Simulation and Experimental Studies of a Multi-Tubular Floating Sea Wave Damper

energies

Article Simulation and Experimental Studies of a Multi-Tubular Floating Sea Wave Damper

Leszek Chybowski ID , Zenon Grz ˛adzieland Katarzyna Gawdzi ´nska* ID Faculty of Marine Engineering, Maritime University of Szczecin, 70-500 Szczecin, Poland; [email protected] (L.C.); [email protected] (Z.G.) * Correspondence: [email protected]; Tel.: +48-914-809-941

Received: 26 March 2018; Accepted: 11 April 2018; Published: 20 April 2018

Abstract: This article explores the issue of shore protection from sea waves and has presented the main methods used for coastal protection. It discusses the construction and operation of the multi-tubular floating sea wave damper that has been developed at the Maritime University of Szczecin by Professor Bolesław Ku´zniewski.This paper presents the results of the research project aimed at creating and examining a prototype of the device. The research aimed to confirm the two hypotheses: “the largest damping force should occur when the damping units are placed at an optimal distance equal to half the length of the wave to be damped” and “a compensation of the horizontal forces caused by the rippling of water should occur in the damping device”. Simulation studies of the behaviour of the device’s buoyancy elements when floating on waves were performed using the ANSYS AQWAWB and AQWA software. The buoyancy components were modelled as TUBE elements with a diameter of 0.11 m and a length of 1.5 m and as triangular and square surface elements. The results of the experimental research and the computer simulation of the operation of the prototype device have also been presented. The external conditions adopted corresponded to the frequency of a wave equal to 0.807 Hz and to the wave height in front of the device which was equal to 0.1 m. Experimental studies were conducted in an auxiliary model basin with dimensions of 60 m × 7 m × 3.12 m at the Ship Hydromechanics Division, Ship Design and Research Centre (CTO S. A.) in Gdańsk(Poland). The study recorded the distribution of the vertical and horizontal forces acting on the prototype device as well as the wave height both in front of and behind the device. Both hypotheses were proven. Simulation and experimental studies have been summarised. A proposal for future works has also been presented.

Keywords: sea waves; damping; shore protection; model basin; load simulation; multi-tubular ﬂoating damper; Ku´zniewski’sdamper

1. Introduction Effective protection of the sea shore remains a valid but still unsolved social issue that forms part of the responsibilities of any public authority. The coastal area is a space of human expansion which includes the majority of hydrotechnical facilities. Furthermore, it is estimated that more than 60% of the world’s population inhabit coastal areas [1]. These areas are directly related to many ﬁelds of human activity, such as industry, trade, agriculture, ﬁshing and tourism. As a rule, hydrotechnical facilities are structures that are subjected to complex mechanical loadings [2–8], among which of primary importance are the hydrotechnical forces associated with water movement [9,10]. The most important factors that cause water movement in coastal zones are surface waves and wave-driven currents [11–13]. Dynamic phenomena occurring in coastal zones [14], including wind-driven sea waves which are a major cause, contribute to coastal erosion and abrasion [15]. Figure1 shows an overview map of the impact of erosion processes on European sea shores. Particularly great coastal

Energies 2018, 11, 1012; doi:10.3390/en11041012 www.mdpi.com/journal/energies Energies 2018, 11, 1012 2 of 20 Energies 2018, 11, x 2 of 20 Energies 2018, 11, x 2 of 20 damage can be observed in Belgium, Denmark, Estonia, France, Spain and Italy. Interesting case Particularly great coastal damage can be observed in Belgium, Denmark, Estonia, France, Spain and studies regarding Mediterranean islands can be found in references [11,12,16]. Italy.Particularly Interesting great case coastal studies damage regarding can be Mediterranean observed in Belgium, islands canDenmark, be found Estonia, in references France, [11,12,16]. Spain and Italy. Interesting case studies regarding Mediterranean islands can be found in references [11,12,16].

FigureFigure 1. ExposureExposure to to coastal coastal erosion erosion in Europe [17]. [17]. Figure 1. Exposure to coastal erosion in Europe [17]. For example, the Polish sea annually claims about 50 hectares of land which have a total value For example, the Polish sea annually claims about 50 hectares of land which have a total value of of 500For million example, zlotys. the The Polish worst sea situationannually isclaims on the about western 50 hectares coast, on of theland Hel which Peninsula have a and total on value the 500 million zlotys. The worst situation is on the western coast, on the Hel Peninsula and on the Vistula Vistulaof 500 millionSpit [1]. zlotys.There areThe areas worst where situation coastal is onregression the western exceeds coast, one on meter the Hel per Peninsulayear. Approximately and on the Spit [1]. There are areas where coastal regression exceeds one meter per year. Approximately 60% to 60%Vistula to 70% Spit of [1]. the There Polish are coastline areas where is exposed coastal to regression erosion caused exceeds by one wave meter movement. per year. EveryApproximately year, the 70% of the Polish coastline is exposed to erosion caused by wave movement. Every year, the country’s country’s60% to 70% territory of the Polishis reduced coastline by about is exposed 340,000 to erosionm2 [18]. caused In recent by wave decades, movement. more than Every 70% year, of thethe territory is reduced by about 340,000 m2 [18]. In recent decades, more than 70% of the Polish coast has Polishcountry’s coast territory has been is affected reduced by by erosive about processes.340,000 m The2 [18]. average In recent annual decades, rate of morecoastline than recession 70% of thein been affected by erosive processes. The average annual rate of coastline recession in the years from thePolish years coast from has 1975 been to affected 1983 was by 0.9erosive m/year. processes. Furthermore, The average it is important annual rate to ofrealise coastline that recessiona coastline in 1975 to 1983 was 0.9 m/year. Furthermore, it is important to realise that a coastline recession at the recessionthe years atfrom the 1975rate ofto only1983 0.10 was m 0.9 per m/year. year means Furthermore, a loss of it land is important area equal to torealise about that 37,000 a coastline m2 per rate of only 0.10 m per year means a loss of land area equal to about 37,000 m2 per year. There are a year.recession There at are the a ratenumber of only of methods0.10 m per of coastalyear means protection a loss whichof land vary area in equal efficiency, to about implementation 37,000 m2 per number of methods of coastal protection which vary in efﬁciency, implementation and operation costs andyear. operation There are costs a number and level of methods of environmental of coastal protectioninterference which [19–22]. vary A in brief efficiency, overview implementation of the basic and level of environmental interference [19–22]. A brief overview of the basic methods is presented in methodsand operation is presented costs and in Figure level of2. environmental interference [19–22]. A brief overview of the basic Figure2. methods is presented in Figure 2.

