Vertical Wave Forces Research Articles

CFD study of a Dual Chamber Floating Oscillating Water Column device

A comprehensive Computational Fluid Dynamics study of a Dual Chamber Floating Oscillating Water Column device fixed in space is presented. Firstly, the numerical wave flume model is calibrated and validated for a simple case of a floating box fixed in space. Spectral components of the vertical wave force on the box are evaluated and the Computational Fluid Dynamics numerical model uncertainty is assessed. Secondly, the numerical wave flume is used to study the hydrodynamics around the Dual Chamber Floating Oscillating Water Column. The wave forces acting on the device when fixed in space are calculated, also free surface elevations and air pressures inside the chambers are evaluated and the efficiency of the device is determined. The present numerical results show that the model can describe properly the two main components of the vertical force of a fixed floating box. Efficiency results of the device show that it is the same whether it is moving or not for the low wave height. For higher wave heights, the efficiency improves when the device is moving due to its resonance mechanisms.

Numerical analysis of the performance of a horizontal porous plate attached to the front of a vertical wall

The dual boundary element method (DBEM) is applied to investigate the wave scattering and wave loads on a vertical wall with a horizontal plate, over wide ranges of relative widths, porosities, relative depths of submergence, inclinations, and relative depths of vertical barrier. The structure rests on a submerged porous breakwater. It is observed that a smaller relative width of the plate is more effective for reducing the vertical load. Furthermore, varying the relative width from 0.2 to 1.0 does not alter the wave transmission noticeably. It is observed that increasing the porosity of the horizontal plate helps to reduce the vertical wave force, but increases the horizontal wave force and wave-induced moment. Moreover, a variation in the relative depth of submergence of horizontal plate from 0.05 to 0.4 has an insignificant effect on wave transmission. However, it helps reduce the vertical load and increases horizontal wave force and moment. It is observed that an anticlockwise rotation of the horizontal plate by 5° reduced the vertical load and moments by 10%–20%. These results would be effective for the optimal design of similar wave barriers.

Wave force reduction due to burial of submarine pipeline: A probability based analysis and comparison with DNVGL-RP-F109

Horizontal and vertical wave forces were assessed on submarine pipeline for different burial depths in soils of four different hydraulic conductivity in random waves of wide range of wave height and periods. Probability analysis is carried out for 99.99% and 98% probability of non-exceedance of vertical and horizontal wave forces on the pipeline. The force reduction due to burial of the pipelines are compared with the recommendations by DNVGL-RP-F109. The effect of changing the wave height, wave period and hydraulic conductivity on the wave forces and its change due to different burial depths are revealed. The wave force values and the quantitative differences due to 99.99% and 98% probability of non-exceedance can be used for risk-based design of buried pipelines. The recommended value of wave force reduction factor for different relative burial depth of the pipeline by DNVGL-RP-F109 is much smaller than the value of wave force reduction factor from the present study. Strong scope exists to revise this code for the betterment of submarine pipeline design engineers. The knowhow revealed in this study will be useful for optimal design of buried submarine pipelines.

Experimental and numerical investigation on wave impacts on box-girder bridges

Climate change could result in more extreme weather events and induce increasing challenges to the low-lying coastal bridges. The structural performance of box-girder bridges under wave impacts was seldom investigated. In this paper, a three-dimensional (3D) computational fluid dynamics (CFD) model is established to simulate the wave-bridge interactions, and laboratory experiments are conducted to investigate wave impacts on a bridge. The experiments and 3D CFD simulations are unique as compared with other relevant studies since they provide the complex wave-bridge interactions through dynamic and spatial analyses. Specifically, time histories of vertical and horizontal wave forces are measured through experiments. The time-dependent pressure distributions, wave-induced forces, and overturning moments on the bridge model are computed with the CFD model. The effects of different parameters on the maximum wave forces are discussed. Also, comparisons of the differences between two-dimensional (2D) and 3D CFD models are conducted. Then, the results are converted to a prototype scale to explore the effects of wave impacts, and prediction formulas are proposed accordingly. This study combining experimental and 3D numerical investigations could help improve understanding of the wave-bridge interaction mechanism, and further aid the optimal and robust designs of coastal bridges.

