Crown Wall Research Articles

The initial stage of the coalescence of a compound drop in an impact regime

The evolution of the regular fine structure of the colored matter distribution produced, when a freely falling multifluid drop spreads in deep water, is for the first time traced using the techniques of engineering photo and video recording. The flow pattern is studied in the initial stage of the formation of a cavity and a crown during the coalescence of a compound drop, whose core is a drop of alizarin ink solution coated with an oil shell. The distributions of the colored fluid at the cavity bottom and the crown walls include streaky structures, whose formation can be due to the processes of the available potential surface energy (APSE) conversion occurring when the contact surfaces of the merging fluids are eliminated. In the experiments the height of the falling drop was varied. The core position in the compound drop was not checked but was determined by separation conditions. The ink core disintegration into fibers was observable in all the experiments. The areas of the cavity and crown surfaces covered by the colored fluid reached maximum at the central position of the core.

Hydraulic Model Experiments and Performance Analysis of Existing Empirical Formulas for Overtopping Discharge on Tetrapod Armored Rubble Mound Structures with Low Relative Freeboard

In coastal structure design incorporating revetments, the assessment of wave overtopping discharge relies on hydraulic model experiments. Numerous empirical formulas have been developed to predict overtopping discharge based on quantitative data from these experiments. Typically, for revetment structures aimed at mitigating wave overtopping, crest height is determined by considering the maximum amplitude of the design wave, resulting in a relatively high freeboard compared to wave heights. However, achieving complete prevention of all wave overtopping would require the crown wall to have substantial crest heights, rendering it economically impractical. Therefore, the concept of limiting discharge has been introduced in the design of revetment structures, aiming to restrict wave overtopping discharge to an acceptable level. Consequently, many coastal structures in real-world settings feature relatively lower freeboard heights than incident wave heights. This study investigated wave overtopping discharge on rubble-mound breakwaters with relatively low freeboard heights through hydraulic model experiments. Furthermore, it conducted a comparative analysis of the predictive capabilities of existing empirical formulas for estimating overtopping discharge using experimental data.

Scour at the rear side of rubble mound revetments due to random wave overtopping: Laboratory experiments

This study presents the physical model experiments on the wave overtopping induced bed level changes at an unprotected rear side of a rubble mound revetment with a crown wall. In the experiments, the wave conditions, the backfill material size, and the backfill depth (vertical distance from the crest level to the rear side bed level) are varied. Two mobility parameters, namely the densimetric overtopping discharge and the relative fall velocity, are introduced to represent the initiation of motion and suspension of the backfill material, respectively. The temporal evolution of scour depth at the rear side is related to the mobility parameter, the number of waves and the backfill depth utilizing regression analyses. The effect of the backfill depth on the scour is found very limited for the available data set. However, the time scale of the scour is found to be related with the backfill depth only. For the present data set, it varied within a range of 1500–16000 number of waves approximately, with an average of 5600 waves. An equilibrium scour profile is reached 3 to 4 times the time scale. The geometry of the scour profile is expressed in terms of the scour depth, based on the equilibrium scour profile data.

Numerical investigation of drop–film interactions with a thixotropic liquid

We investigate numerically the influence of thixotropic effects on the impact of a drop onto a thin film, a fundamental process in many technical systems. Direct numerical simulations are performed with a Volume-of-Fluid (VOF) method based multiphase flow solver whose capabilities are expanded in order to enable simulations of a thixotropic liquid. The thixotropic behavior is modeled by a rate kinetic equation for the structural integrity of the assumed microstructure of the liquid. The corresponding structural parameter is described by an additional VOF-variable. After a validation of the implementations, we vary systematically the two parameters of the thixotropic model for a selected impact scenario in order to identify thixotropic effects during the impact and on the overall impact morphology. The two parameters are the mutation number Mu=texp/tθ as the ratio of the experimental time scale to the time scale of the structural rebuilding and the parameter β, which describes the effectivity of the shear-induced structural disintegration. The parameter study leads to a regime map with three different regimes. For Mu>10, the liquid behaves purely shear-thinning. High shear rates during the early stages of the impact lead to a low apparent viscosity at the crown base and to an enhanced crown growth. For Mu<0.1, the liquid behaves irreversible thixotropic or rheodestructing, respectively. Structural rebuilding is negligible and every deformation leads to a further disintegration of the microstructure. In this regime, a thin region of disintegrated microstructure develops within the liquid, spanning from the location of high shear stresses at the bottom into the crown rim. In between these two regimes, purely thixotropic effects become significant. A complex microstructure develops during the impact, in which features of both regimes occur combined, leading to a pronounced viscosity gradient along the crown wall. A comparison of the resulting maximum crown heights reveals that various combinations of Mu and β values can lead to the same maximum crown height whereas the crown shapes prior to this point in time can be very different.

