European Journal of Mechanics - B/Fluids ( IF 2.6 ) Pub Date : 2021-01-10 , DOI: 10.1016/j.euromechflu.2020.12.013 L. Ullah , A. Samad , A. Nawaz
We present convective instability analyses of the boundary-layer flows originated over cones (with half-angle ) rotating in an otherwise still conducting fluid. A uniform magnetic field (with magnetic strength parameter, ) is acting normally on the surface of each cone. In the non-magnetic case of cones, comparison of present results with existing experimental and theoretical studies lead *to propose that onset of instabilities may be attributed to crossflow (type I) modes and streamline curvature (type II) modes for broad cones (with ) and more slender cones (with ), respectively. For slender cones with half-angle in the vicinity of 25° the presented results validate the hypothesis of centrifugal (type III) modes ( discovered by Garrett et al. (2014)). In the magnetic case, increasing magnetic strength considerably delays the onset of instabilities (due to both type I and type II modes) over each rotating cone with fixed . The stabilising influence of magnetism is in agreement with the meagrely available theoretical studies for magnetic rotating disk case . In addition, our results lead to suggest that streamline curvature mode over each cone with fixed half-angle become sensitive with increasing m. A minimum exists for each fixed half-angle such that whenever the onset of instabilities (in the sense of minimum critical Reynolds numbers) over every cone with half-angle () are commenced by type II mode instead of type I mode whilst the aforementioned conjecture of stabilising effect of magnetism is not violated in the considered range of parameters. Under non-stationary vortices assumption with magnetism, we show that crossflow modes travelling at around 75% of the cone surface are likely to be selected in applications where smooth and frictionless surfaces are used. This finding is in complete agreement with the non-magnetic case of rotating cone in existing studies.
中文翻译:
在均匀磁场内外的旋转锥上边界层流的对流不稳定性
我们对源自圆锥体(具有半角)的边界层流进行对流不稳定性分析 )在其他情况下仍在导电的流体中旋转。均匀的磁场(具有磁强度参数,)正常作用在每个锥体的表面上。在圆锥体的非磁性情况下,将当前结果与现有的实验和理论研究进行比较,可以得出*不稳定现象的起因可以归因于宽圆锥体(具有)的横流(I型)模式和流线曲率(II型)模式。)和更细长的锥体(带有 ), 分别。适用于半角细长锥在25°附近,本文给出的结果验证了离心(III型)模式的假设(由Garrett等人(2014年)发现)。在磁性情况下,增加磁场强度 固定旋转的每个旋转锥大大延迟了不稳定的发生(由于I型和II型模式) 。磁性的稳定作用与旋转磁盘盒的理论研究很少。另外,我们的结果表明,在固定半角的情况下,每个锥体的流线曲率模式随着m的增加变得敏感。最低要求 每个固定的半角都存在 这样每当 每个半角锥的不稳定性的发生(在最小临界雷诺数的意义上)()由II型模式代替I型模式开始,而在所考虑的参数范围内没有违反上述磁场稳定作用的推测。在具有磁性的非平稳涡旋假设下,我们表明,在使用光滑无摩擦表面的应用中,可能会选择在锥面约75%处传播的错流模式。这一发现与现有研究中的非磁性旋转锥情况完全吻合。