Aeration performances of a gabion stepped weir with and without capping

Abstract

The stepped spillway design has been used for more than 3,300 years. A simple structure is the gabion stepped weir. A laboratory study was performed herein in a large size facility. Three gabion stepped weirs were tested with and without capping, as well as a flat impervious stepped configuration. For each configuration, detailed air–water flow measurements were conducted systematically for a range of discharges. The observations highlighted the seepage flow through the gabions and the interactions between seepage and overflow. The air–water flow properties showed that the air concentration, bubble count rate and specific interface data presented lower quantitative values in the gabion stepped weir, compared to those on the impervious stepped chute, while higher velocities were measured at the downstream end of the gabion stepped chute. The re-oxygenation rate was deduced from the integration of the mass transfer equation using air–water interfacial area and velocity measurements. The aeration performances of the gabion stepped weir were lesser than on the flat impervious stepped chute, but for the lowest discharge. For the two configurations with step capping, the resulting flow properties were close to those on the impervious stepped configuration.

Appendix 1: Relationship between void fraction and bubble count rate in self-aerated flows

In self-aerated chute flows, the relationship between void fraction and bubble count rate tends to follow a pseudo-parabolic relationship close to [4, 8, 31]:

$$\begin{aligned} \frac{\hbox {F}}{\hbox {F}_\mathrm{\max }}=4\times \hbox {C}\times \left( {1-\hbox {C}}\right) \end{aligned}$$

(15)

where $\hbox {F}_\mathrm{max}$ is the maximum bubble rate in a cross-section. A more advanced theoretical model was introduced by [31] and [33]:

$$\begin{aligned} \frac{\hbox {F}}{\hbox {F}_\mathrm{\max }}=\frac{1}{\upalpha \times \upbeta }\times \frac{\hbox {C}\times \left( {1-\hbox {C}}\right) }{\hbox {C}_{\mathrm{F}_\mathrm{\max }}^{2}} \end{aligned}$$

(16)

where $\upalpha$ and $\upbeta$ are two correction factors which are functions of the local void fraction and flow conditions, and $\hbox {C}_\mathrm{Fmax}$ is the void fraction for which $\hbox {F}=\hbox {F}_\mathrm{max}$. The first correction parameter $\upalpha$ accounts for the different average sizes of air bubble chord size $\lambda \hbox {a}$ and water droplet chord size $\lambda \hbox {w}$:

$$\begin{aligned} \upalpha =1+\left( {\frac{\lambda _\mathrm{w}}{\lambda _\mathrm{a}}-1}\right) \times \hbox {C} \end{aligned}$$

(17)

with the ratio $\lambda _\mathrm{w}/\lambda _\mathrm{a}$ assumed to be constant within a cross-section and independent of the void fraction. The second correction factor $\upbeta$ takes into account the variation of $\lambda _\mathrm{w}$ and $\lambda _\mathrm{a}$ with the void fraction:

$$\begin{aligned} \upbeta \left( \hbox {C}\right) =1-\hbox {b} \times \left( {1-2\times \hbox {C}}\right) ^{4} \end{aligned}$$

(18)

where b is a characteristic value of the maximum variation of $\upbeta$: i.e., $1-\hbox {b}<\upbeta <1$ [33]. Some typical results are presented in Fig. 7 where Eqs. (15) and (16) are compared with experimental data. Equation (16) compared favourable with the data on both flat impervious and gabion stepped configurations. The best agreement was found for $\lambda _\mathrm{w}/\lambda _\mathrm{a}=2.4$ and b = 0.55 for the flat impervious stepped configuration. and for $\lambda _\mathrm{w}/\lambda _\mathrm{a}=1.6$ and b = 0.52 for the gabion stepped configuration. The values were generally in agreement with the findings of [12] for the same chute slope.