Fully-Developed Pulsating Liquid Flows in a Three-Dimensional Wavy Wall Microtube

Abstract

Influences of a three-dimensional wavy wall on the fully-developed pulsating liquid flows in microtube were studied in this paper. Fully-developed pulsating liquid flows driven by the pulsating pressure gradient in microtube with non-axisymmetric wavy wall were considered. The pulsating pressure gradient can be split into the steady and the oscillatory terms, and therefore the velocities were split into steady and the oscillatory terms in the same way. The analytical and numerical results show that the variations of disturbances are dependent on those of pulsating frequency. When the frequency increases large enough, subsidiary stresses will approach to their asymptotic solutions. In addition, it is found that the subsidiary stress layers gradually become thinner with increasing of the pulsating frequency, and therefore the wall disturbances are difficult to be transmitted to the center of the flow area. At the low frequency of pulsation, the curve shapes of oscillatory subsidiary stresses are nearly consistent with the cases of steady flow. The variations of phase shifts are between the values —π/2 and π/2, which is independent of the choices of parameters (including the choices of oscillatory pressure drop), and the extreme values of them tend to —π/2 and π/2 as the pulsating frequency approaches to infinity.