Choice of urea-spray models in CFD simulations of urea-scr systems
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1 Choice of urea-sray models in CFD simulations of urea-scr systems Andreas Lundström & Henrik Ström Cometence Centre for Catalysis / Chemical Reaction Engineering Deartment of Chemical Engineering and Environmental Science Chemical Reaction Engineering Chalmers University of Technology S Göteborg Sweden andreas.lundstrom@chalmers.se and henrik.strom@chalmers.se
2 Diesel exhaust Heavy-duty diesel engines: high efficiency and cometitive fuel cost Emission legislation being sharened NO x : adverse effects on health and environment Otimize combustion with resect to articles remove NO x in the aftertreatment system Ammonia gives the best SCR erformance 2/24
3 The urea-scr system AdBlue: 32.5-weight% urea in water Thermal decomosition of urea: Hydrolyzation of isocyanic acid: 3/24
4 Outline 1. The investigated urea-scr system 2. Eulerian-Lagrangian modeling in CFD - Force balance - Sub-models for the discrete hase - Heat and mass transfer - Results are influenced by modeling choices 3. Volume of Fluid modeling in CFD - Simulation setu - Comarison of drolet distortion 4. Influence of material data quality 5. Summary 6. Future work 4/24
5 The investigated urea-scr system Single-hase AdBlue injector Drolet size range: µm Pulsating injection Sauter mean diameter: ~ 120 µm Hollow cone sray Mean diameter N : ~ 90 µm Water evaoration and urea decomosition is modeled Drolets hitting walls are logged and removed i.e. no wall-film modeling 5/24
6 Eulerian-Lagrangian modeling in CFD dxi = u i, dt du 18µ C Re m = m u u + F ( ) i, D 2 i, i x dt ρ d 24 External forces to include in the Lagrangian force balance equations (F x ) Sub-models for drolet drag coefficient (C D ), including effects of drolet distortion Sub-model for turbulent disersion of drolets and its sensitivity to the choice of turbulence model Fluent, Inc. 6/24
7 Overview of external forces FORCE DUE TO FORMULA NEGLECT Gravitational force Gravitation F = m g g x ( ρ ρ ) ρ When τ d is small Virtual mass force Acceleration of the surrounding gas d F = C ρ u u u dt ( ) vm vm g d d g ρ d >> ρ g Brownian motion Collisions with molecules F Brownian 216µσT = ξ π d ρ C t 5 2 c Kn < Lift force Velocity gradient 1 F = ρ U πa C L f c L? Rotational force Rotation of drolet 1 F = ρ U πa C L+ R f c L+ R When the lift force is neglected Termohoretic force Temerature gradient F T 2 π µ s( t ) ( 1 3 Kn)( Kn) 6 d C K + CKn 1 T = ρ + C + K + C T x m t? History force Build-u of boundary layer at d t ( U f U ) acceleration 2 FHistory = 6r d πρ f µ τ f dτ t τ? t 0 7/24
8 L ( Re, ) C α = K α + Kα * *0.9 * Estimating lift force effects 1 F = ρ U πa C 2 L 2 2 L f c L ( Re, ) C α = K α + Kα * α c * *0.9 * a U = K K = f U y ( ) ; 0, 1 Re Kurose & Komori (J. Fluid Mech. 384, 1999) The lift force exerienced by drolets within the system is at least two orders of magnitude smaller than their current drag force. Neglecting lift force is effects is thereby justified. 8/24
9 ( Re, ) C α = K α + Kα L * *0.9 * Estimating thermohoretic effects F T = ρ 2 π µ s( t ) ( 1 3 Kn)( Kn) 6 d C K + CKn 1 T + C + K + C T x m t Kn = 2λ d K= k k C s, C t and C m are constants Talbot et al (J. Fluid Mech. 101, 1980) Thermohoretic effects are more ronounced at lower gas flows, but the thermohoretic force is small (< 5%) comared to the drag force for most (> 95%) of the drolet s lifetime within the system. 9/24
10 Estimating history effects d t ( U f U ) 2 FHistory = 6r d πρ τ f µ f dτ t τ Crowe, C. T. Multihase Flow Handbook (2006) t 0 History effects are very sensitive to other modeling choices! 20% 15% Relative imortance * 10% 5% 0% base case + DRW base case + DRW HIGH GAS FLOW LOW GAS FLOW Turbulent disersion of drolets will affect imortance of the history force. *Percent of injected arcels exeriencing F history /F drag higher than 10% for more than 10% of their time in the domain DRW = Discrete Random Walk (model for turbulent disersion of drolets) 10/24
11 Sub-models for the discrete hase Drag coefficient Sherical drag law: C Dshere, 24 1 = 1+ Re Re 6 23 ( Re 1000) Dynamic drag law: ( ) C = C + C C y D, dynamic D, shere D, disk D, shere TAB model: d y C ρ u C σ C µ dy dt C r r r dt 2 2 F g k d l = y b ρl ρl ρl 11/24 Turbulent disersion ( ) = + () u t u u t u = ζ u t 2 k τ e = CL log ( r) ε = min ( τ, t ) L e tcross = τ ln 1 τ u u interaction e cross Crowe et al (CRC Press, 1998)
