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Effect of Spray-Exhaust Gas Interactions on Ammonia Generation in SCR Mixing Sections.

Introduction

Diesel engines in combination with modern charging and diesel injection systems feature constant high torque over a wide speed range and thus remain very popular among all types of internal combustion engines [1]. However, a drawback of diesel engines is the increased production of particulate matter and nitrogen oxides (N[O.sub.x]) caused by their combustion process [2]. Increasingly stringent emission standards and the new worldwide harmonized light duty test cycle (WHTC) with real driving emission measurements represent a major challenge for the development of diesel engines in the future, in particular for maintaining the diesel engine's positive characteristics, such as dynamic driving performance and fuel economy, while drastically reducing emissions [2-4].

For the reduction of N[O.sub.x], only a few of the theoretically possible methods are feasible for use in vehicles. Furthermore, the three-way catalytic converters that are installed in gasoline engines, in which N[O.sub.x] react with hydrocarbons and carbon monoxide at a very high conversion rate for [lambda] = 1, are thus unsuitable for lean-burning diesel engines. Two different systems for the reduction of N[O.sub.x] in diesel engines are being launched on the market at present. The N[O.sub.x] storage catalysts are primarily used for smaller engines, particularly in passenger vehicles, while selective catalytic reduction (SCR) systems are implemented in a range from middle-sized cars to commercial vehicles [5, 6].

Selective Catalytic Reduction of N[O.sub.x]

The applied reducing agent for N[O.sub.x] in SCR systems is ammonia (N[H.sub.3]). However, due to ammonia's toxicity and possible leaks in the tank and piping of SCR systems that could be classified as considerably harmful to the environment and humans, exclusively SCR systems with precursor substances are available or being developed. The European automotive industry reached an agreement in the 1990s to use a standardized 32.5 wt% aqueous urea solution according to DIN 70700 with the brand name AdBlue*, which is sufficiently chemically stable for environmental considerations [6]. The determining factors for the efficiency of SCR systems, for moderate reducing-agent consumption, and for meeting space requirements are sufficient ammonia generation and homogenization upstream from the catalytic converter [7, 8]. The individual steps of N[H.sub.3] generation from the dosing point to the catalytic converter are shown in Figure 1.

Consequent to the injection of urea-water solution (UWS), interactions occur between the droplets and the exhaust gas or wall. First, the water evaporates out of the UWS droplets, followed by the decomposition of urea and the formation of ammonia by thermolysis and hydrolysis before entering the catalytic converter [4, 8]. Possible interactions between the injected droplets and the mixing section wall can lead to wall film formation and unwanted solid depositions. Another drawback of wall film formation is that the reducing agent is not available at the time of injection, meaning that ammonia might be unavailable for N[O.sub.x] reduction or could cause ammonia slip if released at an inconvenient moment.

Spray characteristics have a considerable influence on ammonia generation and thus the efficiency of SCR systems. There are several dosing nozzles/systems available on the market, which basically differ in the number of nozzle holes, injection angle, discharge velocity, and droplet-size distribution. At present, only low-pressure dosing systems are available for application in SCR systems in passenger cars, which feature a droplet-size distribution with a Sauter mean droplet diameter (SMD) of 20 [micro]m to 200 [micro]m. Figure 2 illustrates the broad spectrum of available injection systems with regard to the droplet-size distribution. The discharge velocity of the droplets is 10 m/s to 50 m/s, the injection temperature varies from 303 K to 353 K, and the amount of injected UWS varies from 5 g/h to 120 g/h, contingent on the operation point of the engine. Depending on the employed dosing system, a static mixer can additionally be implemented in the SCR mixing section for better homogenization of the reducing agent ammonia upstream from the catalytic converter. [9-15].

The aim of this study is, on the one hand, to conduct an experimental investigation of the occurring physical and chemical phenomena during UWS injections and ammonia generation in SCR mixing sections. In particular, the focus will be on the decomposition of UWS droplets and wall impingement. On the other hand, the aim is to describe the observed individual steps of ammonia generation and the resulting evoked temperature change in SCR mixing sections. This consideration is of particular importance because the exhaust gas temperature considerably influences the SCR catalyst's temperature, which in turn has a major impact on the efficiency of N[O.sub.x] reduction. In a final step, the objective is to determine the necessary level of detail for simulations of SCR mixing sections by comparing the results of a strongly simplified case study with varying degrees of complexity. The gained results and the in this study composed mathematical framework could serve as a basis for future investigations (e.g., the implementation in CFD codes).

Ammonia Generation in SCR Systems Once the urea-water droplets are injected, water evaporates out of the droplet. The necessary heat is supplied by the exhaust gas through convective heat transport. Subsequently, the generation of ammonia from urea starts and generally occurs over two reactions: the thermolysis of urea and the hydrolysis of isocyanic acid [16]. Urea ((N[H.sub.2])[.sub.2]CO) is decomposed into gaseous ammonia and isocyanic acid (HNCO) during thermolysis with a noticeable conversion rate of urea at temperatures greater than 406 K [7, 17, 18], as shown in Equation 1. The isocyanic acid then reacts during hydrolysis with water vapor to form ammonia and carbon dioxide [7, 17], as in Equation 2.

[mathematical expression not reproducible] Eq. (1)

[mathematical expression not reproducible] Eq. (2)

However, gaseous isocyanic acid is stable in the presence of water vapor for several seconds and at temperatures up to 1000 K. Therefore,

the conversion of isocyanic acid to ammonia occurs almost exclusively in the presence of a catalyst [19, 20]. Concerning the reaction parameters for the thermolysis of urea, rather different suggestions can be found in the literature. Buchholz [21], Fang and Da Costa [22], and Brack et al. [23] have determined the decomposition of urea by means of thermo-gravimetrical analysis (TGA). Further proposals for thermolysis kinetics are made by Ostrogovich and Bacaloglu [24], Birkhold [25], Yim et al. [20], and Rota et al. [26]. The results are presented in Table 1.

In contrast to the thermolysis reaction parameters, the hydrolysis kinetics are widely understood, and different sources are in relatively strong agreement [16, 17, 20, 26]. For instance, Yim et al. [20], Wurzenberger et al. [17], and Rota et al. [26] have achieved independently of one another similar results for the description of the reaction parameters for hydrolysis, as shown in Table 2.

Formation of Undesired Species If the heat for the reaction is provided too slowly, the formation of undesired by-products can occur. Remaining urea can react with previously formed isocyanic acid to form biuret ([C.sub.2][H.sub.5][N.sub.3][O.sub.2]) at temperatures of 433 K, as in Equation 3. At temperatures greater than 466 K, biuret begins to decompose back into urea and isocyanic acid. The urea formed at this temperature is unstable and decomposes further to ammonia and isocyanic acid according to Equation 1 [18, 19].

[mathematical expression not reproducible]Eq. (3)

The production of cyanuric acid ([C.sub.3][H.sub.3][N.sub.3][O.sub.3]) and ammelide ([C.sub.3][H.sub.4][N.sub.4][O.sub.2]) commences simultaneously at a temperature of 448 K. The considerable increase in production rates of both at temperatures of 466 K (when biuret decomposes) leads to the suggestion that cyanuric acid and ammelide are directly generated from biuret, as in Equations 4 and 5 [18].

[mathematical expression not reproducible] Eq. (4)

[mathematical expression not reproducible]Eq. (5)

Furthermore, trimerization of isocyanic acid to cyanic acid is a viable possibility, particularly for fast heating of the reaction mixture, as in Equation 6 [18, 25].

[mathematical expression not reproducible] Eq. (6)

As temperatures exceed 498 K, ammeline production starts, presumably also a result of biuret decomposition. Cyanuric acid, ammelide, and ammeline begin to form a sticky solid matrix. A further temperature increase can cause the additional production of melamine. The initial mass decreases to 5% at a temperature of 623 K and is composed solely of cyanuric acid, ammelide, ammeline, and melamine [18].

Methodology

This study presents an experimental investigation of the occurring mechanisms during ammonia generation from UWS droplets; including the evaporation of water, the thermal decomposition of urea, and droplet-wall interactions. The aim is to mathematically describe the individual steps of ammonia generation and thereby the evoked temperature change in SCR mixing sections. The resulting numerical model is in a final step tested on the necessary level of complexity by varying the degrees of detail for a simplified case study. The logical sequence of the study is displayed in Figure 3.

Numerical Modeling of the Temperature Progression

First, the temperature progression along an SCR mixing section was calculated without any UWS injections by means of two parallel running 1-D numerical simulations. Temperature changes in the pipe wall are considered on the one hand and the change in temperature of the exhaust gas on the other hand. For the simulation of the temperature progression, uniformly distributed cells throughout the mixing section are applied, as shown in Figure 4.

Following the creation of the numerical model, both the cell size and time step used for calculation needed to be defined such that an additional reduction of size or time step would have no further impact on the results. In a final stage, the results of the simulation were compared with experimental data gained from a test engine and could be validated.

The energy balance for a single mixing section cell is described in Equation 7. The changes in temperature are evoked by convective heat transport between the exhaust gas and the pipe wall [Q.sub.conv], heat conductive heat transport from the previous cell to the current [Q.sub.cond in], heat conduction from the current to the next cell [Q.sub.cond out], and heat loss to the environment [Q.sub.loss]. In the case of UWS injections, the temperature change is additionally caused by the evaporation and decom-position of UWS [Q.sub.UWS].