Figure 2. Technical methods of shore protection [22]. Figure 2. Technical methods of shore protection [22]. Figure 2. The following methods are amongTechnical the most methods popular: of shore protection [22]. The following methods are among the most popular:  TheBreakwater—this following methods consists are among of concrete, the most stone popular: or prefabricated structures placed parallel or at  anBreakwater—this angle to the consists shoreline. of concrete, Figure 3 stone shows or prefabricated example breakwaters structures placed made ofparallel patented or at Breakwater—thisprefabricatesan angle to of the consists various shoreline. of types. concrete, FigureOne stone disadvantage 3 shows or prefabricated example to this structuressolution breakwaters is placed the made deepening parallel of patented or of at the an anglewaterprefabricates to the basin shoreline. directlyof various Figure in types. front3 shows One of example the disadvantage structure breakwaters from to this the made solution side of patented ofis the deepening open prefabricates sea, of huge the of implementationwater basin directly cost and in limitsfront of to thewater structure exchange from between the side the sea of the and open the area sea, being huge protected.implementation cost and limits to water exchange between the sea and the area being protected.

Energies 2018, 11, 1012 3 of 20

various types. One disadvantage to this solution is the deepening of the water basin directly in front of the structure from the side of the open sea, huge implementation cost and limits to water Energiesexchange 2018, 11 between, x the sea and the area being protected. 3 of 20 Components installed on the sea bed, below the water surface—barrages, artiﬁcial reefs.  Components installed on the sea bed, below the water surface—barrages, artificial reefs. The The drawbackdrawback to to these these kinds kinds ofof structures is is the the deepening deepening of ofthe the water water basin basin directly directly in front in frontof of the structurethe structure and the and need the for need maintenance for maintenance and systematic and systematic monitoring monitoring of its oftechnical its technical condition. Structurescondition. placed in the beach area—plants, fences, brushwood, geotextiles and geosynthetic materials. Structures The disadvantage placed in theof this beach type area—plants, of solution is fences, the extent brushwood, of intervention geotextiles in the and natural ecosystemgeosynthetic of the dunes. materials. The disadvantage of this type of solution is the extent of intervention Gabion—concrete,in the natural soilecosystem and stone of the ordunes. prefabricated structure located on the slopes of dunes or  Gabion—concrete, soil and stone or prefabricated structure located on the slopes of dunes or cliffs. The disadvantage of this is sublittoral deepening and the slow erosion of its outskirts. cliffs. The disadvantage of this is sublittoral deepening and the slow erosion of its outskirts. Groyne—wooden Groyne—wooden posts posts laid perpendicularlylaid perpendicularly to to the the shoreline shoreline reaching reaching 100–200100–200 m m into into the the sea. A disadvantagesea. A disadvantage of this solution of this solution is low efficiency is low efficiency in sediment-poor in sediment-poor areas, areas, deepening deepening of theof sea bottomthe in frontsea bottom of the in structure, front of the formation structure, of formation erosional of bays erosional and the bays need and forthe periodicneed for periodic maintenance. Refulation—amaintenance. method which consists of collecting sandy material from the sea bottom by dredging Refulation—a and placing method it on which the shorelineconsists of bycollecting means sandy of pipelines. material from Its main the sea drawback bottom by is the need fordredging periodic and repetition placing it ofon the the process shoreline and by themeans extent of pipelines. of environmental Its main drawback intervention is the at the need for periodic repetition of the process and the extent of environmental intervention at place of collection of material. the place of collection of material. Storm surgeStorm barriers—thesurge barriers—the purpose purpose these these structures structures serve serve is the is protectionthe protection of areas of areas located located close to sea level.close Their to sea disadvantages level. Their disadvantages are high maintenance are high maintenance costs and the costs need and to the provide need to large provide amounts of constructionlarge amounts material. of construction material.

Figure 3. Breakwaters made of prefabricates of various types: (A) Dolosse, (B) Accropode, (C) Figure 3. Breakwaters made of prefabricates of various types: (A) Dolosse, (B) Accropode, (C) KOLOS, KOLOS, (D) Tetrapod, (E) Core-loc, (F) A-Jack, (G) Xbloc, (H) Waveblock [19]. (D) Tetrapod, (E) Core-loc, (F) A-Jack, (G) Xbloc, (H) Waveblock [19]. The presented overview of the technical solutions has demonstrated that their huge Thedisadvantage presented lies overview is the fact of thethat technicalin order solutionsto protect hasthe demonstratedcoastal area they that have their to hugebe permanent disadvantage lies isengineering the fact that structures. in order toThis protect fact is the the coastal cause of area their they high have expense, to be permanentadverse impact engineering on the natural structures. Thisappearance fact is the of cause the sea of shore, their highdisruption expense, of the adverse balance impactin adjacent on ecosystems, the natural and appearance reduction of of the the sea shore,recreational disruption value of theof coastal balance areas. in adjacent Furthermore, ecosystems, another drawback and reduction of such of solutions the recreational is that the valuesea of waves often direct their destructive energy towards locations close to the protected area. A possible coastal areas. Furthermore, another drawback of such solutions is that the sea waves often direct solution to these drawbacks is the use of multi-tubular floating dampers presented in [23] (pp. their14–15). destructive energy towards locations close to the protected area. A possible solution to these drawbacks is the use of multi-tubular ﬂoating dampers presented in [23] (pp. 14–15).

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2. Results—Kuźniewski’s Results—Ku´zniewski’s Damper This invention was developed by Professor Bolesław Ku´zniewskiinKuźniewski in 2007 at the Maritime University in Szczecin. The The solution solution was was granted granted the the patent patent PL 210,447 [24] [24] by the Polish Patent Ofﬁce.Office. The object of the invention was a method of shore protection against sea waves during storms and a sea wave damping assembly. ElementsElements ofof thethe prototypeprototype devicedevice areare shownshown inin FigureFigure4 .4.

