## 1 Introduction  
An advantageous compressor design in terms of compactness, weight, and cost is needed for gas turbine engines. This can be accomplished by directly reducing the number of stages required to provide a desired pressure ratio in a multistage compressor. Aerodynamically, the reduction of stages will certainly need to increase the total enthalpy rise, i.e., loading level, of each stage. A highly loaded compressor usually means a high relative Mach number or/and high blade aerodynamic diffusion to achieve this high total enthalpy rise across each stage, which results in a high work coefficient (usually more than 0.5), as discussed by [PERSON] et al. [1]. In order to achieve this goal, increasing the blade speed (hence higher relative inflow Mach number for a rotor) or/and flow deflection (hence higher blade surface diffusion for a rotor or stator) can be employed. These methods usually cause increased deviation angles and aerodynamic losses under much stronger adverse pressure gradient for the highly loaded blades so that the blade performance tends to deteriorate. Considering the successful applications of splitter vanes (SVs) in centrifugal compressors, the cascade arrangement with SVs has been used in supersonic and subsonic axial flow compressors as a flow control method to reduce the deviation angles and losses under the high loading condition by [PERSON] et al. [2], [PERSON] et al. [3], [PERSON] [4], and [PERSON] et al. [5]. The concept is to incorporate a SV in the rear blade passage, thereby increasing solidity locally without substantially increasing throat blockage, which is expected to strengthen flow deflection but reduce the local flow diffusion level on the suction surface of principal blades (PBs). In a subsonic axial compressor cascade investigated by [PERSON] et al. [6], for instance, splittered blades have shown potential to achieve higher pressure ratio, efficiency, and mass flow compared to conventional blade at the studied subsonic condition. However, because of the geometric difference between the PB and the SV, the design procedures of a splittered compressor should be different to those of a conventional one, as shown in Figure 1. Obviously, the incorporation of the extra SVs makes the design freedoms of blade geometry at least double compared to conventional blades, which on the one hand brings extra possibilities for performance improvement, but on the other hand makes the design process much more complicated. Nevertheless, it is the same with the design of conventional blades: blading design also plays a critical role in the design of high-performance splittered compressors. One of the important goals in blading design is to achieve desired velocity triangles (vector diagrams) derived from throughflow computations at different spanwise locations. It is only when the desired velocity triangles are appropriately satisfied that a given work input (for rotors), pressure rise, and flow deflection (for stators) can be achieved. To do that, a model for predicting the reference minimum-loss incidence and deviation angles, which are usually selected as design goals, is required to obtain some blade profile parameters,  
Figure 1: A typical flowchart of the design of a splittered axial flow compressor. Figure 2: A schematic diagram for reference minimum-loss definition. such as camber angle and stagger angle, for the blading design. The reference minimum-loss incidence and deviation angles, which were proposed by [PERSON] [7], are both usually defined at the middle of incidence range between two points corresponding to twice the minimum loss at the loss-to-incidence-angle characteristic line of a certain blade, as shown in Figure 2. Unfortunately, according to the authors' knowledge, few studies on the topic have been openly published for the blades with SVs, except for the work conducted by [PERSON] et al. [3]. However, [PERSON] et al. only considered the variation of deviation angles with the solidity and camber of SVs.