Numerical Study of Efficiency Indices to Evaluate the Effect of Layout Mode of Artificial Reef Unit on Flow Field

Journal of Marine Science and Engineering

Article Numerical Study of Efﬁciency Indices to Evaluate the Effect of Layout Mode of Artiﬁcial Reef Unit on Flow Field

Jiating Zhang 1, Lixin Zhu 1, Zhenlin Liang 1, Liyuan Sun 2, Zhaoyi Nie 1, Jiahao Wang 1, Wude Xie 1 and Zhaoyang Jiang 1,*

1 Marine College, Shandong University, Weihai 264209, China; [email protected] (J.Z.); [email protected] (L.Z.); [email protected] (Z.L.); [email protected] (Z.N.); [email protected] (J.W.); [email protected] (W.X.) 2 Shandong Hydrobios Resources Conservation and Management Center, Yantai 264003, China; [email protected] * Correspondence: [email protected]

Abstract: Artificial reefs (ARs) have been widely used to restore the seabed habitat and protect biodiversity. They can effectively increase the dissolved oxygen content in the bottom water layer by their disturbing effect of upwelling and downwelling. The bottom water is prone to hypoxia in summer due to the extreme weather of the global climate and excessive biomass in some marine ranching in northern China. Therefore, how to effectively use the upwelling effect of artificial reefs to alleviate this problem is a necessary subject of research. Generally, ARs are arranged by different intervals in a unit form on the seafloor, and the flow field effect is different from that of the individual reefs. However, few studies have been focused on the effect of layout mode on the flow field of a unit reef (UR). In this paper, we selected the interval between reefs (IR) and the angle of inflow (AI) as the Citation: Jiating, Z.; Lixin, Z.; influencing factors to study the flow field effect of UR. The upwelling and wake regions of 64 URs Zhenlin, L.; Liyuan, S.; Zhaoyi, N.; Jiahao, W.; Wude, X.; Zhaoyang, J. were presented by the efficiency and disturbance indices related to the flow characteristics and Numerical Study of Efficiency Indices proposed an optimal layout mode having the best performance of the upwelling effect. The results to Evaluate the Effect of Layout Mode showed that the interactions among the AI, the transverse, and longitudinal IRs were significant, and of Artificial Reef Unit on Flow Field. J. the AI has a significant influence on the flow field. These indices were effective and contribute to Mar. Sci. Eng. 2021, 9, 770. https:// the layout optimization of UR. The AI close to 45◦ has a significant influence on the flow field effect doi.org/10.3390/jmse9070770 of UR.

Academic Editors: Kamal Djidjeli and Keywords: unit reef; interval between reefs; angle of inﬂow; efﬁciency index; disturbance index Apostolos Papanikolaou

Received: 12 May 2021 Accepted: 11 July 2021 1. Introduction Published: 15 July 2021 Artiﬁcial reefs (ARs), as man-made permeable structures, are widely used in biodi-

Publisher’s Note: MDPI stays neutral versity conservation and coastal habitat restoration in marine ranching engineering [1–4]. with regard to jurisdictional claims in After the settlement of ARs, a complex hydrodynamic condition is formed in a certain published maps and institutional affil- range around the ARs. For example, due to the block of an AR, a slow flow region full of iations. complex eddies will form behind the AR, also known as the wake region. This turbulent region full of eddies can cause the physical aggregation of plankton, crustaceans, and fish [5–10]. Simultaneously, there is an upwelling region above the AR, which can enhance the exchange and transport of nutrients between the upper and lower water layers and is conducive to the improvement of primary productivity. This is one of the basic principles Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. for AR to perform its function on the flow field. This article is an open access article Moreover, the upwelling has higher chlorophyll concentration (Chl a) and lower sea distributed under the terms and surface temperature (SST), which can also promote the improvement of surface primary conditions of the Creative Commons productivity [11]. For a small-scale area such as marine ranching, nutrient exchange in Attribution (CC BY) license (https:// regional water also needs a continuous driving force. ARs can change the original seabed creativecommons.org/licenses/by/ topography, and the upwelling formed by them plays a necessary role in regulating the 4.0/). flow in a small sea area [12–15].

J. Mar. Sci. Eng. 2021, 9, 770. https://doi.org/10.3390/jmse9070770 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 770 2 of 16

At present, many research results have been obtained based on the analysis of flow field effect of individual AR, mainly focusing on opening ratio, inlet velocity, angle of inflow (AI), and characterization of drag coefficient [9,16–21]. However, AR is generally arranged and released in the form of a combination of several ARs, which is often called AR module, AR set or AR group [22]. In order to facilitate the statistics and expression of the number of ARs, it also called unit reef (UR). Different combinations of UR will produce different flow field effects. Therefore, a reasonable layout mode can effectively promote water exchange, improve water quality, and enhance biodiversity in the areas surrounding ARs [23–27]. The common layout modes of UR were usually in the form of piles, such as rock reefs, which were used to multiply sea cucumber in northern China. Li et al. [28] studied the flow field effect of three kinds of tube artificial reef piles under different inlet velocities. However, this form of layout mode is prone to collapse due to the impact of the ocean current. For large ARs, such as those made of concrete, they were usually arranged in an array combination. Woo et al. [8] presented effective layout modes of labyrinth artificial concrete reef (LTACRs) based on the wake volume. Kim et al. [29] selected four marine forest artificial reefs (MFARs) frequently used in South Korea to simulate the flow field in order to analyze the spreading pattern and range of seaweed spores. The interval between reefs (IR) was determined by the wake length of the single-type AR, and the optimal flat layout mode was selected based on the wake volume and flow characteristics. It was concluded that the major wake length has important significance to guide further research on the IRs. At present, the studies on upwelling only focus on the height and the upwelling flow rate of the individual reefs [9,21], and rarely consider the influence of AR layout mode. In recent years, during high temperatures and rainy summers, the bottom water of AR areas dominated by rock reefs in northern China has formed hypoxic areas. This causes the death of sea cucumbers and other benthic organisms that proliferate in AR areas, which induces ecological and environmental disasters [30–32]. Our previous research [9,13,21] showed that structural optimization can significantly improve the upwelling effect of AR. However, if we want to solve the regional hypoxia phenomenon in marine ranching, it needs to be solved by the upwelling effect of UR, and it is also necessary to optimize the layout mode of UR. A reasonable combination of ARs, such as IRs and AIs, can improve the overall flow field effect of UR and enhance the disturbance efficiency between the bottom and the upper water layer in the artificial reef area. In this article, we adopted the CFD method to analyze the influence of IR and AI on the formation of the flow field of UR, focusing on the effect of the upwelling and wake region with the efficiency index and the disturbance index. This study can provide a scientific reference for the layout optimization of UR.

