Viscous fluid flow in initial segment of two-dimensional channel with porous walls

Abstract

flow in wells. Laminar flows of this type are studied theore t ica l ly in [ i ] and exper imen ta l ly in E2]. In an exper imenta l study of laminaxturbuIent transition flow in pipes and annular channels with porous walls in [3], i t was found that the transition is affected markedIy by flow conditions near the closed front end (bottom of channel) , where the results of [ lJ are not appl icable . In this study we define the nature of the flow in the in i t i a l segment of a two-dimensional channel both for the impermeab le end and for in ject ion or suction of fluid through the end. A f in i te-di f ference method of solution for the Navier-Stokes equations is used. 1. Assume steady flow of a viscous incompressible fluid in a semi infini te two-d imens iona l channel with para l le l pe rmeable wails through which fluid is supplied with the constant ve loc i ty v i. I f we take as the character is t ic ve loc i ty and length the speed of sound v 0 and the channel halfwidth a, in dimensionless var iables this flow is described by