**5. Conclusions**

A modeling work conducted on the understanding of the causes of pre-DPF water injection effects on wall-flow DPF pressure drop, filtration and regeneration response has been presented. A one-dimensional wall-flow DPF model has been applied to explore how the soot mass distribution in the particulate layer formed on the inlet channels walls and the porosity of the particulate layer influence on pressure drop. Good agreemen<sup>t</sup> has been found between experimental data, optical visualization of the monolith channels and modeling of pressure drop. In fact, the modeling results of the pressure drop after pre-DPF water injections events have confirmed that the soot mass on the particulate layer must be moved back as a required condition to reduce the DPF pressure drop.

Although the onset of the soot mass distribution is dependent on the particulate layer porosity, the modeling of the soot loading after every injection event has demonstrated that the particulate layer compaction has a negligible impact. Likewise, parabolic and linear soot mass distribution profiles have been computed obtaining just minor changes to the onset of the soot mass distribution. The main outcomes on the mechanism governing the pressure drop reduction are not sensitive to this parameter.

In agreemen<sup>t</sup> with experimental data obtained in previous works, modeling results indicate that the filtration efficiency is not modified by pre-DPF water injection. The reason lies in the fact that the porous wall is kept saturated acting as a barrier filter. However, the conclusions on the regeneration dynamics during active processes obtained from experimental data have been contradicted by the modeled results. The results obtained in this work evidence that the soot depletion rate when the DPF has been subjected to water injection is non-uniform along the inlet channels, in contrast to the baseline case. In fact, the entering and middle regions are quickly regenerated. This makes the pressure drop rapidly decrease. However, the rear end region of the inlet channels behaves as a plug end, the filtration velocity (mass flow) being very small along this porous wall region. Consequently, the soot oxidation gets mass transfer limited, leading to a slower regeneration end phase than the baseline operating conditions. This behavior points out that optimization of active regeneration strategies should be required in order to take maximum advantage from pre-DPF water injection benefits.

Beyond particular concerns on pre-DPF water injection, the results obtained in this study also contribute to highlight the importance of the soot loading process and how engine operation history can determine the soot structure (recurrent engine stops with water condensation, highly dynamic engine operation, etc.). It would explain pressure drop variability under the same operating conditions, which can cover up the real DPF state and lead to additional engine fuel consumption penalty and substrate durability issues, especially when pressure drop-based control is considered.

**Acknowledgments:** This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through Grant No. TRA2016-79185-R. Additionally, the Ph.D. student Enrique José Sanchis has been funded by a gran<sup>t</sup> from Universitat Politècnica de València with the reference FPI-2016-S2-1355. This support is gratefully acknowledged by the authors.

**Author Contributions:** All authors discussed and agreed on the contents of the manuscript. Pedro Piqueras coordinated the work defining the objectives of the experimental and modeling tasks, guiding the technical discussion of the results and manuscript writing. Enrique José Sanchis contributed to the design of the theoretical study, performed the calculations, analyzed the results and collaborated in the manuscript preparation. José Ramón Serrano and Vicente Bermúdez discussed the results, contributed to manuscript writing and provided technical guidance in experimental phases from the first stages of the project development.

*Appl. Sci.* **2017**, *7*, 234

**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.
