Deposit Formation from Urea Injection: a Comprehensive Modeling Approach

For validation of both the applied simulation models and the new speed-up method, experimental results from an engine test bench, as shown in Fig. 1 a, were used. Its design allows the study of following physical and chemical processes under engine typical OC:

In order to avoid the modeling of complex turbulent flow and hence facilitate the validation of simulation models, a uniform and unidirectional flow with fine-scale and isotropic turbulence was generated in the measurement volume of the optical box. For this reason, an inlet section with a cone angle of 7° followed by an uncoated monolith (CAT1) was implemented (see Fig. 1b). Downstream of the measuring section a second uncoated monolith (CAT2) separated any liquid urea from the exhaust gas.

The measurement volume of the box (200 × 200 × 600 mm) was designed to enable optical access to the deposit formation process mentioned above. A horizontal impingement plate made of widely used steel X5CrNi18-10 with a thickness of 2 mm and the surface roughness Ra < 0.5 μm was placed in the middle of the box. The straight plate allows unhindered propagation of the liquid film with long pathway. The liquid film was produced by an AdBlue injector installed on the topside of the box. AdBlue was supplied by a flexible and mobile supply and control unit. For observation of the liquid film and the formation of solid deposits, the box was equipped with three large borosilicate glasses.

The cooling of the bottom side of the impingement plate was measured with an IR-camera through zinc selenide windows (Zn-Se), which have a high transmissivity in the IR spectrum range. In order to increase the surface emissivity, the bottom side of the plate was varnished with black lacquer. Additionally, a line pattern was carefully scratched in the lacquer for spatial information. For calibration of the IR-camera, two thermocouples were soldered on the plate within the observation area of the camera.

For validation of the simulation models, two experiments were chosen as shown in Table 1. The choice was based on the following criteria:

The OCs of the experiment 1 are typical for a higher load point of a diesel engine. Due to the heat radiation, at the beginning of the experiment the steady state temperature of the impingement plate was approx. 40 °C less than the temperature of the exhaust gas. Nevertheless, it was sufficiently high to cause the Leidenfrost effect during the first 15 s of the experiment. After this time, the critical wall temperature was reached, which triggered wall wetting and the subsequent formation of solid deposits. AdBlue was being injected during the whole experiment. The video recording of the experiment shows a permanent accumulation of solid deposits.

The OCs of the experiment 2 represents a medium load point of a diesel engine. The initial steady state temperature of the impingement plate was approx. 245 °C, which is 30 °C less than the temperature of the exhaust gas. The liquid film was being produced during the first 5 min of the experiment by the injection of AdBlue. Then the injection was stopped. A fast evaporation of the liquid film and a slow decomposition of solid deposits were visually observed during the next 15 min of the experiment.

Two different commercial injectors were applied for the film generation in the experiments 1 and 2. They cover a wide range of droplet Weber-numbers and specific area load, which are known to have a crucial impact on the spray impingement regimes and the wall cooling [6, 34‐36]. The spray characteristics of both injectors are shown in Table 2.

After each experiment, solid deposits were removed from the impingement plate and stored in a hermetic container for chemical analysis. The applied analytical methods are explained in the following chapter.

Deposits generated and sampled from the test rig are subsequently analyzed in terms of chemical composition by thermogravimetric analysis (TGA) and high-performance liquid chromatography (HPLC).

Thermogravimetric analysis is performed in a Netzsch STA 409 C instrument. Deposit samples from the test rig are grinded and an initial sample mass of 10 mg is arranged in a cylindric corundum crucible. Using a constant heating rate of 2 K/min, the sample is heated from 40 to 700 °C. Synthetic air (20.5% O2 in N2) is used as purge gas with a flow of 100 ml/min. Measurements reveal the sample mass loss due to evaporation and chemical reactions over temperature. Normalization by the initial sample mass is performed for the presentation of the measurement results. In addition to measurements on the deposit samples, reference measurements are performed with pure cyanuric acid (Sigma Aldrich, purity ≥ 98%).

For quantitative analysis of the deposits’ composition, HPLC measurements are performed. The method applied for the measurements was specifically designed for chemical characterization of urea deposits and was adapted from previously published methods [37, 38]. It includes urea, biuret, triuret, cyanuric acid, ammelide, ammeline and melamine. A Hitachi VW12 HPLC instrument with a L-2200 sampler is employed for the measurements. Signal analysis is performed downstream the column (Waters IC-PAK Anion HC) by a L-2455 diode array detector. A N2HPO4 buffer solution is used as mobile phase after filtration with a constant flow of 0.5 ml/min at 25 °C. As results reveal a strong sensitivity on pH, the solution was kept at pH = 10.4 constantly. Calibration was performed in advance by standard solutions.

Deposit samples are grinded and dissolved in the eluent. Initially, a sample of 15–20 mg is dissolved in 100 ml of the eluent. Further dilution was required in case of poor solubility of the sample or to meet the respective calibration range of a species. With this method, the composition of the deposit samples can be determined with an accuracy of < 5% for urea, < 10% for biuret, < 30% for triuret, < 10% for cyanuric acid, < 20% for ammelide, < 10% for ammeline and < 20% for melamine.

