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A Numerical Investigation of Moderate Magnetic Reynolds Number Fusion Liquid Metal Magnetohydrodynamic Flows

机译：中磁雷诺数融合液态金属磁流体动流的数值研究

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摘要

In this study, mathematical and numerical methodologies are developed, and an induction-based incompressible magnetohydrodynamic (MHD) flow solver was created, to study moderate Rem liquid metal (LM) MHD flows for fusion blanket design. Most LM MHD flow numerical studies in fusion blanket design have traditionally assumed that the magnetic Reynolds number (Rem) is much less than unity. The Rem, a dimensionless parameter in the magnetic induction equation, is a measure of the ratio of convection to diffusion of the magnetic field. The low Rem approximation, also known as the inductionless or quasi-static approximation, assumes that the applied magnetic field is quasi-static and that the ratio of induced to applied magnetic field strength is much less than unity. This assumption is not valid under certain conditions, however. For example, during unsteady plasma events, such as major disruptions, the applied magnetic field changes on the order of Tesla per milliseconds. The strongly unsteady applied magnetic field requires the use of the magnetic induction formulation. Furthermore, these conditions may lead to high velocities such that Rem is greater than unity.;The objectives of this study are to (1) study the effects of moderate Rem on steady MHD flows, (2) compare approximate magnetic boundary conditions (BCs) with proper far-field magnetic BCs for moderate Rem steady MHD flows and our main objective (3) study flow physics of a flow induced from a strongly unsteady applied magnetic field, similar to conditions expected in the LM during a fusion plasma disruption. We limit our scope of the first two objectives to a simple lid-driven cavity (LDC) flow with a transversely applied magnetic field. For the third objective, we consider a long three-dimensional rectangular enclosure (akin to a blanket module) with no-slip conducting walls on all sides and an unsteady applied magnetic field computed from a plasma code, used for the international thermonuclear experimental reactor (ITER).;The Rem effect on MHD flows was analyzed by considering a LDC MHD flow with a transversely applied magnetic field using proper far-field magnetic BCs. Results show that the flow is mostly two-dimensional (except for the Hartmann layers) when Rem < 100, but becomes more three-dimensional as Rem increases. The integral kinetic energy and velocity distributions indicate that the Rem effect on the flow is negligible for Rem [special character omitted]100 at steady state, suggesting that approximate magnetic BCs are valid in this range under steady-state conditions. While the flow is unsteady, however, the integral kinetic energy deviated significantly with respect to changes in Rem, indicating that the approximate magnetic BCs are likely invalid during flow unsteadiness. For 0 ≤ Re m ≤ 100, the induced magnetic field magnitude increases linearly with Rem while its distribution Remains qualitatively unchanged. The induced magnetic field energy in the flow domain is higher than the applied one for Rem values higher than Rem ∼ 850. First results of linear and non-linear dynamo tests were performed for the LDC flow problem and while both tests were ultimately inconclusive, the results were analyzed and time-local induced magnetic field generation was observed in the non-linear dynamo test.
机译：在这项研究中，开发了数学和数值方法，并创建了基于感应的不可压缩磁流体动力学（MHD）流动求解器，以研究用于熔融毯设计的中等Rem液态金属（LM）MHD流动。传统上，大多数在熔覆层设计中进行的LM MHD流动数值研究都假定雷诺数（Rem）小于一。 Rem是磁感应方程中的无量纲参数，是对流与磁场扩散比的量度。低Rem近似值，也称为无感应近似值或准静态近似值，假定所施加的磁场是准静态的，并且感应磁场强度与所施加磁场强度之比远小于1。但是，此假设在某些条件下无效。例如，在不稳定的等离子体事件（例如重大破坏）期间，所施加的磁场的变化量为每毫秒特斯拉量级。强烈不稳定的磁场需要使用磁感应配方。此外，这些条件可能会导致Rem大于1的高速度。;本研究的目的是（1）研究中等Rem对稳定MHD流的影响，（2）比较近似磁边界条件（BCs）用适当的远场磁BC来实现中等的Rem稳定MHD流动，我们的主要目标（3）研究了由强不稳定磁场施加的流动的流物理学，类似于聚变等离子体破裂过程中LM所预期的条件。我们将前两个目标的范围限制为具有横向施加磁场的简单盖驱动腔（LDC）流。对于第三个目标，我们考虑一个长的三维矩形外壳（类似于毯子模块），在所有侧面上均具有防滑导电壁，并根据等离子代码计算出了不稳定的施加磁场，用于国际热核实验反应堆（通过考虑使用适当远场磁BC的横向施加磁场的LDC MHD流，分析了Rem对MHD流的影响。结果表明，当Rem <100时，流动主要是二维的（除Hartmann层外），但随着Rem的增加，流动变得更加立体。积分动能和速度分布表明，在稳态下，Rem [省略特殊特征] 100对流体的Rem效应可忽略不计，这表明在稳态条件下，该范围内的近似磁性BC有效。然而，尽管流动不稳定，但积分动能相对于Rem的变化却明显偏离，这表明在流动不稳定期间，近似的磁性BC可能无效。当0≤Re m≤100时，感应磁场强度随Rem线性增加，而其分布在质量上保持不变。当Rem值高于Rem〜850时，在流域中感应磁场能量高于所施加的磁场能量。对LDC流动问题进行了线性和非线性发电机测试的第一个结果，尽管这两个测试最终都没有定论，但是分析结果，并在非线性发电机测试中观察到时域感应磁场的产生。

著录项

  • 作者

    Kawczynski, Charles Newlin.;

  • 作者单位

    University of California, Los Angeles.;

  • 授予单位 University of California, Los Angeles.;
  • 学科 Mechanical engineering.;Fluid mechanics.
  • 学位 D.Env.
  • 年度 2018
  • 页码 118 p.
  • 总页数 118
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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