Semi-analytical solutions of pulsating flow in a helically rough-walled microtube

The influence of a helically rough wall surface on fully developed pulsating laminar flows in microtube is investigated through a semi-analytical method. A two-dimensional simple harmonic function is chosen to model helically wavy structure. The velocity and pressure are decomposed into space-averaged and disturbance terms and the corresponding governing equations are established. Pulsating flow is split into a steady term and an oscillatory term based on a given oscillatory pressure drop, and the governing equations for the oscillatory terms are presented together with their steady counterparts. Analytical solutions are obtained for the space-averaged equations and a spectral collocation method is used to solve the disturbance equations numerically. An iterative approach is adopted for the coupled equations with respect to space-averaged velocities and disturbance velocities. The computational results show that a Reynolds stress layer (RSL) and a secondary swirling velocity are present in the rough-walled microtube. The relative amplitude of the waviness of the wall, its wavenumber, and the Reynolds number are found to be important parameters influencing the Reynolds stress and RSL, as well as the space-averaged velocities and pressure drop. The direction of rotation of the swirling velocity is found to depend on the sign of the azimuthal wavenumber. In addition to the parameters of the rough wall and the Reynolds number, both the oscillatory pressure drop and frequency are important factors influencing the pulsating flow and the phase shift of the space-averaged velocity.