Effective Inverse Method for High-loaded Axial Compressor Based on Pre-compression Theory

Document Type : Regular Article


School of Power and Energy, Northwestern Polytechnical University, Xi’an, Shanxi, 710129, China



The S1 stream surface inverse method for a single-stage axial transonic compressor was developed and studied under the guidance of the quasi-three-dimensional viscous design theory, based on computational fluid dynamics (CFD), in order to establish and solve governing equations. The re--adjusted load distribution of the S1 stream surface was imposed to obtain a special profile for the rotor, which is known as S-shaping. This changed the structure and weaken the strength of the shock due to the pre-compression effect. In order to match the inlet flow angle of the downstream stator, inverse modification for multiple S1 stream surfaces of the stator blade was conducted in the present study at the same time. As it is known, the S-shaped profile is commonly applied to supersonic flows. Therefore, NASA stage 37 was selected as the design case to verify whether the present inverse method is effective and reliable. Stage 37 was re-designed by stacking five S1 stream surfaces. The profiles of these surfaces were renewed through the inverse design. The results revealed that, compared to the prototype, the aerodynamic performance of the re-designed one was apparently promoted within the stable working range. The adiabatic efficiency at the design point increased by approximately 0.4%, and the pressure ratio improved by approximately 4.5%. In addition, analysis result for the characteristic line revealed that the performance of the redesigned blades at off-design points significantly improved.


Main Subjects

Ahmadi, M., & Ghaly, W. S. (1998). Aerodynamic inverse design of turbomachinery cascades using a finite volume method on unstructured meshes. Inverse Problems in Engineering, 6, 281–298. https://doi.org/10.1080/174159798088027680##
Baldwin, B. S. (1978, January). Thin-layer approximation and algebraic model for separated turbulent flows. American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, Huntsville, Ala.##
Blazek, J. (2015). Computational Fluid Dynamics: Principles and Applications. Butterworth-Heinemann.##
Chu, W., Liu, Q., & Hu, C. (2009). Principles of Aviation Vane Machines. Northwest University of Technology Press.##
Dang, T. (1995, January). Inverse method for turbomachine blades using shock-capturing techniques. 31st Joint Propulsion Conference and Exhibit.##
Dang, T. Q. (1993). A fully three-dimensional inverse method for turbomachinery blading in transonic flows. Journal of Turbomachinery 115, 354-361. https://doi.org/10.1115/1.2929241##
Hawthorne, W. R., Wang, C., Tan, C. S., & McCune, J. E. (1984). Theory of blade design for large deflections: Part I—Two-dimensional cascade. Journal of Engineering for Gas Turbines & Power, 106, 346–353. https://doi.org/10.1115/1.3239571##
Hield, P. (2008, January). Semi-inverse design applied to an eight-stage transonic axial flow compressor. Turbo Expo: Power for Land, Sea, and Air.##
Hu, J. (2014). Principles of aviation vane machines. National Defense Industry Press.##
Jameson, A., Schmidt, W., & Turkel, E. (1981, June). Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes. 14th fluid and Plasma Dynamics Conference, Palo Alto, CA.##
Lighthill, M. J. (1945). A new method of two-dimensional aerodynamic design. Aeronautical Research
 Council R and M
2112. https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=7C78BA426572BDA97B4D0E6EE7F17043?doi=
Liu, Z. (2017). Research of full three-dimensional viscous inverse design method for multi-stage axial compressor. [PhD. thesis, Northwestern Polytechnical University]. Shaanxi, China.##
Liu, Z., Wu, H., & Tang, X. (2015). Application of improved inverse method boundary condition in turbomachiny. Journal of Engineering Thermophysics, 36, 2132–2136. https://kns.cnki.net/kcms2/article/abstract?v=3uoqIhG8C44YLTlOAiTRKibYlV5Vjs7ir5D84hng_y4D11vwp0rrtYebZZdUY3FI3MkboggYCoQtc_s0u_IXGkFPdma8AsYm&uniplatform=NZKPT##
Medd, A. J., Dang, T. Q., & Larosiliere, L. M. (2003, January). 3D inverse design loading strategy for transonic axial compressor blading. Turbo Expo: Power for Land, Sea, and Air.##
Suder, K. L. (1996). Experimental Investigation of the Flow Field in A Transonic, Axial Flow Compressor with Respect to the Development of Blockage and Loss. Case Western Reserve University.##
Tan, C. S., Hawthorne, W. R., McCune, J. E., & Wang, C. (1984). Theory of blade design for large deflections: Part II—annular cascades.##
Tiow, W. T., & Zangeneh, M. (2000, May). A three-dimensional viscous transonic inverse design method. Turbo Expo: Power for Land, Sea, and Air.##
van Rooij, M., and Medd, A. (2012, June). Reformulation of a three-dimensional inverse design method for application in a high-fidelity CFD environment. In Turbo Expo: Power for Land, Sea, and Air (Vol. 44748, pp. 2395-2403).  https://doi.org/10.1115/GT2012-69891##
Wu, C. H. (1952). A general theory of three-dimensional flow in subsonic and supersonic turbomachines of axial-, radial, and mixed-flow types. National Aeronautics and Space Administration Washington DC.##
Yang, C., Wu, H., and Liang, Y. (2019). A novel three-dimensional inverse method for axial compressor blade surface design. Arabian Journal for Science and Engineering, 44(12), 10169-10179. https://doi.org/10.1007/s13369-019-04083-3##
Yang, J., Liu, Y., Wang, X., & Wu, H. (2016, June). 3D viscous inverse design of turbomachinery using one-equation turbulence model. Turbo Expo: Power for Land, Sea, and Air.##
Yang, J., Liu, Y., Wang, X., & Wu, H. (2017). An improved steady inverse method for turbomachinery aerodynamic design. Inverse Problems in Science and Engineering, 25(5), 633-651. https://doi.org/10.1080/17415977.2016.1178259##
Yang, J., Liu, Z., Shao, F., & Wu, H. (2015). Transpiration boundary condition based on inverse method for turbomachinery aerodynamic design: on the solution existence and uniqueness. Journal of Propulsion Technology, (4), 579–586. https://doi.org/10.13675/j.cnki.tjjs.2015.04.014##
Zangeneh, M., Goto, A., & Harada, H. (1998). On the design criteria for suppression of secondary flows in centrifugal and mixed flow impellers. Journal of Turbomachinery, 120, 723–735. https://doi.org/10.1115/1.2841783##
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. https://doi.org/10.1243/0954406991522167##
Volume 16, Issue 8
August 2023
Pages 1675-1689
  • Received: 12 October 2022
  • Revised: 19 March 2023
  • Accepted: 06 April 2023
  • Available online: 31 May 2023