Random wave forces on the submerged box-girder superstructure of coastal bridges based on potential flow theory

The hydrodynamic performance of the box-girder superstructure under extreme random wave conditions in the actual ocean environment is the focus of coastal bridge designers and researchers. This paper proposed an analytical method to estimate random wave forces on the box-girder superstructure based on the potential flow theory and the correction parameters. The accuracy of the proposed analytical method is validated by the classical problem about the wave force on the rectangular structure, empirical methods proposed by previous researchers, and the hydrodynamic experiment conducted by authors on the wave force of the box-girder superstructure within the application range of the proposed method. With the validated analytical method, a parametric study is carried out to explore the influence of the peak frequency of the incident wave spectra and the structural configuration on the hydrodynamic performance of the submerged box-girder superstructure. Results show that the structural parameter, including the relative deck thickness, girder width, and girder height of the box-girder superstructure affects the horizontal wave force more significantly than the vertical wave force. A larger ratio of wavelength to the width of the box-girder superstructure results in smaller horizontal wave forces when the dimensionless wave number is smaller than 1.0. It is of great significance to consider the effect of actual ocean waves on coastal bridge superstructures using random waves.

A novel tri-semicircle shaped submerged breakwater for mitigating wave loads on coastal bridges part I: Efficacy

Extreme waves generated by hurricanes, together with storm surges, have led to severe damage and even failures in many offshore structures. This paper presents a novel submerged breakwater design suitable for protecting coastal bridges and other infrastructure. The proposed breakwater design is composed of three identical semicircular shells and a rectangular base using the same total volume of construction material as traditional trapezoidal breakwaters. This configuration permits modular construction and quick installation. A high-fidelity numerical wave tank is established to investigate the performance of the new breakwater device under different conditions with varying wave height, water depth, bridge submersion depth, and spacing between the device and the bridge. The extreme wave is simulated using a second-order solitary wave. According to the observation of a typical scenario, based on the numerical simulations, where waves pass over the novel breakwater and then impact the bridge, it is argued that the new design demonstrates an increased effectiveness to dissipate wave energy. Through analysis of the horizontal and vertical wave forces impacting the T-girder bridge deck, the wave loads are shown to be consistently reduced under all parametric studies. Moreover, it is found that the new breakwater offers improved protection when contrasted with the traditional trapezoidal geometry. The work conducted in this study sheds light on the design of high performing submerged breakwater for mitigating wave loads on coastal bridges.

Wave action on a vertical wall with a submerged horizontal plate: Analysis of phase variation of forces and probability of exceedance

In this study, experiments on the wave forces and moments acting on a Vertical Wall (VW) and a VW attached to a horizontal plate (VWHP) subjected to regular and random wave fields were conducted. In the experiments, the phase lag between the horizontal and vertical wave forces was analyzed for the regular waves and the probability density was analyzed for the random waves. The experimental results showed that attaching a horizontal plate with a length equal to the water depth to a VW at a position corresponding to 28.5% of the water depth reduced the 95% non-exceedance value of the normalized horizontal wave force from 1.05 to 0.8 for a relative water depth of d/Lp = 0.1, where d is the water depth and Lp is the wavelength of the peak period. For d/Lp = 0.5, the corresponding reduction was from 0.6 to 0.17. The results of this study can be used to optimize the design of VW- and VWHP-type marine structures.

