Encyclopaedia Index

## TITLE : Hydraulic jump in a supercritical flow

BY : CHAM User Support Team - Dr S V Zhubrin

FOR : Demonstration case

DATE : November, 2000

PHOENICS Version : 3.3.1

### PHYSICAL SITUATION :

- The physical situation simulates the impingement of uniform
supercritical (Froude number is 2.8) water flow on a solid block.
- One symmetric half of the flow is considered due to symmetric
flow pattern.
- In adjusting to the stagnation conditions on the block face the
supercritical stream is expected to undergo an oblique hydrailic
jump.
- A subcritical region is then created between the jump and the body.
- The subcritical flow is deflected round the body and accelerates to
supercritical flow again.
- The task is to compute the distributions of velocities and depths.

### ASSUMPTIONS :

- Hydrostatic pressure
- Incompressible, homogeneous fluid
- Viscous, bed friction and turbulence effects are neglected
- 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= Depth, h
- Pressure, P1= g*h**2/2, i.e.
- RHO1=sqrt(2*P1/g)
- U1, V1 = depth-averaged velocity components

### NUMERICAL DETAILS :

- Cartesian computational grid.
- Boundary conditions:
- Fixed fluxes for inlet mass/momentum and
- Fixed-pressure outlet (equivalent to fixed depth).

### RESULTS :

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

Pictures are as follows :

### THE IMPLEMENTATION

All model settings have been made in VR-Editor of PHOENICS 3.3.1.

The relevant Q1 file can be inspectedby clicking
here.

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