二维下腔室稳态流场降阶模型开发

Development of Reduced Order Model for Steady State Flow Field in Two-dimensional Lower Plenum

  • 摘要: 计算流体力学(CFD)程序基于三维Navier-Stokes(N-S)方程组,可实现三维尺度的模拟。但CFD模拟通常需要较长的计算时间,难以实现快速计算,限制了其应用场景。本文采用本征正交分解(POD)方法和稀疏网格理论,构建了二维压力容器下腔室稳态流场的非侵入式降阶模型。降阶模型的输入为下腔室两个入口的冷却剂质量流量,输出为下腔室速度场分布。基于稀疏网格理论,通过运行全阶CFD下腔室模型生成快照矩阵,并拟合POD系数与降阶模型输入参数之间的映射关系。在测试集上对构建的降阶模型进行测试,结果表明:所构建的降阶模型可以快速得到不同入口流量下的流场分布数据,且精度满足仿真要求。由于降阶模型仅涉及矩阵代数运算,其计算速度远高于全阶CFD模型,拓宽了CFD的应用范围,有望应用于多尺度耦合、数字孪生等对计算速度要求较高的场景。

     

    Abstract: In the field of reactor thermal-hydraulics, system thermal-hydraulic codes have been widely employed to quickly determine the global response characteristics of the primary system. But, duo to the one-dimensional governing equations are adopted, certain local multi-dimensional physical phenomena cannot be accurately captured by the system thermal-hydraulic codes. On the other hand, the multi-dimensional dynamic simulation with high spatial and temporal resolution can be achieved by computational fluid dynamics (CFD) codes using the Navier-Stokes (N-S) equations. However, CFD computation is computationally expensive and time-consuming, requiring extensive computational resources, such as high-performance computing clusters or parallel processing techniques, to solve complex flow problems. This imposes significant limitations on its applications in scenarios requiring rapid computation speed and real-time analysis, such as parametric study, uncertainty quantification, and design optimization. To address this challenge, a non-intrusive reduced order model for predicting the steady state flow field in the lower plenum of a two-dimensional reactor pressure vessel was constructed using the proper orthogonal decomposition (POD) method combined with sparse grids theory in this paper. The input parameters of the reduced order model were the coolant mass flow rates at the two inlets of the lower plenum, while the output was the corresponding velocity field distribution within the lower plenum. Based on the sparse grids theory, the snapshot matrix was first generated by repetitive simulation using the full order CFD lower plenum model, then the mapping relation between the POD coefficients and the input parameters of the reduced order model was fitted. The performance of the constructed reduced order model was tested on an independent test dataset. The results indicate that the developed reduced order model is capable of rapidly predicting velocity field distributions in the lower plenum under different inlet mass flow rate, while maintaining accuracy that meets simulation requirement. Since the operation of the reduced order model involves only matrix algebra calculations instead of solving the N-S equations, its computational speed is significantly higher than that of the full order CFD model. This remarkable improvement expands the applicability of CFD-based simulation to a broader range of engineering problems. Specifically, the proposed reduced order model construction method holds great promise for applications requiring high-speed flow field prediction, such as multi-scale coupling simulation, real-time simulation analysis, and digital twin implementations in nuclear reactor systems and other fluid engineering domains. Furthermore, the developed framework can also be extended to transient flow problems, further enhancing its utility in advanced engineering applications.

     

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