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Hydraulic Analogy for Compressible flow

Hydraulic Analogy for Compressible flow. Simulation and comparison with experimental data. Hydraulic Analogy. 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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Hydraulic Analogy for Compressible flow

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  1. Hydraulic Analogy for Compressible flow Simulation and comparison with experimental data

  2. Hydraulic Analogy

  3. 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.

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

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

  6. Subcritical flow over a bump. • Inlet conditions. • Initial depth h=1m. • Initial velocity v=1.5m/s • Initial Froude Fr=0.479 • Turbulence intensity 5% • The bump is simulated with a porous object, set with a sine function with a minimum porosity of 0.9

  7. Simulation Results • Velocity and depth in the middle of the channel.

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

  9. 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.

  10. Simulation of supercritical flow near an abrupt wall deflection. • Inlet with Fr=4.0 • Initial depth h=50mm. • 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.

  11. Comparison with experimental data in the deflection area. Comparison for dimensionless depth for 50mm deflection.

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

  13. Transverse comparison Dimensionless depth profile at 80cm from the origin of the deflection wall.

  14. Comparison with experimental data in the deflection area. Comparison for dimensionless depth for 100mm deflection.

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

  16. Transverse comparison Dimensionless depth profile at 80cm from the origin of the deflection wall.

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

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

  19. Transverse comparison Dimensionless depth profile at 80cm from the origin of the deflection wall.

  20. Comparison with experimental data in the deflection area. Comparison for dimensionless depth for 200mm deflection.

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

  22. Transverse comparison Dimensionless depth profile at 80cm from the origin of the deflection wall.

  23. 3-D representation of the free surface

  24. 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.

  25. Simulation of supercritical flow at channel expansions. • Standard k-e turbulence model is activated. • Inlet conditions. • Initial depth h=0.3m • Initial velocity u=8.577m/s • Initial Froude Fr=5.0 • Turbulence intensity 5%

  26. Depth and Froude results

  27. 3-D representation of the free surface.

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