In a heavy-duty gas turbine, when hot rotor is left cooled in standstill condition, thermal bow occurs due to natural convection, which may result in high vibrations in a subsequent restart. Usually, a turning gear is immediately started after shutdown of gas turbine to slowly roll and uniformly cool the rotor in order to prevent thermal bow, which is called turning gear operation. The minimum turning time and the acceptable temperature of wheel space are two important indexes of turning gear operation, and their determination highly depends on accurate prediction of thermal bow. This paper proposes an analytical method to predict the thermal bow behavior of rotors with complex structures and investigates the effect of turning time on thermal bow. First, the general form of analytical solution of rotor thermal bow is derived and validated through both finite element analysis and experiments. Then the analytical solution is applied in a heavy-duty gas turbine to predict the most severe thermal bow behavior of the rotor with no turning gear in operation before standstill. Finally, the effect of turning time on thermal bow is investigated, and the indexes to achieve acceptable thermal bow are discussed. Results show that the shape of thermal bow of the gas turbine rotor is close to the first-order mode shape; the peak of the most severe thermal bow reaches 0.7 mm after 3.8 h of cooling and the decrease of thermal bow is much slower than the increase. Besides, the maximum thermal bow of the rotor due to insufficient turning gear operation presents an exponential decay with turning time and lies in linear relationship with the temperature of the same location. These two relationships help determine the minimum turning time and acceptable temperature of wheel space to attain an acceptable bow and thus have practical significance to develop and optimize turning gear operations.
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