**5. Conclusions**

In view of the challenges to manage the gasoline partially premixed combustion in compression-ignited engines, this paper proposes a numerical approach based on multi-dimensional CFD in order to improve the knowledge and understanding of this particular combustion concept. In particular, the presented methodology was specifically developed to capture knocking combustion, allowing an comprehensive analysis of all involved phenomena and their undesired effects.

The proposed methodology allows a realistic estimation of both the cycle-averaged and dispersion values of the main combustion/knock metrics while keeping the computational burden under reasonable values. Thereby it offers the chance to include these parameters in the design process, optimizing them altogether with the rest of relevant emissions and performance metrics.

Combining distinct visualization methods, such as iso-surfaces of temperature and energy release contours, allowed to identify the differences in the combustion process among two extreme cycles, thereby enhancing the understanding the knock phenomenon.

Results revealed that the propensity of the knock onset is reduced as the combustion is delayed towards the expansion stroke. In this sense, cycles with lower burning rates lead to a slight knocking combustion whereas high burning speed cycles tends to significantly increase the knock.

Nonetheless, further efforts must be taken to confirm, through LES simulations, that URANS is capturing all relevant phenomena in the knocking combustion. Moreover, further analysis should be done for providing more insight about the combustion process itself and its related knocking generation mechanisms.

**Author Contributions:** All authors discussed and agreed on the contents of the manuscript. R.N. managed the work defining the objectives of the proposed methodology, guiding the technical discussion of the results and contributing to the critical review of the manuscript. J.G.-S. conducted the research tasks and leaded the investigation process; developed the methodology, performed the simulations, analysed the results and wrote the initial draft. P.J.M.-H. contributed to the manuscript preparation and presentation. J.R.S. discussed the results, contributed to the manuscript review and provided technical guidance in the design of methodology.

**Funding:** The work has been partially supported by the Spanish Ministerio de Economía y Competitividad through gran<sup>t</sup> number TRA2016-79185-R. The equipment used in this work has been partially supported by FEDER project funds "Dotación de infraestructuras científico técnicas para el Centro Integral de Mejora Energética y Medioambiental de Sistemas de Transporte (CiMeT), (FEDER-ICTS-2012-06)" from the operational program of unique scientific and technical infrastructure of the Spanish Ministerio de Economía y Competitividad. In addition, J. Gomez-Soriano is partially supported by an FPI contract (FPI-S2-2016-1353) of the "Programa de Apoyo para la Investigación y Desarrollo (PAID-01-16)" of the Universitat Politècnica de València.

**Acknowledgments:** The authors want to express their gratitude to CONVERGENT SCIENCE Inc. and Convergent Science GmbH for their kind support for the CFD calculations with the CONVERGE software.

**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.
