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.

svz