2. Materials and Methods 2.1. Reef Module In this article, the upwelling reef designed in our previous research [9] was used as the research object, which is composed of four isosceles triangles and right triangles as shown in Figure1. The flow field effect produced by the upwelling reef has a wider range, higher upwelling height, and more complex flow patterns. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 3 of 17 J. Mar. Sci. Eng. 2021, 9, 770 3 of 16 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 3 of 17

Figure 1. TheThe upwelling upwelling reef. reef. Figure 1. The upwelling reef. 2.2. Numerical Numerical Simulation Simulation 2.2.1. Layout Mode 2.2. Numerical 2.2.1.Simulation Layout Mode In this study, nine upwelling reefs were combined into a UR, which is shown in 2.2.1. Layout ModeIn this study, nine upwelling reefs were combined into a UR, which is shown in Fig- Figure2. The IR is measured by the length of the upwelling reef (L). Both the longitudinal In this study,ure 2. nine The upwelling IR is measured reefs wereby the combined length of intothe upwellinga UR, which reef is (L).shown Both in the Fig- longitudinal IR IR (h1) and the transverse IR (h2) were set to 1 L, 4/3 L 5/3 L, and 2 L, respectively. The ure 2. The IR is(h measured1) and the transverseby the length IR (ofh2 )the were upwelling set to 1 L,reef 4/3 (L). L 5/3 Both L, andthe longitudinal2 L, respectively. IR The AI was AI was set to 0◦, 15◦, 30◦, and 45◦ respectively (Figure3). These three influence factors (h1) and the transverseset to 0°, IR15°, (h 230°,) were and set 45° to respectively1 L, 4/3 L 5/3 (FigL, andure 23). L, Theserespectively. three influence The AI was factors and their and their levels produced a total of 64 combinations of ARs. The flow field effects of these set to 0°, 15°, 30°,levels and produced 45° respectively a total of (Fig 64 urecombinations 3). These three of ARs. influence The flow factors field andeffects their of these combi- combinations were used to analyze the interaction among the influencing factors. The levels producednations a total were of 64 used combinations to analyze ofthe ARs. interaction The flow among field effectsthe influencing of these combi-factors. The optimal optimal h1, h2, and AI were identified according to large upwelling and downwelling nations were usedh1, h2 ,to and analyze AI were the identified interaction according among the to largeinfluencing upwelling factors. and Thedownwelling optimal regions. regions. h1, h2, and AI were identified according to large upwelling and downwelling regions.

Figure 2. The UR and AI. Note: θ: angle of inflow. Figure 2. The UR and AI. Note: θ: angle of inﬂow. Figure 2. The UR and AI. Note: θ: angle of inflow.

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Figure 3. Computational domain and the grid division. Figure 3. Computational domain and the grid division. 2.2.2. Governing Equation and Turbulence Model 2.2.2. GoverningANSYS Fluent Equation [33] was and used Turbulence to simulate Model the flow field of URs in this article. The flowANSYS was assumed Fluent [33] to be was Newtonian, used to simulate which is incompressiblethe flow field of and URs viscous in this around article. ARs. The flow wasThe assumed finite volume to be methodNewtonian, was utilized which tois discretizeincompressible the Navier-Stocks and viscous equations. around TheARs. The finitemethod volume of calculating method was the utilized turbulent to motion discretize was the solved Navier by the-Stocks RNG equations.k-ε model, The which method could effectively simulate the flow with a minor turbulence structure and more uniform of calculating the turbulent motion was solved by the RNG k-ε model, which could effec- distribution [34], and it has been well applied in many researches of AR with complex tivelystructures simulate [9,15 the,21 flow,25,28 with,35]. a The minor analysis turbulence of the pressure structure and and velocity more uniform coupling distribution chose [34the], and SIMPLEC it has algorithm, been well and applied the second-order in many researches upwind method of AR was with used complex for spatial structures [9,15,21,25,28,35].discretization. Convergence The analysis was of assumed the pressure as the residualsand velocity fell below coupling 10−5 .chose the SIMPLEC algorithm, and the second-order upwind method was used for spatial discretization. Con- vergence2.2.3. Computational was assumed Domain as the andresiduals Boundary fell Conditionbelow 10−5. The location of ARs and the grid division of the computational domain are shown 2.2.3.in Figure Computational3, and the bottom Domain center and ofBoundary the AR located Condition in the center of the UR was set as the coordinate origin. Although there are 64 combinations of ARs in this study, h1 and h2 haveThe little location effect onof theARs ranges and the of these grid combinations.division of the Gambit computational software was domain used toare estab- shown in Figlishure models 3, and andthe constructbottom center a cuboid of computationalthe AR located domain in the with center200 of m ×the160 UR m was× 100 set m .as the coordinateIn order toorigin. determine Although the appropriate there are 64 numerical combinations simulation of ARs method, in this three study, simulation h1 and h2 have littleschemes effect were on the set. Threeranges small of these domains combinations. with respective Gambit dimensions software of 70 mwas× 60used m × to40 establish m, models100 m ×and80 construct m × 60 m anda cuboid 120 m ×computational100 m × 40 m weredomain separately with added200 m inside× 160 the m cuboid× 100 m. In ordercomputing to determine domain to the achieve appropriate the purpose numerical of grid refinement simulation around method, UR. By contrast,three simulation the schemesrefined were meshing set. method Three small by a domain domains with with 100 respective m × 80 m ×dimensions60 m generated of 70 more m × than60 m × 40 1.5 million unstructured grids for each case, which is more than the other two methods m, 100 m × 80 m × 60 m and 120 m × 100 m × 40 m were separately added inside the cuboid and improved the accuracy and credibility of the simulation results [13,21]. The initial computingboundary domain conditions to wereachieve set asthe follows: purpose of grid refinement around UR. By contrast, the refined meshing method by a domain with 100 m × 80 m × 60 m generated more than 1.5 (1) The inlet boundary condition was set as 0.5 m/s, which is a general practice in millionShandong unstructured Province, grids and for the each turbulent case, which parameters is more were than obtained the other by the two parameters methods and improvedof the the computational accuracy and domain. credibility of the simulation results [13,21]. The initial boundary(2) conditionsThe outlet were of theset computationalas follows: domain was set as a pressure-free outlet with a (1)pressure The inlet gradient boundary of 0. condition was set as 0.5 m/s, which is a general practice in Shandong(3) The Province, top surface and of the the computational turbulent parameters domain was were set as obtained a moving by wall the without parameters shear of the computatiforceonal and domain. the same velocity as the inflow. (4) (2)The The bottom outlet of of the the computational computational domain domain was set was as a set stationary as a pressure no-slip wall-free boundary outlet with a condition. pressure gradient of 0. (3) The top surface of the computational domain was set as a moving wall without shear force and the same velocity as the inflow. (4) The bottom of the computational domain was set as a stationary no-slip wall boundary condition.

