Abstract
The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 106–2.55 · 106) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.
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References
J. K. H. Holger Babinsky, Shock Wave-Boundary-Layer Interactions: Cambridge Aerospace (Cambridge University Press, Cambridge, 2011).
P. K. Chang, “Characteristics of Separated Flows,” in Separation of Flow, Ed. by P. K. Chang (Pergamon Press, Oxford, London–Edinburgh, 1970), Chapter 7, pp. 272–335.
E. H. Hirschel, Basics of Aerothermodynamics (Springer, 2015).
H. Schlichting, Boundary Layer Theory (McGraw, New York, 1960).
R. E. Spall and M. R. Malik, “Goertler Vortices in Supersonic and Hypersonic Boundary Layers,” Phys. Fluids, A: Fluid Dyn. 1 (11), 1822–1835 (1989).
J. J. Ginoux, “On Some Properties of Reattaching Laminar and Transitional High Speed Flows,” Tech. Note K´arm´an Inst. for Fluid Dynamics, No. 53 (Rhode-Saint-Genése, 1969).
V. N. Brazhko, “Periodic Structure of the Flow and Heat Transfer in the Region of Supersonic Flow Reattachment,” Uch. Zap. TsAGI 10 (2), 113–118 (1979).
D. A. de la Chevalerie, A. Fonteneau, L. de Luca, and G. Cardone, “Görtler-Type Vortices in Hypersonic Flows: The Ramp Problem,” Exp. Thermal Fluid Sci. 15 (2), 69–81 (1997).
J. J. Ginoux, “Streamwise Vortices in Reattaching High-Speed Flows—A Suggested Approach,” AIAA J. 9 (4), 759–760 (1971).
G. F. Glotov and E. K. Moroz, “Streamwise Vortices in Supersonic Flows with Separation Regions,” Uch. Zap. TsAGI 8 (4), 44–53 (1977).
Y. Ishiguro, H. Nagai, K. Asai, and K. Nakakita, “Visualization of Hypersonic Compression Corner Flows Using Temperature-and Pressure-Sensitive Paints,” AIAA Paper No. 2007-118 (2007).
T. Kuriki, H. Sakaue, O. Imamura, and K. Suzuki, “Temperature-Cancelled Anodized-Aluminum Pressure Sensitive Paint for Hypersonic Compression Corner Flows,” AIAA Paper No. 2010-673 (2010).
L. de Luca, G. Cardone, and G. G. M. Carlomagno, “Goertler Vortices in Hypersonic Flow Detected by IR Thermography,” in Proc. of the Int. Congr. Instrument. in Aerospace Simulat. Facilities, Saint Louis, France, September 20–23, 1993 (IEEE, 1993).
L. de Luca, G. Cardone, D. A. de la Chevalerie, and A. Fonteneau, “Viscous Interaction Phenomena in Hypersonic Wedge Flow,” AIAA J. 33 (12), 2293–2298 (1995).
G. Simeonides and W. Haase, “Experimental and Computational Investigations of Hypersonic Flow about Compression Ramps,” J. Fluid Mech. 283 (1), 17–42 (1995).
L. de Luca, G. Cardone, D. A. de la Chevalerie, and A. Fonteneau, “Goertler Instability of a Hypersonic Boundary Layer,” Exp. Fluids 16 (1), 10–16 (1993).
V. I. Zapryagaev and I. N. Kavun, “Mechanism of Formation of Streamwise Vortices behind the Reattachment Line of a Supersonic Separated Flow in the Compression Corner,” Uch. Zap. TsAGI 47 (3), 27–37 (2016).
C. Whang and X. Zhong, “Secondary Goertler Instability in Hypersonic Boundary Layers,” AIAA Paper No. 2001-0273 (2001).
S. Navarro-Martinez and O. R. Tutty, “Numerical Simulation of Görtler Vortices in Hypersonic Compression Ramps,” Comput. Fluids 34 (2), 225–247 (2005).
