Numerical Model Applicability Based on a Hydraulic Characteristic Analysis of an Eco-friendly Double-row Submerged Breakwater
Article information
Abstract
In this study, a submerged breakwater with effective wave control and eco-friendly characteristics is developed and proposed. Hydraulic experiments are conducted to compare the hydraulic performance of a submerged breakwater and an eco-friendly double-row submerged breakwater. The hydraulic characteristics are analyzed based on wave reflections and the transmission-splitting method for each experimental cross-section. This splitting technique utilizes Goda’s two-point method, which employs the spectra of two irregular superposed wave fields. In addition, the reliability of the results obtained from the hydraulic experiments is discussed by comparing the results with empirical formulas. The eco-friendly double-row submerged breakwater features approximately half the width of a typical submerged breakwater. Nevertheless, its transmission coefficient (KT) is approximately 20% more effective, and the difference in the average reflection coefficient (KR) values between the two is approximately 0.17. Moreover, the dissipation coefficient (KD) shows a generally similar trend. Based on these experimental results, the hydraulic performance of the eco-friendly double-row submerged breakwater is more efficient regarding wave control, compared with a typical submerged breakwater. These hydraulic characteristics confirm that the numerical model developed for the eco-friendly double-row submerged breakwater accurately reproduces the KT, KR, and KD values within ±5%.
1. Introduction
A coastal area refers to a complex zone that includes both sea and land, based on the coastline. Recently, coastal areas have become spaces where various marine industries and leisure sports take place. Because of their spatial characteristics, coastal areas are constantly exposed to coastal disasters, such as coastal erosion and storm surges. Countermeasures are essential, and various disaster prevention facilities are being installed. Representative disaster prevention facilities for coastal erosion include groynes as well as offshore and submerged breakwaters. Among these, offshore and submerged breakwaters have been designed and constructed parallel to the coastline in the open sea to attenuate the energy of waves approaching the coast. Most structures installed in existing coastal areas are gray structures that use artificial materials, such as cement concrete. The indiscriminate construction of these grey structures poses the risk of causing changes in marine ecosystems, such as algal blooms. Moreover, the possibility of large-scale coastal disasters is increasing, owing to climate change caused by the massive emissions of carbon dioxide due to industrialization. Recently, the government implemented carbon-neutral policies as part of a set of fundamental measures to solve these problems. To achieve carbon neutrality, it is essential to enhance carbon absorption via the creation and expansion of blue carbon in marine and coastal areas as well as green carbon from afforestation. From this perspective, the application and utilization of eco-friendly materials in structures installed in coastal areas are critical.
In the field of rivers, research and river development projects using new eco-friendly materials have begun to simultaneously solve disaster safety issues and river ecosystem problems caused by the indiscriminate development of artificial concrete structures. Recently, to review the applicability of eco-friendly materials to embankments, a new technology was developed to prevent and delay embankment collapse by reinforcing the embankment surface with biopolymer binders extracted from plants and natural aggregates. This technology enhances eco-friendliness (Ahn et al., 2017b; Lee et al., 2024; Park et al., 2015) and verifies safety via full-scale experiments (Ahn et al., 2017a; Kang and Ahn, 2023; Lee et al., 2022). The developed reinforcement material significantly improved the resistance to water flow and safely protected the embankment under high water pressure and fast flow conditions during floods, without the erosion of the surface soil or detachment of the reinforcement material. In addition, because eco-friendly materials were used, the early establishment and growth of vegetation was possible. Hence, the restoration of river ecological functions and durability were simultaneously maximized.
In coastal areas, the urgent development and introduction of an eco-friendly new hybrid submerged breakwater material is necessary. This hybrid submerged breakwater can fulfill the dual role of creating blue carbon through the attachment and growth of seaweed and seagrass while also serving as a disaster prevention facility through wave control. A thorough review of the optimal cross-sectional specifications, double- and multi-row forms, and spacing distances of eco-friendly submerged breakwaters is required to satisfy the economic feasibility and wave control performance needs, compared with those of existing wide submerged breakwaters.
