A robust mixing plane method satisfying interface flux conservation, nonreflectivity and retaining interface flow variation; valid at all Mach numbers and applicable for any machine configuration is formulated and implemented in a vertex based finite volume solver for flow analysis and inverse design. The formulation is based on superposing perturbed flow variables derived from the three-dimensional (3D) characteristics obtained along the flow direction on the exchanged mixed out averaged quantities. The method is extended for low speed applications using low Mach number preconditioning. Subsequently, inverse design runs over a single stage transonic low pressure (LP) turbine configuration conducted at a fixed mass flow boundary condition and spanwise loading condition similar to the baseline generates optimized configurations providing performance improvement while achieving prespecified target meridional load distribution.
Issue Section:
Research Papers
References
1.
Giles
, M.
, 1988
, “Non-Reflecting Boundary Conditions for the Euler Equations
,” MIT Department of Aeronautics and Astronautics, Cambridge, MA, Paper No. CFDL-TR-88-1.2.
Denton
, J.
, and Singh
, U.
, 1979
, Time Marching Methods for Turbomachinery Flow Calculation
, von Karman Institute
, Sint-Genesius-Rode, Belgium
.3.
Holmes
, D. G.
, 2008
, “Mixing Plane Revisited: A Steady State Mixing Plane Approach Designed to Combine High Levels of Conservation and Robustness
,” ASME Turbo Expo, Berlin, Germany, June 9–13, ASME
Paper No. GT2008-51296.10.1115/GT2008-512964.
Hanimann
, L.
, Mangani
, L.
, Casartelli
, E.
, Mokulys
, T.
, and Mauri
, S.
, 2013
, “Development of a Novel Mixing Plane Interface Using a Fully Implicit Averaging for Stage Analysis
,” ASME Turbo Expo, San Antonio, TX, June 3–7, ASME
Paper No. GT2013-94390.10.1115/GT2013-943905.
Moraga
, F.
, Vysohild
, M.
, Smelova
, N.
, Mistry
, H.
, Atheya
, S.
, and Kanakala
, V.
, 2012
, “A Flux-Conservation Mixing Plane Algorithm for Multiphase Non-Equilibrium Steam Models
,” ASME Turbo Expo, Copenhagen, Denmark, June 11–15, ASME
Paper No. GT2012-68660.10.1115/GT2012-686606.
Saxer
, A.
, and Giles
, M.
, 1991
, “Quasi-Three-Dimensional Nonreflecting Boundary Conditions for Euler Equations Calculations
,” J. Propul. Power
, 9
(2
), pp. 263
–271
.10.2514/3.236187.
Anker
, J.
, Schrader
, B.
, Seybold
, U.
, Mayer
, J.
, and Casey
, M.
, 2006
, “A Three-Dimensional Non-Reflecting Boundary Condition Treatment for Steady-State Flow Simulations
,” AIAA
Paper No. 2006-1275.10.2514/6.2006-12758.
Páscoa
, J. C.
, Xisto
, C. M.
, and Göttlich
, E.
, 2010
, “Performance Assessment Limits in Transonic 3D Turbine Stage Blade Rows Using a Mixing-Plane Approach
,” J. Mech. Sci. Technol.
, 24
(10
), pp. 2035
–2042
.10.1007/s12206-010-0713-99.
Tiow
, W. T.
, and Zangeneh
, M.
, 2002
, “A Novel 3D Inverse Method for the Design of Turbomachinery Blades in Rotational Viscous Flow: Theory and Applications
,” Task Q.
, 6
(1
), pp. 63
–78
.10.
Tiow
, W. T.
, and Zangeneh
, M.
, 2002
, “Application of a Three Dimensional Viscous Transonic Inverse Method to NASA Rotor 67
,” J. Power Energy
, 216
(A3
), pp. 243
–255
.10.1243/09576500232018356811.
TURBOdesign Suite,
2013
, TURBOdesign2, Version 5.2.1, Advanced Design Technology Ltd, London.12.
Demeulenaere
, A.
, and Van den Braembussche
, R.
, 1996
, “Three-Dimensional Inverse Method for Turbomachinery Blading Design
,” ASME 41th International Gas Turbine Conference and Exhibit, Birmingham, UK, June 10–13, ASME Paper No. 96-GT-39.10.1115/96-GT-3913.
Rooij
, M.
, and Medd
, A.
, 2012
, “Reformulation of a Three-Dimensional Inverse Design Method for Application in a High-Fidelity CFD Environment
,” ASME Turbo Expo, Copenhagen, Denmark, June 11–15, ASME
Paper No. GT2012-69891.10.1115/GT2012-6989114.
Arbabi
, A.
, and Ghaly
, W.
, 2013
, “Inverse Design of Turbine and Compressor Stages Using a Commercial CFD Program
,” ASME Turbo Expo, San Antonio, TX, June 3–7, ASME
Paper No. GT2013-96017.10.1115/GT2013-9601715.
Page
, J. H.
, Hield
, P.
, and Tucker
, P. G.
, 2013
, “Inverse Design of 3D Multi-Stage Transonic Fans at Dual Operating Points
,” ASME Turbo Expo, San Antonio, TX, June 3–7, ASME
Paper No. GT2013-95062.10.1115/GT2013-9506216.
Weiss
, J.
, and Smith
, W.
, 1995
, “Preconditioning Applied to Variable and Constant Density Flows
,” AIAA J.
, 33
(11
), pp. 2050
–2057
.10.2514/3.1294617.
Darmofal
, D.
, and Siu
, K.
, 1999
, “A Robust Multigrid Algorithm for the Euler Equations With Local Preconditioning and Semi-Coarsening
,” J. Comput. Phys.
, 151
(2
), pp. 728
–756
.10.1006/jcph.1999.621618.
Hall
, M. G.
, 1985
, “Cell-Vertex Multigrid Schemes for Solution of the Euler Equations
,” Numerical Methods for Fluid Dynamics
, K. W.
Morton
, and M. J.
Baines
, eds., Clarendon Press, Oxford
, UK
.19.
Tiow
, W. T.
, 2000
, “Inverse Design of Turbomachinery Blades in Rotational Flow
,” PhD thesis, University College, University of London, London.20.
Denton
, J.
, 1986
, “The Use of a Distributed Body Force to Simulate Viscous Effects in 3D Flow Calculations
,” ASME 31st International Gas Turbine Conference and Exhibit, Düsseldorf, Germany, June 8–12, ASME Paper No. 86-GT-144.10.1115/86-GT-14421.
Jameson
, A.
, Schmidt
, W.
, and Turkel
, E.
, 1981
, “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge–Kutta Time Stepping Schemes
,” AIAA
Paper No. 81-1259.10.2514/6.81-125922.
Swanson
, R. C.
, Radespiel
, R.
, and Turkel
, E.
, 1998
, “On Some Numerical Dissipation Schemes
,” J. Comput. Phys.
, 147
(2
), pp. 518
–544
.10.1006/jcph.1998.610023.
Chima
, R. V.
, 1998
, “Calculation of Multistage Turbomachinery Using Steady Characteristic Boundary Conditions
,” AIAA
Paper No. 98-0968.10.2514/6.98-096824.
TURBOdesign Suite
2013
, Turbodesign CFD 5.2.0, Advanced Design Technology
, London
.25.
ANSYS, 2011, ANSYS CFX 14.0, ANSYS Inc., Canonsburg, PA.
Copyright © 2015 by ASME
You do not currently have access to this content.
