Cross-code comparison of the edge codes SOLPS-ITER, SOLEDGE2D and UEDGE in modelling a low-power scenario in the DTT

As reactor-level nuclear fusion experiments are approaching, a solution to the power exhaust issue in future fusion reactors is still missing. The maximum steady-state heat load that can be exhausted by the present technology is around 10 MW/m2. Different promising strategies aiming at successfully managing the power exhaust in reactor-relevant conditions such that the limit is not exceeded are under investigation, and will be tested in the Divertor Tokamak Test (DTT) experiment. Meanwhile, the design of tokamaks beyond the DTT, e.g. EU-DEMO/ARC, is progressing at a high pace. A strategy to work around the present lack of reactor-relevant data consists of exploiting modelling to reduce the uncertainty in the extrapolation in the design phase. Different simulation tools, with their own capabilities and limitations, can be employed for this purpose. In this work, we compare SOLPS-ITER, SOLEDGE2D and UEDGE, three state-of-the-art edge codes heavily used in power exhaust studies, in modelling the same DTT low-power, pure-deuterium, narrow heat-flux-width scenario. This simplified, although still reactor-relevant, testbed eases the cross-comparison and the interpretation of the code predictions, to identify areas where results differ and develop understanding of the underlying causes. Under the conditions investigated, the codes show encouraging agreement in terms of key parameters at both targets, including peak parallel heat flux (1-45%), ion temperature (2-19%), and inner target plasma density (1-23%) when run with similar input. However, strong disagreement is observed for the remaining quantities, from 30% at outer mid-plane up to a factor 4-5 at the targets. The results primarily reflect limitations of the codes: the SOLPS-ITER plasma mesh not reaching the first wall, SOLEDGE2D not including ion-neutral temperature equilibration, and UEDGE enforcing a common ion-neutral temperature. Potential improvements that could help enhance the accuracy of the code models for future applications are also discussed.

Data-Driven Modeling of Geometry-Adaptive Steady Heat Convection Based on Convolutional Neural Networks

Heat convection is one of the main mechanisms of heat transfer, and it involves both heat conduction and heat transportation by fluid flow; as a result, it usually requires numerical simulation for solving heat convection problems. Although the derivation of governing equations is not difficult, the solution process can be complicated and usually requires numerical discretization and iteration of differential equations. In this paper, based on neural networks, we developed a data-driven model for an extremely fast prediction of steady-state heat convection of a hot object with an arbitrary complex geometry in a two-dimensional space. According to the governing equations, the steady-state heat convection is dominated by convection and thermal diffusion terms; thus the distribution of the physical fields would exhibit stronger correlations between adjacent points. Therefore, the proposed neural network model uses convolutional neural network (CNN) layers as the encoder and deconvolutional neural network (DCNN) layers as the decoder. Compared with a fully connected (FC) network model, the CNN-based model is good for capturing and reconstructing the spatial relationships of low-rank feature spaces, such as edge intersections, parallelism, and symmetry. Furthermore, we applied the signed distance function (SDF) as the network input for representing the problem geometry, which contains more information compared with a binary image. For displaying the strong learning and generalization ability of the proposed network model, the training dataset only contains hot objects with simple geometries: triangles, quadrilaterals, pentagons, hexagons, and dodecagons, while the testing cases use arbitrary and complex geometries. According to the study, the trained network model can accurately predict the velocity and temperature field of the problems with complex geometries, which has never been seen by the network model during the model training; and the prediction speed is two orders faster than the CFD. The ability of accurate and extremely fast prediction of the network model suggests the potential of applying reduced-order network models to the applications of real-time control and fast optimization in the future.

Node generation in complex 3D domains for heat conduction problems solved by RBF-FD meshless method

A novel algorithm is presented and employed for the fast generation of meshless node distributions over arbitrary 3D domains defined by using the stereolithography (STL) file format. The algorithm is based on the node-repel approach where nodes move according to the mutual repulsion of the neighboring nodes. The iterative node-repel approach is coupled with an octree-based technique for the efficient projection of the nodes on the external surface in order to constrain the node distribution inside the domain. Several tests are carried out on three different mechanical components of practical engineering interest and characterized by complexity of their geometry. The generated node distributions are then employed to solve a steady-state heat conduction test problem by using the Radial Basis Function-generated Finite Differences (RBF-FD) meshless method. Excellent results are obtained in terms of both quality of the generated node distributions and accuracy of the numerical solutions.

Simulation and optimization of steady-state heat transfer property measurement platform

This paper studies the measurement technology of heat transfer coefficient of building envelope, explores the main factors affecting the measurement of heat transfer coefficient, uses ANSYS Icepak software to simulate the steady-state heat transfer property measurement platform model, and establishes the virtual prototype of the product. The product design based on Icepak replaces the test on the physical prototype with the simulation on the virtual prototype, We should reduce or even cancel the manufacturing of physical prototype, shorten the R & D process, and cut R & D costs with the improvement of design quality. Through the comparison and analysis with the experimental data of the offline detection platform, the feasibility of using Icepak to simulate the equipment is proved. The software is used to simulate the ther-mal environment in the hot box. Through comparison and analysis, the most uniform upper wi-nd steady-state thermal environment scheme is found.

A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.