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Copyright Â© 2012 SAE International
ABSTRACT
The Selective Catalytic Reduction (SCR) based on Urea Water Solution (UWS) injection is an effective technique to reduce nitrogen oxides (NOx) emitted from diesel engines. A 3D numerical computer model of the injection of UWS and their interaction with the exhaust gas flow and exhaust tubing is developed to evaluate different configurations during the development process of such a DeNOx system. The model accounts for all relevant processes appearing from the injection point to the entrance of the
1. INTRODUCTION
Among various techniques of reducing diesel NOx to levels required by strict worldwide emission regulations, the most realistic solution is
recently, the technology has been applied to mobile diesel engine applications such as heavy duty trucks, ships, etc. The development of
In modern automotive applications, the
In actual exhaust configurations impingement of droplets on the catalyst and the walls cannot be avoided due to the slow evaporation and thermolysis and due to the inertia of the droplets [2]. Especially in passenger car applications [3], where dosing systems without
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distribution of the reducing agent a detailed
2.CFD METHODOLOGY
2.1Evaporation Model Including
Urea Thermolysis
The influence of urea on the evaporation of water from a UWS droplet is investigated theoretically by different evaporation models considering droplet motion and variable properties of UWS and the ambient gas phase. To evaluate the influence of solved urea on the evaporation of water, three different evaporation models are used:
Liquid phase
Rapid Mixing Model (RM Model) [12, 13]:
Within the RM model infinite high transport coefficients are assumed for the liquid phase, resulting in spatial uniform temperature, concentration and fluid properties in the droplet, but the quantities will change in time. The variation of urea
concentration of the droplet can be evaluated by 

dYdtu = âˆ’ mÌ‡mvap 
(1) 
Diffusion Limit Model (DL Model) [14]:
Neglecting internal convection, only diffusive transport of energy and mass are assumed. The diffusion equation for
species and energy in the droplet is solved considering variable fluid properties.
âˆ‚ 


G 

âˆ‚2 
+ 



âˆ‚ 


âˆ‚G 

+ 




âˆ‚ 

âˆ‚Y 


u 
âˆ‚ Yu 
1 

âˆ‚P 
G1 
âˆ‚ 

u 
Gr 
u 

dr 
âˆ‚Yu 


t 
= r2 
w2 
w +Ï 

w + 
u 

w 


dt âˆ’ r 
(2)w 

âˆ‚ 




âˆ‚2 




âˆ‚l 








âˆ‚ 
(3) 

âˆ‚Tt 

= r2 

+ 
w +l1 
âˆ‚w + r 



drdt âˆ’ 
r 
âˆ‚Tw 



âˆ‚wT2 





with 



















d 
= 
Ï lcp, 

















r denotes a radial convective velocity which accounts for the variable density field within the droplet.
Effective Diffusion Model(ED model):
The ED model accounts for internal circulation due to forced convection. It considers internal circulation by an empirical correction of the transport
Gas phase:
For the gas phase the


dmdt 
= âˆ’Ï€Ddrg,refGg,refSh* ln(l+BM) 
(4) 



dTdt 
= mmÌ‡vapcp, 
cp,vap, 
T 
T 
âˆ’h 
(5) 

where, 
BM = 
Yvap,s 
Yvap, 
and 







1 Yvap,s 







BT = ( +BM)x âˆ’ 
1, 
= 
Cp,vap, 
N 
* 
1 


* 



Cp, , 

Le 


dm 



l , 
* 
ln( 
+BT) 

(6) 

dt 
= âˆ’Ï€Dd Cp,vap, 




with 











BT = Cp,vap, vapT 
Ts 







The RM and DL models describe the physical limits of infinite high and only diffusive transport. As the temperature and the urea concentration changes strongly during evaporation,
2
variable fluid properties are used. For the calculations, it is additionally assumed that no crystallization of urea occurs. The droplets are assumed to be spherical throughout the evaporation and decomposition processes [15].
In the modeling of thermolysis rate, there are different formulations for the thermolysis rate in literature The reaction rate is described by an
= âˆ’ re ,A. âˆ’Ea
RT (7)
with the kinetic parameters A=382 1/s, Ea= 2.94e7 J/mol. Birkhold et al. [2] use the experimental data from Kim et al. [9] for a parameter fit and get A=0.42 kg/ms, Ea=69 000 J/mol..
For thermolysis following reaction is considered
(NH2)2CO(s orl) 
NH3(g)+HNCO(g) H=+185KJ/mol 
And rate equation is 
Ea 
dÎ± 

