Purpose

Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism.

Design/methodology/approach

A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation.

Findings

Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 ≤ Ha ≤ 80), inclination angles (0 ≤ γ ≤ 90°) and radii ratios λ ≤ 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at γ = 30°.

Practical implications

This numerical model is selected for its various applications in technology and industry.

Originality/value

To the best of the authors’ knowledge, the influence of the inclination of the cylindrical annulus (ring), with various radii ratio, on natural oscillatory convection under a radial magnetism has never been investigated.

中文翻译：

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充满熔融金属的倾斜圆柱形环空中的磁热对流稳定性

目的

金属冷却的反应器通常使用熔融金属，例如钠，钾或钠和钾的混合物，因为它们具有出色的传热性能，因此反应器可以在更低的压力和更高的温度下运行。本文的目的是研究在径向磁场影响下充满熔融钾的倾斜环中自然对流的稳定性。

设计/方法/方法

在径向磁场的影响下，在倾斜的圆柱环上进行了导电流体自然对流稳定性的数值模拟。上壁和下壁是绝热的，而内部和外部气缸则保持在均匀的温度下。使用有限体积法对控制该流体系统的方程进行了数值求解。SIMPLER算法用于动量方程中的压力-速度耦合。

发现

针对各种哈特曼数（0≤Ha≤80），倾角（0≤γ），以等压线，等温线和环形空间中的流线的形式讨论了解决初始振动状态问题的各种有效参数的数值结果≤90°）和半径比λ≤6。在此调查的数值数据的基础上，建立了具有瑞利数RaCr的临界值和相应频率FrCr的复杂情况之间的相关性稳定性图。环的倾角和半径比对磁对流通量的稳定有重要影响，并且表明通过最强的磁场强度，高的半径比可以获得自然振荡对流的最佳稳定性。环在γ= 30°处的倾斜度。

实际影响

选择该数值模型是因为其在技术和工业中的各种应用。

创意/价值

据作者所知，从未研究过具有不同半径比的圆柱环（环）的倾斜度对径向磁作用下自然振荡对流的影响。