The following studies were conducted to quantitatively compare the wave control performances of double- and multi-row submerged breakwaters with varying spacing distances and optimal cross-sectional specifications. Yun et al. (1995) analyzed the correlation between the permeability, crest depth, and spacing distance of multi-row submerged breakwaters under the same incident wave conditions via numerical model experiments and examined the wave control performance of these breakwaters. They argued that multirow submerged breakwaters with fewer materials could replace existing submerged breakwaters that struggle with long-period wave control. Cho (2006) performed laboratory experiments to analyze the reflection characteristics of impermeable rectangular submerged breakwaters based on their arrangement and spacing, and they reproduced and compared hydraulic experiments using the eigenfunction expansion method. This study confirmed that the location of the first resonance period was consistent, regardless of the structural arrangement, and that the reflection coefficient increased with the number of rows. Ha et al. (2009) applied the boundary integral equation method for short-period waves and a three-dimensional mixed upstream analysis method for solitary waves to perform a numerical analysis on impermeable structures. They also derived the cross-sectional specifications of double-row submerged breakwaters and numerically compared their wave-blocking performances. Lee et al. (2010) found that under limited numerical conditions, double-row submerged breakwaters were effective in controlling short-period and solitary waves. Shih et al. (2013) used a numerical model with the boundary element method to compare and review the water molecule distribution and flow velocity around multirow submerged breakwaters. Behera and Khan (2019) conducted numerical studies on permeable rectangular and trapezoidal submerged breakwaters and compared and analyzed the hydraulic characteristics of these breakwaters based on single- and double-row arrangements. Patil and Karmakar (2021) compared and analyzed the hydraulic characteristics based on various submerged breakwater shapes and cross-sectional specifications by using numerical model experiments with the boundary element method.
This study proposes an eco-friendly double-row submerged breakwater that was made by mixing a biopolymer binder extracted from non-toxic castor oil and natural aggregates. The proposed breakwater displays wave control performance that is similar to those of existing wide submerged breakwaters and allows for the attachment and growth of marine vegetation. The proposed submerged breakwater was analyzed via hydraulic model experiments and compared with the wave control hydraulic performances of existing submerged breakwaters that are composed of concrete blocks. The effectiveness and validity of the numerical model were examined using a Navier–Stokes equation-based numerical wave tank (NWT), the reliability of which has been confirmed in various previous studies related to submerged breakwaters (Hur et al., 2013).
2. Hydraulic Experiment
2.1 Overview of the Hydraulic Experiment and Structure
To compare the hydraulic performances of the existing submerged breakwater and the eco-friendly double-row submerged breakwater, laboratory experiments were conducted in a cross-sectional 2D wave flume. The specifications of the experimental flume, as shown in Fig. 1, are a length of 37.0 m, width of 0.6 m, and height of 1.0 m. To minimize wave reflection on the leeward side of the cross-sectional 2D wave flume, a permeable layer with a constant slope was arranged. A piston-type wave generator was used to stably generate the incident waves. In addition, an impermeable sloped structure with a 1:30 slope was installed up to a height of 0.3 m to facilitate the setting of experimental waves.
Sketch of the 2D wave channel, including the structure
Table 1 lists the cross-sectional conditions of the existing submerged breakwater and the eco-friendly double-row submerged breakwater used in this study. The specifications for each experimental cross-section are illustrated in Fig. 1 for the existing submerged breakwater (A1) and eco-friendly double-row submerged breakwater (D1, D2). The double-row submerged breakwater is composed of front and rear breakwaters. The material used for the eco-friendly double-row submerged breakwater is biopolymer concrete, which is made by combining a biopolymer binder extracted from natural castor oil with natural aggregates to coat the exterior. The interior is composed of rubble and aggregates, whereas the base and walls are made of reinforced concrete, as shown in Fig. 2. The cover blocks of existing submerged breakwaters are composed of concrete tetrapod (TTP) units. The cross-sectional specifications of D1 and D2 in Table 1 show that, compared with the existing wide submerged breakwater, the crest width is nearly halved by the proposed breakwater, which thereby achieves economic efficiency owing to reduced material costs. The reduced crest width allows for a smaller structure size as well as easier onshore manufacturing and installation, which shortens the construction period and effectively reduces the construction costs. The shape of the double-row submerged breakwater was designed to fully attenuate energy, based on wave breaking characteristics. The front breakwater was designed with smaller cross-sectional dimensions than those of the rear breakwater to develop wave nonlinearity, whereas the rear breakwater was designed with larger cross-sectional dimensions to fully dissipate the developed wave nonlinearity and enhance energy attenuation through an increased wave breaking intensity.
