# Influence of the Tip Clearance on the Aeroelastic Characteristics of a Last Stage Steam Turbine
## 5 Discussion  
To understand the tip clearance effects on both the steady and unsteady flow field, the flow structure in the tip region was firstly investigated in both the radial and circumferential direction. The Schlieren figure on 98% of the span surface presented in Figure 12 shows the development of tip clearance vortices in the blade-to-blade direction, as well as the interaction between tip clearance vortex and shocks. The development of tip clearance vortex in the radial direction is presented in Figure 13, which is the contour of the Mach number, as well as the vector of the velocity component at 80% axial chord from the leading edge of the rotor blade. In the no tip gap model, the shock from the neighbor blade trailing edge impinged on the suction surface, and therefore, a clear reflection on the blade is shown in Figure 12. The influence of that shock was more alleviated with the increase of the strength of the tip leakage vortex. The interaction between the tip clearance flow and shock influenced the blade loading on the suction side near the mid-chord, as presented by Region A in Figure 6. Meanwhile, the oscillation of shock is also a source of unsteady aerodynamic force, as discussed in [6]. The reduction of impinging shock strength significantly decreased the amplitude of unsteady pressure in Region A, which reacts as a stabilization effect at the least stable IBPAs in Figures 10c and 11. Although a strong influence on aerodynamic force was caused by this phenomenon, the interaction between tip leakage vortex and the impinging shock from adjacent blade cannot be resolved in the analysis of subsonic turbomachines. From Figure 13, the tip leakage vortex is rotated in the clockwise direction (observed from the trailing edge side), and the local Mach number is relatively lower in the center of vortices. The core of the tip leakage vortex showed a trend of moving away from the blade suction surface, as well as the shroud when the tip gap height was increasing, which is also verified in Figure 12. The increase of flow speed due to tip leakage vortices reduced the pressure among the vortex trajectories, as shown in Region B of Figure 6. Due to the motion of the blade tip, the core of the tip leakage vortex oscillated at the same frequency as blade vibration [19], and the periodical pressure variation among the vortex trajectories produced extra aerodynamic work on the blade suction surface. The extra aerodynamic  
Figure 12: Schlieren figure on 98% of the span surface. The flow direction is from the left to the right. Figure 13: Mach number contour and the vector of velocity at 80% axial chord of the rotor. The suction side of the blade is located on the right side. work presented a destabilizing effect because of the negative phase angle difference between the vortex motion and the blade motion, and the magnitude of the aerodynamic work increased with the strength of the tip leakage vortex. This phenomenon resulted in an increase of the wall work coefficient in Region B of Figures 10c and 11, which was also found in previous research of low-speed turbine cascades [2]. Besides the flow field near the blade tip, the flow field within the top 10% of span height was also influenced by the tip leakage vortex when the tip gap height exceeded a certain value, such as 4.2 mm for the analyzed test case. The well-developed tip leakage vortex in the model with relative large tip gaps accelerated the flow above 90% span in the radial direction compared with the models with no tip clearance or with a small tip gap height, as shown in Region C of Figures 13 and 14. The impact on flow field not only induced a variation in steady blade loading on the aft side of the suction surface (Region C in Figure 6), but also decreased the amplitude of unsteady pressure during blade vibration. The magnitude of positive aerodynamic work in Region C at the least stable IBPAs was thus reduced. The stabilizing effect was present in the models with large tip gap heights, as shown in Figures 10b,c and 11.