NON-AXISYMMETRICAL MODES IN VISCOELASTIC TAYLOR-COUETTE FLOW
NON-AXISYMMETRICAL MODES IN VISCOELASTIC TAYLOR-COUETTE FLOW
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DOI：
10.1016/0377-0257(93)80033-8
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发表时间：
1993-12-01
影响因子：
3.1
通讯作者：
BERIS, AN
中科院分区：
文献类型：
--
作者：
AVGOUSTI, M;BERIS, AN
本文研究了粘弹性Taylor-Couette流在非轴对称扰动下的线性稳定性。一个伪谱生成的，广义代数特征值问题的三维控制方程的线性化组周围的稳态方位角的解决方案。临界本征值的数值计算表明，对于上随体麦克斯韦模型和本文所研究的特定几何和运动学参数组，方位角Couette（基）流在轴对称流之前对非轴对称时间周期扰动变得不稳定，只要弹性数ε（=De/Re）大于某个非零但很小的值（ε> 0.01）。此外，随着ε的增加，不同的本征解族成为不稳定性的开始。特别地，已经发现临界本征解的方位角波数从1到2到3变化，然后随着λ从0.01增加到无穷大而回到2以类似于轴对称粘弹性Taylor-Couette流的方式，（极限环）可以出现后，发病的不稳定性：带状和螺旋，对应于方位和行波，分别。这些模式仅由主流的对称性决定，并且已经在涉及牛顿流体的实验中观察到，但是两个圆柱体反向旋转而不是如这里所考虑的共同旋转。已发现包含非零溶剂粘度（Oldrophil-B模型）对结果有定量影响，但无定性影响。这些理论预测是特别重要的泰勒-库埃特流使用高弹性粘弹性流体中获得的实验数据的解释。
In this work, the linear stability analysis of the viscoelastic Taylor-Couette flow against non-axisymmetric disturbances is investigated. A pseudospectrally generated, generalized algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional governing equations around the steady-state azimuthal solution. Numerical evaluation of the critical eigenvalues shows that for an upper-convected Maxwell model and for the specific set of geometric and kinematic parameters examined in this work, the azimuthal Couette (base) flow becomes unstable against non-axisymmetric time periodic disturbances before it does so for axisymmetric ones, provided the elasticity number epsilon (=De/Re) is larger than some non-zero but small value (epsilon > 0.01). In addition, as epsilon increases, different families of eigensolutions become responsible for the onset of instability. In particular, the azimuthal wavenumber of the critical eigensolution has been found to change from 1 to 2 to 3 and then back to 2 as epsilon increases from 0.01 to infinity (inertialess flow).In an analogous fashion to the axisymmetric viscoelastic Taylor-Couette flow, two possible patterns of time-dependent solutions (limit cycles) can emerge after the onset of instability: ribbons and spirals, corresponding to azimuthal and traveling waves, respectively. These patterns are dictated solely by the symmetry of the primary flow and have already been observed in conjunction with experiments involving Newtonian fluids but with the two cylinders counter-rotatng instead of co-rotating as considered here. Inclusion of a non-zero solvent viscosity (Oldroyd-B model) has been found to affect the results quantitatively but not qualitatively. These theoretical predictions are of particular importance for the interpretation of the experimental data obtained in a Taylor-Couette flow using highly elastic viscoelastic fluids.