**59642 - Stator Blades Manufacturing Geometrical Variability in Axial Compressors and Impact on the Aeroelastic Excitation Forces **

The manufacturing geometrical variability is a source of uncertainty, which cannot be avoided in the realization of a machinery. Deviations of a component geometry from its nominal design are inevitably present due to the manufacturing process. In the case of the aeroelastic forced response problem within axial compressors, these uncertainties may affect the vibration characteristics. For this reason, the impact of geometrical uncertainties due to the manufacturing process onto the modal forcing of axial compressor blades is investigated in this study.

The research focuses on the vibrational behavior of an axial compressor rotor *blisk* (blade-integrated disk) and in particular the amplitude of the forces acting as source of excitation on the vibrating blades (modal forcing). Within this context, the geometry of the upstream stator plays an important role as in general the main harmonics of the rotor excitation forces are produced by its wake. Therefore, small variations of the upstream stators geometries, such as the ones caused by the manufacturing process, may affect the resulting forcing. In particular, the geometrical variability of the upstream stator implies that the hypothesis of a cyclic-symmetrical flow is no longer valid. This may cause the introduction of lower harmonic components in the modal forces, generally referred to as *Low Engine Orders* (LEO).

The geometrical variability is modelled starting from a series of optical surface scans. A set of optical measurements of manufactured stator blades originating from the same nominal design constitutes the baseline dataset on which the geometrical model is built. The measured blades as well as the relative nominal geometry are parametrized to describe the individual blades surfaces. The parameterization is accomplished by slicing the surfaces in radial sections and describing each of these with a set of NACA-like parameters [1]. The measured geometrical deviations from the nominal model can therefore be described as an offset of such parameters. A reduced representation of the variables representing the input uncertainty (noise variables) is obtained via *Principal Components Analysis*. Afterwards a sampling on the reduced noise variables domain can be done to represent the modelled uncertainty and perform an *Uncertainty Quantification* (UQ) on the relative quantities of interest, in this case the modal forcing.

The computation of the modal forcing is done through a CFD solver, computing the unsteady flow field around the rotor blades. The domain considered in this case is a 1.5 stage of the axial compressor, including the rotor and the up- and down-stream stators. The solutions are initialized from a validated steady state solution of the considered compressor rig. The time-dependent pressure field calculated on the rotor blades is projected onto the relative vibrational mode shapes of interests (from structural modal analyzes). The resulting forces are analyzed by means of their spectrum, evaluating the amplitudes for the present engine orders (higher harmonics of the shaft mechanical speed).

The UQ uses Monte Carlo methods to evaluate the impact of the geometrical variability onto the modal forcing. The modelled uncertainty on the geometries is introduced into the CFD solver to compute the deviations on the quantities of interest. A reconstruction of the forces acting on the rotor during one revolution is obtained. This allows to evaluate the uncertainty on the present engine orders as well as the possible rise of LEO for the rotor blades in presence of a mistuned upstream stator.

[1]: Lange A., Vogeler K., Gümmer V., Schrapp H. and Clemen C. (2009). “*Introduction of a Parameter Based Compressor Blade Model for Considering Measured Geometry Uncertainties in Numerical Simulation*.” Proceedings of ASME Turbo Expo. GT2009-59937.

### Stator Blades Manufacturing Geometrical Variability in Axial Compressors and Impact on the Aeroelastic Excitation Forces

#### Paper Type

Technical Paper Publication

#### Description

**Session: **39-01 UQ & Robust Design - Operation and Geometric Uncertainties

**Paper Number: **59642

**Start Time: **June 9th, 2021, 02:15 PM

**Presenting Author: **Marco Gambitta

**Authors: **Marco Gambitta *Brandenburg University of Technology (BTU)*

Arnold Kühhorn *Brandenburg University of Technology (BTU)*

Bernd Beirow *Brandenburg University of Technology (BTU)*

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