(8) 
(âˆ’RT ) 
dt = âˆ’A.( âˆ’ ) . 
where( denotes the urea conversion fraction Î± given by where Î±= re (t=0) re (t))/ re (t=0) Buchholz [16] suggests A=1.e6 1/s, Ea = 7.3e4 J/mol and n=0.3.
All of the above approaches are implemented in FIRE and can be selected in the spray evaporation GUI section. According to the most comprehensive validation related to the automotive SCR application the approach of Birkhold (equation (2.41)) has been established as the default setting. The frequency factor A and activation energy Ea are input parameters in the GUI with default settings as given above
2.2 Mass, Heat Transfer and Evaporation
In the present work, a transfer temperature, uniform gas model derived by Dukowicz [17] is applied. The model assumes spherical symmetry, a quasi steady gas film around the droplet, uniform droplet properties, and phase and thermal equilibrium at the droplet surface. The mass balance of the droplet is given by,

dmdt 
= Ad. 
Ì‡ 





(9) 

where, the time derivative of the droplet mass 


depends on 

the specific 
vapor 
mass 
flux 

vaporizing from or 











d 

condensing on the droplet surface 
Ì‡. The energy balance of 

the droplet is 
â„Ž .Ad . Ì‡ + 
Ad 





d. 
,d.dTdt 
= 
Ë™ 

Ì‡ 

(10) 

By introducing a specific surface energyË™ 
flux 









Ì‡ = 





the balance equations of the massAand energy can 



be 









dm 
= 
Ë™ 
Ì‡vap 







(11) 
dt 
Ì‡ 

+ 
â„Ž 
. Ì‡vapÌ‡ 






d. ,d.dTdt = 
Ë™ 



(12) 
Equations 

provided that the expressions 
Ë™and 
Ì‡vapÌ‡ are known. 
The energy transfer flux Ë™is calculated 

Ë™ = Ad.Î±.( 
g â€“ d) 
(13) 
Î± is a general heat transfer coefficient, which is typically
derived from Nusselt correlations [18]. The fraction of specific 

heat to mass flux at the droplet surface 
Ì‡vap is evaluated based 
on analogy considerations. It is assumedÌ‡that the differential 
equations and boundary conditions for the heat and mass transfer problems are similar. Based on a rigorous theoretical study, Dukowicz [16] derived the following expression,
mÌ‡vap 
= 
âˆž 
Le. vap, 
vap,âˆž 
.(1 
vap, ) 
, ) 
(14) 
qÌ‡ 

