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Kulolu cwaningo, i-hydrodynamics ye-flocculation ihlolwa ngophenyo lokuhlola nolwezinombolo lwenkambu yesivinini sokugeleza kwesiphithiphithi esikalini selabhorethri sokugwedla.Ukugeleza kwesiyaluyalu okuthuthukisa ukuhlanganisa kwezinhlayiyana noma ukuhlukana kwe-floc kuyinkimbinkimbi futhi kucatshangelwa futhi kuqhathaniswe kuleli phepha kusetshenziswa amamodeli amabili esiphithiphithi, okuyi-SST k-ω ne-IDDES.Imiphumela ibonisa ukuthi i-IDDES inikeza ukuthuthukiswa okuncane kakhulu kune-SST k-ω, okwanele ukulingisa ngokunembile ukugeleza ngaphakathi kwe-paddle flocculator.Isilinganiso esifanele sisetshenziselwa ukuphenya ukuhlangana kwemiphumela ye-PIV ne-CFD, nokuqhathanisa imiphumela yemodeli yesiphithiphithi ye-CFD esetshenzisiwe.Ucwaningo luphinde lugxile ekubaleni i-slip factor k, engu-0.18 ngesivinini esiphansi sika-3 no-4 rpm uma kuqhathaniswa nevelu evamile evamile engu-0.25.Ukunciphisa u-k ukusuka ku-0.25 kuye ku-0.18 kukhulisa amandla alethwa oketshezini cishe ngo-27-30% futhi kukhulisa i-velocity gradient (G) cishe ngo-14%.Lokhu kusho ukuthi ukuxuba okujulile kufinyelelwa kunalokho obekulindelwe, ngakho-ke amandla amancane asetshenziswa, ngakho-ke ukusetshenziswa kwamandla kuyunithi ye-flocculation yesikhungo sokuhlanza amanzi okuphuza kungaba ngaphansi.
Ekuhlanzweni kwamanzi, ukungezwa kwama-coagulants kuphazamisa izinhlayiya ezincane ze-colloidal nokungcola, okuhlanganisa ukwenza i-flocculation esiteji se-flocculation.Ama-Flakes ayinhlanganisela ye-fractal eboshwe ngokukhululekile, esuswa ngokulungiswa.Izakhiwo zezinhlayiya kanye nezimo zokuxuba uketshezi zinquma ukusebenza kahle kwenqubo ye-flocculation kanye nokwelashwa.I-flocculation idinga ukuyaluza kancane isikhathi esifushane uma kuqhathaniswa namandla amaningi ukunyakazisa umthamo omkhulu wamanzi1.
Ngesikhathi se-flocculation, i-hydrodynamics yalo lonke uhlelo kanye nekhemistri ye-coagulant-particle interaction inquma izinga lapho ukusabalalisa usayizi wezinhlayiyana ezimile kufinyelelwa khona2.Uma izinhlayiya zishayisana, ziyanamathelana3.I-Oyegbile, i-Ay4 ibike ukuthi ukushayisana kuncike ezindleleni zokuthutha ezinyakazayo ze-Brownian diffusion, i-shear fluid kanye nokuhlalisa okuhlukile.Lapho ama-flakes eshayisana, akhula futhi afinyelele umkhawulo wesayizi othize, okungaholela ekuqhekekeni, njengoba ama-flakes engakwazi ukumelana namandla e-hydrodynamic force5.Amanye alawa ma-flakes aphukile aphinde ahlangane abe amancane noma alingane nosayizi6.Kodwa-ke, ama-flakes aqinile angamelana nala mandla futhi agcine usayizi wawo futhi akhule7.U-Yukselen no-Gregory8 babike ngezifundo ezihlobene nokucekelwa phansi kwama-flakes kanye nekhono lawo lokuvuselela, okubonisa ukuthi ukungahlehliseki kunqunyelwe.Bridgeman, Jefferson9 wasebenzisa i-CFD ukuze alinganisele umthelela wendawo wokugeleza kwencazelo kanye nesiyaluyalu ekwakhekeni kwe-floc nokuhlukana ngama-gradient esivinini endawo.Emathangeni afakwe ama-rotor blades, kuyadingeka ukushintsha isivinini lapho ama-aggregates engqubuzana nezinye izinhlayiya lapho ehlakazeka ngokwanele esigabeni sokuhlangana.Ngokusebenzisa i-CFD nesivinini esiphansi sokuzungeza esingaba ngu-15 rpm, i-Vadasarukkai ne-Gagnon11 zikwazile ukuzuza amanani e-G okuntanta ngama-conical blades, ngaleyo ndlela kuncishiswe ukusetshenziswa kwamandla okuyaluza.Kodwa-ke, ukusebenza ngamavelu aphezulu we-G kungase kuholele ekunyakazeni.Baphenye umthelela wokuxuba isivinini ekutholeni isilinganiso se-velocity gradient ye-pilot paddle flocculator.Zizungeza ngesivinini esingaphezu kuka-5 rpm.