[mathematical expression not reproducible] Eq. (7)

Conductive heat transport for one cell is composed of the thermal conductivity of the pipe [[lambda].sub.cell] divided by the distance from two adjacent cells [l.sub.cell] multiplied by the cross-sectional surface [A.sub.CS] of the pipe and the temperature difference from the pipe walls of two adjacent cells [DELTA][T.sub.cell], as shown in Equation 8.

[mathematical expression not reproducible] Eq. (8)

The forced convection from the exhaust to the pipe wall is determined by the coefficient of heat transfer [[alpha].sub.gas], the surface of an individual cell [A.sub.cell], and the temperature difference between the gas temperature and the pipe wall temperature [DELTA]? of the respective cell, as in Equation 9.

[mathematical expression not reproducible] Eq. (9)

The coefficient of heat transfer is calculated by the product of the dimensionless Nusselt number N[u.sub.x] and the thermal conductivity of the exhaust gas at its mean temperature in the cell [[lambda].sub.gas], divided by a characteristic length, in this case, the inner diameter of the pipe [d.sub.i], as in Equation 10 [28].

[mathematical expression not reproducible] Eq. (10)

The dimensionless Nusselt number is used to characterize the intensity of convective heat transport between a moving fluid and the surface of a body. According to Gnielinski [29], in the case of a fully turbulent flow, the local Nusselt number depends on the dimensionless Reynolds Re and Prandtl number Pr, the inner diameter of the pipe, a friction factor [xi], and the examined position of the pipe x, as in Equation 11.

[mathematical expression not reproducible] Eq. (11)

The friction factor is a function of the dimensionless Reynolds number, as shown in Equation 12 [30].

[xi] = (1.8 x [log.sub.10] Re -1.5)[.sup.-2] Eq. (12)

Heat losses for uninsulated pipes, due to free convection, are a product of the coefficient of heat transfer [[alpha].sub.loss], the surface of an individual cell [A.sub.cell], and the difference between the ambient temperature and the temperature of the pipe wall ([T.sub.amb] - [T.sub.cell]), as in Equation 13.

[mathematical expression not reproducible] Eq. (13)

The coefficient of heat transfer in this case is given by Equation 14 and determined by the product of the dimension-less Nusselt number for free convection around a horizontal cylinder N[u.sub.loss] and the heat conductivity from the surrounding air at the mean temperature of the surrounding air and pipe wall [[lambda].sub.loss], divided by the stream length, which depends on the outer diameter of the pipe [28].

[mathematical expression not reproducible] Eq. (14)

In the case of free convection around a horizontal cylinder, the Nusselt number is, according to [31], defined by the product of the Prandtl number and Grashof number Gr, and a function of the Prandtl number [f.sub.3](Pr), as in Equation 15.

[mathematical expression not reproducible] Eq. (15)

The function [f.sub.3](Pr) describes the effect of the Prandtl number and is given by Equation 16 [28].

[mathematical expression not reproducible] Eq. (16)

The Grashof number comprises the acceleration of gravity g, the stream length, the kinematic viscosity of the surrounding air [v.sub.air] the temperature difference between the pipe wall temperature and the surrounding air ([T.sub.cell] - [T.sub.amb]), and the isobaric volume expansion coefficient [beta], as in Equation 17 [28].

[mathematical expression not reproducible] Eq. (17)

The isobaric volume expansion coefficient for perfect gases can be approximated by the reciprocal temperature of the surrounding gas as in Equation 18 [32].

[mathematical expression not reproducible] Eq. (18)

Heat losses into the atmosphere, due to radiation, are not considered in the simulation model, as in this case their share of the total heat losses is negligibly small.

The change in temperature of the exhaust gas is determined using the temperature of the inflowing exhaust gas [T.sub.gas in] and the emitted or absorbed heat amount in one cell due to forced convection divided by the mass flow [m.sub.gas] and specific heat capacity of the exhaust gas [c.sub.pgas], as in Equation 19.

[mathematical expression not reproducible] Eq. (19)

The thermodynamic properties (e.g., density, specific heat capacity, heat conductivity, and dynamic viscosity) of the exhaust gas were calculated for each at its mean temperature in the cell. The thermodynamic properties of the surrounding air were determined at the mean temperature of the air and the pipe wall. The composition of the exhaust gas was assumed to be the same as the air as diesel engines feature a high global air excess ratio.

Validation of the created numerical model was performed for three distinct operation points (E-OP3, E-OP4, and E-OP5). The engine test bench consisted of a six-cylinder diesel engine with common rail injection, an eddy current brake, and measuring systems. The relevant technical data of the test engine are given in Table 3.

The engine-out parameters for the investigated operation points are presented in Table 4. However, the exhaust gas temperature decreased considerably until the gas reached the SCR system, due to heat losses to upstream components (e.g., DOC, DPF). The actual temperatures of the inflowing exhaust gas into the SCR mixing section are displayed on the right of Table 4.

The applied mixing section for this study is strongly simplified, since it does not feature any deflections or static mixers. However, the simplification measures allowed a detailed analysis of the thermal behavior of SCR mixing sections, particularly during UWS injections, which would otherwise not have been possible to this extent. The relevant dimensions and material parameters of the modeled mixing section are displayed in Table 5.

The temperature progression along the SCR mixing section wall for the validation of the numerical model was monitored with thermocouples at six different positions, as displayed in Figure 5.

Numerical Modeling of UWS Injections

The numerical model for the injection of UWS spray into the SCR mixing section describes the droplet trajectories, the weight loss during water evaporation and ammonia generation, and droplet-wall interactions in the case of wall impingement. In contrast to previous simulations [8, 25], in addition to the change in droplets' temperature and relative velocity, this model considers the temperature change of the exhaust gas and mixing section due to the intermittent UWS injections. Furthermore, the previously described changes in exhaust gas and mixing section temperatures due to convective and conductive heat transport phenomena as well as heat losses to the environment were calculated. The numerical modeling of injections starts after thermal equilibrium is reached between exhaust gas and mixing section.

The amount of 32.5 wt% UWS injected and the frequencies of injections strongly depend on the operation point of the engine. The investigation of UWS injections took place for different partial-load and full-load operation points. The selected operation points were the same as applied for the model validation of the temperature progression in SCR mixing sections without any injections (Table 4). For the amount and frequency of injection, the injection angle (45[degrees]), the initial UWS temperature (353 K), and the injection pressure (5 bar), typical applied values were used. However, instead of the actual duration of one injection, one single time step (~0.5 ms) was taken to inject the respective amount of urea in the simulation model. Moreover, the injector was assumed to have one centered nozzle hole for injection instead of several holes.

The injection velocity was determined to 25 m/s by high speed recording experiments. The droplet-size distribution of the injected UWS droplets was derived from laser diffraction measurements conducted by [33] and approximated by a distribution function according to Rosin-Rammler. The calculation of the spray phenomena is based on the Lagrangian approach, which means the behavior of single droplets from representative size classes is observed instead of explicitly considering each droplet of the spray. In order to minimize computing time, the spray was modeled with three representative size classes instead of the six approximated by [33]. The droplet-size distribution subsequently changed to diameter classes of 85 [micro]m, 171 [micro]m, and 263 [micro]m with a density distribution of 0.37, 0.48, and 0.15, as can be seen in Figure 6.

Following the calculation of a single droplet from each diameter class, the impacts of these droplets on the exhaust gas and mixing section were multiplied by the actual number of droplets for the three considered diameters. The amount of UWS injected, the injection frequency, and the time slice in which the nozzle is open are graphically presented for each operation point in Figure 7.

Droplet Motion The trajectory of a single droplet is determined by the momentum equation, which is derived from the balance of forces. Figure 8 displays the forces affecting a droplet in the exhaust gas flow in the x- and y-directions.

The momentum equation in x- and y-directions is solved by integration, and consequentially the velocity and current position of a single droplet can be determined. The forces affecting an injected droplet are composed of the drag force of the exhaust gas [mathematical expression not reproducible] and the weight and buoyant force of the droplet [mathematical expression not reproducible]; see Equation 20.

[mathematical expression not reproducible] Eq. (20)

The drag force is defined by the cross-sectional area of the drop [A.sub.CS, drop], the exhaust gas density [[rho].sub.gas], he relative velocity between gas phase and drop [mathematical expression not reproducible], and the drag coefficient [c.sub.D], as in Equation 21 [34].

[mathematical expression not reproducible] Eq. (21)

The drag coefficient is specified by the correlation of Schiller and Naumann [35], depending on the droplet's Reynolds number [Re.sub.drop], as in Equation 22.

[mathematical expression not reproducible] Eq. (22)

The droplet's Reynolds number is described by the density of the surrounding gas, the dynamic gas viscosity [[micro].sub.gas], the droplet's diameter [d.sub.drop], and the relative gas velocity, Equation 23.

[mathematical expression not reproducible] Eq. (23)

The weight and buoyant force acting on the droplet is determined by the droplet's volume [V.sub.drop], its density [[rho].sub.drop], the density of the surrounding gas phase [[rho].sub.gas], and gravity [mathematical expression not reproducible] as in Equation 24.

[mathematical expression not reproducible] Eq. (24)

The droplet's total density depends on the current composition of urea and water. The density of urea is assumed constant with [mathematical expression not reproducible] [25] and the density for water is determined according to a correlation formula [28].

