Dezhi Ning

Wave-current interactions with three-dimensional floating bodies

A Time-domain Higher-Order Boundary Element Method (THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies. Through a Taylor series expansion and a perturbation procedure, the model is formulated to the first-order in the wave steepness and in the current velocity, respectively. The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem. Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching. An artificial damping layer is adopted to dissipate the scattering waves. Different from the other time-domain numerical models, which are often focused on the wave-current interaction with restrained bodies, the present model deals with a floating hemisphere. The numerical results of wave forces, wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods. The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry. In this work, the regular and focused wave combined with current interacting with a truss-spar platform is investigated.

Current Effects on Nonlinear Wave Scattering by a Submerged Plate

AbstractOn the basis of a time-domain higher-order boundary element method, a two-dimensional fully nonlinear numerical wave flume is developed to investigate the nonlinear interactions between a regular wave and a submerged horizontal plate in the presence of uniform currents. A two-point method is used to discriminate bound (i.e., nonlinearly forced by and coupled to free waves) and free harmonic waves propagating upstream and downstream from the structure. The proposed model is verified against experimental and other numerical data for wave-current interaction without obstacles and nonlinear wave scattering by a submerged plate in the absence of currents. A first-order analysis shows that the reflection coefficient increases in the following current (i.e., current in the same direction as the incident wave) and decreases in the opposing current (i.e., current in the opposite direction to the incident wave). Moreover, the plate length for the maximum reflection to occur is not sensitive to the current. ...

Analytical Solution of a Wave Diffraction Problem on a Submerged Cylinder

AbstractBased on the methods of variable separation and matching eigenfunction expansion for the velocity potential, an analytical solution is developed for a wave diffraction problem on a submerged vertical cylinder in finite water depth. It is validated by comparison with the results from a higher-order boundary-element method and convergent examinations on the number of expanding models. Numerical examinations are carried out to investigate the influences of submerged depth, cylinder length, and water depth. The wave forces on the submerged cylinder are decreased with the increase of submerged depth. Compared with a floated cylinder, the surge force is always small, whereas the heave force and pitch moment may be larger than those on the floated cylinder at some frequencies. The influence of the cylinder length is also analyzed for surge, heave, and pitch results.

Numerical study of resonance induced by wave action on multiple rectangular boxes with narrow gaps

By introducing a source term into the Laplace equation, a two-dimensional fully nonlinear time-domain numerical wave flume (NWF) is developed to investigate the resonance induced by the interaction between waves and multiple objects with narrow gaps. In the numerical model, the fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface and the constant artificial damping is employed in the gaps to approximate the viscous dissipation due to vortex motion and flow separation. The computational domain is discretized using a higher-order boundary element method (HOBEM). The proposed model is firstly validated against the published experimental data and numerical results of the wave height in the narrow gap between two boxes, the wave heights in the two gaps of three boxes, and wave loads on the boxes. Then, the extensive numerical experiments are performed to study the influences of the number of the boxes and the gap spacing on the resonant frequency, reflected and transmitted wave heights and wave loads on the boxes.

Nonlinear Numerical Investigation on Higher Harmonics at Lee Side of a Submerged Bar

The decomposition of a monochromatic wave over a submerged object is investigated numerically in a flume, based on a fully nonlinear HOBEM (higher-order boundary element method) model. Bound and free higher-harmonic waves propagating downstream the structure are discriminated by means of a two-point method. The developed numerical model is verified very well by comparison with the available data. Further numerical experiments are carried out to study the relations between free higher harmonics and wave nonlinearity. It is found that the nth-harmonic wave amplitude is growing proportional to the nth power of the incoming wave amplitude for weakly nonlinear wave condition, but higher-harmonic free wave amplitudes tend to a constant value for strong nonlinear wave condition.

Numerical and Experimental Investigation of Nonlinear Wave-Current Propagation over a Submerged Breakwater

AbstractThe nonlinear wave-current propagation over a submerged rectangular breakwater on a flat seabed was investigated both experimentally and numerically. Experiments were conducted in a two-dim...

Numerical investigation of solitary wave action on two rectangular boxes with a narrow gap

Based on the time-domain higher-order boundary element method (HOBEM), a two-dimensional numerical wave flume is developed to investigate solitary wave interaction with two rectangular boxes with a narrow gap. In the numerical model, the fully nonlinear boundary conditions are satisfied on the free surface, the mixed Eulerian-Lagrangian method is adopted to track the transient water surface and the fourth-order Runga-Kutta method is used to predict the velocity potential and wave elevation on the free surface. The acceleration potential technique is used to compute the transient wave forces along the wetted object surface. A piston-type wavemaker is used to generate solitary waves. The proposed model is validated by comparing the simulated wave run-up and the wave loads with the published experimental and numerical results of the reflection of a solitary wave from a vertical wall. Then, numerical experiments are performed to study the effects of the narrow gap and the size of each box on the wave run-ups at the two sides of the two-box system and in the narrow gap between two boxes, and the wave loads on the two boxes. The interaction between double solitary waves with a time interval between them with a two-box system is also investigated.

