Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows
Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows
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DOI：
10.1017/jfm.2021.852
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发表时间：
2021-07
影响因子：
3.7
通讯作者：
D. Wan;Guangrui Sun;Mengqi Zhang
中科院分区：
文献类型：
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作者：
D. Wan;Guangrui Sun;Mengqi Zhang
最近Garg等人发现oldyd - b流体的轴对称粘弹性管流是线性不稳定的。莱特牧师。中文信息学报，vol. 121, 2018, 024502)。从非线性的角度来看，这意味着流动可以超临界地过渡到湍流，而不是亚临界牛顿管道流动。粘弹性管道流动的亚临界和超临界分岔的实验证据已被报道，但这些非线性现象尚未在理论上得到检验。在这项工作中，我们通过对线性临界条件周围的扰动进行多尺度展开来研究该流的弱非线性稳定性。扰动参数为雷诺数，其他参数未扰动。导出了三阶金兹堡-朗道方程，其系数表示流的分岔类型。在探索了一个大的参数空间后，我们发现聚合物浓度起着重要的作用：在高聚合物浓度（或小溶剂与溶液粘度比$\beta \lessapprox 0.785$）下，非线性稳定流动，表明流动将发生超临界分岔，而在低聚合物浓度（$\beta \gtrapprox 0.785$）下，流动分岔是亚临界的。结果在质量上与实验观察一致，其中临界$\beta \approx 0.855$。上对流麦克斯韦流体的管道流动可以是线性不稳定的，其分岔类型也是超临界的。在固定值$\beta$下，当$Wi$足够大时，朗道系数与Weissenberg数（$Wi$）的倒数进行标度。本文的分析对粘弹性管道流动中弹性-惯性湍流的超临界和亚临界路径的最新研究提供了理论认识。
Abstract Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. (Phys. Rev. Lett., vol. 121, 2018, 024502). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidence of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expansion of the disturbance around linear critical conditions. The perturbed parameter is the Reynolds number with the others being unperturbed. A third-order Ginzburg–Landau equation is derived with its coefficient indicating the bifurcation type of the flow. After exploring a large parameter space, we found that polymer concentration plays an important role: at high polymer concentrations (or small solvent-to-solution viscosity ratio $\beta \lessapprox 0.785$), the nonlinearity stabilizes the flow, indicating that the flow will bifurcate supercritically, while at low polymer concentrations ($\beta \gtrapprox 0.785$), the flow bifurcation is subcritical. The results agree qualitatively with experimental observations where critical $\beta \approx 0.855$. The pipe flow of upper convected Maxwell fluids can be linearly unstable and its bifurcation type is also supercritical. At a fixed value of $\beta$, the Landau coefficient scales with the inverse of the Weissenberg number ($Wi$) when $Wi$ is sufficiently large. The present analysis provides a theoretical understanding of the recent studies on the supercritical and subcritical routes to the elasto-inertial turbulence in viscoelastic pipe flows.