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J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20212021,, 99,, x 770 FOR PEER REVIEW 55 of of 17 16 (5) The other sides were set as symmetrical boundaries.

2.3. Upwelling Region (5) (5)The The other other sides sides were were set set as as symmetrical symmetrical boundaries. boundaries. As shown in Figure 4, the height and area of upwelling are often used as the indices to2.3. 2.3.describe Upwelling Upwelling the Regionupwelling Region region and characterize the size and velocity profile of a certain plane As[9,21].As shown shown However, in in Figure Figure these 44,, thethe indices heightheight andandof the areaarea sa ofofme upwellingupwelling reference areare plane oftenoften are usedused not asas enough thethe indicesindices to repre- senttoto describe describethe overall the the upwelling upwellingcharacteristics region region ofand and the characterize characterize upwelling the the region size size and and of velocityURs. velocity Therefore, profile profile of of athe a certain certain volume of upwellingplaneplane [9,21]. [9,21 was]. However, adopted thesethese to evaluate indicesindices of of the the the upwelling same same reference reference effect plane plane of areURs are not (Figurenot enough enough 5). to The representto repre- upwelling regionsentthe overallthe in thisoverall characteristicsarticle characteristics mainly of refers theof the upwelling to upwelling a flow region region region ofconcentrated of URs. URs. Therefore,Therefore, on the thethe top volume of AR, of and the velocityupwellingupwelling in the was was y adopted-direction adopted to to inevaluate evaluate this region the the upwelling upwelling is generally effect greater of URs than(Figure 5% 55).). of TheThe the upwellingupwelling inflow velocity [11,23].regionregion Ain in largerthis this article article upwelling mainly mainly refersvolume refers to to acan flow a flow genera region regionte concentrated a concentratedstronger water on onthe ex thetopchange, topof AR, of AR, whichand andthe is ben- the velocity in the y-direction in this region is generally greater than 5% of the inflow eficialvelocity to inimprove the y-direction the exchange in this region efficiency is generally of nutrients greater than between 5% of the different inflow velocitywater layers [11,23].velocity A[ larger11,23]. upwelling A larger volume upwelling can volumegenerate can a stronger generate water a stronger exchange, water which exchange, is ben- [9,21,25]. eficialwhich to is beneficialimprove tothe improve exchange the efficiency exchange efficiencyof nutrients of nutrientsbetween betweendifferent different water layers water [9,21,25].layers [9, 21,25].

FigureFigureFigure 4. 4. 4.Velocity VelocityVelocity profileprofile proﬁle of of the the x x-z- zplane plane ( y (=y 0). 0).= 0).

Figure 5. Upwelling volume. 2.4. Wake Region FigureFigure 5.5. UpwellingUpwelling volume. volume. The wake region is a reflux area behind the AR where the flow velocity is relatively 2.4. Wake Region 2.4.slow Wake and Region the flow pattern is complicated (Figure 6). It is supposed to be the region that providesTheThe wake habitat, wake region region foraging, is a reflux refluxenemy area area avoidance, behind behind the and the AR spawning AR where where the for flowthe marine flow velocity organismsvelocity is relatively is [29]. relatively slowSimilarslow and and to the the flow upwelling flow pattern region, isis complicatedcomplicated it is difficult (Figure (Figurto describe6).e It6). is all It supposed theis supposed characteristics to be to the be of region thethe wakeregion that that providesregionprovides only habitat, habitat, by the foraging, foraging,size of the enemyenemy influence avoidance, avoidance, range or and the and spawningflow spawning velocity for marineoffor a marinecertain organisms plane. organisms Kim [29]. [29]. Similar to the upwelling region, it is difficult to describe all the characteristics of the Similaret al. [5] to proposedthe upwelling the wake region, volume it is concepdifficultt based to describe on the allelement-based the characteristics finite-volume of the wake wake region only by the size of the influence range or the flow velocity of a certain plane. regionmethod. only Therefore, by the size the ofcharacteristics the influence of rangethe wake or theregion flow can velocity be further of a quantitatively certain plane. Kim et al. [5] proposed the wake volume concept based on the element-based finite-volume method. Therefore, the characteristics of the wake region can be further quantitatively

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Kim et al. [5] proposed the wake volume concept based on the element-based finite-volume analyzedmethod. by Therefore, calculating the its characteristics volume, to estimate of the wake the region habitat can space be further of marine quantitatively organisms. The analyzedwateranalyzed region by by calculating calculatingwhere the its itsvelocity volume, volume, in toto the estimateestimate -x-direction the the habitat habitat is spacegreater space of marinethanof marine 5% organisms. of organisms. the inflow The The was waterdefinedwater region regionas the where wherewake the region the velocity velocity in this in article, thethe -x-x-direction-direction as shown is is greaterin greaterFigure than 7.than 5%This 5% of is the ofconsistent inflowthe inflow was with was the defineddefinitiondefined as asthe of the wakeupwelling wake region region volume in in this article,inarticle, this as article,as shown shown which in in Figure Figure can7. Thisprovide 7. This is consistent is a consistent strong with disturbance thewith the definitioneffect,definition promote of of upwelling upwelling the exchange volumevolume efficiency in in this this article, article,of whichthe bottomwhich can provide canwater, provide a strongand help disturbancea strong to break disturbance effect, the strati- promote the exchange efficiency of the bottom water, and help to break the stratification of effect,fication promote of the waterthe exchange body. efficiency of the bottom water, and help to break the strati- the water body. fication of the water body.

