Utafiti unaweka array ya mraba yenye WEC tano ndani ya moonpool ya mviringo yenye openings ili kupunguza athari inayozuia uzalishaji wa nishati ya “near-trapping” modes zinazoweza kutokea katika wave energy converters (WEC) za heaving buoy zilizowekwa karibu. Kwa kufanya ukuta wa moonpool uakisi na kuelekeza mawimbi kwenye maeneo fulani, lengo ni kupunguza kwa kiasi hydrodynamic interaction hasi kati ya WEC. Katika model ya time-domain inayotatua wave radiation na diffraction, moonpool opening width, opening orientation, wall draft na idadi ya openings zilibadilishwa kwa utaratibu.

Moja ya matokeo yaliyo wazi zaidi katika model yalipatikana wakati ratio ya moonpool opening width kwa umbali kati ya WEC jirani ilikuwa w/D=3,0. Katika configuration hii, array interaction factor ilifikia takriban 3 katika baadhi ya hali, na maximum value iliyotolewa katika sehemu ya results ilikuwa q_array=3,1. q_array>1 inaonyesha constructive hydrodynamic interaction ikilinganishwa na isolated WEC reference katika open water kwa frequency ile ile. Kuweka moonpool opening ikitazama incident wave pia kulitoa matokeo chanya katika wave range pana zaidi.

Wave energy haikusambazwa sawasawa ndani ya moonpool. WEC ya nne iliyo upande wa nyuma wa incident-wave direction iliangukia kwenye main energy-focusing region inayotengenezwa na reflections; katika opening-width analysis, individual interaction factor ilifikia takriban 4,7, na katika calculations ambapo moonpool draft iliongezwa ilifikia takriban 5,9–6. Kwa upande mwingine, baadhi ya WEC katika front row zilibaki kuwa less sensitive kwa mabadiliko ya moonpool draft.

Matokeo muhimu ya utafiti si kwamba “openings nyingi zaidi ni bora kila wakati”. Wakati width ya kila opening ilihifadhiwa sawa, mfumo wenye openings mbili ulitoa high energy output katika baadhi ya short-wave conditions. Lakini total opening width ilipohifadhiwa constant, moonpool yenye opening moja ilifanya vizuri kuliko structures zenye openings mbili na tatu; energy conversion ya mfumo wa openings tatu ilipatikana kuwa hadi %24,1 chini ya mfumo wa opening moja katika baadhi ya hali. Tofauti hii inaonyesha kwamba athari ya opening count inapaswa kutathminiwa pamoja na total open area.

Matokeo yanatokana na time-domain numerical model inayotegemea linear potential-flow assumptions, si physical prototype, sea experiment au measurement ya real electricity-generation facility. Model imechunguza regular waves na heave motion pekee. Watafiti pia wanasema kwamba future work inapaswa kuchunguza irregular realistic wave conditions, nonlinear multi-body effects, flexible moonpool walls na advanced PTO control strategies.

Kwa upande wa Uturuki, utafiti unatoa mfano wa kimetodolojia unaoonyesha kuwa arrays za wave energy converters zinaweza kubuniwa si kwa kuongeza tu idadi ya devices, bali pia pamoja na marine structure inayozunguka ambayo inaelekeza wave field. Hata hivyo, utafiti haujamodel wave climate, bathymetry, storm conditions, economic feasibility au local site geometry ya pwani ya Uturuki. Kwa hiyo reported performance increases haziwezi kutafsiriwa kama direct expected production values kwa site yoyote nchini Uturuki.

Tatizo kuu ambalo utafiti unajaribu kutatua ni nini?

Wave energy converters zinapowekwa kama array badala ya moja moja, radiation waves zinazotengenezwa na kila device na diffraction ya incident wave kutoka kwenye devices zinaweza kuathiri motion ya devices jirani. Hydrodynamic interaction hii inaweza kuwa constructive katika baadhi ya frequencies lakini kupunguza energy-capture capacity katika frequencies nyingine.