The numerical modeling of both described experiments was carried out within the CFD code Star-CCM+ v13.06. It consisted of a set of consecutive simulations:

For the modeling of the gas flow in all simulations, a RANS (Reynolds-averaged Navier-Stokes) approach was used with a Lag Elliptic Blending k-ε realizable turbulence model. The heat exchange between solid parts of the box and the exhaust gas was simulated with the help of the conjugate heat transfer model [33]. A combination of the Gray Thermal Radiation and the Surface-to-Surface Radiation model [33] was used to reproduce the cooling of solid walls due to thermal radiation.

The volume mesh of the optical box and the monolith downstream (see Fig. 1a) are shown in Fig. 2. For the modeling of the liquid film, a shell region was created on the topside of the impingement plate. In order to represent the uncoated monolith downstream the box, a volume mesh was extruded from the outlet of the fluid region.

A grid dependency analysis was carried out to optimize the simulation effort and accuracy in the following numerical investigations. Simulations with a cell base size of 2 mm showed reasonable results for the velocity field inside the optical box. Furthermore, the impact of the wall treatment on the convective heat transfer between the gas flow and the impingement plate was studied. For this reason, the temperature field of the plate was modeled with both low and high y⁺ wall treatment approaches at steady-state OC of the experiment 1. The obtained temperature field of the plate is the resulting equilibrium state between the convective heat transfer from the exhaust gas to the plate and the heat loss of the plate due to the heat radiation. As shown in Fig. 3, the simulation result obtained with resolved viscous sublayer (7 prism layers) and low y⁺ wall treatment has a very good agreement with the measurement data. In contrast, the simulation with not resolved viscous sublayer (3 prism layers) and high y⁺ wall treatment overestimated the resulting temperature field by more than 10 °C.

The physical models applied for the simulation of UWS spray and liquid film are mainly based on the work by Fischer [30] and the SCR best practices guide by the software producer [33]. The spray deceleration by the exhaust gas was simulated by the modified Schiller-Naumann drag force model [39]. The modified Wruck impingement heat transfer model [40] was applied for the modeling of heat exchange between the spray and the impingement plate if its surface temperature was above the critical value. The droplet impingement was simulated according to the modified Bai-Onera impingement model [41]. The two-dimensional, finite volume model [33] was applied for the modeling of liquid film. The kinetic model for urea decomposition and by-product formation is integrated by user-coding based on the algorithm of a multi-phase batch reactor model in DETCHEM™ [42].

The modified Schiller-Naumann, Wruck and Bai-Onera models can be found in the final report of the research project “AdBlue Deposits” supported by the Research Association for Combustion Engines. The focus of current work is the applied speed-up method and the coupling of the detailed chemical solver DETCHEM™ with the used CFD code.

In order to speed up the simulation time and hence accomplish the modeling of deposit formation with typical time ranges, a new speed-up method called “injection source approach” was developed. In this approach, the numerical parcels representing the spray are substituted by source terms of mass, momentum and energy that are directly applied to the film and gas phase. The source terms for both phases were calculated simultaneously during a single injection event. The obtained sources can be used as long as the OC remain constant, i.e. as long as the spray deflection and the impingement positions of droplets are not changing. When simulating transient OCs, the source terms must be updated continuously with the specific combination of spray and exhaust mass flow. In the following, the calculation of source terms for the gas and film phase will be described in detail.

The source terms applied to the gas phase should represent the spray behavior in the exhaust gas flow, i.e. mass and energy transfer between the spray and the gas phase as well as the momentum exchange between both phases. Three required source terms can be calculated during an unsteady simulation of one injection cycle. During this simulation, following values should be determined in each fluid cell for each time step:

The values of m_gi, Q_g and p_g were cumulated during the whole simulation time and then normalized to the cell volume and the used injection time.

The obtained data \( \sum {\overline{m}}_{gi} \), \( \sum {\overline{Q}}_g \) and \( \sum {\overline{\overrightarrow{p}}}_g \) are source terms for mass, energy and momentum, respectively. The normalized terms can be applied to each desired injection time.

As mentioned above, the calculation of source terms for the film phase was conducted simultaneously with those for the gas phase. During the unsteady simulation of one injection cycle, properties of the impinging droplets were analyzed and the following values were determined:

According to the applied Bai-Onera impingement model, the sticking mass depends only on the surface temperature and the impact K-number [43].

Where We_n and Oh denote the normal impact Weber number and the Ohnesorge number, respectively.

As long as the OCs are not changing, the impact of the gas flow on the droplets is not changing as well. Droplet trajectories and thus impact K-numbers of droplets will remain the same for each injection. Therefore, only changing surface temperature, due to surface cooling by film evaporation, may lead to a change of the sticking mass. In order to obtain a mass source, which is valid for different surface temperatures T_si, sticking mass \( {m}_{s,{T}_{si}} \) should be calculated for different surface temperatures T_si in advance, e.g. 280, 260, 240, 220, 200 and 160 °C. These values cover the temperature range with the highest changing gradients of the sticking mass. Below the surface temperature of 160 °C, the temperature impact on droplet impingement is considered as negligible [44].

