Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method （FEM） is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient （CG） method with a symmetric successive overelaxlation （SSOR） preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.

A THEORETICAL APPROACH TO THERMAL PROPERTY OF ARRAY OF CYLINDERS EMBEDDED IN HOMOGENEOUS MATRIX

We investigate in this article the thermal coliductivity of array Of cylinders embedded in a homogeneous matrix. Using Green's function, we confirm that the method invented by Rayleigh can be generalized to deal with thermal property of these systems. A technique for calculating effective thermal conductivities of these systems is proposed. As an example, we consider a system with square symmetry, and a neat formula for effective thermal conductivity is derived. We show that the method also includes the proof of Keller theorem.

Numerical investigation on local resonance within an array of C-shaped cylinders in water waves

In this work, computational fluid dynamics (CFD)—based simulations and linear diffraction analysis are carried out to investigate the interaction between water waves and metamaterials composed of an array of C-shaped cylinders. The flow visualization by CFD-based simulations reveals that local resonance is a result of constructive interference between the incident wave and the wave radiated from the cavity of the C-shaped cylinder. The wave-induced water motion inside the cavity acts as a source of generating this radiated wave, which has the same angular wave frequency and wavenumber but opposite propagation direction as the incident wave. In addition, it is found from the CFD-based simulations that the energy dissipation increases as the opening of the C-shaped cylinder becomes shorter and sharper, along with an increase in its outer radius, and the variation trend of energy dissipation is only affected by the outer radius. Meanwhile, except for very small opening lengths, variations in opening length, width, and outer radius do not significantly impact the wave attenuation effect of the C-shaped cylinder array. Moreover, the results obtained by CFD and the linear potential flow model are compared. The linear potential flow theory is proven to be a reliable approach for accurately predicting the local resonant frequency and transmission coefficients within the local resonant band across a range of geometric parameters. However, it is noted that this theory may have limitations when applied to cases with extremely small opening lengths, where it struggles to accurately predict the local resonant frequency and the intensity of local resonance.

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.

Numerical simulation of flow through circular array of cylinders using porous media approach with non-constant local inertial resistance coefficient

Aquatic vegetation zone is now receiving an increasing attention as an effective way to protect the shorelines and riverbeds. To simulate the flow through the vegetation zone, the vegetation elements are often simplified as equidistant rigid cylinders, and in the whole zone, the porous media approach can be applied. In this study, a non-constant inertial resistance coefficient is introduced to model the unevenly distribution of the drag forces on the cylinders, and an improved porous media approach is applied to one circular array of cylinders positioned in a 2-D flume. The calculated velocity profile is consistent with the experimental data.

Wave action by arrays of vertical cylinders with arbitrary smooth cross-section

This paper presents an analytical model to solve the linear wave diffraction problem by arrays of bottom-mounted cylinders with arbitrary smooth cross-section.Based on the assumption of ideal fluid and potential theory,the unknown coefficients of total velocity potential can be solved by system of linear equations,which are obtained from the boundary conditions.The accuracy of the present method is verified by comparing it with the numerical tool in terms of the wave force and wave mn-up.Multiple cylinders with different configurations are tested,the cross-section of which is circular with cosine perturbation.The results show that the proposed method could obtain an accurate prediction of the wave action with multiple cylinder problems.Finally,the diffraction wave is investigated on arrays of bottom-mounted cylinders with different cross-section and layout.The near-trapping problem with effects of the multi-body interaction are also investigated.

The hydrodynamic interactions of an array of truncated circular cylinders as each cylinder oscillates independently with different prescribed modes

An analytical method based on the eigenfunction expansion and the Graf＇s addition theorem for Bessel functions is developed to study the hydrodynamic interactions of an array of truncated circular cylinders with each cylinder oscillating independently in different prescribed modes. The hydrodynamic radiation and diffraction of linear waves by such an array of cylinders are investigated and the analytical solutions of the velocity potentials are obtained. After comparisons for degenerated cases and program verifications, several cases for an array of truncated cylinders with each cylinder oscillating independently in surge, sway, heave, roll, and pitch modes with different prescribed amplitudes, are studied and the hydrodynamic forces and moments acting on the cylinders are obtained.

Predicting submerged vegetation drag with a machine learning-based method

Accurate estimation of the drag forces generated by vegetation stems is crucial for the comprehensive assessment of the impact of aquatic vegetation on hydrodynamic processes in aquatic environments.The coupling relationship between vegetation layer flow velocity and vegetation drag makes precise prediction of submerged vegetation drag forces particularly challenging.The present study utilized published data on submerged vegetation drag force measurements and employed a genetic programming(GP)algorithm,a machine learning technique,to establish the connection between submerged vegetation drag forces and flow and vegetation parameters.When using the bulk velocity,U,as the reference velocity scale to define the drag coefficient,C_(d),and stem Reynolds number,the GP runs revealed that the drag coefficient of submerged vegetation is related to submergence ratio(H^(*)),aspect ratio(d^(*)),blockage ratio(ψ^(*)),and vegetation density(λ).The relation between vegetation stem drag forces and flow velocity is implicitly embedded in the definition of C_(d).Comparisons with experimental drag force measurements indicate that using the bulk velocity as the reference velocity,as opposed to using the vegetation layer average velocity,U_(v),eliminates the need for complex iterative processes to estimate U_(v)and avoids introducing additional errors associated with U_(v)estimation.This approach significantly enhances the model’s predictive capabilities and results in a simpler and more user-friendly formula expression.