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The improved inverse method for axial compressor based on quasi-three-dimensional model

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A Correction to this article was published on 12 March 2024

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Abstract

An improved and steady inverse method based on the time-marching solution of quasi-three-dimensional Navier–Stokes equations for axial compressors is proposed in this work. The main novelty of this paper lies in the derivation of a stable inverse design boundary condition based on the conservation of Riemann invariants in order to redesign the blade quickly, which is established on a reduced-order model. At the same time, in order to simulate the flow field of transonic axial compressors more accurately, the solver takes the blade radius and thickness into consideration in the direct mode. In addition, a detailed inverse design time step method is employed to guarantee the robustness. Two redesigned cases are presented, including a subsonic stream surface and a transonic stream surface. On this basis, a transonic fan is partially redesigned near the hub of the blade. Through the novel three-dimensional verification of ANSYS CFX, the result shows that the inverse method achieves higher efficiency and better effect in the partial redesign of axial compressors, which demonstrates the effectiveness of the new inverse method.

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References

  1. Kuzenov VV, Ryzhkov SV, Varaksin AY (2022) Calculation of heat transfer and drag coefficients for aircraft geometric models. Appl Sci 12(21):11011

    Article  Google Scholar 

  2. Yang J, Wang R, Zhang M, Liu Y (2021) Parametric study of rotor tip squealer geometry on the aerodynamic performance of a high subsonic axial compressor stage. J Braz Soc Mech Sci Eng 43:1–13

    Article  Google Scholar 

  3. Lighthill MJ (1945) A new method of two-dimensional aerodynamic design. Aero.res.council London R & M 2112

  4. Stanitz JD (1952) Design of two-dimensional channels with prescribed velocity distributions along the channel walls. Technical Report Archive & Image Library (1115)

  5. Hawthorne WR, Wang C, Tan CS, Mccune JE (1984) Theory of blade designfor large deflections: Part i—two-dimensional cascade. J Eng Gas Turbines Power 106(2):346–353

    Article  Google Scholar 

  6. Tan CS, Hawthorne WR, McCune JE, Wang C (1984) Theory of blade designfor large deflections: Part ii—annular cascades. J Eng GasTurbines Power 106(2):354–365

    Article  Google Scholar 

  7. Dulikravich G (1995) Shape inverse design and optimization for three-dimensional aerodynamics. In: Aerospace sciences meeting & exhibit

  8. Dang T (1992) A fully three-dimensional inverse method for turbomachinery blading in transonic flows. In: Turbo Expo: Power for Land, Sea, and Air, vol 78934. American Society of Mechanical Engineers, pp 001–01070

    Google Scholar 

  9. Dang T (1995) Inverse method for turbomachine blades using shock-capturing techniques. In: 31st Joint Propulsion Conference and Exhibit, p 2465

  10. Qiu X, Dang T (2000) 3d inverse method for turbomachine blading with splitter blades. In: Turbo Expo: Power for Land, Sea, and Air, vol 78545. American Society of Mechanical Engineers, pp 001–03090

    Google Scholar 

  11. Hield P (2008) Semi-inverse design applied to an eight stage transonic axial flow compressor. In: Asme Turbo Expo: Power for Land, Sea, & Air

  12. Rooij MPCV, Dang TQ, Larosiliere LM (2008) Enhanced blade row matching capabilities via 3d multistage inverse design and pressure loading manager. In: Asme Turbo Expo: Power for Land, Sea, & Air

  13. Rooij MPCV, Dang TQ, Larosiliere LM (2005) Improving aerodynamic matching of axial compressor blading using a 3d multistage inverse design method. In: ASME Turbo Expo 2005: Power for Land, Sea, and Air, vol 6 pt.B

  14. Rooij MV, Medd A (2012) Reformulation of a three-dimensional inverse design method for application in a high-fidelity cfd environment. In: Asme Turbo Expo: 20 Turbine Technical Conference & Exposition

  15. Zangeneh M, Goto A, Harada H (1997) On the design criteria for suppression of secondary flows in centrifugal and mixed flow impellers. J Turbomach 120(4):723–735

