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Research Papers

Comparison of Two Methods for Sensitivity Analysis of Compressor Blades

[+] Author and Article Information
Robin Schmidt

Institute of Fluid Mechanics,
Technische Universität Dresden,
Dresden D-01062, Germany
e-mail: robin.schmidt@tu-dresden.de

Matthias Voigt, Konrad Vogeler

Institute of Fluid Mechanics,
Technische Universität Dresden,
Dresden D-01062, Germany

Marcus Meyer

Rolls-Royce Deutschland Ltd & Co KG,
Blankenfelde-Mahlow D-15827, Germany
e-mail: marcus.meyer@rolls-royce.com

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 14, 2017; final manuscript received June 5, 2017; published online August 16, 2017. Editor: Kenneth Hall.

J. Turbomach 139(11), 111006 (Aug 16, 2017) (8 pages) Paper No: TURBO-17-1065; doi: 10.1115/1.4037127 History: Received May 14, 2017; Revised June 05, 2017

This paper will compare two approaches of sensitivity analysis, namely (i) the adjoint method which is used to obtain an initial estimate of the geometric sensitivity of the gas-washed surfaces to aerodynamic quantities of interest and (ii) a Monte Carlo type simulation with an efficient sampling strategy. For both approaches, the geometry is parameterized using a modified NACA parameterization. First, the sensitivity of those parameters is calculated using the linear (first-order) adjoint model. Since the effort of the adjoint computational fluid dynamics (CFD) solution is comparable to that of the initial flow CFD solution and the sensitivity calculation is simply a postprocessing step, this approach yields fast results. However, it relies on a linear model which may not be adequate to describe the relationship between relevant aerodynamic quantities and actual geometric shape variations for the derived amplitudes of shape variations. Second, in order to better capture nonlinear and interaction effects, a Monte Carlo type simulation with an efficient sampling strategy is used to carry out the sensitivity analysis. The sensitivities are expressed by means of the coefficient of importance (CoI), which is calculated based on modified polynomial regression and therefore able to describe relationships of higher order. The methods are applied to a typical high-pressure compressor (HPC) stage. The impact of a variable rotor geometry is calculated by three-dimensional (3D) CFD simulations using a steady Reynolds-averaged Navier–Stokes model. The geometric variability of the rotor is based on the analysis of a set of 400 blades which have been measured using high-precision 3D optical measurement techniques.

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Figures

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Fig. 1

Model of two-stage compressor

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Fig. 2

Pressure coefficient over axial chord

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Fig. 6

Sensitivity ranking of the CoI

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Fig. 3

Sensitivity ranking of the adjoint method

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Fig. 4

Anthill plot of total pressure loss of stator 3 over rotor 3

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Fig. 5

Pitchwise-averaged axial whirl angle over blade height: (a) and (b) rotor 3

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Fig. 7

Comparison of the sensitivity ranking for adjoint method and MCS + PA

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