Figure 6. Wake region of the x-z plane (y = 0). FigureFigure 6. 6.WakeWake region region of thethex x-z-zplane plane (y (=y = 0). 0).

Figure 7.7.Wake Wake volume. volume. Figure 7. Wake volume. 2.5.2.5. Evaluation Evaluation Index Index 2.5. EvaluationThree-dimensionalThree-dimensional Index indexindex parameters parameters can bettercan better evaluate evaluate the effects the of upwellingeffects of [9upwelling,21] [9,21]andThree-dimensional wakeand wake region region [24,29 ], index[24,29], which parameters is which better thanis better can the two-dimensionalbetter than theevaluate two-dimensional index.the effects The dimension- ofindex. upwelling The di- less indices of the ratio of upwelling volume to reef volume and the ratio of wake volume [9,21] and wake region [24,29], which is better than the two-dimensional index. The di- mensionlessto reef volume indices can quantitatively of the ratio of analyze upwelling the flow volume field effectto reef of volume UR. and the ratio of wake mensionlessvolume to reef indices volume of the can ratio quantitatively of upwelling analyze volume the to flowreef volumefield effect and of the UR. ratio of wake In this article, we presented four indices, ϕ1, ϕ2, ϕ3, and ϕ4, to evaluate the flow volumefieldIn effect tothis reef article, of volume UR, which we canpresented are quantitatively the upwelling four indices, efficiencyanalyze φ1, theφ index,2, flowφ3, theand field wake φ4 ,effect to efficiency evaluate of UR. index, the flow the field effectIn ofthis UR, article, which we are presented the upwelling four indices, efficiency φ1, index,φ2, φ3, theand wake φ4, to efficiency evaluate theindex, flow the field effi- effectciency of indexUR, which of the are downwelling, the upwelling and efficiency the disturbance index, the intensity wake efficiency index of index, the upper the effi- and ciencylower indexwater oflayers the downwelling,near the ARs. Theseand the indicators disturbance are as intensity follows: index of the upper and lower water layers near the ARs. These indicators are as follows: 𝑣 𝜑 𝑣 (1) 𝑣 𝜑 (1) 𝑣 where vup refers to the volume of the upwelling region; vm represents the volume of URs. where vup refers to the volume of the upwelling region; vm represents the volume of URs. 𝑣 𝜑 𝑣 (2) 𝑣 𝜑 (2) 𝑣

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efﬁciency index of the downwelling, and the disturbance intensity index of the upper and lower water layers near the ARs. These indicators are as follows:

vup ϕ1 = (1) vm

where vup refers to the volume of the upwelling region; vm represents the volume of URs.

vw ϕ2 = (2) vm

where vw refers to the volume of the wake region.

vdown ϕ3 = (3) vm

where vdown refers to the volume of the downwelling region (the ﬂow velocity in the -y-direction is greater than 5% of the inﬂow velocity).

vup ϕ4 = (4) vdown The numerical simulation results of 64 URs with different layout modes were imported into CFD-POST to calculate the above four indices, to compare and analyze the interaction among the inﬂuencing factors and verify the effectiveness of these indices.

2.6. Statistics The data were analyzed by SPSS 20.0. The results were analyzed relatively with a single variable and multi-factor analysis of variance. The differences were considered to be signiﬁcant if p < 0.05.

3. Results 3.1. Effects of IR on Flow Field Effect of UR

Figure8 shows the flow field effects of URs with 16 combinations of h1 and h2 at four inflow velocities evaluated by the ϕ1 and ϕ2. Table1 shows the optimal combination of maximum ϕ1 and ϕ2 at each AI. The evaluation results of the indices of ϕ1 and ϕ2 show that the URs formed by the combinations of longitudinal and transverse IRs with the best benefit of the upwelling region also have the better benefit of wake region.

Table 1. The optimal combination of efﬁciency indices.

◦ AI ( ) h1 (L) h2 (L) ϕ1 ϕ2 0 5/3 1 24.51 2.32 15 2 4/3 57.21 4.18 30 4/3 2 73.65 4.98 45 1 2 84.41 6.86

Taking the upwelling volume range of the upwelling as an example, the upwelling can affect the distance of 1 L on both sides of the reef (Figure9). When the h2 is set to 1 L, the superposition of upwelling volume formed between two reefs will not only accelerate the velocity of upwelling, but the height of upwelling will also increase to 5 times that of the reef. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 7 of 17

where vw refers to the volume of the wake region.

𝑣 𝜑 (3) 𝑣

where vdown refers to the volume of the downwelling region (the flow velocity in the -y- direction is greater than 5% of the inflow velocity).

𝑣 𝜑 (4) 𝑣 The numerical simulation results of 64 URs with different layout modes were imported into CFD-POST to calculate the above four indices, to compare and analyze the interaction among the influencing factors and verify the effectiveness of these indices.

3. Results 3.1. Effects of IR on Flow Field Effect of UR

Figure 8 shows the flow field effects of URs with 16 combinations of h1 and h2 at four inflow velocities evaluated by the φ1 and φ2. Table 1 shows the optimal combination of maximum φ1 and φ2 at each AI. The evaluation results of the indices of φ1 and φ2 show J. Mar. Sci. Eng. 2021, 9, 770 8 of 16 that the URs formed by the combinations of longitudinal and transverse IRs with the best benefit of the upwelling region also have the better benefit of wake region.

(a) (b)

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(e) (f)

(g) (h)

Figure 8. EfficiencyFigure 8. indicesEfficiency of fourindices combined of four URscombined with differentURs with AIs different and IRs. AIsNote: and (IRs.a): UpwellingNote: (a): Upwelling efficiency index at 0◦; efficiency index at 0°; (b): Wake efficiency index at 0°; (c): Upwelling efficiency index at 15°; (d): (b): Wake efficiency index at 0◦;(c): Upwelling efficiency index at 15◦;(d): Wake efficiency index at 15◦;(e): Upwelling Wake efficiency index at 15°; (e): Upwelling efficiency index at 30°; (f): Wake efficiency index at 30°; efficiency index at 30◦;(f): Wake efficiency index at 30◦;(g): Upwelling efficiency index at 45◦;(h): Wake efficiency index (g): Upwelling efficiency index at 45°; (h): Wake efficiency index at 45°. at 45◦. Table 1. The optimal combination of efficiency indices.