Nevertheless, the weight and buoyant force are neglected in these investigations, because the droplet's volume is so small that the error made with this simplification is negligible. In the absence of the weight and buoyant force, the momentum equation for a single droplet can be described by transforming Equation 20 and inserting Equation 21, resulting in Equation 25. The droplet's velocity results from integrating the momentum equation, and the droplet's position in the SCR mixing section [mathematical expression not reproducible] determined by integration of the drop-let's velocity.

[mathematical expression not reproducible] Eq. (25)

The time interval applied for the calculation of UWS injections is defined by the cell thickness divided by the mean value of the droplets' relative velocity in x-direction from the different diameter classes. This method was used to ensure that with every repeated time step, the droplets passed one entire cell.

Evaporation of Water The generation of ammonia from urea-water droplets is, according to the results of [4, 25], based on two individual steps: the evaporation of water and the thermal decomposition of urea.

The same behavior was examined by Moeltner [8] for a urea-water droplet on a heating plate. First, the droplet experiences a fast heat-up phase, followed by a mass loss due to the evaporation of water, whereby the droplet's temperature does not change during the evaporation. Within the first second a distinct evaporation of water is apparent, which is recognizable by the partial condensation of the evaporated liquid, as can be seen in Figure 9. Subsequent to the complete evaporation of water, the thermal decomposition of urea begins. The comparison between the mass loss during evaporation and thermolysis reveals that the evaporation of water occurs faster than the thermal decomposition of urea [8].

The driving force for the evaporation is generally the concentration difference between the droplet's surface and the surrounding exhaust gas. The transport phenomena appearing during evaporation are based on diffusion and convection, which implies a simultaneous occurrence of heat and mass transfer. Heat and mass transfer phenomena are considerably influenced by the droplet's Reynolds number, which strongly depends on the droplet's diameter. During a droplet's residence time in an SCR mixing section, the relative velocity between droplet and exhaust gas, and the droplet's diameter are constantly changing. For the creation of the numerical model, a few further assumptions had to be made:

* Spherical symmetry of the droplet;

* Uniform droplet temperature along the radius;

* Uniform physical properties of the inflowing exhaust gas;

* Increased initial temperature of the exhaust gas compared to the droplet; and

* Negligible heat transport processes by radiation.

The heat transport from the exhaust to the droplet is based on convection. The intensity of convective heat transfer depends on the temperature gradient in the droplet's boundary layer and the heat transfer coefficient as a function of physical exhaust gas properties and droplet diameter [36]. However, the evaporation of water is limited more by the diffusion of the developed vapor into the exhaust gas than by heat transport phenomena. The evaporation of water occurs by diffusion in a thin boundary layer between the droplet and the exhaust gas, provided that the relative humidity of the surrounding gas is less than one [37, 38]. Therefore, the mass loss of the droplet during evaporation of water was calculated as a problem limited by diffusion, assuming that the heat supply from the exhaust to the droplet is sufficient at any time.

Equation 26 describes the mass transfer coefficient as a function of the Sherwood number [mathematical expression not reproducible], the diffusion coefficient D, and the droplet's diameter [d.sub.drop], and was developed by Ranz and Marshall from experiments with drops of different liquids and diameters [36, 37].

[mathematical expression not reproducible] Eq. (26)

The diffusion coefficient of water vapor in air is described by Equation 27 according to Schirmer [39]. The variables [T.sub.0] and [p.sub.0] indicate the standard temperature and pressure of 273 K and 101325 Pa.

[mathematical expression not reproducible] Eq. (27)

The temporal mass loss of the droplet can be described by Equation 28. The diffusion process of the developed vapor into the exhaust gas occurs on the droplet's surface and depends on the mass transfer coefficient [k.sub.c] and the driving force for diffusion, which is described by the saturation vapor of UWS [p.sub.s], the relative humidity of the surrounding gas [X.sub.rel], the droplet's temperature [T.sub.drop], and the exhaust gas temperature [T.sub.gas] [37].

[mathematical expression not reproducible] Eq. (28)

The vapor pressure of the droplet can be approximated by applying the laws of Raoult and Dalton. The vapor pressure of pure water can be determined according to Antoine [8]. The vapor pressure of urea can be described by an exponential function in conformity with [9], as in Equation 29.

[mathematical expression not reproducible] Eq. (29)

As mentioned above, the evaporation of water is an isothermal process, and thus the droplet's temperature remains constant until the water is completely evaporated. The specific evaporation enthalpy of water is temperature dependent and can be approximated with a correlation formula [28]. The evaporation of water causes an increase in the exhaust gas volume and thus a rise in the relative gas velocity. The calculation of the current gas velocity occurs by adding the amount of evaporated water to the initial exhaust gas flow [m.sub.gas] and dividing the volume flow rate by the surface of the mixing section. Furthermore, the evaporation of water induces an increase of relative humidity in the exhaust gas, which is considered.

Non-Isothermal Decomposition of Urea Subsequent to the complete evaporation of water, the thermal decomposition of urea starts. The temporal mass loss of a droplet due to thermolysis of urea depends on the reaction rate constant [k.sub.therm], and the current mass of the droplet [m.sub.drop], as in Equation 30.

[mathematical expression not reproducible] Eq. (30)

The droplet's temperature during thermal decomposition of urea is defined by the difference of supplied heat from the exhaust gas and consumed heat by the endothermic reaction. The convective heat transport from the exhaust gas to the droplet depends on the heat transfer coefficient [h.sub.c], the drop-let's surface [A.sub.drop], and the temperature difference between exhaust gas and droplet ([T.sub.gas] - [T.sub.drop]), as in Equation 31 [8].

[mathematical expression not reproducible] Eq. (31)

To calculate the heat transfer coefficient, Ranz and Marshall developed a correlation between the thermal conductivity of the gas [[lambda].sub.gas], the droplet's Reynolds number, the Prandtl number, and the droplet's diameter, as in Equation 32 [36].

[mathematical expression not reproducible] Eq. (32)

The amount of heat consumed by the thermal decomposition of urea is described by the change in the droplet's mass over time multiplied by the reaction enthalpy for thermolysis of urea [40].

[mathematical expression not reproducible]

The change in droplet temperature over time is the result of the thermal balance, which comprises the heat supplied by the exhaust gas and the heat consumed by the endothermic reaction, divided by the droplet's heat capacity [mathematical expression not reproducible] [41] and the current mass of the droplet, as in Equation 33.

[mathematical expression not reproducible] Eq. (33)

The conversion rate of urea to ammonia due to thermal decomposition is calculated for each diameter class. In order to determine the total conversion rate, the individual conversion rates are multiplied by the respective mass fraction and totaled.

Determination of Urea Decomposition Kinetics. The conversion of isocyanic acid to ammonia in the temperature range of exhaust gas occurs almost exclusively in the presence of a catalyst [19, 20]. Hence, ammonia generation for the simulation took place only due to the thermolysis of urea, and hydrolysis was not considered. The temperature-dependent rate constant for the thermolysis of urea was investigated through TGA.

The methodology for the TGA measurements was selected in a way that all factors that potentially influenced the results (e.g., sample and size, flow rate, heating rate, and purge gas) could be investigated without drastically increasing the number of measurements. The urea samples were purchased from Carl Roth GmbH + Co. KG with a purity of [greater than or equal to]99.6% and Merck KGaA with a purity of [greater than or equal to]99.5%, and they were used without any further purification. The two different urea samples were randomly selected for the measurements. The heating rate was varied from 3 K/min to 50 K/min, the purge gas flow rate from 20 ml/min to 80 ml/min, the sample size from 70 [micro]l to 150 [micro]l (aluminum oxide pan), and the purge gas was either synthetic air or nitrogen. In addition to dynamic measurements, isothermal measurements were conducted at different temperatures.

To establish the reaction rate constant for the thermolysis of urea, it is first necessary to determine the reaction order. The differential rate law can be used to determine the reaction order from the experimental data received from the TGA measurement. For instance, at a temperature of 465 K, the reaction order was determined to be 1.0948. Therefore, the thermolysis of urea can be considered a first-order reaction.

After determining the reaction order, the reaction rate constant for various temperatures can be calculated. The resulting reaction rate constants from the different measurements at the respective temperatures were first tested on outliers, according to Grubbs as described in [42, 43]. After detecting and, where appropriate, removing the outliers, the rate constants were tested on significant differences between the applied TGA methods with analysis of variance (ANOVA) for a significance level of [alpha] = 0.05, of as described in [42, 43].

The Grubbs test for outliers revealed that outliers within the test results appeared randomly and thus could not be attributed to any investigated potential influence factor of the TGA measurement. Therefore, the detected outliers were rejected, and further analysis of the test results was conducted without the rejected rate constants. In addition, a one-way ANOVA was used to investigate whether there were any statistically significant differences between the natural logarithm of the reaction rate constants from the different applied methods for the TGA measurements. There is no statistically significant difference at p < 0.05 recognizable between the applied methods (F(11, 101) = 0.4573; p = 0.9250), whereby it can be concluded that the previously defined potential influence factors do not have a significant effect on the resulting reaction rate constants.

The natural logarithm of the determined reaction rate constants at different temperatures were plotted against the reciprocal temperature, which resulted in the Arrhenius plot by which the activation energy [E.sub.A] and the pre-exponential factor A could be calculated. The determined thermolysis kinetics and the comparison with literature are presented below, Figure 13.