Three-dimensional numerical investigation of vortex-induced vibration of a rotating circular cylinder in uniform flow

The vortex-induced vibration (VIV) of an elastically mounted rotating circular cylinder vibrating in a uniform flow is studied numerically. The cylinder is allowed to vibrate only in the cross-flow direction. In the numerical simulations, the Reynolds number, the mass ratio, and the damping ratio are kept constants to 500, 11.5, and 0, respectively. Simulations are performed for rotation rates of α = 0, 0.5, and 1 and a range of reduced velocities from 1 to 13, which covers the entire lock-in regime. It is found that the lock-in regime of a rotating cylinder is wider than that of a non-rotating cylinder for α = 0, 0.5, and 1. The vortex shedding pattern of a rotating cylinder is found to be similar to that of a non-rotating cylinder. Next, simulations are performed for three typical reduced velocities inside the lock-in regime and a range of higher rotation rates from α = 1.5 to 3.5 to investigate the effect of the rotation rate on the suppression of VIV. It is found that the VIV is suppressed when the rotation rate exceeds a critical value, which is dependent on the reduced velocity. For a constant reduced velocity, the amplitude of the vibration is found to increase with increasing rotation rate until the latter reaches its critical value for VIV suppression, beyond which the vibration amplitude becomes extremely small. If the rotation rate is greater than its critical value, vortex shedding ceases and hairpin vortices are observed due to the rotation of the cylinder.The vortex-induced vibration (VIV) of an elastically mounted rotating circular cylinder vibrating in a uniform flow is studied numerically. The cylinder is allowed to vibrate only in the cross-flow direction. In the numerical simulations, the Reynolds number, the mass ratio, and the damping ratio are kept constants to 500, 11.5, and 0, respectively. Simulations are performed for rotation rates of α = 0, 0.5, and 1 and a range of reduced velocities from 1 to 13, which covers the entire lock-in regime. It is found that the lock-in regime of a rotating cylinder is wider than that of a non-rotating cylinder for α = 0, 0.5, and 1. The vortex shedding pattern of a rotating cylinder is found to be similar to that of a non-rotating cylinder. Next, simulations are performed for three typical reduced velocities inside the lock-in regime and a range of higher rotation rates from α = 1.5 to 3.5 to investigate the effect of the rotation rate on the suppression of VIV. It is found that the VIV is suppressed when the ro...

Effect of the PTO damping force on the wave pressures on a 2-D wave energy converter

The information of the wave loads on a wave energy device in operational waves is required for designing an efficient wave energy system with high survivability. It is also required as a reference for numerical modeling. In this paper, a novel system, which integrates an oscillating wave energy converter with a pile-restrained floating breakwater, is experimentally investigated in a 2-D wave flume. The measurements of the wave pressure on the wet-surface of the device are made as the function of the power take-off (PTO) damping force. It is shown that the wave pressure is significantly affected by the PTO system, in particular, at the edges, and the wave pressure varies under different wave conditions. From the results, conclusions can be drawn on how the PTO damping force and wave conditions affect the loads on the device, which is of engineering concern for constructing safe and reliable devices.

Experimental and numerical investigation of the hydrodynamic characteristics of submerged breakwaters in waves

ABSTRACT Ning, D.; Chen, L.; Zhao, M., and Teng, B., 2016. Experimental and numerical investigation of the hydrodynamic characteristics of submerged breakwaters in waves. The interactions between nonlinear, regular waves and submerged breakwaters with rectangular or trapezoidal cross-sections were investigated both experimentally and numerically in this article, with emphasis on the effect of the shape of the breakwater on its hydrodynamic behavior. A series of experiments was carried out and used to validate a numerical model based on a fully nonlinear, two-dimensional boundary-element method. Comparisons among the numerical results of both wave elevations and wave pressures on the structure and the measured data indicate that the present numerical model is very capable of accurately predicting the hydrodynamic characteristics of submerged breakwaters in waves. Furthermore, parametric studies were conducted to investigate the influence of the existence of the seaward and rearward slopes on the effectiveness of the breakwater in reflecting the wave energy.