Effects of passive porous walls on boundary-layer instability

A theoretical study is described of the effects of a passive porous wall on boundary-layer instability. The passive porous wall Is conceived of as a thin porous sheet stretched over a plenum chamber. When disturbances in the form of Tollmien-Schlichting waves propagate along the boundary layer, the fluctuating pressure forces air in and out of the plenum chamber. The basic approach is based on classic linear stability theory fur the flat-plate boundary layer with modified wall boundary conditions. The wall response is represented by a complex admittance (ratio of fluctuating flow rate per unit area to wall pressure) and, therefore, applies to a general class of passive porous, and other interactive, walls. The effects of a wide range of admittance values are studied, A stabilizing effect is obtained when the admittance phase is close to pi /2, and an optimum value of admittance magnitude is also found. A theoretical model is introduced and used to calculate the admittance of the porous panels used in a parallel experimental study, It is shown that it may be possible to manufacture stabilizing porous panels. The stabilizing mechanism is due to the production of a near-wall region of negative Reynolds stress.