Figure 4. Components of the Kuźniewski’s damper prototype. Figure 4. Components of the Ku´zniewski’sdamper prototype. In accordance with the patent claim, the invention is a method of coastal protection consisting of placingIn accordance in the way with of the sea patent waves claim, beneath the invention the rippling is a methodwater at of least coastal one protection unit of the consisting sea wave of placingdamper, in composed the way of seaof verticalwaves beneath tubular the floating rippling elements, water at least and one locating unit of itthe behind sea wave the damper, wave composedtransformation of vertical line (breaking tubular floatingline) and elements, at an economically and locating optimal it behind distance the wave from transformation the shoreline. lineThe (breakingupper edges line) of andthe damping at an economically unit are underneath optimal distance the surface from of the the shoreline. water, while The upperits lower edges edges of theare dampinglocated atunit a distance are underneath from the thebottom surface of the ofthe sea. water, The unit while is itsattached lower edgesto anchoring are located elements at a distance resting fromon the the seabed bottom by means of the sea.of at least The unittwo istie attachedrods. One to of anchoring the benefits elements of the invention resting on is thethat seabed the unit’s by meansweight ofis atless least than two its tiebuoyancy. rods. One of the benefits of the invention is that the unit’s weight is less than its buoyancy.The invention is visualised in Figure 5. The sea wave damping unit (1) contains thirty-four verticalThe elements invention (8) is arranged visualised in infive Figure rows.5. The The vertical sea wave element damping (8) is unit a tube (1) containsclosed at thirty-four both ends verticalwhich constitutes elements (8) a natural arranged float in fivewith rows. a specific The verticalbuoyancy element force. (8) On is each a tube vertical closed tubular at both element ends which (8), constitutesin its top and a naturalbottom floatpart, withthere a is specific a clamp buoyancy (7) which force. is a three-sectional On each vertical bracket tubular connected element by (8), means in its topof bolts. and bottomEach of part,the three there elements is a clamp of the (7) whichbracket is is a equipped three-sectional with a bracket clamp to connected which the by cut-off means top of bolts.of the Eachrigid ofspacer the three (9) is elements attached of using the bracket two bolts. is equipped The spacer with is a a clamp flat bar to whichin the theform cut-off of a triangular top of the rigidtruss spacer with cut-off (9) is attached tops and using a triangle two bolts. inscribed The spacer within is a it. flat The bar spacers in the form (9) combine of a triangular the vertical truss withelements cut-off (8) tops in their and upper a triangle and inscribed lower parts, within forming it. The two spacers rigid (9) trusses combine in two the verticalplanes. elementsIn one row (8) inof theirthe vertical upper andtubular lower elements parts, forming (8) three two top rigid ends trusses of the in tworods planes. (6) are In attached one row ofto thethe verticalbottom tubular of the elementsclamps (7), (8) and three each top endsof the of lower the rods ends (6) areof the attached rods (6) to theare bottom fastened of theto the clamps anchoring (7), and element each of the(5) lowerlocated ends on the of the seabed rods (6)(4). are Figure fastened 5B present to the anchoring a top view element of the (5)device. located The on width the seabed ‘S’ of (4).the Figuredamping5B presentunit (1) ais top4 m, view and ofits the length device. is 8 Them. The width height ‘S’ of of the the damping vertical elements unit (1) is (8) 4 m,is 4 and m. itsThe length device is may 8 m. Thealso heightcontain of thirty the verticalvertical elementselements (8)arranged is 4 m. in The five device rows of may six alsoelements contain [24]. thirty vertical elements arranged in five rows of six elements [24].

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Figure 5. Views of the sea wave damping unit located in the water column [24]; (A) Frontal view; (B) Figure 5. Views of the sea wave damping unit located in the water column [24]; (A) Frontal view; FigureTop view 5. Views (description of the sea in thewave text). damping unit located in the water column [24]; (A) Frontal view; (B) (B) Top view (description in the text). Top view (description in the text). Figure 6 presents a system for coastal protection consisting of three damping units (1) arranged inFigure aFigure row6 behindpresents 6 presents the a wave system a system transformation for for coastal coastal protection line protection (breaking consisting consisting line) (12). of of threeThe three system damping damping can unitsprotect units (1) (1)30 arranged marranged of the in a rowinshoreline a behindrow behind (11). the wavetheEach wave damping transformation transformation unit (1) lineis lineinstalled (breaking (breaking within line) line) the (12). (12). water TheThe column system in can can such protect protect a way 30 30that m m of the of the the shorelineshorelineupper (11). edge (11). Each (2) Each is, damping according damping unit tounit (1)general (1) is installed is recommendations,installed within within the the water placed water column 0.5 column m from in such in the such amean way a way thatwater that the level upperthe edgeupper(10) (2) is,andedge according the (2) lower is, according toedge general (3) is to located recommendations,general 1 mrecommendations, above the placedseabed. 0.5 placedThe m sea from 0.5 wave m the fromdamping mean the water meanunits levelarewater located (10) level and the(10) loweralong and edgethe the shoreline lower (3) is locatededge in at (3) least 1 is m located one above row. 1 the m above seabed. the The seabed. sea wave The sea damping wave damping units are units located are alonglocated the shorelinealong the in atshoreline least one in row.at least one row.

Figure 6. The coastal protection system consisting of three damping units in a row [24] (description

in the text). FigureFigure 6. The6. The coastal coastal protection protection system system consisting consisting of of three three damping damping units units in in a a row row [ 24[24]] (description (description in

thein text). the text).

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The method for sea wave damping featured by the device allows for the dissipation of the The methodmethod forfor sea sea wave wave damping damping featured featured by the by devicethe device allows allows for the for dissipation the dissipation of the energyof the energy of sea waves during a storm and thus protects the shoreline. The height of the vertical energyof sea waves of sea during waves a storm during and a storm thus protects and thus the protects shoreline. the The shoreline. height of The the vertical height element of the vertical ranges element ranges from 0.2 to 1.0 of the dominant wave length. The damping units are to be used for elementfrom 0.2 ranges to 1.0 of from the dominant0.2 to 1.0 of wave the length.dominant The wave damping length. units The are damping to be used units for are the to protection be used for of the protection of coastlines against storm wave damage by means of damping the energy of the sea thecoastlines protection against of coastlines storm wave against damage storm by meanswave damage of damping by means the energy of damping of the sea the wave energy already of the in sea the wave already in the water and at a certain distance from the shoreline. waterwave already and at a in certain the water distance and fromat a certain the shoreline. distance from the shoreline. Installing the damping units at a distance equal to half of the wave length leads to the fact that Installing the damping units units at a distance equal to half of the wave length leads to the fact that horizontal forces caused by movement of the rippling water by the first unit are directed contrary to horizontal forces caused by movement of the rippling water by the first ﬁrst unit are directed contrary to the horizontal forces by the second unit and thus the forces are mutually compensating [1]. A the horizontal horizontal forces forces by by the the second second unit unit and and thus thus the forces the forces are mutually are mutually compensating compensating [1]. A diagram [1]. A diagram of the damping device consisting of two identical units has been presented in Figure 7, diagramof the damping of the devicedamping consisting device ofconsisting two identical of two units identical has been units presented has been in Figure presented7, where in Figure size A is7, where size A is the width of the damping device, size B is the distance between the units, and size C wherethe width size of A theis the damping width of device, the damping size B is device, the distance size B betweenis the distance the units, between and size the Cunits, is the and width size ofC is the width of the units which may not exceed half of the wave length. isthe the units width which of the may units not which exceed may half not of the exceed wave half length. of the wave length.

Figure 7. Diagram of a damping device consisting of two units as seen from the top to down view [1] Figure 7. Diagram of a damping device consisting of two units as seen from the top to down view [1] [1] (description in the text). (description in the text).

