Numerical Simulation of Density Current Evolution in a Diverging Channel

Mitra Javan,Afshin Eghbalzadeh,Masoud Montazeri Namin

doi:10.1155/2012/729597

Mitra Javan, Afshin Eghbalzadeh + Show 1 more

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https://doi.org/10.1155/2012/729597

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Abstract

Numerical Simulation of Density Current Evolution in a Diverging Channel: When a buoyant inflow of higher density enters a reservoir, it sinks below the ambient water and forms an underflow. Downstream of the plunge point, the flow becomes progressively diluted due to the fluid entrainment. This study seeks to explore the ability of 2D width-averaged unsteady Reynolds-averaged Navier-Stokes (RANS) simulation approach for resolving density currents in an inclined diverging channel. 2D width-averaged unsteady RANS equations closed by a buoyancy-modified <svg style="vertical-align:-0.13794pt;width:33.8125px;" id="M1" height="10.7375" version="1.1" viewBox="0 0 33.8125 10.7375" width="33.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan> <tspan style="font-size: 12.50px; " x="9.5522919" y="0">−</tspan> <tspan style="font-size: 12.50px; " x="20.892513" y="0">𝜀</tspan> </text> </g> </g> </svg> turbulence model are integrated in time with a second-order fractional step approach coupled with a direct implicit method and discretized in space on a staggered mesh using a second-order accurate finite volume approach incorporating a high-resolution semi-Lagrangian technique for the convective terms. A series of 2D width-averaged unsteady simulations is carried out for density currents. Comparisons with the experimental measurements and the other numerical simulations show that the predictions of velocity and density field are with reasonable accuracy.

Highlights

When a river enters the relatively quiescent water of a lake or reservoir, it meets water of slightly different temperature, salinity, or turbidity
Unsteady Reynolds-averaged Navier-Stokes (RANS) approach with the statistical turbulence model provides a viable alternative for engineering computations of gravity currents at practical Reynolds numbers, and several such models have been proposed in the literature
The parameter values used in the calculation for the numerical simulation of these cases are summarized in Table 1 which includes inflow rate (q0), inlet temperature (Tinlet), ambient water temperature (T0), divergence half-angle of channel (δ), the bottom slope (S), width of inflow channel (B0), and depth of inflow channel (H0)

Summary

Introduction

When a river enters the relatively quiescent water of a lake or reservoir, it meets water of slightly different temperature, salinity, or turbidity. If the river is lighter than the surface water, it will form an overflow Such a current has been observed in Lake Kootenay in Canada [1]. When the river is heavier than the water of the lake, it sinks and flows as an inclined plume along its morphological channel. Such a current has been reported by Huppert and Simpson [3] in the Wellington Reservoir in Australia. Bournet et al [29] simulated plunging gravity currents in an inclined channel of constant width and in a diverging channel. It is beneficial to develop and validate a new numerical model that can speedily solve the specific problems in hydraulic engineering

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