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.
Issue Section:
Gas Turbines: Structures and Dynamics
Keywords:
aerodynamics,
turbomachinery,
engines,
rotors,
vibrations,
blades,
minimisation,
cost reduction
Topics:
Blades,
Excitation,
Flow (Dynamics),
Rotors,
Turbomachinery,
Vibration,
Damping,
Aerodynamics,
Design
1.
Verdon
, J. M.
, 1993, “Review of Unsteady Aerodynamic Methods for Turbomachinery Aeroelastic and Aeroacoustic Applications
,” AIAA J.
0001-1452, 31
(2
), pp. 235
–250
.2.
Marshall
, J. G.
, and Imregun
, M.
, 1996, “A Review of Aeroelasticity Methods With Emphasis on Turbomachinery Applications
,” J. Fluids Struct.
0889-9746, 10
(3
), pp. 237
–267
.3.
Vahdati
, M.
, Sayma
, A. I.
, and Imregun
, M.
, 2000, “An Integrated Nonlinear Approach for Turbomachinery Forced Response Prediction. Part II: Case Studies
,” J. Fluids Struct.
0889-9746, 14
(1
), pp. 103
–125
.4.
Giles
, M. B.
, 1992, “An Approach for Multi-Stage Calculations Incorporating Unsteadiness
,” ASME Paper No. 92-GT-282.5.
Hall
, K. C.
, 1993, “Deforming Grid Variational Principle for Unsteady Small Disturbance Flows in Cascades
,” AIAA J.
0001-1452 31
(5
), pp. 891
–900
.6.
Hall
, K. C.
, Clark
, W. S.
, and Lorence
, C. B.
, 1994, “A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery
,” ASME J. Turbomach.
0889-504X, 116
(3
), pp. 477
–488
.7.
Clark
, W. S.
, and Hall
, K. C.
, 1995, “A Numerical Model of the Onset of Stall Flutter in Cascades
,” ASME Paper No. 95-GT-0377.8.
Marshall
, J. G.
, and Giles
, M. B.
, 1998, “Some Applications of a Time-Linearized Euler Method to Flutter and Forced Response in Turbomachinery
,” Proc., 8th ISUAAT, Stockholm, Sweden
, T. H.
Fransson
, ed., Kluwer Academic
, Dordrecht, The Netherlands, pp. 225
–240
.9.
Panovsky
, J.
, and Carson
, S. M.
, 1998, “Prediction of Turbine Blade Vibratory Response Due to Upstream Vane Distress
,” ASME J. Turbomach.
0889-504X, 120
(3
), pp. 515
–521
.10.
Hoyniak
, D.
, and Clark
, W. S.
, 1999, “Aerodynamic Damping Predictions Using a Linearized Navier-Stokes Analysis
,” ASME Paper No. 99-GT-207.11.
Suddhoo
, A.
, Giles
, M. B.
, and Stow
, P.
, 2003, “Simulation of Inviscid Blade Row Interaction Using a Linear and a NonLinear Method
.” ISABE Paper 91-7049.12.
Vahdati
, M.
, Green
, J. S.
, Marshall
, J. G.
, and Imregun
, M.
, 1998, “Forced Response Predictions for a HP Turbine Rotor Blade
,” Proc. RTO Applied Vehicle Technology Panel Symposium on Design Principles and Methods for Aircraft Gas Turbine Engines
, NATO Research Technology Organization
, Neully-sur-Seine, France.13.
Green
, J. S.
, and Marshall
, J. G.
, 1999, “Forced Response Predictions Within the Design Process
,” Proc., 3rd European Conference on Turbomachinery-Fluid Dynamics and Thermodynamics
, von Karman Institute for Fluid Dynamics
, Rhode Saint-Genese, Belgium.14.
Sbardella
, L.
, and Imregun
, M.
, 2001, “Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids
,” ASME J. Turbomach.
0889-504X, 123
(3
), pp. 568
–582
.15.
Jameson
, A.
, 1988, “Aerodynamic Design via Control Theory
,” J. Sci. Comput.
0885-7474, pp. 233
–260
.16.
Jameson
, A.
, 1995, “Optimum Aerodynamic Design Using CFD and Control Theory
,” AIAA Paper 1995-1729.17.
Jameson
, A.
