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Roughness-induced transition control is of considerable importance for high-speed vehicles. In this paper, the instability of a roughness-disturbed boundary layer controlled by spanwise-uniform wall-blowing is investigated through BiGlobal and three-dimensional parabolized stability equation (PSE-3D) analysis. Without wall-blowing, symmetric and antisymmetric unstable modes are observed when using BiGlobal analysis, with PSE-3D analysis suggesting that the symmetric mode is the dominant instability. Both modes are associated with the instability of the entire separated shear layer behind the roughness region rather than the components in certain directions, as both the wall-normal shear and the spanwise component resulting from the bending shear layer contribute to the growth of the disturbance. Upstream wall-blowing delays the roughness-induced transition by modifying the wake instability. The antisymmetric mode is the first to disappear as the blowing intensity increases while the symmetric instability is also suppressed. Upstream wall-blowing also reduces both the strength and bending of the shear layer by affecting the inflow boundary layer. This leads to a decrease in the wall-normal and spanwise contributions to the disturbance energy. Downstream wall-blowing achieves a control effect by decelerating the development of the dominant symmetric mode through the direct interaction between wall-blowing and the wake. Although the reduction in shear strength is not as strong as with upstream wall-blowing, downstream wall-blowing still relaxes the bending of the shear layer, which is related to the production of disturbance energy. In conclusion, two-dimensional wall-blowing can delay the roughness-induced transition by modifying the wake structure and instability.
Lu et al. (Sat,) studied this question.