A Molten Solid Approach for Simulating Urea-Water Solution Droplet Depletion

Transcription

1 ILASS Americas 7th Annual Conference on Liqui Atomization an Spray Systems, Raleigh, NC, May 015 A Molten Soli Approach for Simulating Urea-Water Solution Droplet Depletion Shaoping Quan* 1, Mingjie Wang 1, Scott Drennan, Joshua Strotbeck 1, an Ambarish Dahale 1 Convergent Science, Inc Enterprise Lane, Maison, WI USA 1619 E. Common St. Suite 104, New Braunfels, TX 7813 USA Abstract Engine emissions regulations toay have essentially require the use of NOx reuction aftertreatment systems for on an off-roa iesel engines. Injection of Urea-Water Solution (UWS) into the exhaust system is a promising approach to reuce nitrogen oxies (NOx) emitte from iesel engines. The etaile unerstaning of the epletion process that converts UWS to corresponing gases is essential for esigning an efficient UWS injection base SCR systems. In this work, we implemente a reliable numerical moel into CONVERGE to simulate the epletion of UWS roplets. A multi-component roplet spray injection moel is use for injecting UWS roplets. The time rate of change of the roplet raius ue to water evaporation is moelle by the Frossling correlation, while the time rate of change of the roplet raius ue to urea ecomposition is compute using an Arrhenius correlation. A heat transfer equation between the rop an the gas phase is use to moel the heat balance uring the evaporation an/or ecomposition. This moel was valiate against a number of numerical an experimental results with goo agreement. The moel results show excellent agreement with the tren observe in experiments for urea-water solution roplet evaporation, i.e. water evaporation ominates uring the early stage while urea ecomposition plays significant role at the late stage when the roplet temperature is high, is very well preicte. Corresponence shoul be aresse to Shaoping Quan at shaoping.quan@convergecf.com