Jambo ambalo utafiti unalenga hasa ni near-trapping modes. Katika spacings fulani za WEC na wavelengths fulani, free-surface waves kati ya devices zinaweza kutengeneza strong local oscillations. Utafiti unakubali kuwa modes hizi zinafanya iwe vigumu kwa WEC array kukusanya nishati kwa uthabiti na kwa ufanisi katika wave-period range pana.

Suluhisho linalopendekezwa ni kuweka WEC ndani ya circular, partially open moonpool badala ya kuziacha kabisa katika open water. Moonpool wall inaakisi sehemu ya incident na scattered waves kurudi ndani, ikitengeneza focusing region maalum na hivyo kufidia sehemu ya negative interaction katika WEC array.

WEC tano zimepangwaje?

Model ilitumia cylindrical WEC tano zenye geometric properties sawa. WEC nne ziliwekwa kwenye circle kuunda square arrangement, na WEC ya tano ikawekwa katikati ya moonpool na array. Kila WEC iliunganishwa na independent power take-off (PTO) system.

Umbali kati ya centers za WEC jirani D ulifafanuliwa kwa kutumia characteristic length l ya WEC moja, kwa namna ambayo D=2l. Moonpool radius iliwekwa kuwa R=2D. Katika basic computational geometry, values za l=10 m, D=20 m na R=40 m zilitumiwa.

Kwa nini moonpool inatumika kama energy focuser?

Waves zinazoingia kupitia moonpool opening zinaingiliana na WEC za ndani huku pia zikiakisiwa na curved moonpool wall. Free-surface wave-field maps zinaonyesha kuwa wave-crest na trough regions hazijasambazwa symmetrically au homogeneously ndani ya moonpool. Hasa, high wave-amplitude regions zinatokea karibu na WEC ya nne iliyo nyuma ya incident-wave direction.

Watafiti wanatafsiri eneo hili kama main energy-focusing point inayotengenezwa na reflections kutoka moonpool wall. Kwa hiyo, si incident wave energy pekee bali pia reflected wave energy inaweza kuchangia WEC motion.

Dirichlet na Neumann near-trapping modes zinaonyesha nini?

Utafiti unachunguza kwa kina near-trapping cases mbili za characteristic. Katika maelezo makuu ya chanzo, kl/π ≈ 1,0 condition inafafanuliwa kama Dirichlet mode, huku kl/π ≈ 0,5 condition ikifafanuliwa kama Neumann mode.

Katika free-surface maps, maximum wave amplitude inaonekana kutokea mara nyingi karibu na WEC ya nne katika short- na long-wave conditions. Kwa Neumann mode, heave response amplitude ratios za WEC ya pili, ya tatu na ya nne katika wave direction zilitolewa kuwa takriban 0,29, 0,38 na 0,40. Hii inaonyesha kwamba energy focusing inaweza kuongeza WEC-motion response kadiri unavyoenda nyuma katika wave direction.

Source-internal terminology note: Katika sehemu inayojadili moonpool draft, kl/π ≈ 0,5 condition inaitwa kwanza Neumann mode, lakini katika sentensi inayofuata condition hiyo hiyo imeandikwa “Dirichlet mode”. Kwa kuwa definition ya awali ya utafiti na free-surface analysis zinatoa kl/π ≈ 0,5 kama Neumann na kl/π ≈ 1,0 kama Dirichlet, kuna terminological inconsistency katika source text. Makala hii ya Verianla haifichi kosa hili la source.

Opening width ilibadilisha performance vipi?

Opening widths nne zilichunguzwa: 20, 40, 60 na 80 m. Hizi zinawakilisha kwa mtiririko huo w/D=1,0; 2,0; 3,0 na 4,0. Opening width ilipoongezwa kutoka 1,0D hadi 3,0D, array interaction factor kwa ujumla iliongezeka, lakini ilipopandishwa hadi 4,0D, performance ilipungua tena.

Optimum opening ratio iliamuliwa kuwa w/D=3,0. Katika geometry hii, wave-focusing effect ilikuwa nguvu kuliko negative near-trapping effect kati ya WEC katika hali nyingi. Utafiti unaonyesha q_array karibu 3 katika kl/π=2,0 na katika sehemu ya results unaripoti maximum array interaction factor ya q_array=3,1.

