## 2 Methodology  
Developed injectors can inject hydrogen into cylinders at pressures ranging from 10 to 300 bar, with various designs featuring different hole counts and injection angles. Rather than designing a completely novel injector, this study aims to optimize the cap configuration of a standard hydrogen injector platform commonly used in heavy-duty applications. This allows the results to be directly applicable to existing engine architectures and manufacturing constraints while still achieving performance and emission improvements through geometric tuning. For this purpose, CFD combustion simulations were carried out to systematically evaluate and optimize various injector blow cap configurations, with the goal of enhancing gross thermal efficiency and indicated cylinder power while preventing abnormal combustion behavior, such as knocking events. [PERSON]'s hydrogen-fueled research engine [19] specifications showed in Table 1 were adopted as the reference model due to their industrial relevance, public data availability,and their geometric similarity to current heavy-duty hydrogen engine concepts. This engine was developed specifically for long-haul truck applications, making it well-suited for assessing injector optimization strategies under realistic conditions. Hydrogen injection was modeled to occur between \(-140\)\({}^{\circ}\)CA and \(-70\)\({}^{\circ}\)CA. The baseline configuration employed a low-pressure direct injection (LPDI) system with an injection pressure of 25 bar. This configuration was preferred due to the use of a lower-pressure fuel pump and its safer operational characteristics for heavy-duty engine conditions. LPDI systems exhibit sensitivity to injector design parameters such as hole count and injection angle. At low injection velocities, mixture formation is more readily simulated and validated through numerical methods [18]. Based on these considerations, an LPDI-based setup was considered appropriate for the optimization study. Although similar optimization strategies could also be applied to HPDI systems and may yield valuable design insights, this study focused solely on LPDI configuration due to its applicability and implementation within the selected engine concept. The optimization focused on two primary parameters to achieve an appropriate air-fuel mixture and optimal engine performance while minimizing NO\({}_{\mathrm{x}}\) emissions: injector hole count and injection angle. The hole count was varied between three and five, and the injection angle ranged from \(15^{\circ}\) to \(33^{\circ}\). These parameter ranges were determined based on the geometric feasibility to accommodate the hole configurations on the injector tip. Converge CFD v3.2 software was employed to carry out the CFD combustion cases, and CAESES v4.4.2 software was utilized for optimization to maximize indicated brake mean effective pressure and minimize NO\({}_{\mathrm{x}}\) emissions. Before the optimization study, a full-cycle CFD combustion simulation was conducted over two cycles (1440 CA Total Duration) without a blow cap injection hole design to establish the initial conditions for optimization. The optimization study began at \(-145\) CA before TDC and concluded at \(+50\) CA after the top dead center to reduce computation time and costs. MAP-type CFD initialization was applied to the simulation, mapping in-cylinder pressure, temperature, and species distribution directly into the computational domain with 2.6% H\({}_{2}\)O EGR. As a result, the optimization study was initiated in the same manner as the full-cycle simulation, where the cylinder domain was pre-charged with combustion residuals. The EGR level used in this setup was calculated from the baseline CFD analysis and fixed at 2.6% throughout the optimization process. This approach ensured consistency in evaluating the effects of injection parameters. A study by [PERSON] et al.