Reduced-Order Models for the Calculation of Thermal Transients of Heat Conduction/Convection FE Models

On-line calculation of temperature and thermal stresses at critical locations of structural components is currently performed in nuclear and aeronautical applications in order to assess fatigue damage accumulation and residual life. Since it is not possible to use full-scale finite element models because of the large calculation times, ad-hoc simplified algorithms are developed and employed. Thermal stresses commonly arise because of temperature gradients within the component due to heat exchange between the solid and the surrounding fluid. Commonly on-line monitoring methods are based on the assumption that time histories of the temperatures of the fluids around the component are known (e.g., measured) and are used as the inputs for the calculation of temperature and thermal stress at the critical locations of the component. If the temperatures of the surrounding fluid can not be measured, they must be numerically computed integrating an FE model of the fluid in the thermal FE model of the component; as a result, the size of the coupled thermal model is further increased. In the present work, a methodology is developed to reduce the size of thermal models including not only the FE model of the component but also the coupled fluid model. In detail, Guyan reduction and component mode synthesis are applied to a coupled thermal FE model, in order to reduce the size of the problem and to make it suitable for on-line calculations. The appropriate mathematical formulation for the reduction of the fluid FE model has been developed. Two reduction methods are proposed and are applied to the axial symmetric FE model of a turbine disk pointing out their capabilities and limitations for on-line temperature calculation.

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