Hydraulic Analogy for Compressible flow

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Hydraulic Analogy for Compressible flow

• Simulation and comparison with experimental data

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Hydraulic Analogy
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Solved equations and variables

• The general transport equation
• Is solved in 2-D for the variables
• P1
• U1
• V1
• Standard k-e turbulence model is activated.

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Implementation in PHOENICS

• The following settings must be made in the Q1
  file in order to activate the hydraulic analogy
  ecuations.

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Subcritical flow over a bump.

• Geometry.

A 7m long, 2.1m width channel with a 0.1m high
and 1m long bump was considered.
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Subcritical flow over a bump.

• Inlet conditions.
• Initial depth h1m.
• Initial velocity v1.5m/s
• Initial Froude Fr0.479
• Turbulence intensity 5
• The bump is simulated with a porous object, set
  with a sine function with a minimum porosity of
  0.9

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Simulation Results

• Velocity and depth in the middle of the channel.

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Simulation Results

• 3-D representation of the free surface.
• Comparision with analytical results

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Simulation of supercritical flow near an abrupt
wall deflection.

• Geometry.

A 2.5m long and 0.5m wide with a variable 1m long
deflection was simulated.
Experimental reference Hager W., Jimenez O., et
al. Supercritical flow near an abrupt wall
deflection Journal of Hydraulic Research. V32-1.
1994.
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Simulation of supercritical flow near an abrupt
wall deflection.

• Inlet with Fr4.0
• Initial depth h50mm.
• Turbulence intensity 5.
• Simulations were performed with the same inlet
  conditions. Four different deflection widths were
  considered. 50, 100, 150 and 200mm.
• Simulations results are compared with
  experimental data.

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Comparison with experimental data in the
deflection area.
Comparison for dimensionless depth for 50mm
deflection.
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Transverse comparison
Dimensionless depth profile at 40cm from the
origin of the deflection wall.
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Transverse comparison

• Dimensionless depth profile at 80cm from the
  origin of the deflection wall.

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Comparison with experimental data in the
deflection area.

• Comparison for dimensionless depth for 100mm
  deflection.

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Transverse comparison
Dimensionless depth profile at 40cm from the
origin of the deflection wall.
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Transverse comparison

• Dimensionless depth profile at 80cm from the
  origin of the deflection wall.

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Comparison with experimental data in the
deflection area.
Comparison for dimensionless depth for 150mm
deflection.
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Transverse comparison

• Dimensionless depth profile at 40cm from the
  origin of the deflection wall.

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Transverse comparison

• Dimensionless depth profile at 80cm from the
  origin of the deflection wall.

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Comparison with experimental data in the
deflection area.

• Comparison for dimensionless depth for 200mm
  deflection.

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Transverse comparison

• Dimensionless depth profile at 40cm from the
  origin of the deflection wall.

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Transverse comparison

• Dimensionless depth profile at 80cm from the
  origin of the deflection wall.

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3-D representation of the free surface
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Simulation of supercritical flow at channel
expansions.

• Geometry

A 14m long, 2.1m witdth channel was considered.
Expansion length is 3.0m. Expansion ratio is
1.1667.
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Simulation of supercritical flow at channel
expansions.

• Standard k-e turbulence model is activated.
• Inlet conditions.
• Initial depth h0.3m
• Initial velocity u8.577m/s
• Initial Froude Fr5.0
• Turbulence intensity 5

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Depth and Froude results
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3-D representation of the free surface.