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Research Papers

Multipoint Design Optimization of a Transonic Compressor Blade by Using an Adjoint Method

[+] Author and Article Information
Jiaqi Luo

Postdoctoral Researcher
e-mail: jiaqil81@gmail.com

Chao Zhou

Assistant Professor
e-mail: czhou@pku.edu.cn
College of Engineering,
Peking University,
Beijing 100871, China

Feng Liu

Professor
Department of Mechanical and
Aerospace Engineering,
University of California,
Irvine, CA 92697-3975
e-mail: fliu@uci.edu

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 29, 2013; final manuscript received July 7, 2013; published online September 27, 2013. Editor: Ronald Bunker.

J. Turbomach 136(5), 051005 (Sep 27, 2013) (10 pages) Paper No: TURBO-13-1087; doi: 10.1115/1.4025164 History: Received May 29, 2013; Revised July 07, 2013

This paper presents the application of a viscous adjoint method to the multipoint design optimization of a rotor blade through blade profiling. The adjoint method requires about twice the computational effort of the flow solution to obtain the complete gradient information at each operating condition, regardless of the number of design parameters. NASA Rotor 67 is redesigned through blade profiling. A single point design optimization is first performed to verify the effectiveness and feasibility of the optimization method. Then in order to improve the performance for a wide range of operating conditions, the blade is redesigned at three operating conditions: near peak efficiency, near stall, and near choke. Entropy production through the blade row combined with the constraints of mass flow rate and total pressure ratio is used as the objective function. The design results are presented in detail and the effects of blade profiling on performance improvement and shock/tip-leakage interaction are examined.

