波状壁の上を通過する粘弾性流体のせん断流れの数値解析

Abstract

A two-dimensional shear flow of a viscoelastic fluid over a wavy wall was numerically analyzed by the finite difference method. The upper convected Maxwell (UCM) model was used as the constitutive equation, and the unsteady flow problem was solved numerically using the stream function-vorticity method. Variables are discretized using a staggered grid with uniform mesh width. The volume penalization method was used to represent the moving upper wall and the fixed lower wavy wall that induces a vorticity perturbation. The flow in an infinitely long channel is computed using periodic boundary conditions in the flow direction. The results show that the vorticity intensifies over the wavy surface with positive and negative vorticity stripes, at which extreme wall-normal velocity fluctuations are also observed. At relatively high Deborah numbers, the lower ends of these extreme fluctuation regions are close to the critical line associated with a change of type of the governing partial differential equations in a Couette flow. In contrast, the upper ends of the extreme fluctuation region are close to the critical layer of the shear flow, where the flow velocity coincides with the viscoelastic Alfvén wave speed.