Hydrodynamic Efficiency Analysis of a Flexible Hydrofoil Oscillating in a Moderate Reynolds Number Fluid Flow
Abstract
:1. Introduction
2. Problem Formulation
2.1. Oscillating and Deformable Hydrofoil
2.2. Fluids Dynamics Equations
2.3. Structure Dynamics Equations
2.4. Fluid-Structure Interaction Coupled Problem
3. Numerical Resolution
3.1. Heaving Reference Frame Validation
3.2. FSI Implicit Coupling Scheme Validation
3.3. Mesh and Time Step Convergence Analysis
4. Results and Discussion
4.1. Analysis of the Flow in the Wake of the Hydrofoil
4.2. Flexibility Influence on the Hydrodynamic Forces
4.3. Flexibility Influence on the Power Extraction Efficiency of the Hydrofoil
4.4. Fluid Pressure and Vorticity Fields Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Abbreviations
NACA | National Advisory Committee for Aeronautics |
LEV | Leading-edge vortex |
Mean value of a over one motion period | |
Flow velocity [m/s] | |
Free-stream velocity [m/s] | |
Vorticity in z-direction [1/s] | |
p | Flow pressure [Pa] |
Density [kg/m] | |
Re | Nombre de Reynolds [-] |
Angle of attack [°] | |
h | Vertical position [m] |
T | Motion period [s] |
c | Hydrofoil chord length [-] |
Dimensionless x-projection of the hydrodynamic forces [-] | |
Dimensionless y-projection of the hydrodynamic forces [-] | |
Dimensionless torque of the hydrodynamic forces [-] | |
Dimensionless extracted power [-] | |
Efficiency [-] | |
Dimensionless oscillating frequency [-] | |
Dimensionless time [-] | |
Mass density | |
Structure local displacements | |
Young’s modulus |
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Designation (−) | hydrofoil 1 | hydrofoil 2 | hydrofoil 3 |
Density (kg/m) | 1420 | 1420 | 1420 |
Young’s Modulus (GPa) | 1.0 | 0.1 | 0.01 |
Poisson’s Coefficient (−) | 0.35 | 0.35 | 0.35 |
Solvers | Cells | Time Steps/Cycle | ||
---|---|---|---|---|
Blackburn & Henderson [34] | 422 | 2000 | 1.414 | 1.776 |
Kinsey & Dumas [2] | 65,600 | 2000 | 1.412 | 1.755 |
Present | 75,000 | 2000 | 1.467 | 1.761 |
Relative deviations with [34] | - | - | 3.75% | 0.84% |
(-) | (-) | (°) | [mm] | |
---|---|---|---|---|
Experiment [41] | 0.80 | 0.045 | 0.2 | 1.48 |
Numerical—Ansys [23] | 0.85 | 0.058 | 0.17 | 1.5 |
Numerical—OpenFoam | 0.74 | 0.058 | 0.22 | 1.35 |
Relative deviations with [41] | 7.5% | 22% | 10% | 8.5% |
Mesh 1 | Mesh 2 | Mesh 3 | Mesh 4 | |
---|---|---|---|---|
° | 0.189 | 0.220 | 0.219 | 0.219 |
° | 2.26 | 2.26 | 2.27 | 2.27 |
° | 3.91 | 3.72 | 3.75 | 3.75 |
Hydrofoil 1 | Hydrofoil 2 | Hydrofoil 3 | |
---|---|---|---|
° | 0.2197 | 0.2567 | 0.3166 |
° | 2.279 | 2.442 | 2.878 |
° | 3.746 | 4.026 | 4.374 |
° | 5.088 | 6.119 | 6.070 |
° | 8.258 | 8.655 | 13.72 |
° | 12.87 | 15.75 | 21.66 |
° | 13.99 | 17.84 | 20.45 |
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Brousseau, P.; Benaouicha, M.; Guillou, S. Hydrodynamic Efficiency Analysis of a Flexible Hydrofoil Oscillating in a Moderate Reynolds Number Fluid Flow. Energies 2021, 14, 4370. https://doi.org/10.3390/en14144370
Brousseau P, Benaouicha M, Guillou S. Hydrodynamic Efficiency Analysis of a Flexible Hydrofoil Oscillating in a Moderate Reynolds Number Fluid Flow. Energies. 2021; 14(14):4370. https://doi.org/10.3390/en14144370
Chicago/Turabian StyleBrousseau, Paul, Mustapha Benaouicha, and Sylvain Guillou. 2021. "Hydrodynamic Efficiency Analysis of a Flexible Hydrofoil Oscillating in a Moderate Reynolds Number Fluid Flow" Energies 14, no. 14: 4370. https://doi.org/10.3390/en14144370
APA StyleBrousseau, P., Benaouicha, M., & Guillou, S. (2021). Hydrodynamic Efficiency Analysis of a Flexible Hydrofoil Oscillating in a Moderate Reynolds Number Fluid Flow. Energies, 14(14), 4370. https://doi.org/10.3390/en14144370