The pulsating laminar flow in a rectangular channel

The finite difference method is used to solve the task of the developed pulsating laminar flow in a rectangular channel. The optimum of the difference scheme parameters was determined. Data on the amplitude and phase of the longitudinal velocity oscillations, the hydraulic and friction drag coefficients, the shear stress on the wall have been obtained. Using the dimensionless value of the frequency pulsations two characteristic regimes — the quasisteady-state regime and the high-frequency regime have been identified. In the quasi-steady-state regime, the values of all hydrodynamic quantities at each instant of time correspond to the velocity value averaged over the cross section at a given moment of time. It is shown that in the high-frequency regime, the dependences on the dimensionless oscillation frequency of oscillating components of hydrodynamic quantities are identical for rectilinear channels with a different cross-sectional form (round pipe, flat and a rectangular channels). The effect of the aspect ratio of the rectangular channel sides channel on the pulsating flow dynamics has been analyzed.