An integration design platform is under development for the design of the China Fusion Engineering Test Reactor (CFETR). It mainly includes the integration physical design platform and the integration engineering design platform. The integration engineering design platform aims at performing detailed engineering design for each tokamak component (e.g., breeding blanket, divertor, and vacuum vessel). The vacuum vessel design and analysis module is a part of the integration engineering design platform. The main idea of this module is to integrate the popular CAD/CAE software to form a consistent development environment. Specifically, the software OPTIMUS provides the approach to integrate the CAD/CAE software such as CATIA and ANSYS and form a design/analysis workflow for the vacuum vessel module. This design/analysis workflow could automate the process of modeling and finite element (FE) analysis for vacuum vessel. Functions such as sensitivity analysis and optimization of geometric parameters have been provided based on the design/analysis workflow. In addition, data from the model and FE analysis could be easily exchanged among different modules by providing a unifying data structure to maintain the consistency of the global design. This paper describes the strategy and methodology of the workflow in the vacuum vessel module. An example is given as a test of the workflow and functions of the vacuum vessel module. The results indicate that the module is a feasible framework for future application.
The China Fusion Engineering Test Reactor (CFETR) is a superconducting tokamak currently under conceptual design. The objectives of CFETR are to achieve 50~200 MW fusion power and steady-state operation with a duty cycle between 0.3 and 0.5 in order to demonstrate the feasibility of fusion energy and the self-sustainability of the fuel cycle [
The design work of CFETR involves many complex components such as the core plasma, breeding blanket, and divertor. Data exchange and iteration are necessary between different components as well as between physics design and engineering design. Thus, a comprehensive system code is required to perform the consistent global design of CFETR. A system code aims at self-consistent optimization of the key factor in the design of a tokamak. Several system codes have been developed by different organizations (SYCOMORE by CEA [
These system codes greatly improve the efficiency of tokamak conceptual design. But they have few connections with the detailed engineering design and analysis of tokamak components. The CFETR integration design platform comprises both the physical design platform and the engineering design platform [
This manuscript describes the development of the engineering design and analysis module of the vacuum vessel (VV) in integration engineering platform. Section
As one of the modules in the engineering platform, the VV design and analysis module has a basic function to conduct VV modeling and FE analysis about VV. Based on the results of FE analysis, further sensitivity analysis and optimization of geometric parameters could be done. With reference to previous experience of VV engineering design, the basic conceptual workflow of VV module is shown in Figure
Conceptual workflow of VV module.
The dashed box in Figure
Firstly, the input and output data are described as follows.
The input of VV module includes geometric parameters of VV (main input), material properties of VV for FE analysis, shape and current of PF/TF coils for FE analysis, structural loads (i.e., coolant pressure), structure criterion.
The output of VV module includes final design model of VV, final geometric parameter of VV, results of FE analysis.
Interfaces are built into the VV module to facilitate the data exchanges of the input and output. Five interfaces have been developed to realize these exchanges: Interface between material databases Interface between assessment criterion databases Interface between working condition databases Interface between GASC [ Interface between PF/TF modules
The data for exchanging through these interfaces are all arranged in TXT files with a predefined standard data structure. The consistency of data and model should be kept from the beginning to the end.
Generally, the procedure of a single run of the VV module is shown in Figure
The VV module starts from the geometric parameters of VV, which means the model of VV should be parameterized at first to give a set of parameters that could describe the shape and structure of VV. The parameterization of CFETR VV will be discussed in the next chapter. The initial values of geometric parameters of VV are determined according to results of GASC (General Atomics System Code, [
CFETR device radial space distribution.
This step involves modeling the VV in CAD and CAE software with the former geometric parameters. The parameters and the equations between these parameters are defined in both CATIA and ANSYS to achieve the parameterization of VV, ensuring the automatic rebuilding of the model with the changing of geometric parameters afterwards. The model/parameter interaction between CAD model and CAE model means that both the model and the parameters are transferred from CAD to CAE. Instead of using the CAD model directly, the complex part of the model could be rebuilt in CAE to improve the success rate of model conversion.
This step involves performing FE analysis based on the parameterized VV model in CAE. The FE analysis includes electromagnetic analysis, thermal analysis, and structural analysis. The results of electromagnetic and thermal analysis will be used in structural analysis to realize indirect coupling.
This step involves outputting the model, geometric parameters, and results of FE analysis to the external database. The engineering platform will manage the utilization of these data in subsequent modules.
The sensitivity analysis and optimization loop are performed based on the single-run process. The steps for sensitivity analysis and optimization are as follows.
