Onset of convection induced by centrifugal buoyancy in a rotating cavity
Onset of convection induced by centrifugal buoyancy in a rotating cavity
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DOI：
10.1017/jfm.2017.451
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发表时间：
2017-08
影响因子：
3.7
通讯作者：
D. Pitz;O. Marxen;J. Chew
中科院分区：
文献类型：
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作者：
D. Pitz;O. Marxen;J. Chew
离心力引起的流动发生在旋转系统中，与其他体力相比，离心力较大，这对地球物理学家和涉及快速旋转和不稳定温度梯度的工程问题都是有意义的。在这项数值研究中，我们采用了与燃气轮机内部空气系统中浮力诱导流动的基础研究相关的几何构型，分析了由两个平面绝缘盘所包围的旋转圆柱腔中的离心浮力的开始。通过线性稳定性分析，得到了不同半径比下的离心瑞利数Ra和相应的对流开始临界方位波数的临界值。利用直接的数值模拟，我们积分了从静止状态开始的解，并在其上添加了小的正弦扰动，表明非线性三元相互作用在能量饱和之前就发生了。在所考虑的最低瑞利数下，最终状态是一个受圆盘存在影响的极限环振荡，其频谱由某一模式及其谐波所主导。我们证明，在这种情况下，极限环振荡只有在无滑移端壁存在的情况下才会出现。对于被认为是混沌运动的最大的$Ra，即使在湍流区，由线性分析得到的临界波数最终也变得最有能量。
Flows induced by centrifugal buoyancy occur in rotating systems in which the centrifugal force is large when compared to other body forces and are of interest for geophysicists and also in engineering problems involving rapid rotation and unstable temperature gradients. In this numerical study we analyse the onset of centrifugal buoyancy in a rotating cylindrical cavity bounded by two plane, insulated disks, adopting a geometrical configuration relevant to fundamental studies of buoyancy-induced flows occurring in gas turbine’s internal air systems. Using linear stability analysis, we obtain critical values of the centrifugal Rayleigh number $Ra$ and corresponding critical azimuthal wavenumbers for the onset of convection for different radius ratios. Using direct numerical simulation, we integrate the solutions starting from a motionless state to which small sinusoidal perturbations are added, and show that nonlinear triadic interactions occur before energy saturation takes place. At the lowest Rayleigh number considered, the final state is a limit-cycle oscillation affected by the presence of the disks, having a spectrum dominated by a certain mode and its harmonics. We show that, for this case, the limit-cycle oscillations only develop when no-slip end walls are present. For the largest $Ra$ considered chaotic motion occurs, but the critical wavenumber obtained from the linear analysis eventually becomes the most energetic even in the turbulent regime.