I-Korpijärvi, i-Ahlstedt12 isebenzise amamodeli amane ahlukene esiphithiphithi ukuze itadishe inkambu yokugeleza ebhentshini lokuhlola ithangi.Balinganise inkambu yokugeleza nge-laser Doppler anemometer ne-PIV futhi baqhathanisa imiphumela ebaliwe nemiphumela elinganisiwe.U-de Oliveira kanye no-Donadel13 bahlongoze enye indlela yokulinganisa ama-gradient esivinini kusuka ezakhiweni ze-hydrodynamic kusetshenziswa i-CFD.Indlela ehlongozwayo yahlolwa kumayunithi ayisithupha e-flocculation ngokusekelwe ku-helical geometry.ihlole umthelela wesikhathi sokugcina kuma-flocculant futhi yahlongoza imodeli ye-flocculation engasetshenziswa njengethuluzi lokusekela ukwakheka kweseli okunengqondo ngezikhathi zokugcina eziphansi14.U-Zhan, You15 uhlongoze imodeli ye-CFD ehlanganisiwe nebhalansi yabantu ukuze ilingise izici zokugeleza nokuziphatha kwe-floc ngokugeleza okugcwele kwesikali.Llano-Serna, Coral-Portillo16 uphenye izici zokugeleza ze-Cox-type hydroflocculator endaweni yokuhlanza amanzi e-Viterbo, e-Colombia.Nakuba i-CFD inezinzuzo zayo, kukhona futhi ukulinganiselwa okufana namaphutha ezinombolo ekubaleni.Ngakho-ke, noma yimiphi imiphumela yezinombolo etholiwe kufanele ihlolwe ngokucophelela futhi ihlaziywe ukuze kufinyelelwe eziphethweni ezibucayi17.Kunezifundo ezimbalwa ezincwadini zokuklanywa kwama-baffle flocculators avundlile, kuyilapho izincomo zokuklanywa kwama-hydrodynamic flocculators zilinganiselwe18.I-Chen, i-Liao19 isebenzise ukusetha kokuhlola okusekelwe ekusabalaleni kokukhanya kwe-polarized ukukala isimo sokuhlukanisa ukukhanya okuhlakazekile kusuka ezinhlayiyeni ngazinye.I-Feng, i-Zhang20 isebenzise i-Ansys-Fluent ukuze ilingise ukusatshalaliswa kwama-eddy currents nokushwibeka endaweni yokugeleza ye-coagulated plate flocculator kanye ne-inter-corrugated flocculator.Ngemva kokulingisa ukugeleza koketshezi oluyaluzayo ku-flocculator kusetshenziswa i-Ansys-Fluent, i-Gavi21 yasebenzisa imiphumela ukuze idizayine i-flocculator.U-Vaneli no-Teixeira22 babike ukuthi ubudlelwano phakathi kwe-fluid dynamics ye-spiral tube flocculators kanye nenqubo ye-flocculation kusaqondwa kabi ukusekela umklamo onengqondo.U-de Oliveira noCosta Teixeira23 bafunde ukusebenza kahle futhi babonisa izakhiwo ze-hydrodynamic ze-spiral tube