Quantitative comparison of 2D and 3D shock control bumps for drag reduction on transonic wings

In this paper, the design spaces of the 2D and 3D shock control bumps on an infinite unswept natural laminar flow wing are investigated by adopting an optimization enhanced parametric study method. The design space spanned by the design variables are explored through a series of design optimization and their landscapes around the optima are revealed. The effects of the bump spacing, bump length, and Mach number are investigated respectively around the optima. The maximum cross-sectional area, bump incident angle, and aspect ratio are found to be important design parameters. The associated flow physics is discussed in relation to these parameters. The comparative performance of the 2D and 3D bumps are explained in the context of the transonic area rule. Two types of flow separation are identified by varying the bump aspect ratio at off-design conditions. It is concluded that the 2D and 3D shock control bumps can have nearly the same performances at optimal designs with similar cross-sectional areas. Some practical design principles and guidelines are suggested.