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Unsteady inverse problem of type B for 2-D transonic flow: A variational formulation

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Journal of Shanghai University (English Edition)

Abstract

A family of variational principles (VP) has been developed for the unsteady inverse problem of the second type IB. It opens new ways for the inverse shape design of unsteady airfoils and can serve as key basis of multipoint inverse shape design of steady airfoils and cascades.

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References

  1. Dulikravich G. S., Aerodynamic shape design and optimization: status and trends, J. Aircraft, 1992, 29(6): 1020–1025

    Article  Google Scholar 

  2. Liu G. L., Advances in research on inverse & hybrid problems of turbomachine aerothermodynamics in China, Inverse Problems in Engrg, 1995, 2(1): 1–27

    Google Scholar 

  3. Nixon D. (ed.), Unsteady Transonic Aerodynamics, Progress in Astron. & Aeronautics (Vol. 120), AIAA, Washington D.C., 1989

    Google Scholar 

  4. Liu G. L., Variational formulation of 2-D unsteady transonic aerodynamics of oscillating cascades, Proc. 5th Intl. Symp. Unsteady Aerodynamics & Aeroelasticity of Turbomachines & Propellers, Beijing, China, Sep. 1989: 76–85

  5. Liu G. L., Formulation of inverse problem of 2-D unsteady flow around oscillating airfoils by VP, Acta Aerodynamica Sinica, 1996, 14(1): 1–6 (or: Proc. Intl. Conf. Aerohydroelasticity, Beijing, China, Oct, 1993: 82–97)

    Google Scholar 

  6. Liu G. L & Guo J. H., Variable-domain variational formulation of inverse problem of 2-D unsteady flow, AIAA Paper 1998, 98: 0124

    Google Scholar 

  7. Finlayson B. A., The Method of Weighted Residuals & VP, AP, New York, 1972

    Google Scholar 

  8. Liu G. L., A general variational theory of multipoint inverse design of 2-D transonic airfoils based on an artificial airfoil-oscillation concept, Inverse Problems in Engrg Mechanics, (ed. by M. Tanaka & G. S. Dulikravich,) Elsevier, Amsterdam, 1998: 391–398

    Google Scholar 

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Project supported by the National Natural Science Foundation of China (59876017)

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Liu, G. Unsteady inverse problem of type B for 2-D transonic flow: A variational formulation. J. of Shanghai Univ. 3, 1–3 (1999). https://doi.org/10.1007/s11741-999-0020-9

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  • DOI: https://doi.org/10.1007/s11741-999-0020-9

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