Scour caused by rectangular impinging jets in cohesionless beds

Abstract

An experimental investigation was conducted to obtain a better predictor of the depth of scour caused by impinging jets on cohesionless beds. The variables of importance considered in this study were the unit discharge, q, the velocity of impingement, Vi, the thickness of the jet at impingement, bi, the tailwater depth TW, the angle of impingement, δ, the particle size diameter, dn, the submerged specific density of the particle, (G - 1), and the gravity acceleration, g. Dimensional analysis indicated that the dimensionless depth of scour, Y/(q2/g)1/3 was related to the Froude number to the jet at impingement, Vi/(g bi)0.5, the dimensionless tailwater depth, TW/(bi cos δ), and the dimensionless fall velocity w/(g bi)0.5. The fall velocity of the particle, w, is approximately equal to (g (G - 1) dn)0.5, for particles whose dn > 0.1 mm. A large facility was built at Colorado State University to conduct the tests. The Dam Foundation Erosion (DFE) Facility consists of a tailbox whose dimensions are 16.76 m by 9.14 m, conveyance structures and a diffuser that contains a nozzle. The diffuser was mounted on a supporting structure above the tailbox. The cross section of the nozzle is 3.05 m by 0.087 m and the angle of issuance can be changed in 5 degrees increments. Water was conveyed from Horsetooth Reservoir by pipelines to the testing site and water was released as a jet. The experimental phase of this study was divided in two parts. In the first part, the bed material was 19.05 mm roadbase. A constant discharge of 2.735 m3/s was released by a diffuser impinging the tailwater at four different water depths for each angle of issuance. The angles of issuance with respect to the vertical were 15, 25 and 35 degrees. An increase in the tailwater depth always caused a decrease in the depth of scour when the angle of issuance remained constant. Furthermore, the scour hole was shallower as the angle of issuance departed from vertical. The geometric characteristics of the scour hole were documented and a strong correlation between the downstream slope and the angle of impingement was found. A second test series was conducted to study the erodibility of fractured rock. Fractured rock was simulated using concrete blocks. They were fluted on one side, flat on the other side and were 0.39 m long, 0.20 m wide, and 0.064 m thick. The specific gravity of the blocks was 1.65. Three thousand six hundred blocks were placed in two layers at a 45 degree angle pointing into the flow. Scour tests were conducted under minimum tailwater conditions. The upper layer was dislodged at a unit discharge of 0.372 m2/s. The bottom layer was dislodged at a unit discharge of 0.650 m2/s. In both test series, the degree of aeration of the jet was high. Instrument measurement of air concentration yielded values between 90% and 98% when the unit discharge was 2.735 m3/s. This was confirmed visually, because the jet expanded as it fell. The thickness of the jet at issuance was 0.087 m, and the thickness of the jet at impingement varied between 1.80 m and 2.00 m. Additional data was obtained from the studies conducted by Thomas (1953), Hallmark (1955) and Lencastre (1961) to complement the database obtained during the experimental phase of this study. The jets were formed at an overfall and photographic records indicate that the amounts of air entrained was not appreciable. During the data analysis, it was necessary to separate the expression developed for compact jets and it was determined that the scour caused by highly aerated jets cannot be predicted using the expression obtained for compact jets. It was shown that air entrainment affects the scouring capacity of the jet. The expression obtained using dimensionless analysis was validated for compact jets first. A second expression was obtained for highly aerated jets. The effects of power dissipation of the jets after they impinge the tail water surface are more pronounced in highly aerated jets. Fractured rock can be treated as a collection of large cohesionless materials, provided that there is no cementing material between the blocks. The spherical equivalent diameter of the blocks is used to obtain a characteristic particle size, dn. The dislodgement of the blocks is controlled by the depth of the rock layers. The unit discharge, tailwater depth, angles of impingement, particle size, and the degree of aeration of jets, proved to be major factors in the prediction of the ultimate depths of scour holes.