Finite Element Analysis for NEG coated vacuum chamber based on ANSYS Workbench

The Hefei Advanced Light Facility (HALF) is a diffraction limited storage ring (DLSR) being constructed. As the main component of the storage ring vacuum system, the vacuum chamber transports the beam and withstands the thermal effect of synchrotron radiation simultaneously. The thermal and mechanical condition of the vacuum chamber of HALF were quantitatively analysed by means of ANSYS Workbench in this work. Combining the Computational Fluid Mechanics (CFD) and Finite Elements Analysis (FEA), the temperature and thermal stress maps of the vacuum chamber were calculated. The CFD calculation displays that the heat transfer coefficient between the water and the chamber is 7966-13093 W/(m2·°C). The thermal-mechanical simulation shows that the maximum temperature and thermal stress are 53.5 °C and 42.1 MPa, respectively. The static structural analysis was performed on vacuum chamber under the ultra-high vacuum condition, with the maximum stress of 1.7 MPa and the maximum deformation of 0.0003 mm. These results show that the vacuum chamber meets the design requirements and provide a critical theoretical basis for the design of the vacuum system of HALF.


Introduction
The new generation of diffraction limited storage rings (DLSR) employs small magnet units and compact lattice in design for the purpose of lower emittance [1].The size of the vacuum chamber is limited by the compact physical design, and most of the chambers in the straight section are simple tubular chamber [2].The Hefei Advanced light facility (HALF) is a DLSR and its vacuum chamber is designed to be as small as 22 mm in diameter and 1 mm thickness.It noteworthy that the reduction in the diameter of the vacuum chamber will cause the challenge of attaining ultra-high vacuum, which is required to improve the beam lifetime.However, coating the non-evaporable getter (NEG) film onto the inner walls of the vacuum chamber provides an efficient solution and have been used in many accelerators [3][4][5].
The vacuum chamber transports beam while withstands little heat load of the synchrotron radiation.The water flow in the cooling channels of the vacuum chamber can take away the heat which accumulated on the light-receiving surface in time, thus achieving the effect of thermal releasing [6].In addition, the appropriate fabrication material contributes to the dissipation of the thermal power.Taking into account the mechanical properties, process conditions and fabrication of the materials, CuCrZr was preliminarily chosen as the material for vacuum chamber of HALF [7].On account of the significantly improved performance of HALF, it is essential to evaluate the thermal effect of synchrotron radiation on the vacuum chamber.Besides, the vacuum chamber with thin wall may exhibit large deformation resulting from insufficient rigidity in ultra-high vacuum, and its strength needs to be analysed.
In this article, the three-dimensional (3D) model of the vacuum chamber with an internal diameter of 22 mm was established.The finite element software ANSYS Workbench was used for thermal and static structural analysis.The CFD was also applied to calculate the temperature distribution and thermal stress distribution of the vacuum chamber due to the synchrotron radiation-induced heat load.And the stress and deformation of the vacuum chamber under the ultra-high vacuum condition were simulated.

Finite Element Model
The finite element software ANSYS Workbench and Windows 7 Operating Platform were used for analysis.The vacuum chamber with the length of 835 mm is taken as the analysis object and the 3D model is established in SolidWorks as shown in Fig. 1.The applied material is CuCrZr and its mechanical parameters are listed in Table 1.The ANSYS smart sub-work was chosen, and the mesh size of light-receiving surface was set to 2 mm for better calculation accuracy.

CFD Simulation
In order to simulate the working state, the fluid condition in the cooling channels is calculated by CFD.The diameter of cooling channel is 8 mm, the inlet flow is set to 5 L/min, and the flow velocity of the cooling water can be calculated using the formula, (1) where v is the flow velocity of the cooling water, q is the flow, d is the diameter of the water channel.
The flow velocity of the cooling water was calculated as 1.658 m/s.During the cooling process, the fluid flow is assumed to be steady-state.The water flow condition is set to turbulent regime and the standard k-ε model is chosen.The temperature and flow velocity of the inlet water are 20 °C and 1.658 m/s, respectively.According to the CFD simulation, a relatively accurate heat transfer coefficient of cooling water is displayed in Fig. 2. It found that the heat transfer coefficient between the water and the chamber is 7966-13093 W/(m 2 •℃).

Thermal-mechanical Simulation
Firstly, the absorbed radiation power on the chamber wall was set, which serves as the basis for calculating the thermal load.For the sake of safety, the radiation heat power received by the vacuum chamber was set to 1000 W, which is much bigger than the practical value provided by the physical design of the HALF.Assuming that the heat load uniformly distributed on the surface, the heat flow was applied as seen in Fig. 3. Based on the calculated convective heat transfer coefficient in Fig. 2, the temperature distribution of vacuum chamber is analysed, see Fig. 4. It can be seen that the maximum temperature of the vacuum chamber is mainly distributed on the light-receiving surface, with a maximum value of 53.5 ℃.Due to the existence of temperature gradient and constraint, the different degrees of deformation and stress will generate in the vacuum chamber.Fixed constraints are set on the flange part of the vacuum chamber, according to the practical application.The thermal induced stress distribution of the vacuum chamber is presented in Figure 5.And the maximum stress is 42.1 MPa.The maximum temperature and stress of vacuum chamber are within the safe range in combination with the engineering criteria, as shown in Table 2.It found that the cooling water is sufficient for heat dissipation and the thermal deformation of the chamber has less influence on its structure.The superior thermal conductivity and good mechanical properties make CuCrZr a suitable material for vacuum chambers, and the thermal simulation results meet the requirements of HALF.

Static Structural Simulation
The vacuum specification for particle accelerator is much lower than the atmosphere, and the average dynamic pressure of the vacuum system of the Hefei light source is around 2.0e-7 Pa during the operation.The strength of the vacuum chamber with 1 mm wall thickness was evaluated by static structure analysis.The external surface of the chamber is set to be approximately equal to a standard atmospheric pressure.The added fixed constraints are the same as those in the thermal-mechanical simulation.Considering the effect of gravity, gravitational acceleration is also included in the boundary conditions.
The mechanical stress and deformation maps of the vacuum chamber under the ultra-high vacuum condition are presented in Fig. 6 and Fig. 7, respectively.The maximum stress is 1.7 MPa (Fig. 6) and the maximum deformation is 0.0003 mm (Fig. 7).Stress and structural deformation are found to be lower enough for the basic design.The vacuum chamber with a wall thickness of 1 mm has sufficient structural strength in ultra-high vacuum.

Conclusion
In this paper, the safety and reliability of NEG coated vacuum chamber based on HALF and CuCrZr material are analysed based on ANSYS Workbench.The temperature and thermal stress distribution of the small-diameter vacuum chamber are simulated by combining CFD and FEA.The result of CFD calculation indicates that the heat transfer coefficient between the water and the chamber is 7966-13093 W/(m 2 •℃).The maximum temperature and thermal stress of the vacuum chamber are 53.5 ℃ and 42.1 MPa, respectively, both within the design criteria for CuCrZr.The maximum stress and deformation of the vacuum chamber under the ultra-high vacuum condition are 1.7 MPa and 0.0003 mm, respectively.The FEA results of the vacuum chamber show a good performance and meet the design criteria.
The subsequent research work will be close to the engineering application, testing the photon desorption yield of NEG coated vacuum chamber and performing thermal-mechanical simulation of other types of vacuum chambers.

Figure 2 .
Figure 2. Heat transfer coefficient between the water and the chamber.

Table 1 .
Mechanical Parameters of CuCrZr