enhancement of Interpolation in 2012R2
0.00 %
10.00 %
20.00 %
30.00 %
40.00 %
50.00 %
60.00 %
70.00 %
80.00 %
90.00 %
100.00 %
0.001 µm 0.01 µm 0.1 µm 1.0 µm 10.0 µm 100.0 µm
r1
r1 center
r1.5
r1.5 center
r2
r2 center
r3
r3 center
r4
r4 center
2012 R1: Interpolation from
cell-centered velocities
2012 R2: Interpolation from
original staggered grid
Voxel length 3 µm in 2012R2
same quality as
Voxel length 2 µm in 2012R1
200x200x200 (=8 Mio) in 2012R2
same quality as
300x300x300 (=27 Mio) in 2012R1
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Decreasing Efficiency by Changed Pathways
0 %
10 %
20 %
30 %
40 %
50 %
60 %
0 1000 2000 3000 4000 5000
To
tal F
iltr
ati
on
Eff
icie
nc
y
Time / s
Total Filtration Efficiency by Weight
=> Effect can explain
decreasing efficiencies!
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Reentrainment & Lingering
Observations from numerous simulations:
Larger particles get sieved!
Local flow field does not flip direction => particles stay sieved.
=> Larger particles do not re-entrain (in significant numbers)!
Initially, particles pass the clean filter quickly.
Small particles pass through filter cake slowly
(in later stages of filtration, assuming sieving model)
=> This is most likely not the main explanation!
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Flow
Simulation Results
(GeoDict 2012R2 Version)
Tomography cut-out
Oil filtration
Adhesion model: sieving
No re-entrainment
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0 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
0 200 400 600 800 1000 1200 1400 1600 1800 2000
To
tal F
iltr
ati
on
Eff
icie
nc
y
Time / s
resolution 1 µm
resolution 2 µm
Total Efficiency by Weight
Efficiency is initially
decreasing!
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Fractional Filtration Efficiency
0.00 %
10.00 %
20.00 %
30.00 %
40.00 %
50.00 %
60.00 %
70.00 %
80.00 %
90.00 %
100.00 %
0 s 500 s 1000 s 1500 s 2000 s
1 µm
5 µm
9 µm
15 µm
25 µm
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Summary and Outlook
Summary:
Decreasing efficiencies can be explained by simulation
=> No re-entrainment, but explained geometrically
Improvements needed:
More accurate particle tracking / flow field interpolation
Global time concept: particles can continue in the next batch
Future improvements:
Enhance fractional efficiency determination (Filtech 2013)
Reconsider sieving criterion w.r.t. resolution dependency