Stepped cascades are recognised for both aeration potential and energy dissipation, and have been employed in hydraulic structures for over 3,500 years. Yet little detailed information exists on their performance, especially pertaining to low-gradient cascades. This study presents a detailed investigation of both the macro and micro-scale flow properties on a low-gradient cascade (3.4º slope). Research is conducted on two large-size physical models: a 24m long multi-step cascade (10× 2.4m long steps), and a single-step model with identical step height and length. The large size of the model allows near full-scale data acquisition under controlled flow conditions, minimising potential scale effects. The study comprises three distinct components: 1. A global investigation of the general flow properties of nappe flow on a low-gradient, multi-step cascade. Unforeseen three-dimensional characteristics of the flow, including supercritical shockwaves and sidewall standing-waves downstream of nappe impact, are identified and examined by the study. Although comparable to similar phenomena at channel bends and expansions, these have not been previously described on stepped cascades. Energy dissipation on the cascade is investigated, and is found to be over twice that observed for a smooth chute of similar gradient. 2. A complete characterisation of the air-water structure of flow in a nappe regime. Significant outcomes of the analysis include: ⊕ Air-concentration Distribution: The air-concentration distribution at the lower nappe of the free-falling jet shows good agreement with an analytical solution of the diffusion equation. The experimental results from the study, and a reanalysis of existing data, indicate a distinct relationship between the turbulent diffusivity in the shear layer and distance from the step brink. This contradicts earlier investigations that assumed constant diffusivity. Strong aeration of the flow, with a large volume of spray, occurs downstream of the nappe impact. Depth-averaged air concentrations of 40% to 50% are observed within the spray region, decreasing towards the downstream end of the step. ⊕ Velocity Distribution: A theoretical analysis of the momentum transfer process imparts an improved understanding of the momentum transfer and velocity redistribution within the free-falling jet. An analytical solution based on twodimensional wake flow is developed, superseding existing solutions based upon a monophase free-mixing layer. ⊕ Bubble-frequency Distribution: A quasi-parabolic relationship between bubble frequency and time-average air concentration across a cross-section is observed. A theoretical explanation for the parabolic relationship is developed, and two correction factors are introduced to provide a better representation of the experimental data. ⊕ Air-bubble and Water-droplet Size Distributions: Chord-length distributions are compared with standard probability distributions, showing good agreement with standard Weibull, gamma and log-normal probability distributions within various regions of the flow on the step. A computer model is developed to model interaction between a bubbly transition from water to air and fluctuations of the free surface. 3. A parallel investigation of the oxygen aeration efficiency of a stepped cascade. Measured air-water property data is used to calculate the air-water interface area in bubbly flow, and to estimate the theoretical aeration efficiency of the stepped cascade based upon the integration of the mass transfer equation. The aeration performance of the stepped cascade model is also measured experimentally in terms of dissolved oxygen content. This analysis allows a unique, successful comparison of experimental dissolved oxygen measurements with the numerical integration of the mass transfer equation.
| Identifer | oai:union.ndltd.org:ADTP/253641 |
| Creators | Toombes, Luke |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
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