AI (°) h1 (L) h2 (L) φ1 φ2 0 5/3 1 24.51 2.32 15 2 4/3 57.21 4.18 30 4/3 2 73.65 4.98 45 1 2 84.41 6.86

Taking the upwelling volume range of the upwelling as an example, the upwelling can affect the distance of 1 L on both sides of the reef (Figure 9). When the h2 is set to 1 L, the superposition of upwelling volume formed between two reefs will not only accelerate the velocity of upwelling, but the height of upwelling will also increase to 5 times that of the reef.

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FigureFigureFigure 9. Transverse 9.9. TransverseTransverse influence inﬂuenceinfluence range rangerange of ofupwellingof upwellingupwelling of of theof thethe upwelling upwelling upwelling reef reef reef (y- ( zy( y-plane).z-zplane). plane).

FigureFigureFigure 10 1010shows showsshows that thatthat the thethe length lengthlength of oftheof thethe wake wakewake region regionregion is isaboutis aboutabout 2 L. 22 L.TheL. TheThe velocity velocityvelocity contour contourcontour diagramsdiagramsdiagrams of oftheof thethe section sectionsection in inxin-direction xx-direction-direction show showshow that thatthat the thethe coverage coveragecoverage area areaarea of oftheof thethe backflow backflowbackflow or orslowor slowslow flowflowflow at attheat thethe position positionposition of of1of L 11 LandL andand 4/34/3 4/3 L behind LL behindbehind the thethe reef reefreef is ismuchis muchmuch larger largerlarger than thanthan the thethe areas areasareas at attheat thethe positionpositionposition of of5/3of 5/35/3 L and L and 2 L. 2 L.TheL. TheThe section sectionsection between betweenbetween 1 L 11 and LL andand 4/3 4/34/3 L behind L behind the thethe reef reefreef is inisis inthein thethe core corecore areaareaarea of oftheof thethe wake wakewake region region region and and and full full full of of vorticesof vortices, vortices, where where, where the the the current current current velocity velocity velocity decreases decreases decreases sharply. sharply. sharply. If the h1 of the combined reefs is set in this section, the inflow velocity of the post AR will be If theIf the h1 ofh1 theof the combined combined reefs reefs is setis set in thisin this section, section, the the inflow inflow velocity velocity of theof the post post AR AR will will much lower than the initial velocity of inflow, which will affect the efficiency index of UR. be bemuch much lower lower than than the the initial initial velocity velocity of inflow,of inflow, which which will will affect affect the the efficiency efficiency index index of of The results show that the section between 5/3 L and 2 L behind the reef is a good choice UR.UR. The The results results show show that that the the section section between between 5/3 5/3 L andL and 2 L 2 behindL behind the the reef reef is ais good a good for the h1 of UR. This indicates that the selection of the h1 of UR should consider the extent choicechoice for for the the h1 ofh1 UR.of UR. This This indicates indicates that that the the selection selection of theof the h1 ofh1 URof UR should should consider consider the the of the wake region generated by AR. If the h1 is 2 L, the wake region volume of AR is the extentextent of theof the wake wake region region generated generated by byAR. AR. If the If the h1 ish1 2is L, 2 theL, the wake wake region region volume volume of ARof AR largest, and the ϕ2 of UR is also the largest, about 2.59. is theis the largest, largest, and and the the φ2 φof2 URof UR is alsois also the the largest, largest, about about 2.59. 2.59.

◦ FigureFigureFigure 10. 10. 10.The TheThe volume volumevolume of oftheof thethe wake wakewake region regionregion of ofthofe theth upwellinge upwellingupwelling reef reefreef with withwith the thethe AIAI AIof of0°.of 0 0°..

Similarly,Similarly,Similarly, under underunder conditions conditionsconditions of ofotherof otherother AIs, AIs,AIs, the thethe optimal optimaloptimal transverse transversetransverse and andand longitudinal longitudinallongitudinal IR IR IR dependsdependsdepends on on onthe thethe extent extentextent of oftheof thethe upwelling upwellingupwelling and andand wake wakewake region regionregion of ofanof an anupwelling upwellingupwelling reef. reef.reef. 3.2. Effects of AI on the Flow Field of URs 3.2.3.2. Effects Effects of AIof AIon onthe the Flow Flow Field Field of URsof URs Figures 11 and 12 show the changes of the upwelling and wake volumes produced FiguresFigures 11 11and and 12 12show show the the changes changes of theof the upwelling upwelling and and wake wake volumes volumes produced produced by each combined UR at different AIs. The results show that the volumes of upwelling by each combined UR at different AIs. The results show that the volumes of upwelling andby each wake combined regions generallyUR at different demonstrate AIs. The a rising results trend show with that the the increase volumes of of AI, upwelling and the andand wake wake regions regions generally generally demonstrate demonstrate a rising a rising trend trend with with the the increase increase of AI,of AI, and and the the

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J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20212021, 9, ,9 x, 770FOR PEER REVIEW 10 of10 17 of 16

maximum value basically occurs when the AI is 45°, and a few of them occur when the AI is 30°. The statistical analysis results (Table 2) showed that the interactions among the h1, maximummaximum value value basically basically occurs occurs when when the the AI AI is is45°, 45 and◦, and a few a few of them of them occur occur when when the the AI AI 2 h , and◦ AI were significant, and the AI had the most significant influence on the flow field1 isis 30°. 30 The. The statistical statistical analysis analysis results results (Table (Table 2)2 showed) showed that that the the interactions interactions among among the the h , h1, (2p = 0.000 < 0.05). hh, 2and, and AI AI were were significant, significant, and and the the AI AI had had the the most most significant significant influence influence on onthe the flow flow field field (p( p= =0.000 0.000 < <0.05). 0.05).

Figure 11. The maximum and minimum upwelling volumes of URs with different h1, h2, and AI. Figure 11. The maximum and minimum upwelling volumes of URs with different h1, h2, and AI. Figure 11. The maximum and minimum upwelling volumes of URs with different h1, h2, and AI.

Figure 12. The maximum and minimum wake volumes of URs with different h1, h2, and AI. Figure 12. The maximum and minimum wake volumes of URs with different h1, h2, and AI.