2 Introuction An efficient way to reuce nitric oxies, i.e. NOx, in exhaust systems emitte from iesel engine combustion is using ammonia as an agent in selective catalytic reuction with the following catalytic reaction. 4NO + 4NH + 3O > 4N + 6H O (1) 3 However, because ammonia is gaseous, poisonous an also explosive, urea-water solution (UWS) is usually use to generate the gaseous ammonia in the SCR system to reuce NOx emission for greater convenience an safety in storage an transport. The challenge face by a Urea/SCR system esigner is to achieve a goo istribution of ammonia upstream of the SCR catalyst in as short a istance as possible without causing urea eposition. Hence, atomization an evaporation of UWS is critical in Urea/SCR system performance. Urea-water solution is injecte into upstream of the SCR catalyst. The liqui UWS then goes through primary an seconary breakup an becomes roplets; the roplets interact with the hot exhaust gas an evaporate. The UWS roplets finally are converte into water vapor, gaseous ammonia an iso-cyanic aci. There are two major approaches that were propose in the literature to moel the evaporation an the ecomposition of UWS roplets. These two approaches iffer in how they treat the conversion of urea to NH3 an HNCO. The multi-component approach treats the urea in the UWS as a liqui that evaporates an then unergoes gas phase ecomposition. The molten soli approach treats the urea in the UWS as a soli that ecomposes. These approaches have been reviewe an iscusse by others[1-]. One approach believes that water evaporates first from UWS an then the leftover soli urea unergoes thermal ecomposition [1,3-5]. For the ecomposition, there are two ways [4], i.e., 1) the soli urea unergoes evaporation to gaseous urea, an then the gaseous urea ecomposes into gaseous NH3 an HNCO; or ) the soli urea irectly ecomposes into gaseous NH3 an HNCO. This approach is often calle the molten soli metho. The other approach uses a multicomponent concept in which urea an the water of the UWS roplet unergo evaporation at same time with ifferent evaporation rate, an the liqui urea can be irectory converte to gaseous NH3 an HNCO by evaporation [, 6]. This metho is usually calle the multi-component urea evaporation approach. The above two approaches were use wiely to moel urea-water solution interaction with the exhaust gas. Kim et al [7] employe the molten soli approach an simulate the spray injection of urea-water solution, an compare their numerical results with their experimental ata. The comparison showe goo agreement after tuning the Arrhenius parameters for urea ecomposition. Using the molten soli metho, Birkhol et al [4] numerically simulate the evaporation an ecomposition of a UWS roplet with an initial iameter of 70µm an foun that the evolution of the roplet iameter following the D rules. The slopes for evaporation an ecomposition are ifferent. The water evaporates much faster than the urea ecomposes. These authors then valiate their numerical approaches by comparing their results against the observations by Kim et al [7] for the urea-water solution injection case. Nayak [8] compute the evaporation an ecomposition of a single stationary roplet using the molten soli scheme, an the simulation results qualitatively agree with the experimental ata by Wang et al [5]. Nayak further stuie the spraywall interaction incluing urea eposition in film an on the wall. Birkhol et al [9] employe the evaporation approach by assuming the vapor pressure of the urea being an exponential function of the roplet temperature to simulate the injection of UWS an the spray wall interaction. Their simulation results agree well with the experiments by Kim et al [7] an their own experimental ata after tuning the kinetic parameters. Using evaporation law for each component of the bi-component UWS roplets, Yi [10] evelope a multi-imensional CFD moel to simulate the injection an mixing of urea-water solution in SCR systems. Abu-Ramanan et al [] implemente a numerical moel to simulate the epletion an ecomposition process of urea-water solution roplets. The urea epletion was moele using two approaches, i.e. the evaporation an the molten soli. These authors showe that the vaporization approach preicte much better results than the molten soli metho oes. Abiin et al [6] evelope a semi-1d approach an couple this approach with a 3D moel to simulate a full SCR system. UWS roplet epletion was moele by vaporization an molten soli schemes. However, these authors showe that the results obtaine by the molten soli approach showe better agreement with the test ata. In this paper, we focus on implementing a molten soli base approach into the multi-imensional CFD software CONVERGE [11] to simulate the evaporation an ecomposition of UWS an valiating the approach against the existing numerical an/or experimental results. Overview of Droplet Injection an Coupling between Gas an Liqui Phases The urea-water solution is injecte or introuce to the simulation using a multicomponent approach. For all of the simulations reporte in this paper, ABlue (contains 3.5% urea an 67.5% water) is use. The same kin of solution was also use in the work one by