WithWith aa constantconstant unitunit width,width, thethe greatestgreatest dampingdamping effecteffect occursoccurs whenwhen thethe spacingspacing betweenbetween thethe unitsWith is equal a constant to half the unit wave width, length. the greatest The increase damping in the effect unit’s occurs width when enhances the spacing damping between efficiency the units is equal to half the wave length. The increase in the unit’s width enhances damping efficiency efficiency andand simultaneouslysimultaneously increasesincreases thethe widthwidth ofof thethe device.device. ItIt followsfollows thatthat thethe greatestgreatest attenuationattenuation effecteffect andcan be simultaneously achieved when increases the width the of width the damping of the device. device It is follows equal to that the the wave greatest length, attenuation which has effect been can be achieved when the width of the damping device is equal to the wave length, which has been specifiedspecified inin thethe patentpatent application.application. specifiedKuźniewski’s in the patent damper application. was subjected to experimental tests conducted in a 60 m × 7 m × 3.12 m Kuźniewski’sKu´zniewski’sdamper damper was subjected to experimentalexperimental teststests conductedconducted inin aa 6060 mm× × 77 mm ×× 3.12 m modelmodel basinbasin (auxiliary(auxiliary pool)pool) atat thethe ShipShip HydromechanicsHydromechanics Division,Division, ShipShip DesignDesign andand ResearchResearch CentreCentre model(CTO S. basin A.) in (auxiliary Gdańsk pool)(Poland). at the Figure Ship Hydromechanics8 showns the already Division, immersed Ship Design device and in the Research course Centre of the (CTO S.S. A.)A.) in in Gdańsk(Poland). Gdańsk (Poland). Figure Figure8 showns 8 showns the the already already immersed immersed device device in the in course the course of the of tests. the tests.tests.

Figure 8. The damping device in the course of tests in the model basin of the Ship Hydromechanics Figure 8. The damping device in the course of tests in the model basin of the Ship Hydromechanics Division, Ship Design and Research Centre (CTO S. A.) in Gdańsk. Division, Ship Design and Research Centre (CTO S.S. A.)A.) inin Gda´nsk.Gdańsk.

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A simulation and experimental plan was developed for the damping device prototype to determine its performance and parameters and to conﬁrm the following hypotheses:

The largest damping force should occur when the damping units are placed at an optimal distance equal to half the length of the wave to be damped. compensation of the horizontal forces caused by the rippling of water should occur in the damping device.

The examination was carried out to measure both the vertical and horizontal forces caused by the rippling water and, subsequently, to analyse the results of the measurements of the forces in order to perform:

a harmonic analysis of the horizontal forces acting on the damping units; a harmonic analysis of the waves that trigger these forces; an analysis of the compensation of the horizontal forces.

3. Studies and Discussion

3.1. Simulation Studies The tested wave damping device was designed in such a way that the distance between the two damping segments was 1.2 m, which corresponds to half the wave length. The length of the simulated wave has to be equal to 2.4 m with amplitude of 0.05 m. Such waves were obtained at the auxiliary model basin at the Ship Design and Research Centre in Gda´nsk.The speed c of the wave propagation depends not only on the length λ of the waves, but also on the depth h of the water [1]. In the general λ case, if: h < 2 then wave speed, c, is equal to:

r g c = tan h(κ · g) (1) κ

= 4π2 2 where: κ T2g is the wave number, g = 9806 m/s is acceleration due to gravity, T is the wave period and tanh is the hyperbolic tangent. The dependence of the main parameters of the wave from its period for the deep water area is given in Table1.

Table 1. The values of wave number κ, wave speed c, wave length λ and wave frequency f as a function of the wave period T, for deep water waves.

2 q κ = 4π g = = 1 T T2g c = κ tan h(κ · g) λ cT f T [s] [rad/m] [m/s] [m] [Hz] 0.8866 5.1217 1.3837 1.2268 1.1279 1.2399 2.6187 1.9351 2.3993 0.8065 1.5185 1.7460 2.3699 3.5987 0.6585 1.7336 1.3396 2.7056 4.6904 0.5768

Due to the small amplitude of the examined waves (0.05 m) relative to the depth h (3 m) of the water, the speed c and wave length λ can also be expressed using the period T:

gT c = (2) 2π Based on Table1 and the values obtained from Equation (2), it can be seen that the calculations for c, l and f for the deep water waves also showed the same values for small amplitude waves. For the Energies 2018, 11, 1012 8 of 20 tested wave length l = 2.4 m, wave period T = 1.2399 s (frequency f = 0.807 Hz) and phase speed of wave c = 1.9359 m/s. Energies 2018, 11, x 8 of 20 3.1.1. Load Simulation of One Buoyancy Element the tested wave length l = 2.4 m, wave period T = 1.2399 s (frequency f = 0.807 Hz) and phase speed of Awave single c = buoyancy1.9359 m/s. element was made from PE HD 100 polyethylene tube for water systems, with an outer diameter of f z = 0.11 m and wall thickness g = 0.0066 m. The total length of one tube L = 1.5 m. PE HD3.1.1. 100 Load polyethylene Simulation has of One a density Buoyancy of 980 Element kg/m 3, slightly less than the density of water. The other parametersA withsingle regard buoyancy to aelement single tube,was made which from are PE required HD 100 inpolyethylene the load simulation tube for water process, systems, took the followingwith values:an outer diameter of fz = 0.11 m and wall thickness g = 0.0066 m. The total length of one tube L = 1.5 m. PE HD 100 polyethylene has a density of 980 kg/m3, slightly less than the density of water. The tube mass m = 3.139 kg other parameters with regard to a single tube, which are required in the load simulation process, 2 2 momentstook the following of inertia: values: Jxx = Jyy = 0.5885 kg m ,Jzz = 0.0095 kg m , weight of water displaced at immersion h = 1.4 m, m = 13.539 kg.  tube mass m = 3.139 kg z z A diagram ofmoments the immersion of inertia: and Jxx = installationJyy = 0.5885 kg of m a2, single Jzz = 0.0095 buoyancy kg m2, element is presented in Figure9. Vertical line numberweight 5 of keeps water thedisplaced element at immersion in the vertical hz = 1.4 position. m, mz = 13.539 It was kg. attached to the bottom of the basin atA one diagram end andof the to immersion the lower and end installation of the tube of at a the single other. buoyancy The horizontal element is lines presented numbers in 1–4 preventedFigure the 9. buoyancyVertical line element number from5 keeps moving the element along in the the horizontal vertical position. direction. It was At attached one end, to they the were attachedbottom to the of simulatedthe basin at basin one end bottom, and to while the lower at the end other of the they tube were at the fastened other. The to the horizontal tube at lines a distance of 0.25numbers m and 1–4 1m prevented measured the from buoyancy the lower element end from of themoving tube. along The the modelling horizontal procedure direction. At of one the tube end, they were attached to the simulated basin bottom, while at the other they were fastened to the element required the division of a tube of length L = 1.5 m into multiple smaller parts of 0.25 m each, tube at a distance of 0.25 m and 1m measured from the lower end of the tube. The modelling whichprocedure resulted inof the 6 equal tube tubeelement segments. required Allthe division the lines of were a tube made of length of artificial L = 1.5 fibresm into withmultiple a carbon fibre coresmaller (sailboat parts of line 0.25 with m each, a diameter which resulted of 0.008 in m).6 equal The tube tensile segments. strength All EtheA oflines the were line made (the productof of Young’sartificial modulus fibres with and a carbon the line’s fibre cross-sectional core (sailboat line area), with a determined diameter of 0.008 experimentally m). The tensile in strength the material 5 durabilityEA of laboratory the line (the at product the Maritime of Young’s University modulus in and Szczecin, the line’s was cross-sectional EA = 10 N. area), The calculated determined elastic experimentally in the material durability laboratory at the Maritime University in Szczecin, was EA = constants k = EA/L for the respective lengths of line were equal to: 105 N. The calculated elastic constants k = EA/L for the respective lengths of line were equal to: 5 5 for a vertical line of length L5 = 1.61 m, k5 = 10 /1.61 = 0.62 10 N/m,  for a vertical line of length L5 = 1.61 m, k5 = 105/1.61 = 0.62 105N/m, for a horizontal lines of length L = 1.0 m, k = k = k = k = 105N/m.  for a horizontal lines of 1length L1 = 1.01 m, 2k1 = k32= k3 4= k4 = 105N/m.