    Article  Google Scholar 

  16. Tiow W, Zangeneh M (2000) A three-dimensional viscous transonic inverse design method. In: Turbo Expo: Power for Land, Sea, and Air, vol 78545. American Society of Mechanical Engineers, pp 001–03089

    Google Scholar 

  17. Zangeneh M, Goto A, Harada H (1999) On the role of three-dimensional inverse design methods in turbomachinery shape optimization. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213(1):27–42

  18. Ramamurthy R, Ghaly W (2010) Dual point redesign of an axial compressor airfoil using a viscous inverse design method. In: Asme Turbo Expo: Power for Land, Sea, & Air

  19. Jin-Guang Y, Zhen-De L, Fu-Yong S, Hu W (2015) A study of applications of 3d viscous inverse method based on transpiration boundary conditions for turbomachinery aerodynamic design. J Propulsion Technol 36(5):8

    Google Scholar 

  20. Jin-Guang Y, Zhen-De L, Fu-Yong S, Hu W (2015) Transpiration boundary condition based on inverse method for turbomachinery aerodynamic design: on the solution existence and uniqueness. J Propuls Technol 4:579–586

    Google Scholar 

  21. Zhao-wei L Research of full three dimensional viscous inverse design method for multi-stage axial compressor. PhD thesis, Northwestern Polytechnical University

  22. Liu Y, Wang X, Yang J, Wu H (2017) An improved steady inverse method for turbomachinery aerodynamic design. Inverse Probl Sci Eng 25(5):633–651

    Article  MathSciNet  Google Scholar 

  23. Yang C, Wu H, Liang Y (2019) A novel three-dimensional inverse method for axial compressor blade surface design. Arab J Sci Eng 44(12):10169–10179

    Article  Google Scholar 

  24. Jameson A, Schmidt W, Turkel E (1981) Numerical solution of the euler equations by finite volume methods using runge kutta time stepping schemes. In: AIAA, fluid and plasma dynamics conference, 14th, Palo Alto, CA, June 23-25, 1981. 15 p

  25. Baldwin BS (1978) Thin-layer approximation and algebraic model for separated turbulent flows. pp 78-257

  26. Blazek J (2015) Computational fluid dynamics: principles and applications, third edition. Elsevier, Amsterdam

    Google Scholar 

  27. Strazisar AJ, Wood JR, Hathaway M, Suder KL (1981) Laser anemometer measurements in a transonic axial-flow fan rotor. J Eng Gas Turb Power 103(2):430–437

    Article  Google Scholar 

  28. Niehuis R, Bohne A, Hoynacki A (2003) Experimental investigation of unsteady flow phenomena in a three-stage axial compressor. Proc Instit Mech Eng Part A: J Power Energy 217(4):341–348

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Power and Energy, Northwestern Polytechnical University, 127 West Youyi Road, Beilin District, Xi’an, 710072, Shaanxi, People’s Republic of China

    Haijian Lou, Hu Wu, Qing Tang & Jinguang Li

  2. Institute of Engineering Thermophysics, Chinese Academy of Sciences, 11 Beisihuanxi Road, Beijing, 100190, People’s Republic of China

    Chen Yang

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  1. Haijian Lou
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  2. Hu Wu
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  4. Qing Tang
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Correspondence to Hu Wu.

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Technical Editor: William Wolf.

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The original version of the article was revised: In the original publication of the article, two equations have been incorrectly cited on page 6 in the paragraph under equation 16. The correct statement should read “Equation 15 presents that by averaging the virtual velocities of the suction and pressure surfaces to obtain the displacement of the camber, while an optimal time step is given in Eq. 16, in order to converge at the fastest rate during the inverse calculation.”

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Lou, H., Wu, H., Yang, C. et al. The improved inverse method for axial compressor based on quasi-three-dimensional model. J Braz. Soc. Mech. Sci. Eng. 46, 6 (2024). https://doi.org/10.1007/s40430-023-04586-z

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