# Influence of the Tip Clearance on the Aeroelastic Characteristics of a Last Stage Steam Turbine
## 6 Conclusions  
The influence of the tip gap height on the aeroelastic stability of a realistic-scale last-stage steam turbine model was investigated in this paper. Five tip gap heights from 0-5% of chord length were  
Figure 14: Contour of radial velocity on the 92% span surface.  
analyzed. The numerical results showed that the global aerodynamic damping at the least stable inter-blade phase angle increased with the tip gap height till it equaled 5% of chord length. The tip clearance effects on blade aeroelastic stability were classified into three types of mechanisms.  
The primary cause of the variation in total aerodynamic damping was the interaction between the tip clearance vortex and the trailing edge shock from the adjacent blade. Another mechanism was the acceleration of the flow near the aft side of the suction surface in the tip region due to the well-developed tip leakage vortex when the tip clearance height was greater than 2.5% chord. These two mechanisms reduced the magnitude of the local aerodynamic work coefficient at the least stable IBPAs and thus caused a stabilizing effect. Meanwhile, a negative influence on the aeroelastic stability was presented along with the tip clearance vortex trajectory due to the oscillation of tip leakage vortex during blade vibration. The destabilizing effect was enhanced with the increase of the strength of tip clearance vortex and the tip gap height.  
As a result, a continuous increase of tip gap height will eventually decrease the aerodynamic damping at the least stable IBPA for the test case, i.e., there will be a special tip gap height that is most aeroelastically stable for the analyzed turbine. Due to the interaction between the tip clearance flow and the shock from the adjacent blade, the magnitude of the special gap height with maximum aerodynamic damping in this steam turbine model was much larger than that in low-speed turbine cascades; however, the interaction between tip leakage vortex and shocks cannot be resolved in analyses of low-speed turbines. Experimental analysis on the tip clearance effects on the turbomachinery flutter characteristics of a transonic cascade is planned to be carried at KTH.  
Conceived of and designed the numerical simulation, T.S. and P.P.; performed the simulation and analyzed the data, T.S. and M.Z.; writing, original draft preparation, T.S.; writing, review and editing, M.Z., P.P., and A.H.; supervision, P.P. and A.H.  
This work is supported by the Special Funds of the Foshan Technology Innovation Team of China (No. 2016 lt100123).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} \(b\) & blade height \\ \(c\) & blade chord length \\ \(f\) & modal frequency \\ \(h_{max}\) & maximum blade vibration amplitude \\ \(n\) & nodal diameter \\ \(\vec{\mu}\) & vector normal to surface element \\ \(N\) & number of blades \\ \(p_{ref}\) & reference pressure \\ \(p_{i}\) & imaginary component of the unsteady pressure \\ \(W\) & aerodynamic work coefficient \\ \(W_{zero}\) & aerodynamic work done to the blade per blade oscillating period \\ \(\alpha\) & \(h_{max}/c\) \\ \(\sigma\) & inter-blade phase angle \\ \(\Xi\) & aerodynamic damping coefficient \\ \(\omega\) & angular frequency; natural frequency \\ \(\omega^{*}\) & reduced frequency \\ AETR & Aeroelasticity Test Rig \\ CFD & computational fluid dynamics \\ IBPA & inter-blade phase angle \\ KTH & Kungliga Tekniska Hogskolan (Royal Institute of Technology) \\ RPM & round per minute \\ URANS & unsteady Reynolds-averaged Navier-Stokes \\ \end{tabular}