Figure 9. Diagram of the immersion of one buoyancy element in the basin. Figure 9. Diagram of the immersion of one buoyancy element in the basin.

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Energies 2018, 11, x 9 of 20 Computer calculations of the loads were performed using the ANSYS AQWA OFFSHORE v 12.1 Computer calculations of the loads were performed using the ANSYS AQWA OFFSHORE v software (ANSYS Inc., Canonsburg, PA, USA). A view of the element modelled has been shown in 12.1Energies software 2018, 11 ,(ANSYS x Inc., Canonsburg, PA, USA). A view of the element modelled has been shown 9 of 20 Figure 10. in Figure 10. Computer calculations of the loads were performed using the ANSYS AQWA OFFSHORE v 12.1 software (ANSYS Inc., Canonsburg, PA, USA). A view of the element modelled has been shown in Figure 10.

Figure 10. Example pressures and motion results for the buoyancy element modelled in ANSYS FigureAQWA 10. ExampleOFFSHORE. pressures and motion results for the buoyancy element modelled in ANSYS AQWA OFFSHORE. TheFigure results 10. Example of the calculations pressures and of motion the horizontal results for forces the buoyancy in horizontal element lines modelled 1–4 and in ANSYSthe vertical AQWA OFFSHORE. Theforces results in the vertical of the line calculations 5 with wave of amplitude the horizontal of 0.05 forces m are shown in horizontal in Figure lines 11. Fluctuations 1–4 and the of the vertical vertical force of line 5 were within the range of 94.1–95.4 N. The average value of the signal was forces in the vertical line 5 with wave amplitude of 0.05 m are shown in Figure 11. Fluctuations of equalThe to 94.75 results N, ofand the the calculations amplitude ofwas the 0.65 horizontal N. There forces was, therefore,in horizontal almost lines a constant1–4 and linethe tensionvertical the verticalforces in force the vertical of line line 5 were 5 with within wave amplitude the range of of 0.05 94.1–95.4 m are shown N. The in averageFigure 11. value Fluctuations of the signalof the was caused by the buoyancy force of a single tube. Water rippling had a minimal effect on the vertical equalforces.vertical to 94.75 The force N, forces andof line in the the 5 amplitudewere horizontal within wasline the range 0.65rangeN. around of There 94.1–95.4 the was, average N. therefore, The value average were almost value equal a of constant to the zero, signal and line wasthe tension causedamplitudeequal by to the 94.75 buoyancyof these N, and oscillations the force amplitude of in a the single was lower 0.65 tube. lines N. Water Therewas approximately was, rippling therefore, had 2 aalmostN, minimal while a constant in effectthe upper line on tension thelines vertical it forces.wascaused The approximately forcesby the inbuoyancy the 9 N. horizontal force of a line single range tube. around Water therippling average had a value minimal were effect equal on tothe zero, vertical and the amplitudeforces. ofThe these forces oscillations in the horizontal in the line lower range lines around was the approximately average value 2 were N, while equal into thezero, upper and the lines it amplitude of these oscillations in the lower lines was approximately 2 N, while in the upper lines it was approximately 9 N. was approximately 9 N.

Figure 11. The results of the computer calculations of the forces in the lines with wave amplitude of 0.05 m (vertical line: number 5, horizontal lines: numbers 1–4).

Figure 11. The results of the computer calculations of the forces in the lines with wave amplitude of Figure0.05 11. mThe (vertical results line: of number the computer 5, horizontal calculations lines: numbers of the 1–4). forces in the lines with wave amplitude of 0.05 m (vertical line: number 5, horizontal lines: numbers 1–4).

Energies 2018, 11, 1012 10 of 20

Energies 2018, 11, x 10 of 20 Figure 12 presents the same processes, but was obtained with an amplitude twice as large (0.1 m). The rangeEnergiesFigure of2018 ﬂuctuations, 1112, xpresents ofthe the same vertical processes, force but in was line obtained 5 was increased with an amplitude and was twice in the as large range (0.1 10 from of m). 20 85 to 105 N.The The range average of fluctuations value of thisof the signal vertical remained force in line at 94.75 5 was N, increased and the and maximum was in the amplitude range from increased 85 to to 10 N.105 The N.Figure amplitude The average12 presents of value the the signalsof same this processes,signal of the remained horizontal but was at obtained 94.75 forces N, inwithand the thean lower amplitudemaximum lines twice amplitude (numbers as large increased 1 (0.1 and m). 2) was approximatelyTheto 10 range N. The of 5 fluctuationsamplitude N, and in of the of the the top signals vertical lines of (numbersforce the horizontalin line 4 5 and was forces 5) increased it approximatelyin the and lower was lines in equalledthe (numbers range 25from 1 N.and 85 It to2) can be 105was N.approximately The average 5value N, and of thisin the signal top linesremained (numbers at 94.75 4 and N, 5)and it approximatelythe maximum amplitudeequalled 25 increased N. It can clearly seen that the signals of the lower and upper horizontal forces were in opposite phases. tobe 10clearly N. The seen amplitude that the signals of the ofsignals the lower of the and horizontal upper horizontal forces in forcesthe lower were lines in opposite (numbers phases. 1 and 2) was approximately 5 N, and in the top lines (numbers 4 and 5) it approximately equalled 25 N. It can be clearly seen that the signals of the lower and upper horizontal forces were in opposite phases.

Figure 12. Results of the computer calculations of the forces in the lines with wave amplitude of 0.1 Figurem 12.(verticalResults line ofnumber the computer 5, horizontal calculations lines numbers of the 1–4) forces [1]. in the lines with wave amplitude of 0.1 m (verticalFigure line 12. number Results 5,of horizontalthe computer lines calculations numbers of 1–4) the [forces1]. in the lines with wave amplitude of 0.1 mFigure (vertical 13 showsline number an overview 5, horizontal of the lines signals numbers of the1–4) horizontal [1]. forces as determined from second Figure11 to 17 13 of shows the simulation. an overview The of opposite the signals phases of theof the horizontal signals of forces the forces as determined in the upper from lines second 11 to(numbers 17Figure of the 3–4) 13 simulation. showscompared an overview to Theforces opposite inof thethe lowersignals phases lines of the of(numbers horizontal the signals 1–2) forces were of theasclearly determined forces seen. in from the uppersecond lines 11 to 17 of the simulation. The opposite phases of the signals of the forces in the upper lines (numbers 3–4) compared to forces in the lower lines (numbers 1–2) were clearly seen. (numbers 3–4) compared to forces in the lower lines (numbers 1–2) were clearly seen.

