Oscillatory entry flow in a plane channel with pulsating walls

An analysis is made of the unsteady flow of an incompressible viscous fluid in the entrance region of a parallel-sided channel whose walls pulsate in a prescribed manner. The flux of fluid entering the channel oscillates cosi nusoidally with time so that there is always an inflow at the entrance. The time-dependent Navier-Stokes equations are solved numerically using the fi nite difference method. Axial velocity profiles at various distances from t he entrance of the channel are found at different instants of time during o ne period of oscillation of the flux of fluid entering the channel. It is s hown that for large values of frequency of pulsation f(o) of the channel wa lls oscillating sinusoidally with time, back flow occurs near the channel w alls at a certain location far downstream from the entrance section at a ce rtain instant of time. It is also found that at a subsequent time there is flow reversal at the same location across the entire cross-section of the c hannel. For sufficiently small values of f(o), such back flow does not occu r. The effect of variation of the phase difference in the oscillation of en try flux of fluid and the channel wall oscillation on the time intervals in which wall sheer stress does not vanish is also determined. No proper entr y length could be found when f(o) not equal 0. (C) 2001 Elsevier Science Lt d. All rights reserved.