The adjoint method plays an important role in the aerodynamic design of turbomachinery. However, most optimization objects are only local parts of the fluid domain in turbomachinery, such as blade or end-wall. In this study, a novel parameterization method is adopted in the adjoint optimization framework to merge all design spaces together and then a typical multi-row compressor, Stage 35, is optimized by the in-house adjoint optimizer, TurboSim_un. The adiabatic efficiency of STAGE 35 is improved by 1.7%. Results show that the intersection of shock wave and boundary layer is weakened and the performance in mainstream is significantly improved.
SuXRYuanX. Adjoint boundary sensitivity method to assess the effect of nonuniform boundary conditions. Chinese Journal of Aeronautic2021; 35: 12–16.
2.
ChenLChenJ. Aerodynamic optimization design for high pressure turbines based on the adjoint approach. Chinese Journal of Aeronautics2015; 28(3): 57–69.
3.
ZhangQXuSRYuXJ, et al.Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method. Chinese Journal of Aeronautics2021; 35: 17–21.
4.
LionsJ. Optimal control of systems governed by partial differential equations. New York: Springer-Verlag, 1971.
5.
JamesonA. Aerodynamic design via control theory. Journal of Scientific Computing1988; 3(3): 233–260.
6.
DreyerJMartinelliL. Hydrodynamic shape optimization of propulsor configurations using continuous adjoint approach. 15th AIAA Computational Fluid Dynamics Conference, CA,USA. American Institute of Aeronautics and Astronautics, 2001.
7.
YangSLiuF. Optimum aerodynamic design of cascades by using an adjoint equation method. 41st Aerospace Sciences Meeting and Exhibit, CA,USA. American Institute of Aeronautics and Astronautics, 2003.
8.
HeLWangDX. Concurrent blade aerodynamic-aero-elastic design optimization using adjoint method. Journal of Turbomachinery2011; 133(1): 11–21.
9.
LuoJQLiuFZhouC. Multi-point design optimization of a transonic compressor blade by using an adjoint method. Proceedings Of the ASME Turbo Expo2013; 136: 10.
10.
DutaMCGilesMBCampobassoMS. The harmonic adjoint approach to unsteady turbomachinery design. Int J Numer Meth Fl2002; 40: 23–32.
11.
VerstraeteTMullerMullerJD. CAD-based adjoint optimization of the stresses in a radial turbine. Proceedings Of the ASME Turbo Expo2017; GT2017-65005: 8.
12.
TalnikarCWangQQLaskowskiGM. Unsteady adjoint of pressure loss for a fundamental transonic turbine vane. Proceedings of the Asme Turbo Expo, NY, USA, The American Society Of Mechanical Engineers, 2016.
13.
JohnAShahparSQinN. Alleviation of shock-wave effects on a highly loaded axial compressor through novel blade shaping. Proceedings of the ASME Turbo Expo, NY, USA, The American Society Of Mechanical Engineers, 2016.
14.
PiniMPersicoGDossenaV. Robust adjoint-based shape optimization of supersonic turbomachinery cascades. Proceedings of the Asme Turbo Expo, NY, USA, The American Society Of Mechanical Engineers, 2014.
15.
YangJXiongJTMcBeanI, et al.Performance impact of manufacturing variations for multistage steam turbines. J Propul Power2017; 33: 31–36.
16.
ShankaranSMartaA. Robust optimization for aerodynamic problems using polynomial chaos and adjoints. Proceedings of the ASME Turbo Expo2012; 8: 17–27.
17.
FengZPLiHTSongLM, et al.Aerodynamic inverse design optimization for turbine cascades based on control theory[J]. Science China Technology Sciences2013; 56: 308–323.
18.
JiLCYuJLiWW, et al.Study on aerodynamic optimal super/transonic turbine cascade and its geometry characteristics[J]. Proceedings of the Institution of Mechanical Engineers Part G-Journal of Aerospace Engineering2017; 231: 435–443.
19.
JohnAShahparSQinN. Novel compressor blade shaping through a Free-Form Method[J]. Journal of Turbomachinery2017; 139(8): 081002.
20.
ArensKRentropPStollSO, et al.An Adjoint approach to optimal design of turbine blades[J]. Applied Numerical Mathmatics2005; 53: 93–105.
21.
LuoJQXiongJTLiuF, et al., Secondary flow reduction by blade redesign and endwall contouring using an adjoint optimization methodProceedings Of the Asme; 7. Pts a-C: pp. 547–562, 2010.
22.
SongH. Development and research of discrete adjoint optimization system for turbomachinery aerodynamic shape design[D], Beijing, China, Beijing Institute of Technology, 2017.
CoquillartS. Extended Free-Form Deformation: a sculpturing tool for 3D geometric modeling[J]. Computer Graphics1990; 24(4): 187–196.
25.
CelestinaMMulacR. Assessment of stage 35 with APNASA. 47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition2009; 1057: 1057.
26.
XuSRRadfordDMeyerM, et al.Stabilisation of discrete steady adjoint solvers[J]. Journal of Computational Physics2015; 299(15): 175–195.
27.
VerstraeteTGarreauMAlsalihiZ, et al.Multidisciplinary optimization of a radial turbine for micro gas turbine application. 7th European Conference on Turbomachinery : fluid dynamics and thermodynamics ETC 2007, Athens, Greece, National Technical University of Athens, 2007. 1–9.
