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.

A new method for rapid shock loss evaluation and reduction for the optimization design of a supersonic compressor cascade

“…However, in these works, the second passage shock is simply modeled as an entire normal shock and the influences of shock-boundary layer interaction and back pressure on second passage shock strength and shape are not fully considered, which may result in significant disparity for shock loss prediction in the cases or operating conditions far away from the modeling case. Recently, a shock loss model has been developed by Sun et al 8 and applied to the optimization design of a transonic profile L030-6 resulting in 2% increment of total pressure recovery by reducing the terminal passage shock losses and shock-induced viscous losses. But in this model, the flow acceleration in cascade passage is neglected by considering the downstream Mach number of the first passage shock as the preshock Mach number of the terminal passage shock, which has discrepancy with the actual flow observed in experiments and reduces its usability in other cascades.…”

“…Recently, a shock loss model has been developed by Sun et al. 8 and applied to the optimization design of a transonic profile L030-6 resulting in 2% increment of total pressure recovery by reducing the terminal passage shock losses and shock-induced viscous losses. But in this model, the flow acceleration in cascade passage is neglected by considering the downstream Mach number of the first passage shock as the pre-shock Mach number of the terminal passage shock, which has discrepancy with the actual flow observed in experiments and reduces its usability in other cascades.…”

A Three-Dimensional Design to Study the Shock Waves of Linear Cascade with Reduced Mass Flow Requirements

“…Their model was applied to two supersonic cascades, resulting in a significant reduction of 20% and 16% in the total pressure loss coefficient. Furthermore, Sun et al [22] conducted research to determine the primary source of shock losses. By developing a shock loss mechanism and validating the results, it was identified that the main source of loss in the supersonic cascade is the terminal passage shock loss.…”

Supersonic Compressor Cascade Shape Optimization under Multiple Inlet Mach Operating Conditions

“…In [2], a multi-objective optimization of a 2D S-shaped supersonic profile, operating at a unique incidence condition, was conducted using a Kriging-assisted evolutionary algorithm in order to minimize total pressure losses and to maximize the pressure ratio. In [3,4], one-dimensional analytical shock-loss models were developed to predict overall total pressure losses. Upon these models, optimizations were conducted to reduce losses on two baseline geometries, acting on profile shape and thickness distribution.…”