## 1 Introduction  
During the last decade, governments around the world have implemented strict regulations for reducing greenhouse gas emissions and energy consumption. This will help to protect the environment and control the effects of global warming. It is estimated that the transport sector is responsible for about 30% of the world's greenhouse gas emissions, and internal combustion engine vehicles (ICEV) contribute close to 70% of that emission [1]. The automotive industry has developed several power train concepts, which include hybrid vehicles, electric vehicles, and fuel cell vehicles, in order to reduce the carbon footprint of the industry. Fuel Cell Electric Vehicles (FCEVs) are one of the ideal solutions to the global warming and energy crisis. They have zero carbon dioxide emissions and high system efficiency while having a long driving distance and short refilling time [2, 3]. If renewable energy sources, such as hydrogen are used, FCEVs will be more environmentally friendly and can reach net-zero emission [4]. Hydrogen is readily available in nature in various forms, which will make hydrogen-fueled FCEVs indispensable in the future in terms of performance and environmental friendliness [1, 5, 6, 7]. The electric power in the hydrogen-fueled FCEVs is generated through the electrochemical reaction of hydrogen and oxygen (air) in the fuel cell stack [1]. The air compressor supplies compressed air from the atmosphere to the fuel cell stack while the turbo blower supplies hydrogen from the compressed hydrogen tank and water is released as the by-product. The air compressor is one of the most important auxiliary components of the FCEV, that determines the cost, efficiency, performance, and power density of the system [8; 9; 10]. The centrifugal compressor is considered the most ideal air compressor, when compared with other types (such as screw, scroll, and roots), because of its ability to provide oil-free clean air at high efficiency, favorable NVH (noise, vibration, harshness) performance, and at a smaller energy footprint [4; 8; 11; 12]. However, centrifugal compressors generally have narrow operating ranges and tend to operate near the surge line and flow instabilities at these operating conditions lead to undesirable pressure pulsation [11]. Therefore, to improve the performance of hydrogen FCEVs, as well as other centrifugal compressor applications, it is important to improve the pressure ratio and operating range of the centrifugal compressor [13]. The flow field in the centrifugal compressor is 3-dimensional and highly complex. Composed of many flow phenomena such as shock waves, tip leakage vortices, wakes, reverse flows, and the interactions among them. These flow phenomena greatly affect the performance of the centrifugal compressor and their occurrence need to be thoroughly understood to improve the performance of the centrifugal compressor [14]. In the previous studies, [PERSON] et al. [14] performed a computational fluid dynamics (CFD) analysis of the transonic centrifugal compressor with a double splitter blade using the k-omega turbulence model and analyzed the vortical flow structures by visualizing the vortex structure using CFD analysis. The experimental results and CFD analysis results were compared for the relative velocity distribution at various locations of the blade. They observed that the changes in pitch velocity affected by the shock wave due to the transonic were the same in both results. [PERSON] et al. [13] performed unsteady numerical calculations of two different centrifugal compressors at 160,000 rpm by experimental and numerical investigations and revealed that the internal flow structures were related to the operating range. In compressors with a narrow operating range, the compressors' characteristics become unstable at low flow rates. It was predicted that the blockage caused by the tip leakage vortex breakdown can stabilize the flow field and improve performance.