3 Birkhol et al [4] an Wang et al [5]. In our Lagrangian particle tracking metho, the momentum coupling between the gas phase an the iscrete phase is through the rag forces, an popular rag moels have been implemente, such as the perfect sphere an ynamic rag moels. The governing equations, such as conservation of momentum, species, an energy are solve using a PISO (Pressure Implicit with Splitting of Operator) base algorithm. A secon orer central scheme is use to iscretize the convection an iffusion terms. The resulte linear system is solve with an SOR (Successive Over-Relaxation) metho. The etails of the numerical schemes can be foun in [11]. In our scheme, the water of UWS roplet evaporates in a way which is ifferent from the way that urea ecomposes. Therefore, in the following sections, we will escribe the two ifferent steps. Water Evaporation of the roplet The Frossling correlation [1] is use to moel the raius change rate of the roplet ue to evaporation of the water: r t ρgd ρ r l B Sh =, () where r is the roplet raius, ρ g is the air ensity, ρ l is the liqui ensity, an D enotes the mass iffusivity of the water vapor in the air. The parameter B is efine as B Y Y =, (3) 1 * 1 1 * Y1 * where Y1 is the vapor mass fraction at the roplet surface, an Y1 is the vapor mass fraction. The Sherwoo number is efine as 1/ 1/3 ln(1 + B ) Sh = ( Re Sc ), (4) B where Re is the roplet Reynols number base on the air properties an the roplet raius, an Sc is the Schmit number of air. The vapor mass fraction at the roplet surface is compute as M * CH n m Y1 =, (5) pgas MC 1 nh + M m mix pv where p gas is the air pressure an p v is the vapor pressure, M is the molecular weight, an the subscript mix stans for the mixture. Urea Thermal Decomposition of the roplet Urea ecomposes into ammonia an isocyanic aci as (NH ) CO NH +HNCO. (6) 3 In the molten soli approach, this ecomposition is moelle by an Arrhenius formula [4]: m ( Ea/ RT ) = π r Ae, (7) t where m is the roplet mass, D stans for the roplet iameter, R is the universal gas constant, an T enotes the roplet temperature. Equation (7) can be written as 4πρ r 3 t 3 ( Ea/ RT ) = π r Ae. (8) The above equation can be simplifie to r t ( Ea/ RT ) 1 Ae =, (9) ρ r where A is prefactor an Ea enotes the activation energy. For the simulations in Birkhol et al [4], A=0.4 kg/sm an Ea= J/kmol are ientifie from regression analysis of the experimental ata. As the ecomposition of urea only become evient when the temperature is above 45K [4], the ensity of urea is use for ρ in the above equations. Heat Transfer to the Droplet The roplet temperature change ue to the heat transfer from/to the gas phase can be moelle by two approaches. The first one assumes that the roplet can be heate up instantaneously to a uniform temperature. This assumption usually applies to small-size roplet, i.e., the roplet iameter is less than several hunre micrometers. The heat transfer equation is written as T Cm = π rk gnu( Tg T) t (10) m m + Hvap + Hcmp t vap t cmp where C is the specific heat capacity of the rop, an k g is the air/gas thermal conuctivity. It shoul be note that the heat exchange ue to the water evaporation is calculate base on the mass change ue to the evaporation, while the mass change ue to urea ecomposition is use for the heat loss calculation ue to thermal ecomposition. The Nusselt number is calculate by 1/ 1/3 ln(1 + B ) Nu = ( Re Pr ), (11) B where Pr is the Prantl number. Equations (), (9) an (10) are solve in a couple an implicit fashion until a converge solution is reache. For large roplet, the above assumption may introuce observable errors. A heat equation for spherically symmetric evaporating roplet with no recirculation [13] is use, i.e.

4 T 1 T ρc = kr t r r t, (1) with a bounary conition for heat transfer at the surface (neglecting the raiative heat flux), T k = h Tg T( Rt,) + t ρ H r= R r + ρ H vap cmp t vap r t cmp, (13) where r is the istance from the roplet centroi, k is the roplet thermal conuctivity, an h is the convection coefficient between the surrouning gas an the roplet. The parameter h is calculate using the Nusselt number (Equation 11). Equation (1) with the bounary conition equation (13) is solve numerically using a finite volume metho by iscretizing the roplet into N number of spherical shells of equal volume. Since the roplet raius is a function of time, Leibnitz s rule for ifferentiation uner integral sign is use when applying finite volume iscretization to the time erivative term for the outermost shell. The final form obtaine by volume integrating the governing equation over a typical shell is given by: 3 3 r r 1 k T T T = r r1 t 3 ρ C r r= r r r= r1,(14) r + rt ( r,) t t where r 1 an r are the inner an the outer raii of a spherical shell, an r is a function of time only for the outermost shell (where r =r ). The time integration scheme is fully implicit where the time step is the same as the one in the flui solver. The roplet is re-iscretize every time step to account for shrinking size ue to evaporation an ecomposition. Numerical Results an Valiations To valiate our scheme, the single UWS roplet evaporation an ecomposition case by Birkhol et al [4] is simulate. The roplet has an initial iameter of 70 µm, an initial temperature of 300 K. The roplet sits in a box fille with gas (3% of O an 77% N ). The gas pressure is 0.11MPa an the temperature of the gas is 673 K. The gas is at still. For this simulation, the prefactor an the activation energy from Birkhol et al [4] are use. As the roplet is small in size, the first approach for heat transfer to the roplet is use. Figure 1 shows a comparison of the evolution of the roplet surface area ( D ), which is non-imensionalize by the initial roplet surface area ( D ), between our results an the results by Birkhol et al [4]. In the figure, the black ash-otte line represents the result 0 from CONVERGE using soli urea vapor pressure from [14] with some moification to account for temperature effects. It can be seen that our simulation preicts two processes, i.e., evaporation an thermal ecomposition which is evience by the two istinct slopes of the ata lines. This agrees well with the preiction by Birkhol et al [4]. However, it is also seen that the result that uses urea soli vapor pressure preicts faster ecomposition. To further investigate the ifference, the roplet temperature is isplaye in Figure. Again, we can see that the trens are very similar, i.e. the roplet was heate up very quickly at the very early stage; then the roplet maintains a relatively constant temperature for a relatively long perio; an then the roplet was heate up very quickly to a temperature very close to the surrouning gas temperature; then the temperature is kept as a constant. Combining figures (1) an (), we can see that the water evaporation ominates the early stages where the temperature oes not vary much, an after the water totally evaporates, the urea starts thermally ecomposing. The final steay temperature of the roplet is ifferent for the two simulations. We believe the ifference is because of the vapor pressure use for the simulation, as the Nusselt number (equation (11)) is a function of the vapor pressure. To further valiate our schemes, the simulations are performe for the experimental case in Wang et al [5]. As the roplet iameter in Wang et al [5] is on the orer of 1 mm, the secon approach for computing the heat transfer balance is employe. The vapor pressure from [14] with moifications which account for the temperature effects is use for all the simulations. In orer to properly valiate our schemes, a curve fitting is conucte to obtain the prefactor A an the activation energy Ea using the ata from the experiments [5]. To perform the fitting, equation (9) is rewritten as r r 0 ρ = Ae t r 0 ( Ea/ RTg ) [14] Taking the natural logarithm of the above equation, we get, Ea ln( ρku) = ln( A) Tg R where k u is the slope for each case in Wang et al [5] for a temperature range from 473K to 673K. The fitting gives A=0.16 kg/sm an Ea= J/kmol.