Figure 13. Determined signals of the horizontal forces [1].

Figure 13. Determined signals of the horizontal forces [1]. Figure 13. Determined signals of the horizontal forces [1].

Energies 2018, 11, 1012 11 of 20 Energies 2018, 11, x 11 of 20

Both wave wave amplitudes amplitudes of of 0.05 0.05 m and m and 0.10 m 0.10 conﬁrmed m confirmed the fact the that fact the wavethat the amplitude wave amplitude decreased decreasedexponentiallyEnergies 2018 exponentially, 11 along, x with along the depth. with Atthe the depth. depth At equal the depth to half equal the wave to half length, the wave the wavelength, motion the 11 of wave 20 was motiondamped was by asdamped much asby 23as timesmuch [ 15as ].23 times [15]. Both wave amplitudes of 0.05 m and 0.10 m confirmed the fact that the wave amplitude 3.1.2.decreased Load Modelling exponentially of Two along Elements with the depth. At the depth equal to half the wave length, the wave 3.1.2. Load Modelling of Two Elements motion was damped by as much as 23 times [15]. The diagram in Figure 14 shows the distribution of two buoyancy elements attached using vertical The diagram in Figure 14 shows the distribution of two buoyancy elements attached using lines to the basin bottom and connected to each other at a distance equal to half the length of the wave. vertical3.1.2. linesLoad toModelling the basin of bottom Two Elements and connected to each other at a distance equal to half the length of A view of the modelled elements is shown in Figure 15. the wave.The A diagram view of inthe Figure modelled 14 shows elements the is distribution shown in Figure of two 15. buoyancy elements attached using vertical lines to the basin bottom and connected to each other at a distance equal to half the length of the wave. A view of the modelled elements is shown in Figure 15.

Figure 14. A diagram of the distribution of two buoyancy elements spaced at a distance equal to half Figure 14. A diagram of the distribution of two buoyancy elements spaced at a distance equal to half the wave length. theFigure wave 14. length. A diagram of the distribution of two buoyancy elements spaced at a distance equal to half the wave length.

FigureFigure 15. 15. Example Example pressures pressures and and motion motion resultsresults forfor the pairpair ofof buoyancybuoyancy elements elements modelled modelled using using Figure 15. Example pressures and motion results for the pair of buoyancy elements modelled using ANSYSANSYS AQWA AQWA OFFSHORE. OFFSHORE. ANSYS AQWA OFFSHORE. TheseThese are are two two identical identical elements elements as as shown shown in Figure 9,9, attachedattached to to the the bottom bottom of of the the basin basin with with identicalidentical lines lines and and at at the the same same depth. depth. The The fundamental fundamental difference difference here here lay lay in in the the use use of of rigid rigid connectorsconnectors between between the the two two tubes tubes instead instead ofof horizontalhorizontal lines.lines. TheThe connectors connectors are are at at a adepth depth equal equal to to thethe depth depth of ofthe the horizontal horizontal lines lines in in Figure Figure 9.9. FiguresFigures 16 andand 1717 presentpresent the the results results of of the the computer computer

Energies 2018, 11, 1012 12 of 20

These are two identical elements as shown in Figure9, attached to the bottom of the basin with identical lines and at the same depth. The fundamental difference here lay in the use of rigid connectors between the two tubes instead of horizontal lines. The connectors are at a depth equal to the depth of the horizontalEnergies 2018 lines, 11, x in Figure9. Figures 16 and 17 present the results of the computer simulation 12 of 20 of the Energies 2018, 11, x 12 of 20 valuessimulation of the forces of the in values the vertical of the forces line and in the rigid vertical connectors line and respectively, rigid connectors at wave respectively, amplitudes at wave equal to 0.05 m and 0.10 m. simulationamplitudes of equal the valuesto 0.05 ofm andthe forces0.10 m. in the vertical line and rigid connectors respectively, at wave amplitudes equal to 0.05 m and 0.10 m.

Figure 16. The results of the computer calculations of the forces in the vertical lines and rigid Figureconnectors 16. The resultsat the amplitude of the computer of the wave calculations equal to 0.05 of the m forces[1]. in the vertical lines and rigid connectors at theFigure amplitude 16. The of the results wave of equal the computer to 0.05 m calculations [1]. of the forces in the vertical lines and rigid connectors at the amplitude of the wave equal to 0.05 m [1].

Figure 17. The results of the computer calculations of the forces in the vertical lines and rigid connectors at the amplitude of the wave equal to 0.10 m [1]. Figure 17. The results of the computer calculations of the forces in the vertical lines and rigid Figureconnectors 17. The resultsat the amplitude of the computer of the wave calculations equal to 0.10 of the m forces[1]. in the vertical lines and rigid connectors at theThe amplitude joints between of the wave the equal connectors to 0.10 m and [1 ]. the tubes are articulated. The advantage of rigid connectorsThe joints is that between they can the transfer connectors the compression and the tubesand extension are articulated. forces. The advantage of rigid connectors is that they can transfer the compression and extension forces.

Energies 2018, 11, 1012 13 of 20

EnergiesThe 2018 joints, 11, x between the connectors and the tubes are articulated. The advantage of rigid connectors 13 of 20 is that they can transfer the compression and extension forces. 3.2. Experimental Studies 3.2. Experimental Studies The test site is presented in Figure 18. The first prototypes of the damping device were constructedThe test from site is polyethylene presented in Figure tubes 18 with. The a first diameter prototypes of 0.11 of the m damping and length device of 1.5 were m constructed installed verticallyfrom polyethylene at the vertices tubes of with equilateral a diameter triangles of 0.11 with m and sides length equal of 1.5 to m0.505 installed m. The vertically studies atundertaken the vertices haveof equilateral demonstrated triangles the correctwith sides functioning equal to 0.505 of the m. first The prototype studies undertaken of the damping have demonstrated device, but the the resultscorrect of functioning the damping of were the first considered prototype to ofbe the insufficient. damping The device, results but obtained the results clearly of the indicated damping that were theconsidered main issue to standing be insufficient. in the way The of results creating obtained the second clearly prototype indicated was that an the increase main issuein the standing damping in forcethe wayof the of first creating prototype. the second To improve prototype the was damping an increase properties in the of damping the device, force a ofsingle the first row prototype. of rigid elementsTo improve was the attached damping vertically properties to of each the device, of the a unit’s single trusses row of rigidthat wereelements made was of attached water-resistant vertically plywoodto each of with the a unit’s thickness trusses of that 0.02 were m, a made width of of water-resistant 0.1 m and a length plywood of 1.5 with m. a Twelve thickness additional of 0.02 m, elementsa width were of 0.1 added m and to a lengththe first of damping 1.5 m. Twelve unit from additional the side elements of the wave were direction, added to while the first the damping second unitunit which from the affects side the of the already wave partially direction, damped while the waves second was unit reinforced which affects with eighteen the already additional partially items.damped waves was reinforced with eighteen additional items.

