**Session: **24-01 Compressor aerodynamic damping

**Paper Number: **82935

**82935 - A Digital Twin of Compressor Blisk Manufacturing Geometrical Variability for the Aeroelastic Uncertainty Quantification of the Aerodynamic Damping **

This study is centered on the aeroelastic problem for axial compressors blisk airfoils in presence of geometrical uncertainties. The combined problem of structural dynamics and unsteady aerodynamics is of interest for these machines due to the stress induced by the blades vibration. In this field, deviations from the nominal cyclic symmetry (in geometry, material or fluid properties) are generally referred to as mistuning. In particular, the geometrical mistuning is addressed resulting from the manufacturing process of blisk airfoils. The impact of these uncertainties on the aeroelastic problem is evaluated, focusing on the aerodynamic damping.

The analysis of the manufacturing geometrical variability is approached in a probabilistic manner. A model representing the uncertainty is created starting from a dataset of optical surface scans. The measured geometries are parameterized in order to numerically describe the differences from the nominal geometry with a set of variables. The creation of a mean geometry of the measured blades allows to simplify the description of the uncertainty, which can be then modelled describing the distributions of geometrical deviations over the blade height. In order to create a stochastic model for the geometrical uncertainty, a data reduction method is implemented in the model. This aims to describe the variability within a minimum required accuracy while using a minimal set of variables. For this purpose, an Autoencoder is used to define a compressed representation of the dataset of interest. The method is based on the training of a Neural-Network, which tries to represent the identity function for the given data while forcing a variables reduction in the intermediate layers. A regularization method for the reduced variables is also introduced in order to avoid correlations and normalize the distributions.

The computation of the aerodynamic damping is performed using a CFD solver. A steady-state representation of the investigated axial compressor rig is validated using available experimental data. The unsteady computations are done for one configuration at one shaft speed, which is representative of two relevant crossings in the Campbell diagram for the studied blisk. This indicates resonance conditions for two vibrational mode shapes of the component. The *Aerodynamic Influence Coefficients* (AIC) method is used to calculate the aerodynamic damping curve for the two vibrational mode shapes of interest. This allows to obtain the damping values over the different inter-blade phase angles with one single solution per mode shape, while reducing the domain to a sub-assembly of the investigated blisk. The *Uncertainty Quantification* (UQ) uses the implemented geometrical variability model and the defined solution method for the calculation of the aerodynamic damping. To describe the input uncertainty (manufacturing geometrical variability) the space of the variables resulting from the Autoencoder data reduction is used. A sampling is generated, representing with each sample a set of three mistuned blades. For each sample, the three resulting blade surfaces are inserted in the AIC setup, representing the vibrating blade as well as the relative direct upstream and downstream blades. This allows to evaluate the uncertainty on the amplitude and phase of the influence coefficients relative to the three blades and finally on the aerodynamic damping curve.

The data reduction provided by the Autoencoder proved to be very efficient, especially if compared to linear methods as the principal components analysis. This allowed to include in the UQ multi-passage variations for a better representation of a real geometry. The output uncertainty on the aerodynamic damping could therefore be evaluated taking these effects in consideration. The results can be combined in an aeroelastic reduced order model with the mistuning of the mechanical properties of the component to represent the mistuned blades vibrations.

**Presenting Author: **Marco Gambitta *Brandenburg University of Technology (BTU)*

**Presenting Author Biography: **Marco Gambitta is a mechanical engineer, currently working as PhD student at the Brandenburg Technical University (BTU) in Cottbus, Germany. He completed his studies at the University of Trieste, Italy, with the master in Mechanical Engineering in 2018. He worked as an intern in Rolls-Royce Deutschland, where he wrote his mater thesis on manufacturing geometrical variability and robust design in axial compressors. Since 2018, he is employed at the BTU Cottbus as a PhD student, conducting his research in collaboration with Rolls-Royce Deutschland on axial compressor blades geometrical variability and its impact on the aeroelastic problem.

**Authors:**

*Brandenburg University of Technology (BTU)*

Bernd Beirow

*Brandenburg University of Technology (BTU)*

Sven Schrape

*Rolls-Royce Deutschland Ltd. & Co. KG*

### A Digital Twin of Compressor Blisk Manufacturing Geometrical Variability for the Aeroelastic Uncertainty Quantification of the Aerodynamic Damping

#### Paper Type

Technical Paper Publication