Bubble curtains in a lock-exchange flow: the importance of transient dynamics in the curtain-driven regime

TL;DR

This work investigates bubble curtains at a lock gate to mitigate saltwater intrusion in a lock-exchange flow, emphasizing the transient curtain-driven regime. It combines multiphase large-eddy simulations with a semi-analytical, five-volume mass-conservation model to capture time-dependent density changes and the resulting effectiveness $E(t)$, across parameters $Fr_{air}$, $\sigma$, and $\tilde{L}$. A central finding is that transient dynamics dominate curtain performance, with an optimal $Fr_{air}$ around $0.91$ yielding maximal effectiveness near $E \approx 0.81$, and that the flow organizes into two recirculation cells from which secondary gravity currents emerge. The study provides scaling laws for the recirculation-cell velocity $\tilde{U}_c \approx 0.15(Fr_{air}+1)$ and mixing time $\tilde{\tau}_{mix} \approx 1/[0.15(Fr_{air}+1)]$, and demonstrates how finite-domain effects govern the approach to steady state, offering practical guidance for designing curtain-based mitigation in real locks.

Abstract

Bubble curtains are line bubble plumes that are used to mitigate saltwater intrusion in shipping locks. When the lock gate that separates the saline seawater from the fresh river water is opened, a lock-exchange flow is initiated. Placing a bubble curtain at the gate location disrupts this flow and reduces saltwater infiltration. For practical applications, it is useful to quantify the effectiveness of the bubble curtain as a function of the governing parameters of the problem. To achieve this goal, we performed multiphase large eddy simulations that accurately reproduce previous experimental results including the two regimes of operation: the break-through and the curtain-driven regimes. This paper focusses on the curtain-driven regime and aims to unravel the temporal evolution of the effectiveness of bubble curtains. The detailed spatial and temporal information obtained from the simulations and the flexibility to vary the governing parameters allowed us to overcome several previous experimental limitations. In addition, the simulations were used to obtain parameters to build a semi-analytical model. Both the simulations and the semi-analytical model clearly describe and help to understand the time evolution of the density field and the effectiveness of the bubble curtain. These results show that the time elapsed since the opening of the gate and the transient dynamics are crucial for determining the effectiveness of bubble curtains.

Figures (23)

• Figure 1: Schematic of a laboratory scale lock with a bubble curtain placed at the centre. The annotations $L$, $W$, and $H_d$ depict the length, width and height of the tank, respectively. The blue line represents the level of the free-surface at $z=H$.
• Figure 2: Snapshots of contours of volume fraction of salt water $\alpha_s$ at $z = 0$ for two simulations: a) one in the breakthrough regime ($\hbox{Fr}_{air}=0.5$, $\sigma=1.040$, $\tilde{L}=7.69$) and b) one in the curtain-driven regime ($\hbox{Fr}_{air}=3.24$, $\sigma=1.005$, $\tilde{L}=15.4$). The location of the bubble curtain is shown with grey shading. For simulation in the curtain-driven regime, we highlight the two recirculation cells with intermediate density using rectangles. On the left side, the cell extends until $\tilde{x}\approx-4$ and on the right side until $\tilde{x}\approx3$. From each of these recirculation cells, a secondary gravity current emerges.
• Figure 3: Plot of effectiveness $E$ vs Froude number $\hbox{Fr}_{air}$, comparing the simulation results (blue circles) obtained in the present study and experimental data of bacot2022bubble (red squares). The effectiveness is computed at the end time $t_{end}$ of the experiments or simulations. The analytical solution proposed by bacot2022bubble for $t_{end}\to \infty$ is shown by the solid red curve. The dashed line represents the optimal $\hbox{Fr}_{air}$ ($\approx 0.91$) where $E$ is maximum that separates the breakthrough and curtain-driven regimes which are typically observed to the left and right of the dashed line, respectively.
• Figure 4: Schematic representation of the recirculation cell with length $L_c$ and the secondary gravity current on the fresh side of the lock. The control volumes chosen to establish mass and volume conservation are also depicted.
• Figure 5: Non-dimensional velocity scale in the recirculation cell, $\tilde{U}_c$, computed using \ref{['eq:velocity_scale_flux']} versus the proposed scaling in \ref{['eq:velocity_cell_dimensionless_2']}. The solid black line represents a perfect match with $\tilde{U}_c= 0.15( \hbox{Fr}_{air}+1)$.