## 3 Results
### Effects of Large Backsweep Angle on S-CO\({}_{2}\) Compressor Performance
In order to understand the reason why the backsweep angle change affects the efficiency, the compressor loss distribution with varying angle was analyzed as shown in Figures 20-23. It is again noted that the percentage of blade loading loss is minimized at \(-70^{\circ}\) which achieves the highest efficiency. Figure 20 shows the change in blade loading loss, clearance loss and mixing loss with increasing backsweep angle. All three losses are associated with the pressure loading on the blade. The blade loading loss is due to the flow separation resulting from the pressure load difference between the suction side and the pressure side. In this respect, the inclination of the blades to the radial direction reduces the pressure loading and it alleviates the secondary flow and the tip clearance flow. As the backsweep angle increases, less pressure loading per unit length on the blade is expected, which results in reducing the strength of the vortex at the blade tip. This means that the clearance loss decreases as the backsweep angle increases. Mixing loss is derived from mixing of the high momentum fluid on the pressure side and the low momentum fluid on the suction side. Decrease of pressure load means a reduction in the difference of fluid momentum between the pressure side and suction side, and the mixing loss decreases as the backsweep angle increases. This physical insight corresponds to the results of Figure 20. Also, as the blade angle becomes more-flat, the radius increases as shown in Figure 24. This is because the pressure ratio of the compressor is assumed to be constant even if the backsweep angle changes. As the backsweep angle increases, smaller tangential component of absolute velocity is obtained. As a result, the diameter of the impeller is increased, as shown in Figure 24, to maintain the same outlet pressure. Thus, as shown in Figures 21 and 22, the skin friction loss, leakage loss, and the disk friction loss tend to increase because those are proportional to the impeller size. The compressor design is optimized to have the best efficiency as the backsweep angle changes. Therefore, the optimal incidence angle was chosen to minimize incidence loss, and consequently, as shown in Figure 23, the incidence loss is always zero regardless of the change in the backsweep angle. Figure 25 shows the effects of the off-design performance and the surge limit while backsweep angle varies. As shown in Figure 15, if the mass flow rate decreases, the angle of relative velocity, \(W_{2}\), remains the same. On the other hand, the tangential component of the absolute velocity, \(C_{\text{w}2}\), increases. Since the product of \(U_{2}\) and \(C_{\text{w}2}\) has increased in comparison with the high mass flow rate condition, the work per unit of mass flow rate at the low mass flow rate condition has increased considerably. Thus, a backward sweep impeller can achieve higher pressure ratio as the mass flow rate is decreased. Also, this feature allows stable compressor operation in wider range because the surge limit is conservatively set as the point where the gradient of pressure ratio becomes zero. Figure 16: Distribution of tip speed at impeller exit. Figure 17: dh/dP of S-CO\({}_{2}\) and air with respect to temperature. Figure 15: Effect of the backsweep angle at impeller exit on velocity triangles. Figure 19: Distribution of relative Mach number. Figure 20: Distribution of internal losses with backsweep angle variation. Figure 18: Sound speed variation near the critical point. Figure 21: Distribution of internal losses with backsweep angle variation. Figure 20.0 Distribution of external losses with backsweep angle variation.