| Citation: | KANG Wei, WANG Yanqing, XU Quanyong, et al. Discrete-adjoint optimization of axial turbine blade using free-form deformation[J]. Journal of Aerospace Power, 2024, 39(11):20220943 doi: 10.13224/j.cnki.jasp.20220943 |
A discrete-adjoint CFD method based on the free-form deformation was developed for aerodynamic performance optimization of the axial turbine stage. Optimization analysis of the two-dimensional turbine stator and single turbine stage was carried out, and the optimal shape of the blade shape under the constraints was given. In the stator blade optimization, the leading edge radius and thickness of the blade obtained were significantly reduced. The total pressure recovery coefficient decreased by 12.44% after optimization, while the flow outlet angle was constrained to −74.66° with the variance of 0.047% during the optimization. For the single-stage turbine optimization problem, the camber of the rotor blade was enhanced, and the total efficiency was improved by 0.79% considering the rotation effect. The constraint condition lied in the flow outlet angle with the variance of 0.068% during the optimization. The results showed the effectiveness of the proposed method on the aerodynamic performance optimization of turbine stage. Compared with the traditional finite difference method, the discrete adjoint method costed only 3% CPU time for single-stage optimization.
| [1] |
LI Zhihui,ZHENG Xinqian. Review of design optimization methods for turbomachinery aerodynamics[J]. Progress in Aerospace Sciences,2017,93: 1-23. doi: 10.1016/j.paerosci.2017.05.003
|
| [2] |
RATNAWEERA A,HALGAMUGE S K,WATSON H C. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J]. IEEE Transactions on Evolutionary Computation,2004,8(3): 240-255. doi: 10.1109/TEVC.2004.826071
|
| [3] |
王晓鹏. 遗传算法及其在气动优化设计中的应用研究[D]. 西安: 西北工业大学,2000. WANG Xiaopeng. Genetic algorithm and its application in aerodynamic optimization design[D]. Xi’an: Northwestern Polytechnical University,2000. (in Chinese
WANG Xiaopeng. Genetic algorithm and its application in aerodynamic optimization design[D]. Xi’an: Northwestern Polytechnical University, 2000. (in Chinese)
|
| [4] |
韩忠华. Kriging模型及代理优化算法研究进展[J]. 航空学报,2016,37(11): 3197-3225. HAN Zhonghua. Kriging surrogate model and its application to design optimization: a review of recent progress[J]. Acta Aeronautica et Astronautica Sinica,2016,37(11): 3197-3225. (in Chinese
HAN Zhonghua. Kriging surrogate model and its application to design optimization: a review of recent progress[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(11): 3197-3225. (in Chinese)
|
| [5] |
GILES M B,PIERCE N A. An introduction to the adjoint approach to design[J]. Flow,Turbulence and Combustion,2000,65(3/4): 393-415. doi: 10.1023/A:1011430410075
|
| [6] |
PAPOUTSIS-KIACHAGIAS E M,GIANNAKOGLOU K C. Continuous adjoint methods for turbulent flows,applied to shape and topology optimization: industrial applications[J]. Archives of Computational Methods in Engineering,2016,23(2): 255-299. doi: 10.1007/s11831-014-9141-9
|
| [7] |
ARENS K,RENTROP P,STOLL S O,et al. An adjoint approach to optimal design of turbine blades[J]. Applied Numerical Mathematics,2005,53(2/3/4): 93-105.
|
| [8] |
PAPADIMITRIOU D I,GIANNAKOGLOU K C. Compressor blade optimization using a continuous adjoint formulation[R]. ASME Paper GT2006-90466, 2006.
