# A New Method for Rapid Optimization Design of a Subsonic Tandem Blade
## 4 Optimization for Tandem Blades
### Optimization for a Double-Stage Transonic Compressor with Tandem Blades
#### 4.2.2 Numerical Simulation Results and Analyses  
The comparisons of baseline and optimized compressor characteristics, normalized by the results at the DE point, are shown in Figure 22. The effect of tandem stator optimization on pressure rise and efficiency is negligible at design speed. However, the compressor characteristic is obviously modified at 80% design speed: the efficiency increases approximately 2 points at the CO (cooperating) point, with an overall improvement along the equal engine speed line. Additionally, mass flow rises nearly 1.6% at the choke point. The characteristics of the front and rear stages at 80% design speed are shown in Figure 23; both the efficiency and mass flow of each stage increase significantly in the whole  
Figure 21: Operating conditions of the tandem stator at design speed and off design speed. (**a**) Incidence range; (**b**) inlet Mach number.  
operating conditions. Note that compressor performance improvement benefits from the modification of the tandem stator only, which indicates that the flow capacity enhancement of the tandem stator has a great impact on the matching characteristic of the double-stage transonic compressor at low speeds.  
\(\bullet\) Discussions for Flow Details At 80% Design Speed, CO Point  
The CO points of baseline and optimized compressors at 80% design speed are marked in their respective characteristic maps. As shown in Figure 24, the FB isentropic Mach number distributions at 10%, 50%, and 90% blade heights illustrate obviously different flow status in the two tandem stators: the Mach number decreases about 0.1, and the location of passage shock moves forward for the 10% chord length. The phenomena stated above indicate that the rear stage tandem stator operates away from the deep choke condition at the CO point. A similar tendency can be reflected in the Mach contours near the blade surface, as shown in Figure 25. Compared to the baseline tandem stator, the optimized scheme has a weaker and forward-moving passage shock and, as a consequence, a smaller separation zone induced by shock-boundary layer interaction.  
Figure 23: Characteristics of front and rear stages, 80% design speed.  
Figure 22: Characteristics of a double-stage compressor.  
* Discussions for flow details at design speed, DE point As stated above, the inlet Mach number along the spanwise varies from 0.95 to 0.8 at design speed, so the shock wave near the FB SS should be controled to avoid a rapid increase of loss. The FB isentropic Mach numbers at the DE point are shown in Figure 26; due to the forward-load of FB, the suction spike Mach number increases from 1.0 to 1.05 at the hub and mid-span and the location moves forward for the 5% chord length. The Mach contours near the blade surface show that the FB SS normal shock enhances slightly (Figure 27). Nevertheless, the tandem stator is still operating at good status.  
Figure 26: FB surface isentropic Mach number at 100% design speed at the DE point. (**a**) 10% blade height; (**b**) 50% blade height; (**c**) 90% blade height.  
Figure 24: FB surface isentropic Mach number at 80% design speed at the CO point. (**a**) 10% blade height; (**b**) 50% blade height; (**c**) 90% blade height.  
Figure 25: Mach contours near the blade surface at 80% design speed at the CO point. (**a**) Original; (**b**) modified.