Abstract
Results of experiments aimed at studying the linear and nonlinear stages of the development of natural disturbances in the boundary layer on a swept wing at supersonic velocities are presented. The experiments are performed on a swept wing model with a lens-shaped airfoil, leading-edge sweep angle of 45°, and relative thickness of 3%. The disturbances in the flow are recorded by a constant-temperature hot-wire anemometer. For determining the nonlinear interaction of disturbances, the kurtosis and skewness are estimated for experimentally obtained distributions of the oscillating signal over the streamwise coordinate or along the normal to the surface. The disturbances are found to increase in the frequency range from 8 to 35 kHz in the region of their linear development, whereas enhancement of high-frequency disturbances is observed in the region of their nonlinear evolution. It is demonstrated that the growth of disturbances in the high-frequency spectral range (f > 35 kHz) is caused by the secondary instability.
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References
D. Arnal, G. Casalis, and J. C. Juillen, “Experimental and Theoretical Analysis of Natural Transition on ‘Infinite’ Swept Wing,” in Laminar-Turbulent Transition (Springer-Verlag, Berlin, 1990), pp. 311–325.
H. L. Reed and W. S. Saric, “Stability of Three-Dimensional Boundary Layers,” Ann. Rev. Fluid Mech. 21, 235–284 (1989).
A. V. Boiko, G. R. Grek, A. V. Dovgal, and V. V. Kozlov, Origination of Turbulence in Near-wall Flows (Nauka, Novosibirsk, 1999) [in Russian].
H. Bippes, “Basic Experiments on Transition in Three-Dimensional Boundary Layers Dominated by Crossflow Instability,” Prog. Aerospace Sci. 35, 363–412 (1999).
D. I. A. Poll, “Some Observations on the Transition Process on the Wind Ward Face of a Long Yawed Cylinder,” J. Fluid Mech. 150, 329–356 (1985).
Y. Kohama, “Some Expectations on the Mechanism of Cross-Flow Instability in a Swept-Wing Flow,” Acta Mech. 66, 21–38 (1987).
T. M. Fischer and U. Dallmann, “Primary and Secondary Stability Analysis of a Three-Dimensional Boundary-Layer Flow,” Phys. Fluids A 3, 2378–2391 (1991).
P. Nitschke-Kowsky and H. Bippes, “Instability and Transition of a Three-Dimensional Boundary Layer on a Swept Flat Plate,” Phys. Fluids 31, 786–795 (1988).
Y. Kohama, W. S. Saric, and J. A. Hoos, “A High-Frequency, Secondary Instability of Cross-Flow Vortices that Leads to Transition,” in Proc. Conf. on the Boundary Layer Transition and Control, Cambridge, April 8–12, 1991 (Roy. Aeronaut. Soc., London, 1991), pp. 4.1–4.13.
H. Deyhle and H. Bippes, “Disturbance Growth in an Unstable Three-Dimensional Boundary Layer and Its Dependence on Environmental Conditions,” J. Fluid Mech. 316, 73–113 (1996).
M. Kawakami, Y. Kohama, and M. Okutsu, “Stability Characteristics of Stationary Crossflow Vortices in Three-Dimensional Boundary Layer,” AIAA Paper No. 99-0811 (1999).
V. G. Chernoray, A. V. Dovgal, V. V. Kozlov, and L. Loefdahl, “Experiments on Secondary Instability of Streamwise Vortices in a Swept-Wing Boundary Layer,” J. Fluid Mech. 534, 295–325 (2005).
A. V. Boiko, V. V. Kozlov, V. V. Syzrantsev, and V. A. Shcherbakov, “Experimental Investigation of High-Frequency Secondary Disturbances in a Swept-Wing Boundary Layer,” Prikl. Mekh. Tekh. Fiz. 36(3), 74–83 (1995) [Appl. Mech. Tech. Phys. 36 (3), 385–393 (1995)].
E. White and W. Saric, “Secondary Instability of Crossflow Vortices,” J. Fluid Mech. 525, 275–308 (2005).
M. R. Malik, F. Li, M. M. Choudhari, and C.-L. Chang, “Secondary Instability of Crossflow Vortices and Swept-Wing Boundary-Layer Transition,” J. Fluid Mech. 399, 85–115 (1999).
P. Wassermann and M. Kloker, “Transition Mechanisms Induced by Travelling Crossflow Vortices in a Three-Dimensional Boundary Layer,” J. Fluid Mech. 483, 67–89 (2003).
W. Koch, F. P. Bertolotti, A. Stolte, and S. Hein, “Nonlinear Equilibrium Solutions in a Three-Dimensional Boundary Layer and Their Secondary Instability,” J. Fluid Mech. 406, 131–174 (2000).
T. S. Haynes and H. L. Reed, “Simulation of Swept-Wing Vortices Using Nonlinear Parabolized Stability Equations,” J. Fluid Mech. 405, 325–349 (2000).
M. Högberg and D. Henningson, “Secondary Instability of Crossflow Vortices in Falkner-Skan-Cooke Boundary Layers,” J. Fluid Mech. 368, 339–357 (1998).
