Analytical Heat Transfer Correlation for a Multistage Steam Turbine in Warm-Keeping Operation With Air

Due to the growing share of volatile renewable power generation, conventional power plants with a high flexibility are required. This leads to high thermal stresses inside the heavy components which reduces the lifetime. To improve the ability for fast start-ups, information about the metal temperature inside the rotor and the casing are crucial. Thus, an efficient calculation approach is required which enables the prediction of the temperature distribution in a whole multistage steam turbine. Considerable improvements of the computing power and numerical simulation tools today allow detailed investigations of the heat transfer and the flow phenomena by conjugate-heat-transfer (CHT) simulations. However, these simulations are still restricted to smaller geometries mostly by the number of elements. This leads to coarser numerical meshes for larger geometries, and thus, to a reduced accuracy. A highly accurate three-dimensional-CHT simulation of a whole multistage steam turbine can only be conducted with huge computational expense. Therefore, a simplified calculation approach is required. Heat transfer correlations are a commonly used tool for the calculation of the heat exchange between fluid and solid. Heat transfer correlations for steam turbines have been developed in a multitude of investigations. However, these investigations were based on design or to some extent on part-load operations with steam as the working fluid. The present paper deals with the theoretical investigation of steam turbine warm-keeping operation with hot air. This operation is totally different from the conventional operation conditions, due to a different working fluid with low mass flow rates and a slow rotation. Based on quasi-steady transient multistage CHT simulations, an analytical heat transfer correlation has been developed, since the commonly known calculation approaches from the literature are not suitable for this case. The presented heat transfer correlations describe the convective heat transfer separately at vane and blade as well as the seal surfaces. The correlations are based on a CHT model of three repetitive steam turbine stages. The simulations show a similar behavior of the Nusselt-number in consecutive stages. Hence, the developed area related heat transfer correlations are independent of the position of the stage. Finally, the correlations are implemented into a solid body finite element model and compared to the fluid-dynamic simulations.