## 4 Summary and Conclusions  
The main results of this study are summarized below in bullet points.  
Regarding the conventional piston:  
* At no-EGR condition (21% O\({}_{2}\)), the reduction of KL is more prominent when increasing the OME\({}_{\rm X}\) quantity in the blend, which agrees with what can be found in the literature.
* The OME\({}_{\rm X}\) content in the blend reduces the amount of soot formed, even at 15% O\({}_{2}\). However, results confirm that only OME\({}_{\rm X}\) (up to 50%) is insufficient to avoid the increase because of the reduction of ambient oxygen.  
Regarding the radial-lips piston:
* The avoidance of flame-to-flame interaction achieved by the radial-lips feature results in lower soot formation close to the bowl wall. In addition, the redirection of flames toward the center of the piston takes advantage of the oxygen available and significantly improves soot oxidation.
* The addition of OME\({}_{\rm X}\) improves the radial-lips piston geometry benefits. In the most unfavorable condition (15% O\({}_{2}\)), the addition of OME\({}_{\rm X}\) can extend the KL reduction achieved by the novel piston geometry from 17% (0 Ox) up to 70% (50 Ox) during the late stage of combustion.
* Results show that 30% and 50% OME\({}_{\rm X}\) in the blend, in combination with the radial-lips piston, can provide similar soot levels with 15% and 21% O\({}_{2}\). This confirms the potential of this combined solution to reduce soot levels when using EGR significantly.  
The reported synergy between OME\({}_{\rm X}\) and the radial-lips concept represents a promising solution to mitigate the existing soot-NO\({}_{\rm X}\) trade-off. It opens a path to using temperature reduction strategies like EGR to minimize NO\({}_{\rm X}\) formation without compromising soot emissions.  
This study has analyzed the potential of different OME\({}_{\rm X}\)-Diesel blends (0%, 30%, and 50%) in combination with a novel radial-lips piston geometry under high EGR rate condition (15% O\({}_{2}\)). However, this work presents some limitations that future works should overcome. As previously mentioned, only the duration of the main injection was modified to compensate for the lower LHV of OME\({}_{\rm X}\) to reach the same engine load for all cases. Future studies should explore further improvement and optimization of the injection strategy for the blends by modifying other parameters, such as the number of injections, the injection pressure, or the delay between pulses. In addition, the study analyzed the combustion behavior in an optical engine, which has certain limitations in terms of operating conditions compared to more conventional engines. Therefore, to extend the application of the results presented here, a similar study in a full-metal version of a single-cylinder engine would be beneficial to analyze the exhaust emissions and corroborate what has been observed inside the cylinder and has been reported in this work.  
Conceptualization, J.V.P.; Data curation, F.L. and F.J.T.; Formal analysis, F.L.; Investigation, F.J.T. and C.T.; Methodology, C.M.; Project administration, J.V.P.; Resources, J.V.P.; Software, F.J.T.; Supervision, C.M.; Writing--original draft, F.J.T.; Writing--review & editing, C.M., F.L. and C.T. All authors have read and agreed to the published version of the manuscript.  
This work has been partially funded by Universitat Politecnica de Valencia through the program of access contracts for PhD research staff in Research Structures of the Universitat Politecnica de Valencia with reference PAID-10-22. The presence of [PERSON] at Universitat Politecnica de Valencia was funded by the \"Short Term Mobility (STM) Program\" of the Italian National Research Council.  
Not applicable.  
The authors declare no conflict of interest.