Fitt, A.D. and Lattimer, T.R.B.
A high-Reynolds-number cross-flow with injection and suction
Quarterly Journal of Mechanics and Applied Mathematics, 50, (1), . (doi:10.1093/qjmam/50.1.47).
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The effect upon a high-Reynolds-number cross-flow of an upstream injection slot and a downstream suction slot of given geometries and strengths is examined. It is shown that the problem may be reduced to a single nonlinear singular integrodifferential equation. It transpires that, in the resulting flow, a total of five different regimes may be identified. For critical suction, the suction strength is just sufficient to reingest all of the previously injected flow. For weaker suctions, the flow is either subcritical, in which case the injected flow that cannot be reingested forms a layer downstream of the suction slot, or subsubcritical, in which case the lowpressure region produced by the injection is of sufficient strength that the ‘suction’ slot exhausts, rather than ingests, fluid. For suctions stronger than the critical value, the flow is supercritical, and the suction slot ingests some of the cross-flow as well as the previously injected flow, leading to an order-of-magnitude increase in the mass flow into the slot. Finally, for supersupercritical flow, when the suction strength is an order of magnitude larger than in cases previously considered, the injection slot is effectively absent and the mass flow into the slot once again jumps by an order of magnitude. In each case the equation governing the flow is solved asymptotically and numerically. Some limiting cases are also identified in which closed-form solutions may be determined.
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