Natural Cooling and Startup of Steam Turbines: Validity of the Over-Conductivity Function

The temperature drop during natural cooling and the way in which the steam turbine restarts have a major impact on the cyclic lifetime of critical parts and on the cyclic life of the whole machine. In order to ensure the fastest startup without reducing the lifetime of the turbine critical parts, the natural cooling must be captured accurately in calculation and the startup procedure optimized. During the cool down and restart, all turbine components interact both thermally and mechanically. For this reason, the thermal analyst has to include, in his numerical model, all turbine significant parts—rotor, casings together with their internal fluid cavities, valves, and pipes. This condition connected with the real phenomenon lead-time—more than 100 hours for natural cooling—makes the analysis time-consuming and not applicable for routine projects. During the past years, a concept called “over-conductivity” was introduced by Marinescu et al. (2013, “Experimental Investigation Into Thermal Behavior of Steam Turbine Components—Temperature Measurements With Optical Probes and Natural Cooling Analysis,” ASME J. Eng. Gas Turbines Power, 136(2), p. 021602) and Marinescu and Ehrsam (2012, “Experimental Investigation on Thermal Behavior of Steam Turbine Components: Part 2—Natural Cooling of Steam Turbines and the Impact on LCF Life,” ASME Paper No. GT2012-68759). According to this concept, the effect of the fluid convectivity and radiation is replaced by a scalar function K(T) called over-conductivity, which has the same heat transfer effect as the real convection and radiation. K(T) is calibrated against the measured temperature on a Alstom KA26-1 steam turbine (Ruffino and Mohr, 2012, “Experimental Investigation on Thermal Behavior of Steam Turbine Components: Part 1—Temperature Measurements With Optical Probes,” ASME Paper No. GT2012-68703). This concept allows a significant reduction of the calculation time, which makes the method applicable for routine transient analyses. The paper below shows the theoretical background of the over-conductivity concept and proves that when applied on other machines than KA26-1, the accuracy of the calculated temperatures remains within 15–18 °C versus measured data. A detailed analysis of the link between the over-conductivity and the energy equation is presented as well.