When water conduits operate with velocities exceeding 20-25 m/sec, high-vacuum regions are created, which result in the development of cavitation, followed by heavy erosion of the concrete, and in many cases by damages to the hydraulic equipment and the steel facings of concrete surfaces.This article presents some results of work carried out at the S. u Zhuk Scientific-Research Department of the All-Union Design and Scientific-Research Institute for Hydraulic Structures (NIS Gidroproekta), which permit preparing recommendations for the prevention of hazardous cavitation erosion of elements of hydraulic structures.Cavitation on Surface Irregularities of Water Conduits. In order to prevent cavitation erosion, the allowable dimensions of irregularities on the surfaces of water conduits should be specified for each structure.The degree of cavitation under a flow is determined by the cavitation index [1?. ]')o~ --/OjWoo c% in which L,e --2g P~,is thecharacteristicpressureinkg/mZ, v~oisthevelocityinm/sec, Pv is the saturated vapor pressure of the fluid in kg/m 2, and y is the unit weight of water, in kg/m 3.

Tunnel spillways are widely used in medium-and high-pressure hydraulic works. It is therefore an important and pressing task to improve the constructions used in these types of spillways and to develop optimal and reliable spillway structures.With this in mind, we would like to turn the reader's attention to essentially novel (i.e., in terms of configuration and operating conditions) vortex spillways which utilize vortex-type flows [1, 2, 3, 4]. On the one hand, these types of spillways make possible large-scale dissipation of the kinetic energy of the flow on the initial leg of the tailrace segment, and, as a consequence, flow rates of slightly vortex-type and axial flows through the subsequent legs that do not produce cavitation damage. On the other hand, the dangerous effect of high flow rates on the streamlined surface decreases over the length of the initial tailrace leg as a consequence of the increased pressure on the wall caused by the effect of centrifugal forces.A number of structural studies of tunnel spillways for hydraulic works such as the Rogunskii, Teri, Tel'mamskii, and Tupolangskii hydraulic works based on different operating principles have now been completed. These constructions may be divided into the following basic groups:-vortex-type (or so-called single-vortex type) spillways with smooth dissipation of the flow energy throughout the length of the tunnel when L r > (60 --80)hT or (60 --80)dT (where dT and hT are the diameter and height of the tunnel; cf. Fig. 1), while the cross-section of the tunnel is either circular or near-circular throughout its length.-vortex-type spillways with increasingly greater dissipation of the energy of the vortex-type flow over a shorter length Lr -< (60 --80)hT of a noncircular section river diversion tunnel (horseshoe-shaped, square, triangular) which is connected to the eddy chamber either by means of an energy-dissipation (expansion) chamber (Fig. 2) [5, 6] or by means of a smooth transition leg [7]; -spillways with two or more interacting vortex-type flows in energy-dissipation discharge chambers [8] or in special energy dissipators that have been termed "counter-vortex energy dissipators" [2, 4].The terminal portion of the tailrace tunnel of a vortex spillway may be constructed in the form of a ski-jump bucket, a stilling basin, or special structures depending on the flow rate at the exit from the tunnel and on the conditions in the channel downstream. The hydraulic system used to link the flow to the tailrace canal may involve the use of either overflowtype or free-fall type structures.Vortex spillways with smooth or accelerated [7] dissipation of energy over the entire length of the water conduit represent the simplest and most promising types of hydraulic structures.Techniques of designing vortex spillways have now been developed and published in numerous studies [2, 7, 8]; in particular, techniques are now available for calculating the hydraulic resistance of individual legs of a route and the flow rates and pressures in vortex-type flow. Howeve...

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At the present time, in the hydraulic engineering practice wide use is made of spillway structures with flow deflection in different portions of the flow route. They include whirl spillways, antiwhirl dissipators, shaft spillways with elbows in the taikace tunnel, and whirl gates.The integral flow characteristics required for design of spillways having bent portions, such as the discharge, the specific energy in the sections, and the averaged pressure at the limit, can be theoretically determined with sufficient accuracy for engineering analyses [1]. However, although there has been extensive study of helical flows in cylindrical water conduits, no methods are available for determining the flow velocity near the conduit lining required for predicting cavitation. This fact is a consequence of the attempt to approximate the velocity profile on the whole for the section.To solve specific engineering problems, search of the velocities in the entire flow section is not necessary. It is sufficient to know the local kinematic structure of the flow at the conduit walls for calculation of the cavitation numbers in its individual defects, such as projections from the formwork joints, uncut reinforcement, coarse aggregate of the concrete, etc.As a rule, the size of the above-mentioned defects does not exceed 2% with respect to the conduit diameter.Investigations intended to search for the mathematical relation and the velocity profile in the wall zone were performed on a shaft spillway model with deflected flow within the limits of the tailrace horizontal tunnel.The model was made of fiberglass with a wall roughness K e = 0.012 mm, a diameter of the tailrace tunnel with flow deflection d = 187 mm, and a head on the spillway model of about 1500 mm. If in a first approximation it is considered that for the helical flows the handbook data at the turbulent regime limits obtained for axial flows in pipelines are correct, the flow in the models can be classified as pertaining to the field of smooth pipes with respect to the hydraulic resistance.The velocity measurements were carried out by means of a laser Doppler anemometer installation which operated in accordance with the scheme of a backward light dispersion scheme. The system made it possible to perform measurements of the axial component of the flow velocity in the measuring elliptic volume, the linear dimension of which in a direction perpendicular to the flow direction was 0.10-0.15 mm.As kinematic characteristic after direct computer data processing, the time-average values of the axial components of the flow velocity at the measurement point v z and the turbulence intensity vz'/v 100%.The experiments reduced to demonstration of the simplest assumption, namely to the correctness, for the wall zone of the flows with deflection (zone thickness of no more than 0.02d), of the mathematical approximation of the velocity profile recommended in the reference literature for axial flows (smooth pipe region):

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