## 1 Introduction
The regenerative pump works at small flow rates and a high compression ratio, providing the advantages of low vibrations, high reliability, and the ability to work without lubrication [14; 15]. The claw pump is a rotary positive displacement pump with built-in compression, the main advantages of which include simple construction, structural compactness, and oil-free operation [16]. The scroll pump operates by the meshing of two scrolls with tight clearance, which has the advantages of high efficiency, a wide range of adjustable flow, low noise, and vibration [17; 18]. The Roots pump also belongs to the positive displacement machine and its advantages include high reliability, low cost, and permission with reversible rotation. The main disadvantage of the Roots pump is low efficiency since there is no built-in compression within the machine. However, this built-in compression is unimportant in the specific application in the hydrogen recirculation because the pressure difference required is relatively small. Therefore, the Roots pump is a distinguished choice for hydrogen recirculation in the fuel cell system. For example, the hydrogen recirculation pump used in the fuel cell system of the Toyota Mirai is a Roots pump with two straight lobes [19]. Although the Roots pump has already been used for hydrogen recirculation in the fuel cell system, it is hard to find published papers related to the Roots pump for this application except for one primary simulation work from the reference [20]. The majority of the papers about the Roots pump were related to applications as air blowers and vacuum pumps. Nevertheless, all these studies provided invaluable insights and helpful information for the development of the Roots pump for hydrogen recirculation. It was demonstrated by the research that the performance of the Roots pump is strongly influenced by the rotor profile and port position. The sealing performance of Roots vacuum pumps and volume efficiency have been improved by using a profile comprising five arcs [21] or a new design profile using an extended cycloid curve with a variable trochoid ratio [22]. The rotor profile has been optimized based on the calculated backward leakage from each of the four clearances within the Roots vacuum pump, and the results enabled the optimum rotor profiles to be developed [23]. The pressure distribution in a Roots blower with three lobes was simulated by the 2D model and validated by testing data [24]. The transient flow field in the Roots blower was investigated by the Reynolds-Averaged Navier-Stokes computational modeling, which agreed well with the experimental results [25]. Moreover, some research has shown that the performance of the Roots pump with helical rotors and multi-lobes is better than that with straight rotors and two-lobes [26; 27; 28]. Research has shown that the rotor profile significantly influences the flow field and consequent the performance of the Roots pump. Therefore, the development of a Roots pump with a new rotor profile for hydrogen recirculation in fuel cell systems and testing of its performance map were the research objectives in this study. The effects of the rotor profile design, port position, and structure of the pump on the performance are discussed and presented in the paper. A prototype of three-lobe Roots pump with helical rotors having a theoretical capacity per rotation of 0.135 L was fabricated, based on which an extensive experimental study was carried out through the test rig built especially for evaluating the performance of the Roots pump. The flow rate and power consumption of the prototype were measured under various operating conditions of rotation speed, suction pressure, and pressure difference. The comparison of the performance for the Roots pump working and being tested with air, helium, and hydrogen is also presented in this paper. Finally, the designed Roots pump was successfully integrated into three PEM fuel cell systems, with output powers of 60, 80, and 110 kW, respectively.