Abstract
A novel three-dimensional inverse method based on the time-accurate solution of Navier–Stokes equations for axial compressor design is proposed in this work. The main novelty lies in the derivation of an inverse design boundary condition established on the conservation of Riemann invariant in order to directly design the blade surface. Specifically, a dynamic mesh technique is employed to update the grids and reduce the computational costs. In addition, some restrictions are imposed on the blade surface movement in order to avoid unrealistic airfoil profiles and guarantee computational robustness. Two redesign procedures are presented, including shock wave strength restrain for the NASA Rotor 37 stage and integrated controlled diffusion airfoil concept design for the Stage 35. Results indicate that this novel inverse method is effective for detailed axial compressor design.
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Abbreviations
- 2D:
-
Two-dimensional
- 3D:
-
Three-dimensional
- CDA:
-
Controlled diffusion airfoil
- CFD:
-
Computational fluid dynamics
- CFL:
-
Courant–Friedrichs–Lewy
- LU-SGS:
-
Lower–upper symmetric Gauss–Seidel
- MCA:
-
Multiple circular arc airfoil
- NURBS:
-
Non-uniform rational B-spline
- RANS:
-
Reynolds-averaged Navier–Stokes equations
References
Sanz, J.M.: Automated design of controlled-diffusion blades. J. Turbomach. 110(4), 540–544 (1988)
Sanz, J.M.: Lewis Inverse Design Code (LINDES): Users Manual. NASA Lewis Reasearch Centre, Cleveland (1987)
Dang, T.: A fully three-dimensional inverse method fo turbomachinery blading in transonic flows. J. Turbomach. 115(2), 354–361 (1993)
Dang, T.: Inverse method for turbomachine blades using shock-capturing techniques. In: 31st Joint Propulsion Conference and Exhibit, San Diego, CA (1995)
Dang, T.; Van, M.P.C.; Larosiliere, L.M.: Design of aspirated compressor blades using three-dimensional inverse method. In: Proceedings of ASME Turbo Expo2003, Atlanta, Georgia (2003)
Daneshkhah, K.; Ghaly, W.: An inverse blade design method for subsonic and transonic viscous flow in compressors and turbines. Inverse Probl. Sci. Eng. 14(3), 211–231 (2006)
Arbabi, A.; Ghaly, W.; Medd, A.: Aerodynamic inverse blade design of axial compressors in three-dimensional flow using a commercial CFD Program. In: Proceedings of ASME Turbo Expo 2017, Charlotte, NC (2017)
Qiu, X.; Ji, M.; Dang, T.: Three-dimensional viscous inverse method for axial blade design. Inverse Probl. Sci. Eng. 17(8), 1019–1036 (2009)
Roidl, B.; Ghaly, W.: Redesign of a low speed turbine stage using a new viscous inverse design method. J. Turbomach. 133(1), 2681–2691 (2011)
Van Rooij, M.P.C.; Dang, T.; Larosiliere, L.M.: Improving aerodynamic matching of axial compressor blading using a three-dimensional multistage design method. J. Turbomach. 129(1), 108–118 (2007)
Van Rooij, M.P.C.; Dang, T.; Larosiliere, L.M.: Enhanced blade row matching capabilities via 3D multistage inverse design and pressure loading manager. In: Proceedings of ASME Turbo Expo 2008, Berlin, Germany (2008)
Van Rooij, M.P.C.; Medd, A.J.: Reformulation of a three-dimensional inverse design method for application in a high-fidelity CFD environment. In: Proceedings of ASME Turbo Expo 2012, Copenhagen, Denmark (2012)
Zangeneh, M.; Goto, A.; Harada, H.: On the design criteria for suppression of secondary flows in centrifugal and mixed flow impellers. J. Turbomach. 120(4), 723–735 (1998)
Zangeneh, M.; Goto, A.; Harada, H.: On the Role of three-dimensional inverse design methods in turbomachinery shape optimization. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 213(1), 27–42 (1999)
Tiow, W.T.; Zangeneh, M.: A three-dimensional viscous transonic inverse design method. In: Proceedings of ASME Turbo Expo 2000, Munich, Germany (2000)
Watanabe, H.; Zangeneh, M.: Design of the blade geometry of swept transonic fans by 3D inverse design. In: Proceedings of ASME Turbo Expo 2003, Atlanta, Georgia (2003)
Sun, G.; Sun, Y.; Wang, S.: Artificial neural network based inverse design: airfoils and wings. Aerosp. Sci. Technol. 42, 415–428 (2015)
Shumal, M.; Nili-Ahmadabadi, M.; Shirani, E.: Development of the ball-spine inverse design algorithm to swirling viscous flow for performance improvement of an axisymmetric bend duct. Aerosp. Sci. Technol. 52, 181–188 (2016)
Yang, J.; Liu, Y.; Wang, X.; et al.: An improved steady inverse method for turbomachinery aerodynamic design. Inverse Probl. Sci. Eng. 25(5), 633–651 (2017)
Ferlauto, M.: A pseudo-compressibility method for solving inverse problems based on the 3D incompressible Euler equations. Inverse Probl. Sci. Eng. 23(5), 798–817 (2015)
Jameson, A.; Schmidt, W.; Turkel, E.: Numerical solutions of the euler equations by finite volume methods using Runge–Kutta time-stepping schemes. In: 14th Fluid and Plasma Dynamics Conference, Alto, CA (1981)
Steger, J.L.; Warming, R.F.: Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys. 40(2), 263–293 (1981)
Yoon, S.; Jameson, A.: Lower–upper symmetric-Gauss–Seidel method for the Euler and Navier–Stokes equations. AIAA J. 26(9), 1025–1026 (1988)
Baldwin, B.; Lomax, H.; Thin-layer approximation and algebraic model for separated turbulent flow. In: 16th AIAA Aerospace Sciences Meeting, Huntsville, Alabama (1978)
Giles, M.: UNSFLO: A Numerical Method for the Calculation of Unsteady Flow in Turbomachinery. Gas Turbine Laboratory, Massachusetts Institute of Technology, Cambridge (1991). (GTL Report 205)
Liu, Z.; Wu, H.: A new three-dimensional viscous inverse design method for axial compressor blade. In: Proceedings of ASME Turbo Expo 2016, Seoul, South Korea (2016)
Reid, L.; Moore, R.D.: Design and Overall Performance of Four Highly Loaded, High Speed Inlet Stages for an Advanced High-Pressure-Ratio Core Compressor. Lewis Research Center, NASA, Washington (1978). (NASA-TP-1337)
Suder, K.L.: Experimental Investigation of the Flow Field in a Transonic, Axial Flow Compressor with Respect to the Development of Blockage and Loss. Lewis Research Center, NASA, Washington (1996). (NASA-TM-107310)
Denton, J.D.: Lessons from rotor 37. J. Therm. Sci. 6(1), 1–13 (1997)
Hobbs, D.E.; Weingold, H.D.: Development of controlled diffusion airfoils for multistage compressor application. J. Eng. Gas Turb. Power 106(2), 271–278 (1984)
Dang, T.; Damle, S.; Qiu, X.: Euler-based inverse method for turbomachine blades, part 2: three-dimensional flows. AIAA J. 38(11), 2007–2013 (2000)
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This work was supported by the National Natural Science Foundation of China (Grant Number 51076131).
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Yang, C., Wu, H. & Liang, Y. A Novel Three-Dimensional Inverse Method for Axial Compressor Blade Surface Design. Arab J Sci Eng 44, 10169–10179 (2019). https://doi.org/10.1007/s13369-019-04083-3
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DOI: https://doi.org/10.1007/s13369-019-04083-3