Cross-section conditions of structures
Porous biopolymer submerged breakwater
Five capacitive wave gauges (WGs) were installed in the experimental flume. WGs 1–3 were positioned at the front of the structure, whereas WGs 4 and 5 were placed at the rear. Wave gauges were set to acquire water level fluctuation data at fixed points in front of and behind the structure at intervals of 50 Hz.
2.2 Wave Conditions
In this study, 40 experimental conditions were established by combining 4 wave heights and 10 periods at the same water depth, as listed in Table 2. Three cross sections were targeted for the experiment: the existing submerged breakwater and two eco-friendly double-row submerged breakwaters with different spacing distances. The model used in the laboratory experiment accurately represented the hydraulic phenomena of the prototype. The Froude similarity law was applied to analyze the hydraulic characteristics of the existing submerged breakwater and the eco-friendly double-row submerged breakwater, as gravity is the dominant external force acting on fluid motion. The scale ratio was set to 1:20, considering the size and performance of the experimental facilities and measuring equipment, including the wave flume used in the laboratory experiments.
Incident wave conditions used in this study
The wave conditions were as follows. The model wave heights (Hi) ranged from 2.50 to 10.00 cm, and the periods (Ti) ranged from 0.89 to 2.91 s. According to the 1:20 scale, the prototype wave heights (Hi) ranged from 0.5 to 2.0 m, and the periods (Ti) ranged from 4.0 to 13.0 s. Thus, all the conditions were represented by the model specifications. The wavelengths (Li) ranged from 107.10 to 424.50 cm, and the wave steepness (Hi/Li) ranged from 0.006 to 0.093. Each experimental wave was an irregular wave that was generated based on the Bretschneider–Mitsuyasu spectrum, as given by Mitsuyasu (1969) in Eq. (1):
Fig. 3 compares the theoretical values of the Bretschneider– Mitsuyasu spectrum with the experimentally measured values. Fig. 3(a) represents wave case O1 (Hs = 2.50 cm, Ts = 0.89 s), Fig. 3(b) represents wave case O19 (Hs = 7.50 cm, Ts = 1.79 s), and Fig. 3(c) represents wave case O28 (Hs = 10.00 cm, Ts = 2.24 s). In addition, when setting the experimental waves in the laboratory experiment, the position of the experimental wave setup was determined based on whether the wave was breaking. Therefore, the wave data measured in front of the impermeable sloped structure were compared with the wave condition spectra in this study.
Comparison of measured data and data obtained via the Bretschneider–Mitsuyasu theoretical spectrum
2.3 Wave Reflection and Transmission Splitting Method
To analyze the hydraulic performance of the existing submerged breakwater and the eco-friendly double-row submerged breakwater, the wave reflection coefficient (KR) and transmission coefficient (KT) were calculated from the water level fluctuation data measured at the front and rear of the structures by using the incident and reflected wave separation methods of Goda and Suzuki (1976). The wave dissipation coefficient (KD) was calculated using Eq. (2):
2.4 Experimental Results
2.4.1 Wave field
Figs. 4–6 show the wave fields around the structures at regular time intervals (t/Ti = 1/5) under wave case O19 (Hs = 7.50 cm, Ts = 1.79 s) for the existing submerged breakwater and the eco-friendly double-row submerged breakwater. Fig. 4 illustrates the experimental cross-section for the existing submerged breakwater (A1), whereas Figs. 5 and 6 represent the experimental cross-sections for the eco-friendly double-row submerged breakwaters (D1, D2) with spacing distances of 110 and 75 cm, respectively.