M. R. Malik, F. Li, and C.-L. Chang, “Nonlinear Crossflow Disturbances and Secondary Instabilities in Swept-Wing Boundary Layers,” in Nonlinear Instability and Transition in Three-Dimensional Boundary Layers (Kluwer, Dordrecht, 1996), pp. 257–266.
C. Mielke and L. Kleiser, “Investigation of Transition to Turbulence in a 3D Supersonic Boundary Layer,” in Laminar-Turbulent Transition (Springer-Verlag, Berlin, 2000), pp. 397–402.
F. Li and M. Choudhary, “Spatially Developing Secondary Instabilities in Compressible Swept Airfoil Boundary Layers,” Theoret. Comput. Fluid Dyn. 25, 65–84 (2011).
W. S. Saric and H. L. Reed, “Supersonic Laminar Flow Control on Swept Wings Using Distributed Roughness,” AIAA Paper No. 2002-0147 (2002).
Yu. G. Ermolaev, A. D. Kosinov, V. Ya. Levchenko, and N. V. Semenov, “Instability of a Three-Dimensional Boundary Layer,” Prikl. Mekh. Tekh. Fiz. 36(6), 50–54 (1995) [Appl. Mech. Tech. Phys. 36 (6), 840–843 (1995)].
N. V. Semionov, Yu. G. Ermolaev, A. D. Kosinov, and V. Ya. Levchenko, “Experimental Investigation of Development of Disturbances in a Supersonic Boundary Layer on a Swept Wing,” Teplofiz. Aeromekh. 10(3), 357–368 (2003) [Thermophys. Aeromech. 10 (3), 347–358 (2003)].
N. V. Semionov and A. D. Kosinov, “Method of Laminar-Turbulent Transition Control of Supersonic Boundary Layer on a Swept Wing,” Teplofiz. Aeromekh. 14(3), 353–357 (2007) [Thermophys. Aeromech. 14 (3), 337–342 (2007)].
N. V. Semionov, Yu. G. Ermolaev, and A. D. Kosinov, “Evolution of Disturbances in a Laminarized Supersonic Boundary Layer on a Swept Wing,” Prikl. Mekh. Tekh. Fiz. 49(2), 40–46 (2008) [Appl. Mech. Tech. Phys. 49 (2), 188–193 (2008)].
Yu. G. Ermolaev, A. D. Kosinov, and N. V. Semionov, “Experimental Investigation of Stability of a Supersonic Boundary Layer on a Swept Wing at M = 2,” Uch. Zap. TsAGI 42(1), 3–11 (2011).
G. L. Kolosov, A. V. Panina, A. D. Kosinov, et al., “Spatial Wave Structure of Controlled Disturbances in a Three-Dimensional Supersonic Boundary Layer,” Vestn. Novosib. Gos. Univ., Ser. Fiz. 6(4), 5–15 (2011).
S. A. Gaponov and B. V. Smorodskii, “Linear Stability of Three-Dimensional Boundary Layers,” Prikl. Mekh. Tekh. Fiz. 49(2), 3–14 (2008) [Appl. Mech. Tech. Phys. 49 (2), 157–166 (2008)].
A. D. Kosinov, N. V. Semionov, and Yu. G. Yermolaev, “Disturbances in Test Section of T-325 Supersonic Wind Tunnel,” Preprint No. 6-99 (Inst. Theor. Appl. Mech., Sib. Branch, Russian Acad. of Sci., Novosibirsk, 1999).
E. N. L’vovskii, Statistical Methods of Constructing Empirical Formulas (Vysshaya Shkola, Moscow, 1988) [in Russian].
M. Kendall and R. L. Kimmel, “Nonlinear Disturbances in Hypersonic Laminar Boundary Layer,” AIAA Paper No. 91-0320 (1990).
A. D. Kosinov and A. I. Semisynov, “Character of Evolution of Natural Disturbances in a Supersonic Boundary Layer on a Flat Plate,” Teplofiz. Aeromekh. 10(1), 41–46 (2003) [Thermophys. Aeromech. 10 (1), 39–44 (2003)].
N. Chokani, D. A. Bountin, A. N. Shiplyuk, and A. A. Maslov, “Nonlinear Aspects of Hypersonic Boundary-Layer Stability on a Porous Surface,” AIAA J. 43(1), 149–155 (2005).
N. V. Semionov, A. D. Kosinov, and Yu. G. Yermolaev, “Experimental Study of Turbulence Beginning of Supersonic Boundary Layer on Swept Wing at Mach Numbers 2–4,” J. Phys. Conf. Ser. 318, 1–10 (2011).
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Original Russian Text © Yu.G. Yermolaev, A.D. Kosinov, N.V. Semionov.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 55, No. 5, pp. 45–54, September–October, 2014.
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Yermolaev, Y.G., Kosinov, A.D. & Semionov, N.V. Experimental study of nonlinear processes in a swept-wing boundary layer at the mach number M=2. J Appl Mech Tech Phy 55, 764–772 (2014). https://doi.org/10.1134/S0021894414050058
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DOI: https://doi.org/10.1134/S0021894414050058