flocculator ngokusebenzisa izivivinyo ze-physics kanye nokulingiswa kwe-CFD.Abacwaningi abaningi baye bahlola amashubhu ahlanganisiwe noma ama-tube flocculators ahlanganisiwe.Kodwa-ke, ulwazi oluningiliziwe lwe-hydrodynamic mayelana nokuphendula kwalezi ziphehli kumiklamo ehlukahlukene nezimo zokusebenza zisantuleka (Sartori, Oliveira24; Oliveira, Teixeira25).U-Oliveira no-Teixeira26 bethula imiphumela yasekuqaleni evela ezilinganisweni zethiyori, zokuhlola kanye ne-CFD ye-spiral flocculator.U-Oliveira no-Teixeira27 bahlongoze ukusebenzisa ikhoyili evunguzayo njenge-coagulation-flocculation reactor ehlanganiswe nesistimu yokukhipha umchamo evamile.Babika ukuthi imiphumela etholiwe yokusebenza kahle kokususwa kwe-turbidity ihluke kakhulu kuleyo etholwe ngamamodeli asetshenziswa kakhulu ukuze kuhlolwe i-flocculation, iphakamisa ukuqapha lapho kusetshenziswa amamodeli anjalo.U-Moruzzi kanye no-de Oliveira [28] bafanekisela indlela yokuziphatha yesistimu yamagumbi agelezayo aqhubekayo ngaphansi kwezimo ezihlukahlukene zokusebenza, okuhlanganisa ukuhluka kwenani lamakamelo asetshenzisiwe kanye nokusetshenziswa kwamagreyidi esivinini seseli esimisiwe noma esikalini.I-Romphophak, Le Men29 PIV izilinganiso zesivinini esisheshayo kuzihlanzi zejethi ezinezinhlangothi ezimbili.Bathole ukuzungeza okunamandla okubangelwa i-jet endaweni ye-flocculation kanye namazinga alinganiselwe endawo kanye nesilinganiso esisheshayo.
U-Shah, u-Joshi30 ubika ukuthi i-CFD inikeza enye indlela ethokozisayo yokuthuthukisa amadizayini kanye nokuthola izici zokugeleza ezibonakalayo.Lokhu kusiza ukugwema ukusetha okubanzi kokuhlola.I-CFD isetshenziswa ngokwandayo ukuhlaziya izimboni zokuhlanza amanzi namanzi angcolile (Melo, Freire31; Alalm, Nasr32; Bridgeman, Jefferson9; Samaras, Zouboulis33; Wang, Wu34; Zhang, Tejada-Martínez35).Abaphenyi abaningana benze izivivinyo kumishini engakwazi ukuhlola (i-Bridgeman, i-Jefferson36; i-Bridgeman, i-Jefferson5; i-Jarvis, i-Jefferson6; i-Wang, i-Wu34) kanye nama-disc flocculators ane-perforated31.Abanye basebenzise i-CFD ukuhlola ama-hydroflocculators (Bridgeman, Jefferson5; Vadasarukkai, Gagnon37).I-Ghawi21 ibike ukuthi ama-flocculator ayimishini adinga ukunakekelwa njalo njengoba evame ukuphuka futhi adinga ugesi omningi.