A Hybrid Surrogate Model for the Prediction of Solitary Wave Forces on the Coastal Bridge Decks

To facilitate the establishment of the probabilistic model for quantifying the vulnerability of coastal bridges to natural hazards and support the associated risk assessment and mitigation activities, it is imperative to develop an accurate and efficient method for wave forces prediction. With the fast development of computer science, surrogate modeling techniques have been commonly used as an effective alternative to computational fluid dynamics for the establishment of a predictive model in coastal engineering. In this paper, a hybrid surrogate model is proposed for the efficient and accurate prediction of the solitary wave forces acting on coastal bridge decks. The underlying idea of the proposed method is to enhance the prediction capability of the constructed model by introducing an additional surrogate to correct the errors made by the main predictor. Specifically, the regression-type polynomial chaos expansion (PCE) is employed as the main predictor to capture the global feature of the computational model, whereas the interpolation-type Kriging is adopted to learn the local variations of the prediction error from the PCE. An engineering case is employed to validate the effectiveness of the hybrid model, and it is observed that the prediction performance (in terms of residual mean square error and correlation coefficient) of the hybrid model is superior to the optimal PCE and artificial neural network (ANN) for both horizontal and vertical wave forces, albeit the maximum PCE degrees used in the hybrid model are lower than the optimal degrees identified in the pure PCE model. Moreover, the proposed hybrid model also enables the extraction of explicit predictive equations for the parameters of interest. It is expected that the hybrid model could be extended to more complex wave conditions and structural shapes to facilitate the life-cycle structural design and analysis of coastal bridges.

Harmonic Analyses of Hydrodynamic Characteristics for Gap Resonance Between Fixed Box and Vertical Wall

Two marine structures arranged side by side with a narrow gap may suffer from violent free-surface resonance, which would cause green water on deck, dramatically raise hydrodynamic loads on structures and seriously threaten the operation safety. The CFD-based open-sourced software, OpenFOAM®, is employed to simulate the two-dimensional fluid resonance inside a narrow gap between a fixed box and a vertical wall induced by regular waves with different wave heights. The topographies with various plane slopes are placed in front of the wall. The focus of this article is on the influences of the incident wave height and the topographic slope on the nonlinear characteristics of various hydrodynamic parameters (including the wave height in the gap, the vertical wave force, and the horizontal wave force on the box) during gap resonance. The ratios of their high-order to the corresponding 1st-order components under different sets of the incident wave height and the topographic slope are analyzed. It is found that the relative importance of all the high-order components increases gradually with the incident wave height for all the three parameters. The topographic influence on them closely depends on the type of the parameters and the incident wave height. In addition, the occurrence of the 2nd-order gap resonance phenomenon can cause the 2nd-order wave height and horizontal force to be significantly larger than the corresponding 1st-order components.

Higher-order harmonic induced wave resonance for two side-by-side boxes in close proximity

Wave resonance in a narrow gap formed by two boxes in the side-by-side arrangement is investigated by employing a numerical wave flume based on the OpenFOAM® package. In the present study, the main focus lies in the exploration of the nonlinear resonant behavior induced by the second- and third-order harmonic components which occur around half and one third of the resonant frequencies. A wide range of incident wave frequencies is considered, by which the higher-order harmonic induced wave resonance at lower wave frequencies is discussed. By the harmonic analysis, it is revealed that at the resonant frequency the first-order harmonic component dominates the wave resonance and the second-order effect is minor, which coincides with the conclusion drawn in the previous study. However, around half or one third of the resonant frequencies, the first-order harmonic component is in good agreement with the linear potential flow solutions, but the second- or third-order harmonic component is significant, causing the corresponding higher-order harmonic induced wave resonance. In addition, the numerical results show that the second- and third-order harmonic induced wave resonances only influence the wave properties inside the narrow gap, such as the wave response in the narrow gap and the horizontal wave forces on the boxes. The wave responses around the two-box system, the vertical wave forces on the boxes and the reflection and transmission coefficients are hardly affected by the wave resonance around the corresponding half and one third of the resonant frequencies. The higher-order harmonic induced normalized wave elevation in the narrow gap increases with the increase in incident wave height, implying the increased influence of the free surface nonlinearity.

