Shock–wave drag of profile flowing by transonic gas flow: history, achievements, problems

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Abstract

This paper presents a review of works on the theory of profile drag and contains an attempt to review the process of basic ideas development about the physical processes that take place at transonic airfoil flow. It should be noted that this field of aerodynamics was replete with erroneous statements at the early stages of its development. The accumulation of experimental data and the improvement of the mathematical apparatus have made it possible to eliminate inaccuracies in the formulation of problems, as well as to significantly improve the mathematical models describing this phenomenon. Nevertheless, a few problems remain unsolved at the present time, requiring further delving into the physics of the phenomenon and improving the mathematical apparatus.

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About the authors

A. S. Petrov

Central Aerohydrodynamic Institute

Author for correspondence.
Email: aspetrov1906@rambler.ru
Russian Federation, Zhukovsky

G. G. Soudakov

Central Aerohydrodynamic Institute

Email: soudakov@mail.ru
Russian Federation, Zhukovsky

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Supplementary files

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2. Fig. 1. Scheme of flow around the profile in the presence of a local supersonic zone

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3. Fig. 2. Wave drag coefficient for the NACA–0012 airfoil: angle of attack α = 0, Reynolds equations, k–ω SST turbulence model

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4. Fig. 3. Shock wave height: angle of attack α = 0, Reynolds equations, k–ω SST turbulence model. The dependence is approximately linear. Deviations from the linear dependence are caused by the shock wave shift downstream with increasing M1 and decreasing curvature of the profile surface at the shock base point (see formula (4.7))

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5. Fig. 4. The M1 number before the shock wave: angle of attack α = 0, Reynolds equations, k–ω SST turbulence model. The curve with diamond-shaped markers was obtained visually from the M1 field, the curve with square markers was obtained from the maximum entropy jump on the shock wave. The dependence is essentially nonlinear.

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6. Fig. 5. Position and shape of the supersonic zone: M¥ = 0.73 – occurrence of the supersonic zone, M¥ = 0.75 – occurrence of the shock

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7. Fig. 6. Distribution of Mach numbers by the height of the supersonic zone

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8. Fig. 7. Comparison of theoretical, calculated and experimental values ​​of shock wave height

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9. Fig. 8. Comparison of the values ​​of wave resistance (5.12) with experimental data [38]

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