A numerical study of the triggering mechanism of a lock-release density current

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Abstract

A numerical study on the effects induced by the impulsive vertical removal of a lock-gate at the interface between two fluids of different densities is presented. This configuration represents the typical setup of those experiments commonly employed for investigating density currents in the laboratory. Experimentally induced effects resulting from opening the lock-gate are expected to occur, but the evaluation of these dynamics and their impact on the evolution of the laboratory density current produced in such a manner are not easy to estimate. Despite the fact that numerical studies are often concerned with lock-release density currents, the triggering mechanism which occurs in the early stages of the evolution of the fluid flow is commonly neglected. Here a comparison is established between the case when the triggering mechanism is completely neglected and a series of cases where, in contrast, this effect is taken into account. The withdrawal of the lock-gate is modeled either by employing a zero-thickness lock-gate or by accounting for the volumetric nature of the lock-gate. Subsequently the influence of speed on the withdrawal of the lock-gate is assessed. The numerical results suggest that the density current is mainly affected by the constraining effect of the lock-gate on the flow and by the responses of the submerged fluid and the free surface to the displacement of the lock-gate. These differences lead to improved physical modeling and numerical simulation validation in the case where the physics of the lock-gate is accounted for. Such differences can be very important particularly in particulate-laden flows, where small changes in initial conditions may lead to longer-term divergence as a result of positive feedback effects. The work has significant implications for physical modeling of density currents and a series of recommendations are made for the standardization of experimental protocols. Finally, the approach adopted here for the moving gate is applicable to civil and environmental engineering problems including dam-break flows and sluice gate modeling.

Introduction

The attention devoted to gravity currents, either natural or man made, is justified by the widespread occurrence of such phenomena across very disparate environments. Be it katabatic winds and sea breezes in the atmosphere, deep thermohaline circulation, estuarine hyperpycnal intrusions, or turbidity currents in water bodies, the mechanics which trigger and control the evolution of such processes are essentially the same [1], [2], [3]. When fluids with different density interface each other in a gravitational field, a reciprocal motion is started which results in one of the two intruding underneath the other. Despite their frequent and ubiquitous occurrence, investigation of the fluid dynamics of density currents has been fostered mainly by laboratory scale analysis and mathematical modeling rather than by direct observation because of the magnitude and the unpredictability of these phenomena.

One of the most remarkable advancements in the field of density currents was achieved by means of the simplest experiment conceivable: the lock-release experiment. The setup employed by Martin and Moyce [4] for the physical simulation of the dam-break test case was later revisited and extensively exploited for the in-depth exploration of the fluid mechanics of density currents. This laboratory device entails a straight rectangular tank with transparent sidewalls and a removable “lock-gate” located near one end of the channel. Thus the tank is divided into a long section, initially occupied by the ambient fluid alone and a small compartment, the “lock-box”, where the dense fluid is housed before the flow is started, Fig. 1(b). The experiment is initiated by the sudden removal of the lock-gate which allows the dense and ambient fluid to come into contact and gives rise to a typical density current. The lock-gate is sometimes constrained between small binaries (i.e., guides) in order to facilitate its vertical withdrawal and minimize the disturbances generated by horizontal oscillations. The lock-release experiment has been broadly employed throughout the entire history of the research on gravity flows either in its standard setup [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] and in modified versions purposely designed for specific investigative requirements [17], [18], [19], [20], [21], [22], [23].

Not only does the lock-gate setup represent a suitable device for experimental observation, it also constitutes an appropriate test case for numerical analysis. The simple rectangular geometry makes the lock-gate experiment a valuable candidate for high-resolution DNS and LES models [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], but RANS models have also been successfully employed with different turbulent modeling approaches [36], [37], [38], [39]. The effort to obtain accurate numerical models is motivated by the capability of these models to support the data analysis of experimental measurements, and on the requirement for realistic predictive tools. Validation against experiments have demonstrated the high degree of accuracy at which numerical models can produce estimates of the front velocity and front displacement [30], [31], [32] and deposition rates from particle-laden gravity currents [27]. The capability of the numerical models to capture the realistic shape of the density currents and the overall concentration field was demonstrated in [25], [26], [28]. Direct comparison between the shape of the dense intrusion observed in the experiment of [9] and that predicted by numerical simulation was established by Ooi [40], Hoyes [41] and Paik et al. [42] respectively by means of LES, DNS and k-ϵ RANS models.