Wall Impingement In particular, droplets ofgreater diameters cannot be entrained by the exhaust gas and impinge on the wall of the mixing section. The occurring interactions between wall and UWS droplets have a great influence on the decomposition and thus ammonia generation. A vast number of different physical phenomena can occur, which are commonly described as regimes in literature [8, 25, 34]. The most important regimes for droplet-wall interactions in the case of a dry surface, classified by Bai and Gosman [44, 45], are presented below.

* Deposition: For the deposition regime, the adhesion of the droplet on the surface is dominant. With increasing droplet velocity the adhering droplet loses its spherical shape and forms a lenticular film. On wet surfaces, coalescence with the existing film appears. On hot surfaces, the film starts to boil and thus merges into the breakup regime.

* Splash: The splash regime characterizes an atomization of primary droplets into smaller secondary droplets due to high kinetic energy on dry or wet cold surfaces.

* Break-up: The breakup regime describes a decay of the primary droplets into smaller secondary droplets on hot surfaces. In contrast to the splash regime, the disintegration is thermally initiated at comparably smaller impact velocities.

* Rebound: The rebound regime denotes the reflection of droplets on hot dry surfaces. A vapor cushion prevents direct wall contact, and the droplets rebound. This effect is commonly known as the Leidenfrost effect.

The most relevant parameters determining the droplet-wall interactions are the droplet's diameter and velocity perpendicular to the surface, the density, the surface tension, the viscosity and the boiling temperature of the liquid, as well as the properties of the wall (e.g., temperature, heat capacity, thermal conductivity, roughness, or wall film height) [25, 34]. These influencing factors can be described by dimensionless characteristic numbers. The Weber number (We) is the quotient of the droplet's inertia force and its surface tension [[sigma].sub.drop], and thus a parameter for the stability of the droplet against acting gas forces and impingement in accordance with [25, 34], Equation 34.

[mathematical expression not reproducible] Eq. (34)

The droplet's Reynolds number describes the ratio of inertia to viscous forces, Equation 23. The viscous forces counter vibrations and wall film formation during impingement. The combination of Reynolds and Weber number leads to the dimensionless K-number, which is relevant for the above mentioned regime classification, Equation 35 [34].

[mathematical expression not reproducible] Eq. (35)

The influence of the wall temperature to the regime classification is expressed by the quotient of the wall temperature and the droplet's boiling temperature, Equation 36 [25, 34].

[mathematical expression not reproducible] Eq. (36)

Kuhnke [34] applied the two dimensionless numbers K and T to classify the above mentioned regimes, which is schematically presented in Figure 10. The critical temperature quotient [T*.sub.crit] was determined to 1.1 for alcohols and fuels by Kuhnke, which presents the shift from deposition/splash to rebound/break-up regime. Birkhold [25] adapted [T*.sub.crit] for UWS, Equation 37. In the case of a 32.5 wt% aqueous urea solution, [T*.sub.crit] amounts to 1.37.

[mathematical expression not reproducible] Eq. (37)

Discussion of Results

In the first approach, the validation of the numerical model to describe the temperature progression in an SCR mixing section without UWS injection took place. The comparison of the empirically obtained wall temperatures with the results from the numerical model occurred after thermal equilibrium was reached between exhaust gas and mixing section. The observation of empirically determined and calculated temperature progression along the mixing section reveals good correlation and is presented in Appendix A: Figure A.1.

The next step was to verify the assumption that water completely evaporates before the thermolysis of urea occurs as well as to determine the kinetics for the thermolysis of urea by means of TGA. In the final stage, droplet injections and ammonia generation (due to thermolysis of urea) with all interactions between the droplets and the exhaust gas or wall were implemented in the simulation model. The model-based investigations were validated by means of thermographic and laser diffraction measurements. On the basis of this numerical model, the necessary level of complexity could be investigated by varying the degrees of detail for a simplified case study.

Staged Decomposition of UWS

The assumption for the created numerical model that water completely evaporates out of the injected UWS droplet before the thermolysis of urea occurs could be verified with various isothermal TGA measurements. Figure 11 exemplifies the progress of mass loss over time for UWS and pure water at a temperature of 353 K; air was used as purge gas at a flow rate of 60 ml/min.

The mass loss progression of water is clearly faster than the mass loss of UWS, which can be explained by the decrease of vapor pressure in the mixture due to dissolved urea [41]. Furthermore, a complete mass loss of water occurs, whereas for the UWS only the mass fraction of 67.5% water evaporates and urea remains. The gained results are in strong agreement with the previously presented investigation of a UWS droplet on a heating plate (Figure 9) conducted by Moeltner [8]. Moreover, the simulated results presented in Figure 12 are in good conformity with the experimental observation, which in turn supports the validity of the created numerical model.

Kinetics of Thermolysis

The TGA was conducted without determining the emerged gaseous products; hence the temperature range to define the Arrhenius parameters needed to be chosen in a segment where it could be ensured that weight loss would occur exclusively due to thermolysis. The temperature range was from 419 K to 502 K in at least 10 K intervals. The Arrhenius plot of the results from the urea TGA measurements is displayed in Appendix B: Figure B.1. The pre-exponential factor thereby amounts to A = 6.047x[10.sup.6] [s.sup.-1] and the activation energy to [E.sub.A] = 89317 J/mol (coefficient of determination of 0.9979).

To facilitate comparison of the determined temperature-dependent thermolysis rate constant according to Arrhenius, the constant is displayed in Figure 13 in linearized form together with the rate constants found in literature [20-26].

Figure 13 reveals considerable differences between the rate constant progressions subjected to temperature. The determined rate constant from the urea measurements proposes a smaller rate of thermolysis for low temperatures but implies a steeper rise of the reaction rate at high temperatures than the proposed kinetics of Rota et al. [26], for instance. However, findings in the literature indicate that the span in which the determined rate constant is located corresponds closely to the proposed rate constants of [9, 21, 23, 26]. Therefore, the temperature-dependent rate constant from the urea TGA measurements was applied for the pursuant investigations and implementation in the simulation model.

Simulation of UWS Injections

The initial investigation of UWS injections into a simplified mixing section occurred for the three distinctive operation points E-OP3, E-OP4, E-OP5 (Table 4) and is presented in Figure 14. The applied diameter classes for the simulation were 85 [micro]m, 171 [micro]m, and 263 [micro]m, determined from the droplet-size distribution shown in Figure 6.

Droplet-wall interactions appear for all three diameters at each operation point. A comparable stronger deflection of the smallest diameter occurs, which is explained by the weaker inertia due to their smaller mass. In addition, a stronger deflection of the droplets for E-OP5 in comparison to E-OP3 and E-OP4 is apparent. Although the density of the exhaust gas is lower for E-OP5 due to its relatively high temperature, the increased mass flow rate and thus velocity overcompensate for the density and cause the enhanced deflection. Due to the prompt wall impingement of the droplets after injection, the evaporation of water persists and no ammonia generation during the flight phase of the droplets occurs. Table 6 reveals the distinctions between density, exhaust gas velocity, and dynamic viscosity for the three considered operation points.

Wall Impingement The occurring droplet-wall interactions are discussed on the basis of the gained parameters from the simulation. For this purpose, it is in a first step necessary to determine the droplets' Reynolds number, Equation 23, and the Weber number, Equation 24, for the three diameter classes at the moment of impingement, Appendix C: Table C.2. The required parameters include the droplet's diameter, velocities, density, and surface tension (Appendix C: Table C.1), as well as the density and dynamic viscosity of the exhaust gas (Table 6).

The combination of the Reynolds and Weber number leads to the dimensionless K-number, as in Equation 35, which determines the horizontal position in the regime classification for droplet-wall interactions in accordance with Kuhnke [34] and Birkhold [25] (Figure 10). The resulting K-numbers are displayed in Table 7.

The temperature-related vertical position in the regime classification is dependent on the wall temperature and the droplet's boiling temperature, Equation 36. The wall temperature at the point of impingement is directly derived from the simulation model, Appendix C: Table C.3. The droplet's boiling temperature at the moment of impingement is subjected to the urea-water composition and thus to the preceding evaporation of water. The urea mass fraction is obtained from the simulation results, Appendix C: Table C.4. The boiling temperature of the binary urea-water mixture with varying molar compositions is approximated by means of the laws of Raoult and Dalton, Equation 29, and is stated for the investigated droplet-size classes in Appendix C: Table C.5.

Figure 15 depicts the vertical classification of the droplet-wall interaction regimes as a function of the wall temperature and the mass fraction of urea at a pressure of 101325 Pa. The diagram reveals the critical temperature quotient [T*.sub.crit] proposed by Birkhold [25] and the temperature ratio for varying wall temperatures on the primary y-axis; the boiling temperature at the time of impingement is displayed on the secondary y-axis; all as a function of the urea mass fraction.

Figure 15 can be applied to determine the vertical position in the described regime classification (above [T*.sub.crit] rebound or break-up, below [T*.sub.crit] deposition or splash) on the basis of the urea mass fraction and the wall temperature. The developed diagram is generally valid for interactions of droplets with dry surfaces; which not only includes the mixing section wall, but also other components in the after-treatment system (e.g., static mixers).

Table 8 presents the temperature ratio and the respective critical temperature quotient for the three investigated droplet-size classes and operation points derived from Figure 15. The temperature ratios T are below the critical values [T*.sub.crit] for all diameter classes for E-OP3, whereas the ratios are above this limit for all investigated size classes for E-OP4 and E-OP5.

