## 4 Conclusions  
This study proposes a multi-zone model to predict diesel/DMG combustion and regular emissions. Based on this model, numerical studies were conducted to investigate a CI engine fueled with different proportions of diesel-DMG blends at a constant engine speed of 1500 rpm and full load. In addition, the effects of EGR rate on performance, as well as the combustion and emission characteristics of a dual-fuel engine are also discussed. The major conclusions are summarized as follows:  
* Increasing the energy share of DMG to 20% of the diesel input energy leads to an increase in ITE and IMEP. Compared to the original diesel engine, the increase is 9.7% for ITE and 9.2% for IMEP, indicating that DMG has the potential to improve engine power and fuel economy. Moreover, methanol has a lower price compared with diesel, which is beneficial for reducing total fuel cost.
* The addition of DMG increases in-cylinder pressure, average temperature, and HRR, makes the temperature distribution and local equivalence ratio more homogenous, and reduces both CA10-90 and CA50. These effects are because the main componentsof DMG are hydrogen, CO, and gaseous methanol, which have fast burning speeds and high combustion temperatures, and therefore improve the combustion efficiency.
* For regular emissions, CO and soot emissions are reduced, HC emissions increase at low substitution levels and decrease at relative higher substitution levels, and NOx emissions decrease with an increase in the DMG substitution ratio. These trends are caused by the high combustion temperature and rich oxygen content of DMG.
* At 15% DMG substitution ratio, ITE and IMEP decrease with an increase in the EGR rate. However, the power and the fuel economy of the dual-fuel engine with less than 20% EGR rate are still higher than that of the original engine without EGR.
* The dilution effect and increased heat capacity caused by EGR have a negative effect on combustion efficiency and result in a decline in the maximum in-cylinder pressure, average temperature, and HRR. However, the high combustion speed and oxygenated nature of DMG partly compensate for this deterioration effect. Thus, the maximum in-cylinder pressure, average temperature, and HRR of the dual-fuel engine with lower EGR rates are still higher than that of the original engine.
* The application of EGR reduces the oxygen concentration, temperature, and pressure inside the engine cylinder. Therefore, CO and soot emissions of the dual-fuel engine increase, HC emissions remain at a similar level, and NOx emissions are drastically decreased with increasing EGR rate.
* The dual-fuel engine outperforms the original engine in power, fuel economy, and regular emissions once the DMG substitution ratio and EGR rate are optimized.  
Overall, the addition of DMG in diesel improves engine performance and reduces HC, CO, and soot emissions. Although the presence of DMG leads to worsened NOx emissions, an optimal EGR rate can mitigate this effect. However, there are still unresolved issues. For instance, all the findings thus far were obtained under stable operating conditions. Further research is required to investigate conditions across a broad range of engine speeds and loads, incorporating diverse injection strategies.  
B.L., resources, writing--review and editing, supervision, funding acquisition; Y.C., investigation, validation, data curation; F.Z., writing--review, funding acquisition; H.X., conceptualization, visualization, writing--original draft, software. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China (Grant No. 52205147), the National Natural Science Foundation of China (Grant No. 52005168), and an open grant from the Hubei Provincial Key Laboratory of Modern Manufacturing Quality Engineering (KFJ)-2020009).  
Not applicable.  
The data used to support the findings of this study are available from the author upon request.  
The authors declare no conflict of interest.