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Modelling hydraulic jumps: IDDES versus experiments

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Abstract

The present paper analyses the advantages and limitations of using numerical modelling to simulate hydraulic jumps at high Froude numbers. Two hydraulic jumps of the same Froude number (7.5) but different Reynolds numbers were simulated using Improved Delayed Detached Eddy Simulation. The free surface was captured using the Volume of Fluid multiphase model with a High-Resolution Interface-Capturing technique. Flow properties including velocity, total pressure and air concentration profiles were compared with experimental results at different streamwise locations. It was observed that while the simulations were able to accurately capture the velocity and pressure fields, the air concentration values were over predicted, although the air concentration distribution was successfully reproduced. Since the simulations capture the complete three-dimensional flow field, further analysis of different physical mechanisms contributing to air entrainment are also carried out. The turbulent kinetic energy and the vorticity field were examined to understand the air–water flow dynamics. The coherent structures responsible for air entrainment were identified using vortex identification techniques. The influence of these structures on the air-entrainment mechanisms is presented with pertinent discussions.

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Abbreviations

\(C\) :

Mean air concentration (–)

\(C_{mean}\) :

Depth-averaged air concentration (–)

\(C_{max}\) :

Local maximum mean air concentration (–)

\(d_{0}\) :

Height of gate opening (m)

\(d_{1}\) :

Supercritical flow depth at jump toe (m)

\(d_{2}\) :

Tailwater depth (m)

C α :

Sharpening factor used in the VOF model (–)

F1 :

Inlet Froude number (–)

g:

Acceleration due to gravity (m s−2)

K:

Mean curvature of free surface (m−1)

\(L_{r}\) :

Length of the roller (m)

p :

Mean total pressure (Pa)

p max :

Maximum mean total pressure (Pa)

Re:

Reynolds number (–)

St:

Strouhal number (–)

Sr :

Additional mass source term in VOF model (kg m−3 s)

Sαi :

Source or sink of the ith phase in the VOF model (–)

\(T\) :

Time period of jump toe oscillations in CHJ (s)

\(t\) :

Time (s)

\(U\) :

Mean x-component of velocity (m s−1)

U m :

Maximum value of U at any x-location (m s−1)

\(U_{1}\) :

Velocity at the jump toe (m s−1)

α :

Volume fraction (–)

η :

Free-surface elevation (m)

μ :

Dynamic viscosity of the fluid (kg m s−1)

μa :

Dynamic viscosity of the air (kg m s−1)

μw :

Dynamic viscosity of the water (kg m s−1)

ρ :

Density of the fluid (kg m−3)

ρa :

Density of the air (kg m−3)

ρw :

Density of the water (kg m−3)

σ :

Surface tension (N m−1)

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Windsor, Windsor, ON, Canada

    Vimaldoss Jesudhas & Ram Balachandar

  2. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, China

    Hang Wang

  3. Department of Mechanical Engineering, ESTACA West Campus, Laval, France

    Frederic Murzyn

Authors
  1. Vimaldoss Jesudhas
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  2. Ram Balachandar
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  3. Hang Wang
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  4. Frederic Murzyn
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Correspondence to Frederic Murzyn.

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Jesudhas, V., Balachandar, R., Wang, H. et al. Modelling hydraulic jumps: IDDES versus experiments. Environ Fluid Mech 20, 393–413 (2020). https://doi.org/10.1007/s10652-019-09734-5

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