Ukusebenza kwe-paddle flocculator kuncike kakhulu ku-hydrodynamics ye-reservoir.Ukuntuleka kokuqonda okulinganiselwe kwezinkambu zejubane lokugeleza kulawo ma-flocculator kuphawulwe ngokucacile ezincwadini (Howe, Hand38; Hendricks39).Isisindo samanzi sonke singaphansi kokunyakaza kwe-impeller ye-flocculator, ngakho-ke kulindeleke ukushelela.Ngokuvamile, isivinini soketshezi singaphansi kwesivinini se-blade nge-slip factor k, echazwa njengesilinganiso sesivinini somzimba wamanzi nesivinini sesondo lesigwedlo.I-Bhole40 ibike ukuthi kunezici ezintathu ezingaziwa okufanele zicatshangelwe lapho uklama i-flocculator, okungukuthi i-velocity gradient, i-drag coefficient, kanye nesivinini esihlobene samanzi esihlobene nensingo.
I-Camp41 ibika ukuthi uma ucubungula imishini yejubane eliphezulu, isivinini singaba ngu-24% wesivinini se-rotor futhi siphezulu njenge-32% yemishini yejubane eliphansi.Uma ingekho i-septa, u-Droste no-Ger42 basebenzisa i-ak value engu-0.25, kuyilapho endabeni ye-septa, k isukela ku-0 iye ku-0.15.I-Howe, i-Hand38 iphakamisa ukuthi u-k usebangeni lika-0.2 ukuya ku-0.3.I-Hendrix39 ihlobanise isici esishelelayo nesivinini sokuzungeza isebenzisa ifomula yokuhlola futhi yaphetha ngokuthi isici esishelelayo sasingaphakathi kwebanga elisungulwe yi-Camp41.I-Bratby43 ibike ukuthi i-k icishe ibe ngu-0.2 ngesivinini se-impeller sisuka ku-1.8 siye ku-5.4 rpm futhi sikhuphuke siye ku-0.35 ngesivinini se-impeller sisuka ku-0.9 siye ku-3 rpm.Abanye abacwaningi babika amanani anhlobonhlobo e-drag coefficient (Cd) ukusuka ku-1.0 kuye ku-1.8 kanye namavelu e-coefficient k ashelelayo ukusuka ku-0.25 ukuya ku-0.40 (Feir ne-Geyer44; Hyde kanye no-Ludwig45; Harris, Kaufman46; van Duuren47; kanye ne-4 Brat8by kanye ne-Marais8by ).Izincwadi azibonisi inqubekelaphambili ebalulekile ekuchazeni nasekulinganiseni u-k kusukela emsebenzini we-Camp41.
Inqubo ye-flocculation isuselwe kusiphithiphithi ukuze kube lula ukungqubuzana, lapho i-velocity gradient (G) isetshenziselwa ukukala i-turbulence/flocculation.Ukuxuba kuyinqubo yokuhlakaza amakhemikhali ngokushesha nangokulinganayo emanzini.Izinga lokuxuba likalwa nge-velocity gradient:
lapho i-G = i-velocity gradient (isekhondi-1), P = okokufaka kwamandla (W), V = umthamo wamanzi (m3), μ = i-viscosity eguquguqukayo (Pa s).
Lapho inani le-G liphezulu, lixubene kakhulu.Ukuxutshwa okuphelele kubalulekile ukuze kuqinisekiswe ukuhlangana okufanayo.Izincwadi zibonisa ukuthi imingcele ebaluleke kakhulu yokuklama isikhathi sokuxuba (t) kanye ne-velocity gradient (G).Inqubo ye-flocculation isuselwe kusiphithiphithi ukuze kube lula ukungqubuzana, lapho i-velocity gradient (G) isetshenziselwa ukukala i-turbulence/flocculation.Amanani edizayini ajwayelekile ka-G angu-20 kuya ku-70 s–1, t iyimizuzu engu-15 kuya kwengama-30, futhi i-Gt (engenasici) ingu-104 kuya ku-105. Amathangi okuhlanganisa okusheshayo asebenza kahle kakhulu ngamavelu e-G angu-700 kuya ku-1000, ngokuhlala kwesikhathi. cishe imizuzu emi-2.