A physical model study on the hydraulic performances of vertical breakwaters with retreated wave walls

This paper describes a 2D physical model study on the hydraulic performances of composite vertical breakwaters with retreated wave walls. The research is an expansion of a previous experimental study by the same Authors: a very large number of experiments, in the order of 2,000, have been carried out by exploring and varying a wide range of wave and geometrical parameters of the structure, to investigate their effect and importance. In order to make feasible the execution of this large number of tests, a small-scale wave flume was used and regular wave conditions were reproduced. The influence of the wave wall retreat has been investigated in terms of wave-induced forces, reflection coefficients and wave overtopping discharges, comparing the hydraulic performances of structures with retreated walls with those of a flushed wall configuration under the same wave conditions. The large number of experiments allowed to formulate a detailed description of the complex phenomena at hand, providing statistical indicators that can be used as guidelines for preliminary design purposes of such structures, quantifying the relevant sources of uncertainty. The analysis confirmed and extended the previous findings and indicates that, on average, the hydraulic performances of structures with retreated crown wall vary significantly from those of flushed wall configurations. Specifically: (I) the forces acting on the wave wall increase of a factor up to 1.5, due to the occurrence of impulsive loads; (II) the forces acting on the caisson trunk decrease of a factor up to 0.91; (III) the global forces can decrease reaching a minimum reduction factor of 0.87, although some dangerous exceptions, in which equal or larger loads, than those occurring for standard flushed wall configuration, have been registered; (IV) the reflection coefficients decrease of a factor up to 0.83; (V) the wave overtopping discharges increase up to 2.55 times those with flushed walls.

2D And 3D Physical Model Testing For The Rehabilitation On The Frioul Port Breakwater (France)

A white archipelago anchored in the Mediterranean Sea 2 km off the coast of Marseille (France), the port of Frioul is made up of the Pomègues islands (to the south) and Ratonneau (to the north). It is protected on the west side by the Berry breakwater (renovated in 1984), and on the east side by the Condorcet breakwater (figure 1.a). The port was built in the early 1820s (Berry breakwater) to take care of the quarantine of ships coming from areas infected by yellow fever, then developed in the 1850s (Condorcet breakwater in the East) to make it a military port. The current findings highlight that the eastern breakwater is seriously damaged and must be rehabilitated (figure 1.b). Accordingly, the rehabilitation solution, which consists to replace the actual rock armour unit, was physically modelled, and tested for its hydraulic stability and the overtopping performance as well as the forces and pressures acting on the crown wall. The process includes recreation of breakwater cross sections in a 2D wave flume at a scale of 1:35 (figure 2.a), and a optimized breakwater configuration proposed in a 3D wave basin at a scale of 1:50 (figure 2.b). These two campaigns made it possible to compare and optimize the design, first with the state of the art (Van Gent, M., et van der Werf, I., 2019) (Mares-Nasarre and van Gent, M., 2020), then with the observations and measurements collected from the modeling.

Parametric Analysis Of Wave-Induced Forces And Overtopping On Composite Vertical Breakwaters With Retreated Crown Wall