The determined K-numbers (Table 7) and temperature ratios with respect to the critical temperature quotient (Table 8) allow a prediction of the occurring droplet-wall interaction regime at the moment of impingement (Figure 10) in accordance with Bai and Gosman [44, 45]. Table 9 reveals that the droplet-wall interactions for all size classes at E-OP3 can be classified as deposition; the adhesion of the droplet on the surface is dominant and wall wetting can occur. For E-OP4 and E-OP5, the droplets with an original diameter of 85 [micro]m will rebound on the wall, whereas droplets with an initial size of 171 [micro]m and 263 [micro]m experience a thermally induced break-up.

The occurring droplet-wall interactions for all diameter classes at E-OP3 increase the opportunity for wall film formation. The heat, which is required for the evaporation of water and the thermolysis of urea, is supplied by heat transfer processes from the wall and the exhaust gas to the wall film. Furthermore, the extent of wall film formation is dependent on the available heat.

Experiment vs. Simulation Figure 16 presents a thermographic measurement of the SCR mixing section during UWS injections at E-OP3. The predicted deposition regime, describing the adhesion of the droplet on the surface and the possibility of wall wetting, is evident due to the distinct cooling of the mixing section wall at the impingement points of UWS. The occurring wall wetting and the thereby caused cooling of the mixing section wall can cause unwanted solid depositions. Moreover, the availability of ammonia for the reduction of N[O.sub.x] is delayed by this indirect route. The thermographic measurement was further conducted for E-OP4 and E-OP5. However, as predicted by the simulation model, no wall wetting and thus no cooling of the mixing section wall was evident.

Furthermore, laser diffraction measurements (Malvern Spraytec 10 K) were conducted for E-OP3 to examine the validity of the simulation model. The droplet size distribution in the mixing section was determined 0.15 m downstream of the UWS-injection position. According to the model-based investigations, a small part of the droplet spectrum directly follows the exhaust gas flow and can be detected by laser diffraction. Droplets of larger diameter classes are undetectable since droplet-wall interactions occur because of their inertia. Due to the comparatively low wall temperatures at E-OP3, the deposition regime prevails in the case of droplet-wall interactions. Figure 17 presents the comparison of the simulation model and the experimental results. The observation of empirically determined and calculated droplet spectrum reveals a good conformity, which in turn strengthens the model's validity.

Case Study In the final step of this study, the self-defined aim is to determine, on the one hand, influencing factors to avoid droplet-wall interactions and thus solid depositions or delays in ammonia generation on the basis of a strongly simplified case study. On the other hand, the necessary level of complexity for an accurate calculation of the occurring physical and chemical phenomena in SCR mixing sections is investigated.

An important parameter for the prevention of droplet-wall interactions is the droplet-size distribution of the injected UWS spray. The initial investigation (Figure 14) revealed that the least deflection of droplets occurs for E-OP3. Therefore, this operation point is applied to determine the critical diameter at which the droplet is no longer able to impinge on the wall under the given circumstances. Figure 18 displays the trajectories of different droplet diameters for E-OP3. The injection angle amounts to 45[degrees], injection pressure to 5 bar, injection velocity to 25 m/s, and initial UWS temperature to 353 K. On the basis of this diagram, the critical diameter for a certain mixing section geometry (length and diameter) can be determined.

In the event of this simplified case study, the length of the mixing section is 0.55 m and its diameter is 0.06 m. Hence, the critical diameter must be in between 50 [micro]m and 100 [micro]m, more precisely 61 [micro]m, which represents the biggest diameter class of the optimized spray. The two smaller diameters for the optimized spray were calculated by reducing the initial diameters by the same amount as the biggest diameter (263 [micro]m) of the initial spray distribution was decreased. The optimized diameter classes amount thus to 20 [micro]m, 40 [micro]m, and 61 [micro]m with the same density distribution as for the initial droplet spectrum; see Figure 6.

After reduction of the initial droplet-size distribution, factors that could improve the conversion rate from urea to ammonia during flight phase and their effect on the temperature progression of the SCR mixing section were examined. By means of the developed numerical model it is possible to modify the injection angle and velocity, the initial droplet temperature, and the relative humidity of the surrounding exhaust gas. With respect to the extent of this paper, Figure 19 only presents one exemplary optimization of ammonia generation in SCR mixing sections for the three investigated operation points. Although, counterflow injection is still in the development phase, particularly due to comparatively greater deposit formation and injector clogging, the injection angle was in this optimization modified from 45[degrees] to 155[degrees]. Moreover, the initial droplet velocity was modified from 25 m/s to 20 m/s, and the reduced droplet-size distribution was applied.

The counterflow injection positively affects ammonia generation due to an increase in residence time and a temporarily more pronounced heat and mass transfer, as the relative velocity is comparatively higher at the beginning of injection than for co-flow [46]. These two effects even compensate for the stronger cooling of the exhaust gas for counterflow injection. In general, an increased injection velocity for counterflow injection causes an enhanced residence time and thus a better conversion rate. Nevertheless, higher injection velocities lead to stronger droplet deflection, which causes droplet-wall interactions. Therefore, the droplets' velocity was decreased from 25 m/s to 20 m/s for the optimization scenario. It is also important to mention that the injection velocity directly correlates with the injection pressure and in turn with the droplet-size distribution of the spray. However, different SCR systems for the suggested parameters are in development or already established on the market (see Figure 2) [33, 47-50].

The tendencies concerning deflection of the droplets at the three operation points are comparable to the basic situation with bigger diameter classes (see Figure 14), but the conducted optimization prevents undesired droplet-wall interactions for all operation points. Moreover, the evaporation of water can be concluded in the mixing section. The earliest start of urea decomposition is at E-OP3 and the latest at E-OP5. The reason for that is the comparatively longer residence time of the droplet at E-OP3 due to the lower gas velocity.

Figure 20 presents the temperature progression of the exhaust gas and the mixing section wall at the entrance, middle, and exit, exemplarily for the optimized droplet spectrum - no droplet-wall interactions occur - at E-OP5.

The temperature progression reveals that the mixing section temperature is not affected by spray-exhaust gas interactions, although the exhaust gas experiences a temporal strong cooling. The decrease in the temperature of the mixing section wall of about 15 K from entrance cell to exit cell can be explained by heat loss to the environment and less heat available in the exhaust gas at the end of the mixing section.

The pronounced temporal cooling of the exhaust gas can be explained on the one hand with the relatively fast evaporation of water after injection. On the other hand, the distinct cooling can also be traced back to the calculation method. As mentioned above, instead of injecting the respective amount of UWS during several milliseconds, the amount was injected in a single time step, which in turn caused a more intense local cooling. However, the exhaust gas is able to recover from the temporal cooling until the next injection of UWS starts, even for the displayed E-OP5 where the amount of UWS injected and the injection frequencies are the highest (see Figure 7). It can thus be concluded that it is satisfactory to simulate a single injection for further investigations of spray-exhaust gas interactions instead of intermittent injections, as it is possible to retrieve the initial situation between every injection.

Figure 21 displays the mass loss for the three different diameter size classes from the moment of injection to the exit of the mixing section during one injection, exemplarily for the optimized situation of E-OP3. The four considered scenarios are composed of scenario 1: calculated with the presented model; scenario 2: calculated without considering the temperature change in the exhaust gas due to evaporation and thermolysis; scenario 3: considering the temperature change in the exhaust gas due to evaporation/thermolysis but not including the temperature changes along the mixing section because of heat losses to the environment; and scenario 4: calculated without any temperature changes and, therefore, the same temperature along the mixing section.

There are no significant differences evident between the distinct calculation methods. Furthermore, a mass loss due to thermolysis is only recognizable for the smallest diameter class, whereas Figure 19 displays that for all diameter classes it is possible to completely evaporate the water. Although the thermolysis of urea theoretically starts for every diameter class in the mixing section, the heat-up phase of the bigger diameter classes is comparably slow and thus so is the conversion rate, which is why no noticeable mass loss of urea can be seen.

For clarification, Table 10 contrasts the urea conversion for the four investigated scenarios. The comparatively greatest conversion can be achieved with a constant temperature along the mixing section (scenario 4). Nevertheless, all conversion rates are similar in magnitude. As a result, it can be concluded that it is not extremely essential to consider all evoked temperature changes along the mixing section due to droplet-exhaust gas interactions, thus computing time can be reduced.

The conversion rate from urea to ammonia during flight phase is generally low, yet different investigations proved the thermolysis of urea to be also a catalytic reaction [22, 51]. Another approach for an SCR system could be a relatively short inlet section for the evaporation of water so as to not considerably influence the catalyst's temperature and so the ammonia generation would already take place on the catalytic converter. This intended system could improve the availability of ammonia for N[O.sub.x] reduction, even for highly transient load profiles.

In summary, the presented mathematical framework could in a further step be transferred to more complex geometries (e.g., implementation of a static mixer), which would be valuable for the development of broader SCR models. Furthermore, the created numerical model is capable of determining the occurring droplet-wall interaction regime, which is essential for the prediction of possible wall film formation and depositions. On the basis of the quantification of UWS amount and composition interacting with the mixing section wall, the wall film temperature could be captured with the simulation model. The further implementation of deposition kinetics (e.g., as proposed by [52]) would enable to estimate the chemical composition of the urea deposits, which would facilitate the mitigation of the depositions along the SCR mixing section.

Conclusions

This survey presents, on the one hand, an experimental investigation of the occurring physical and chemical phenomena during UWS injections into SCR mixing sections. On the other hand, the observed individual steps of ammonia generation and thereby the evoked temperature changes in SCR mixing sections are described.

