## 1 Introduction
[25] used a single-cylinder optical engine to study the effect of hydrogen injection timing on the mixture formation before and after intake valve closure. It qualitatively evaluated the formation of the in-cylinder mixture using the PLIF method and OH chemiluminescence. [PERSON] et al. [26; 27] combined experimental and numerical simulation to investigate the effects of different injection strategies on the mixture distribution. The results showed that the simulation results had the smallest deviation from the experimental data, and the mesh resolution mainly affected the jet penetration length in the simulation, whereas the jet penetration length had a limited effect on the mixture formation. Owing to the convenience of the numerical simulations, more information on the spatial distribution of hydrogen in the cylinder can be obtained. [PERSON] et al. [28] used GT-Power software to study the optimal hydrogen injection timing under different engine speeds and equivalent ratios. The results showed that the equivalence ratio and engine speed strongly influenced the optimum injection timing and engine performance. The optimal hydrogen injection timing was delayed when the mixture was richer. Different hydrogen injection timings should be used according to the equivalence ratio and speed. [PERSON] et al. [29] analyzed the mixture formation process through computational fluid dynamics (CFD) simulation, providing predictions for using a newly designed nozzle in internal combustion engines. [PERSON] et al. [30] used numerical simulations to study the in-cylinder hydrogen concentration distribution of a port fuel injection (PFI) H\({}_{2}\)ICE, and found that the location of nozzle holes, the diameter of nozzle holes, and the timing of hydrogen injection all had certain effects on the homogeneity of the hydrogen-air mixture in the cylinder. Reasonable matching of these parameters could improve the homogeneity of the mixture and make the exothermic combustion reaction more reasonable. [PERSON] et al. [31] studied the effect of different injection parameters on hydrogen-air mixture formation and optimized the combustion chamber geometry to achieve acceptable thermal efficiency. It was also concluded that injection pressure had the smallest impact on the formation and combustion of the mixture. Many studies have been conducted on hydrogen injection strategies, nozzle positions, and other factors affecting mixture formation in H\({}_{2}\)ICEs. However, owing to the wide flammability of hydrogen, lean combustion is the most suitable condition for hydrogen combustion. For small-to-medium-power internal combustion engines requiring less fuel mass, ultra-lean combustion is very sensitive to the mixture distribution, and further research is needed on hydrogen injection strategies and combustion chamber matching for mixture formation under ultra-lean combustion conditions. Therefore, this study aims to explore the formation of homogeneous mixtures and stable combustion by using three-dimensional CFD software (AVL-Fire) based on a direct-injection H\({}_{2}\)ICE modified from a diesel engine. Considering the in-cylinder flow and mass transfer field of the H\({}_{2}\)ICE as a starting point, this study focuses on the effects of hydrogen injection timing, nozzle hole number, injection direction, and combustion chamber geometry on the mixture formation process.