vap, 
, 
.( 
vap, 

3.1
The physical mechanisms occurring during the interaction of spray with a wall are very complex, because the behavior of the impinging droplet is influenced by a variety of parameters such as droplet properties like velocity, diameter, fluid properties
3
and surface properties like wall temperature, surface roughness or wall film height [19]. Thus
3.2 Spray Impingement Heat Transfer
The cooling of the wall due to spray impingement plays an important role, because only if the dimensionless wall temperature T*(ratio of wall temperature to saturation temperature) decreases below the critical value (usually1.4) deposition of droplets will occur and a wall film will develop. The implemented heat transfer model is based on the approach of Wruck[11]. When a droplet impinges on a hot wall, a short period of direct contact between fluid and solid exists until a vapor cushion is formed. For small droplets the heat transferred during this direct contact is determining the total heat transfer, because of the insulation effect of the vapor cushion [11].The heat transfer is calculated assuming the contact by two semi infinite bodies, droplet and wall, which are in contact for a certain time with an effective contact area. It is based on one dimensional transient heat conduction in both contact partners
Figure 1. Regime map for UWS of
3.3Wall film Modelling
Deposition of droplets leads to a wall film which is modeled with a 2D finite volume method in the Fire v8 wall film module [8]. Gas and wall film flow are treated as separate single phases, coupled by
3.4Continuity Equation
The continuity equation transformed into conservation of film thickness assuming a spatially constant wall film thickness in a cell, equation can be solved explicitly, if velocity components and the source term are known.. development of a wall film using physical properties like kinematic viscosity and the surface tension. The viscosity increases with increasing urea concentration [22] and leads to an increase of the film thickness and shear stress and a tendency to a laminar film profile [22]. For high urea concentrations the above approach may only be a rough estimation of the film dynamics. The viscosity increases with increasing urea concentration [21] and leads to an increase of the film thickness and shear stress and a tendency to a laminar film profile [22]. For high urea concentrations the above approach may only be a rough estimation of the film dynamics. Evaporation and thermolysis from wall film is based on Fickâ€™s law of diffusion. Wall film energy equation and the evaporation routines are coupled in this study through a time step adaptation to avoid numerical instabilities and to solve the steep gradients of heating and evaporation of the wall film. The influence of flow conditions, exhaust tube properties and spray parameters on the film formation can be evaluated with the developed model. The derived models implemented in the
4.CFD MODEL
The amount of UWS injected into gas stream is set to produce a stoichiometric amount of ammonia inside the converter. Due to the toxicity and handling problems of ammonia, the non toxic and commonly available reducent urea is used, and is injected in front of the SCR converter. The present study allows to judge different SCR exhaust system configurations with respect to conversion and local distribution of reducing agent. For our study emphasis is given to on evaporation followed by hydrolysis and thermolysis of UWS which are contributing for formation and distribution of ammonia. The simulation is done considering the gas phase reaction module of Fire v8.3 to characterize the ammonia distribution along entry to the SCR.
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Inlet 
Homogeneous reactions 
Outlet (rear) 
Location of the injector
Figure. 2 Typical SCR system for CFD study
Table 1: Properties of Urea Water Solution
Exhaust 

Exhaust temperature 

Wall temperature 
300 K 
Flow rate 
0.23575 kg/sec 
Spray 

Injection velocity 
5 27 m/s 
Injection temperature 
293 K 
Injection mass in the SCR domain 
0.4gms 
5.RESULTS AND DISCUSSION
Spray Validation: To evaluate the influenc e of varying injection velocities, CFD simulations are done for injection UWS of 0.4gms in SCR domain for 0.4 secs from an orifice of 0.1mm outer diameter and at various injection velocities of 5 27m/s with average particle sizes of
5
Figure. 3 Variation of droplet diameter at 623K after 0.4sec
water 
0.0805 




5m/sec 









0.08 











10m/sec 











0.0795 




15m/sec 



of 







0.079 




20m/sec 



fraction 











27m/sec 



0.0785 











673K 



0.078 







Mass 








0.0775 


















0.077 








0.0765 

















0 
0.2 
0.4 
0.6 
0.8 
1 
Residence time sec
Figure.4 Variation of mass fraction of water with residence time at various injection velocities
water 
0.088 




8.3m/sec 

















0.086 




10.8m/sec 











0.084 








of 

















fraction 
0.082 







0.08 








Mass 
0.078 

















0.076 

















0 
0.2 
0.4 
0.6 
0.8 
1 
Residence time, s
Figure. 5 Variation of mass fra ction of water with residence time for two different exhaust gas velocities at UWS injection velocity 27m/sec at 673K
5.1 Droplet Evaporation Characteristics
Some studies have been done on droplet evaporation at different temperature for the droplet sizes higher than the droplet which are really seen in SCR applications [23].Main objectives of our study are to understand the evaporation characteristics of UWS droplet in various ambient temperatures numerically for stationary droplet. So far, to our knowledge, there have been few useful experimental data capable of quantifying the evaporation of UWS droplet over a wide range of temperatures for moving droplets. As typically appeared in the evaporation process of multicomponent fuel droplet or emulsified mixture droplet, the phenomenon of violent droplet fragmentation which is often referred to as micro explosion is also observed during the evaporation of UWS droplets at elevated temperatures[23]. More volatile component trapped in droplet interior due to diffusional resistance can be heated beyond local boiling point and hence undergoes internal superheating. This may eventually lead to the onset of homogeneous nucleation, whose extremely rapid rate of gasification causes intense internal pressure
Figure 6. A sample photograph of evaporating UWS Droplet [23]

