Three-dimensional stability, receptivity and sensitivity of non-Newtonian flows inside open cavities
Three-dimensional stability, receptivity and sensitivity of non-Newtonian flows inside open cavities
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DOI：
10.1088/0169-5983/47/1/015503
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发表时间：
2015-02
影响因子：
1.5
通讯作者：
V. Citro;F. Giannetti;J. Pralits
中科院分区：
文献类型：
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作者：
V. Citro;F. Giannetti;J. Pralits
我们研究了具有剪切相关粘性的流体在开方腔内流动的稳定性。分析是在使用简正波分解的线性理论的背景下进行的。采用Carreau粘性模型对不可压缩柯西方程进行了有限元离散。为了了解流动的感受性特征，对直接本征模和伴随本征模的特性进行了分析和讨论。此外，我们通过建立由直接特征函数和伴随特征函数之间的乘积得到的空间映射来识别对空间局部化反馈更敏感的流动区域。分析表明，定常流动的第一个整体线性不稳定性是定常或非定常的三维分叉，这取决于幂指数n的大小。失稳机制总是位于空腔内部，线性稳定性结果表明与经典的盖子驱动空腔问题有很强的联系。
We investigate the stability properties of flows over an open square cavity for fluids with shear-dependent viscosity. Analysis is carried out in context of the linear theory using a normal-mode decomposition. The incompressible Cauchy equations, with a Carreau viscosity model, are discretized with a finite-element method. The characteristics of direct and adjoint eigenmodes are analyzed and discussed in order to understand the receptivity features of the flow. Furthermore, we identify the regions of the flow that are more sensitive to spatially localized feedback by building a spatial map obtained from the product between the direct and adjoint eigenfunctions. Analysis shows that the first global linear instability of the steady flow is a steady or unsteady three-dimensionl bifurcation depending on the value of the power-law index n. The instability mechanism is always located inside the cavity and the linear stability results suggest a strong connection with the classical lid-driven cavity problem.