Flow of Wall Jet Near Channel Exit at Moderate Reynolds Number

The wall jet flow near channel exit at moderate Reynolds Number, emerging from a two-dimensional channel, is examined theoretically in this study. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface, flow in the outer layer region and the flow in the core region. The fluid is assumed to be Newtonian and it is found that the jet contracts downstream from the channel exit. The influence of inertia on the shape of free surface, the velocity and stress is emphasized and the higher order boundary layer is explored. To leading order, the problem is similar to the case of the free jet (Tillett) [1] with different boundary conditions. A similarity solution can be carried out using a similarity variable problem which is then solved as an initial-value problem, where the equation is integrated subject to the boundary conditions and a guessed value of the slope at the origin. The slope is adjusted until reasonable matching is achieved between the solution and the asymptotic form at large θ. The level of contraction is essentially independent of inertia, but the contraction moves further downstream with increasing Reynolds number. The present work provides the correct conditions near exit, which are required to determine the jet structure further downstream. If the jet becomes thin far downstream, a boundary layer formulation can be used with the presently predicted boundary conditions for steady and possibly transient flows.