Temporal and spatial distributions of surface elevations around wave cases A1 and O19
Temporal and spatial distributions of surface elevations around wave cases D1 and O19
Temporal and spatial distributions of surface elevations around wave cases D2 and O19
As shown in Fig. 4, wave breaking occurred at the crest of the submerged breakwater as the wave crest propagated. The waves propagating behind the structure exhibited a reduction in wave height owing to the breaking and dispersion of the wave crests. In addition, the return flow owing to the difference in water levels on the front and rear sides of the structure can be observed. This phenomenon is particularly noticeable in cases with relatively larger wave heights among the irregular waves.
Figs. 5 and 6 show that although the combined crest widths of the front and rear breakwaters of the eco-friendly double-row submerged breakwater is nearly half that of the existing submerged breakwater, the wave heights of the waves propagating behind the structure are further reduced. This hydraulic characteristic indicates that the front breakwater of the eco-friendly double-row submerged breakwater increases the nonlinearity of the waves and that the rear breakwater induces wave breaking with stronger nonlinearity, thereby effectively controlling the waves. The wave height reduction owing to the spacing distance between the front and rear breakwaters of the eco-friendly double-row submerged breakwater appears to be approximately the same.
Based on the above, the changes in the wave fields from the recorded video data qualitatively confirmed the hydraulic wave control performance for the existing and eco-friendly double-row submerged breakwaters reviewed in this study. In the following sections, the hydraulic performance for each experimental cross-section is quantitatively assessed via the wave transmission, reflection, and dissipation coefficients.
2.4.2 Wave transmission coefficients
Fig. 7 shows the wave transmission coefficient (KT) as a function of the wave steepness (Hi/Li) for different experimental cross-sections by using the incident and reflected wave separation methods of Goda and Suzuki (1976). In the figure, the black circles (
) represent the results for the existing submerged breakwater, whereas the blue squares (
) and red diamonds (
) represent the results for the eco-friendly double-row submerged breakwater. The spacing distances for the eco-friendly double-row submerged breakwaters D1 and D2 were 110 and 75 cm, respectively. The calculation of KT for an existing submerged breakwater considers the ratio of the crest depth to incident wave height (R/Hi) and the ratio of the crest width to incident wave height (B/Hi), as proposed by the empirical formula of van der Meer et al. (2005). The trend line of Eq. (3), according to the experimental conditions, is indicated by a black dashed line (- - -) in Fig. 6. The solid lines (━) represent the trend lines for each experimental cross-section based on the wave steepness.
Distribution of transmission coefficients
Fig. 7 shows that KT generally decreases as the wave steepness increases, regardless of whether it is for an existing submerged breakwater or eco-friendly double-row submerged breakwater. The wave control ability of the existing submerged breakwater was similar to the results of the empirical formula of van der Meer et al. (2005). Although the values of KT for the eco-friendly double-row submerged breakwater showed slight differences based on the experimental conditions, the trend of KT relative to the spacing between the front and rear breakwaters was nearly identical. On average, the wave control ability of the eco-friendly double-row submerged breakwater was approximately 20% higher than that of the existing submerged breakwater. This is because the material properties and cross-sectional shape of the eco-friendly double-row submerged breakwater increased the wave nonlinearity at the front breakwater and then followed this with wave breaking at the rear breakwater. Therefore, it can be concluded that the eco-friendly double-row submerged breakwater, which has a crest width that is half that of the existing submerged breakwater, still possesses adequate wave control capabilities.
2.4.3 Wave reflection coefficients
Fig. 8 shows the wave reflection coefficient (KR) as a function of the wave steepness (Hi/Li) for different experimental cross-sections by using the incident and reflected wave separation methods of Goda and Suzuki (1976). The symbols represent the KR values for the respective experimental cross-sections discussed previously. The calculation of KR for an existing submerged breakwater considers the ratio of the crest depth to the incident wave height (R/Hi), as proposed by the empirical formula of van der Meer et al. (2005). This empirical formula is represented by Eq. (4) and has the same significance as does the aforementioned trendline.
