Abstract
The problem of calculating the nonstationary aerodynamic characteristics of a cascade of thin lightly loaded airfoils in a subsonic flow with the formation of thin separation zones of finite extent is solved approximately. As in [1–5], an approach based on a linear small-perturbation analysis, within which the flow is assumed to be inviscid, is employed and the boundaries of the unsteady separation zones are simulated by oscillating lines of contact discontinuity. However, instead of the requirement of a given fixed pressure at the boundary of the separation zone, used in [1–5], this study proposes a more general condition according to which on each element of length of the thin separation layer the pressure oscillates with an amplitude proportional to the local value of the amplitude of its thickness oscillations. The problem is reduced to a system of two singular integral equations which can be solved numerically.
Similar content being viewed by others
References
P. V. Perumal and F. Sisto, “Lift and moment prediction for an oscillating airfoil with a moving separation,”Trans. ASME, Ser. A, J. Engin. for Power96, No.4, (1974).
S. B. Bogomolov and V. É. Saren, “Cascaded airfoils vibrating in a separated incompressible flow,” in:Aeroelasticity of Turbomachinery Blading [in Russian], Tr. TsIAM, Issue 6, No. 2393 (1991), p. 57.
H. B. Tou and G. J. Hancock, “Inviscid theory of two-dimensional aerofoil/spoiler configurations at low speed. Pt. IV. Oscillatory aerofoil/spoiler characteristics,”Aeronaut. J.,91, 410 (1987).
R. M. Chi, “Unsteady aerodynamics in stalled cascade and stall flutter prediction,” ASME Paper, No. C2/Aero-1 (1980).
R. M. Chi, “Separated flow unsteady aerodynamic theory,”J. Aircr.,22, 956 (1985).
V. N. Kotovskii, M. I. Nisht, and R. M. Fedorov, “Mathematical simulation of unsteady separated flow past cascaded airfoils,”Dokl. Akad. Nauk SSSR,263, 1326 (1982).
P. R. Spalart, “Simulation of rotating stall by vortex method,”J. Propulsion and Power,1, 235 (1985).
F. Sisto, S. Thangam, and A. Abdel-Rahim, “Computational prediction of stall flutter in cascade airfoils,”AIAA J.,29, 1161 (1991).
I. H. Tuncer, J. C. Wu, and C. M. Wang, “Theoretical and numerical studies of oscillating airfoils,”AIAA J.,28, 1615 (1990).
Y. Shida, K. Kuwahara, K. Ono, and H. Takami, “Computation of dynamic stall of a NACA-0012 airfoil,”AIAA J.,25, 408 (1987).
D. L. Hulf, “Numerical simulation of unsteady viscous, transonic flow over isolated and cascaded airfoils using a deforming grid,” AIAA Pap., No. 1316, (1987).
S. Yashima and H. Tanaka, “Torsional flutter in stalled cascade flow,” Trans. ASME, Ser. A, J. Eng. for Power,100, No. 2 (1978).
H. Tanaka, I. Fujimoto, and S. Ishii, “Aerodynamic response of a blade in pitching oscillation with partial and full separation,”Proc. of the Second Intern. Symp. Aeroelast. Turbomach., Lausanne (1980).
M. E. Goldstein, “Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry,”J. Fluid Mech.,154, 509 (1985).
O. S. Ryzhov, “Excitation of unstable oscillations in the boundary layer by a source in the potential flow zone,”Dokl. Akad. Nauk SSSR,304, 820 (1989).
A. G. Munin, V. M. Kuznetsov, and E. A. Leont'ev,Aerodynamic Noise Sources [in Russian], Mashinostroenie, Moscow (1981).
K. K. Butenko and A. A. Osipov, “Calculation of unsteady supersonic flow past a plane plate cascade subjected to the action of free-stream vortex inhomogeneities,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 152 (1986).
F. D. Gakhov,Boundary Value Problems [in Russian], Fizmatgiz, Moscow (1958).
Additional information
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–191, January–February, 1995.
Rights and permissions
About this article
Cite this article
Osipov, A.A., Reent, K.S. Cascaded thin lightly loaded airfoils vibrating in a subsonic separated flow. Fluid Dyn 30, 149–156 (1995). https://doi.org/10.1007/BF02029940
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02029940