Figure 12. The maximum and minimum wake volumes of URs with different h1, h2, and AI. TableTable 2. 2. TheThe interaction interaction among among factors. factors.

Table 2. The interactionFactorsFactors among factors. Evaluation Evaluation Index Index p p

Factors Evaluationφ1ϕ 1Index 0.000p0.000 AI*h1*h2 φ2 0.000 AI*h1*h2 φ1 ϕ2 0.0000.000 φ3ϕ 0.0000.000 AI*h1*h2 φ2 3 0.000 φ3 0.000 ItIt is is supposed supposed that that the the rectangle rectangle type formed inin thethe frontfront sideside of of AR AR with with the the AI AI of of 45 ◦ 45°has hasIt less is less supposed resistance resistance that than than the the rectanglethe plane, plane, and type and this formedthis structure structure in the interacts frontinteracts side with with of the AR the other with other ARsthe ARs AI on ofon both 45°bothsides has sides toless form to resistance form a higher a higher than velocity velocitythe plane, upwelling upwellin and this region,g region, structure accelerates accelerates interacts the the with flow flow the velocity velocity other aroundARs around on the boththemiddle middle sides ARs, to ARs, form and and a produceshigher produces velocity a a stronger stronger upwellin upwelling.upwellg region,ing. The Theaccelerates confluence confluence the offlow of these these velocity fluids fluids around greatly greatly theupliftsuplifts middle the the ARs,upwelling upwelling and produces and and forms forms a stronger a alarger larger rangeupwell range ofing. of upwelling upwelling The confluence volume. volume. of Therefore, these Therefore, fluids the thegreatly IR IRcan can upliftsbebe further further the upwellingextended extended when and when forms the the AI AIa islarger is45° 45 and◦ rangeand th thereere of upwellingis isenough enough spacevolume. space to toformTherefore, form the the wake the wake region.IR region.can beInIn furtheraddition, addition, extended the the distance distance when between the between AI is ARs 45° ARs and also also th increasesere increases is enough the the extent space extent of to ofthe form the wake wakethe region,wake region, region. which which Inisis addition,formed formed on onthe the thedistance right right side between side behind behind ARs the the also ARs ARs increases and and converges converges the extent into intoof thethe the largestwake largest region, wake wake region.which region. isTherefore,Therefore, formed on the the the AI AI rightof ofthe theside URs URs behind can can be setthe be betweensetARs between and 30° converges and 30◦ 45°,and intoand 45◦ ,thethe and bestlargest the effect best wake on effect theregion. flow on the Therefore,flow field the is theAI of AI the at URs 45◦. can While be set the between AI is set 30° between and 45°, 0 and◦ and the 15 best◦ the effect effect on onthe the flow flow

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ﬁeld is relatively poor, especially at 0◦ direction, due to the obvious blocking action among the reefs.

3.3. Effect of URs on Water Exchange In general, the production of upwelling will inevitably form part of downwelling to achieve water exchange. Strong water exchange can not only promote the exchange of nutrients and improve water quality but also indirectly provide abundant food for fish. Figure 13 describes the water disturbance efficiency of each UR with different h1, h2, and AI. The ϕ4 represents the volume ratio of upwelling and downwelling. The closer its value is, the better the water exchange effect will be. To reflect the exchange range of upwelling and downwelling more visually, the lowest 5% of the flow velocity in upwelling and downwelling volume is eliminated to reduce the influence of turbulence. Generally, the upwelling is concentrated in the front and upper part of the front reefs, and the downwelling is generally formed at the rear of the reefs. When the h1, h2, and AI are different, the effective upwelling and downwelling extents of each UR are also different which indicates that they have different disturbance abilities upon water exchange. When ◦ the AI is 0 , the ϕ4 of all URs are relatively high, basically above 3, and the maximum value is 7.52 in the layout mode with h1 of 1 L and h2 of 4/3 L. It is speculated that the lateral currents on both sides of the reef converge, and create a wider and higher upwelling region above the reef. The smaller the h1 is, the stronger the convergence capacity is. Therefore, the effect of upwelling generated is the best when the h1 of 1 L. When the h1 is 4/3 L, the rear reef is located in the wake region of the front reef. The initial inflow velocity of the rear reef is smaller than that of the front reef when h1 is 1 L (Figure 11). In the process of the flowing descent, a large number of fluids with a velocity of less than 5% of the inflow velocity were eliminated due to the weak disturbance ability, resulting in the volume of downwelling generated by the rear reef being much smaller than that of the front reef. Therefore, the volume of upwelling formed by this combined UR is large, the volume of downwelling is small, and the disturbance ability upon water is low. When the AI is 15◦, the ϕ4 of each combined UR is above 2, and the maximum value can be obtained when the h1 is 4/3 L and h2 is 2 L, about 3.92. This may be due to the deflection of the AI, leading to a distance difference with the front reef. When the h1 is 4/3 L and the h2 is 2 L, the distance between the front reefs perpendicular to the direction of the inflow is small. This is conducive to the formation of flow with a high range and high ascent velocity, and, at the same time, merges with the upwelling generated by the blocking of reefs in the middle of UR. The further increase of h1 allows the initial inflow velocity of the rear reefs on the left side to develop, resulting in a larger range of upwelling. However, the downwelling is mainly concentrated on the right side of the rear reefs, and there is no strong disturbance between different water layers due to the slow and weak downwelling. When the AI is 30◦ ◦ or 45 , the ϕ4 is about 1. This indicates that the volumes of upwelling and downwelling ◦ produced by each UR are almost equal, and the values of ϕ4 are greater than those of 0 ◦ ◦ and 15 . When the AI is 45 , all the URs have the largest ϕ4 and the best disturbance effect. It can be inferred that when the AI is close to 45◦, the triangular tip structure formed in the front of the AR will help to generate an upwelling region with a higher velocity. The velocity of upwelling will further increase with the change of IR and AI, resulting in a larger volume of downwelling. This makes the disturbance between the water layers more intense, and the amplitude of rising and falling is more obvious. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 12 of 17 J. Mar. Sci. Eng. 2021, 9, 770 12 of 16

