Converging narrow-channel flow of a super-critical fluid

The solution of a supercritical fluid flowing into a constricted narrow channel is presented in this study. The compressible Navier-Stokes equations in the lubrication limit coupled with the energy equation and the isothermal and non-isothermal van der Waals fluid and perfect gas have been solved. In order to find the semi-analytical solution of these non-linear coupled equations, homogenization technique in the transverse direction has been applied. Because of the high compressibility and high thermal expansion of supercritical fluids, waviness is observed in the flow and thermal fields near the exit of the channel. This effect is attributed to the channel constriction where the slope is maximum, where a strong coupling between the pressure and density gradients exists. Moreover, the density difference between the exit and inlet of the channel drastically increases when one approaches the critical point, corroborating the data from existing literature.