The assumption that water completely evaporates before the decomposition of urea starts could be verified with various TGA measurements. Furthermore, it was possible to determine the kinetics for the thermolysis of urea by means of TGA, which correspond closely to other proposed kinetics in the literature.

The created numerical model is able to determine the droplets' trajectories, their mass loss due to evaporation and decomposition of urea, and the change in the droplets' temperature. In contrast to previous studies, the created numerical model additionally considers the change in temperature of the exhaust gas and mixing section due to the intermittent UWS injections, heat losses to the environment, and convective and conductive heat transport. The cell size and time step of the numerical model were determined in a way that a further reduction of size or time has no further impact on the results. The observation of empirically determined and calculated temperature progression and droplet size distribution along the mixing section revealed a good correlation between experiment and simulation. The calculation of the spray phenomena was based on the Lagrangian approach, which means the behavior of single droplets from representative size classes is observed instead of explicitly considering each droplet of the spray. The impacts of these droplets were multiplied by the actual number of droplets for the three considered diameters.

In the case of the initial simulation scenario of UWS injections into the simplified SCR mixing section; droplet-wall interactions occurred for all three diameter classes at the investigated partial- and full-load operation points. On the basis of the gained parameters from the numerical model, a classification to the occurring droplet-wall interaction regime at the moment of impingement in accordance with Bai and Gosman was possible. The droplet-wall interactions for all size classes at E-OP3 can be classified as deposition, where the adhesion of the droplet on the surface is dominant and wall wetting can occur. At E-OP4 and E-OP5, the droplets with an original diameter of 85 [micro]m can be assigned to the rebound regime; droplets with an initial diameter of 171 [micro]m and 263 [micro]m experience a thermally induced break-up. Thermographic measurements of the SCR mixing section during UWS injections revealed the same results concerning droplet-wall interactions as predicted with the simulation model.

In a final step, influencing factors to avoid wall impingement and the necessary level of detail for an accurate calculation of UWS injections into SCR mixing sections were examined. An important parameter for the prevention of droplet-wall interactions is the droplet-size distribution of the spray. Therefore, the critical diameter was determined by means of the numerical model at which the droplet is no longer able to impinge on the wall and the initially defined diameters were reduced accordingly. Furthermore, factors that could positively influence the efficiency of ammonia generation were analyzed. For instance, a counterflow injection positively affects ammonia generation because of an increase in residence time and a temporarily more pronounced heat and mass transfer. However, a generally poor conversion rate during the flight phase of the droplets is apparent.

The analysis of the essential degree of detail for an accurate calculation revealed that the exhaust gas is able to recover from the considerable temporal cooling until the next UWS injection starts. In addition, the urea conversion is not significantly influenced by simulating the UWS injection without a temperature change along the mixing section. It can thus be concluded that it is satisfactory to simulate a single injection and it is not required to consider all evoked temperature changes along the mixing section for further investigations of spray-exhaust gas interactions.

In conclusion, the created numerical model is capable of describing the individual steps during ammonia generation in SCR mixing sections and the effects on the temperature behavior of the exhaust gas and mixing section. This detailed description, in turn, can serve as a strong basis for future investigations (e.g., implementation in CFD codes).

Contact Information

Dr. Lukas Moeltner

MCI Management Center Innsbruck

Maximilianstrabe 2

6020 Innsbruck, Austria

lukas.moeltner@mci.edu

Phone: +43 512 2070-4132

Nomenclature

Latin Letters
A.                  pre-exponential factor/surface
[C.sub.D]           drag coefficient
[C.sub.P]           specific isobaric heat capacity
d                   diameter
D                   diffusion coefficient
[E.sub.A]           activation energy
F                   force
g                   acceleration of gravity
Gr                  Grashof number
h                   specific enthalpy
[h.sub.c]           heat transfer coefficient
K                   K-number (regime classification)
k                   chemical rate constant
[k.sub.c]           mass transfer coefficient
l                   length
m                   mass
m                   mass flux
M                   molar mass
Nu                  Nusselt number
p                   pressure
Pr                  Prandtl number
Q                   heat flux
R                   universal gas constant
Ra                  Rayleigh number
Re                  Reynolds number
Sc                  Schmidt number
Sh                  Sherwood number
t                   time
t                   temperature
[T*.sub.crit]       critical temperature coefficient
v                   velocity
V                   volume
We                  Weber number
x                   current position
[X.sub.rel]         relative humidity
A.                  [s.sup.-1]/[m.sup.2]
[C.sub.D]           -
[C.sub.P]           J-(mol-K)[.sup.-1]
d                   m
D                   [m.sup.2] x s
[E.sub.A]           J-(mol-K)[.sup.-1]
F                   N
g                   m x [s.sup.-2]
Gr                  -
h                   J x [kg.sup.-1]
[h.sub.c]           W x ([m.sup.2] x K)[.sup.-1]
K                   -
k                   [s.sup.-1]
[k.sub.c]           m x [s.sup.-1]
l                   m
m                   kg
m                   kg x [s.sup.-1]
M                   kg x [kmol.sup.-1]
Nu                  -
p                   Pa
Pr                  -
Q                   J x [s.sup.-1]
R                   J x (mol x K)[.sup.-1]
Ra                  -
Re                  -
Sc                  -
Sh                  -
t                   s
t                   K
[T*.sub.crit]       -
v                   m x [s.sup.-1]
V                   [m.sup.3]
We
x                   m
[X.sub.rel]         -


Greek Letters
[alpha]   coefficient of heat transfer   W x [m.sup.-2] x [K.sup.-1]
[beta]    isobaric volume expansion      [K.sup.-1]
          coefficient
[lambda]  thermal conductivity/air-fuel  W x [m.sup.-1]-[K.sup.-1]/-
          equiv. ratio
[micro]   dynamic viscosity              Pa x s
[nu]      kinematic viscosity            [m.sup.2] x [s.sup.-1]
[xi]      friction factor                -
[rho]     density                        kg x [m.sup.-3]
[sigma]   surface tension                N x [m.sup.-1]


Subscripts

0 - initial

air - air

amb - ambient

boil - boiling

cell - cell

cond - conductive heat transport

conv - convective heat transport

CS - cross sectional

drop - droplet

exp. - experiment

evap. - evaporation

gas - exhaust gas

hydro. - hydrolysis

i - inner

in - inflowing

loss - heat losses

max - maximal

o - outer

ortho - orthogonal

out - outflowing

rel - relative

sim. - simulation

therm. - thermolysis

total - total

urea - urea

w - weight

wall - wall

x - current position

Definitions/Abbreviations

ANOVA - analysis of variance

[C.sub.2][H.sub.5][N.sub.3][O.sub.2] - biuret

[C.sub.3][H.sub.3][N.sub.3][O.sub.3] - cyanuric acid

[C.sub.3][H.sub.4][N.sub.4][O.sub.2] - ammelide

C[O.sub.2] - carbon dioxide

E-OP - experimentally validated operation point

HNCO - isocyanic acid

[H.sub.2]O - water

MS - mixing section

(N[H.sub.2])[.sub.2]CO - urea

N[H.sub.3] - ammonia

N[O.sub.x] - nitrogen oxides

orig. - original

S - scenario

SCR - selective catalytic reduction

TGA - thermogravimetric analysis

UWS - urea-water solution

References

[1.] Weibbaeck, M., "Erfuellung zukuenftiger Emissionsanforderungen fuer Diesel SUV's," Forschungsgesellschaft Kraftfahrwesen mbH Aachen, 15. Aachener Kolloquium Fahrzeug- und Motorentechnik, Tagungsband Nr. 1506, 2006.

[2.] Andersson, J., Trevisan, A., and Vries, S., "N[O.sub.x-] und N[O.sub.2-]Vorteile Moderner SCR-Systeme," MTZ Extra 11, 2015.

[3.] Schatz, A., Knorr, T., and Ellmer, D., "Elektrischer Heizkatalysator zur Optimierung der Emissionen von Mildhybridsystemen," MTZ 02:46-52, 2016.

[4.] Fischer, S., "Simulation of the Urea-Water-Solution Preparation and Ammonia-Homogenization with a Validated CFD-Model," Dissertation, TU Wien, Wien, 2012.

[5.] Koebel, M., Elsener, M., and Kleemann, M., "Urea-SCR: A Promising Technique to Reduce N[O.sub.x] Emissions from Automotive Diesel Engines," Catalysis Today 59:335-345, 2000.

[6.] Mollenhauer, K. and Tschoeke, H., Handbuch Dieselmotoren, Third Edition, (Berlin, Springer Verlag, 2007), ISBN:978-3-540-72165-9.

[7.] Birkhold, F., Meingast, U., Wassermann, P., and Deutschmann, O., "Analysis of the Injection of Urea-Water-Solution for Automotive SCR DeNOx-Systems: Modeling of Two-Phase Flow and Spray/Wall-Interaction," SAE Technical Paper 2006-01-0643, 2006, doi:10.4271/2006-01-0643.

[8.] Moeltner, L., "Tropfen/Abgas- und Tropfen/Wandinteraktionen von AdBlue[R] bei der selektiven katalytischen Reduktion von Stickoxiden," (VDI Verlag, 2014), Fortschritt-Berichte VDI Reihe 12 Nr. 785, ISBN:978-3-18-378512-4.