5 are two stages, i.e., the water evaporation stage that occurs first an the urea thermal ecomposition stage that happens later. Our simulations agree well with the experiments for the water evaporation stage. Although the slope for the urea ecomposition stage matches closely with the results of the experiments, the transition point from the water evaporation stage to the urea thermal ecomposition stage has observable ifferences. The transition of the experiments is earlier than one of the simulations. This might be of some water trappe in the experiments. The mechanism for the water entrapment is not clear an is not moelle in the simulations. Figure 1. Evolution of the UWS roplet surface area. The black ash-otte line is the results using the soli urea vapor pressure from [14]. Figure 3. Comparison of evolution of the UWS roplet surface area for the cases with T g=373 K, r 0= mm, an T g=43 K, r 0=0.379 mm between simulations an experiments by Wang et al [5]. Figure. Temperature evolution of the cases in figure 1. Figures 3-5 show the comparison of the evolution of the UWS roplet surface area between our simulations an the experiments by Wang et al [5]. For lower temperature, i.e. the surrouning gas temperature is less than 45 K, the roplet mainly unergoes water evaporation. This trens matches with the experimental preiction. For the case with T g=373 K, r 0= mm, our simulations uner-estimates the evaporation, while for the cases with T g=43 K, r 0=0.379 mm, our simulation agrees well with the experiment. It can be seen that urea ecomposition is very minimal after t/ D 0 > 80 (s/mm ). For higher gas temperature cases, we clearly can see there Figure 4. Comparison of evolution of the UWS roplet surface area for the cases with T g=473 K, r 0=0.435 mm, an T g=53, r 0=0.485 mm between simulations an experiments by Wang et al [5].