lapho u-P engamandla anikezwa uketshezi yi-flocculator blade ngayinye, uN isivinini sokuzungeza, b ubude beblade, ρ ukuminyana kwamanzi, r irediyasi, futhi u-k yi-coefficient yokushelela.Lesi sibalo sisetshenziswa ku-blade ngayinye ngayinye futhi imiphumela ifinyezwa ukunikeza inani lamandla okufakwayo kwe-flocculator.Ukuhlola ngokucophelela le zibalo kubonisa ukubaluleka kwesici sokushelela k ohlelweni lokuklama i-flocculator ye-paddle.Imibhalo ayisho inani eliqondile lika-k, kodwa kunalokho incoma ububanzi njengoba kushiwo ngaphambili.Nokho, ubudlelwane phakathi kwamandla P kanye ne-coefficient k eshelelayo buyi-cubic.Ngakho-ke, inqobo nje uma wonke amapharamitha afana, isibonelo, ukushintsha k kusuka ku-0.25 kuya ku-0.3 kuzoholela ekwehleni kwamandla adluliselwa ku-fluid nge-blade cishe ngo-20%, futhi ukunciphisa k kusuka ku-0.25 kuya ku-0.18 kuzokwandisa.cishe ngo-27-30% i-vane ngayinye Amandla anikezwe uketshezi.Ekugcineni, umthelela we-k ekwakhiweni kwe-paddle flocculator esimeme udinga ukuphenywa ngokubalwa kobuchwepheshe.
Ukulinganisa okunembile kwe-empirical of slippage kudinga ukugeleza ngeso lengqondo nokulingiswa.Ngakho-ke, kubalulekile ukuchaza isivinini se-tangential se-blade emanzini ngesivinini esithile sokujikeleza emabangeni e-radial ahlukene ukusuka ku-shaft nasekujuleni okuhlukene ukusuka emanzini ukuze kuhlolwe umphumela wezikhundla ezihlukene ze-blade.
Kulolu cwaningo, i-hydrodynamics ye-flocculation ihlolwa ngophenyo lokuhlola nolwezinombolo lwenkambu yesivinini sokugeleza kwesiphithiphithi esikalini selabhorethri sokugwedla.Izilinganiso ze-PIV zirekhodwa ku-flocculator, okwenza amakhonco esivinini esilinganiso sesikhathi abonisa isivinini sezinhlayiya zamanzi ezizungeze amaqabunga.Ngaphezu kwalokho, i-ANSYS-Fluent CFD isetshenziselwe ukulingisa ukugeleza okushwibekayo ngaphakathi kwe-flocculator nokudala amakhonco esivinini esilinganiso sesikhathi.Imodeli ye-CFD eyaba umphumela yaqinisekiswa ngokuhlola ukuxhumana phakathi kwemiphumela ye-PIV ne-CFD.Okugxilwe kulo msebenzi kuwukubala inani le-coefficient k, okuyipharamitha yedizayini engenasici ye-paddle flocculator.Umsebenzi owethulwe lapha unikeza isisekelo esisha sokulinganisa i-coefficient yesiliphu k ngesivinini esiphansi sika-3 rpm no-4 rpm.Imiphumela yemiphumela ifaka isandla ngqo ekuqondeni kangcono i-hydrodynamics yethangi le-flocculation.
I-flocculator yaselabhorethri iqukethe ibhokisi elingaphezulu elivulekile elingunxande elinobude obuyi-147 cm, ukuphakama okungama-39 cm, ububanzi obuyi-118 cm, nobude obuyi-138 cm (Fig. 1).Inqubo yokuklama eyinhloko eyakhiwe yi-Camp49 yasetshenziselwa ukuklama i-paddle flocculator yesikali selabhorethri futhi isebenzise izimiso zokuhlaziywa kobukhulu.Isikhungo sokuhlola sakhiwe eLabhorethri Yobunjiniyela Bezemvelo yaseLebanese American University (Byblos, Lebanon).
