Solving of the inverse problem for a multielement airfoil in a compressible viscous gas flow

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Abstract

An iterative method for solving the inverse problem for a multielement (slotted) airfoil at high speeds in a viscous compressible flow, using RANS methods, has been developed. It is an evolution of a similar method developed earlier by the authors for low speed conditions. The method is based on the well-known principle of residual correction, according to which corrections to the current geometry are generated on the basis of the difference between the target and current pressure distribution. A brief description of the algorithm and the methods used is given. Examples for the slotted airfoil design corresponding to the target pressure distribution are given, including cases with the shock waves existence.

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About the authors

A. L. Bolsunovsky

Central Aerohydrodynamic Institute

Author for correspondence.
Email: bolsmail@mail.ru
Russian Federation, Zhukovsky

N. P. Busoverya

Central Aerohydrodynamic Institute

Email: bolsmail@mail.ru
Russian Federation, Zhukovsky

S. V. Gerasimov

Central Aerohydrodynamic Institute

Email: bolsmail@mail.ru
Russian Federation, Zhukovsky

M. A. Gubanova

Central Aerohydrodynamic Institute

Email: bolsmail@mail.ru
Russian Federation, Zhukovsky

References

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  8. Bolsunovsky A.L., Buzoverya N.P., Gubanova I.A. et al. Solution of the inverse problem for a multi-element airfoil in the framework of RANS-equations // TsAGI Sci. J., 2021, vol. 52, no. 3. (in Russian)
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Supplementary files

Supplementary Files
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2. Fig. 1. Calculated and experimental [1] pressure distribution on a multi-link profile, M = 0.2, Re = 9×106, α = 16°

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3. Fig. 2. NASA slotted wing concept [6]

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4. Fig. 3. The principle of constructing residual correction methods

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5. Fig. 4. Structure of the method used

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6. Fig. 5. Splitting of the pressure discrepancy into subsonic and supersonic parts.

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7. Fig. 6. Structured multi-block grid

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8. Fig. 7. Vortex features on the panels of a multi-link contour

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9. Fig. 8. Example of solving the inverse problem for M = 0.5, ∆Су, ∆Сx – changes in the integral characteristics compared to the characteristics of the original profile

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10. Fig. 9. Example of solving the inverse problem for M = 0.6

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11. Fig. 10. Convergence of the solution of the inverse problem at M = 0.6

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12. Fig. 11. Mach number field in the mode M = 0.768, Cy = 0.75

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13. Fig. 12. Pressure distribution in the mode M = 0.768, Cy = 0.75

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14. Fig. 13. Calculated polars of cut and insulated profiles

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