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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Adjoint Harmonic Sensitivities for Forced Response Minimization

[+] Author and Article Information
Mihai C. Duta

Oxford University Computing Laboratory,  University of Oxford, Oxford OX1 2QD, UKmihai.duta@comlab.ox.ac.uk

Michelle S. Campobasso

Oxford University Computing Laboratory,  University of Oxford, Oxford OX1 2QD, UKsergio.campobasso@comlab.ox.ac.uk

Michael B. Giles

Oxford University Computing Laboratory,  University of Oxford, Oxford OX1 2QD, UKmike.giles@comlab.ox.ac.uk

Leigh B. Lapworth

 Aerothermal Methods Group, Rolls-Royce plc., P.O. Box 31, Derby DE24 8BJ, UKleigh.lapworth@rolls-royce.com

J. Eng. Gas Turbines Power 128(1), 183-189 (Mar 01, 2003) (7 pages) doi:10.1115/1.2031227 History: Received October 01, 2002; Revised March 01, 2003

This paper presents an adjoint analysis for three-dimensional unsteady viscous flows aimed at the calculation of linear worksum sensitivities involved in turbomachinery forced response predictions. The worksum values are normally obtained from linear harmonic flow calculations but can also be computed using the solution to the adjoint of the linear harmonic flow equations. The adjoint method has a clear advantage over the linear approach if used within a rotor forced vibration minimization procedure which requires the structural response to a large number of different flow excitation sources characterized by a unique frequency and interblade phase angle. Whereas the linear approach requires a number of linear flow calculations at least equal to the number of excitation sources, the adjoint method reduces this cost to a single adjoint solution for each structural mode of rotor response. A practical example is given to illustrate the dramatic computational saving associated with the adjoint approach.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Comparison between the standard iteration and GMRES convergence histories for a turbine flutter case; GMRES (applied either from the initial conditions or from a restart) is a stable solver

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Figure 2

Comparison between the measured and the computed midspan distribution of the unsteady pressure amplitude for the 11th standard configuration at the subsonic flow condition

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Figure 3

Comparison between the imaginary part of the worksum value and the logarithmic decrement output by an independent nonlinear viscous code

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Figure 4

Variation of the absolute value of the aerodynamic forcing work sum with the value of the extremal phase shift for the 1T and 2F modes of rotor vibration

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Figure 5

The midspan distribution of the unsteady pressure amplitude computed as a response to the datum inlet flow harmonic perturbation and to the perturbations phase shifted with ±180 deg

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