Composite vertical breakwaters are monolithic structures often used to protect port basins, especially in deep-water conditions. At present, the design of these structures is mainly based on Goda's formulae (Goda, 2010) or on the probabilistic design tools (PROVERBS) proposed by Oumeraci et al. (2001), while their hydraulic performance in terms of overtopping can be predicted by using the tools described in the EurOtop Manual (EurOtop Manual, 2018). Due to the size of these structures, the optimization and the improvement of the hydraulic performances (e.g. reduction of wave loads, wave overtopping, etc.) of these breakwaters can lead to significant economic saving. Typically, designers try to make small geometric changes without modifying the main geometrical dimensions of these structures. One of these technical solutions consists in placing the cast-in-situ concrete crown wall at a retreated position with respect to the front caisson face. It is assumed that the retreat of the crown wall, for geometric reasons, induces a time lag between the loads acting on the lower front external seawall face and on the crown wall of the caisson; furthermore, this could introduce a change in the pulsating nature of the loads, introducing also turbulent dissipations, consequently reducing the reflection coefficient and modifying the wave overtopping. To the best authors’ knowledge, in the literature there is a lack of guidelines to consider the effects of crown wall retreat in terms of wave actions and hydraulic performance of the structure. Recently, Romano &amp; Bellotti (2023), based on physical model tests, provided a first experimental insight on the increase/reduction of the wave loads acting on deep water vertical breakwaters with retreated crown wall.

Seismic stability evaluation of rubble mound breakwater: Shake table tests and numerical analyses

Rubble mound (RM) breakwaters are coastal structures constructed to provide tranquil condition around the port areas. After past earthquakes such as the 2004 Indian Ocean earthquake and the 2011 Great East Japan earthquake, it was found that stability of breakwater not only depends on the wave action but seismic motions also play an important role for this. Very limited studies are available for the stability evaluation of RM Breakwater under earthquake motions by conducting physical model tests. To the end, an attempt has been made in the study to evaluate the stability of RM breakwater subjected to earthquake loadings. A series of shaking table tests conducted to evaluate the seismic behaviour of the RM breakwater. A prototype RM breakwater is modelled on two layers of seabed foundation soil. Different amplitudes of sinusoidal seismic motions (foreshocks and main shock) are provided at the base of the model. Later, the breakwater stability was evaluated for real earthquake motions. Various parameters such as settlement, horizontal displacement, acceleration-time histories and excess pore water pressure were measured during the tests. Deformation pattern was also studied by photos and videos captured during the tests. During the mainshock, the crown wall settled by 111 % more comparable to second foreshock; and the structure laterally displaced by more than 200 % comparable with first foreshock. The peak acceleration of input wave amplified while it was travelling from bottom to the crest of breakwater. The excess pore water pressure was maximum beneath the rubble mound, in loose sand and it was five times more during the mainshock compared to first foreshock. Due to loss in bearing capacity of foundation soil, the breakwater collapsed. Also, the effects like rolling down of armor units, densification and slumping of core material, shear deformation of breakwater body were observed during the main shock. Thus, the breakwater failed during the mainshock. Numerical analyses were also executed for both sinusoidal and real earthquake motions to make clear the mechanism of the breakwater behaviour subjected to the earthquake loadings.

Statistical assessment of the wave loads at walls through two-phase CFD modeling of the effects of air compressibility

The modeling of wave impacts against coastal structures requires the analysis of hundreds or thousands of waves to be statistically meaningful. Long irregular wave attacks, when affordable, can be performed experimentally, but may be inadequate to track the air entrapment and account for air compressibility, which, instead, plays a key role in the wave impacts. On the other hand, long simulations are generally avoided in numerical modeling for computational effort and numerical stability reasons, even more so when two-phase flows and air compressibility are involved. In such a context, this paper presents, for the first time, the application of a plug-in suite developed in the OpenFOAM® environment to the representation of long time series of irregular waves impacting against coastal defenses while solving two compressible fluids. To this purpose, such a plug-in compressible suite was applied to reproduce recent 2D experiments of wave overtopping and wave impacts at smooth dikes with crown walls. The numerical stability of the compressible solver and its adequacy to accurately reproduce the wave reflection and the wave overtopping are first verified by comparing the numerical results with the laboratory tests. Second, the improved representation of the wave pressures and wave forces at the walls obtained with the plug-in compressible suite is shown by comparing its results with the corresponding ones obtained with the incompressible solver. Specifically, the plug-in suite—accounting for the effects of the air compressibility during the impact events—outperforms the incompressible native solver in the capture of the pressure peaks, in the reproduction of the time–pressure trace, and in the statistical analysis of the pressure distribution along the crown wall.

