Research on the Numerical Calculation Method for the Flow Field of Oil-Immersed Converter Transformers Based on Unstructured Collocated Grids
Xin Jiwei1, Li Lin1, Liu Gang2
1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China; 2. Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense North China Electric Power University Baoding 071003 China
Abstract：Non-physical oscillations may arise from the upwind finite element method when solving the two-dimensional steady-state incompressible Navier-Stokes equations, and mesh generation in complex geometries can cause large computational errors. In addition, the structured staggered-grid finite volume method has limitations for complex geometries and boundary conditions. Thus, this paper proposes a finite volume method based on unstructured collocated grids. The proposed method utilizes an unstructured mesh constructed from irregular triangles, which offers flexibility and adaptability in handling complex flow geometries. A collocated grid arrangement for velocity and pressure is adopted to avoid additional interpolation operations when velocity and pressure are stored on different grids in a staggered grid configuration. The Rhie-Chow interpolation method is employed to eliminate spurious pressure oscillations. Furthermore, delayed correction high-order schemes and second-order central difference schemes are used to discretize the convection and diffusion terms, respectively. The SIMPLE algorithm is employed to optimize the solution process, thereby reducing memory and computational costs. In terms of sparse matrix storage, the COO format is used. It does not require additional calculations to recover the original matrix, which is easier to implement than CSR and CSC formats, thus saving storage space. The PARDISO solver, based on super node technology, is employed to improve computational efficiency and avoid convergence issues with iterative methods. This solver requires less memory and supports single-node decomposition, outperforming MUMPS and WSMP solvers. Finally, under-relaxation techniques are incorporated to optimize convergence performance and ensure the stability of the numerical solution. Accordingly, a flow field calculation program was developed for triangular and quadrilateral meshes, and the computational time for both types of meshes with a similar number of nodes was compared. By optimizing the under-relaxation factor combination, numerical simulations were performed for the classical driven cavity flow problem, and the results were compared with those obtained from COMSOL finite element simulation software and Ghia's vorticity-stream function method. The results show that the proposed method agrees with Ghia's computation for the horizontal velocity distribution along the vertical centerline and the vertical velocity distribution along the horizontal centerline at Reynolds numbers Re=100 and Re=3 200. The proposed method provides higher computational accuracy than the finite element method. When handling complex geometries and boundary conditions, the proposed method demonstrates greater flexibility and applicability than the structured staggered grid finite volume method. Finally, the method is applied to the oil flow analysis in oil-immersed converter transformers, verifying its accuracy and practicality for real engineering applications.
辛纪威, 李琳, 刘刚. 基于非结构化同位网格的油浸式换流变压器流场数值计算方法研究[J]. 电工技术学报, 2025, 40(24): 7832-7845.
Xin Jiwei, Li Lin, Liu Gang. Research on the Numerical Calculation Method for the Flow Field of Oil-Immersed Converter Transformers Based on Unstructured Collocated Grids. Transactions of China Electrotechnical Society, 2025, 40(24): 7832-7845.
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