A HIGH-REYNOLDS-NUMBER CROSS-FLOW WITH INJECTION AND SUCTION

The effect upon a high-Reynolds-number cross-Row of an upstream inject ion slot and a downstream suction slot of given geometries and strengt hs is examined. It is shown that the problem may be reduced to a singl e nonlinear singular integrodifferential equation. It transpires that, in the resulting flow, a total of five different regimes may be ident ified. For critical suction, the suction strength is just sufficient t o reingest all of the previously injected flow. For weaker suctions, t he flow is either subcritical, in which case the injected flow that ca nnot be reingested forms a layer downstream of the suction slot, or su bsubcritical, in which case the low-pressure region produced by the in jection is of sufficient strength that the 'suction' slot exhausts, ra ther than ingests, fluid. For suctions stronger than the critical valu e, the flow is supercritical, and the suction slot ingests some of the cross-flow as well as the previously injected flow, leading to an ord er-of-magnitude increase in the mass flow into the slot. Finally, for supersupercritical Row, when the suction strength is an order of magni tude larger than in cases previously considered, the injection slot is effectively absent and the mass Bow into the slot once again jumps by an order of magnitude. In each case the equation governing the flow i s solved asymptotically and numerically. Some limiting cases are also identified in which closed-form solutions may be determined.