Regardless of the resolution of the numerical model, the interval elapsing between the removal of the lock-gate and the stage where the density current has reached a quasi-steady front velocity is systematically ignored. The work of [23] is the only exception where the focus was placed on the initial phase of evolution of the flow; however, in this case a circular sector-shaped lock-release experiment was investigated. The possible inaccuracies of employing a numerical model where the initial effects of the lock-gate are neglected is discussed in [42]. Although concerned with Rayleigh–Taylor instabilities, the work of [43] provides an accurate insight into the process of initiating an experiment by removing a horizontally sliding gate at the interface between two fluids of differing densities.

By examining the experimental observations from [9], [44], [21], [22], the dense intrusion is seen to develop a head immediately after the removal of the lock-gate. As opposed to numerical models, asymmetry between the dense intrusion and the ambient fluid backflow always occurs, even when devices are employed [22] for casting analogous boundary conditions at the channel bed and at the free surface. Most numerical models, on the other hand, agree on the fact that the dense intrusion initially undergoes a rotation during which dense and ambient fluid maintain a symmetric evolution [36], [24], [30], [29], [32]. Ultimately, the features found in the experiments are accompanied by the development of eddies along the entire extent of the contact interface of the fluids. Here it is examined to what degree the lock-gate constitutes a significant disturbance in the experiment and it is assessed whether the physical representation of lock-release density currents can be improved by accounting for the full description of the experimental setup. Moreover, the processes involved in the lock-gate removal are investigated to ascertain categorically what these disturbances are, and to what extent they disrupt the natural evolution of the density current. These questions are addressed through implementation of the triggering mechanism of a lock-release density current into a CFD model. Such analysis will also highlight the relevant laboratory-induced effects which may be important to be aware of during the experimental procedure. Additionally, the numerical techniques described here are equally applicable to similar problems such as dam-break case studies [4], [45], [46], [47], [48] and sluice gate modeling [49], [50], [51].

Section snippets

Work development

The process investigated constitutes a simplified case of fluid–structure interaction modeling. The effects of the fluid on the solid is not relevant to the present analysis, thus reducing the problem to a one-way interaction where only the response of the fluid to the motion of the solid is investigated. The lock-gate may be expected to affect the fluid in its proximity in the following ways:

  • The moving panel represents a constraint on the spontaneous, symmetrical development of the bottom and

Governing equations and lock-gate modeling

In the experimental investigation of [9], and hence in the numerical simulations, the dense flow initially occupies the lock box with a horizontal extent x0= 0.3 m and a vertical depth H= 0.2 m. The reduced gravity g=g(ρ1ρ0)/ρ0=0.12m s2 is used. The numerical simulations presented in this paper are all performed in a two-dimensional reference frame. In the case of the zero-thickness lock-gate, the simulation is performed in a closed 2D rectangular domain Fig. 1(a). In the case of the

Results from the zero-thickness lock-gate model

Two simulations are performed with the zero-thickness lock-gate. Model-I was defined with a stress-free condition prescribed for the vertical velocity on the wall of the lock-gate. Model-II was designed with a source of momentum at the lock-gate equivalent to the speed of withdrawal. This implies that, in the stress-free zero-thickness model-I, only the constraint to the free flow is accounted for, while both the constraint and the gate-induced shear are taken into account by model-II. No

Results from the volumetric lock-gate model

Here, a more realistic description of the lock-gate is employed where the thickness of the panel and the shear produced on the fluid are accounted for along with the motion of the free-surface. This approach is found to be suitable for capturing the full set of processes associated with the withdrawal of the lock-gate.

A comparison between the evolution of the isocontours of concentration predicted by the numerical model and the experimental dataset from [9] is presented in Fig. 8(a–c). In

Front velocities

The analysis of the velocity at the head of the density current is crucial for assessing the accuracy of a simulation. While laboratory measurements of the temporal evolution of the fluid velocity are commonly performed at fixed locations across the channel[63], [12], [15], [16], numerical models usually refer to the velocity of the foremost point of the density current as the reference parameter for the head velocity (e.g., [32]). Here the estimate of the front velocity and horizontal velocity

Discussion

The role of the lock-gate in a lock-release experiment is summarized hereafter based on the numerical simulations presented before. Discussion concerning the limited reproducibility of the very early evolution of lock-release density current by means of numerical models is also addressed. According to the analysis performed in the previous sections, eight distinct terms appear to play a role in determining the initial evolution of a lock-release density current. In the following sections each

Concluding remarks

The role played by the lock-gate in the early development of lock-release gravity currents has been investigated by means of a series of CFD numerical models. From the comparison of the numerical output with the experimental measurements of [9], which these simulations are based on, evidence was brought that an improvement in the predictive capability of the shape of the density current during the early stage of evolution is achieved when the physics associated with the removal of the lock-gate

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