Figure 13. The ϕ of URs. Figure 13. The φ4 of4 URs. 3.4. Flow Field Characteristics of the Optimal URs 3.4. Flow Field Characteristics of the Optimal URs According to the results of Section 3.1, these URs with the optimal IRs at each AI were selectedAccording as the to object the results of further of Section analysis, 3.1, these and theirURs with flow the field optimal effects IRs were at evaluatedeach AI were by the selected as the object of further analysis, and their flow field effects were evaluated by the defined efficiency indices. As shown in Figure 15, the ϕ1 and ϕ2 gradually increase with defined efficiency indices. As shown in Figure 15, the φ1 and φ2 gradually increase with ◦ the increase of AI. The maximum ϕ1 and ϕ2 are generated by the URs with the AI of 45 , thewhich increase means of AI. that The the maximum AI has a moreφ1 and obvious φ2 are influencegenerated onby thethe flowURs fieldwith effectthe AI than of 45°, the IR. which meansAs shown that inthe Figures AI has a14 more and obvious15, the upwelling influence on is mainlythe flow concentrated field effect than over the the IR. front reefs.As shown The upwellings in Figures generated 14 and 15, by the URs upwell withing different is mainly layout concentrated modes are over almost the symmetri- front reefs.cal inThe their upwellings inflow directions. generated by Except URs forwith the different strong upwellinglayout modes around are almost the front symmet- reefs, the ricalvolumes in their of inflow upwelling directions. generated Except by for other the strong reefs in upwelling UR are relatively around the small front and reefs, dispersed the volumesdue to of the upwelling flow blocking generated effect by of other the frontreefs reefs.in UR Theare relatively height of small the upwelling and dispersed is about duefive to timesthe flow that blocking of individual effect of ARs. the front The horizontalreefs. The height span of of each the upwelling AR module is about in this five layout timesis about that of two individual times the ARs. length The of horizontal the upwelling span reef.of each The AR upwelling module volumein this layout of UR is with aboutAI of two 15 ◦times(Figure the 15lengthb) is significantlyof the upwelling larger reef. than The that upwelling with AI volume of 0◦ (Figure of UR with15a). AI It seemsof 15°that (Figure the second 15b) is rowsignificantly of ARs in larger the UR than further that with enhances AI of the0° (Figure upwelling. 15a). With It seems the increasethat theof second the AI, row the of upwelling ARs in the of UR UR further tends enhanc to spreades the to theupwelling. right, and With the the ARs increase in the of leftmost the AI,row the produceupwelling the of longest UR tends horizontal to spread span to of the upwelling, right, and approximately the ARs in the 23 leftmost times the row length produceof the upwellingthe longest reef.horizontal Its height span of of upwelling upwelling, is approximately about 6 times 23 the times length the of length the reef. of In theFigure upwelling 16c, thereef. height Its height of upwelling of upwelling volume is about with 6 times AI of the 30◦ lengthis about of the 6 times reef. theIn Figure length of 16c,the the reef, height and of the upwelling horizontal volume span is with about AI 28 of times. 30° is Theseabout 6 show times that the the length upwelling of the reef, deflects, andincreases, the horizontal and spreads span tois theabout right 28 furthertimes. withThese the show increase that ofthe the upwelling AI. The upwelling deflects, in- height creases,of UR and with spreads AI of 45 to◦ the(Figure right 15 furtherd) is about with 8the times increase the length of the ofAI. the The reef, upwelling and the horizontalheight J. Mar. Sci. Eng. 2021, 9, x FOR PEERof UR REVIEW with AI of 45° (Figure 15d) is about 8 times the length of the reef, and the horizontal13 of 17 span is about 23 times. The spans of upwelling formed on both sides are the same, and the spanenclosed is about space 23 times. formed The above spans theof upwelling UR is the largestformedamong on both the sides four are layout the same, modes. and the enclosed space formed above the UR is the largest among the four layout modes.

FigureFigure 14. UpwellingUpwelling and and wake wake efficiency efﬁciency indices indices of the of optimal the optimal URs with URs AI with of 0°, AI 15°, of 030°,◦, 15 and◦, 3045°◦,. and 45◦.

(1) Lateral view

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J. Mar. Sci. Eng. 2021, 9, 770 13 of 16 Figure 14. Upwelling and wake efficiency indices of the optimal URs with AI of 0°, 15°, 30°, and 45°.

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(1) Lateral view

(2) Vertical view

FigureFigure 15. 15. UpwellingUpwelling volume volume of of the the optimal optimal layout layout with with the the AI AI of of 0°, 0◦ ,15°, 15◦ ,30°, 30◦ ,and and 45° 45◦ (m(m3)3. ).

TheThe extent extent of the wakewake regionregion generatedgenerated by by each each UR UR is is basically basically the the same same when when the the AI ◦ AIis 0is .0°. With With the the deflection deflection of of the the AI, AI, the the wake wake flow flow isis graduallygradually concentratedconcentrated in the right rearrear of of the the right right reefs reefs and and connected connected as as a a wh wholeole wake wake region region (Figure 16).16). Combined Combined with with thethe analysis analysis of of upwelling upwelling volume, volume, these these results results show show that that the the flow flow field field effect effect of of UR UR is is the the ◦ mostmost efficient efficient when when the the AI AI is is 45°. 45 .

Figure 16. Wake volume of the optimal layout with the AI of 0°, 15°, 30°, and 45° (m3).

3.5. Influence of Inflow Velocity on the Flow Field

As stated above, the UR with h1 of 1 L, h2 of 2 L, and the AI of 45° has the best flow field effect. The efficiency indices were used to evaluate the influence of inflow velocity on the flow field effect of the optimized UR. As shown in Figure 17, these indices of the optimized UR fluctuate slightly under the condition of inflow velocity variation, which indicates that the flow field of UR is little affected by the variation of inflow velocity. This is similar to the result of individual AR [25,36,37].

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(2) Vertical view

Figure 15. Upwelling volume of the optimal layout with the AI of 0°, 15°, 30°, and 45° (m3).

The extent of the wake region generated by each UR is basically the same when the AI is 0°. With the deflection of the AI, the wake flow is gradually concentrated in the right

J. Mar. Sci. Eng. 2021, 9, 770 rear of the right reefs and connected as a whole wake region (Figure 16). Combined14 with of 16 the analysis of upwelling volume, these results show that the flow field effect of UR is the most efficient when the AI is 45°.