[9.] Birkhold, F., Meingast, U., Wassermann, P., and Deutschmann, O., "Modeling and Simulation of the Injection of Urea-Water-Solution for Automotive SCR-DeN[O.sub.x]-Systems," Applied Catalysis B: Environmental 70(1):119-127, 2007, doi:10.1016/j.apcatb.2005.12.035.

[10.] Calvo-Zuecco, S. et al., "Harnstoff-SCR-Systeme im Fokus, Neue Herausforderungen bei der Entwicklung von Abgasanlagen," Motorentechnische Zeitschrift 09, 2007.

[11.] Zheng, G., Sampath, M., Alcini, W., Salanta, G. et al., "Design Improvements of Urea SCR Mixing for Medium-Duty Trucks," SAE Technical Paper 2013-01-1074, 2013, doi:10.4271/2013-01-1074.

[12.] Zhan, R., Li, W., Eakle, S., and Weber, P., "Development of a Novel Device to Improve Urea Evaporation, Mixing and Distribution to Enhance SCR Performance," SAE Technical Paper 2010-01-1185, 2010, doi:10.4271/2010-01-1185.

[13.] Alano, E., Jean, E., Perrot, Y., Brunel, J. et al., "Compact SCR for Passenger Cars," SAE Technical Paper 2011-01-1318, 2011, doi:10.4271/2011-01-1318.

[14.] Seo, J., "Aftertreatment Package Design for SCR Performance Optimization," SAE Technical Paper 2011-01-1135, 2011, doi:10.4271/2011-01-1135.

[15.] Zheng, G., Palmer, G., Salanta, G., and Kotrba, A., "Mixer Development for Urea SCR Applications," SAE Technical Paper 2009-01-2879, 2009, doi:10.4271/2009-01-2879.

[16.] Kleemann, M., Elsener, M., Koebel, M., and Wokaun, A., "Hydrolysis of Isocyanic Acid on SCR Catalysts," Industrial & Engineering Chemistry Research 39:4120-4126, 2000.

[17.] Wurzenberger, J. and Wanker, R., "Multi-Scale SCR Modeling, 1D Kinetic Analysis and 3D System Simulation," SAE Technical Paper 2005-01-0948, 2005, doi:10.4271/2005-01-0948.

[18.] Schaber, P., Colson, J., Higgins, S., Thielen, D. et al., "Thermal Decomposition (Pyrolysis) of Urea in an Open Reaction Vessel," Thermochimica Acta 424:131-142, 2004, doi:10.1016/j.tca.2004.05.018.

[19.] Yi, Y., "Development of a 3D Numerical Model for Predicting Spray - Urea Decomposition and Mixing in SCR Systems," SAE Technical Paper 2007-01-3985, 2007, doi:10.4271/2007-01-3985.

[20.] Yim, S. et al., "Decomposition of Urea into N[H.sub.3] for the SCR Process," Industrial & Engineering Chemistry Research 43:4856-4563, 2004, doi:10.1021/ie034052j.

[21.] Buchholz, F., "Einsatz von festem Harnstoff als Reduktionsmittel fuer die NOx-Minderung nach dem SCR-Verfahren," Dissertation, Universitaet Karlsruhe (TH), Karlsruhe, 2000.

[22.] Fang, H.L. and DaCosta, H.F., "Urea Thermolysis and N[O.sub.x] Reduction with and without SCR Catalysts," Applied Catalysis B: Environmental 46(4):17-34, 2003.

[23.] Brack, W. et al., "Kinetic Modeling of Urea Decomposition Based on Systematic Thermogravimetric Analyses of Urea and Its Most Important By-Products," Chemical Enigneering Science 106:1-8, 2014.

[24.] Ostrogovich, G. and Bacaloglu, R., "Die Kinetik der Thermolyse von Harnstoff und der darauffolgenden Umwandlungen," III. Revue Roumaine de Chimie 10:1125-1135, 1965.

[25.] Birkhold, F., "Selektive katalytische Reduktion von Stickoxiden in Kraftfahrzeugen: Untersuchung der Einspritzung von Harnstoffwasserloesung," Dissertation, Karlsruher Institut fuer Technologie, Karlsruhe, 2007.

[26.] Rota, R., Antos, D., Zanoelo, E., and Morbidelli, M., "Experimental and Modeling Analysis of the N[O.sub.x]OUT Process," Chemical Engineering Sience 57:27-38, 2002.

[27.] Moeltner, L., Hohensinner, M., and Schallhart, V., "Experimental and Numerical Analysis of Low Temperature N[O.sub.x-]Conversion in Urban Busses," SAE Technical Paper 2016-01-8076, 2016, doi:10.4271/2016-01-8076.

[28.] VDI e.V, VDI Heat Atlas, (Berlin, Springer-Verlag, 2010), ISBN:978-3-540-77877-6.

[29.] Gnielinski, V., "Ein neues Berechnungsverfahren fuer die Waermeuebertragung im Uebergangsbereich zwischen laminarer und trubulenter Rohrstroemung," Forschung im Ingenieurwesen 61(9):240-248, 1995, doi:10.1007/BF02607964.

[30.] Konakov, P.K., "Eine neue Formel fuer den Reibungskoeffizienten glatter Rohre," Berichte der Akademie der Wissneschaften der UdSSR, 51(7), 1946, Band LI, 503-506.

[31.] Churchill, S. and Chu, H., "Correlation Equations for Laminar and Turbulent Free Convection for a Horizontal Cylinder," International Journal of Heat and Mass Transfer 18:1049-1059, 1975.

[32.] Moran, M.J. and Shapiro, H.N., Fundamentals of Engineering Thermodynamics, Fifth Edition, (Hoboken, John Wiley & Sons, 2004), ISBN:9780471317135.

[33.] Moeltner, L., Fischer, S. et al., "New Approaches and Development Methods to Minimize N[O.sub.x-]Emissions of Diesel Engines," 31. Internationales Wiener Motorensymposium, Fortschritts-Berichte VDI, Reihe 12, Nr. 716, 2010, 374-394.

[34.] Kuhnke, D., "Spray/Wall-Interaction Modelling by Dimensionless Data Analysis," Dissertation, TU Darmstadt, Darmstadt, 2004.

[35.] Schiller, L. and Naumann, A., "Ueber die grundlegende Berechnung bei der Schwerkraftaufbereitung," Zeitschrift des Vereins Deutscher Ingenieure 77(12):318-320, 1933.

[36.] Ranz, W. and Marshall, W., "Evaporation from Drops," Chemical Engineering Progress 48:141-146, 1952.

[37.] Wozniak, G., Zerstaeubungstechnik, (Heidelberg, Springer Verlag, 2003), ISBN:3-540-41170-4.

[38.] Ebrahimian, V., Nicolle, A., and Habchi, C., "Detailed Modeling of the Evaporation and Thermal Decomposition of Urea-Water-Solution in SCR Systems," AIChE Journal 58(7):1998-2009, 2012.

[39.] Schirmer, R., "Diffusionszahl von Wasserdampf-Luftgemischen und die Verdampfungsgeschwindigkeit," VDI-Beilage, Verfahrenstechnik 6:170, 1938.

[40.] Kabo, G.Y., Miroshnichenko, E.A., Frenkel, M.L., Kozyro, A.A. et al., "Thermochemistry of Urea Alkyl Derivatives," Bull. Acad. Sci. USSR, Div. Chem. Sci. 39:662-667, 1990.

[41.] Gambino, M. and Bros, J.P., "Capacite calorifique de l'uree et de quelques melanges eutectiques a base d'uree entre 30 et 140[degrees]C," Thermochim. Acta 127:223-236, 1988.

[42.] Sachs, L. and Hedderich, J., Angewandte Statistik-Methodensammlung mit R, Twelfth Edition, (Berlin, Springer Verlag, 2006), ISBN:3-540-32160-8.

[43.] Lazic, R., Design of Experiments in Chemical Engineering, (Weinheim, Wiley-VHC Verlag GmbH&Co.KGaA, 2004), ISBN:3-527-31142-4.

[44.] Bai, C. and Gosman, A., "Development of Methodology for Spray Impingement Simulation," SAE Technical Paper 950283, 1995, doi:10.4271/950283.

[45.] Bai, C. and Gosman, A., "Mathematical Modeling of Wall Films Formed by Impinging Sprays," SAE Technical Paper 960626, 1996, doi:10.4271/960626.

[46.] Moeltner, L., Giovannini, A., and Schallhart, V., "Analysis of Heat and Mass Transfer on Free Moving Urea/Water-Droplets in SCR-Systems by Numerical Methods," International Journal of Mechanics, 10:138-144, 2016, ISSN: 1998-4448.

[47.] Larsson, P., Lennard, W., Andersson, O., and Tunestal, P., "A Droplet Size Investigation and Comparison Using a Novel Biomimetic Flash-Boiling Injector for AdBlue Injections," SAE Technical Paper 2016-01-2211, 2016, doi:10.4271/2016-01-2211.

[48.] Gaynor, P., Reid, B., Hargrave, G., Lockyer, T. et al., "An Experimental Investigation into DEF Dosing Strategies for Heavy Duty Vehicle Applications," SAE Int. J. Engines 8(3):1196-1206, 2015, doi:10.4271/2015-01-1028.

[49.] Hua, L., Zhao, Y., Hu, J., Tao, T. et al., "Comparison Between Air-Assisted and Airless Urea Spray for Diesel SCR System by PDA and CFD," SAE Technical Paper 2012-01-1081, 2012, doi:10.4271/2012-01-1081.

