# Influence of the Tip Clearance on the Aeroelastic Characteristics of a Last Stage Steam Turbine
## 4 Results
### Tip Cleanance Flow Effects on Blade Loading  
The blade loading in the steady state at 80%, 90%, and 98% span of the rotor surface is shown in Figure 5. There exists an interaction between 98% span line and the blade tip of the tip gap 8.4-mm model, which is revealed in Figure 1. Therefore, the numerical results of the tip gap 8.4-mm model near the leading edge on the 98% span surface are missing. The distribution of pressure at 80% and 90% span was qualitatively similar for all five models, which is consistent with the previous research [8], that the tip clearance flow majorly influences the local flow field near the tip. With the increase of tip gap height, a decrease in surface pressure was shown at the whole pressure side and the aft side of the suction side on 80% and 90% span. On 98% span, a more significant unloading effect on the pressure surface was shown, and the pressure decreased in the most of suction side, but not near the blade leading edge. The mononucleosis variation in the loading on the pressure surface was due to the absorbing effect of the well-development tip clearance flow in the large tip gap size models  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Tip Gap** & **Tip Gap** & **Node Number in** & **Number of** \\  & **Size/Chord** & **Size/Ave.Blade** & **Rotor Domain** & **Layers in the** \\  & **(\%)** & **Length (\%)** & **(million)** & **Tip Gap** \\ \hline No Tip Gap & 0 & 0 & 0.856 & - \\ Tip Gap 2.10 mm & 1.25 & 0.228 & 1.37 & 31 \\ Tip Gap 4.20 mm & 2.50 & 0.457 & 1.72 & 61 \\ Tip Gap 6.30 mm & 3.75 & 0.685 & 1.72 & 61 \\ Tip Gap 8.40 mm & 5.0 & 0.913 & 1.72 & 61 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geometry parameter of the five models.  
Figure 3: Fluid mesh: (**a**) blade surface and hub and (**b**) blade shroud.  
Since the majority of aerodynamic work variation due to tip clearance flow in turbines occurs on the tip region of the blade suction side [8], the distribution of blade loading on the suction side of the blade is highlighted in Figure 6. The pressure on both the front and aft part of the blade suction side was decreasing with the increase of tip gap height, and the difference was not in a linear relationship with the tip gap height, according to Figure 5c. Specifically, there were three dominant regions of loading difference, as marked in Figures 5 and 6: A: near the middle chord of the blade suction side, from 90% span to blade tip; B: the front half of suction surface, parallel to the shroud surface and close to blade tip; and C: the aft side of blade suction side above 90% span.  
Figure 4: Normalized difference in mass flow and total to static isentropic efficiency of the five rotor models.  
Figure 5: Blade loading in steady state at **(a)** 80%, **(b)** 90%, and **(c)** 98% span for the five studied models; the abscissa is the ratio of chord coordinates to the length of the chord, in which \(-1\)–\(0\) indicate the trailing edge to the the leading edge on the suction surface and \(0\)–\(1\) indicate the leading edge to the trailing edge on the pressure surface.