## 1 Introduction  
Most compressors currently use the radial inlet as the upstream component [1]. As the radial inlet transports working fluids from the pipelines to the impeller inlet, it should provide a uniform flow field for the impeller to guarantee the compressor good performance. Due to the complex configuration of the radial inlet, the flow field in it shows complicated three-dimensional characteristics, which means that a uniform flow field can barely be obtained in the radial inlet, and it harms the performance of the compressor [2]. Generally, the radial inlet causes a 1% to 4% and a 2% to 4% decrease in efficiency and total pressure of the compressor, respectively, compared with the axial flow inlet [3, 4]. Therefore, researchers investigating the flow characteristic of the radial inlet through experiments and numerical simulations is meaningful for the compressor. [PERSON] et al. [5] reviewed the radial inlet from the internal flow in the radial inlet and its effects on the compressor performance [6], and summarized the design of the structure and optimum method in the radial inlet [7]. Using three-hole probes, [PERSON] et al. [8] measured the flow parameter distribution at the exit of the radial inlet and compared the experiment and simulation. [PERSON] et al. [9] measured the flow in the radial inlet and observed the flow loss and distortions caused by flow separations and vortices. Through different conditions,Zhang et al. [10] analyzed the relationship between the bent torsional methods and the compressor performance based on the experiments. [PERSON] et al. [11] and [PERSON] et al. [12] respectively investigated the effects of upstream and swirling distortions based on S-duct and bent pipes in the single-stage centrifugal compressor and found that the geometry greatly influenced the downstream flow field. Based on the development of technology, the optimization methods are suitable for engineering design. [PERSON] et al. [13] simplified the structure of the radial inlet by parameterized design model analysis, which improved the precision and efficiency of the radial inlet design. With the assistance of the computational fluid dynamics technique, an optimization approach for the radial inlet design of the meridian plane was developed by [PERSON] [14] to obtain a 1.26% improvement in the polytropic efficiency. [PERSON] et al. [15] optimized the radial inlet structure by proposing an optimization method to increase the efficiency by a new design parameter. The parameter had a significant impact on the total pressure loss and the circumferential non-uniformity in the radial inlet. In addition, adding the guide vane could improve the flow field and weaken the negative impact of the radial inlet [16]. [PERSON] et al. [17] added the vanes in the radial inlet, which resulted in the flow loss increasing and the flow distortion decreasing. Through optimizing the profile of vanes in the radial inlet, the flow separation loss was further reduced, which increased the efficiency of the compressor. [PERSON] et al. [18] added the guide vanes in the radial inlet and increased the efficiency by 4.97% over different operating conditions for the compressor. Most of the literature indicates that the radial inlet has a significant effect on the safety of the downstream impeller. By reviewing the unsteady aerodynamic loads in the centrifugal compressor, [PERSON] et al. [19] considered that the flow characteristic in the radial inlet is an essential factor for analyzing the safety of the impeller that cannot be ignored. During the compressor operation, [PERSON] et al. [20] found that the radial inlet excited aerodynamic load on the impeller, but the impeller had a slight effect on the flow field of upstream the impeller, i.e., in the radial inlet. In the radial inlet, [PERSON] et al. [21] added the guide vanes to protect the impeller by providing a uniform flow field and decreasing the aerodynamic load on the impeller at the machine rotation frequency.