Principal component analysis on 3D scanned compressor blades for probabilistic CFD simulation

The Principal Component Analysis (PCA) is a widely applied method for describing geometric variability of turbo–engine airfoils. It converts correlated measured coordinates into a set of mode shapes and uncorrelated modal amplitudes. The paper discusses the required steps to apply this method to 3D scanned compressor blades. Transformation laws are derived for translating the unstructured scan into the analysis mesh for performing the PCA and also for translating geometric mode shapes from the analysis mesh to the CFD mesh. Several sampling technologies are discussed concerning their applicability for correctly modelling the statistics of the modal amplitudes matrix. The mentioned points were integrated into a process chain that is applied to a high–pressure compressor stage (HPC) of a jet–engine represented by a stator–rotor–stator configuration. Within a Monte– Carlo simulation (MCS) 500 probabilistic realizations of the compressor blade were created and the impact of the manufacturing variability on the performance of the HPC stage is investigated. The post–processing of the probabilistic simulation reveals the sensitivity of the HPC stage performance on the individual mode shapes and derived geometric features.

[1]  Carsten Clemen,et al.  Introduction of a Parameter Based Compressor Blade Model for Considering Measured Geometry Uncertainties in Numerical Simulation , 2009 .

[2]  Ramana V. Grandhi,et al.  Probabilistic System Reliability for a Turbine Engine Airfoil , 2004 .

[3]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[4]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[5]  Sanjay R. Arwade,et al.  Computational Analysis of Randomness in Structural Mechanics , 2011 .

[6]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[7]  Ramana V. Grandhi,et al.  Probabilistic Analysis of Geometric Uncertainty Effects on Blade Modal Response , 2003 .

[8]  John D. Duffner.  The effects of manufacturing variability on turbine vane performance , 2008 .

[9]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[10]  Alok Sinha,et al.  Vibratory Parameters of Blades From Coordinate Measurement Machine (CMM) Data , 2005 .

[11]  Caroline Marie Lamb,et al.  Probabilistic performance-based geometric tolerancing of compressor blades , 2005 .

[12]  Alexander Lange,et al.  Probabilistic CFD Simulation of a High-Pressure Compressor Stage Taking Manufacturing Variability Into Account , 2010 .

[13]  David L. Darmofal,et al.  Impact of Geometric Variability on Axial Compressor Performance , 2003 .

[14]  Alok Sinha,et al.  Vibratory Parameters of Blades From Coordinate Measurement Machine Data , 2008 .