12 Drolet heat and mass transfer (d = 30 µm) Stage of evaoration or decomosition A. Evaoration of water B. Heating of urea C. Decomosition of urea (at constant temerature ~ 425 K) Heat and mass balances dt dm mc = ha( T T) + h dt dt Ni = kc( ci, s ci, ) s va dt mc = ha T T dt ( ) s ( ) ( ) d d 4k c T T = ( Red ) ln 1+ dt ρ c d h,, decomosition 12/24
13 Eulerian-Lagrangian modeling results u g 70 m/s T g = 400 C Mass fraction of water in drolet Mass fraction of ammonia in ie 13/24
14 Results are influenced by model choices HIGH GAS FLOW CASE Decomosition efficiency: 21.4% Wall hit: 4.4% (u g 70 m/s, T g = 400 C) Switching to a dynamic drag law decreases wall hit with 43% Simulating turbulent disersion increases wall hit with 37% Using both the dynamic drag law and turbulent disersion increases wall hit with 47% LOW GAS FLOW CASE (u g 25 m/s, T g = 300 C) Decomosition efficiency: 32.9% Wall hit: 20.9% Simulating turbulent disersion increases decomosition efficiency with 14% 14/24
15 Exlanations for model choice sensitivity Dynamic drag coefficient seeds u drolet adatation to the gas flow large effect on wall hit at high gas flows Turbulent disersion will increase heat and mass transfer rates at low relative velocities increases decomosition efficiency at low gas flows Turbulent disersion redicts small drolets/urea articles on injector side of ie will be thrown towards the wall increases extent of wall hit and redicts different variety of drolet tyes at the walls Drolet roerties at wall hit crucial for wall modeling! 15/24
16 Turbulence model Pie Y-coordinate [m] /24 RSM u (lane) 0.08 RSM v (main gas flow direction) RNG k-e u v Turbulent fluctuating velocity [m/s] Turbulent fluctuating velocity across the ie cross-section in a fully develoed turbulent flow for a high gas flow case (u g 75 m/s) in a straight exhaust gas ie Changing from RNG k-ε to a Reynolds stress model will increase wall hit with 9.6% for a straight ie with a high gas flow ( 70 m/s).? Modeling turbulent disersion increases the sensitivity to the choice of turbulence model!
17 Volume of Fluid modeling Used in conjunction with Eulerian-Lagrangian modeling to give a detailed resolution of individual drolet behavior Heat and Momentum transfer May only be used on a small number of drolets 17/24
18 Comarison of drolet distortion VOF and TAB simulations for 50 and 100 (µm) drolets in a 70 (m/s) gas flow 50 (µm) 100 (µm) VOF and TAB simulations agree well in redicting drolet oscillation frequency and amlitude 18/24
19 Comarison of drag forces VOF, Dynamic- and Sherical-drag law simulations of 300 and 100 (µm) drolets in 70 (m/s) gas flow under constant material roerties Dynamic drag law gives a better descrition of real drolet drag than the sherical drag law. 19/24
20 AdBlue material data The need for good data in simulations? 80 Kinematic viscosity of Urea (cst) Measurements of: viscosity density surface tension Temerature [ o C] mass fraction of Urea [%W] 20/24
21 Results of changed viscosity Drolet distortion during evaoration: D = 200 (µm) in 75 (m/s) flow during 0.5 % of total evaoration time a) Comarison between UW solution viscosity and using a constant viscosity of (Pas) b) Comarison between UW solution viscosity and using ure water viscosity TAB modeling results of drolet oscillations deends on material data 21/24
22 Effects on drag Drag coefficient redicted using TAB and sherical drag law models for: UW-solution with roerty deendent or constant viscosity Dynamic drag law alicable for ~0.3% of total evaoration time Prediction of drag is insensitive to changes in material roerties 22/24
23 Summary Choice of models influences the results! Lagrangian force balance Drag force and gravitational force History force? Drag coefficient TAB model rovides good descritions of drolet distortion Turbulent disersion Large effects Sensitivity to the choice of turbulence model Material data Material data quality is of minor imortance when redicting drag 23/24
24 Future work Continued work comaring evaoration rates for VOF and Eulerian-Lagrangian modeling Develoment of urea-decomosition kinetics Wall-drolet interaction modeling 24/24
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