◦ ◦ ◦ ◦ 3 Figure 16.FigureWake volume16. Wake of volume the optimal of the layout optimal with layout the AI with of 0the, 15 AI, of 30 0°,, and 15°, 45 30°,(m and). 45° (m3).

3.5.3.5. Influence Influence of of Inflow Inflow Velocity Velocity on on the the Flow Flow Field Field ◦ AsAs stated stated above, above, the the UR UR with with hh11 ofof 1 1 L, L, hh22 ofof 2 2 L, L, and and the the AI AI of of 45° 45 hashas the the best best flow flow fieldfield effect. effect. The The efficiency efficiency indices indices were were used used to to evaluate evaluate the the influence influence of of inflow inflow velocity velocity onon the the flow flow field field effect effect of of the the optimized optimized UR. UR. As As shown shown in in Figure Figure 17,17, these these indices indices of of the the optimized UR fluctuate slightly under the condition of inflow velocity variation, which J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEWoptimized UR fluctuate slightly under the condition of inflow velocity variation,15 ofwhich 17 indicatesindicates that that the the flow flow field field of of UR UR is is little little affected affected by by the the variation variation of of inflow inflow velocity. velocity. This This isis similar similar to to the the result result of of individual individual AR AR [25,36,37]. [25,36,37].

FigureFigure 17. The 17. Theefficiency efficiency indices indices of the of theoptimal optimal UR. UR. 4. Conclusions 4. Conclusions Artificial reefs laid on the seafloor can not only retard the flow to form a slow flow area forArtificial fish to choose reefs laid their on habitats, the seafloor but also can generatenot only upwellingretard the andflow downwelling to form a slow to promoteflow areathe for exchange fish to choose and mixing their ofhabitats, water betweenbut also watergenerate layers. upwelling However, and in downwelling the construction to of promoteARs, multiplethe exchange individual and mixing reefs are of oftenwater used between to form water UR tolayers. expand However, the influence in the rangecon- of structionthe flow of ARs, field inmultiple the AR individual area, to obtain reefs relatively are often strongused to inter-layer form UR to disturbance. expand the influence rangeHowever, of the flow the flowfield fieldin the effect AR area, of UR to isobtain not simply relatively a linear strong superposition inter-layer disturb- of several ance.ARs. How to obtain a relatively large and complex flow field environment as far as possible isHowever, the first problem the flow to field be solved.effect of In UR this is article,not simply we considered a linear superposition the longitudinal of several interval ARs.(h 1How), transverse to obtain interval a relatively (h2), large and the and angle complex of inflow flow field (AI) asenvironment the influencing as far factors as possi- of UR ble is the first problem to be solved. In this article, we considered the longitudinal interval (h1), transverse interval (h2), and the angle of inflow (AI) as the influencing factors of UR layout. Considering the impact force of the water around ARs, the layout mode of flat laying was usually chosen. Nine upwelling reefs were finally selected and combined into a UR, forming 64 different combinations for numerical simulation analysis. The upwelling efficiency index (φ1), wake efficiency index (φ2), downwelling efficiency index (φ3), and disturbance intensity index between water layers (φ4) were defined as the comprehensive evaluation standard for the flow field effect of UR, and the layout mode of UR is further optimized. The conclusions are summarized as follows:

(1) The h1, h2, and AI have a significant influence on the flow field effect of UR. Among the three influencing factors, AI has the most significant influence on the flow field. With the increase of the AI, the efficiency indices of upwelling, wake, and downwelling increase gradually. When the AI is 45°, the disturbance efficiency of UR is the highest. (2) Therefore, in the layout process of URs, the direction of current in the local sea area should be the first consideration, and the best AI of AR should be at 45° to the direction of current as far as possible. If the current is multiple direction, the proportion of the main current or its prevailing time should be considered, so as to better play the disturbance effect of the UR. (3) The combination of ARs with h1 of 1 L and h2 of 2 L has the highest upwelling volume (4641.6 m3) and downwelling volume (3266.91 m3) and has the optimal layout among the 64 URs. Its disturbance index (φ4) is 1.4, which indicates a good disturbance effect. (4) The inflow velocity has little influence on the flow field effect of UR, which is consistent with the results of the individual reefs.

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layout. Considering the impact force of the water around ARs, the layout mode of flat laying was usually chosen. Nine upwelling reefs were finally selected and combined into a UR, forming 64 different combinations for numerical simulation analysis. The upwelling efficiency index (ϕ1), wake efficiency index (ϕ2), downwelling efficiency index (ϕ3), and disturbance intensity index between water layers (ϕ4) were defined as the comprehensive evaluation standard for the flow field effect of UR, and the layout mode of UR is further optimized. The conclusions are summarized as follows:

(1) The h1, h2, and AI have a significant influence on the flow field effect of UR. Among the three influencing factors, AI has the most significant influence on the flow field. With the increase of the AI, the efficiency indices of upwelling, wake, and downwelling increase gradually. When the AI is 45◦, the disturbance efficiency of UR is the highest. (2) Therefore, in the layout process of URs, the direction of current in the local sea area should be the first consideration, and the best AI of AR should be at 45◦ to the direction of current as far as possible. If the current is multiple direction, the proportion of the main current or its prevailing time should be considered, so as to better play the disturbance effect of the UR. (3) The combination of ARs with h1 of 1 L and h2 of 2 L has the highest upwelling volume (4641.6 m3) and downwelling volume (3266.91 m3) and has the optimal layout among the 64 URs. Its disturbance index (ϕ4) is 1.4, which indicates a good disturbance effect. (4) The inflow velocity has little influence on the flow field effect of UR, which is consistent with the results of the individual reefs.

Author Contributions: Conceptualization, Z.J. and Z.L.; methodology, J.Z.; software, J.Z.; validation, J.Z., Z.N. and J.W.; formal analysis, J.Z.; investigation, L.Z., Z.N.; resources, Z.J.; data curation, J.W., W.X.; writing—original draft preparation, J.Z.; writing—review and editing, Z.J.; visualization, J.Z.; supervision, L.S.; project administration, Z.L.; funding acquisition, Z.J. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number 41771544, and the Fundamental Research Funds for the Central Universities, grant number 2019ZRJC006. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The numerical calculations in this article were performed on the supercomputing system in the Supercomputing Center, Shandong University, Weihai. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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