Study on vorticity diffusion laws under oscillating flow and its influences on dissipation loss

In this paper, the vorticity-stream function method is proposed to study the incompressible oscillating flow in the channel of Stirling regenerators. The vorticity field and velocity field in the channels of the parallel-plate regenerator are investigated. The plate spacing and oscillating frequency and kinematic viscosity of the working medium are unified as a dimensionless number e. The results showed that when e is ∼7, the “velocity overshoot” phenomenon occurs in the flow field, and this phenomenon becomes more evident with the increase of e and it gradually approaches the wall of the channel. The phase relationship between the pressure drop and the flow rate was obtained; the results showed that the phase of the flow rate lags behind the pressure drop, and the phase difference is influenced by spacing, frequency, and kinematic viscosity, with the maximal phase difference being 90°. The viscous dissipation loss in the channel was obtained based on the characteristic relationship between the cumulative flow and the pressure drop, and the wasted power of helium crossing a single channel was calculated to be less than 50 W when the frequency is no more than 100 Hz and the plate spacing is greater than 0.5 mm (given a swept volume of 500 ml). The results obtained in this paper verified the application of the vorticity-stream function method in oscillating flows, and the advantage of low resistance of helium over nitrogen was theoretically demonstrated in the relatively high frequency range.