UNSTEADY SLOT SUCTION FROM A HIGH-REYNOLDS-NUMBER CROSS-FLOW

The problem of unsteady suction from a high-Reynolds-number cross-flow into a slot is considered in the case where the suction is driven by a rime-dependent slot pressure. The model uses linearised asymptotics based on a small parameter that defines the suction strength. An integ ro differential equation is derived for the mass flow into the slot an d this is solved for various time-dependent slot pressures of practica l interest. Closed-form expressions are also found for the shape of th e shear layer dividing the external flow from the fluid in the slot. F or a step function change in the slot pressure, a non-monotonic decay to the steady solution is observed, and for an oscillatory slot pressu re there is a phase lag between the slot pressure and the mass flow. F or rapidly changing slot pressures it is shown that slot injection can occur, even when the slot pressure remains below the free-stream pres sure.