Geosynthetic reinforced rubble mound breakwater for mitigation of tsunami-induced damage

Several rubble mound breakwaters (RMB) were damaged and even collapsed during the past tsunamis. The main reasons for the failure of the breakwaters occurred due to the combined effects of seepage and scouring. Limited articles are available dealing with the behaviour of RMB during the tsunami. Furthermore, few available articles are related to developing countermeasures for the RMB against tsunamis. Therefore, an attempt has been made in the study to determine the exact behaviour of the RMB under the action of the tsunami. In addition, the main aim of the present study is to develop countermeasures to make the breakwater tsunami resilient. The present study proposes a novel geosynthetics-reinforced RMB to mitigate tsunami-induced breakwater damage. Based on the available information, this is the first time geosynthetics have been used in the RMB to mitigate tsunami-induced damage. Geogrid layers, geobags, sheet piles and crown walls (with shear keys) are adopted as countermeasure elements against the tsunami. Since the height of a tsunami can exceed its design tsunami height, tsunami waves were allowed to overflow the breakwater in physical model tests. Comparative analyses between the reinforced and unreinforced RMB were performed by conducting physical model tests, analytical tools, and numerical simulations.

THE INFLUENCE OF A CROWN WALL ON WAVE OVERTOPPING OVER BREAKWATERS

This paper investigates the influence of a crown wall on wave overtopping on rubble mound breakwaters. Existing data is used to modify the EurOtop overtopping formula updated by Eldrup et al. (2022) to cover the influence of the crown wall. The effect of raising the wall above the armour crest (elevated wall) or lowering the wall below the armour crest (lowered wall) is investigated. A crown wall at the armour crest level is considered as the reference case. By increasing the elevation of either the armour crest or the crown wall, overtopping is reduced and by lowering either of them, overtopping increases. The influence of the crown wall height, elevated or lowered compared to the armour crest, is not considered accurately in the present design guidelines and thus corrections are suggested. For an elevated wall, a modified crest width has been defined, to better describe the presence of the armour crest in front of the wall. For the lowered wall the effective freeboard might be taken as the average of the wall and armour freeboards. The improvement compared to existing methods is significant, especially for breakwaters with a large elevated wall. The proposed modifications to the EurOtop Manual increase the range of applicability with respect to the wall configuration.

MODELLING WAVE OVERTOPPING AND WAVE IMPACTS BY MEANS OF IMAGE CLUSTERING TECHNIQUES

The experimental modelling of the wave-structure interaction processes is a very complicated issue, due to the highly non-linear turbulent flow conditions, including wave breaking and air entrainment (Stringari et al., 2021). Recently, Formentin et al. (2021) demonstrated that videography can provide a reliable representation of the wave breaking, of the wave overtopping and of the wave impact at walls. They filmed laboratory tests of wave overtopping at smooth dikes with crown walls (Formentin et al., 2018; Palma et al., 2020) with a low-cost full-HD camera and compared the results of the video-cluster analysis applied to its records with the measurements obtained through traditional techniques. They derived accurate quantitative estimations of free-surface elevation, wave overtopping discharge, volumes, velocities and celerities. The aim of this paper is to further investigate the possibilities of the videography by focusing on the analysis of the wave impacts at the walls and on the detection of the amount of air entrapped during the impacts themselves.

MODELLING WAVE-STRUCTURE INTERACTION WITH A NEW COMPRESSIBLE TWO-PHASE FLOW SOLVER

This contribution presents and investigates the effects of the air entrainment and air compressibility on the shape and magnitude of the wave impacts occurring at crown walls on top of sea defenses. To this purpose, a new solver, developed in the OpenFoam environment to represent the wave interactions with impermeable and porous coastal structures, accounting for the fluid compressibility, is checked against recent laboratory tests of wave overtopping and wave impacts. By comparing the first results of this new code to the ones obtained with the native solver dealing with incompressible fluids exclusively, significant advances in the representation of the pressure signals and peaks at the walls seem to be achieved.