Kwa WEC ya nne katika w/D=3,0, individual interaction factor ilifikia takriban q_single=4,7. Watafiti wanahusisha hili na kuhamishwa kwa energy iliyoreflectiwa na moonpool wall kwenda nyuma ya array na WEC ya nne kuwa katika energy-focusing region.

Opening inapaswa kuelekezwa vipi kwa incident wave?

Moonpool opening ikitazama incident wave ilitoa matokeo bora zaidi. Wakati incident wave angle β=0°, waves zilizoakisiwa kutoka inner moonpool wall zinaelekezwa kwa ufanisi zaidi kwenye rear part ya WEC array.

β ilipobadilishwa kutoka 0° hadi 15°, 30° na 45°, overall energy-conversion performance ilipungua na useful wave range ikawa nyembamba. Kwa mfano karibu na Neumann mode, q_array iliripotiwa kuwa takriban 0,86 kwa β=0° na takriban 0,30 kwa β=45°.

Kwa hiyo watafiti wanapendekeza diagonal inayounganisha corner WEC mbili za square array na center WEC ilinganishwe na incident-wave direction, na centerline ya moonpool opening ifuate direction hiyo pia.

Moonpool draft iliathiri WEC gani zaidi?

WEC draft ilihifadhiwa d=2,0 m, huku moonpool draft ikibadilishwa kuwa d_mp=1,0; 2,0; 3,0 na 5,0 m. Performance ya front WEC katika low-wave-number region ilibaki relatively insensitive kwa mabadiliko ya draft, lakini WEC ya nne iliathirika kwa wazi.

Moonpool-wall draft ilipoongezeka, reflecting surface ya kina zaidi iliundwa na, kulingana na tafsiri ya watafiti, wave-energy transfer kwenda rear focusing region iliimarika. Individual interaction factor ya WEC ya nne ilifikia takriban 5,9 katika baadhi ya wave conditions; katika abstract matokeo haya yameelezwa kuwa takriban q=6.

Numerical-consistency note: Source inasema katika sehemu hiyo hiyo kwamba d_mp=5 m case ni %49,1 higher kuliko d_mp=2 m case. Hata hivyo, values 0,90 na 0,71 zilizotolewa mara moja kabla yake hazionyeshi difference ya %49,1 kati ya numbers hizi mbili maalum. Sehemu ya conclusion tena inatumia expression ya “hadi %49,1” increase. Kwa hiyo %49,1 imehifadhiwa kama overall maximum iliyoripotiwa katika source; haijawasilishwa kama direct arithmetic result ya kl/π≈0,5 point.

Kwa nini kuzungusha moonpool opening kulipunguza performance?

Opening centerline ilichunguzwa kwa kuzungushwa kwa β_mp=0°, 30° na 45° relative to incident wave. Kadiri angle ilivyoongezeka, moonpool opening iliondoka kwenye wave direction na kuelekeza waves zinazoingia na wall kwenda desired focusing direction kukadhoofika.

Utafiti unasema useful dimensionless wavelength range yenye q_array>1 ilipungua hadi %36,7 pamoja na deviation ya opening orientation. β_mp=0° arrangement ilitambuliwa kama most effective overall layout ambapo WEC ya tatu na ya nne zinaweza kuzidi isolated WEC reference katika open water kwa long na short waves.

Je, kutumia openings nyingi ni bora?

Matokeo yanabadilika kulingana na aina mbili tofauti za comparison. Ikiwa width ya kila opening inahifadhiwa sawa, configuration yenye openings mbili inaweza kutoa very high energy-focusing performance katika baadhi ya short-wave conditions. Source inaripoti kwamba two-opening structure ilifikia maximum q_array=3,1 na, chini ya same individual opening width, inaweza kutoa values hadi %107 na %138 higher kuliko one- na three-opening designs kwa mtiririko huo.

