In the current study, we present a mathematical and computational fluid dynamics (CFD) model for simulating open-cycle linear Faraday-type continuous-electrode channels of magnetohydrodynamic (MHD) power generators, operating on combustion plasma. The model extends the Favre-averaged Navier-Stokes equations to account for the electric properties of the flowing plasma gas and its reaction to the applied magnetic field. The model takes into account various effects, such as the Lorentz force, turbulence, compressibility, and energy extraction from the plasma, and it adopts an electric potential technique along with the low magnetic Reynolds number (Rem) approximation. The model is numerically implemented using the multiphysics open-source computer programming environment "OpenFOAM," which combines the finite volume method (FVM) and the object-oriented programming (OOP) concept. The capabilities of the model are demonstrated by simulating the supersonic channel of the large-scale pulsed MHD generator (PMHDG) called "Sakhalin", with the aid of collected data and empirical expressions in the literature about its tested operation. Sakhalin was the world's largest PMHDG, with a demonstrated peak electric power output of 510 MW. Sakhalin operated on solid-propellant plasma (SPP), and it had a single supersonic divergent Faraday-type continuous-electrode channel with a length of 4.5 m. We check the validity of the model through comparisons with independent results for the Sakhalin PMHDG. Then, we process our three-dimensional simulation results to provide scalar characteristics of the Sakhalin channel, one-dimensional profiles along the longitudinal centerline, and three-dimensional distributions in the entire channel.

翻译：本研究提出了一种用于模拟燃烧等离子体驱动的磁流体动力发电机开式循环线性法拉第型连续电极通道的数学与计算流体动力学模型。该模型扩展了Favre平均Navier-Stokes方程，以考虑流动等离子体气体的电学特性及其对施加磁场的响应。模型综合考虑了洛伦兹力、湍流、可压缩性及等离子体能量提取等多种效应，采用电势技术结合低磁雷诺数近似方法。该模型通过结合有限体积法与面向对象编程理念的多物理场开源计算编程环境"OpenFOAM"实现数值求解。通过利用文献中关于"萨哈林"大型脉冲磁流体动力发电机测试运行的实测数据与经验表达式，模拟其超音速通道，展示了该模型的仿真能力。萨哈林曾是世界最大的脉冲磁流体动力发电机，实测峰值电功率输出达510兆瓦。该发电机采用固体推进剂等离子体，配备单通道超音速扩张法拉第型连续电极通道，通道长度为4.5米。通过与萨哈林脉冲磁流体动力发电机的独立结果进行对比验证模型有效性，进而处理三维仿真结果，提供萨哈林通道的标量特征参数、沿纵向中心线的一维分布曲线以及整个通道内的三维场分布。