# A New Method for Rapid Optimization Design of a Subsonic Tandem Blade
## 1 Introduction  
Increasing the compressor aerodynamic load is of great significance for shortening the axial length of the aero-engine and reducing the weight of the structure. Due to the potential to break the aerodynamic load limit, the tandem blade has been widely investigated.  
Earlier studies were launched to investigate the tandem blade potential performance advantages compared with conventional configurations. In the 1970s, high-loaded tandem blades were investigated by the Pratt and Whitney group using a single-stage test rig [1; 2]. [PERSON] [3; 4] optimized the multistage axial compressor with tandem blades, and the results showed that blade loss decreased approximately 20 percent relative to conventional blades. [PERSON] [5] summarized the physical mechanism of the multiblade system represented by tandem and splitter blades: the interaction between the two blades changes the distribution of circulations. For the tandem blade, the forward blade undertakes the whole incidence range and part of the aerodynamic load; the aft blade undertakes a higher load in a relatively stable operating condition.  
There are more degrees of freedom during the tandem blade design and optimization process, such as the relative position, the solidity ratio, and the camber ratio of FB and AB. It is necessaryto investigate the extent of the optimal parameters, which has become a hot issue in recent years. [PERSON] [6] et al. established mathematic models to assess tandem blade loss based on experiment results and investigated the mechanism of the flow affected by key design parameters. [PERSON] [7; 8] et al. pointed out that the optimal relative position between FB and AB is AO \(\approx\) 0 and PP \(\approx\) 0.7-0.8. [PERSON] [9] presented a model to predict splitter blade minimum-loss incidence and deviation angle. This is a constructive effort to guide splitter blading design into becoming a conventional design process, which also provides a beneficial reference to developing an empirical model for tandem blades. In addition, [PERSON] [10], [PERSON] [11], and [PERSON] [12; 13] indicated that optimal design parameters may change in design and off-design conditions; for instance, a larger pitch-wise blade distance will lead to a simultaneous increase of the loss and choke margins [14].  
The CFD-combined numerical optimization algorithm has been adopted in the tandem blade design, which presented further enhancements of blade performance: [PERSON] [15] et al. optimized a 2D tandem airfoil with a multiobjective genetic algorithm and an artificial neural network method; [PERSON] and [PERSON] [16] pointed out several principles for transonic tandem blade design based on asynchronous multiobjective genetic algorithm results. [PERSON] [17; 18] conducted a reverse optimization on the basis of 2D and 3D simulations and showed the feasibility of a prescribed velocity distribution concept applied to tandem blades.  
In conclusion, the combination of conventional airfoil configurations (such as C4, CD airfoil, and double circular airfoil) is a simple and practical pattern in tandem blade design. However, it should be emphasized that the aerodynamic interaction between FB and AB is ignored. In this article, based on existing design experience for tandem blades and conventional airfoils, we try to develop a rapid method for fully improving tandem blade performance potential. Firstly, the aerodynamic interaction mechanisms between FB and AB are investigated. Secondly, based on the combination with conventional airfoils, optimization concepts are put forward to fully utilize the gap flow between FB and AB. Thirdly, the \"camber line modification method\" is developed to conduct rapid tandem blade optimization based on conventional airfoils. Lastly, the optimization method and concepts are verified in both a 2D blade model and a transonic compressor with tandem blades.