Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body
Abstract
:1. Introduction
2. Formulation of the Hydrodynamic Problem
3. Hydrodynamic Forces
4. Numerical Results
4.1. Validation
4.2. Test Cases
4.2.1. Coaxial Bottom-Mounted Porous Cylindrical System
4.2.2. Bottom-Mounted Porous Compound Cylindrical Body
4.2.3. Free Floating Porous Compound Cylindrical Body
5. Conclusions
- The presence of the porous cylindrical surface reduces the hydrodynamic forces on the inner cylinder, as well as the wave run up. This could be beneficial for minimizing the environmental impact on pile-supported marine structures;
- Sloshing phenomena due to the fluid motion in the fluid volume confined between the porous surface and the inner cylinder are notable. Accordingly, sloshing phenomena create resonant peaks in the trends of the hydrodynamic loads and the wave elevations;
- In addition, resonances at specific wave numbers are encountered in the drift forces and the wave run-up. At the corresponding wave numbers, the porous surface cannot dissipate the wave energy, thus enhancing the wave impact on the porous system;
- The presence of the outer porous cylinder causes an increase on the hydrodynamic forces and added mass, which are bounded by the limiting cases G = 0 and G ≫ 1 On the other hand, the damping coefficient is not bounded by these limiting cases due to the existence of the additional porous damping, which increases the values of the total damping coefficient;
- The chosen porosity plays a key role in reducing/controlling the forces and moments on a system under consideration by dissipating the wave energy. The permeability of the outer porous surface increases with the increase of G, enhancing the wave impact on the inner cylinder. Hence, G needs to be chosen so as to have the optimum impact on the inner cylinder in addition to reducing the resonance effects.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Wave amplitude | |
k | Wave number |
ω | Wave frequency |
d | Constant water depth |
h | Distance between the bottom of the body and the seabed |
h1 | Distance between the bottom of the porous surface and the seabed |
α | Radius of the porous cylindrical surface |
b | Radius of the coaxial cylinder |
Velocity potential around the porous body, k = I, II, III | |
Velocity potential of the undisturbed incident regular wave | |
Scattered velocity potential | |
Diffraction velocity potential | |
Radiation velocity potential, j = 1,3,5 | |
Complex velocity amplitude of body motion in j-th direction | |
m-th Bessel function of first kind | |
Neumann’s symbol | |
Principal unknowns of the diffraction and radiation problems, ℓ = D, 1, 3, 5; k= I, II, III | |
S | Body’s impermeable wetted surface |
Generalized normal vector | |
μ | Dynamic viscosity |
γ | Material constant |
ρ | Fluid density |
Porous coefficient | |
τ | Opening rate of the material |
ε | Wave slope |
m-th order Hankel function of first kind | |
m-th order modified Bessel function of second kind | |
Orthonormal eigenfunctions | |
m-th order modified Bessel function of first kind | |
Fourier coefficients defined by the solution of the corresponding diffraction and radiation problems | |
Horizontal exciting forces | |
Vertical exciting forces | |
M | Overturning moment |
Hydrodynamic reaction forces | |
Added mass coefficients | |
Damping coefficients | |
Mean drift wave forces | |
Gravity acceleration | |
M | Generalized mass matrix |
First-order translations vector | |
R | Rotational transformation matrix |
First-order translational accelerations of body’s center of gravity | |
Relative wave elevation | |
Vertical distance of the body’s center of gravity from the seabed |
Appendix A
Appendix B
- for , then:
- for then:
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τ | 0.037 | 0.08 | 0.12 | 0.22 | 0.41 | 0.60 |
G | 0.100 | 0.468 | 1.015 | 3.118 | 9.309 | 17.482 |
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Konispoliatis, D.N.; Chatjigeorgiou, I.K.; Mavrakos, S.A. Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body. Fluids 2021, 6, 320. https://doi.org/10.3390/fluids6090320
Konispoliatis DN, Chatjigeorgiou IK, Mavrakos SA. Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body. Fluids. 2021; 6(9):320. https://doi.org/10.3390/fluids6090320
Chicago/Turabian StyleKonispoliatis, Dimitrios N., Ioannis K. Chatjigeorgiou, and Spyridon A. Mavrakos. 2021. "Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body" Fluids 6, no. 9: 320. https://doi.org/10.3390/fluids6090320