This step consists of analyzing the sensitivity of each geometric parameter corresponding to the output of FE analysis. The sensitivity analysis could screen out the parameters with high sensitivities as the driving parameters for the subsequent optimization. The parameters with higher sensitivity have greater influence on the output, which means they should be taken into consideration in the optimization.
In this step, the optimization loop in Figure
In order to boost the efficiency of optimization, the response surface method (RSM) and optimization algorithm (e.g., sequential linear programming, self-adaptive evolutionary programming) [
As shown in Figure
VV workflow in OPTIMUS.
As shown in Figure
The CFETR VV design is a 316 L SS double-wall toroidal structure. To consider the use of central space as efficiently as possible and the manufacturing difficulty, the CFETR VV has a D-shaped cross section and each D-shaped cross section is formed by one straight line and five arcs which are tangential to each other [
The thickness of the inner shell and outer shell is 50 mm with a gap of 0.18 m reserved for in-wall shielding (IWS), baking, and cooling system for inboard area as well as a gap of 0.28 m for the outboard area at the equatorial plane. The vessel has eight vertical and eight equatorial ports for auxiliary heating, diagnostics, and remote maintenance and eight divertor ports for reassembly of divertor, utility feed-through, and vacuum pumping. The maximum size inside the VV is about 6,220 mm in the horizontal direction and 10,270 mm in the vertical direction [
VV CAD model of CFETR.
Parametric modeling offers two advantages for design: one is to facilitate the modification of the design module and the other is to promote validity and accuracy of transformation between CAD model and CAE model. Direct transformation from CAD model to CAE model mostly depends on the performance of CATIA and ANSYS, which does not have high reliability. Geometric parameters could bridge these two programs. For the complex part of the model, by using the same parameters for modeling in each program, the consistency of the model could be maintained as much as possible.
Take the parameterization of D-shape cross section as an example. The D-shape cross section contains one straight line and five arcs. Only the upper half of the cross section is considered since the lower half has the same structure. The detailed geometric elements of the upper half are shown in Figure
Geometric elements of upper half cross section of VV.
Main geometric parameters of VV.
Geometric parameters of port cross sections. (a) Cross section of the upper port; (b) cross section of the equatorial port; (c) cross section of the lower port.
The detailed design parameters were shown in Table
Geometry parameters of CFETR VV (unit: mm).
Name | | | | | | | | | | |
Value | 3702.7 | 3417.8 | 2870 | 1834.2 | 4410.3 | 6601.7 | 2729.6 | 2452.6 | 3148.3 | 3150 |
| ||||||||||
Name | | | | | | | | | rad_hor | len_hor |
Value | 1438.7 | 4014.8 | 6323.2 | 2192.1 | 3069.7 | 3046.8 | 1750 | 2200 | 100 | 1500 |
| ||||||||||
Name | dis_up | shor_up | rad_up | len_up | waist_up | hg_up | | shor_low | rad_low | len_low |
Value | 4460 | 650 | 200 | 1430 | 3820 | 1315.7 | 6540.9 | 826 | 100 | 1480 |
| ||||||||||
Name | waist_low | | ang_low | | | | | secn | ang | |
Value | 2188 | 11250 | 76 deg | 50 | 50 | 60 | 60 | 16 | 6 deg |
Along with these parameters, the constraint equations have been established in both CATIA and ANSYS. When one parameter changes, the model automatically changes and keeps smooth joins everywhere. But the allowed value range of each parameter was restricted to make sure the vessel is big enough to contain the plasma and small enough to fit inside the coils.
ANSYS v15.0 was adopted for performing the FE analyses of VV, which include electromagnetic field analysis, thermal analysis, and structural analysis. With the same FE model, these analyses could be coupled indirectly. The EM force distribution and temperature distribution are, respectively, read from result files from electromagnetic analysis and thermal analysis.
The mechanical loads acting on the VV can be divided into four independent categories.
Taking all the mechanical loads into consideration is the objective of VV module but only loads listed in Table
Types of loads performed in VV module.
Type of load | Type of analysis |
---|---|
EM forces from MD event | Electromagnetic analysis |
Nuclear heat during normal operation | Thermal analysis |
Coolant pressure | Structural analysis |
Gravity (dead weight) | Structural analysis |
The results of FE analysis are used to examine the structural strength of VV. Stresses are extracted and classified into four types according to ASME-VIII [ General Primary Membrane Stress ( Local Primary Membrane Stress ( Primary Bending Stress ( Secondary Stress (
Referring to ASME-VIII-2 and ITER VV design criterion [
Design criterion of mechanical strength.
