## 1 Introduction  
With the aggravation of the energy crisis and global warming, reducing the use of fossil fuels has become a tough problem. From 2014 to 2020, China's hydrogen production rose from 16 million tons to 25 million tons. Hydrogen, as a promising renewable energy carrier and carbon-free fuel, has significant and unique physical and chemical properties [1; 2; 3]. The burning velocity of hydrogen is much higher than other fuels, such as gasoline; therefore, it is an alternative engine fuel that could effectively enhance combustion in and improve the efficiency of internal combustion engines [4; 5; 6]. As a carbon-free fuel, fueling engines with hydrogen can significantly reduce their emissions. There is no doubt that higher combustion temperatures lead to higher NOx emissions [7; 8; 9; 10]. Nevertheless, due to the greater flammability limit of hydrogen, hydrogen-fueled engines can work under lean-burn conditions, resulting in the reduction of NOx emissions. As a result, hydrogen-fueled engines can achieve lower emissions and higher efficiency [11]. However, there are also many challenges for hydrogen-fueled engines. Firstly, due to the low ignition energy of hydrogen, such engines are more prone to backfire [12]. Fortunately, supercharger systems can increase the intake pressure to limit backfire [13; 14; 15]. Secondly, hydrogen has low density and small molecules, so it is very easy for it to escape through the shell of the storage device. Therefore, the storage of hydrogen is the key problem that must be properly solved in the development of hydrogen-fueled engines [16]. To fully utilize its advantages for combustion and avoid its disadvantages regarding storage, researchers have considered mixing hydrogen with fossil fuels to form blending fuel [17]. Numerous studies on hydrogen blending fuel have been conducted. Since the combustion rate of diesel is relatively slow, it can be effectively improved by adding hydrogen, which has significant implications for diesel engines [18; 19]. With the addition of 10% hydrogen, efficiency increased and emissions decreased [20; 21]. Moreover, a reactivity controlled compression ignition (RCCI) mode has been used to increase the efficiency of diesel/hydrogen engines [22]. With hydrogen direct injection, pre-ignition in diesel engines can be attenuated, improving their limitations and emissions. Since mixing hydrogen and natural gas before injection into the cylinder can simplify the fuel injection system, there are many studies about hydrogen/natural gas engines [23; 24; 25; 26]. The combustion rate of natural gas is worse than that of gasoline. Hydrogen has been found to help natural gas by increasing the combustion rate and decreasing the cyclic variation [27], especially under lean-burn conditions [28]. Studies have found that, with the addition of hydrogen, the combustion rate clearly increased, leading to higher efficiency and low cyclic variation [29]; combustion became more complete, leading to less emissions [30]; and the combustion temperature rose, leading to more NO\({}_{\text{X}}\) emissions [31]. With regard to gasoline engines, hydrogen can be injected into such engines in two ways: hydrogen intake port injection (HPFI) and HDI. [PERSON] et al. have published several studies on HPFI [32; 33; 34]. Hydrogen addition was found to improve engine efficiency, decrease emissions, extend the lean burn limit [32], speed up the cold-starting process [33] and reduce the idle speed [34]. [PERSON] et al. have mainly focused their research on HDI [35; 36; 37; 38; 39; 40; 41; 42; 43]. Compared with a pure gasoline engine, HDI resulted in a quicker combustion rate and higher combustion temperature [35; 36], which led to higher efficiency and fewer emissions [37]. The hydrogen in HDI is not homogeneous but stratified, which is controlled by the injection strategy [38]. With better stratification of hydrogen distribution, combustion was found to occur faster and more quickly led to lower cyclic variations and higher efficiency [39].