A Numerical Study of the behaviour on Lock Volume Variations in Lock-Exchange Density Current in Cold Fresh Water

Abstract

The behaviour of warm discharge through lock-exchange was investigated numerically, with the assumption that density was taken as a quadratic function of temperature. Simulations were conducted eleven different times varying barrier position. This work as presented here is practical and can also enhance policy making towards the protection of the aquatic ecosystems. Such behaviours are evident in lakes, especially in holomictic lakes and warm discharge from thermoelectric power generating plants. The sudden increase in water temperature after discharge may leads to ”thermal shock” killing aquatic life that has become acclimatised to living in a stable temperate environment. The aim of this investigation is to better fathom and as well, gain more insight into such flows. The results show that regimes of flow is dependent on the size of the lock volume. The general behaviours here are dependent on lock volume, density difference and Reynolds number. Effects of back reflected waves on the propagation speed was not significant for small lock volume simulations. A rapid collapsing behaviour of fluid was noticed for simulations with small lock volume, and the velocity decreases with increase in lock volume in this same phase. Propagation speed is not totally independent of the lock volume. Cabbeling was also key at the point where water masses meet, and as well the development of Kelvin-Helmholtz instabilities. Relations that describes the various regimes of flow are given in Table (1 - 11). Though, there are little variations in the scaling laws as compared to the earlier studied cases where density difference was by the means of salt water. Lastly, it will be interesting if measures can be taken to eliminate the effect of this back reflected waves in other to properly fathom the behaviour in thepropagation of the frontal speed after the slumping phase.

Propagation Speed of the Frontal Head Through Lock-Exchange Density Current in Cold Fresh Water: Simulations without the Effect of Back-reflected Waves

“…Results here show that the velocity with which the current travels with in the second regime of flow, is higher within the first time frame than those by [3,9,23] with the effect of back reflected waves (see Fig. 4(a), 5(a) with a linear scale).…”

“…4(a), 5(a) with a linear scale). Meanwhile, speed of the current in the first regime of flow appear more like those by [3,23] with small lock volume. This is also evident in Table 1 and 2, where we have obtained some empirically determined data set that represent the best fit power laws obtained by linear regression of logU dc1 on logτn.…”

“…4(a), 5(a)). It is also worth noting that the speedy movement of fluid in this collapsing phase might not only be to the influence of the small lock volume [23] but also to the fact that denser fluid could flow from two fronts. Unlike those where denser fluid is positioned at one end of the container [2,3,23].…”

“…3(f -j)) even as the penetrating sharp head of the current advances forward, leaving fluid that have attained φin = 0 at the rear. But then, simulations with increased lock volume have shown that a ground flow of warm but dense fluid from the rear continue to replenish this head, enabling the frontal head to penetrate the ambient fluid faster [23]. Though, density difference between ambient fluid and dense fluid is very small, thus mixture requires just a little mixing before attaining φin = 0.…”

“…It has been established that gravity currents usually undergo either two or three distinct phases of flow and these include: a slumping phase, self-similar phase and viscous phase [9,11,23] but that this is also dependent on the lock volume. This authors [23] have established that number of distinct phases of flow are dependent on the lock volume (i.e., two phases of flow when the lock volume is big and three phases of flow when the lock volume is small). Thus, having identified two regimes here, we can the say that the lock volume used is fairly big.…”