This document discusses spray modeling for lean NOx trap aftertreatment system design. It presents Eaton Corporation's aftertreatment system for reducing NOx and PM emissions. Computational fluid dynamics (CFD) was used to optimize fuel preparation and distribution through injection modeling. Both test-based and CFD-based injection modeling were performed and validated. CFD results showed that smaller droplet sizes and optimized mixer placement improved fuel uniformity and vaporization. CFD modeling aided in comparing injector performances and selecting mixers for the aftertreatment system design.

1. © 2008 Eaton Corporation. All rights reserved.
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Spray Modeling for Lean NOx Trap
Aftertreatment System Design
Lokanath Mohanta
Milind S Kulkarni
Eaton Technologies Pvt Ltd, Pune, India
James McCarthy, Jr.
Eaton Corporation, Southfield, MI, USA
SAE INDIA
International Mobility Engineering
Congress & Exposition, Chennai
2009

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Topics
• Introduction to Eaton Aftertreatment System
• Modeling Approach
• Test based Injection Modeling
• Injection Modeling through CFD
• Validation of Computational Model
• Results
• Performance Comparison of Injectors
• Mixer Selection
• Conclusion

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Introduction
Eaton Aftertreatment system
NOx < 0.27 gm/kW-h
PM < 0.02 gm/kW-h
Working
• Lean NOX Trap (LNT) stores the NOX
• During LNT regeneration, Reformer produces H2
and CO, which are used to purge the LNT
• LNT releases the NOX as Nitrogen and NH3
• Selective Catalytic Reduction (SCR) uses the
released NH3 and treats the slipped NOX
• Diesel Particulate Filter (DPF) traps the Particulate
Matter (PM)
Product Differentiator
• Single fluid system [Dosing System needed]
• Independent of urea infrastructure
• Flexible, customized and smaller packaging
• Scalable with engine power (size)
# Ref: Hu, DEER Conf 2006, McCarthy, SAE2009-01-2835
Emission Regulation for Highway Vehicle#
Eaton Aftertreatment System#

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Topics
• Introduction to Eaton Aftertreatment System
• Modeling Approach
• Test based Injection Modeling
• Injection Modeling through CFD
• Validation of Computational Model
• Results
• Performance Comparison of Injectors
• Mixer Selection
• Conclusion

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EAS modeling Approach…
Role of CFD
• Optimize fuel preparation path
• 100% fuel vaporization
• Uniform flow and fuel distribution
Challenges
• Fuel injection modeling
Computational Domain
Exh Flow In
InjectorMixer-1Mixer-2Reformer
Boundary Condition
• Inlet – Transient Profile
• Reformer - Porous media
• Mixers: Zero Thickness wall
• Walls: Convective in steady
environment
Fuel Droplet Tracking
• Lagrangian method [DPM]
Exh Flow Out
Inlet: Transient Profile Boundary Condition
0
5
10
15
20
25
30
0 5 10 15 20 25 30
Time [sec]
ExhMassFlux[kg/m^2-s]
0
100
200
300
400
500
600
Fueling[gpm];Temperature[K]
B25 Exhaust Mass Flux (kg/m^2-2) B25 Exhaust Temperature (K)
B25 Exhaust O2 Concentration (%) B25 Fuel Mass Flow (grams/min)
0
2
4
6
8
10
O2Concentration[%]

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Test based Fuel Injection Modeling
Advantages of Test based Injection Modeling
• Need not to model injector geometry
• Independent of Multiphase flow and atomization model
• Turn around time ~ 24-48 hours on 4GB HP Work station
Input for CFD Spray Modeling#
Droplet Distribution
Spray Cone Angle
Spray characterization using
Laser Diagnostic #
Test Output
 Spray Cone Angle (Φ)
 Droplet Diameter
 Droplet Velocity
# Ref: McCarthy, Spray and Atomization 2009
Φ

