An analytical and numerical study on the start-up flow of slightly rarefied gases in a parallel-plate channel and a pipe

摘要

The paper presents results of an investigation of the response of an incompressible fluid in a circular micropipe and a parallel-plate microchannel to a sudden time-independent pressure drop. Solutions of the problem were obtained analytically using the Laplace transform technique and numerically using the lattice Boltzmann method. The unsteady velocity profiles in the pipe and in the channel were obtained with the help of the infinite series solutions validated against numerical simulations. In line with the expectations, the flow asymptotically tends to the fully developed pattern, which is attained quicker for smaller Knudsen numbers. The solution enabled also obtaining relations to estimate the hydraulic resistance coefficient. (C) 2015 AIP Publishing LLC.