FigureFigure 18. 18. DiagramDiagram of of the the testing testing stand stand for for damping damping device device prototypes: prototypes: (A (A) frame) frame unit; unit; (B (B) damping) damping units;units; ( (CC)) rail rail system; system; ( D ()D force) force measurement measurement system; system; (E) immersion (E) immersion adjustment adjustment system; (F system;) immersion (F) immersionmeasurement measurement system [25 system]. [25].

The metrological parameters of the generator allowed the production of a wave with the The metrological parameters of the generator allowed the production of a wave with the assumed assumed length of 2.4 m with an accuracy of 0.005 m. To measure the profile of the wave, resistance length of 2.4 m with an accuracy of 0.005 m. To measure the profile of the wave, resistance probes were probes were used with an uncertainty range of less than 0.0015 m at a 95% confidence level. Since the used with an uncertainty range of less than 0.0015 m at a 95% confidence level. Since the sinusoidal sinusoidal wave generated can be seen as an ergodic phenomenon, the Tps2* section for the probe S2 wave generated can be seen as an ergodic phenomenon, the Tps2* section for the probe S2 can be used can be used for the analysis and development of the measurement data which was recognized to be for the analysis and development of the measurement data which was recognized to be undistorted. undistorted. While in the case of the probe S1, a section was used that was equal to the first one in While in the case of the probe S1, a section was used that was equal to the first one in terms of parameter terms of parameter values, but shifted back in time by 22 s. This is shown schematically in Figure 19. values, but shifted back in time by 22 s. This is shown schematically in Figure 19.

Energies 2018, 11, x 14 of 20 Energies 2018, 11, 1012 14 of 20 Energies 2018, 11, x 14 of 20

Figure 19. The pattern for the selection of data for the determination of average amplitudes (with Figuremeasurement 19. The number pattern 24for as the an selectionexample). of The data light for greenthe determination colour indicates of average the selected amplitudes time sections (with measurementfor the analysis. numbernumber 2424 asas an an example). example). The The light light green green colour colour indicates indicates the the selected selected time time sections sections for forthe the analysis. analysis. Figure 20 presents the measurement results of the wave height, H1, in front of the device and H2 behindFigure 20the presentspresents damping thethe device. measurementmeasurement Figure results21 results shows of of the thethe wave measurementwave height, height, H1, H1,results in in front frontof ofthe theof horizontal the device device and forceand H2 H2behindsensors behind the for damping thethe dampingsame device. sample: device. Figure 1.1; Figure 2.1; 21 showsthis 21 sample shows the measurement wasthe measurementtagged resultsas pom36 results of thein the horizontalof theMaritime horizontal force University sensors force sensorsforreport. the same for the sample: same 1.1;sample: 2.1; this1.1; sample2.1; this was sample tagged was as tagged pom36 as in pom36 the Maritime in the UniversityMaritime University report. report.

FigureFigure 20.20. ResultsResults ofof thethe wavewave heightheight measurement.measurement. Figure 20. Results of the wave height measurement. The prototype functioned properly and in accordance with the project thesis, and demonstrated damping properties in accordance with the report of the Ship Hydromechanics Division, Ship Design and Research Centre (CTO S. A.) of approximately 30%, as shown in Figure 22. However, these damping values were considered unsatisfactory. The conclusions from this series of tests was that further investigation was needed in order to create another prototype with much better damping characteristics through the application of additional dissipative elements that would also limit the circular motion of the rippling water molecules in the vertical direction. It was assumed that this was to be achieved with a limited number of elements that would not violate the above condition of stability. This device structure

Energies 2018, 11, x 15 of 20

Energies 2018, 11, 1012 15 of 20

was positively experimentally tested. The additional dissipative elements were cords made of round Energiesplastic 2018 (polyethylene,, 11, x PE) elements that are used in swimming pools to distinguish swimming lanes. 15 of 20

Figure 21. Results of horizontal force measurement.

The prototype functioned properly and in accordance with the project thesis, and demonstrated damping properties in accordance with the report of the Ship Hydromechanics Division, Ship Design and Research Centre (CTO S. A.) of approximately 30%, as shown in Figure 22. However, these damping values were considered unsatisfactory. The conclusions from this series of tests was that further investigation was needed in order to create another prototype with much better damping characteristics through the application of additional dissipative elements that would also limit the circular motion of the rippling water molecules in the vertical direction. It was assumed that this was to be achieved with a limited number of elements that would not violate the above condition of stability. This device structure was positively experimentally tested. The additional dissipative elements were cords made of round plastic (polyethylene, PE) elements that are used in swimming pools to distinguishFigureFigure swimming 21. 21. ResultsResults lanes. ofof horizontalhorizontal force force measurement. measurement.

FigureFigure 22. 22.GraphsGraphs displaying displaying the the wave wave height height in frontfrontof of and and behind behind the the damping damping device device with with no no additionaladditional dissipative dissipative elements. elements.

TableTable 2 2 provides provides an an overview overview of the the results results of of the the experimental experimental study study of wave of wave damping. damping. MeasurementsMeasurements marked marked with with an an asterisk asterisk (*) (*) are for for devices devices with with additional additional dissipative dissipative elements, elements, negative draught means surfacing, and Hs1 and Hs2 mark the wave height in front and behind the damping device respectively.

Figure 22. Graphs displaying the wave height in front of and behind the damping device with no additional dissipative elements.

Table 2 provides an overview of the results of the experimental study of wave damping. Measurements marked with an asterisk (*) are for devices with additional dissipative elements,

Energies 2018, 11, x 16 of 20 negative draught means surfacing, and Hs1 and Hs2 mark the wave height in front and behind the damping device respectively.

Table 2. The test results of the damping device, with the same value of draught for both units Energies(attempt2018 ,15,37711, 1012 and 15,378) developed by the Ship Design and Research Centre. 16 of 20