Fluid resonance in the narrow gap of a box-wall system under cnoidal wave action

Fluid resonance within a narrow gap formed by a box in close proximity to a plane wall under cnoidal wave action is investigated using the Computational Fluid Dynamics (CFD) package OpenFOAM®. Fluid resonance behavior excited by the second-order harmonic component of the incident cnoidal waves is concerned. Numerical simulations show the large second-order induced wave height in the gap which increases as the incident wave height gets larger or the water depth gets shallower. The large double-frequency component of the cnodial waves is the major reason for the phenomenon. Harmonic analysis indicates that the CFD results can be represented well by a second-order approximation, and the free surface nonlinearity is an indispensable factor in the action of the cnoidal incident wave. Similar phenomenon is also found in the horizontal wave force. However, the second-order induced resonance within the gap has insignificant effect on the vertical wave force.

A comparative study on lateral displacements of movable T-deck and Box-deck under solitary waves

From the field observations of bridge deck failures under extreme waves, it is shown many bridge decks were laterally displaced at varying displacements on the pier caps, and some decks with large lateral displacements even fell into the water. The repair cost varies with the lateral deck displacement, especially between different bridge states (Fixed state, Partially-displaced state, Falling-down state) after the disaster. To the author's knowledge, a comparative study of lateral displacements for T-deck and Box-deck under extreme waves has not been conducted. This paper discusses some fundamental questions related with the lateral deck displacement: (1) What are the influences of three essential parameters (relative clearance, wave height, deck weight) on the lateral displacements for two kinds of bridge decks? (2) Which kind of bridge deck is safer under the extreme solitary waves? In other words, is the lateral displacement of T-deck always larger or smaller than the Box-deck? (3) Does a larger horizontal or vertical wave force on two decks always induce a fiercer lateral motion response? (4) What is the most vulnerable condition for the failures of T-deck and Box-deck? Motivated by these questions, a comparative research on the wave-deck interactions for two movable decks under solitary waves is conducted by a numerical model solving the Navier-Stokes equations. A total of 330 numerical experiments based on this model have been designed to dynamically study the lateral responses of two bridge shapes under various conditions. This study provides researchers an insight into the dynamic properties for T-deck and Box-deck under solitary waves, and improves our understanding of the fragility of two decks under extreme waves.

Dual boundary element analysis for a pair of inverted T-type porous barriers having nonlinear pressure drop

In the present study, scattering of gravity waves by different wave barrier configurations is analyzed under the assumptions of small amplitude wave theory. The wave past barriers are assumed to follow a nonlinear pressure drop boundary condition . The boundary value problem is solved using iterative Dual Boundary Element Method (DBEM) which facilitates the problem-solving in a single domain. Based on the hydrodynamic characteristics, it is revealed that a pair of inverted T-type porous barrier is effective for wave damping application. Further, a parametric analysis is carried for the inverted T-type barrier to understand the effect of porosity, relative submergence of the barrier, relative spacing between the barriers and relative width of barriers on wave scattering, wave forces and moments. It is observed that increasing the porosity of the inverted T-type twin barrier increases the wave transmission but reduces the wave forces and moments. It is revealed that the relative depth of submergence h 1 / h significantly affects the wave scattering and wave loads on the twin inverted T barrier. Varying the relative spacing between the inverted T-type barrier, S / h from 0 to 1 does not change the wave transmission significantly but changes the wave forces and moments appreciably. It is recommended to increase the value of relative width of the wave barrier, B / h , only if wave transmission need to be reduced considerably for a selected porosity, the relative depth of submergence and relative spacing between the barrier, but at the expense of higher vertical wave force and wave-induced moments. The study results are expected to be useful for optimized design of inverted T-type wave barrier for a wide range of wave conditions.

Hydrodynamic characteristics of a vertical wall with an immersed horizontal plate subjected to regular and random waves

Experimental investigations on wave transmission, reflection, dissipation, forces, moments, run-up, and run-down were conducted on a vertical wall (VW) and on a vertical wall fixed with an immersed horizontal plate (VWHP) for a wide range of regular and random waves. It was found that wave reflection can be reduced by 25%–35% using a VWHP (with plate length equal to water depth with a submergence of 28.6% of the water depth) and that dissipation can be increased by 25%–35%. The normalized significant inline wave force on the VWHP can be reduced from 0.8 to 0.1 for 0.1 <d/Lp <0.5. The global inline wave force on the VWHP can be reduced by >50% for d/Lp > 0.3, when compared to VW, which is beneficial in the design of horizontal sliding. The vertical wave forces on the VWHP were significantly higher and increased significantly for lower values of d/Lp, especially for d/Lp = 0.1. The wave-induced moment is 10–20% less for the VWHP compared to that for the VW, which is also useful for the design against overturning, especially if the results are used for the design of caissons with D/L > 1, where D is the width of the caisson.

