Assessment of CFD Solvers and Turbulent Models for Water Free Jets in Spillways
Abstract
:1. Introduction
2. Numerical Modelling
2.1. Comparison of the Used Solvers
- subscript defines the phase;
- —phase fraction;
- —velocity;
- —pressure;
- —combined turbulent (Reynolds) and viscous stress;
- —inter-phase momentum transfer term.
2.2. Turbulence Models
- —turbulent kinetic energy;
- —effective diffusivity for ;
- —turbulent kinetic energy production rate;
- —turbulent kinetic energy dissipation rate;
- —effective diffusivity for ;
- , and —model coefficients, , , ;
- —turbulent kinetic energy production rate;
- —model coefficient, ;
- —internal source term for k
- —turbulent kinetic energy dissipation rate;
- —effective diffusivity for ;
- —viscosity;
- —closure coefficient;
- —lending function;
- ;
- —internal source term for .
2.3. Mesh
- —vertical distance (m);
- —vertical distance of the point with C = 0.5 in the upper nappe to the floor (m);
- —vertical distance of the point with C = 0.5 in the lower nappe to the floor (m);
- —approach flow depth (m);
- —flow velocity (m/s);
- —potential velocity of the flow at a cross-section (m/s);
- —distance from the step (m).
2.4. Boundary Conditions
2.5. Numerical Schemes
3. Results and Discussion
3.1. Velocity
3.2. Air Concentration
3.3. Turbulence Intensity
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Features | interFoam | twoPhaseEulerFoam |
---|---|---|
Formulation | Euler-Euler (VOF) | Euler-Euler (Dispersed) |
Phases | Two continuous | One continuous One dispersed |
Mass and momentum equations | One set of equations | Two sets of equations |
Interphase mass and momentum transfer | No | Yes |
Mesh | Sub-Domains | Cell Dimensions (mm) | Number of Cells in a Cross-Section of the Jet | Total Number of Cells of the Mesh | y+ |
---|---|---|---|---|---|
1 | All domain | 2.00 | ≈15 | 86.430 | 150 |
2 | Far from the jet Jet and vicinity | 2.00 1.00 | ≈30 | 227.545 | 75 |
3 | Far from the jet Jet and vicinity | 2.00 0.25 | ≈120 | 2.074.297 | 75 |
Term | interFoam | twoPhaseEulerFoam |
---|---|---|
convection | Gauss Van Leer | Gauss Van Leer |
artificial compression | Gauss linear | Gauss Van Leer |
momentum transport | Gauss linear Upwind grad(U) | Gauss upwind |
turbulence | Gauss upwind | Gauss upwind |
Inlet Turbulence Intensity (%) | interFoam (%) | twoPhaseEulerFoam (%) |
---|---|---|
10.00 | 1.86 | 2.67 |
1.00 | 1.83 | 2.65 |
0.10 | 1.93 | 2.66 |
0.01 | 1.87 | 2.75 |
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Muralha, A.; Melo, J.F.; Ramos, H.M. Assessment of CFD Solvers and Turbulent Models for Water Free Jets in Spillways. Fluids 2020, 5, 104. https://doi.org/10.3390/fluids5030104
Muralha A, Melo JF, Ramos HM. Assessment of CFD Solvers and Turbulent Models for Water Free Jets in Spillways. Fluids. 2020; 5(3):104. https://doi.org/10.3390/fluids5030104
Chicago/Turabian StyleMuralha, António, José F. Melo, and Helena M. Ramos. 2020. "Assessment of CFD Solvers and Turbulent Models for Water Free Jets in Spillways" Fluids 5, no. 3: 104. https://doi.org/10.3390/fluids5030104