Shock loss model and blade profile optimization design of a supersonic cascade

Abstract

With the improvement of single-stage compressor load, the inflow velocity and relative Mach number at blade tip of compressor are further increased. Using supersonic blade profile to design highly loaded compressor is an effective method to satisfy the requirements of the compressor aerodynamic design. In the internal flow of a blade row, detached shock is caused at the leading edge of supersonic cascade, and complex passage shock structure is produced by shock and boundary layer interaction at blade surface. Establishing shock loss calculation method for detached shock and passage shock and optimizing the blade profile according to the shock loss mechanisms are effective means to design high-efficiency compressors. The earlier studies of shock loss calculation model in supersonic compressor cascade have shown that shock loss of the detached shock at leading edge is related to leading edge radius and inlet Mach number. Therefore, several shock loss models for detached shock are established and proved to be effective. In previous studies on passage shock loss, the changes in geometry of passage shock, which is caused by shock and boundary layer interaction, are not fully considered. So, it is necessary to do further study on passage shock loss model. Based on the internal flow characteristics in supersonic cascade, passage shock loss model is proposed. Physics-based passage shock geometry, which is determined by static pressure rise, Mach number before wave fronts and blade profile curvature, is applied for this passage shock loss model. Near the blade surface, passage shock geometry is transformed into lambda-type shock that is composed of two branch oblique shocks, and oblique shock relationships are used to calculate their total pressure losses. Away from the blade surface, passage shock geometry is very close to the normal shock shape, so that normal shock relationships are used for loss calculation.