|
| [9] |
李伟伟,季路成,伊卫林. 基于伴随方法的多级叶轮机三维叶片优化设计[J]. 工程热物理学报,2014,35(11): 2164-2167. LI Weiwei,JI Lucheng,YI Weilin. Blade shape optimization of multistage turbomachinery by adjoint method[J]. Journal of Engineering Thermophysics,2014,35(11): 2164-2167. (in Chinese
LI Weiwei, JI Lucheng, YI Weilin. Blade shape optimization of multistage turbomachinery by adjoint method[J]. Journal of Engineering Thermophysics, 2014, 35(11): 2164-2167. (in Chinese)
|
| [10] |
罗佳奇,杨婧. 基于伴随方法的单级低速压气机气动设计优化[J]. 航空学报,2020,41(5): 623368. LUO Jiaqi,YANG Jing. Aerodynamic design optimization of a single low-speed compressor stage by an adjoint method[J]. Acta Aeronautica et Astronautica Sinica,2020,41(5): 623368. (in Chinese
LUO Jiaqi, YANG Jing. Aerodynamic design optimization of a single low-speed compressor stage by an adjoint method[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(5): 623368. (in Chinese)
|
| [11] |
ECONOMON T D,PALACIOS F,COPELAND S R,et al. SU2: an open-source suite for multiphysics simulation and design[J]. AIAA Journal,2016,54(3): 828-846. doi: 10.2514/1.J053813
|
| [12] |
REID L,MOORE R. Design and overall performance of four highly loaded,high speed inlet stages for an advanced high-pressure-ratio core compressor[R]. NASA-TP-1337,1978.
|
| [13] |
STEPHAN B,GALLUS H E,NIEHUIS R. Experimental investigations of tip clearance flow and its influence on secondary flows in a 1-1/2 stage axial turbine[R]. ASME Paper 2000-GT-0613,2000.
|
| [14] |
刘晓冬,张沛良,何光洪,等. 基于伴随方法的飞翼布局多目标气动优化设计[J]. 西北工业大学学报,2021,39(4): 753-760. LIU Xiaodong,ZHANG Peiliang,HE Guanghong,et al. Multi-objective aerodynamic optimization of flying-wing configuration based on adjoint method[J]. Journal of Northwestern Polytechnical University,2021,39(4): 753-760. (in Chinese doi: 10.1051/jnwpu/20213940753
LIU Xiaodong, ZHANG Peiliang, HE Guanghong, et al. Multi-objective aerodynamic optimization of flying-wing configuration based on adjoint method[J]. Journal of Northwestern Polytechnical University, 2021, 39(4): 753-760. (in Chinese) doi: 10.1051/jnwpu/20213940753
|
| [15] |
ZHANG Pengfei,LU Juan,SONG Liming,et al. Study on continuous adjoint optimization with turbulence models for aerodynamic performance and heat transfer in turbomachinery cascades[J]. International Journal of Heat and Mass Transfer,2017,104: 1069-1082. doi: 10.1016/j.ijheatmasstransfer.2016.08.103
|
| [16] |
AGROMAYOR R,ANAND N,PINI M,et al. Multirow adjoint-based optimization of NICFD turbomachinery using a computer-aided design-based parametrization[J]. Journal of Engineering for Gas Turbines and Power,2022,144(4): 041008. doi: 10.1115/1.4052881
|
| [17] |
HUANG Huang,EKICI K. A discrete adjoint harmonic balance method for turbomachinery shape optimization[J]. Aerospace Science and Technology,2014,39: 481-490. doi: 10.1016/j.ast.2014.05.015
|
| [18] |
PÉREZ-ARRIBAS F,PÉREZ-FERNÁNDEZ R. A B-spline design model for propeller blades[J]. Advances in Engineering Software,2018,118: 35-44. doi: 10.1016/j.advengsoft.2018.01.005
|
| [19] |
周荐辉,樊未军,田晓沛,等. 某小型高速离心叶轮的优化设计[J]. 航空动力学报,2009,24(9): 2122-2127. ZHOU Jianhui,FAN Weijun,TIAN Xiaopei,et al. Optimized design of a small type high speed centrifugal compressor[J]. Journal of Aerospace Power,2009,24(9): 2122-2127. (in Chinese
ZHOU Jianhui, FAN Weijun, TIAN Xiaopei, et al. Optimized design of a small type high speed centrifugal compressor[J]. Journal of Aerospace Power, 2009, 24(9): 2122-2127. (in Chinese)
|
| [20] |
SAMAREH J. Aerodynamic shape optimization based on free-form deformation[R]. AIAA 2004-4630,2004.
|