# Effect of Rotational Speed Variation on the Flow Characteristics in the Rotor-Stator System Cavity
## 1 Introduction  
With the popularization of frequency conversion technology in fluid machinery, the demand for variable-speed operation of fluid machinery, such as fans and compressors, is gradually increasing. Clearance flow in fluid mechanics is common in the small cavities formed by the rotor and stator, and using the fluid mechanics as a complete computational domain reduces the accuracy of calculations within the cavities. By simplifying this clearance flow to a rotor-stator cavity flow, the internal flow characteristics can be accurately analyzed and subtle changes can be more easily captured. When the rotating speed changes, the characteristics of the flow in the cavity change to varying degrees. Under the action of high-speed rotation and wall shear stress, the clearance flow of the rotor-stator system has an important impact on the system stability. Many researchers have studied the cavity flow in the rotor-stator system. [PERSON] and [PERSON] [1] used a rotor-stator system experiment to analyze the critical Reynolds number of the Ekman laminar boundary layer quantitatively. [PERSON] and [PERSON] [2, 3] also studied the influence of different rotating speed discs on the flow in the cavity through experiments, obtained the torque coefficient of the disc, and made theoretical predictions. [PERSON] et al. [4] indicated that the Ekman boundary layer has a stable three-dimensional axisymmetric structure at a critical speed. When the speed continues to increase, a second transition process to unsteady flow occurs. In recent years, some research has focused on improving the calculation accuracy of turbulence models. [PERSON] and [PERSON] [5] studied the boundary layer flow fielddistribution at different Mach numbers by using improved implicit large-eddy simulation. The results obtained by this improved turbulence model are basically consistent with the experimental data and direct numerical simulation (DNS) results. [PERSON] et al. [6] used DNS and linear stability analysis to analyze the boundary layer of a shrouded rotor-stator system and increased the rotational Reynolds number from 0 to 4 \(\times\) 10\({}^{5}\). The transition process of the boundary layer from laminar to turbulent flow can be clearly observed. [PERSON] et al. [7; 8] applied DNS to calculate numerically the rotor-stator system and quantitatively analyzed the value of the velocity change in the rotor boundary layer and the critical Reynolds number. [PERSON] et al. [9] simulated the model of an axial jet entering the rotor-stator cavity using high-precision DNS and obtained the distribution of the local Nusselt number along the rotor, which is basically consistent with the experimental results. [PERSON] et al. [10] mathematically explained the problem in DNS simulation of rotating disc flow, that is, the rotating disc can still maintain global linear stability under the influence of strong instability. [PERSON] et al. [11] adopted high-precision DNS to compare the numerical simulation results of adiabatic rotor/stator and rotor/rotor cavities with experimental results, verifying the accuracy of the improved numerical calculation method. Numerous researchers have used the method of combining the rotor-stator system test and numerical simulation to do in-depth study. [PERSON] and [PERSON] [12] selected the shear stress transport (SST) \(k\)-\(\omega\) turbulence model for numerical calculations and increased the mass flow in the rotor-stator system by changing the cavity geometry to reduce the inlet static pressure. [PERSON] et al. [13] tested the rotor-stator cavity, obtained the distribution of pressure and heat transfer on the rotor at different rotating speeds and flow rates, and estimated the windage torque coefficient. Based on the linearized complex Ginzburg-Landau equation and experimental results, [PERSON] [14] concluded that there is a linear global instability in the boundary layer of the rotating disc, which may be caused by the local instability at the edge of the disc. [PERSON] et al.