High Reynolds number flow past a flat 'plate with strong blowing

Abstract

For the uniform flow past a semi-infinite flat plate subject to a blowing velocity profile equal to C(Uv/x),½ the conventional boundary-layer approximations break down as C approaches 0middot;6192. Here, we consider the structure of the flow for large Reynolds numbers R when C exceeds this critical value. It is shown that, for C > 0·6192, a region containing injected fluid O(R-1/3)) in thickness forms directly above the plate. To a first approximation the flow in this region is inviscid and the pressure a function of x only. This blowing region is separated from the free stream by a free shear boundary layer of thickness O(R-½). Thus the flow domain consists of three distinct regions which interact to yield a similarity solution valid for large values of Rx. This solution is then extended to higher order by expanding the stream function in each region in powers of (Rx)-1/3 and evaluating the first four terms in the resulting series using standard matching techniques. Finally, more general blowing profiles which also lead to boundary-layer ‘blow off’ are considered and an expression, valid far downstream of boundary-layer detachment, is derived for the position of the streamline separating the injected fluid from that of the free stream. For the case of uniform blowing the blowing region takes on the shape of a wedge, indicating that no solution can exist for the corresponding external flow if the plate is truly semi-infinite.