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

Hydraulic Hydraulic Analogy for Analogy for

Compressible Compressible flowflowSimulation and comparison Simulation and comparison

with experimental datawith experimental data

Hydraulic AnalogyHydraulic Analogy

Compressible Flow Free Surface Flow

h

P2 h

Sound speed Surface wave speed

Mach Froude

Shock Wave Hydraulic Jump

Subsonic Flow Subcritical Flow

Sonic Flow Critical Flow

Supersonic Flow Supercritical Flow

Solved equations and Solved equations and variablesvariables

The general transport equation:The general transport equation:

Is solved in 2-D for the variables:Is solved in 2-D for the variables: P1P1 U1U1 V1V1

Standard Standard k-k-turbulence model is turbulence model is activated.activated.

iSvt

iSvt

Implementation in Implementation in PHOENICSPHOENICS

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

Subcritical flow over a Subcritical flow over a bump.bump.

Geometry.Geometry.

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

Subcritical flow over a Subcritical flow over a bump.bump.

Inlet conditions.Inlet conditions. Initial depth Initial depth h=1m.h=1m. Initial velocity Initial velocity v=1.5m/sv=1.5m/s Initial Froude Initial Froude Fr=0.479Fr=0.479 Turbulence intensity 5%Turbulence intensity 5%

The bump is simulated with a The bump is simulated with a porous object, set with a sine porous object, set with a sine function with a minimum porosity function with a minimum porosity of 0.9of 0.9

Simulation ResultsSimulation Results

Velocity and depth in the middle of Velocity and depth in the middle of the channel.the channel.

Simulation ResultsSimulation Results 3-D representation of the free 3-D representation of the free

surface.surface.

Comparision with analytical Comparision with analytical resultsresults Analitical results Simulation

Depth [m] Velocity [m/s] Depth [m] Velocity [m/s]

Initial conditions 1 1.5 0.99 1.51

Bump 0.859 1.745 0.874 1.731

Simulation of supercritical Simulation of supercritical flow near an abrupt wall flow near an abrupt wall

deflection.deflection. Geometry.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.

Simulation of supercritical Simulation of supercritical flow near an abrupt wall flow near an abrupt wall

deflection.deflection. Inlet with Inlet with Fr=4.0Fr=4.0 Initial depth Initial depth h=50mm.h=50mm. Turbulence intensity 5%.Turbulence intensity 5%. Simulations were performed with the Simulations were performed with the

same inlet conditions. Four different same inlet conditions. Four different deflection widths were considered. 50, deflection widths were considered. 50, 100, 150 and 200mm.100, 150 and 200mm.

Simulations results are compared with Simulations results are compared with experimental data.experimental data.

Comparison with Comparison with experimental data in the experimental data in the

deflection area.deflection area.

Comparison for dimensionless depth for 50mm deflection.

Transverse comparisonTransverse comparison

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

Transverse comparisonTransverse comparison

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

Comparison with Comparison with experimental data in the experimental data in the

deflection area.deflection area.

Comparison for dimensionless depth for 100mm deflection.

Transverse comparisonTransverse comparison

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

Transverse comparisonTransverse comparison

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

Comparison with Comparison with experimental data in the experimental data in the

deflection area.deflection area.

Comparison for dimensionless depth for 150mm deflection.

Transverse comparisonTransverse comparison

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

Transverse comparisonTransverse comparison

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

Comparison with Comparison with experimental data in the experimental data in the

deflection area.deflection area.

Comparison for dimensionless depth for 200mm deflection.

Transverse comparisonTransverse comparison

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

Transverse comparisonTransverse comparison

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

3-D representation of the 3-D representation of the free surfacefree surface

Simulation of supercritical Simulation of supercritical flow at channel expansions.flow at channel expansions.

GeometryGeometry

A 14m long, 2.1m witdth channel was considered. Expansion length is 3.0m. Expansion ratio is 1.1667.

Simulation of supercritical Simulation of supercritical flow at channel expansions.flow at channel expansions.

Standard Standard k-k-turbulence model is turbulence model is activated.activated.

Inlet conditions.Inlet conditions. Initial depth Initial depth h=0.3mh=0.3m Initial velocity Initial velocity u=8.577m/su=8.577m/s Initial Froude Initial Froude Fr=5.0Fr=5.0 Turbulence intensity 5%Turbulence intensity 5%

Depth and Froude resultsDepth and Froude results

3-D representation of the 3-D representation of the free surface.free surface.