To investigate the root causes of peculiar SCR system performances, 3D-CFD analyses have been carried out using the commercial software CONVERGE CFD v2.4 [17]. In particular, the different mixers’ geometries and flow configuration affect the vorticity distribution of the exhaust gases, the UWS spray evolution, and consequently the mixing process as well as the uniformity of flow and species concentration at the SCR inlet. Liquid film development and urea deposit formation are influenced as well by the geometries of the mixers. In this context, numerical analyses can be considered complementary to the experimental campaign, since they allow to obtain additional information concerning the phenomena happening within the exhaust lines, which cannot be acquired during experimental tests, providing useful insights on the key aspects influencing NOx conversion efficiency and deposit formation.
Simulations were performed considering the whole aftertreatment system and the two different mixing subsystems. The operating conditions considered featured an inlet mass flow rate of 125 kg/h and a fixed temperature of 250 °C, corresponding to test case 1 of the experimental campaign (Table 1). Preliminary steady-state single-phase simulations were performed to calculate gas flow field and pressure drops within the systems and initialize multi-phase transient simulations, which were then used to investigate UWS spray development, liquid film formation, and NH3 mixing. In particular, since the aim of the numerical analysis was the characterization of the systems in terms of flow uniformity and mixing between the exhaust gases and the UWS, the inlet gas composition was set to represent air, and NOx emissions have not been included. Consequently, all the reactions inside the SCR systems were not modeled in the numerical simulations. The DOC, DPF, and SCR catalysts have been modeled as porous regions in the numerical analysis, and the pressure loss coefficients have been calibrated to match the available experimental data in terms of pressure losses inside each component. The virtual representation of the DOC has been further simplified substituting the real perforated plate element with a dedicated porous region of 5-mm thickness.
An inflow boundary condition was used to represent engine exhaust gases entering the exhaust line, with constant values of mass flow rate and temperature. A turbulence intensity equal to 10% has been assumed on the inflow boundary, with a turbulence length scale representing a fully developed flow condition. Regarding the outlet boundary of the system, a constant static pressure of 1 bar has been imposed. Following this approach, the inlet pressure of the system remained unconstrained and dependent on the pressure losses inside the system. As far as thermal boundaries are concerned, details are provided in section 4.2 of the paper.
The computational domain was discretized with a base grid size of 5 mm. To correctly characterize UWS spray and mixing phenomena, different grid refinements were implemented: firstly, fixed embedding has been placed along the UWS injector’s hole axes, reaching a minimum grid size of 0.625 mm. Then, an adaptive mesh refinement (AMR) technique has been applied (minimum grid size 0.625 mm), to allow mesh refinements where high velocity and temperature gradients grew up.
The Reynolds-averaged Navier-Stokes (RANS) RNG κ − ϵ model [18] has been used to characterize the turbulence inside the system, as suggested in the case of a rotating flow [19]. The kinetic and thermal boundary layers have been described with a law-of-the-wall approach, and scalable wall functions have been implemented. The target for the near-wall cells y+ was in the range of 30–150, obtained with the AMR technique. The O’Rourke and Amsden heat transfer model has been employed to account for turbulence heat transfer to the walls [20].
Regarding the liquid/gas coupling, Lagrangian and Eulerian approaches have been employed for the liquid and gas phases, respectively. Liquid AdBlue was simulated, with water and urea physical properties modeled as a function of temperature, using a specific size distribution for droplet initialization which was derived from the injector’s manufacturer datasheet. A trapezoidal injection rate profile has been considered for UWS injection, with an injection frequency of 4 Hz, and each injection duration is of about 24 ms. A Kelvin-Helmholtz model [21] which was calibrated in a previous activity for a similar injector [22] has been adopted to account for droplets breakup. Other relevant settings adopted in 3D-CFD simulations were derived from [22] and are reported in Table 2.
Table 2 Summary of the spray and liquid film models implemented in the 3D-CFD simulations to simulate the UWS UWS Decomposition and Deposit Risk Evaluation
The UWS decomposition could be modeled inside a 3D-CFD analysis through different methodologies. For example, simplified models describe only the process of urea thermolysis and hydrolysis using lumped reactions, while more elaborated models consider detailed urea reaction schemes and by-product formations [15]. Simplified models have been broadly applied confirming their validity in an extensive range of exhaust temperatures [29]; however, their main drawback is the lack of urea deposit formation predictiveness. To overcome this limitation, in the present work, a simplified model for the UWS decomposition has been used, the so-called Molten Solid approach [30], together with a user-defined deposit risk index derived from the work of Smith et al. [12]. In this way, an optimal balance between the computational cost needed by the UWS decomposition model and the correct characterization in terms of deposit risk on the mixer region has been obtained. Some details concerning the molten solid approach and the deposit risk index definition are given in the following paragraphs.
According to the molten solid approach, urea decomposition starts only after the complete evaporation of water from each UWS droplet. The decomposition of solid urea into gaseous ammonia and isocyanic acid is modeled with an Arrhenius equation, whose coefficients are obtained from [31]. In addition, hydrolysis of isocyanic acid is modeled using a dedicated reaction mechanism [32].
