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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