## 3 Analysis of Aerodynamic Characteristics of the Basic Tandem Blade
### Loss Mechanism of the Tandem Blade in Typical Operating Conditions  
In a conventional supersonic blade, the passage shock moves out of the channel and then coalesces with the leading edge shock with the increase of outlet static pressure. The supersonic tandem blade experiences a similar process. Due to the fact that flow field structures vary in different outlet static pressure conditions, it is necessary to analyze the flow characteristic and the loss mechanism in typical operating conditions to provide clear guidance for future optimum design. Figure 5 shows the proportion of the FB loss to the total loss in different outlet static pressures. It should be noted that the FB outlet reference surface is set between FB and AB during counting the FB loss. Consequently, the mixing loss of the FB wake in AB passage is counted into the AB loss. In the statistical method described, the FB loss proportion at the DE point exceeded 50%. Furthermore, the FB loss proportion increased with the outlet pressure, and it accounts for more than 80 percent of the total loss at the near stall (NS) point. In conclusion, controlling the FB loss in all operating conditions is the first priority in supersonic tandem blade optimization.  
For further understanding of the supersonic tandem blade loss mechanism, the flow field structures in two typical operating conditions (DE and NS point) were analyzed in detail.  
* DE point  
According to the Mach contour plots at the DE point (Figure 5(a)), there is an obvious double-shock wave structure in the FB passage. Due to the transonic tandem rotor requiring a high stall margin,  
Figure 4: The inlet flow conditions of AB (Aft Blade). (**a**) AB inlet Mach Number, (**b**) AB incidence  
Figure 5: The proportion of the FB loss to the total loss at inlet Mach number 1.2.  
the rotor tip element needs to operate in a deep choke point, which makes the shock position move downstream of the blade passage. The FB passage shock intersects at 60 percent of the chord length in the pressure side and near the trailing edge in the suction side. On the other hand, the Mach number upstream of the shock on the AB suction side exceeds 1.3, and this leads to a strong shock wave/ boundary layer interaction and subsequent separation near the AB trailing edge.  
According to the entropy increment contours at the DE point (Figure 7a), the main physical mechanisms that lead to entropy increment can be summarized as follows: the shock wave loss in FB passage, mixing loss of the FB wake, and the separation loss of the AB boundary layer. Therefore, aiming to reduce the loss at the DE point, the intensity of FB leading edge shock, FB passage shock, and AB suction side shock should be controlled appropriately.  
* NS point  
Since the FB loss proportion accounts for as much as 80 percent of the total loss at the NS point, controlling the increased rate of the FB loss in the positive incidence condition is the key method to increase the incidence range.  
According to the Mach number contours and entropy increment contours at the NS point (Figures 6b and 7b), the main physical mechanisms that lead to loss include the FB suction side shock loss, the FB shock wave/boundary layer interaction loss, and the FB wake mixing loss. It should be emphasized that these losses are all related to the intensity of the FB suction side shock. Therefore,  
Figure 6: The Mach contour plots at inlet Mach number 1.2. NS: Near Stall. (**a**) at the DE point, (**b**) at the NS point.  
Figure 7: The entropy increment contours at inlet Mach number 1.2. (**a**) at the DE point, (**b**) at the NS point.  
aiming at increasing the incidence range, the FB suction side shock intensity growth rate with the incidence should be controlled carefully.