Distribution of reflection coefficients
Fig. 8 shows that the KR for the existing submerged breakwater slightly decreases as the wave steepness increases, with a difference of approximately 0.24 to 0.03 from the empirical formula of van der Meer et al. (2005). This difference is likely owing to the use of TTP cover blocks for the existing submerged breakwater in this study, as opposed to the various cover blocks considered in the empirical formula. Moreover, the KR value of the eco-friendly double-row submerged breakwater was approximately 80% higher than that of the existing submerged breakwater, with an average KR difference of approximately 0.17. This was attributed to the material properties and porosity of the eco-friendly double-row submerged breakwater. The difference in KR between D1 and D2 based on the spacing distance is likely attributable to the resonance effects of the reflected waves from the front and rear breakwaters.
2.4.4 Wave dissipation coefficients
Fig. 9 shows the wave dissipation coefficient (KD) as a function of the wave steepness (Hi/Li), as calculated via the correlation equation for KT and KR from Goda and Suzuki (1976), which is shown in Eq. (2). Each symbol represents the KD value for the respective experimental cross-section, as previously discussed. The trend line derived from the empirical formula proposed by van der Meer et al. (2005) is shown in Eq. (2) for the KT and KR correlations.
Distribution of dissipation coefficients
Fig. 9 shows that the KD increases as wave steepness increases and that the trends for KD from the empirical formula by van der Meer et al. (2005) are similar for all the experimental cross-sections (A1, D1, and D2). This similarity indicates that the smaller KT and larger KR values align consistently with the wave steepness. Comparing the eco-friendly double-row submerged breakwater with the existing submerged breakwater, the KD values are, on average, approximately 4% lower.
3. Numerical Model Applicability
3.1 Overview of the Numerical Model
A 2D numerical wave tank (LES-WASS-2D; Hur and Choi, 2008) was used to evaluate the hydraulic characteristics of the developed double-row submerged breakwater. The numerical analysis method applied in this 2D numerical wave tank is a 2D Navier–Stokes solver based on the porous body model (PBM) for simulating the flow around permeable structures and the volume of fluid (VOF) method for modeling complex free surfaces. In addition, to simulate the fluid resistance within the permeable structures, a highly nonlinear 2D numerical analysis method was utilized. This method considered the energy dissipation owing to turbulent, laminar, and inertial resistance based on the characteristics of the porous media.
3.2 Governing Equations
The governing equations are the continuity equation in Eq. (5), which incorporates the wave-source terms and fluid resistance in permeable media, and the modified Navier–Stokes equation in Eq. (6):
Here, vi represents the flow velocity in the x and z directions, q* is the source flow density, γv is the volume porosity, γi is the permeability in the x and z directions, t is the time, ρ is the water density, P is the pressure, νT is the sum of the kinematic and eddy viscosities of water, Dij is the strain rate tensor, Si is the surface tension term based on the continuous surface force (CSF) model (Brackbill et al., 1992), Qi is the wave source term, Ri is the fluid resistance term owing to the permeable media, gi is the gravitational acceleration term, and Ei represents the energy dissipation term.
In the VOF method, F denotes the volume fraction occupied by fluid in each cell (Hirt and Nichols, 1981). The fluid resistance of permeable media (Ergun, 1952; Sakakiyama and Kajima, 1992), the turbulence model (Smagorinsky, 1963), and other numerical model details were described by Lee et al. (2016).
3.3 Verification of the Numerical Wave Tank (NWT)
The hydraulic characteristics obtained from the 2D laboratory experiments conducted in this study were compared to ensure the validity and reliability of the numerical wave tank. The reflection, transmission, and dissipation coefficients for both the conventional submerged breakwater (A1) and eco-friendly double-row submerged breakwater (D2, with S = 75 cm) were verified. The numerical wave tank verification was performed under the same wave conditions as those used in the laboratory experiments, with 200 irregular waves being used in the laboratory experiment and 100 waves being reproduced in the numerical model to reduce the computational load. Fig. 10 shows a comparison between the experimental and numerical results. Figs. 10(a) and 10(b) compare the experimental and numerical results for the conventional submerged breakwater (A1) and eco-friendly double-row submerged breakwater (D2), respectively. Red circles and diamonds (
,
) indicate the reflection coefficient (KR), blue circles and diamonds (
,
) indicate the transmission coefficient (KT), and black circles and diamonds (
,
) indicate the dissipation coefficient (KD). The solid black line (━) represents the central line indicating the agreement between the calculated and experimental values, whereas the black dashed lines (- - -) represent the ±10% range. The porosity of the permeable media was applied to incorporate the physical properties of the conventional and eco-friendly submerged breakwaters into the numerical model. A porosity of 0.5 was applied for the conventional submerged breakwater composed of TTP, whereas a porosity of 0.4 was applied for the bio-polymer concrete of the eco-friendly double-row submerged breakwater, as certified by an fiti testing & research institute.
