Abstract
The linear stage of short-wave Görtler vortices in the boundary layer near a concave surface is studied for the regime of weak hypersonic viscid-inviscid interaction at high Reynolds and Görtler numbers. It is assumed that the gas is perfect and the viscosity is a linear function of the enthalpy. It is found that neutral vortices are located near the surface if it has zero temperature. When the surface is heated, the vortices move away from it, whereas all newly incipient vortices are located near the surface. It is shown that the growth rate of the vortices has a maximum and the heating of the surface has a stabilizing effect on the vortices.
Similar content being viewed by others
References
P. Hall, “Taylor-Görtler vortices in fully developed or boundary-layer flows: linear theory,”J. Fluid Mech.,124, 475–494 (1982).
P. Hall, “The linear development of Görler vortices in growing boundary layers,”J. Fluid Mech.,130, 41–58 (1983).
V. V. Bogolepov, L. M. Degtyarev, O. M. Drozdova, and I. I. Lipatov, “Asymptotic structure of Taylor-Görtler vortices in boundary layers,” Preprint No. 156, Inst. Applied Mathematics, Acad. of Sci. of the USSR (1988).
V. V. Bogolepov and I. I. Lipatov, “Asymptotic analysis of the evolution of Görtler vortices in a liquid boundary layer near a concave surface,” Preprint No. 8, Central Aerohydrodynamic Institute, Zhukovskii (1990).
S. N. Timoshin, “Asymptotic analysis of spatially unstable spectrum of Görtler vortices,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 32–41 (1990).
V. V. Bogolepov and I. I. Lipatov, “Asymptotic theory of Görtler vortices in a liquid boundary layer,”Prikl. Mekh. Tekh. Fiz., No. 3, 58–68 (1992).
H. Görtler, “Uber eine dreidimensionale instabilitat laminarer grenzschichten an concaven wanden,”ZAMM,21 No. 2, 250–252 (1941).
P. Hall, “On the nonlinear evolution of Görtler vortices in non-parallel boundary layers,”IMA J. Appl. Math.,29, No. 2, 173–196 (1982).
P. Hall, “The nonlinear development of Görtler vortices in growing boundary layers,”J. Fluid Mech.,193, 243–266 (1988).
V. V. Bogolepov, “The nonlinear development of Görtler vortices in the near-wall portion of a boundary layer,”Izv. Ross. Nauk, Mekh. Zhidk. Gaza, No. 1, 29–35 (1994).
V. N. Brazhko, “Periodic flow structures and heat exchange in supersonic region of reattachment,”Uch. Zap. TsAGI,10, No. 2, 113–119 (1979).
R. Kobayashi and Y. Kohama, “Taylor-Görtler instability of compressible boundary layers,”AIAA J.,15, No. 12, 1723–1727 (1977).
R. E. Spall and M. R. Malik, “Görtler vortices in supersonic and hypersonic boundary layers,”Phys. Fluids,A1, 1822–1835 (1989).
P. Wadey, “On the linear development of Görtler vortices in compressible boundary layers,”Eur. J. Mech.,11, 231–248 (1992).
I. I. Lipatov, “Influence of compressibility on Görtler vortices structure at high Reynolds number,” in:Proc. 8th Couette-Taylor Meeting, Nice, France (1993).
V. V. Bogolepov and I. I. Lipatov, “The effect of compressibility of the development of Taylor-Görtler vortices at high reynolds numbers,”Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 36–47 (1997).
P. Hall and Y. Fu, “On the Görtler vortex instability mechanism at hypersonic speeds,”Theor. Comput. Fluid Dynam.,1, 125–134 (1989).
A. H. Dando and S. O. Seddougui, “The compressible Görtler problem in two-dimensional boundary layers,”IMA J. Appl. Math.,51, 317–332 (1993).
Y. Fu, P. Hall, and N. D. Blackaby, “On the Görtler instability in hypersonic flow: Sutherland law and real gas effects,”Philos. Trans. Roy. Soc., London,A342, 451–476 (1993).
J. K. Hayes and P. F. Probstein,Hypersonic Flow Theory, Academic Press, New York (1959).
V. V. Bogolepov, “Görtler vortices incipience in compressible boundary layer near strongly cooled surface,” in:Effects of Organized Vortex Motion on Heat and Mass Transfer, Abstracts of Euromech Colloquium 327, Kiev (1994).
V. V. Bogolepov, “Investigation of surface temperature influence of Görtler vortices incipience,” AIAA Paper No. 95-2297 (1995).
V. V. Bogolepov and I. I. Lipatov, “Structure of a disturbed boundary layer near a cold surface,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 19–27 (1991).
A. M. O. Smith, “On the growth of Taylor-Görtler vortices along highly concave walls,”Quart. Appl. Math.,13, No. 3, 233–262 (1955).
V. V. Voevodin and Yu. A. Kuznetsov,Matrices and Calculations [in Russian], Nauka, Moscow (1984).
Additional information
Central Aerohydrodynamic Institute, Zhukovskii 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 67–76, September–October, 1998.
Rights and permissions
About this article
Cite this article
Bogolepov, V.V. Investigation of the spectrum of short-wave Görtler vortices in a gas. J Appl Mech Tech Phys 39, 710–718 (1998). https://doi.org/10.1007/BF02468041
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02468041