NUMERICAL INVESTIGATION OF TRANSONIC SHOCK WAVE CHARACTERISTICS ON SUPERCRITICAL AIRFOILS UNDER VARIOUS FLOW CONDITIONS

Abstract

This study numerically investigates transonic shock wave characteristics over supercritical airfoils using the OpenFOAM-based open-source solver TSLAeroFoam. The numerical setup is validated through comparison with benchmark transonic experimental results. A parametric study is conducted by varying the Mach number from 0.72 to 0.78 and the angle of attack from 3° to 7° to evaluate their effects on shock position, strength, shock–boundary layer interaction, and associated aerodynamic coefficients including lift, drag, and moment. Results indicate that increasing the angle of attack causes shock to move upstream toward the leading edge. Increasing the Mach number leads to a reduction in pressure on the lower surface and a corresponding decrease in lift coefficient. At a fixed angle of 3°, the lift coefficient dropped from nearly 0.71 to 0.60 as Mach number increased from 0.72 to 0.78. Additionally, the lift-to-drag ratio decreased significantly with both Mach number and angle of attack, dropping from approximately 37 to 16 at 3°, and from 12 to 8 at 7° for Mach numbers 0.72 and 0.78, respectively. The findings collectively demonstrate that both Mach number and angle of attack influence shock wave behavior and aerodynamic performance in transonic flows, with stronger effects observed at higher values of both parameters.

Keywords

• CFD
• OpenFOAM
• RAE2822
• Shock
• Transonic
• Wave

References

1. A. O. Yüksel, Ö. Kandemir, L. Uğur, Y. Ostovan, and E. Ayan, “Aerodynamic Buffet Onset Boundary Estimation of a Jet Trainer Aircraft,” in AIAA SCITECH 2023 Forum, 2023, p. 2119.
2. O. Kocaaslan, K. M. Güleren, B. H. Saracoğlu, and T. Yasa, “Dönen Patlama Motorlarindaki Oluşan Dalga Yapısının Sayısal Olarak İncelenmesi,” Isı Bilimi ve Tekniği Dergisi, vol. 44, no. 1, pp. 33–45, 2024.
3. F. Sartor, M. Clement, D. Sipp, and R. Bur, “Dynamics of a shock-induced separation in a transonic flow: a linearized approach,” in 43rd AIAA Fluid Dynamics Conference, 2013, p. 2735, doi: 10.2514/6.2013-2735.
4. X. Liu and L. Squire, “An investigation of shock/boundary-layer interactions on curved surfaces at transonic speeds,” Journal of Fluid Mechanics, vol. 187, pp. 467–486, 1988, doi: 10.1017/S0022112088000527.
5. H. T. B. Ngoc and N. M. Hung, “Study of separation phenomenon in transonic flows produced by interaction between shock wave and boundary layer,” Vietnam Journal of Mechanics, vol. 33, 2011, doi: 10.15625/0866-7136/33/3/210.
6. B. Lee, “Self-sustained shock oscillations on airfoils at transonic speeds,” Progress in Aerospace Sciences, vol. 37, pp. 147–196, 2001, doi: 10.1016/S0376-0421(01)00003-3.
7. A. Alshabu and H. Olivier, “Unsteady Wave Phenomena on a Supercritical Airfoil,” AIAA Journal, vol. 46, pp. 2066–2073, 2008, doi: 10.2514/1.35516.
8. M. Farahani and A. Jaberi, “Experimental Investigation of Shock Waves Formation and Development Process in Transonic Flow,” Scientia Iranica, vol. 24, pp. 2457–2465, 2017, doi: 10.24200/SCI.2017.4309.

