The last stage blades of a low-pressure (LP) steam turbine were reported to have been experiencing flow instability associated with higher than normal back pressure level. The phenomenon is identified as one of the serious potential causes of last stage blade failures and, therefore, can be one of the major factors that limit the operational flexibility of steam turbines. Thus, for failure prevention, it becomes necessary to determine the operating conditions under which turbulent instability is likely to occur.
This paper presents a novel approach that can quantitatively predict turbulent flow instability by comparing aerodynamic damping and structural damping. To assess its applicability, turbulent flow instability was investigated in conjunction with three fundamental vibration modes of last stage blades of a LP steam turbine. The stability considerations were based on a quasi-steady power-per-vibration-cycle approach. The aerodynamic work per cycle of vibration mode of a bladed disk was calculated from the time integral of the product of the periodic time varying force and the specified harmonic vibration amplitude. A finite element based blade model was constructed to obtain modal characteristics at an operating speed. The aerodynamic forces were obtained from a two-dimensional cascade analysis for viscous compressible flow with a second-order Reynolds-stress model. The computational nodes were generated by employing a body-fitted algebraic grid generation technique. The unsteady compressible Navier-Stokes equations were solved for the flows around the blade airfoil region to determine aerodynamic damping. The nonlinear material damping energy of the bladed disk was calculated as a function of the vibration amplitude by using the Lazan’s power law. The turbulent instability was determined by the net power flow to die bladed disk at various amplitudes of vibration. Some computed results for die last stage of a LP steam turbine are presented in this paper.