Ashrafi N, Khayat RE
Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, Canada N6A 5B9.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1455-67. doi: 10.1103/physreve.61.1455.
The effect of weak shear thinning on the stability of the Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow, becomes lower as the shear-thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows, which coincides with the onset of a supercritical bifurcation. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, a Hopf bifurcation emerges, which exists only for shear-thinning fluids.
在窄间隙极限下，研究了弱剪切变稀对卡雷奥 - 伯德流体泰勒 - 库埃特流稳定性的影响。采用伽辽金投影法从质量守恒和动量方程推导出一个低阶动力学系统。与牛顿系统相比，本方程通过粘度在速度分量中包含额外的非线性耦合。研究发现，对应于基本（库埃特）流稳定性丧失的临界泰勒数随着剪切变稀效应的增加而降低。也就是说，剪切变稀倾向于促使泰勒涡旋流的出现。与牛顿流体类似，库埃特流和泰勒涡旋流之间存在稳定性交换，这与超临界分岔的开始相吻合。然而，与牛顿模型不同的是，当泰勒数达到临界值时，泰勒涡旋胞状结构会依次失去稳定性。此时，出现霍普夫分岔，这仅存在于剪切变稀流体中。