1.1 



Simulated 







1 



Experiment 




al 







2(mm2/mm2) 
0.9 



373K 





0.8 











i 





2/D 
0.7 




o 





D 






0.6 
a 










0.5 





0 
20 
40 
60 
80 



t/D 2(sec/mm2) 





i 



1.2 




Simulated

1 





Experimental 











) 
0.8 






423K 

2(mm2/mm2 









0.6 



















i 









2/D 
0.4 








Do 










0.2 










b 


















0 



















0 
20 
40 
60 
80 
100 






t/D 2(sec/mm2) 










o 



6

1.2 












Simulated 


1 




Experimental 









0.8 




473K 

) 







2(mm2/mm2 







0.6 







0.4 







i 







2/D 















o 







D 








0.2 








c 






0 







0 
50 
100 
150 
200 
250 
300 




t/D 2(sec/mm2) 







i 



Figure
As shown in Fig
Thermolysis of the droplets: Once

0.082 





0.081 



300DEG573K 






of water 
0.08 



350DEG623K 





0.079 



400DEG673K 

fraction 





0.078 











Mass 
0.077 











0.076 





0.075 





0 
0.2 
0.4 
0.6 
0.8 
Residence time, s
Figure 4. Variation of mass fraction of water with residence time





573K 








Concentration 




623K 






673K 



















3 






NH 













0.00E+00 




a 








0 
0.2 
0.4 
0.6 
0.8 
1 
Residence time, s







573K 

















of HCNO 






623 K 








673K 
























fraction 






















Mass 











































b 















0.00E+00 























0 
0.2 
0.4 
0.6 
0.8 
1 
Residence time, s
7
5.2 Spray Wall Interaction
Birkhold et al[8] developed spray wall interaction model for UWS and which Spray impingement on hot surfaces, can lead to a better spatial distribution of the reducing agent due to thermal breakup. This also yields better conversion to ammonia, because small droplets with an enha nced heat and mass transfer are generated. Additionally heat is transferred from the hot surface to the droplets durin g contact and accelerates evaporation. As the film is transport ed downstream in regions with less spray impingement, the evaporation of water from the film leads to higher urea concenntrations. After evaporation of water is completed, thermolysis of urea begins in these areas. Spray impact also results in cooling of surfaces and can lead to wall film formation if the surface temperature decreases below a critical value. The critical transition temperature for UWS is determined within this study. Spray impact also results in cooling of surfaces and can lead to wall film formation if the surface temperature decreases below a critical value. The influence of flow conditions , exhaust tube properties and spray parameters on the film for mation can be evaluated with the developed model.. The spray wall deposition behavior is monitored using 3 major parameters of wall deposition namely wall film deposition, film deposition area and evaporated mass from the wall.
Wall deposition: The simulated results obtaine d for total film mass with respect to residence times are compared at 573K and 623K .The wall film deposition occurs at higher rates at lower temperature, due slow evaporation of UW S droplets and thermal decomposition. However the film for mation at later stages found to proceed at same rates for bot h temperatures 573K and 623K.Film deposited at lower te mperature will undergo further evaporation and thermolysis thereby showing similar trend as that of higher temperature at later stages








mass,kg 














film 
573K 


623K 










Total 

























0 

















0 
0.1 
0.2 
0.3 
0.4 
0.5 





Residence time,s 



Figure. 5 Variation of total film mass with residence time
Film deposition area: It is evide nt from the Regime map for

