Laminar pulsating flow at the initial segment of a flat channel

A method is proposed for solving the problem of a pulsating quasistationary flow in a channel, based on the use of calculation results for stationary flow. This approach is applicable at low relative oscillation frequencies (for Womersley numbers less than one). The solution to the system of stationary equations of motion and continuity in the initial section of a flat channel was carried out by the finite difference method using an iterative implicit unconditionally stable scheme. The hydrodynamic characteristics of a developing pulsating laminar flow in a flat channel have been studied. The results of calculating the longitudinal velocity component and the Poiseuille and Euler numbers are presented as a function of the relative amplitude of the oscillation of the cross-sectional average velocity $A$ and dimensionless length of the channel. It was found that for $A$ values exceeding unity, the period-averaged coefficients of hydraulic resistance and friction resistance near the inlet to the channel are significantly higher than these values for a stationary flow. It has been shown that in order to achieve a pulsating flow with large amplitudes of oscillations, it is necessary to create a time-average pressure drop approximately three times higher $($at $A = 5)$ than for a stationary flow.