Characteristics of wave forces on pile group foundations for sea-crossing bridges

The pile group foundation of sea-crossing bridges has various structural forms, and its wave force characteristics are complex. In this study, the Morrison equation and the boundary element method were utilized to establish a calculation model for predicting the maximum wave forces on the pile group foundation with a square pile cap. Moreover, hydrodynamic models of pile group foundations were designed according to the gravity similarity criterion. On this basis, the model test and analytical calculation were carried out to investigate the effect of pile spacings, pile slopes, conical slopes (on the top of the pile cap), and wave parameters on wave forces of pile group foundations. In addition, impact characteristics of waves on the foundation were also analyzed. The results shown that larger pile spacings and pile slopes reduced the wave forces on the foundation, but this relationship weakened with the rise of the water level. The inclined pile could be regarded as a vertical pile for calculating wave forces at high water level. The conical slope increased the water-blocking area on the pile cap, which led to the increase of wave forces on the foundation. When the wave only acted on the pile group, the wave forces on the single pile firstly decreased then increased with the increase of frequencies, and lower wave frequencies (larger periods) induced stronger nonlinear factors of the waves. When the water level was near the bottom of the pile cap, larger wave periods increased the vertical wave forces on the pile cap. The wave impact mainly occurred in the time range from the pile cap first contacting with the wave to the wave crest reaching the middle of the pile group foundation.

Experimental investigations on wave impact pressures under the deck and global wave forces and moments on offshore jacket platform for partial and full green water conditions

The wave induced dynamic pressures under the deck and the global wave forces and moments on an offshore platform model were measured for three different model orientations and for partial and full green water conditions in random wave fields of different energy levels. It is found that for partial and full green water conditions, the global vertical wave force dominates when compared to horizontal wave forces. The orientation of the structure to wave direction has some effect, only for 22.5° orientation of the deck to wave direction. Shoreward maximum wave force can reach 3 times the maximum seaward wave force. For zero air gap condition, the highest value of normalized peak vertical force can reach a value of 42, which is 5 times higher than the normalized significant uplift force value. The normalized downward peak force value can reach as high as 8 for full green water condition due to the weight of overrunning water staying on the top of deck slab. For zero air gap condition, the normalized peak impact pressure under the deck can reach as high as 13.2 and 21.5 near the leading and trailing bottom side of the deck.

Application of a VARANS based resistance-type porosity model on simulating wave interactions with perforated caisson sitting on a rubble-mound foundation

Rubble-mound foundation can be regarded as a form of porous structure that is widely used in engineering practice. Porous medium flow must be considered when simulating wave interactions with perforated caisson sitting on a rubble-mound foundation. In this paper, volume-averaged/Reynolds averaged Navier-Stokes (VARANS) equations are adopted to describe the flow inside and outside the porous structure. Moreover, they are combined with the volume averaged k−ε model to simulate the turbulence effect. In addition, the three-step finite element method is applied to solve VARANS equations numerically, and the CLEAR-VOF method is applied to capture the free fluid surface. The resistance-type porosity numerical model is proposed and verified by several test cases and then used to simulate wave interactions with perforated caisson sitting on a rubble-mound foundation. The porosity model gives reliable results compared to the experiments with respect to the wave height, the pressure distribution, and the total vertical wave force. The model can be adopted to study the wave interaction with perforated caisson sitting on a rubble-mound foundation and used for the design of such caisson in engineering practice.