CONFINED-CREST IMPACT: THE INFLUENCE OF THE TOE BERM ON THE IMPULSIVE LOAD CONDITIONS

Composite vertical breakwaters are coastal structures used to defend port basins from waves in intermediate and deep water conditions. In order to safely use the inner side of harbors, it is important to limit wave overtopping. Parapet walls are used for this purpose. To improve the hydraulic efficiency of the parapet wall with a fixed crown wall height, the wall can be shaped giving rise to a recurved overhand toward the sea. Its function is to deflect back the incident waves. Recently, it has been shown that the interaction between non-breaking waves and recurved parapet can induce impulsive pressures due to the confinement of the incident wave crest deflected seaward by the overhanging structure. The new physical phenomenon has been called “Confined-Crest Impact (C-CI)” as shown by Castellino et al. 2018. This physical phenomenon can induce “unexpected” structural failure (Dermentzoglou et al., 2020). More recently, Castellino et al. (2021) extended the Goda’s formulae, which define the maximum pressures along a vertical breakwater, considering the “C-CI” induced by the presence of a recurved parapet. The conducted studies have concerned a vertical breakwater without any berm at the toe of the caisson. The purpose of this research is to extend this last work to a composite vertical breakwater based on a foundation berm.

APIA PORT BREAKWATER RECONSTRUCTION

Samoa is located in the South Pacific Ocean, about halfway between Hawaii and New Zealand. The first wharf at Apia (185m long) was constructed in 1966 and a 100m long breakwater with 8t Dolos armor units was constructed in 1988-89 to provide shelter. Following large cyclones in the early 1990s, the breakwater was rehabilitated in 1996 with larger 20t Dolos armor units. In 2003 a solid concrete crown wall added to the breakwater to mitigate wave transmission into the harbor. There is limited toe and scour protection and multiple units have broken legs, cracks and rust stains from corroding steel reinforcement. The design intent of the breakwater upgrading project is to improve resilience to extreme climatic and natural disaster events. Reconstructing the breakwater with a higher crest, larger roundhead, new concrete armor units, toe support and a scour apron was selected as the most appropriate option to meet the design criteria. Physical modelling was undertaken to verify and optimize the design. Wave calibration indicated good correlation with numerical modelling and showed that for offshore wave heights of ~11.5m and greater the near structure wave height is depth limited (Hs ~9.1m). The physical model testing indicated that the existing 20t Dolos units on the rear slope are unstable under the 1percent AEP event as the base units have limited rock toe support. Further model testing was undertaken using 16m3 Xblocs on the leeside which was successful and detailed design was completed accordingly.

Statistical Analysis of the Wave Runup at Walls in a Changing Climate by Means of Image Clustering

This contribution builds on an existing methodology of image clustering analysis, conceived for modelling the wave overtopping at dikes from video records of laboratory experiments. It presents new procedures and algorithms developed to extend this methodology to the representation of the wave runup at crown walls on top of smooth berms. The upgraded methodology overcomes the perspective distortion of the native images and deals with the unsteady, turbulent and bi-phase flow dynamics characterizing the wave impacts at the walls. It accurately reconstructs the free surface along the whole structure profile and allows for a statistical analysis of the wave runup in the time and spatial domain. The effects of different structural configurations are investigated to provide key information for the design of coastal defences. In particular, the effects of increased sea levels in climate change scenarios are analysed. Innovative results, such as profiling of the envelopes of the runup along the wall cross and front sections, and the evidencing of 3D effects on the runup are presented. The extreme runup is estimated for the definition of the design conditions, while the envelopes of the average and minimum runup heights are calculated to assess the normal exercise conditions of existing structures.

On viscoelastic drop impact onto thin films: axisymmetric simulations and experimental analysis

This study investigates the effect of fluid elasticity on axisymmetric droplets colliding with pre-existing liquid films, using both numerical and experimental approaches. The numerical simulations involve solving the incompressible flow momentum equations with viscoelastic constitutive laws using the finite volume method and the volume of fluid (VOF) technique to track the liquid’s free surface. Here, the Oldroyd-B model is used as the constitutive equation for the viscoelastic phase. Experiments are also performed for dilute viscoelastic solutions with 0.005% and 0.01% (w/w) polyacrylamide in 80:20 glycerin/water solutions, in order to ensure the validity of the numerical solution and to investigate the elasticity effect. The formation and temporal evolution of the crown parameters are quantified by considering the flow parameters, including the fluid’s elasticity. The results indicate that the axisymmetric numerical solutions reasonably agree with the experimental observations. Generally, the fluid’s elasticity can enlarge the crown dimension at different thicknesses of the fluid film. Moreover, at intermediate values of the Weissenberg number, the extensional force in the crown wall can control the crown propagation. Furthermore, the results reveal that the effects of the Weber number and the viscosity ratio on this problem are more significant at higher values of the Weissenberg number.

