## 2 Numerical Calculation Model  
### Geometric Model and Mesh Model  
The primary structure of the SSRF's DCM is illustrated in Figure 1, comprising a liquid nitrogen cooling circuit, the first crystal, the second crystal, and a micro-adjustment mechanism for the second crystal. In the cooling circuit of the second crystal, seven monitoring points (p1-p7) are arranged to detect the fluid's motion state. Liquid nitrogen supplied by the pump enters the cooling circuit through the inlet. It initially flows into the cooling circuit of the first crystal, carrying away the heat generated by the first crystal before reaching the second crystal. After cooling the second crystal, the liquid nitrogen flows towards the outlet. The micro-adjustment mechanism for the second crystal, as depicted in Figure 1, connects the upper and lower parts through a flexible hinge, with the upper part equipped with a spring to balance gravity. The structural mesh of the DCM is illustrated in Figure 2, where the inner surface of the pipelines belongs to the fluid-solid coupling interface. Therefore, a double layer of hexahedral elements was used to discretize the pipelines. The hinges serve as the primary deformation components, with the most diminutive geometric dimensions near the axis of rotation, resulting in minimal stiffness. The reasonableness of the discretization of the hinges is crucial for the accuracy of solid domain simulations. At the axis of rotation of the hinge, this research employed four layers of hexahedral elements to capture the geometric shape more accurately. The smallest mesh size at this location is only 0.076 mm. As for the spring used to balance gravity, this research employed a more accurate solver with built-in standard spring properties without mesh partitioning. During the simulation, fixed constraints were applied to the clamping plate at the upper end of the flexible hinge and both ends of the cooling circuit for the second crystal. Heat exchange in the cooling system primarily occurs in the U-shaped circuit of the first crystal, and at the inlet and outlet of the curved pipes in the second crystal circuit; fixed supports are designed for the pipes. Therefore, fluid movement has a minimal impact on crystal vibration before the fixed support of the first crystal circuit and after the fixed support of the second crystal circuit. The focus is on the region from the inlet of the U-shaped circuit for the first crystal to the outlet of the second crystal circuit. The mesh partitioning for the fluid domain is depicted in Figure 3. For the inlet mesh of the fluid, the  
Figure 1: DCM structure and cooling system. Figure 2: Finite element model of mechanical structure. outer layer uses hexahedral mesh elements with a height of 0.3 mm to place the fluid near the wall in the logarithmic region [7]. This facilitates solving the motion state of the fluid near the wall using the k-\(\varepsilon\) wall function method. In this paper, a mesh independence test is performed on the above mesh. The above mesh is Case 4 in Table 1. In the structural domain, the hinge is a critical deformation component. Through Table 1 and Figure 4, it is observed that by adjusting the mesh size of the hinge, the maximum predicted equivalent stress in Case 4 no longer undergoes significant changes under the influence of gravity. This indicates that the simulation results are independent of the mesh. In the thermal-fluid coupling analysis, the maximum temperature of the first crystal in Case 4 no longer changes. Considering both accuracy and efficiency in the calculations, this paper adopted Case 4 for numerical simulations. Figure 4: The variation trends of temperature and stress in the mesh independence test. The abscissa corresponds to the 5 cases of mesh in Table 1. The blue line represents the temperature change trend, monitoring the maximum temperature on the surface of the first crystal, while the red line represents the stress change trend, monitoring the maximum equivalent stress of the flexible hinge.