Measurement Number Draught Hs1 Hs2 Damping Error Table 2. The test results of the damping [m] device, [m] with the same value [m] of draught for [%] both units (attempt [%] 15,377 and36 15,378) developed−0.0500 by the Ship Design 0.1101 and Research 0.0712 Centre. 35.5 1.4 26 −0.0500 0.1068 0.0798 25.3 1.4 Measurement Number Draught Hs1 Hs2 Damping Error 37 * 0.2000 0.1109 0.0920 17.0 1.4 38 * 0.1500 [m] 0.1086 [m] 0.0865 [m] [%] 20.3 [%] 1.4 39 * 36 0.1000− 0.0500 0.1091 0.1101 0.0712 0.0785 35.5 28.0 1.4 1.4 40 * 26 0.0500− 0.0500 0.1094 0.1068 0.0798 0.0631 25.3 42.3 1.4 1.4 41 * 37 * 0.0000 0.2000 0.1086 0.1109 0.0920 0.0486 17.0 55.3 1.4 1.4 38 * 0.1500 0.1086 0.0865 20.3 1.4 42 * 39 * −0.0500 0.1000 0.1097 0.1091 0.0785 0.0371 28.0 66.2 1.4 1.4 43 * 40 * −0.1000 0.0500 0.1096 0.1094 0.0631 0.0375 42.3 65.8 1.4 1.4 44 * 41 * −0.1000 0.0000 0.1443 0.1086 0.0486 0.0394 55.3 72.7 1.4 1.0 45 * 42 * 0.0000− 0.0500 0.1406 0.1097 0.0371 0.0511 66.2 63.7 1.4 1.1 43 * −0.1000 0.1096 0.0375 65.8 1.4 46 * 0.0000 0.1565 0.0540 65.5 1.0 44 * −0.1000 0.1443 0.0394 72.7 1.0 45 *(*) devices with 0.0000 additional 0.1406 dissipative 0.0511 elements. 63.7 1.1 46 * 0.0000 0.1565 0.0540 65.5 1.0 The highest damping efficiency(*) devices was with obtained additional dissipative for measurement elements. number 44, which exceeded 70%. Figures 23–25 present the course of the vertical and horizontal forces in the device and the The highest damping efﬁciency was obtained for measurement number 44, which exceeded 70%. value of compensation of the horizontal forces for the device equipped with additional dissipative Figures 23–25 present the course of the vertical and horizontal forces in the device and the value of elements.compensation of the horizontal forces for the device equipped with additional dissipative elements. TheThe results results presented presented show show that thethe applicationapplication of of Ku´zniewski’sdamper Kuźniewski’s damper can attenuate can attenuate waves waves in a in a widewide range range of of values—by tens tens of of percent percent up up to values to values greater greater than 70%.than They 70%. also They demonstrated also demonstrated the the highhighlevel level of of possible possible compensation compensation of the of horizontal the horizontal forceswith forces small with amplitudes small amplitudes of vertical forces.of vertical forces.These These results results have have proven proven the validity the validity of the assumptions of the assumptions for the tested for device.the tested device.

FigureFigure 23.23. DistributionDistribution of of horizontal horizontal forces 1.11.1 andand 2.1 2.1 and and the the course course of theof the vertical vertical force force 1.3 with 1.3 awith a significantlysigniﬁcantly smaller smaller amplitude. amplitude.

Energies 2018, 11, 1012 17 of 20 EnergiesEnergies 2018 2018, 11,, x11 , x 17 of 17 20 of 20

FigureFigureFigure 24. 24. 24.CompensationCompensation Compensation of of the of the the horizontal horizontal horizontal forces forces forces 1.1 1.1 1.1and and and 2.1. 2.1. 2.1.

Figure 25. Amplitude spectrum of the compensation value of the horizontal forces 1.1 and 2.1. FigureFigure 25. 25. AmplitudeAmplitude spectrum spectrum of of the the compensation compensation value value of of the the horizontal horizontal forces forces 1.1 1.1 and and 2.1. 2.1. 4. Conclusions 4.4. Conclusions Conclusions The experimental tests, performed at the model basin of the Ship Hydromechanics Division, TheThe experimental experimental tests, tests, performed performed at at the the model model basin basin of of the the Ship Ship Hydromechanics Hydromechanics Division, Division, Ship Design and Research Centre (CTO S. A.) in Gdańsk (Poland), have confirmed that the damping ShipShip Design Design and and Research Research Centre Centre (CTO (CTO S. S. A.) A.) in in Gdańsk Gda´nsk(Poland), (Poland), have have confirmed conﬁrmed that that the the damping damping device functioned in accordance with the design assumptions. The results demonstrated damping of devicedevice functioned functioned in in accordance accordance with with the the design design assumptions. assumptions. The The results results demonstrated demonstrated damping damping of waves by more than 70% and a high level of compensation of horizontal forces. The results of the wavesof waves by more by more than than 70% 70% and and a high a high level level of ofcompensation compensation of ofhorizontal horizontal forces. forces. The The results results of of the the experimental studies were consistent with those obtained by means of computer simulations. experimentalexperimental studies studies were were consistent consistent with with those those obtained obtained by by means means of of computer computer simulations. simulations. TheThe physical physical basis basis for for the the presented presented device device concept concept is ais representation a representation of of the the assumption assumption describeddescribed in thein the scientific scientific literature literature that that the the motion motion of moleculesof molecules of ripplingof rippling water water occurs occurs in thein the layer layer

Energies 2018, 11, 1012 18 of 20

The physical basis for the presented device concept is a representation of the assumption described in the scientific literature that the motion of molecules of rippling water occurs in the layer of thickness that is near half of the wave length and occurs in vertical planes along the lines of partly closed circles. The simulation calculations showed that the horizontal forces acting on a single tube immersed vertically in rippling water occurring by the upper end of the tube were much stronger than the horizontal forces appearing at the bottom end of the tube. In addition, the simulation calculations for two tubes immersed in rippling water placed at a distance equal to half the wave length and tied to each other with a rigid connector demonstrated the maintenance of a stable position which implies a compensation for the horizontal forces. The modular design of the damping device allows for any configuration and size of the structure. The design work was supported by cutting-edge computer modelling software. The design features of the device ensure its durability, stability in rippling water and the possibility to adjust the damping force by attaching the required number of highly dissipative elements to both units. The experimental research undertaken provides confirmation of the two hypotheses: “the largest damping force should occur when the damping units are placed at an optimal distance equal to half the length of the wave to be damped” and “a compensation of the horizontal forces caused by the rippling of water should occur in the damping device”. The positive results of the experimental studies, after their verification and further development in more complex sea conditions, including those associated with the use of new structural materials [26,27], create the possibility for practical application of the new method of coastal protection against storm waves.

5. Patents Ku´zniewskiB., Sposób ochrony brzegu przed falami morskimi i zespół tłumi ˛acyenergi˛efal morskich [The manner of embankment protection against sea waves and unit dampening energy of sea waves]. Patent PL 210447, Polish Patent Ofﬁce, 23.03.2007.

Acknowledgments: The article is a tribute to the scientific oeuvre of Professor Bolesław Ku´zniewski (22 June 1935–20 August 2017), inventor and innovator, outstanding specialist in the field of applied fluid mechanics and the creator of the solution presented in this article. The article has presented the results of studies that are part of the research project N R03 0028 04 funded by the National Centre for Research and Development (Poland) titled ‘Nowy sposób ochrony brzegów przed falami morskimi’ (A new method for coastal protection against sea waves) under the leadership of Zenon Grz ˛adziel.The publication costs was covered from the grant of the Ministry of Science and Higher Education of Poland No. 1/S/IESO/17 titled ‘Increasing operational effectiveness of complex technical systems by systematic development and implementation of innovations using novel materials and modifying the object’s structure’ performed at the Institute of Marine Propulsion Plants Operation, Faculty of Marine Engineering, Maritime University of Szczecin. Author Contributions: Leszek Chybowski wrote the paper, performed the analysis of the state-of-the-art, consolidated the data, recalculated the data in the tables, and built the conclusions. Zenon Grz ˛adzielbuilt mathematical models and performed simulations. Katarzyna Gawdzińskaparticipated in the analysis of the state-of-the-art as well as in building conclusions. Conflicts of Interest: The authors declare no conflict of interest.

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