, 1999, “Re-Engineering the Design Process Through Computation
,” AIAA J.
0001-1452 Aircr., 36
(1
), pp. 36
–50
.18.
Giles
, M. B.
, and Pierce
, N. A.
, 2000, “An Introduction to the Adjoint Approach to Design
,” Flow, Turbul. Combust.
1386-6184, 65
(3–4
), pp. 393
–415
.19.
Florea
, R.
, and Hall
, K. C.
, 2001, “Sensitivity Analysis of Unsteady Inviscid Flow Through Turbomachinery Cascades
,” AIAA J.
0001-1452, 39
(6
), pp. 1047
–1056
.20.
Hall
, K. C.
, and Thomas
, J. P.
, 2002, “Sensitivity Analysis of Coupled Aerodynamic∕Structural Dynamic Behavior of Blade Rows
,” Proc., 7th National Turbine Engine HCF Conference
.21.
Thomas
, J. P.
, Hall
, K. C.
, and Dowell
, E. H.
, 2003, “A Discrete Adjoint Approach for Modeling Unsteady Aerodynamic Design Sensitivities
,” AIAA Paper 2003-0041.22.
Giles
, M. B.
, Duta
, M. C.
, Müller
, J.-D.
, and Pierce
, N. A.
, 2003, “Algorithm Developments for Discrete Adjoint Methods
,” AIAA J.
0001-1452, 41
(2
), pp. 198
–205
.23.
Duta
, M. C.
, 2002, “The Use of The Adjoint Method for the Minimisation of Forced Vibration in Turbomachinery
,” PhD thesis, University of Oxford, United Kingdom.24.
Duta
, M. C.
, Giles
, M. B.
, and Campobasso
, M. S.
, 2002, “The Harmonic Adjoint Approach to Unsteady Turbomachinery Design
,” Int. J. Numer. Methods Fluids
0271-2091, 40
(3–4
), pp. 323
–332
.25.
Moinier
, P.
, 1999, “Algorithm Developments for an Unstructured Viscous Flow Solver
,” PhD thesis, University of Oxford, United Kingdom.26.
Giles
, M. B.
, 1990, “Nonreflecting Boundary Conditions for Euler Equation Calculations
,” AIAA J.
0001-1452, 28
(12
), pp. 2050
–2058
.27.
Spalart
, P. R.
, and Allmaras
, S. R.
, 1994, “A One-Equation Turbulence Model for Aerodynamic Flows
,” Rech. Aerosp.
0034-1223, pp. 5
–21
.28.
Campobasso
, M. S.
, and Giles
, M. B.
, 2003, “Effect of Flow Instabilities on the Linear Analysis of Turbomachinery Aeroelasticity
,” AIAA J. Propul. Power
0748-4658, 19
(2
), pp. 250
–259
.29.
Smith
, S. N.
, 1971, “Discrete Frequency Sound Generation in Axial Flow Turbomachines
,” Tech. Rep. CUED∕A-Turbo∕TR 29, University of Cambridge, Department of Engineering, Cambridge, United Kingdom.30.
Whitehead
, D. S.
, 1988, “Classic Two-Dimensional Methods
,” AGARD Manual on Aeroelasticity in Axial-Flow Turbomachines
, AGARD-AG-298, M.
Platzer
and F. O.
Carta
, eds., Vol. 1
, NATO Advisory Group for Aerospace Research and Development
, Neully-sur-Seine, France.31.
Telionis
, D. P.
, 1981, Unsteady Viscous Flows
, Springer
, New York, pp. 156
–158
, Chap. 4.32.
Fransson
, T. H.
, et al., 1999, “Viscous and Inviscid Linear∕Nonlinear Calculations Versus Quasi Three-Dimensional Experimental Cascade Data for a New Aeroelastic Turbine Standard Configuration
,” ASME J. Turbomach.
0889-504X, 121
, pp. 717
–725
.33.
Vahdati
, M.
, Sayma
, A. I.
, Marshall
, J. G.
, and Imregun
, M.
, 2001, “Mechanisms and Prediction Methods for Fan Blade Stall Flutter
,” AIAA J. Propul. Power
0748-4658, 17
(5
), pp. 1100
–1108
.Copyright © 2006
by American Society of Mechanical Engineers
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