## 1 Introduction  
In the 21 st century, the energy crisis, environmental pollution, and climate change have become major challenges to the world because of the use of fossil fuels. After the 2015 United Nations Climate Change Conference (Paris meeting), the participating countries began to attach importance to the application of hydrogen energy in various industries [1]. In this context, proton exchange membrane fuel cells (PEMFCs) fueled by hydrogen have become the most widely used type and research focus due to their advantages of high efficiency, cleanliness, low temperature, and fast start-stop response [2; 3; 4; 5; 6]. Improving the performance of PEMFCs and reducing their cost are key issues for their research and development. Among the systems in PEMFCs, the air supply system has an energy consumption rate of 20-30% of the output power of the fuel cell stack [7], as well as a cost of 15-20% of the total costs [8]. Therefore, its comprehensive performance has a crucial impact on the system efficiency and cost of PEMFCs [9]. The air supply system is responsible for providing air as an oxidant for the chemical reactions of fuel cells, usually consisting of an air filter, compressor, intercooler, and humidifier. As the core component of the air supply system, the PEMFC air compressors that are widely studied and applied currently include centrifugal, root, and screw types. The screw compressor has high reliability, simple control, a high single-stage pressure ratio, and high adiabatic efficiency under wide operating conditions [10], thus attracting the attention of many scholars. In the developmental history of screw compressors, the introduction of oil injection technology in the 1960s led to rapid development. Oil injection technology has brought four advantages for screw compressors: (a) the direct drive of the male rotor to the female rotor has become possible due to the lubricating effect of oil, which also reduces the requirement for the machining accuracy of the screw rotor profile; (b) reliable sealing of compressor clearances has been achieved, effectively improving volumetric efficiency; (c) the temperature during the compression and discharge processes has been effectively reduced, making the internal working process more complete and reducing the risk of component failure caused by high-temperature deformation; and (d) the meshing noise and airflow noise inside the compressor have been significantly suppressed, reducing the noise pollution of the compressor from the source. Therefore, oil-injected screw compressors are widely used in various fields such as air compression, refrigeration, and petrochemicals, and there are many related literature studies on them [11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. However, PEMFCs require clean and oil-free compressed air; therefore, screw compressors used in air supply systems should be oil free. Dry twin-screw air compressors emerged very early, with no liquid sprayed into the rotor cavity, and synchronous gears and bearings are still lubricated with oil or grease. Due to the oil-free design inside the compression chamber, the compressed air produced by the dry twin-screw compressor is relatively clean. However, this also brings the disadvantage of large leakage, which explains as to why dry screw air compressors usually have high rotational speed. In addition, a cooling jacket is required by dry screw air compressors. Due to the double hole shape of the cylinder in the screw compressor, the expansion of its entire surface is uneven. Therefore, cooling jackets are often arranged around the cylinder to ensure that its shape does not change. However, there is currently a lack of specific research on the effectiveness of cooling jackets. Conducting experiments is one of the methods used to study the performance of screw compressors. Although there are relatively few publicly available studies on dry screw compressors [10], previous experimental studies on water-injected screw compressors can be referenced. [PERSON] et al.