The unsteady aerodynamic parameters of 3D blade cascades oscillating in incompressible flow are determined with account for blade geometry and the influence of the steady hydrodynamic loads acting on the blades. On the assumption of separationless flow and harmonic blade oscillations, the corresponding boundary-value problem for the amplitude function of the unsteady velocity potential component is solved in the linear formulation, using a finite-element method. Test calculation results are presented and an example of calculating the unsteady aerodynamic parameters of a hydro-turbine model is given.Here, Φ is the perturbed-flow velocity potential. We introduce the cylindrical coordinates (r 1 , θ , x) fitted to the rotating cascade. In this coordinate system, the relative fluid velocity W is 0015-4628/05/4001-0034 

ON THE SAYANO-SHUSHENSK HYDRO POWER PLANT UDC 621.51:534 V. B. Kurzin and V. S. Seleznev It is demonstrated that the level of vibrations of turbines on the Sayano-Shushensk hydro power plant is enhanced by the capability of a compressible fluid to perform its own hydroacoustic oscillations (which can be unstable) in the turbine duct. Based on the previously obtained results of solving the problem of natural hydroacoustic oscillations in the turbine duct and some ideas about turbine interaction with an unsteady compressible fluid flow, results of full-scale studies of turbine vibrations and seismic monitoring of the dam of the Sayano-Shushensk hydro power plant before and during the accident are analyzed.Introduction. Various possible reasons were given after the accident on the Sayano-Shushensk hydro power plant (HPP), which happened on August 17, 2009. These reasons were analyzed in much detail in [1]. Some versions of the accident are based on the assumption that the turbine was subjected to a certain pulsed high-power action (something like a hydraulic hammer), which exceeded the safety margin of the structure. These versions, however, do not agree with the results of seismic monitoring of the dam of the Sayano-Shushensk HPP before and during the accident. The main reason for the accident is assumed to be the fatigue failure of the fixtures of the turbine cover of the power-generating unit No. 2, which was induced by the high level of turbine vibrations in the standard operation mode. This fact was established by the technical commission investigating the reasons for the accident.The elevated level of turbine vibrations on the Sayano-Shushensk HPP (as compared with vibrations obtained for its model) was observed in full-scale tests performed back in 1988. It was shown [2, 3] that emergence of such vibrations is caused by the effect of water compressibility on turbine interaction with the unsteady flow, which was ignored in design of the Sayano-Shushensk HPP. The study of this problem was continued in [4,5]. Based on results of these studies, certain restrictions were imposed on operation of power-generating units of the Sayano-Shushensk HPP. It should be noted, however, that the hydrodynamic problem in [4,5] (results of these studies were used as a basis for the version described in [1]) was considered in a linear formulation and in a quasi-steady approximation. It is convenient to use the solution of this problem in such a formulation for engineering calculations, but the solution is rather rough and does not explain some qualitative features observed in experiments. In addition, there is a mistake in [4,5].In the present work, based on the theory of cascades in an unsteady flow [6-8] and on the laws of aeroacoustics, we study the qualitative effect of nonlinearity and reduced frequency of vibrations on turbine interaction with an unsteady compressible fluid flow, which was partly taken into account in [2, 3], but skipped in [4,5]. Using the data obtained, we analyze the results of full-scale studies of turbi...

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In the theory of turbomachinery elasticity, it is welt known that the introduction of even a small nonuniformity in cascades can affect the stability of blade vibrations in a flow and increase considerably the dynamic stresses in individual blades with forced vibrations of the cascades. For gas turbomachines, for which the natural frequencies of blade vibrations depend only slightly on the ambient medium, this problem has been adequately studied. For hydraulic turbines, there have been few studies in this direction. In the present work, we examine the effect of small geometric nonuniformity of hydraulic-turbine cascades on the natural frequencies and modes of their vibrations in a quiescent liquid.1. Formulation of the Problem. We study free vibrations of a hydraulic-turbine cascade of sufficiently thin blades. The cascade is located between two coaxial cylinders in a quiescent, ideal, incompressible liquid. In contrast to the model studied in [1], we shall assume that the cascade has small geometric nonuniformity because of inaccurate manufacture and assembly.The geometric parameters of the cascade are assumed to be specified. We introduce a homogeneous cascade with blades of identical thickness h(r0m), where r0m are the radius vectors of the centroidal surfaces S~ ) of the blades. The geometric nonuniformity of the cascade considered is then given by the functions 6rm(r0m) = rm -r0m, ~hn~(r0m) = hm(rm) -h(r0m). where w~ ) is the natural frequency of first-mode vibrations of the ruth blade the and w(D is the natural frequency of the corresponding uniform cascade. The introduction of the second small parameter r is due to the fact the order of smallness of the quantities in relations (1.2) and (1.3) can be different. Assuming that the interaction between the blades is realized only via the liquid, we obtain a matrix system of equations that describe the free vibrations of the blade cascade considered: N-1