Lakini kutoka engineering perspective, total open area inapohifadhiwa fixed, result inageuka. Total opening width ikiwa equal, one-opening moonpool ilionyesha performance hadi %26,7 higher kuliko two-opening model katika long-wave conditions. Vivyo hivyo, one 60 m opening iliongeza energy conversion hadi %24,1 ikilinganishwa na three 20 m openings.

Kwa hiyo main conclusion ya utafiti haiwezi kurahisishwa kuwa “openings mbili ni bora zaidi” au “opening moja ni bora kila wakati”. Result inategemea kama individual opening width au total opening width ndiyo inayowekwa constant katika comparison.

Matokeo yanayoungwa mkono na utafiti

• Moonpool yenye opening inaweza kuongeza hydrodynamic interaction factor ya WEC array juu ya open-water reference katika numerical model iliyochunguzwa.
• w/D=3,0 ratio ilitoa best overall performance kati ya opening ratios zilizochunguzwa.
• Kulinganisha moonpool opening na incident-wave direction kuliimarisha energy focusing.
• Kwa sababu WEC ya nne iko katika main energy-focusing region ndani ya moonpool, inaweza kuonyesha constructive interaction kubwa zaidi kuliko WEC nyingine.
• Kuongeza moonpool draft kunaweza kupanua useful wave range hasa kwa WEC iliyo rear of array.
• Total opening width ikiwa sawa, openings nyingi zinaweza kuongeza energy leakage na kuondoa advantage ya one-opening structure.

Mambo ambayo utafiti haujathibitisha

• System haijajaribiwa baharini kwenye physical prototype.
• Real electrical energy delivered to grid haijapimwa.
• Annual energy production katika real irregular sea states haijahesabiwa.
• Storm, extreme-wave au survival conditions hazijathibitishwa.
• Economic analysis ya moonpool construction cost au levelized cost of electricity haijafanywa.
• Contribution ya nonlinear multi-body effects kwa real-system performance haijathibitishwa na model hii.
• Idealized wall approach imetumiwa badala ya flexible moonpool walls.

Mbinu na Matokeo ya Utafiti

Basic mathematical assumptions

Model imejengwa ndani ya linear potential-flow theory. WEC motions zimechukuliwa kuwa small-amplitude na device motion imewekewa kikomo cha vertical translation pekee, yaani heave degree of freedom.

Total velocity potential imeelezwa kama combination ya radiation potentials zinazotokana na motion ya kila WEC, incident-wave potential na total diffraction potential:

\[ \phi = \sum_{j=1}^{N} u_j\phi_j^R+\phi^I+\phi^D \]

Hapa \(u_j\) inawakilisha vertical motion velocity ya WEC ya j; \(\phi_j^R\) radiation potential ya WEC husika; \(\phi^I\) incident wave na \(\phi^D\) diffraction potential.

Hydrodynamic solution ilifanywaje?

Boundary-element approach inayotegemea Rankine panel method ilitumiwa kwa wetted surfaces zote na free surface. Integral equation yenye Green function iligawanywa kwenye four-node panels juu ya surface na kutatuliwa kwa collocation-point method.

Fourth-order Runge–Kutta method ilitumika kusasisha free surface kwa muda. Artificial damping zone ilifafanuliwa katika outer region ili kupunguza reflection ya scattered waves kutoka computational boundary; damping term iliongezwa kwenye free-surface kinematic na dynamic boundary conditions.

Mwanzoni, buffer function ilitumika kuruhusu gradual development ya incident/scattered wave field na kuzuia sudden loading ya numerical solution. Buffer duration kwa kawaida ilichukuliwa kuwa incident-wave periods mbili.

PTO system ilimodeliwaje?

Kila WEC ilichukuliwa kuwa na independent linear PTO unit. Ingawa general PTO force imeelezwa kwa inertia, damping na elastic components, katika energy-capture analyses M_PTO=0 na K_PTO=0 zilichukuliwa, na mechanical energy extraction ikamodeliwa hasa kupitia linear PTO damping coefficient C_PTO.

