^{1}

^{1}

^{2}

^{1}

^{2}

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

When a river enters the relatively quiescent water of a lake or reservoir, it meets water of slightly different temperature, salinity, or turbidity. Three configurations may occur. First, 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 [

In this paper, the model employing the Boussinesq form of the width-averaged unsteady RANS equations in conjunction with a buoyancy-extended

In this study, we focus on flows with relatively small density differences for which the usual Boussinesq approximation can be assumed to be valid—that is, all variations in density can be neglected except for the buoyancy term. Incorporating the Boussinesq hypothesis to relate the Reynolds stresses with the mean rate of strain tensor via an eddy viscosity, 2D width-averaged unsteady RANS equations for incompressible, stratified flow read as

Side shear stress terms that appear on the boundaries, due to the width averaging, are equal to zero, and slipping conditions are assumed.

The dispersion terms due to lateral nonuniformities of the flow quantities, which appear in the width-averaging of the 3D equations, are neglected [

The eddy viscosity is modeled by the buoyancy-modified

In the above equations,

In the above equations,

The turbulent Prandtl number

Density is assumed to be linearly related to the mean volumetric concentration through the equation of state as

Nonuniform bathymetry of the computational domains is handled by the sigma-type body-fitted grids which fit the vertical direction of the physical domain. The finite-volume integration method is used for different terms in the governing equations. A fractional step [

The boundaries of the computational domain are inlet, outlet, free-surface, and solid walls. In the absence of wind shear, the net fluxes of horizontal momentum and turbulent kinetic energy are set equal to zero at the free surface. Flat, slip boundary condition of zero velocity gradient normal to the surface is applied, and the pressure is set equal to the atmospheric value at the surface. The dissipation rate

The wall function approach is used to specify boundary conditions at the bottom of the channel in order to avoid the resolution of viscous sublayer. The first grid point off the wall (center of the control volume adjacent to the wall) is placed inside the logarithmic layer based on the buoyancy velocity

On the other hand, if the first grid node from the wall locates within the viscous layer

At the inlet, known quantities are specified for the inflow velocity, the concentration of the density current source, and the current thickness, while turbulent kinetic energy and dissipation rate at the inlet are estimated as follows [

In this section, we report numerical results for density currents from continuous sources along with comparisons with the experimental and numerical results of Johnson and Stefan [

The parameter values for the numerical simulations of the continuous density currents in an inclined diverging channel.

Presented by | |||||||
---|---|---|---|---|---|---|---|

Johnson and Stefan [ | 0.0018 | 19.9 | 39.9 | 20 | 0.052408 | 0.091 | 0.17 |

Bournet et al. [ | 15 | 10 | 20 | 7 | 0.025 | 20 | 2 |

Plan and longitudinal section view of diverging channel with sloping bottom at the experiment of Johnson and Stefan [

Plan

Longitudinal section

We first present the comparison of the numerical solutions and experimental measurements published by Johnson and Stefan [

Simulated dimensionless temperature distribution of the Johnson and Stefan experiment [

Comparison of simulated dimensionless temperature and experimental results of Johnson and Stefan [

In the second stage, we present the comparison of the solutions and numerical results published by Bournet et al. [

Plan and longitudinal section view of diverging channel with sloping bottom at the simulation of Bournet et al. [

Plan

Longitudinal section

In the upstream region of the channel (

To compare numerical solutions with the results of Bournet et al. [

Simulated Velocity Field (a) the results of Bournet et al. [

Comparison of simulated iso-contours (dashed lines) of temperature distribution and the results of Bournet et al. [

Figure

Sequential snapshots of density distributions computed at selected time instants (note that the

A series of 2D width-averaged URANS simulations are carried out to resolve continuous density currents in an inclined diverging channel. Comparison of the numerical solutions with available experimental measurements and numerical results leads to the conclusion that 2D width-averaged unsteady RANS simulations using a buoyancy-extended

Detailed comparisons have shown in general that this two-dimensional width-averaged model can be applied to the simulation of the density current in reservoirs which the Froude number of the inlet dense flow and divergence half-angle of reservoir