Gangfu Zhang

Hydraulics of the developing flow region of stepped spillways. I: Physical modeling and boundary layer development

AbstractOn a stepped spillway, the steps act as macroroughness elements, contributing to enhanced energy dissipation and significant aeration. In a skimming flow, the upstream flow motion is nonaerated, and the free surface appears smooth and glossy up to the inception point of free-surface aeration. In this developing flow region, a turbulent boundary layer grows until the outer edge of the boundary layer interacts with the free surface and air entrainment takes place. The flow properties in the developing flow region were documented carefully in a large stepped spillway model (1V:1H; h=0.10  m). The upstream flow was controlled by a broad-crested weir and critical flow conditions were observed along most of the weir crest, although the pressure distributions were not hydrostatic at the upstream and downstream ends. Downstream of the broad crest and upstream of the inception point, the free surface was smooth, although some significant free-surface curvature was observed for all discharges. The boundary ...

Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways

In high-velocity chute flows, free-surface aeration is often observed. The phenomenon is called self-aeration or white waters. When the turbulent shear stresses next to the free-surface are large enough, air bubbles are entrained throughout the entire air–water column. A rapidly-varied flow region is observed immediately downstream of the inception point of free-surface aeration. An analytical solution of the air diffusion equation is proposed and the results compare well with new experimental data. Both experiments and theory indicate that the flow bulking spans over approximately 3–4 step cavities downstream of the inception point of free-surface aeration on a stepped chute. Further downstream the void fraction distributions follow closely earlier solutions of the air diffusion equation. The application of the diffusion equation solution to prototype and laboratory data shows air bubble diffusivities typically larger than the momentum transfer coefficient. The result highlights however a marked decrease in the ratio of air bubble diffusivity to eddy viscosity with increasing Reynolds number. The finding might indicate some limitation of laboratory investigations of air bubble diffusion process in self-aerated flows and of their extrapolation to full-scale prototype applications.

Gabion Stepped Spillway: Interactions between Free-Surface, Cavity, and Seepage Flows

AbstractOn a gabion stepped chute, the steps contribute to the dissipation of turbulent kinetic energy, free-surface aeration may be intense, and there are complex interactions between the free-surface flow and seepage motion. Detailed measurements were conducted in a relatively large gabion stepped spillway model. Using a combination of high-speed movies and phase-detection probe measurements, the air–water flow properties in the step cavities and in the gabions were documented. Strong air–water exchanges between seepage and stepped cavity flows were observed. The data showed a complex bubbly seepage motion in the gabions associated with a high level of interactions between seepage and free-surface flows, leading to a modification of the step cavity recirculation and lesser flow resistance.

Hydraulics of the Developing Flow Region of Stepped Spillways. II: Pressure and Velocity Fields

AbstractIn skimming flow on a stepped spillway, the upstream flow motion is nonaerated and a turbulent boundary layer develops until the outer edge of the boundary layer interacts with the free surface; that is, at the inception point of air entrainment. Herein, new experiments were performed in the developing flow region on a large 1  V∶1  H stepped spillway model with step height h=0.10  m. The flow properties in the developing flow region were carefully documented. In the developing boundary layer, the velocity distributions followed a 1/4.5th power law at the step edges. Detailed velocity and pressure measurements showed some rapid flow redistribution between step edges and above step cavities. The application of the momentum integral equation indicated an average friction factor of 0.18, which is close to the observed air-water-flow friction factor of 0.23, suggesting that the spatially averaged dimensionless shear stress was comparable in the developing flow and fully aerated flow regions.

Application of optical flow methods to aerated skimming flows above triangular and trapezoidal step cavities

ABSTRACT Stepped chutes are built to provide safe flood passage in dams. The steps are associated with strong turbulence generation, which allow air to be entrained from the free surface. The present work adopts a non-intrusive local optical flow technique to examine the effects of partial cavity blockage on the mean and turbulent properties in aerated skimming flows in two large-size stepped chute models. The partial cavity blockage was found to be associated with decreased mean velocities in the overflow. The step edge was identified as the most significant source of turbulent production. General increases in turbulence levels and large scale turbulent motions were identified for the partially blocked cavities, which could be linked to a reduction in mutual sheltering between adjacent roughness elements. It was implied that the cavity blockage might have some effects on the velocity gradient fluctuations.

Turbulence and Energy Dissipation in the Developing Non-Aerated and the Fully-Developed Aerated Flows on a Stepped Spillway

Stepped spillways are characterised by highly turbulent air-water flows and a large rate of energy dissipation compared to smooth chutes. Herein, detailed measurements were performed in both the developing non-aerated and fully-developed air-water flow regions on a large 1V:1H stepped spillway model. In the developing flow region, large total pressure fluctuations and turbulence intensities were recorded next to the pseudo-bottom. Downstream of the inception point, large total pressure fluctuations were recorded, which were mainly induced by density fluctuations. The water turbulence intensities in the air-water flow region did not differ significantly from those in the developing flow region. The steps generated significant form loss, amounting to about 50% of the upstream total energy regardless of discharge. Similar rates of energy dissipation and friction factors were found between the developing non-aerated and fully-developed air-water flow regions. The energy dissipation on stepped chutes was found to be sensitive to the chute slope and relatively little affected by the air-bubble diffusion.

Free-Surface Aeration in a Steep Stepped Spillway

Self-aeration has important civil and environmental applications in stepped chutes, ranging from cavitation protection to enhanced air-water mass transfer. Air bubble entrainment occurs when the turbulent stresses in the boundary layer exceed the combined effects of surface tension and buoyancy. The governing equations for air diffusion in the rapidly-varied region next to and in the gradually-varied region away from the inception point of aeration are introduced. New and existing solutions to these equations are discussed and compared with new experimental data. An analytical model for flow bulking is introduced. The concept of negative diffusivity is discussed.