Katika kila simulation condition, optimum PTO damping coefficient iliyofafanuliwa na utafiti ilitumika. Approach hii si detailed “wave-to-wire” model ya real generator, power electronics na power-conversion chain; inawakilisha mechanical damping effect ya PTO.

Interaction factors zina maana gani?

Energy-capture performance ya WEC moja ndani ya moonpool ililinganishwa na power ya isolated WEC katika open water na individual interaction factor ikafafanuliwa:

\[ q_{\mathrm{single},j}= \frac{P_j}{P_{\mathrm{iso}}} \]

Total interaction factor ya array ilitolewa kama:

\[ q_{\mathrm{array}}= \frac{P_n}{N P_{\mathrm{iso}}} = \frac{1}{N}\sum_{j=1}^{N}q_{\mathrm{single},j} \]

. Hapa q>1 inamaanisha constructive interaction na q<1 destructive interaction relative to isolated WEC reference katika open water. Value hii si direct electrical percentage efficiency kwa maana ya kawaida; ni dimensionless hydrodynamic interaction measure relative to reference WEC power production.

Mesh na time-step sensitivity

Numerical sensitivity test ilifanywa katika regular-wave condition ya A₀=1 m, ω=1,75 rad/s, β=0° na h=70 m. Surface resolutions tatu zililinganishwa:

Katika time-step sensitivity, dt=T/20, T/30 na T/40 zililinganishwa na dt=T/30 solution ikatumika kama choice inayofaa kati ya computational load na numerical accuracy.

Numerical model ilivalidate vipi?

Kwa model validation, linear-array problem ya cylindrical semi-submerged WEC tatu iliyochapishwa awali ilihesabiwa tena. Katika reference geometry, WEC radius ilikuwa a=1 m, draft d=0,5 m, neighboring WEC spacing D=8a na water depth h=20a.

Mean interaction-factor curves zilizohesabiwa kwa new Rankine source method zililinganishwa na reference results za Ning na wenzake na good agreement ilionekana. Validation hii inaunga mkono uwezo wa numerical method ku-reproduce similar linear WEC-array problem; haimaanishi kuwa new moonpool geometry imevalidate kwa physical experiment.

Opening-width analysis

Main numerical findings

Main methodological boundaries ya utafiti

Model inachunguza WEC tano katika vertical-motion degree of freedom pekee. Translational na rotational motions nyingine zinazoweza kutokea katika real systems hazikutumika katika main parametric model. Watafiti pia wanaorodhesha wazi multi-body nonlinear effects katika enclosed water region kama future-work topics.

Analyses zinategemea regular-wave conditions. Irregular real sea states na long-term energy production zimetajwa kama maeneo yanayohitaji validation ya baadaye.

Moonpool wall imetazamwa kama idealized hydrodynamic boundary. Effect ya wall flexibility kwa energy capture imeachwa kama topic ya utafiti tofauti.

PTO systems zimewakilishwa na independent linear mechanical damping elements. Watafiti wanapendekeza future coordinated-control strategies ambapo kila PTO inaweza kurekebisha stiffness na damping independently kulingana na internal wave field.

Maelezo ya Chanzo na Mbinu

Tam özgün çalışma adı: Wave energy extraction performance of heaving buoy WEC arrays deployed within an energy-focusing moonpool

Waandishi na mpangilio: Yong Cheng; Jianyou Yu; Deshuang Yu; Saishuai Dai; Zhiming Yuan; Atilla Incecik; Gang Wang.

Equal contribution/co-first authorship: Hakuna statement ya co-first authorship au equal contribution katika version iliyopakiwa.

Corresponding author: Deshuang Yu.

Corresponding-author email: yudsh@cafs.ac.cn

Taasisi: Fishery Engineering Research Institute, Chinese Academy of Fishery Sciences, Beijing 100141, China; School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China; Naval Architecture, Ocean and Marine Engineering Department, University of Strathclyde, Glasgow, United Kingdom.

Author affiliations: Yong Cheng: Chinese Academy of Fishery Sciences na Jiangsu University of Science and Technology; Jianyou Yu: Jiangsu University of Science and Technology; Deshuang Yu: Chinese Academy of Fishery Sciences; Saishuai Dai, Zhiming Yuan na Atilla Incecik: University of Strathclyde; Gang Wang: Chinese Academy of Fishery Sciences.

