# Experimental and Numerical Research on End-Wall Flow Mechanism of High-Loading Tandem Stators
## 3 Loss Distribution of Tandem Stators  
Due to the interaction between the FB and the RB, the loss composition and distribution in tandem stators differed from those in conventional stators. To analyze the variation in loss characteristics of tandem stators, the total pressure loss coefficients were computed for three distinct regions: the root region (\(\omega_{\text{h}}\)), the mid-span region (\(\omega_{\text{m}}\)) and the tip region (\(\omega_{\text{s}}\)). Total pressure loss coefficients (\(\omega\)) were defined as \((Pt_{1}-Pt_{2})/(1/2\rho V_{1}^{2})\), where \(Pt_{1}\) and \(Pt_{2}\) were the total pressure of stator inlet and outlet, respectively. \(\rho\) was airflow density. \(V_{11}\) was the inlet velocity of the front blade. This calculation was performed using a two-dimensional flow tube method with a flow ratio allocation of 30%:40%:30% across these regions, taking into account their spanwise distribution characteristics and individual flow structure contributions. Figure 11 depicted the variation of the total pressure loss coefficient for tandem stators in different regions, where the root region, mid-span region, and root region were represented by hub, mid, and shroud, respectively. As the flow coefficient decreased, it was observed that the total pressure loss coefficient initially declined and then increased for all three regions, while the loss in the tip region decreased at NS. At NS, the relationship among the losses in these three regions followed the order: \(\omega_{\text{h}}\) > \(\omega_{\text{m}}\) > \(\omega_{\text{s}}\). Additionally, the rate of loss growth in the root and mid-span regions became nearly identical, which was different from the behavior observed in conventional stators. Combined with Figure 9, it was able to be inferred that this particular trend was closely associated with the development of the FB corner separation within the RB, as it migrated along the spanwise direction. The loss variations in the FB and RB, as well as their proportion to the overall losses in a tandem stator, could be better understood by examining the losses of each component separately. Due to the minimal axial gap between the FB and RB, it was challenging to arrange measurement points at the FB outlet during the experiment. Therefore, numerical simulation was necessary to supplement the outlet parameters of the FB for analyzing its losses. To this end, a computational extraction plane was positioned at the trailing edge exit of the FB, as illustrated in Figure 12. Since parts of the root and tip regions of the FB extend into the RB channel, the cross-sectional data obtained can only be used to calculate  
Figure 11: Variation of total pressure loss at the root, tip and mid-span region of the tandem stator. blade row-specific parameters that correspond to total parameters, such as total pressure and total temperature. Figure 13 presented the calculated losses for the FB, RB, and the tandem stator (donated as \"Total\"), along with the percentage contribution of FB loss. The RB loss included boundary layer losses on the blade surface, mixing losses due to the wake of the FB, and corner separation losses in the RB channel. With the decrease in flow coefficient, the variation trend of the FB loss followed a pattern similar to that observed in conventional stators, which was initially decreasing and then increasing. However, the RB loss behaved differently. It experienced a steady decline as the flow coefficient reduced, with only a slight increase near the stall point. Moreover, the proportion of the FB loss consistently exceeded 60% across the entire operating range, reaching up to 70% near the stall point. This significant dominance of the FB loss component decisively influenced the overall total loss of the tandem stator. With the decrease in flow coefficient, the variation trend of the FB loss followed a pattern similar to that observed in conventional stators--initially decreasing and then increasing. However, the RB loss exhibited different behavior.