[50.] Roy, S., Barman, J., and Khan, R., "Development of Air less Urea Dozing Architecture for Better Optimum Spray Characteristics and to Avoid Urea Crystallization," SAE Technical Paper 2017-28-1927, 2017, doi:10.4271/2017-28-1927.

[51.] Bernhard, A., "Catalytic Urea Decomposition, Side-Reactions and Urea Evaporation in the Selective Catalytic Reduction of NOx," Dissertation, ETH Zurich, Zurich, 2012.

[52.] Zhang, H., Xi, Y., Su, C., and Liu, Z., "Lab Study of Urea Deposit Formation and Chemical Transformation Process of Diesel Aftertreatment System," SAE Technical Paper 2017-01-0915, 2017, doi:10.4271/2017-01-0915.

Appendix A: Temperature Progression along the SCR Mixing Section

Appendix B: Kinetics of Thermolysis

Appendix C: Simulation of UWS Injections
TABLE C.1 Droplet's diameter, velocities, and density at
the moment of impingement for the three investigated
droplet-size classes and operation points.

d/[micro]m                       orig. 85 [micro]m  orig. 171 [micro]m

E-OP3                              76                 166
E-OP4                              73                 165
E-OP5                              69                 161
[V.sub.total]/(m x [s.sup.-1])   orig. 85 [micro]m  orig. 171 [micro]m
E-OP3                              18.74              22.50
E-OP4                              26.52              24.89
E-OP5                              50.14              35.24
[[rho].sub.UWS/(kg x [m.sup.-3)  orig. 85 [micro]m  orig. 171 [micro]m
E-OP3                            1123               1090
E-OP4                            1138               1093
E-OP5                            1162               1099
[V[.sub.ortho]/(m x [s.sup.-1])  orig. 85 [micro]m  orig. 171 [micro]m
E-OP3                               7.89              14.12
E-OP4                               8.98              14.57
E-OP5                              10.79              15.44

d/[micro]m                       orig. 263 [micro]m

E-OP3                             259
E-OP4                             258
E-OP5                             256
[V.sub.total]/(m x [s.sup.-1])   orig. 263 [micro]m
E-OP3                              23.62
E-OP4                              24.86
E-OP5                              30.64
[[rho].sub.UWS/(kg x [m.sup.-3)  orig. 263 [micro]m
E-OP3                            1085
E-OP4                            1086
E-OP5                            1089
[V[.sub.ortho]/(m x [s.sup.-1])  orig. 263 [micro]m
E-OP3                              15.76
E-OP4                              16.02
E-OP5                              16.49

[c] SAE International

TABLE C.2 Reynolds and Weber number for the different
droplet-size classes at the moment of impingement.

[Re.sub.drop]/-  orig. 85 [micro]m  orig. 171 [micro]m

E-OP3             15.84              60.49
E-OP4             17.14              61.8
E-OP5             21.79              94.78
We/-             orig. 85 [micro]m  orig. 171 [micro]m
E-OP3             70.38             481.97
E-OP4             89.08             508.91
E-OP5            124.82             563.81

[Re.sub.drop]/-  orig. 263 [micro]m

E-OP3             104.97
E-OP4             106.25
E-OP5             173.03
We/-             orig. 263 [micro]m
E-OP3             932.43
E-OP4             961.08
E-OP5            1009.58

[c] SAE International

TABLE C.3 Wall temperatures at the points of impingement.

       [T.sub.wall]/K

E-OP3  476
E-OP4  567
E-OP5  654

[c] SAE International

TABLE C.4 Mass fraction of urea at the moment
of impingement for the three droplet-size classes.

[m.sub.urea]/[m.sub.total]/-  orig. 85 [micro]m  orig. 171 [micro]m

E-OP3                         0.45               0.36
E-OP4                         0.49               0.36
E-OP5                         0.56               0.38

[m.sub.urea]/[m.sub.total]/-  orig. 263 [micro]p

E-OP3                         0.34
E-OP4                         0.34
E-OP5                         0.35

[c] SAE International

TABLE C.5 Droplet's boiling temperature at the time
of impingement.

[T.sub.boll]/K  orig. 85 [micro]m  orig. 171 [micro]m

E-OP3           379.3              377.5
E-OP4           380.3              377.5
E-OP5           382.4              377.5

[T.sub.boll]/K  orig. 263 [micro]m

E-OP3           377.1
E-OP4           377.1
E-OP5           377.3

[c] SAE International


Verena Schallhart and Lukas Moeltner, MCI Management Center Innsbruck

History

Received: 16 Oct 2017

Revised: 14 Mar 2018

Accepted: 26 Mar 2018

e-Available: 22 May 2018

Keywords

Selective catalytic reduction,

Diesel engines, NOx,

Urea-water solution,

Decomposition of urea

Citation

Schallhart, V. and Moeltner, L., "Effect of Spray-Exhaust Gas Interactions on Ammonia Generation in SCR Mixing Sections," SAE Int. J. Fuels Lubr. 11(2):181-200, 2018, doi:10.4271/04-11-02-0009.
TABLE 1 Comparison of the reaction parameters A in [s.sup.-1]
and [E.sub.A] in J/mol for the thermolysis of urea in accordance
with Arrhenius.

Buchholz [21]              [mathematical expression not reproducible]
Fang and Da Costa [22]     [mathematical expression not reproducible]
Brack et al. [23]          [mathematical expression not reproducible]
Ostrogovich and Bacaloglu  [mathematical expression not reproducible]
[24]
Birkhold [25]              [mathematical expression not reproducible]
Yim et al. [20]            [mathematical expression not reproducible]
Rota et al. [26]           [mathematical expression not reproducible]

[c] SAE International

TABLE 2 Reaction parameters A in [s.sup.-1] and [E.sub.A] in J/mol
for the hydrolysis of isocyanic acid in accordance
with Arrhenius.

Wurzenberger et al. [17]  [mathematical expression not reproducible]
Yim et al. [20]           [mathematical expression not reproducible]
Rota et al. [26]          [mathematical expression not reproducible]

[c] SAE International

TABLE 3 Technical data of the test engine.

Cylinders             V6

Displacement          2987 c[m.sup.3]
Rated power at speed  165 kW at 3800 [min.sup.-1]
Maximum torque at     510 Nm at 1600 [min.sup.-1] to 3800 [min.sup.-1]
speed
Compression ratio     18:1
Injection system      Common rail direct injection

[c] SAE International

TABLE 4 Engine-out parameters and gas temperature at
the entrance of the SCR system for the investigated
operation points.

Operation  Mass flow/      Temperature    Temperature SCR
point      (kg [h.sup.1])  exhaust gas/K  entrance/K

E-OP 3     100             523            510
E-OP 4     200             623            600
E-OP 5     350             723            683

[c] SAE International

TABLE 5 Dimensions and material parameters of the
considered SCR mixing section.

Length                     0.550 m
Inner diameter             0.060 m
Wall thickness             0.001 m
Material                   1.4301 austenitic stainless steel
Density                 7900 kg x [m.sup.-3]
Specific heat capacity   500 J x (kg x K)[.sup.-1]
Thermal conductivity      15 W x (m x K)[.sup.-1]

[c] SAE International

TABLE 6 Density, velocity, and dynamic viscosity
of the inflowing exhaust gas for the three operation points.

       Gas density/   Gas velocity/  Dynamic
       kgx[m.sup.-3]  mx[s.sup.-1]   viscosity/Pa-s

E-OP3  0.692          14.2           2.76 x [10.sup.-5]
E-OP4  0.588          33.4           3.08 x [10.sup.-5]
E-OP5  0.517          66.5           3.36 x [10.sup.-5]

[c] SAE International

TABLE 7 K-numbers for the investigated droplet-size classes
and operation points at the moment of impingement.

K/-    orig. 85 [micro]m  orig. 171 [micro]m  orig. 263 [micro]m
E-OP3  16.71              61.17                97.64
E-OP4  19.18              63.25                99.53
E-OP5  24.21              74.10               115.23

[c] SAE International

TABLE 8 Temperature ratios and the respective critical
temperature quotient for all investigated droplet-size classes
and operation points.

T/[T*.sub.crit]       orig. 85 [micro]m  orig. 171 [micro]m

E-OP3                 1.255/1.442        1.261/1.392
E-OP4                 1.491/1.464        1.502/1.392
E-OP5                 1.710/1.504        1.731/1.403

T/[T*.sub.crit]       orig. 263 [micro]m

E-OP3                 1.262/1.380
E-OP4                 1.504/1.380
E-OP5                 1.733/1.386

[c] SAE International

TABLE 9 Regime classification for the investigated
droplet-size classes and operation points in accordance to Bai
and Gosman [44, 45].

Regime  orig. 85 [micro]m  orig. 171 [micro]m  orig. 263 [micro]m

E-OP3   Deposition         Deposition          Deposition
E-OP4   Rebound            Break-up            Break-up
E-OP5   Rebound            Break-up            Break-up

[c] SAE International

TABLE 10 Comparison of the urea conversion for the four
considered scenarios at E-OP3.

                   S1                  S2

Urea conversion/-  3.45 x [10.sup.-6]  3.67 x [10.sup.-6]

                   S3                  S4


Urea conversion/-  3.74 x [10.sup.-6]  3.98 x [10.sup.-6]

[c] SAE International
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Author:Schallhart, Verena; Moeltner, Lukas
Publication:SAE International Journal of Fuels and Lubricants
Article Type:Technical report
Date:May 1, 2018
Words:12650
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