Encyclopaedia Index

## TITLE : A whirlpool in a pond

BY : CHAM User Support Team - Dr S V Zhubrin

FOR : Demonstration case

DATE : November, 2000

PHOENICS Version : 3.3.1

### PHYSICAL SITUATION :

• Steady free surface turbulent flow of water recirculating under influence of bottom stresses and internal blockage in an open pond.
• The task is to simulate the velocity distribution along with free water surface elevation.

### ASSUMPTIONS :

• Hydrostatic pressure
• Incompressible, homogeneous fluid
• Non-varying bed topography
• Shallow flow: small vertical scale relative to horizontal
• Well-mixed-in-depth flow: uniform vertical distributions

### SHALLOW-WATER MODELLING:

• Two-dimensional treatment of three-dimensional flows with the local depth calculated as part of solution.
• Depth-averaged version of Navier-Stokes equations;
• Equations solved by analogy to isentropic, compressible gas flow:
• Density, RHO1= Water density*Depth
• Pressure, P1= g*RHO1**2/(2*water density), i.e.
• RHO1=sqrt(2*water density*P1/g)
• U1, V1 = depth-averaged velocity components.

### NUMERICAL DETAILS :

• Cartesian computational grid.
• Effective-viscosity turbulence model
• Boundary conditions:
• Fixed fluxes for inlet mass/momentum and
• Fixed-pressure outlet (equivalent to fixed depth).
• Bottom stresses are calculated by relating them to the velocities via Chezy's coefficient.

### RESULTS :

The plots show the distribution of velocity and water depth (free surface elevation) within the pond.

Pictures are as follows :

### THE IMPLEMENTATION

All model settings have been made in VR-Editor of PHOENICS 3.3.1. The relationships for bottom stresses are introduced via PLANT menu.

The relevant Q1 file can be inspectedby clicking here.

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