G. G. Chernyi, Introduction to Hypersonic Flow (Academic Press, New York, London, 1961).
D. Ault and D. Van Wie, “Comparison of Experimental Results and Computational Analysis for the External Flowfield of a Scramjet Inlet at Mach 10 and 13,” in Proc. of the 4th Symp. Multidisciplinary Analysis and Optimization, Cleveland (USA), September 21–23, 1992; https://doi.org/10.2514/MMAO92.
Z. Hong-jun and S. Qing, “Experimental Investigation of Leading Edge Bluntness Effects on Hypersonic Two-Dimensional Inlet,” Procedia Eng. 99, 1582–1590 (2015).
V. Ya. Borovoy, “Effect of Bluntness of Gas-Compressing Ramps on Starting of a Model Inlet,” Uch. Zap. TsAGI 47 (3), 56–70 (2016).
K. Heffner, A. Chpoun, and J. Lengrand, “Experimental Study of Transitional Axisymmetric Shock-Boundary Layer Interactions at Mach 5,” AIAA Paper No. 93-3131 (1993).
S. G. Mallinson, S. L. Gai, and N. R. Mudford, “Leading-Edge Bluntness Effects in High Enthalpy, Hypersonic Compression Corner Flow,” AIAA J. 34 (11), 2284–2290 (1996).
H. K. Cheng, J. Gordon Hall, T. C. Golian, amd A. Hertzberg, “Boundary-Layer Displacement and Leading-Edge Bluntness Effects in High-Temperature Hypersonic Flow¡” J. Aerospace Sci. 28 (5), 353–381 (1961).
M. S. Holden, “Boundary-Layer Displacement and Leading-Edge Bluntness Effects on Attached and Separated Laminar Boundary Layers in a Compression Corner. 2. Experimental Study,” AIAA J. 9 (1), 84–93 (1971).
J. Bibin and K. Vinayak, “Effect of Leading Edge Bluntness on the Interaction of Ramp Induced Shock Wave with Laminar Boundary Layer at Hypersonic Speed,” Comput. Fluids 96, 177–190 (2014).
V. Y. Borovoy, A. S. Skuratov, and I. V. Struminskaya, “On the Existence of a Threshold Value of the Plate Bluntness in the Interference of an Oblique Shock with Boundary and Entropy Layers,” Fluid Dyn. 43 (3), 369–379 (2008).
V. E. Mosharov and V. N. Radchenko, “Measurements of Heat Flux Fields in Short-Duration Wind Tunnels by Temperature-Sensitive Paints,” Uch. Zap. TsAGI 38 (1/2), 94–101 (2007).
W. Saric, “Görtler Vortices,” Annual Rev. Fluid Mech. 26 (1), 379–409 (1994).
V. N. Zhigulev and A. M. Tumin, Emergence of Turbulence (Nauka, Moscow, 1987) [in Russian].
I. V. Egorov, A. V. Fedorov, and V. G. Soudakov, “Direct Numerical Simulation of Disturbances Generated by Periodic Suction–Blowing in a Hypersonic Boundary Layer,” Theoret. Comput. Fluid Dyn. 20 (1), 41–54 (2006).
H. Ludeke and P. Lrogmann, “Numerical and Experimental Investigations of Laminar/Turbulent Boundary Layer Transition,” in Proc. of the Europ. Congr. on Computational Methods in Applied Sciences and Engineering, Barcelona, September 11–14, 2000.
V. V. Shvedchenko, “3D Secondary Separation at Supersonic Flow over the Compression Ramp,” TsAGI Sci. J. 41 (6), 631–650 (2010). 989
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Original Russian Text © P.V. Chuvakhov, V.Ya. Borovoy, I.V. Egorov, V.N. Radchenko, H. Olivier, A. Roghelia.
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Chuvakhov, P.V., Borovoy, V.Y., Egorov, I.V. et al. Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow. J Appl Mech Tech Phy 58, 975–989 (2017). https://doi.org/10.1134/S0021894417060037
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DOI: https://doi.org/10.1134/S0021894417060037