choice of urea-spray models in cfd simulations of urea … · choice of urea-spray models ......

Competence Centre for Catalysis - KCK

Choice of urea-spray modelsin CFD simulations

of urea-SCR systems

Andreas Lundström & Henrik Ström

Competence Centre for Catalysis / Chemical Reaction Engineering

Department of Chemical Engineering and Environmental ScienceChemical Reaction Engineering

Chalmers University of TechnologyS - 412 96 Göteborg

Sweden

E-mail: [email protected]@chalmers.se and

mailto:[email protected]

mailto:[email protected]

2/24 Competence Centre for Catalysis - KCK

Diesel exhaust

• Heavy-duty diesel engines: high efficiency and competitive fuel cost

• Emission legislation being sharpened• NOx: adverse effects on health and environment• Optimize combustion with respect to particles →

remove NOx in the aftertreatment system• Ammonia gives the best SCR performance


The urea-SCR system

• Thermal decomposition of urea:

• Hydrolyzation of isocyanic acid:

AdBlue: 32.5-weight% urea in water


Outline

1. The investigated urea-SCR system2. Eulerian-Lagrangian modeling in CFD

- Force balance- Sub-models for the discrete phase- Heat and mass transfer- Results are influenced by modeling choices

3. Volume of Fluid modeling in CFD- Simulation setup- Comparison of droplet distortion

4. Influence of material data quality5. Summary6. Future work


The investigated urea-SCR system

Single-phase AdBlue injector Droplet size range: 5 – 300 µm

Pulsating injection Sauter mean diameter: ~ 120 µm

Hollow cone spray Mean diameterN: ~ 90 µm

• Water evaporation and urea decomposition is modeled

• Droplets hitting walls are logged and removed – i.e. no wall-film modeling


Eulerian-Lagrangian modeling in CFD

( )

,

,,2

Re1824

ip i

p i D pp p i p i x

p p

dx udt

du Cm m u u F

dt dµ

ρ

=

= − +

Fluent, Inc.

• External forces to include in the Lagrangian force balance equations (Fx)

• Sub-models for droplet drag coefficient (CD), including effects of droplet distortion

• Sub-model for turbulent dispersion of droplets and its sensitivity to the choice of turbulence model


Overview of external forcesFORCE DUE TO FORMULA NEGLECT

Gravitational force GravitationWhen τd is small

Virtual mass force Acceleration of the surrounding gas

Brownian motion Collisions with molecules

Lift force Velocity gradient ?Rotational force Rotation of droplet

When the lift force is neglected

Termophoretic force Temperature gradient

?

History force Build-up of boundary layer at acceleration ?

( )pg p x

p

F m gρ ρ

ρ

−=

( )vm vm g d d gdF C u u udt

ρ= − − gd ρρ >>

5 2

216Brownian

p p c

TFd C t

µσξπ ρ

=∆

Kn < 0.015

2 212L f c LF U a Cρ π=

2 212L R f c L RF U a Cρ π+ +=

( )( )( )

26 Kn 11 3 Kn 1 2 2 Kn

p s tT

m t

d C K C TFC K C Tπ µ

ρ+ ∂

= −+ + + x∂

( )0

26p

p

tf p

History p f ft p

d U UdF r d

tτπρ µ τ

τ

−= ⋅

−∫


Estimating lift force effects

2 212L f c LF U a Cρ π=

( )* *0.9 *1.10 1Re ,L pC K Kα α α= +

( )* *0.9 *1.10 1Re ,L pC K Kα α α= +

( )*0 1; , Re p

c

a U K K fU y

α ∂= =

∂

Kurose & Komori (J. Fluid Mech. 384, 1999)

The lift force experienced by droplets within the system is at least two orders of magnitude smaller than their current drag force. Neglecting lift force is effects is thereby justified.


Estimating thermophoretic effects

( )( )( )

26 Kn 11 3 Kn 1 2 2 Kn

p s tT

m t

d C K C TFC K C T xπ µ

ρ+ ∂

= −+ + + ∂

2Kn =pdλ

( )* *0.9 *1.10 1Re ,L pC K Kα α α= +

Talbot et al (J. Fluid Mech. 101, 1980)

K =p

kk

Cs, Ct and Cm are constants

Thermophoretic effects are more pronounced at lower gas flows, but the thermophoretic force is small (< 5%) compared to the drag force for most (> 95%) of the droplet’s lifetime within the system.


Estimating history effects

( )0

26p

p

tf p

History p f ft p

d U UdF r d

tτπρ µ τ

τ

−= ⋅

−∫

Crowe, C. T. Multiphase Flow Handbook (2006)

History effects are very sensitive to other modeling

choices!

0%

5%

10%

15%

20%

base case + DRW base case + DRWHIGH GAS FLOW LOW GAS FLOW

Relative importance* Turbulent dispersion of

droplets will affect importance of the history

force.