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Axis
Spool wall
Wall
SwirlChamber Point of
Injection
Axis
Direction Vector
• Axial
• Swirl
Axis
Spool wall
Wall
SwirlChamber Point of
Injection
Axis
Injection Modeling through CFD
Step -1 : Geometry Details
Multiphase Flow Simulation
(Volume of Fluids -- VOF)
Step-2: Droplet Modeling [DPM]
Pressure Swirl Atomizer (Break up
& Coalescence)
• Droplet Distribution
• Droplet Diameter
• Spray Cone Angle
• Pressure Drop
2- D Axisymmetric VOF Domain 2- D Axisymmetric DPM Domain
Injector Geometry
Step-1 - VOF Step-2
Computational Domain
for Droplet Modeling

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0
10
20
30
40
50
60
70
80
Half Cone Angle ( Deg) SMD(Micron)
Experiment
Simulation
fuel
Air
• VOF Simulation
• Turbulence Model : κ−ε RNG and RSM
• Surface Reconstruction : HRIC Scheme
• DPM Simulation
• Initial Droplet Diameter through Linearized
Instability Sheet Atomization model
• Initial distribution follows the Rosin-Rammler
Distribution
Results :
Pre-Spray and Spray Characterization
Effect of turbulence model: a) κ−ε model b)
RSM model
Formation of Liquid Sheet at the exit of injector
Time Taken: 20-30 days on same m/c
Comparison of spray half cone angle and SMD
Droplet diameter distribution through simulation
Droplet
Diameter (µm)

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Topics
• Introduction to Eaton Aftertreatment System
• Modeling Approach
• Test based Injection Modeling
• Injection Modeling through CFD
• Validation of Computational Model
• Results
• Performance Comparison of Injectors
• Mixer Selection
• Conclusion

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Validation of the CFD Model
Validation Approach
• Mass Fraction correlated with Test Temp
Temperature Distribution from Test @ Reformer Face
Mass fraction of vapor from CFD model @ Reformer Face
Operating condition-1 Operating condition-2
CFD Predictions are in Qualitative Agreement with Test
Aftertreatment Engine Test Cell
It is observed from the test that the
temperature is low where the fuel
concentration is high and vice versa

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Topics
• Introduction to Eaton Aftertreatment System
• Modeling Approach
• Test based Injection Modeling
• Injection Modeling through CFD
• Validation of Computational Model
• Results
• Performance Comparison of Injectors
• Mixer Selection
• Conclusion

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Results :
Performance Comparison of Injectors
Comparison of wall wetting and Mass Fraction contour
Exhaust System with Spray A
Exhaust System with Spray B
Smaller droplets : Higher fuel uniformity and Better vaporization
• Spray A [ Large Droplets ]
• Fuel uniformity is low
• Higher wall wetting
• Spray B [ Small Droplets]
• Higher fuel uniformity
• Low wall wetting
Diameter distribution of droplets
Spray B
Spray A
High
Low

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Results :
Mixer Selection
Case-1
Contour of fuel mass fraction at the Reformer Face
Comparison of profile at the Reformer Face
Case-2
Liquid Fuel Vapor
Case-2: Optimized configuration based on CFD findings
Injector
Mixer-1
Mixer-2
Reformer
Injector
Mixer-1
Reformer
Case-1 Case-2
Flow
Direction
Role of Mixer
• Increase Fuel uniformity
• Enhanced vaporization
Fuelingrate
Time
Low
High

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Topics
• Introduction to Eaton Aftertreatment System
• Modeling Approach
• Test based Injection Modeling
• Injection Modeling through CFD
• Validation of Computational Model
• Results
• Performance Comparison of Injectors
• Mixer Selection
• Conclusion

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Conclusion
• Test based Injection modeling proved successful to model the
spray behavior. Results validated on aftertreatment hardware.
• Injection modeling through CFD
• 2-D Axi-symmetric VOF model predicted the spray cone angle
accurately.
• DPM Model predicted a representative distribution of the droplets.
• CFD with Test based injection Modeling was used to optimize the
mixing and fuel distribution in the exhaust.
• Injection modeling through CFD can be used independent of test
to generate the spray characteristics.

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Acknowledgement
• EATON Aftertreatment Team,
• Pune, India
• Southfield, USA
• Galesburg, USA
• Santa Clara, USA
• Fluent Support
• FLUENT Support, MI, USA
• Fluent Support, Pune India