磁流体力学均匀湍流中磁雷诺数效应研究  

Investigation of the Magnetic Reynolds Number Effects on MHD Homogeneous Turbulence

作　　者：许珂 高振勋[1] 钱战森 李椿萱[1] Xu Ke;Gao Zhenxun;Qian Zhansen;Li Chunxuan(School of Aeronautic Science and Engineering,BeihangUniversity,Beijing100191,China;Chinese Aeronautical Establishment,Beijing 100029,China)

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100191 [2]中国航空研究院,北京100029

出　　处：《气动研究与试验》2025年第1期94-102,共9页Aerodynamic Research & Experiment

摘　　要：目前针对航空航天领域的磁流体模拟因其低磁雷诺数特性会忽略感生磁场。然而湍流的多尺度特征会引起磁场的多尺度脉动,此时较小的感生磁场也会对流动产生明显的效果。本文通过提出的考虑感生磁场的跨磁雷诺数模型对磁雷诺数0.06~60的均匀湍流开展数值模拟并与无磁场及低磁雷诺数的结果进行对比,结合摄动展开以及磁场能量守恒等方法,分析了磁雷诺数效应。分析发现,对于磁流体湍流,即使磁雷诺数在10-2也不能直接忽略感生磁场。进一步研究给出了感生磁场谱与速度谱的解析关系,并发现感生磁场谱相对速度谱的时间延迟效应,且时间尺度以及磁场能量尺度均正比于磁雷诺数。根据磁场脉动强度将湍流发展过程分为上升阶段和衰减阶段,同时发现磁雷诺数效应描述的是磁流体的电感效应。磁雷诺数越大,电感效应越强,上升阶段与衰减阶段磁场能量对流体造成的影响也会越大,磁场的时间历史效应会更明显。通过本文研究发现低磁雷诺数假设对于包含高频脉动的湍流流动失效,因此后期研究低磁雷诺数磁流体湍流时仍然需要考虑感生磁场所代表的电感效应。ln the field of aerospace,magnetohydrodynamic(MHD)simulations typically ignore the induced magnetic field due to the low magnetic Reynolds number characteristic.However,the multiscale nature of turbulence can cause multiscale magnetic field fluctuations,and in this case,even a small induced magnetic field can have a significant effect on the flow.By employing the proposed trans-magnetic Reynolds number model that accounts for the induced magnetic field,numerical simulations of homogeneous turbulence with magnetic Reynolds numbers ranging from 0.06 to 60 were conducted and compared with results under conditions of no magnetic field and low magnetic Reynolds numbers.Using perturbation expansions and methods like magnetic field energy conservation,the effects of the magnetic Reynolds number were analyzed.The analysis revealed that for MHD turbulence,even when the magnetic Reynolds number is as low as 10,the induced magnetic field cannot be directly neglected.Further studies provided the analytical relationship between the induced magnetic field spectrum and the velocity spectrum,and discovered the time delay effect of the induced magnetic field relative to the velocity field.Both the time scale and magnetic field energy scale were found to be proportional to the magnetic Reynolds number.Based on the intensity of magnetic field fluctuations,the turbulence development process was divided into a rising phase and a decaying phase.It was also found that the magnetic Reynolds number effect describes the induction effect of MHD.The larger the magnetic Reynolds number,the stronger the inductive effect,and the greater the impact of magnetic field energy on the fluid during both the rising and decaying phases.The time history effect of the magnetic field also becomes more pronounced.The study in this paper reveals that the low magnetic Reynolds number assumption fails for turbulent flows with high-frequency fluctuations.Therefore,in future research on lowmagnetic Reynolds number magnetohydrodynamic turbulence,it is still nece

关 键 词：磁流体力学 均匀湍流 低磁雷诺数 磁雷诺数 跨磁雷诺数模型 

分 类 号：O361.3[理学—流体力学] V211.3[理学—力学]