*Percent of injected parcels experiencing Fhistory/Fdrag higher than 10% for more than 10% of their time in the domain

DRW = Discrete Random Walk (model for turbulent dispersion of droplets)


Sub-models for the discrete phase• Drag coefficient

• Turbulent dispersion

Crowe et al (CRC Press, 1998)

( ) ( )

( )( )

2

log

min ,ln 1

e L

interaction e crosse

crossp

u t u u t

u u

kC r

t tLt

u u

ζ

τε

ττ

τ

′= +

′ ′=

⎧ = −⎪⎪= ⎨ ⎡ ⎤⎛ ⎞⎪ ⎢ ⎥⎜ ⎟= − −

⎜ ⎟⎪ −⎢ ⎥⎝ ⎠⎣ ⎦⎩

( )Re 1000p ≤

( ), , , ,

2 2

2 2 3 2TAB model:

D dynamic D sphere D disk D sphere

g k d lF

b l l l

C C C C y

C CCd y u dyydt C r r r dt

ρ σ µρ ρ ρ

= + − ⋅

= − −

Dynamic drag law:2 3

,24 11 Re

Re 6D sphere pp

C ⎛ ⎞= +⎜ ⎟⎝ ⎠

Spherical drag law:


Droplet heat and mass transfer

(dp = 30 µm)

( )( ), ,

p pp p s p vap

i c i s i

dT dmm c hA T T h

dt dtN k c c

∞

∞

⎧= − + ∆⎪

⎨⎪ = −⎩

( )pp p s p

dTm c hA T T

dt ∞= −

( ) ( ) ( ),

,

4 1 0.23 Re ln 1p p pd

p p p decomposition

d d c T Tkdt c d hρ

∞ ∞∞

∞

⎡ ⎤−= + +⎢ ⎥

∆⎢ ⎥⎣ ⎦

Stage of evaporation or decomposition

Heat and mass balances

A. Evaporation of water

B. Heating of urea

C. Decomposition of urea(at constant temperature ~ 425 K)


Eulerian-Lagrangian modeling results

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.675

Mass fraction of water in droplet

ug ≈ 70 m/s

Tg = 400°C

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003 0.0032

Mass fraction of ammonia in pipe


Results are influenced by model choices

• HIGH GAS FLOW CASE

• Switching to a dynamic drag law decreases wall hit with 43%• Simulating turbulent dispersion increases wall hit with 37%• Using both the dynamic drag law and turbulent dispersion

increases wall hit with 47%

• LOW GAS FLOW CASE

• Simulating turbulent dispersion increases decomposition efficiency with 14%

(ug ≈ 70 m/s, Tg = 400°C)

Decomposition efficiency: 21.4% Wall hit: 4.4%

(ug ≈ 25 m/s, Tg = 300°C)

Decomposition efficiency: 32.9% Wall hit: 20.9%


Explanations for model choice sensitivity

• Dynamic drag coefficient speeds up droplet adaptation to the gas flow ⇒ large effect on wall hit at high gas flows

• Turbulent dispersion will increase heat and mass transfer rates at low relative velocities ⇒ increases decomposition efficiency at low gas flows

• Turbulent dispersion predicts small droplets/urea particles on injector side of pipe will be thrown towards the wall ⇒ increases extent of wall hit and predicts different variety of droplet types at the walls

Droplet properties at wall hit crucial for wall modeling!


Turbulence model

2 3 4 5 6 7-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Turbulent fluctuating velocity [m/s]

Pipe

Y-c

oord

inat

e [m

]

RSM u´ (plane)RSM v´ (main gas flow direction)RNG k-e

u

v

Turbulent fluctuating velocity across the pipe cross-section in a fully developed turbulent flow for a high gas flow case (ug ≈ 75 m/s) in a straight exhaust gas pipe

Changing from RNG k-ε to a Reynolds stress model will increase wall hit with 9.6% for a straight pipe with a high gas flow (≈ 70 m/s).

?Modeling turbulent dispersion increases the sensitivity to the

choice of turbulence model!


Volume of Fluid modeling

• Used in conjunction with Eulerian-Lagrangian modeling to give a detailed resolution of individual droplet behavior– Heat and Momentum transfer

• May only be used on a small number of droplets


Comparison of droplet distortion

VOF and TAB simulations for 50 and 100 (µm) droplets in a 70 (m/s) gas flow

100 (µm) 50 (µm)

VOF and TAB simulations agree well in predicting droplet oscillation frequency and amplitude


Comparison of drag forces

VOF, Dynamic- and Spherical-drag law simulations of 300 and 100 (µm) droplets in 70 (m/s) gas flow under constant material properties

Dynamic drag law gives a better description of real droplet drag than the spherical drag law.


AdBlue material data

• The need for good data in simulations?

Measurements of:viscositydensitysurface tension

mass fraction of Urea [%W]

Tem

pera

ture

[o C]

Kinematic viscosity of Urea (cSt)

0.9 0.95 1 1.05

1.1 1.15 1.21.25 1.3

1.351.4

0.951

1.05

1.05

1.1

1.1

1.15

1.15

1.2 1.25

1.3

30 35 40 45 50 55 60 65 7020

30

40

50

60

70

80


Results of changed viscosityDroplet distortion during evaporation:

Dp = 200 (µm) in 75 (m/s) flow during 0.5 % of total evaporation time

b) Comparison between UW solution viscosity and using pure water viscosity

a) Comparison between UW solution viscosity and using a constant viscosity of 0.0007 (Pas)

TAB modeling results of droplet oscillations depends on material data


Effects on drag

Drag coefficient predicted using TAB and spherical drag law models for:

UW-solution with property dependent or constant viscosity

Dynamic drag law applicable for ~0.3% of total evaporation time

Prediction of drag is insensitive to changes in material properties


Summary

• Choice of models influences the results!• Lagrangian force balance

– Drag force and gravitational force– History force?

• Drag coefficient– TAB model provides good descriptions of droplet distortion

• Turbulent dispersion– Large effects– Sensitivity to the choice of turbulence model

• Material data– Material data quality is of minor importance when predicting drag


Future work

• Continued work comparing evaporation rates for VOF and Eulerian-Lagrangian modeling

• Development of urea-decomposition kinetics

• Wall-droplet interaction modeling

choice of urea-spray models in cfd simulations of urea … · choice of urea-spray models ......

Documents