Thermal Stress

Preliminary numerical study of the assembly

In mechanical and aeronautical applications characterized by high safety requirements and expensive maintenance costs (e.g., aircraft engines, nuclear power plants), assessment of fatigue damage accumulation due to thermal transients is performed by on-line fatigue-monitoring systems.  This allows the evaluation real-time of damage accumulation in component-critical locations—that is, where a fatigue crack is expected to appear.
Fatigue monitoring systems are made of several modules assembled together. Each module is used to evaluate one of the parameters that affects the fatigue damage of the component (i.e., temperature and thermal stresses) and it is based on ad hoc algorithms, because finite element (FE) commercial codes are too time consuming for on-line applications.
At AERMEC Laboratory, reduced order models and efficient algorithms are developed for the on-line calculation of temperature and thermal stresses at the critical locations of mechanical components.

It is neither necessary nor possible to monitor the whole component

In details, in the case of temperature calculation, the reduced order models are based on the Component Mode Synthesis approach, orginally developed in the field of structural dynamics and here extended to the thermal analyses. The FE model is reduced retaining a set of master nodes at critical locations , where temperature must be computed, and including a set of slave modes in order to improve the accuracy of the model in simulating transients.
Substructuring is also a feasible option, successfully employed in case of turbine disks. In this case, the component is divided into substructures (superelements) and the nodes lying at the interfaces are included in the set of master nodes and used to connect the reduced substructures together.
The classical approach has been applied to linear thermal models with constant coefficients and also extended to non-linear models with variable convective coefficients.  Furthermore, the case of a thermal model surrounded by an advection network has been analyzed, showing the shortcomings of the classical formulation due to the non-simmetry of the reduced thermal matrices.  As a result a novel approach has been proposed and successfully applied to a test case. The new approach is based on an original reduction technique similar to the well known Guyan reduction, but able to reducee exactly also non-symmetrical systems such as thermal components wurrounded by a flow path.
In the field of thermal stress monitoring, the Green’s Functions Technique (GFT) has been explored. According to the GFT, it is possible to compute the thermal stress time history at a given point of a linear model from the time history if the inputs, by means of the convolution integral, provided that the thermal stress time history due to a unit step of the input is given.
In this frame, the activity of the research group of the AERMEC Laboratory has been initially focused on the extension of the GFT to thermo-mechanical models with variable convective coefficients together with the reduction techniques developed for the temperature monitoring.
As a result a system made of two modules in series with each other has been developed. The first module computes the temperatures at critical points and at the boundaries characterised by non-linear convective coefficient. The second module, uses the time history of the gas temperatures and the temperatures computed at the first module, to compute the thermal stress transients at the critical locations.