基于OpenFOAM的投影法磁流体求解器开发与验证

在开源计算流体力学C++工具包OpenFOAM环境下开发了低磁雷诺数条件下的磁流体求解器，并进行了验证。采用投影算法求解动量方程和压力泊松方程；采用非结构网格同位相容守恒算法求解电势泊松方程、感应电流和洛伦兹力；采用边界耦合方法求解流固耦合电势场。通过对均匀磁场下导电方管和导电圆管内的完全发展磁流体层流的数值模拟和解析解的对比，对求解器进行了验证。进一步对非均匀强磁场作用下导电方管和导电圆管内完全发展磁流体层流进行了数值模拟，并与ALEX实验结果进行了比较。数值解和实验结果吻合良好。所开发的求解器可用于复杂结构强磁场作用下磁流体的数值模拟研究。

Development and validation of magnetohydrodynamic solver with projection in OpenFOAM environment

Magnetohydrodynamic flow solver with low magnetic Reynolds number in open source CFD environment of OpenFOAM was developed and validated. Four step projection methods were used to solve the momentum equation and the mass conservative equation. The consistent and conservative schemes based on collocated unstructured grid were applied to solve the electric potential Poisson equation, the induced electric current and the Lorentz force. A multi-region technique coupled by the boundary was also developed to solve magnetohydrodynamic flow with electric conducting walls. The solver was verified and validated by simulating duct and pipe flow with conducting walls under uniform magnetic field. Furthermore, the multi-region MHD solver was also validated by simulating liquid metal flows subject to a non-uniform magnetic field in an electrically conducting rectangular duct and pipe. The pressure distribution was compared with the ALEX experimental data. The results show that the solver has a good accuracy and can be used in the numerical study of MHD flows in fusion environment.