Aina ya chanzo: Preprint version ya time-domain hydrodynamic numerical modeling/simulation research.

Peer-review status: Huu ni preprint ambao haujapitia peer review; results zinapaswa kutathminiwa kwa kuzingatia publication stage hii.

Jukwaa: SSRN.

SSRN record number iliyochunguzwa: 6934160.

DOI: 10.2139/ssrn.6934160.

Publication date ya SSRN version iliyochunguzwa: 13 Juni 2026.

Official preprint link:SSRN 6934160

Version check: SSRN inaonyesha multiple version records chini ya title hiyo hiyo. File iliyochunguzwa ni 67-page version yenye SSRN 6934160 watermark. SSRN pia ina older 68-page version yenye ID 6845150. Scientific content haijaunganishwa kimya kimya kati ya versions hizi.

Peer-reviewed publication: Katika bibliographic check, separate peer-reviewed journal version na peer-reviewed publication DOI iliyothibitishwa kwa uhakika kupitia official publisher record kwa title hii haikuweza kutambuliwa. Kwa hiyo journal au peer-reviewed DOI information haijabuniwa.

License: Open Creative Commons au equivalent reuse license haikupatikana katika uploaded version. Kwa hiyo original figures za source hazijanakiliwa moja kwa moja katika makala.

Funding: National Key Research and Development Program (2024YFD2400804); National Natural Science Foundation of China (52571295, 52271278, 52111530137); Royal Society Newton Advanced Fellowships (NAF\R1\180304).

Conflict of interest: Waandishi wanatangaza kuwa hakuna known financial conflict of interest au personal relationship inayoweza kuathiri results za utafiti.

Data availability: Uploaded version haina separate data-availability statement.

CRediT author contributions: Yong Cheng: validation, formal analysis, writing-original draft, funding acquisition na conceptualization. Jianyou Yu: methodology, software, data curation, writing-original draft na supervision. Deshuang Yu: formal analysis na writing-original draft. Saishuai Dai: formal analysis na data curation. Zhiming Yuan: review/editing na supervision. Atilla Incecik: funding acquisition na supervision. Gang Wang: supervision.

Numerical validation: Mesh na time-step sensitivity analyses zilifanywa, kisha Rankine panel/BEM model ililinganishwa na previously published three-WEC reference problem na good agreement ikaripotiwa. Validation hii ni ya numerical method; si physical-experiment validation ya new five-WEC–moonpool system.

Source-internal terminology inconsistency: Katika utafiti mzima kl/π≈1,0 imefafanuliwa kama Dirichlet na kl/π≈0,5 kama Neumann mode, lakini katika Sehemu 3.3 kl/π≈0,5 inaitwa Neumann na Dirichlet katika paragraph ile ile.

Source-internal numerical consistency note: Katika Sehemu 3.3, values za qarray=0,71 na 0,90 zimetolewa kwa dmp=2 m na 5 m kwa mtiririko huo katika kl/π≈0,5, kisha statement ya %49,1 increase inatumiwa. Kwa sababu direct ratio ya explicit values hizi mbili haiendani na %49,1 increase, value ya %49,1 imehifadhiwa kama overall maximum iliyoripotiwa katika conclusion ya utafiti, lakini haijawasilishwa kama direct arithmetic result ya numbers hizi mbili.

Main scientific boundary: Findings ni numerical results zilizopatikana katika linear potential-flow framework kwa kutumia idealized geometry, regular waves, heave-only WEC motion na linear PTO mechanism. Real sea site, irregular waves, full electrical-production chain, long-term structural reliability na economic performance hazijathibitishwa katika utafiti huu.

Scientific-content principle: Method, formulas, wave-field interpretations na performance values katika makala hii ya Verianla zinategemea uploaded 67-page study. External sources zilitumiwa tu kwa bibliographic version, date na DOI verification; hakuna new scientific result kutoka external sources iliyoongezwa kwenye main narrative.