Modeling Low Engine Order Vibrations on Last Stage Blade of Steam Turbines Operating at Low Volumetric Flow

A safe operation of  LP steam turbine last stage blades requires an accurate assessment of synchronous and asynchronous flow induced vibrations. Numerical evaluations of such phenomena at the design conditions are common and reliable, yet when operating at low load or island mode operation, the onset of low engine order (LEO) excitations due to rotating instabilities (RI) occurrence or exhaust interaction lead the numerical prediction not trivial. LEO excitations arise from flow instabilities (RI or exhaust diffuser interaction) of geometrical non uniformity (random mistuning), and may lock in low frequency mode-shapes generating high vibration responses. In such conditions, avoiding any potential Campbell’s crossing is impractical, so the development of accurate numerical prediction procedure become mandatory to ensure a wider steam turbine flexibility.

The paper is intended to fill this gap, by proposing a numerical procedure able to tackle this emerging design issue. The developed procedure is based on full annulus unsteady simulations of the last steam turbine stages and the exhaust diffuser, trying to retain in the model all the key geometrical aspects. Unsteady results are then postprocessed by means of an in-house tool able to extract the rotating forcing function associated to each LEO excitations present in the time spectrum. Aerodynamic forcing functions are finally used to solve the forced response problem with a modal work approach that also considers aerodynamic damping.

The obtained numerical results in terms of blade vibration amplitude are in line with the literature where several experimental investigations of LEO vibrations are reported. This confirms the capability of the proposed strategy to predict LEO vibrations in steam turbine last rotors that is now ready to be further validated with in field data.