Some Features of a Laminar Flow Stability Loss in a Pipe

Abstract

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.