The numerical evaluation of the urea deposit formation risk in this study was based on an empirical approach, developed from an experimental campaign carried out by Smith et al. to characterize the major factors influencing deposit formation [12]. According to Smith et al., the liquid film is mandatory for the formation of solid deposits, and its development could follow seven different paths. In particular, the progress of secondary reactions and the formation of species such as biuret, ammelide, and cyanuric acid leads to the formation of solid deposits. The formation of deposits is related to different conditions of liquid film thickness, velocity, temperature, and isocyanic local concentrations. In particular, liquid film thickness should be lower than a critical threshold to allow deposit formation, and film velocity should be higher than a critical value. In addition, film temperature should be higher than 160 °C, since secondary reactions leading to deposits formation have been observed to become evident above this temperature during specific experiments. Nevertheless, HNCO concentrations in the gas flowing above the liquid film must be able to sustain reactions; therefore, a minimum isocyanic acid concentration threshold exists.
It should be noticed that, differently from Smith et al. [12], in this study liquid film having temperatures above 250 °C does not contribute to deposit formation, consistently with the Kuhnke wall film model, which describes liquid film deposition only below 250 °C. In the present work, a dedicated subroutine has been developed to identify the liquid film development paths, based on the above-mentioned criteria, using a customized index. Liquid film developing towards the critical path has been used to identify the zones of the exhaust systems in which deposit formation is expected. Since the modeling methodology allowed the identification of the liquid film evolving towards the deposit formation path rather than the detailed description of solids by-products nucleation and growth, the customized index has been referred to as deposit formation risk index.
Thermal Boundary Conditions and Conjugate Heat Transfer
As far as thermal boundaries are concerned, different conditions were adopted along with the system. Adiabatic conditions were assumed for surfaces placed away from the UWS injection and mixing regions since thermal boundaries in these zones are expected to have a negligible impact on the 3D-CFD simulations results. On the contrary, a correct description of the temperature field in the mixer region is critical achieving realistic 3D-CFD results, since UWS impinging on solid walls contributes to their cooling and could cause liquid film formation, affecting not only the availability of NH3 at SCR inlet but also the formation of solid deposits within the exhaust systems.
A 3D-CHT simulation methodology is therefore mandatory to describe the evolution of gas, liquid, and solid temperatures in the mixer region. However, the computational cost associated with such analysis is significant and increases with the extensions of the solid mesh. To reduce as much as possible the computational effort associated with the CHT analysis, preliminary transient simulations were carried out with adiabatic walls to identify all the boundaries showing significant liquid film formation. The simulated time at this stage was coincident with a couple of injection periods.
Following the results of the preliminary analyses, a 3D solid mesh was created to describe the components showing significant liquid film formation, while other boundaries were modeled as adiabatic walls. Thin peripheral solids exposed to external insulation and showing liquid film formation, for which thermal penetration depth was considered small, were modeled using 1D-CHT boundary conditions. The latter consists in modeling heat transfer in thin solid thickness through a 1D thermal network, at the end of which on one side the gas temperature and heat transfer coefficient linked to the 3D-CFD simulation are imposed, and on the other side a bulk constant temperature is adopted (assumed equal to 250 °C in the present study).
The peripheral solids modeled using 1D-CHT boundary conditions were the plate placed between the wings in geometry A and the bell-shaped cup placed downstream of the injector in geometry B. Figure 9 shows an example of the different thermal boundaries adopted in the final simulation setup, for geometry B. The bottom section of the intermediate pipe placed downstream of the injector has been represented as a 3D solid region, for which CHT modeling is enabled (green surfaces). Furthermore, the downstream bell-shaped cup has been represented as a 1D-CHT boundary (blue surfaces).
Lastly, considering that the timescale of solid thermal dynamics is in the order of minutes, while the timescale of injection events is in the order of milliseconds, a conventional 3D-CFD transient simulation to describe steady-state system conditions was not feasible due to prohibitive computational costs. To overcome this issue, the super-cycling approach [17] has been used, which iterates between fully-coupled gas-solid transient and solid-only steady-state solvers, to speed up simulation convergence towards steady-state system thermal conditions. Further details concerning the super-cycling modeling strategy can be found in [17, 22].
In the present application, the super-cycling model has been applied for each 0.25 s, starting in correspondence with the first injection event. Almost 40 UWS injection events have been simulated in the final transient simulations, used to assess system performance.
Uniformity Index
The distribution of the velocity and species concentration on a reference surface can be synthetically represented by the uniformity index (UI) calculation. In particular, it is known that in SCR applications, a high level of uniformity on catalyst inlet section is correlated to better performances in terms of NOx conversion [33]. In the present work, the definition of the uniformity index, UI, is based on the expression of Eq. (6), referred as an example of the velocity distribution on a selected section of interest:
$${\displaystyle \begin{array}{c} UI=1-\frac{1}{2}{\sum}_i\frac{A_i}{A_{tot}}\frac{\left|\overline{v_i}-\overline{v_{avg}}\right|}{\overline{v_{avg}}},\end{array}}$$
(6)
where Ai is the face area of a single cell, Atot is the total area of the considered section, \(\overline{v_i}\) is the face value of the velocity in one single computational cell, and \(\overline{v_{avg}}\) is the surface average velocity on the considered section. Time-averaged concentration and velocities are considered in the calculation, consistently with experimental procedures.