New flexible operational regimes with fast start-ups and fast-changing load cycles for steam turbines require calculation procedures for determining optimal start-up times in order not to exceed the limits of thermal stress for the steam turbine parts.
This work presents a start-up time calculation for various kinds of industrial steam turbines. An analytical approach for estimating the optimal thermal load of a turbine from quasi-steady or steady condition is developed. The geometry of the respective turbine components, the changing of the steam parameters and heat transfer effects during the start-up procedure are taken into account while observing the respective material properties and stress limits. The temperature distributions of the respective turbine parts are calculated with a one-dimensional numerical algorithm of Fourier’s heat conduction equation. Three-dimensional influences of the geometry and of the the heat flux are considered analytically by adjusting the numerical solutions of elementary bodies (e.g. one-dimensional plate). The start-up time calculation is performed in small time steps to guarantee the stability of the numerical solution. The unsteady stress analysis for the start-up procedure does not uniquely identify one critical component. The calculation must be repeated for each time step to identify the component which limits the start-up gradient. Other boundary conditions, such as restricted speed ranges of the rotor with minimum transients and time for synchronization with the electrical grid, are considered by the model too and can further limit the start-up gradient and lead to slower start-up procedures. The one-dimensional calculation models were verified with a three-dimensional FEA of the casing and a two axis symmetrical FEA of the rotor. The results for the temperature distribution are presented and compared to the one-dimensional results.
The final result of the analytical approach for an optimized start-up time calculation is verified with two typical start-up calculations, one for a generator drive steam turbine and one for a mechanical-drive steam turbine.