9. H. Olivier and I. Klioutchnikov, “A numerical study of pressure/shock waves interactions in transonic airfoil flow using optimized WENO schemes,” in 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010, p. 924. doi: 10.2514/6.2010-924.
10. F. Sartor, C. Mettot, R. Bur, and D. Sipp, “Unsteadiness in transonic shock-wave/boundary-layer interactions: experimental investigation and global stability analysis,” Journal of Fluid Mechanics, vol. 781, pp. 550–577, 2015, doi: 10.1017/jfm.2015.510.
11. E. Bénard, J.-C. Huang, and S. Raghunathan, “Experimental investigation of unsteadiness in transonic shock boundary layer interaction,” in 45th AAAF Symposium of Applied Aerodynamics, 2010, pp. 22–24.
12. P. Bruce, I. Coman, G. Holt, and J. Harvey, “Experimental investigations into transonic shock wave unsteadiness,” in 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2011. p. 1050.
13. W. Chyu and K. Kuwahara, “Computations of transonic flow over an oscillating airfoil with shock-induced separation,” in 20th Aerospace Sciences Meeting, 1982, p. 350.
14. Z. Hu, L. Zhu, X. Mo, and K. Shen, “Numerical study on transonic shock wave buffeting of airfoil,” Journal of Physics: Conference Series, 2024, doi: 10.1088/1742-6596/2879/1/012032.
15. H. Liu, J. Sun, P. Li, D. Zheng, Y. Tao, and Z. Sun, “Investigation on transonic buffet of airfoil within ground effect,” Aerospace Science and Technology, vol. 161, p. 110094, 2025.
16. J. Carter, D. Edwards, and M. Hafez, “Analysis of Transonic Shock Induced Separated Flow Including Normal Pressure Gradients.,” 1983. doi: 10.2514/6.1985-371.
17. A. Vorobiev, S. Gordeyev, E. Jumper, S. Gogineni, A. Marruffo, and D. J. Wittich, “A Low-Dimensional Model of Shock-Wake Interaction Over Turrets at Transonic Speeds,” in 45th AIAA Plasmadynamics and Lasers Conference, 2014, p. 2357.
18. Z. S. Moghadam and A. Jahangirian, “Numerical Study of Active Shock Wave-Turbulent Boundary Layer Interaction Control for Transonic Aerodynamics,” in 30th Congress of the International Council of the Aeronautical Sciences, 2016.
19. S. Matsuo, K. Yokoo, J. Nagao, Y. Nishiyama, T. Setoguchi, H. D. Kim, and S. Yu, “Numerical Study on Transonic Flow with Local Occurrence of Non-Equilibrium Condensation,” Open Journal of Fluid Dynamics, vol. 03, pp. 42–47, 2013, doi: 10.4236/ojfd.2013.32A007.
20. A. Frede and D. Gatti, “Investigation of blowing and suction for turbulent flow control on a transonic airfoil,” International Journal of Heat and Fluid Flow, vol. 113, p. 109769, 2025.
21. L. Zhang, S. Ma, F. Liu, and X. Cui, “Numerical Investigation for Separation Characteristics of Transonic Shock Oscillations Based on Parallel Computing,” Journal of Physics: Conference Series, vol. 1631, 2020, doi: 10.1088/1742-6596/1631/1/012152.
22. B. Li, X. Zhou, L. Luo, and W. Du, “Effects of number of bleed holes on shock-wave/boundary-layer interactions in a transonic compressor stator,” Journal of Thermal Science, vol. 33, no. 2, pp. 611–624, 2024.
23. B. Li, G. Mu, L. Luo, W. Du, and X. Zhou, “Effect of combined boundary layer suction on the separation control in a highly loaded transonic compressor cascade,” Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 238, no. 2, pp. 217–231, 2024.
24. N. Berizzi, D. Gatti, G. Soldati, S. Pirozzoli, and M. Quadrio, “Aerodynamic performance of a transonic airfoil with spanwise forcing,” Journal of Fluid Mechanics, vol. 1010, p. A18, 2025.
25. T. Liu, X. Chen, Z. Tian, and J. Li, “Prediction of transonic shock buffet over supercritical airfoil OAT15A based on zonal detached-eddy simulation,” Applied Sciences, vol. 14, no. 21, p. 9628, 2024.
26. O. V. Özdemir, H. Amiri, and U. C. Küçük, “RAE M2129 S-Shaped Air Intake CFD Analysis Using OpenFOAM,” in 2023 10th International Conference on Recent Advances in Air and Space Technologies (RAST), 2023, pp. 1–6.
27. M. N. Kaya, S. Satcunanathan, M. Meinke, and W. Schröder, “Leading-Edge Noise Mitigation on a Rod–Airfoil Configuration Using Regular and Irregular Leading-Edge Serrations,” Applied Sciences, vol. 15, no. 14, p. 7822, 2025.
28. E. Canli, H. Kucuksariyildiz, and K. Carman, “Impact assessment of new generation high-speed agricultural tractor aerodynamics on transportation fuel consumption and related phenomena,” Environmental Science and Pollution Research, vol. 30, no. 3, pp. 6658–6680, 2023.
29. M. Manolesos, Y. Celik, H. Ramsay, R. Karande, B. Wood, I. Dinwoodie, I. Masters, M. Harrold and G. Papadakis, “Performance improvement of a Vestas V52 850kW wind turbine by retrofitting passive flow control devices,” in Journal of Physics: Conference Series, vol. 2767, no. 2, 2024.
30. M. E. Tolu, O. Babayiğit, and D. N. Özen, “Investigation of the effects of rib application on cooling in a turbine blade,” Konya Journal of Engineering Sciences, vol. 13, no. 1, pp. 11–24, 2025.
31. K. K. You, J. H. Ha, and S. C. Lee, “An Automated Aerodynamic Analysis System in Missile Based on Open-Source Software,” International Journal of Aeronautical and Space Sciences, vol. 24, no. 3, pp. 592–605, 2023.
32. NextFOAM, “NextFOAM CFD Framework”, 2025. [Online]. Available: https://github.com/nextfoam/nextfoam-cfd. [Accessed: Jun. 6, 2025].
33. P. H. Cook, M. C. P. Firmin, and M. A. McDonald, Aerofoil RAE 2822: pressure distributions, and boundary layer and wake measurements. AGARD Advisory Report AR-138, 1979.