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References

Suder, K. L., and Celestina, M. L., 1996, “Experimental and Computational Investigation of the Tip Clearance Flow in a Transonic Axial Compressor Rotor,” ASME J. Turbomach., 118(2), pp. 218–229. [CrossRef]
Van Zante, D. E., Strazisar, A. J., Wood, J. R., Hathaway, M. D., and Okiishi, T. H., 2000, “Recommendations for Achieving Accurate Numerical Simulation of Tip Clearance Flows in Transonic Compressor Rotors,” NASA TM 210347.
Kirtley, K. R., Beach, T. A., and Adamczyk, J. J., 1990, “Numerical Analysis of Secondary Flow in a Two-Stage Turbine,” AIAA Paper No. 1990-2356. [CrossRef]
Oyama, A., Liou, M. S., and Obayashi, S., 2004, “Transonic Axial-Flow Blade Shape Optimization Using Evolutionary Algorithm and Three-Dimensional Navier–Stokes Solver,” J. Propul. Power, 20(4), pp. 612–619. [CrossRef]
Zhao, G., Chen, F., Song, Y., and Wang, Z., 2005, “Optimization Design of Compressor Cascade With Swept and Curved Blades,” AIAA Paper No. 2005-336. [CrossRef]
Jang, C. M., Samad, A., and Kim, K. Y., 2006, “Optimal Design of Swept, Leaned and Skewed Blades in a Transonic Axial Compressor,” ASME Paper No. GT2006-90384. [CrossRef]
Samad, A., Kim, K. Y., Goel, T., Haftka, R. T., and Shyy, W., 2008, “Multiple Surrogate Modeling for Axial Compressor Blade Shape Optimization,” J. Propul. Power, 24(2), pp. 302–310. [CrossRef]
Mengistu, T., and Ghaly, W., 2004, “Single and Multipoint Shape Optimization of Gas Turbine Blade Cascades,” AIAA Paper No. 2004-4446. [CrossRef]
Benini, E., 2004, “Three-Dimensional Multi-Objective Design Optimization of a Transonic Compressor Rotor,” J. Propul. Power, 20(3), pp. 559–565. [CrossRef]
Lian, Y., and Liou, M. S., 2005, “Multi-Objective Optimization of Transonic Compressor Blade Using Evolutionary Algorithm,” J. Propul. Power, 21(6), pp. 979–987. [CrossRef]
Bonaiuti, D., and Zangeneh, M., 2009, “On the Coupling of Inverse Method and Optimization Techniques for the Multiobjective, Multipoint Design of Turbomachinery Blades,” ASME J. Turbomach., 131(2), p. 021014. [CrossRef]
Jameson, A., 1988, “Aerodynamic Design Via Control Theory,” J. Sci. Comput., 3(3), pp. 233–260. [CrossRef]
Jameson, A., 2003, “Aerodynamic Shape Optimization Using the Adjoint Method,” (VKI Lecture Series on Aerodynamic Drag Prediction and Reduction), von Karman Institute of Fluid Dynamics, Rhode-St-Genèse, Belgium.
Yang, S., Wu, H., and Liu, F., 2003, “Aerodynamic Design of Cascades by Using an Adjoint Equation Method,” AIAA Paper No. 2003-1068. [CrossRef]
Wu, H., and Liu, F., 2005, “Aerodynamic Design of Turbine Blades Using an Adjoint Equation Method,” AIAA Paper No. 2005-1006. [CrossRef]
Luo, J., Xiong, J., Liu, F., and McBean, I., 2010, “Secondary Flow Reduction by Blade Redesign and Endwall Contouring Using an Adjoint Optimization Method,” ASME Paper No. GT2010-22061. [CrossRef]
Luo, J., Liu, F., and McBean, I., 2011, “Optimization of Endwall Contours of a Turbine Blade Row Using an Adjoint Method,” ASME Paper No. GT2011-46163. [CrossRef]
Luo, J., Xiong, J., Liu, F., and McBean, I., 2011, “Three-Dimensional Aerodynamic Design Optimization of a Turbine Blade by Using an Adjoint Method,” ASME J. Turbomach., 133(1), p. 011026. [CrossRef]
Wang, D., and He, L., 2010, “Adjoint Aerodynamic Design Optimization for Blades in Multi-Stage Turbomachines—Part I: Methodology and Verification,” ASME J. Turbomach., 132(2), p. 021011. [CrossRef]
Wang, D., He, L., Wells, R., and Chen, T., 2010, “Adjoint Aerodynamic Design Optimization for Blades in Multi-Stage Turbomachines—Part II: Validation and Application,” ASME J. Turbomach., 132(2), p. 021012. [CrossRef]
Strazisar, A. J., Wood, J. R., Hathaway, M. D., and Suder, K. L., 1989, “Laser Anemometer Measurements in a Transonic Axial-Flow Fan Rotor,” NASA TP 2879.
Arnone, A., 1993, “Viscous Analysis of Three-Dimensional Rotor Flows Using a Multigrid Method,” NASA TM 106266.
Puterbaugh, S. L., and Brendel, M., 1997, “Tip Clearance Flow-Shock Interaction in a Transonic Compressor Rotor,” J. Propul. Power, 13(1), pp. 24–30. [CrossRef]
Chima, R. V., 1998, “Calculation of Tip Clearance Effects in a Transonic Compressor Rotor,” ASME J. Turbomach., 120(1), pp. 131–140. [CrossRef]
Hah, C., Rabe, D. C., and Wadia, A. R., 2004, “Role of Tip-Leakage Vortices and Passage Shock in Stall Inception in a Swept Transonic Compressor Rotor,” ASME Paper No. GT2004-53867. [CrossRef]
Van Ness, D. K., Corke, T. C., and Morris, S. C., 2009, “Tip Clearance Flow Control in a Linear Turbine Cascade Using Plasma Actuation,” AIAA Paper No. 2009-300. [CrossRef]
Biollo, R., and Benini, E., 2009, “Shock/Boundary-Layer/Tip-Clearance Interaction in a Transonic Rotor Blade,” J. Propul. Power, 25(3), pp. 668–677. [CrossRef]
Kim, J. H., Choi, K. J., Husain, A., and Kim, K. Y., 2011, “Multiobjective Optimization of Circumferential Casing Grooves for a Transonic Axial Compressor,” J. Propul. Power, 27(3), pp. 730–733. [CrossRef]
Liu, F., and Zheng, X., 1994, “Staggered Finite Volume Scheme for Cascade Flow With a k-ω Turbulence Model,” AIAA J., 32(8), pp. 1589–1597. [CrossRef]
Liu, F., and Zheng, X., 1996, “A Strongly-Coupled Time-Marching Method for Solving the Navier–Stokes and k-ω Turbulence Model Equations With Multigrid,” J. Comput. Phys., 128(2), pp. 289–300. [CrossRef]
Spalart, P. R., and Allmaras, S. R., 1992, “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper No. 1992-0439. [CrossRef]
Dunham, J., and Meauze, G., 1998, “An AGRAD Working Group Study of 3D Navier–Stokes Codes Applied to Single Turbomachinery Blade Rows,” ASME Paper No. 98-GT-50.
Denton, J. D., 1993, “Loss Mechanisms in Turbomachines,” J. Turbomach., 115(4), pp. 621–656. [CrossRef]
Denton, J. D., and Xu, L., 2002, “The Effects of Lean and Sweep on Transonic Fan Performance,” ASME Paper No. GT2002-30327. [CrossRef]

Figures

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Fig. 1

Comparisons of operating characteristics of Rotor 67

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Fig. 2

Spanwise distributions of total pressure ratio, total temperature ratio and flow turning

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Fig. 3

Blade profiles perturbed by shape function

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Fig. 4

Comparisons of gradients

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Fig. 5

Contours of relative isentropic Mach number on the blade surface (a) pressure side and (b) suction side

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Fig. 6

Blade profiles and distributions of relative isentropic Mach number at different spans

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Fig. 7

Spanwise distributions of (a) total pressure ratio and adiabatic efficiency and (b) total temperature ratio and flow turning

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Fig. 8

Contours of relative Mach number at different axial locations (a) 40% chord, (b) 80% chord, and (c) 110% chord

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Fig. 9

Pressure contours on a blade-to-blade stream surface at the blade tip (a) reference and (b) optimized

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Fig. 10

Operating characteristics of the reference and the optimized blades (a) total pressure ratio and (b) adiabatic efficiency

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Fig. 11

Contours of relative Mach number on a blade-to-blade stream surface at the blade tip (a) near P.E. and (b) near stall

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