10 






9 



8 


area,cmÂ² 
7 


6 


5 
623K 



Film 
4 



3 






2 



1 
573K 


0 




0 
0.1 
0.2 
0.3 
0.4 
0.5 


Residence time,s 



Figure 6. Variation of Film area with 
residence time 
Evaporated mass: The deposited UWS over the surface evaporates; the evaporation rate aries with film thickness and the temperature. The simulated results of evaporated mass are compared at temperatures 573 K and 623K. (Fig.7). More quantity of film mass getting eva porated at lower temperature compared to that at higher te mperatures since more mass accumulates at lower temperatures in the form of film.















































mass,kg 


































































































































































Evaporated 








623K 
















































573K 















































































































































































0 







































































































































































0 
0.1 
0. 2 





0.3 
0.4 


0.5 







Residen ce time,s 








Figure.7 Variation of evaporated mass with residence time
8
ACKNOWLEDGMENT
Authors would like to thank Department of Mechanical Engineering of Canara Engineering College, Manipal Institute of Technology and NITK Surathkal for the support to write this paper.
NOMENCLATURE
a thermal conductivity
Aarea
,Spalding numbers heat capacity,
Cdrag
Ddiameter,
g 
gravity 
h 
heat of reaction 
h 
specific enthalpy, 

Lewis number 
m 
mass, 
pÌ‡ 
mass flow 
pressure 

Q 

Ë™energy flux

Nusselt number 

Re 
Reynolds number 

qË™ 
specific energy flux 

r 
radius, 

Sh 
Sherwood number 

t 
time, 

T 
temperature, 

u 
velocity, 
) 
w 
dimentionless radius, (r/ 

vapour mass fraction 

Y 
mass fraction 

Greek symbols
Î±heat transfer coefficient
heat conductivity,
Ïdensity
diffusion coefficient,
Subscipts
âˆž ambient
d,g droplet,gas
l,vap 
liquid, vapor 
ref reference
D drag
[ â„ ]
[m 2]
[ â„ K]
[m]
[m/s] [J/mole][ â„ ]
[k[â„kg]
[Pa]
[W]
[W/m[ 2] m]
[s] [K] [m/s]
[W/m2/K] [W/m K] [Kg/[ â„3]
g gas phase
Superscipts
ï€ªcharacteristic
6.CONCLUSION
In the present work, simulation is done for evaporation characteristics in UWS injection and spray wall interaction. The simulated results of single droplet evaporation at various ambient temperatures are compared with the experimental results of Wang et al[23]. Droplet evaporation at various injection velocities are compared and found increased evaporation for lower injection velocities. As microexplosion occurs at higher temperatures the numerical results are able to predict the droplet fate unless some change in boundary conditions or using user defined functions.The three parameters of the film deposition wall film deposition, film deposition area, evaporated mass from the wall are taken to account to study the behavior of wall film deposition. Thus the formation of a wall film can be calculated precisely as well as the secondary breakup of droplets at the wall. The spray wall deposition found to be varying with temperature and residence time, the variation seems to follow the kunkhe spray wall interaction map. The rebound and thermal breakup of the droplets significant factors at elevated temperatures which lead to depletion of spray wall thickness. The spray film formation at later stages found to proceed at same rates for both temperatures.
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[1]M. Koebel, M. Elsener, and T Marti.
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urea  
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Vienna, Austria, 2005 


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[9]J.Y. Kim, S.H. Ryu, and J.S. Ha. Numerical prediction on the characteristics of
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[11]N. W. Wruck. Transientes Sieden von Tropfen beim Wandaufprall. PhD thesis, RWTH Aachen, 1998
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of
[16]Buchholz, â€œEinsatz von festem Harnstoff als Reduktionsmittel fÃ¼r die
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[18]Verein Deutscher Ingenieure, editor.
BerechnungsblÃ¤tter fÃ¼r den WÃ¤rmeÃ¼bergang.VDI Verlag,DÃ¤sseldorf, 6th edition, 1991.
[19]Chr. Mundo, M. Sommerfeld, and C. Tropea. Dropletwall collisions: Experimental studies of the deformation and
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[22]L. Jaeger, J. NÂ´yvlt, S. HorÂ´aË†cek, and J. Gottfried.Viskosit Â¨aten von Harnstoffwasserl Â¨osungen. Collection Czech. Chem. Commun.,
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ACKNOWLEDGMENTS
Authors would like to thank Department of Mechanical Engineering of Canara Engineering College, Manipal Institute of Technology and NITK Surathkal for the support to write this paper.
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