Numerical Analysis of the Blade Forces Caused by Wake/Blade Interaction in the Last Stage of a Steam Turbine

Abstract

In a steam turbine stage there is an interaction between blades and the flow field. The blades are subjected to the forces caused by the flow field, but also the flow field is affected by the blades and its movement. The nozzle wakes cause uneven pressure field downstream and produce alternating forces on blades which lead to blade vibrations. Some of the vibrations originated in this way may damage the blades and affect the turbine performance. The results of numerical computations about the forces acting on the blades as a result of the variations in the flow field in the axial clearance rotor-stator in the last stage of a 110 MW steam turbine are presented. The analysis is focused on discussing the pressure field because it is necessary for further computation of the useful life time. The flow field was resolved using computational fluids dynamics and the computed pressure field was integrated around the blades to get the forces acting on blades. These computed dynamical forces will be used in the blade useful life estimation and in the investigation to the failure causes of these blades. The Navier-Stokes equations are resolved in two and three dimensions using a commercial program based on finite-volume method. 2-D and 3-D geometry models were built to represent the dimensional aspects of the last stage of the turbine. Periodic boundary conditions were applied to both sides of a periodic segment of the 2-D and 3-D models with the purpose of reducing computational efforts. The computations were conducted in steady state and transient conditions. The results show that the force magnitude acting on blades has an harmonic pattern. Finally a Fourier analysis was used to determine the coefficients and frequency of a Fourier equation which can be used to calculate the alternating stresses on the blade in order to predict the useful life of the blades. Also, the pressure and velocity fields are shown between the diaphragm and rotor blades along the axial clearance.