| | | | |
---|---|---|---|---|
Temp. | | | | |
20°C | 147 | 221 | 221 | 441 |
100°C | 147 | 221 | 221 | 441 |
200°C | 130 | 195 | 195 | 520 |
Generally, there are dozens of parameters to describe a VV (Table
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs [
A variance approach to calculate global sensitivity index (Sobol index) based on response surface method is provided in VV module. Response surfaces are also known as meta models, surrogates, emulators, auxiliary models, and so forth. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response, which is easy to estimate and apply. OPTIMUS has a wide range of methods in building RSM models, including least square method based on Taylor expansion and user-defined expansion, interpolation method based on Krigin method, and Radial Basis Function (RBF) method [
Local sensitivity analysis is also particularly useful when screening high dimensional models. One at a time (OAT) is a choice. The principle of OAT is simple: each parameter is varied successively from a given nominal value while keeping the other parameters constant. Repeating this procedure a limited number of times for each parameter, one can obtain a rough idea of its effect on output parameters [
Local optimization search algorithm and global optimization search algorithm both are available in the module. The former includes sequential linear programming method and sequential square programming method. The latter includes self-adaptive evolutionary programming method (SAE) and differential evolutionary programming method [
After all, the response surface method is only an approximation to FE analysis; it cannot completely replace the FE analysis. The results of the optimization need to be verified by FE analysis. Combining this method with FE analysis, the global optimization could be realized with high efficiency.
In order to test the function of VV module, an example was performed. Table
Results of sensitivity analysis.
Parameter | Impact on FE results | ||
---|---|---|---|
(delta stress/MPa) | |||
I | II | III | |
| 48.3 | 39.9 | 54.2 |
| 5.7 | 37.2 | 38.7 |
| 2.2 | 3.1 | 2.3 |
| 0.1 | 6.4 | 5.1 |
| 0.3 | 11.6 | 14.7 |
| 0.5 | 12.8 | 11.8 |
| 0.1 | 14.5 | 13.5 |
| 2.8 | 9.4 | 10.4 |
| 0.3 | 3.5 | 3.4 |
| 0.2 | 5.3 | 4.8 |
Then, optimization was performed to get the optimum value of
Table
Results comparison of RSM and FE analysis.
| | von Mises/MPa | Mass/ton | |||
---|---|---|---|---|---|---|
I | II | III | ||||
Results from RSM | 50.62 | 30.08 | 146.9 | 279.5 | 424.0 | 84.107 |
Results from FE analysis | 50.62 | 30.08 | 142.7 | 269.6 | 376.5 | 84.162 |
Error | — | — | 2.9% | 3.7% | 12.6% | 0.06% |
The function of VV module was tested by using a workstation with a configuration of the hardware as shown in Table
Configurations of hardware.
Hardware | Model |
---|---|
CPU | Xeon E5-2680v3 2.50 GHz × 2 |
Memory | Samsung DDR4 2133 MHz (64 GB) |
GPU | Nvidia Quadro K6000 (with GPU acceleration) |
The average calculation time of individual FE analysis is about 6 hours and 48 minutes. According to the SAE (self-adaptive evolutionary) method, optimization without RSM usually needs to perform FE analysis 100 to 300 times. Thus, the calculation time is at least 600 hours. But, with RSM method, the results are calculated through response surface instead of FE software. The calculation based on response surface is very fast. It takes less than 5 seconds to accomplish 100 to 300 calculations on response surface. But building the response surface still needs a couple of calculations on FE software. In this case, the FE analysis is performed 24 times to build the response surface. And 186 times of calculations were performed on response surface for the optimization. The calculation time of the overall procedure of optimization with RSM is 163 hours and 13 minutes. Without RSM, the same 186 calculations should have been performed on FE software, which will take nearly 1264 hours and 48 minutes. Even if the number of calculations is more or less different on FE software, the calculation time is still more than 600 hours. Therefore, with the help of RSM, the calculation can achieve a higher efficiency.
The VV design and analysis module of CFETR engineering design platform provides a new approach to conduct engineering design and parameter optimization of the vacuum vessel. The integration of different software made it possible to allow automation and analysis. Combined with RSM, the module gives a more efficient way for engineers to realize the global geometric optimization.
The integration design platform is still under development. Currently, the basic framework has been established. The interfaces and iteration between modules are still planned for future development. For vacuum vessel module, in the next work plan, new analyses such as seismic analysis and buckling analysis should be added to this module and the RSM also should be improved to achieve a higher accuracy.
The authors declare that they have no competing interests.
This work is supported by the National Magnetic Confinement Fusion Research Program of China (Grants nos. 2014GB110001 and 2014GB110002). The authors would like to express their thanks to Vincent Chen, Xuebing Peng, Zhengping Luo, Yong Guo, Nan Shi, and Kun Xu from the CFETR integration platform team.