6 Figures 6-7 emonstrate the evolution of the roplet surface temperature for all of the cases in Figures 3-5. It can be seen that for cases with a higher gas temperature, the roplet surface temperature increases sharply at the early stage, an then oes not vary much, an then increases abruptly to close to the gas temperature. These changes in temperature correspon to the two stages of the UWS roplet iminishing. Figure 5. Comparison of evolution of the UWS roplet surface area for the cases with T g=573 K, r 0=0.460 mm, an T g=63, r 0= mm between simulations an experiments by Wang et al [5]. Figure 6. Surface temperature for the above UWS roplet T g=373 K, T g=43 K, an T g=473 K. Conclusion This paper presents a numerical metho for simulating the evaporation an/or ecomposition of a urea-water solution roplet. The roplet is initialize using a multicomponent approach, i.e., containing a portion of urea an a portion of water. The evaporation of water is moelle using the Frossling correlation, while the ecomposition of the urea is compute using an Arrhenius formula, which is often refer as the molten soli approach. The roplet temperature, require for the evaporation/ecomposition moel, is compute using two ifferent approaches. If the roplet size is smaller than a critical value, then the roplet temperature is assume constant throughout its volume. Otherwise it is etermine by solving a 1D heat iffusion equation. A number of simulations of iminishing of a single UWS roplet have been performe an compare with the available experimental an numerical results, an the results agree well. For higher gas temperatures, i.e., greater than 45 K, the epletion of UWS roplet occur at two istinct stages: the early water evaporation stage an the late urea ecomposition stage. These two stages are evience by the abrupt slope change in the evolution of the UWS roplet surface area. Acknowlegement The author woul like to thank Eric Pomraning, Peter Kelly Senecal, Keith Richars, Meizhong Dai, an Katie Beutel for their comments an suggestions. References Figure 7. Surface temperature for the above UWS roplet with T g=53 K, T g=573 K, an T g=63 K. 1. Munnannur, A., an Liu, Z. G., Development an Valiation of a Preictive Moel for DEF Injection an Urea Decomposition in Mobile SCR DeNOx Systems, SAE Technical Paper Abu-Ramaan, E., Saha, K., an Li, X. G., Moeling of the Injection an Decomposition Process of Urea-Water Solution Spray in Automotive SCR systems, SAE Technical Paper , Yim, S. D., Kim, S. J., Baik, J. H., Nam, I. S., Mok, Y. S., Lee, J. H., Cho, B. K., an Oh, S. H., Decomposition of Urea into NH3 for the SCR Porcess, Inustrial & Engineering Chemistry Research, 43: , 004.

7 4. Birkhol, F., Meingast, U., Wassermann, P., an Deutschmann, O., Moeling an simulation of the injection of urea-water solution for automotive SCR DeNOx-systems, Applie Catalysis B: Environmental, vol. 70 pp , Wang, T. J., Baek, S. W., Lee, S. Y., Kang, D. H., an Yeo, G. K., Experimental investigation on evaporation of urea-water solution roplet for SCR applications, AIChE Journal, 55: , Abiin, Z., Das, K., an Roberts, C., 3D-Semi 1D Coupling for a Complete Simulation of an SCR System, SAE Technical Paper, , Kim, J. Y., Ryu, S. H., an Ha, J. S., Numerical preiction on the Characteristic of Spray-Inuce Mixing an Thermal Decomposition of Urea Solution in SCR System, Technical Conference of the ASME Internal Combustion Engine Division, Nayak, N. S., The Evaporation an Spray Wall Interaction Behavior of Urea Water Solution (UWS) in Selective Catalystic Reuction (SCR) Systems of Moern Automobiles, SAE Technical Paper , Birkhol, F., Meingast, U., Wassermann, P., an Deutschmann, O., Analysis of the Injection of Urea-water solution for Automotive SCR DeNOx- Systems: Moeling of Two-phase Flow an Spray/Wall-Interaction, SAE Technical Paper, , Yi, Y. Development of a 3D numerical moel for preicting spray, urea ecomposition an mixing in SCR systems, SAE Technical Paper Richars, K. J., Senecal, P. K., an Pomraning, E.,CONVERGE (Version.) Manual, Convergent Science, Inc., Maison, WI, Amsen, A. A., O Rourke, P. J., an Butler, T. D., KIVA-II: A computer program for chemically reactive flow with sprays, Los Alamos National Laboratory Report No. LA MS, Sazhin, S. S., Krutitskii, P. A., Guesev, I. G., Heikal, M. R., Transient heating of an evaporating roplet with presume time evolution of its raius, International Jouranal of Heat an Mass Transfer, vol. 54 pp , Avogaro.chem.iastate.eu/MSDS/urea.htm

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