Due to the fact that spray droplets evaporate in the hot exhaust gas and hence have different concentrations of water and urea, \( {m}_{s,{T}_{si}} \) should be determined for each species:Where the c_i is the current species concentration in the impinging droplet.

Where h is the impingement heat transfer coefficient, A_cont effective contact area, T_di temperature of an impinging droplet and c the droplet count in a parcel.

The values \( {m}_{si,{T}_{si}} \), \( {\mathrm{Q}}_{,{T}_{si}} \), \( {\overrightarrow{p}}_f \) and m_di ∙ T_di were cumulated during the entire simulation time for each surface cell and then normalized to the cell area and the used injection time. In order to obtain mass and heat sources, which are valid for the current surface temperature, a linear interpolation between pre-calculated values of \( \varSigma {\overline{m}}_{si,{T}_{si}} \) or \( \varSigma {\overline{Q}}_{T_{si}} \), respectively, was carried out. The cumulated value \( \varSigma {\overline{\overrightarrow{p}}}_f \) was the source term of momentum applied to the film region during injection time.

In order to obtain the correct mass averaged temperature of the species produced by the mass sources, the cumulated product of m_di ∙ T_di must be divided by the cumulated impinged mass:

A kinetic model for urea decomposition adapted from Brack et al. [11] is implemented to the CFD model by user-coding. The numerical algorithm of the DETCHEM™ Multiple Phase Tank Reactor (MPTR) package [45] is translated to user-defined functions. This procedure establishes an interface between the CFD code and the 0D chemistry model in the fluid film. Concentration, temperature and pressure data are transferred from the CFD code to the user code for each liquid film cell in each time step. From these data, reaction rates are calculated by the user-coded algorithm. The complex chemistry model can call resulting production terms in the fluid film in order to update the species concentrations in each time step. No interface exists between the user code and the Lagrangian phase, as urea decomposition was found to be negligible in the simulations due to small droplet lifetime. All physical processes, e.g. gas-liquid equilibria, are calculated in the CFD code independently from the user code.

The numerical model implemented to the user code represents a 0D batch reactor model containing one gaseous and multiple condensed, ideally mixed phases. Besides the gaseous (g) phase, one liquid (l), one aqueous (aq) and multiple solid (s) phases are considered. The phase volumes are assumed to be layered on top of each other and connected by an interface of defined size. Here, the interface area is equal to the cell area. Phase transitions are implemented by two different species, as the species are assigned to respective phases. Reaction rates r_k are expressed by an extended Arrhenius termwhere A_k represents the pre-exponential factor, β_k the temperature exponent, E_{A, k} the activation energy, R the gas constant and ῦ_ik the concentration exponent. For evaporation and condensation, reaction rates are calculated by Eq. (6) representing Herz-Knudsen equation and Eq. (7) based on kinetic gas theory. α_c denotes an accumulation factor, M_i the specific molar mass and h the Henry constant given by Eq. (8).c_i and ρ_i represent the species concentration and density in the respective phases. \( {p}_i^{vap} \) denotes the vapor pressure. Production rates \( {\dot{n}}_{ik} \) for the species i for homogeneous and heterogeneous reactions are given by Eqs. (9) and (10) in dependence on the stoichiometric coefficient ν_ik as well as the phase volume V_j and interface area A, respectively.

Species and enthalpy conservation Eqs. (11) and (12) are solved by the LIMEX solver [45].

k_w denotes the heat transfer coefficient, T^extern the external temperature given by the heating rate. Total enthalpy H is expressed by

The kinetic parameters were adapted and enhanced based on the work of Brack et al. [11] by kinetic data derived from TGA. The applied kinetic scheme is given by Table 4 in the supplemental material. The model considers urea, biuret, triuret, cyanuric acid and ammelide. Since the MPTR model considers multiple condensed phases, pseudo-liquid species are defined in the fluid film model in StarCCM+, which represent solid or aqueous species. Thermophysical properties for all relevant species are summarized in a species database, which is implemented to StarCCM+. A detailed description of the implemented property data for all relevant species in the respective phases is given in the supplemental material.

In the user code, type definitions for variables and functions, mathematical functions and user accessible data are loaded. A user function is created, which results in an array containing production terms for all relevant species in the units of mol/kg/s. The numerical and kinetic algorithm for calculating the production terms is implemented to the user function. Based on the specific mole fraction, which is transferred from the CFD code, mixture densities and molar concentrations of all species present in the liquid film are calculated. In the CFD code, the liquid film represents liquid, aqueous and solid phase. The total amount of each species and the volume of each phase are determined in order to calculate the species concentrations for each phase (l, aq and s).

After compilation to a user library, the user code is loaded to Star-CCM+. In the fluid film model, the user function is integrated to the complex chemistry model as species source.