管道层流稳定性损失的一些特征

G. Voropaiev, O. Baskova
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摘要

尽管在恒定半径的管道中稳定流动看起来很简单,但这种转变的原因和过程的问题仍然存在争议。特别是由于抛物型剖面稳定性损失的必要条件不满足,轴对称泊泽维尔流的线性水动力稳定性理论没有给出任何雷诺数下的轴对称增长本征解,因为在线性化的动量守恒方程中,表征扰动与初速度剖面相互作用的项被去掉了。本文基于三维非定常Navier-Stokes方程组的数值解和能量传递方程,研究了变参数下管道初始段流动对流稳定损失的阶段。本研究的可变参数为:非等温流动中产生的动态粘度系数的雷诺数、大小和梯度符号。将近壁区二次轴对称大尺度环面涡结构的产生与板上层流边界层过渡区的托尔曼-施里希汀波进行了类比。分析了这些环面涡结构的轴对称性和稳定性的丧失,导致下游形成相当规则的纵向涡结构,它们之间的非线性相互作用导致流动的混沌化。这些截面的长度取决于雷诺数、动态粘度系数梯度的大小和符号。
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SOME FEATURES OF A LAMINAR FLOW STABILITY LOSS IN A PIPE
Despite the seeming simplicity of the steady flow in a pipe of constant radius, the question of the cause and process of the transition remains debatable. Especially since the necessary condition for the stability loss of parabolic profile is not satisfied, and the linear theory of hydrodynamic stability for an axisymmetric Poiseuille flow does not give growing axisymmetric eigen solutions for any Reynolds numbers, since the terms characterizing the interaction of disturbances with the initial velocity profile drop out in the linearized equations of momentum conservation. The report presents the results of the study of stages of convective stability loss for the flow at the initial section of the pipe depending on the variable parameters based on the numerical solution of the three-dimensional system of unsteady Navier-Stokes equations and the equation energy transfer. The variable parameters in this study were: Reynolds number, magnitude and gradient sign of the dynamic viscosity coefficient arising in nonisothermal flows. An analogy of the arising secondary axisymmetric large-scale toroidal vortex structures in the near-wall region to Tollmien-Schlichting waves in the region of the transition of the laminar boundary layer on the plate is shown. The subsequent loss of axisymmetry and stability of these torus-like vortex structures is analyzed, which leads to the formation of fairly regular longitudinal vortex structures downstream, the nonlinear interaction of which leads to chaotization of the flow. The lengths of these sections are determined depending on the Reynolds number, the magnitude and sign of the gradient of the dynamic viscosity coefficient.
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