TOOMBES, L. (2002). "Experimental Study of Air-Water Flow Properties on Low-Gradient Stepped Cascades."
Ph.D. thesis, Dept of Civil Engineering, The University of Queensland. (
PDF version at EprintsUQ)
Study period : 1996-2001 (Ph.D. project)
Stepped cascades are recognised for both aeration potential and energy dissipation, and have been employed in hydraulic structures for over 3,500 years. This study presents a detailed investigation of both the macro and micro-scale flow properties on a low-gradient cascade (3.4 deg 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. Significant outcomes of theair-water flow analysis include:
- Air-concentration distribution: The air-concentration distribution at the lower nappe of 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.
-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 parallel investigation of the oxygen aeration efficiency of the stepped cascade was conducted. Measured air-water property data were 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 (
TOOMBES and CHANSON 2005).