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A plane, turbulent, nonbuoyant, vertical jet in shallow water is simulated numerically using a three-dimensional computation model employing standard

Turbulent jets have been used extensively for discharging effluent into rivers, lakes, and coastal environments. Detailed theoretical and experimental studies of free, turbulent jets (circular or plane jets in an infinite extent of ambient fluid) have been reported by Albertson et al. [

Gutmark et al. [

Kuang et al. [

Layout of vertical jet in shallow water.

The free jet regions (ZFE and ZEF) in cases of plane jet impingement on solid surface (Case I) and plane jet issuing vertically upward in a still ambient fluid of finite depth (Case II) are similar. However in ZEF for Case II, Kuang et al. [

Due to the difficulty of obtaining an analytical solution, especially in the zones of surface impingement and horizontal jets, the problem of a jet issuing vertically upward in shallow water is studied using physical models. Numerical models have been adopted increasingly to study complex flow problems. To numerically model turbulent flows, the selection of an appropriate turbulence scheme is essential. The two most common turbulence closure schemes are the

The mass and momentum equations, which constitute the Reynolds-averaged Navier-Stokes (RANS) equations, are given by

A constitutive relationship is required to relate the turbulent normal and shear stresses to mean flow velocities and is achieved through the use of turbulent eddy viscosity. The relationship is given by

In the case of the standard

In the

The

In this study, the experimental data collected by Kuang et al. [

A computational fluid dynamics model, FLOW-3D, developed by Flow Science, Inc., is used to numerically solve the RANS equations. The Flow-3D software provides several options for the turbulent closure scheme including Prandtl mixing length model, two-equation models, and large eddy simulation model. In this study,

The geometry of the experimental setup, as given by Kuang et al. [

To model the scenario as two-dimensional flow in the FLOW-3D model, only one cell needed to be specified in the

Mesh configuration.

The computational results obtained using the

Growth rate and virtual origin comparison.

Characteristics | Kuang et al. [ | RNG scheme | |
---|---|---|---|

Growth rate ( | 0.1 | 0.104 | 0.117 |

Virtual origin ( | 5.0 | 0.51 | −0.61 |

The variation of longitudinal velocity (

Centerline velocity variation.

Variation of centerline turbulent velocity fluctuations.

The variations of longitudinal (

Profiles of longitudinal velocity in ZFE.

Profiles of longitudinal velocity in ZEF.

Profiles of longitudinal velocity in ZSI.

The simulated results of the lateral velocity profiles across the width of the jet are compared to the measured and/or theoretical velocity profiles in Figures

Profiles of lateral velocity in ZFE.

Profiles of lateral velocity in ZEF.

Profiles of lateral velocity in ZSI.

The zone of surface impingement is where the flow turning and acceleration take place. Starting with zero horizontal velocity, the

The predicted turbulent kinetic energy (TKE) profiles across the jet at different locations along the jet are shown in Figures

Profiles of turbulent kinetic energy in ZFE.

Profiles of turbulent kinetic energy in ZEF.

Profiles of turbulent kinetic energy in ZSI (

The variations of lateral velocity in the zone of horizontal jets (ZHJ) predicted by the

Profiles of lateral velocity in ZHJ (

Profiles of lateral velocity in ZHJ (RNG scheme).

Recirculation zone predicted using RNG scheme.

Decay of maximum lateral velocity in ZHJ.

A plane turbulent jet issuing vertically upward in shallow water depth has been simulated using a three-dimensional computational model employing the

In the ZFE and ZEF, the vertical velocities are overpredicted by the RNG scheme. The lateral velocities are underpredicted by both schemes in the ZFE with RNG scheme providing a better fit. While in the ZEF, the RNG scheme progressively underpredicts the lateral velocity with an increase in distance from the nozzle. The TKE is overpredicted (by about 30%) near the center of the jet by the RNG scheme in ZFE. The TKE profiles predicted using the RNG scheme do not preserve self-similarity shown by the measured data and the values are overpredicted near the center. The

The onset of ZSI, based on the centerline variation of TKE, is accurately predicted by both schemes. The vertical velocities are underpredicted by both schemes in this zone, with RNG unable to accurately predict the shape of the profile near the surface. The lateral velocities are predicted more accurately by the RNG scheme in ZSI. The TKE is predicted accurately near the center of the jet and underpredicted at the outer edges by both schemes in this zone.

In the zone of horizontal jets, the lateral velocity in the forward direction and the recirculation zone underneath the surface jet are better predicted by the

A measure of the jet growth

Growth rate of the jet

Empirical coefficient

Empirical coefficient

Empirical coefficient

Width of the nozzle

Water depth in the tank (26 cm)

Turbulent kinetic energy per unit mass

Piezometric pressure

Prandtl number for

Prandtl number for

Source term in RNG scheme

Mean rate of strain

Time

Time-averaged velocity components

Velocity in the

Maximum lateral velocity in the zone of horizontal jets

Turbulent normal and shear stresses

Velocity in the

Centerline velocity in the

Jet velocity at the nozzle

Coordinate direction

Coordinate directions in

Coordinate direction

Distance to the virtual origin

A constant

Kinematic viscosity of the fluid

Combination of the fluid and turbulent kinematic viscosity

Turbulent eddy viscosity

Density of fluid

Kronecker delta

Dissipation rate of turbulence per unit mass

Empirical coefficient

Empirical coefficient

A function of

A constant.