Surface gravity wave scattering by multiple slatted screens placed near a caisson porous breakwater in the presence of seabed undulations

In the present study, the effectiveness of using multiple slatted screens placed in front of a caisson porous breakwater to dissipate the incident wave energy is analyzed. To model the water flow through the slatted screens, a quadratic (nonlinear) pressure drop condition which involves both the inertial and drag effects is considered. Further, for thick porous structure, the well known Sollitt and Cross (1972) model is used. To handle the nonlinear boundary conditions, an iterative multi-domain boundary element method (BEM) is used. The numerical convergence of the multi-domain BEM based solutions is presented. Energy identities for flow past a single slatted screen, multiple slatted screens and for the present problem are derived. The study shows that the minimum reflection coefficient (<1%) and maximum wave energy dissipation (>98%) can be obtained by using four slatted screens. Further, for moderate values of perforation-effect Keulegan-Carpenter number (KC), the reflection coefficient attains maximum for b1λ≈n2,n=1,2,3,⋯ (b1 is the distance between the rigid caisson and the front slatted screen, λ is the incident wavelength) irrespective of the variations in the number of slatted screens. Further, the transmission coefficient, horizontal and vertical wave forces acting on the rigid caisson attain maximum for b1/λ≈0.55n, and minimum occurs for 2n+14<b1λ<3n+26,n=0,1,2,3,⋯. The Bragg resonance in the reflection coefficient occurs at Bragg value ≈1.6 irrespective of the variations of KC number. Moreover, the reflection coefficient increases around the Bragg value for higher values of KC number without altering the peak value in the reflection coefficient.

Hydrodynamic analysis of a seaside quarter-circular breakwater with an array of porous cages using DBEM

ABSTRACT The gravity wave interaction with an array of porous cages in the presence of a seaside submerged quarter-circular porous breakwater (QCPBW) is analyzed within the framework of linearized water wave theory. A quadratic pressure drop is adopted for the wave past the porous structures to capture the effect of wave height on the energy dissipation. The boundary value problem is solved using the iterative Dual Boundary Element Method (DBEM). The numerical code is validated with known results in the literature. One or upto four units of submerged and bottom fixed porous cages are considered. The effect of porosity on QCPBW and porous cages are investigated pragmatically to study the scattering and wave forces. It is found that introducing a single porous cage with 10% porosity at the rear side of a QCPBW with a porosity of 25% can reduce the wave transmission coefficient by about 50% for relative water depth . Increasing the porosity of the single cage from 10% to 40% has a significant reduction on the horizontal and vertical force coefficients on the cage, whereas the change is insignificant on QCPBW. The horizontal wave force is three to four times higher when compared to the vertical wave force for both QCPBW as well as on the porous cage. For a system comprising four units of cages, both the horizontal and vertical wave forces on cage 1, 2, 3, and 4 reduce progressively (cage 2 is at the lee side of cage 1 and so on). The results of the present study can be used for the optimal design of open sea porous systems.

Calculating the Wave Force on Partially Immersed Large-Scale Horizontal Cylinders

Large-scale interceptors constitute the main structure of offshore self-driven floating marine litter collection devices, and the structural stability of such interceptors under the action of waves directly influences the overall safety of the device. When the ratio of the diameter of a horizontal cylinder in such interceptors to the incident wavelength is larger than 0.25, the wave force can be calculated by using the diffraction theory, by considering the problem as that of the interaction between the waves and a partially immersed large-scale horizontal cylinder. In this study, an analytical approach to calculate the wave force on a partially immersed large-scale horizontal cylinder was formulated by using the stepwise approximation method. Physical model tests were conducted to investigate the effects of different factors (wave height, period, and immersion depth) on the wave force on a large-scale horizontal cylinder under conditions involving short-period waves. The results show that both horizontal and vertical wave forces on the cylinder increase as the wave height (immersion depth) increases in most cases. The vertical wave force decreases with the decrease of the period. For the horizontal wave force, it increases with the decrease of the period when the wavelength is larger than the diameter of the cylinder and decreases with the decrease of the period when the wavelength is smaller than the diameter of the cylinder.