Non-stationary flows in channels with permeable walls

Abstract

A flow of inviscid fluid in a plane or axisymmetric semi-infinite channel is considered. One wall of the channel is permeable, and injection or suction of fluid takes place through the other wall at constant lengthwise intensity, while the wall itself moves according to a prescribed law. The flow is assumed to be turbulent. An equation for the stream function is obtained, and a relation connecting the law of motion of the wall with the intensity of injection (suction) is chosen such that the equation has a selfsimilar solution. An approximate representation for the selfsimilar solution is found, and viscous drag in the motions at large Reynolds numbers is estimated. The process of constructing an approximate solution when the wall moves slowly is discussed. An approximate solution of the problem of stationary flows in channels with permeable walls, valid over a whole range of variation in the characteristic Reynolds number R, was constructed in /1/. It was shown that by virtue of the specific features of the problem (no slippage at the walls), the profiles of the velocity vector components vary insignificantly as R varies. A method given earlier in /1/ is used here to obtain selfsimilar solution of non-stationary problems in the limiting case when R → ∞.