Chute aerators introduce a large air discharge through air supply ducts to prevent cavitation erosion on spillways. There is not much information on the microcosmic air bubble characteristics near the chute bottom. This study was focused on examining the bottom air-water flow properties by performing a series of model tests that eliminated the upper aeration and illustrated the potential for bubble variation processes on the chute bottom. In comparison with the strong air detrainment in the impact zone, the bottom air bubble frequency decreased slightly. Observations showed that range of probability of the bubble chord length tended to decrease sharply in the impact zone and by a lesser extent in the equilibrium zone. A distinct mechanism to control the bubble size distribution, depending on bubble diameter, was proposed. For bubbles larger than about 1-2 mm, the bubble size distribution followed a-5/3 power-law scaling with diameter. Using the relationship between the local dissipation rate and bubble size, the bottom dissipation rate was found to increase along the chute bottom, and the corresponding Hinze scale showed a good agreement with the observations.
The rock mass can be assumed to be homogeneous material from the macroscopic view, but it is a heterogeneous material at a mesoscopic scale and its physico-mechanical properties are discontinuous in space. Therefore, it is necessary to research the generation and development of pre-peak micro cracks in rocks and frictional characteristics between post-peak mineral particles from macro-meso and multi-scale perspectives to know the substantive characteristics of rock failure and instability. This paper, based on the manifold cover concept, proposes a new discrete element numerical method (i.e. Manifold Particle Discrete) combining with the particle contact model, so as to introduce the concept of stress boundary. This method can be applied to the entire process of analyzing rock failure. By analyzing the manifold cover and ball particle model, this paper constitutes the ball unit cover function of three-dimensional manifold cover, establishes tetrahedron units, obtains the equilibrium equation and compatible equation of the MPD model. It also verifies the accuracy of the proposed numerical method and the feasibility of rock failure analysis through numerical examples.
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