Numerical Analysis and Load-Carrying Capacity Estimation of Reinforced Concrete Slab Culvert Rehabilitated with a Grouted Corrugated Steel Plate

Two laboratory tests were conducted to investigate the mechanical properties and develop a load-carrying capacity estimation method for reinforced concrete (RC) slab culverts rehabilitated with a grouted corrugated steel plate (CSP). Subsequently, 216 numerical models of RC slab culverts rehabilitated with different shapes of CSPs and grout strengths were established to investigate the influence of these parameters and the arch effect on the rehabilitated system. A mechanical model was proposed based on the elastic center method, and a load-carrying capacity estimation method of RC slab culverts rehabilitated with grouted CSPs was established and verified. It was concluded that the load-carrying capacity of the rehabilitated system increased with a decrease in the radius of the side walls and crown at a constant radius of the CSP haunch. At a constant radius of the side walls and CSP crown, the load-carrying capacity of the rehabilitated system increased with an increase in the haunch radius. The most effective way to improve the load-carrying capacity of the rehabilitated system was to increase the radius of the haunches and reduce the radius of the arch crown and side wall. The arch effect of the grout was related to the load type. The load-carrying capacity of the rehabilitated system was the highest when the CSP was similar to or the same as the arch axes of the grout. The most important function of the grout was to provide strong lateral restraint for the CSP, reducing the required span and improving the load-carrying capacity of the CSP. In addition, the shear strength of the grout contributed to improving the load-carrying capacity by exerting an arch effect or experiencing shear failure. The proposed load-carrying capacity estimation method is applicable to rehabilitated systems with a box or arch-type CSP. Our findings provide guidance for engineers to design similar rehabilitated systems.

Interaction between medium-long period waves and smoothed mound breakwater with crown wall based on experiments and multi-phase simulations

Laboratory and numerical investigations of the wave force during the interaction between medium-long period waves and a smooth mound breakwater with crown wall were conducted. Multi-phase smoothed particle hydrodynamic model and constraint interpolation profile model were used and verified. A comparison of the pressure peaks shows that the accuracies of the two models are similar. A new formula is presented to estimate the wave force on the crown wall under medium-long period waves. With an increase in the wave period, the pulsating force on the crown wall gradually occupies the main component. The wave force on the slope increases with an increase in the wave period. The slope wave force with crown wall was compared to that without crown wall. The crown wall had little effect on the slope wave force. The Neelamani method overestimated the slope wave force. A new prediction method is proposed to significantly improves accuracy.

Numerical Study of Heat Transfer During Oblique Impact of a Cold Drop on a Heated Liquid Film

Abstract A three-dimensional study of a cold droplet impacting obliquely on a heated solid flat surface covered with a hot liquid layer has been performed. The drop Weber number, liquid film thickness, and drop impact angle are set to a range from 100 to 800, 0.1 to 0.4, and 0 deg to 60 deg, respectively. The interface evolution and thermal behavior of the drop impingement is well captured using coupled level set and volume of the fluid method (CLSVOF). The code is validated against previously published results both qualitatively and quantitatively. The results show that in the case of oblique drop impact, the crown dynamics and wall heat flux distribution exhibit an asymmetric pattern, with secondary droplets generated solely on the downstream side, as opposed to normal drop impact in which the secondary drops generated around the circumference of the crown. Based on heat flux values, two distinct region within the liquid film exist: (i) impact region around the impact point and (ii) undisturbed region far from the impact region characterized by the impact dynamics. A parametric analysis further reveals that for a moderate Weber number, asymmetric behavior increases as the drop impact angle increases, resulting in a reduction in heat transfer from the solid surface. However, for a drop impacting at an angle of 28 deg, increased asymmetry due to a increase in the Weber number results in significant cooling of the impact region. Furthermore, it is also found that a thinner liquid film promotes higher heat transfer from the solid surface, resulting in a higher wall heat flux.