The example of a plane jet flow into a rectangular cavity ("dead end") is used in comparing the capabilities of different approaches to numerical simulation of self-oscillatory turbulent flows characterized by global quasi-periodic oscillation of all flow parameters. The calculations are performed for two flow modes, of which the first one is statistically steady according to the available experimental data, and the second one is self-oscillatory. In both cases, three approaches are used to describe the turbulence, namely, the method of large eddy simulation (LES) in combination with the subgrid model of Smagorinsky, and steady and unsteady Reynolds averaged Navier-Stokes equations (SRANS and URANS) with two well-known differential models of turbulence. In the case of the first flow mode, all three approaches produce qualitatively similar and quantitatively close results. In the case of the second (self-oscillatory) mode, a steady-state solution of Reynolds equations may only be obtained in half the domain using the symmetry boundary conditions; within the framework of the other two approaches, the solutions turn out to be unsteady-state. In so doing, their characteristics calculated using the LES and URANS methods differ significantly from each other; in the case of URANS, they further depend on the model of turbulence employed. The best results as regards the accuracy of prediction of the amplitude-frequency characteristics of self-oscillation are produced by the use of the LES and three-dimensional URANS methods. A similar inference may be made with respect to the mean flow parameters. From this standpoint, the worst results are those obtained from calculations involving the use of the symmetry boundary conditions on the geometric symmetry plane of the flow.

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Translated from Gidrotekhnicheskoe Stroitel 'stvo, No. 2, February 2011, pp. 9 -18. Basic information on the in-service tunnel spillway at the Irgana HPP, and also requirements for smoothing irregularities in its surfaces in contact with the flow are presented. A method is proposed for determination of requirements for the surface of the spillway with a tolerance for cavitation damages. Results of experimental investigations and analyses are presented. Keywords:Irgana hydroproject, surfaces of steeply inclined section of spillway in contact with flow, cavitation damages, flow parameters, rectangular projections, permissible height of irregularities.The in-service tunnel spillway at the Irgana hydroproject, which was built on the Avarskoe Koisu River in the Republic of Daghestan, consists of a water intake with a radial gate, steeply inclined section, and discharge tunnel. The spillway is intended to pass design flows of 2000 m 3 /sec in a 10,000-year flood, and 1320 m 3 /sec in a 1000-year flood. The spillway is designed for gravity flow over its entire length. The differential in water levels over its steeply inclined section is approximately 75 m (Fig. 1). The profile of the intake head of the spillway is configured in Kriger coordinates with a profiling head of 15.8 m. For a distance of 20.61 m along the horizontal, the spillway narrows down from 18 to 8 m in plan. In cross-section, the steeply inclined section of the in-service tunnel spillway (SISTS) is troughshaped with a dome configured as the arc of a circle with a radius of 4 m. The thickness of the reinforced-concrete lining of the steeply inclined section of the tunnel is 0.7 m, and the protective layer for the reinforcement in the lining does not exceed 0.1m. Its design is discussed in detail in [1].Requirements for the treatment of irregularities in the concrete surface of the SISTS, which is past over by a highvelocity flow, were formulated on the basis of hydraulic studies that had been performed early-on in the design stage, proceeding from prevention of cavitation. There were no particular difficulties encountered in fulfilling this condition either in preventing cavitation over the uniform natural roughness of the concrete surface, or in the case of shelves, but it was necessary to dress similar protrusions and local roughness (reinforcing rods and other metallic components, large aggregate). Fulfillment of this condition for projections on the most cavitation-prone sections -immediately downstream beyond the constriction in the planform of the SISTS -could be realized with their smoothing at an angle of less than 90°to the concrete surface where the height was 4, and even 2 mm. Smoothing of projections of such a height on the concrete surface could hardly be implemented over the area of the spillway surface in contact with the flow, which is approximately 2200 m 2 , including 1600 m 2 of lateral walls.Procedure for determination of requirements for spillway surface with tolerance for cavitation damages. A tolerance for irregularities compris...