Comparison between the measured and numerical wave characteristics
Figs. 10(a) and 10(b) show that the calculated values generally fell within 10% of the experimental values. For the eco-friendly double-row submerged breakwater in Fig. 10 (b), most wave conditions were reproduced within a high accuracy of ±5%. This indicates that the numerical model can adequately review the hydraulic performance of the eco-friendly double-row submerged breakwater, considering its material properties and cross-sectional shape, with higher precision than that of the conventional TTP submerged breakwater. Fig. 10(a) shows the verification of the hydraulic performance of the conventional submerged breakwater and further supports the validity and reliability of the numerical model.
4. Conclusions
In this study, hydraulic experiments were conducted to compare and analyze the hydraulic characteristics and wave control performance of a developed eco-friendly double-row submerged breakwater with those of a conventional submerged breakwater. Changes in the wave patterns around the eco-friendly double-row submerged breakwater and conventional submerged breakwater were discussed, based on the video data of the hydraulic experiments. The transmission, reflection, and dissipation coefficients of the waves were calculated by applying incident and reflected wave separation methods to the acquired water level data. The reliability of the experiments was ensured via comparison with empirical formulas and trend lines for submerged breakwaters. In addition, a strong nonlinear 2D numerical model was used to verify the hydraulic characteristics and review the applicability of an eco-friendly double-row submerged breakwater. This study was conducted under limited conditions of hydraulic experiments, and the main results are as follows.
(1) The breaking wave process based on the cross-sectional characteristics of the eco-friendly double-row submerged breakwater and conventional submerged breakwater was confirmed. The combined crest widths of the front and rear structures of the eco-friendly double-row submerged breakwater showed wave control capabilities similar to those of the conventional submerged breakwater, which had a crest width that was reduced by half. These results are attributable to the increased wave nonlinearity and occurrence of breaking waves, owing to the cross-sectional shape and material characteristics of the double-row structure.
(2) When comparing the transmission coefficients of a conventional submerged breakwater and the developed eco-friendly double-row submerged breakwater, the wave control capability of the eco-friendly double-row submerged breakwater was approximately 20% superior, regardless of the distance between the front and rear structures.
(3) The eco-friendly double-row submerged breakwater, consisting of front and rear structures, showed relatively higher reflection coefficients, compared with those of the conventional submerged breakwater, owing to the resonance phenomena caused by the periodic components of the reflected waves that result from the cross-sectional shape and material characteristics. The dissipation coefficient increased with the wave steepness, showing a similar trend within 5%.
(4) The numerical model was validated by comparing the experimental and calculated values of the hydraulic characteristics. The hydraulic performance of the eco-friendly double-row submerged breakwater, considering its cross-sectional shape and material characteristics, was well reproduced within ±5%, and the hydraulic characteristics of the conventional submerged breakwater were also reproduced with an accuracy within ±10%, thereby confirming the expanded applicability of the numerical model.
Based on the experimental results, the hydraulic performance of the developed eco-friendly double-row submerged breakwater was deemed efficient, and its applicability was confirmed via numerical verification, thereby enabling the optimal cross-sectional specifications and arrangement shapes to be numerically reviewed. Therefore, future studies will focus on reviewing the hydraulic performance of the developed eco-friendly double-row submerged breakwater as a composite underwater structure utilizing underwater vegetation. Moreover, an expansion to a 3D numerical analysis will be conducted to review the changes in the physical environment of the surrounding sea area and coastline based on 3D specifications.
Notes
No potential conflict of interest relevant to this article was reported.
This study is supported by the Korea Institute of Marine Science and Technology Promotion (KIMST) and funded by the Ministry of Oceans and Fisheries, Korea (RS-2023-00256687).