I-eksisi evundlile itholakala ekuphakameni okungama-60 cm ukusuka phansi futhi ithatha amasondo amabili okugwedla.Isondo ngalinye lokugwedla liqukethe ama-paddles angu-4 anama-paddles angu-3 ku-paddle ngayinye ngesamba sama-paddles angu-12.I-Flocculation idinga ukuyaluza okuthambile ngesivinini esiphansi esingu-2 kuya ku-6 rpm.Isivinini esivame kakhulu sokuxuba kuma-flocculator ngu-3 rpm no-4 rpm.Ukugeleza kwe-flocculator yesikali selabhorethri yakhelwe ukumela ukugeleza endaweni yethangi le-flocculation yesikhungo sokuhlanza amanzi okuphuza.Amandla abalwa kusetshenziswa i-equation yendabuko 42.Kuzo zombili izivinini zokuzungezisa, igrediyenti yesivinini \(\stackrel{\mathrm{-}}{\text{G}}\) sikhulu kuno-10 \({\text{sec}}^{-{1}}\) , inombolo kaReynolds ikhombisa ukugeleza kwesiyaluyalu (Ithebula 1).
I-PIV isetshenziselwa ukuzuza izilinganiso ezinembile neziningi zama-velocity we-fluid velocity ngasikhathi sinye enanini elikhulu kakhulu lamaphoyinti50.Ukusetha kokuhlola kufaka phakathi i-paddle flocculator ye-lab-scale, uhlelo lwe-LaVision PIV (2017), kanye ne-Arduino yangaphandle ye-laser trigger.Ukuze udale amaphrofayili esivinini esinesilinganiso sesikhathi, izithombe ze-PIV zarekhodwa ngokulandelana endaweni efanayo.Isistimu ye-PIV ilinganiswa ngendlela yokuthi indawo eqondiwe ibe maphakathi nobude bezinkemba ezintathu zengalo ethile yokugwedla.I-trigger yangaphandle iqukethe i-laser etholakala ohlangothini olulodwa lobubanzi be-flocculator kanye nesamukeli senzwa ngakolunye uhlangothi.Ngaso sonke isikhathi lapho ingalo ye-flocculator ivimba indlela ye-laser, isignali ithunyelwa kusistimu ye-PIV ukuze ithwebule isithombe ngeleza ye-PIV nekhamera evunyelaniswe neyunithi yesikhathi ehlelekayo.Emkhiwaneni.2 ibonisa ukufakwa kwesistimu ye-PIV kanye nenqubo yokutholwa kwesithombe.
Ukurekhodwa kwe-PIV kwaqalwa ngemva kokuba i-flocculator isetshenziswe imizuzu engu-5-10 ukuze kujwayeleke ukugeleza futhi kucatshangelwe inkambu yenkomba efanayo ye-refractive.Ukulinganisa kufinyelelwa ngokusebenzisa ipuleti lokulinganisa elicwiliswe ku-flocculator futhi libekwe phakathi nendawo yobude be-blade yentshisekelo.Lungisa indawo yelaser ye-PIV ukuze wenze ishidi lokukhanya eliyisicaba ngaphezu kwepuleti lokulinganisa.Rekhoda amanani akaliwe wejubane ngalinye lokuzungezisa leblade ngayinye, futhi izivinini zokuzungezisa ezikhethelwe ukuhlolwa zingu-3 rpm no-4 rpm.
Kukho konke ukurekhodwa kwe-PIV, isikhawu sesikhathi esiphakathi kwama-laser pulses amabili samiswa kububanzi obusuka ku-6900 ukuya ku-7700 µs, obuvumele ukukhishwa kwezinhlayiyana okuncane okungamaphikseli angu-5.Ukuhlolwa komshayeli kwenziwa enanini lezithombe ezidingekayo ukuze kutholwe izilinganiso ezinembile zesikhathi esimaphakathi.Izibalo zeVector ziqhathaniswe kumasampula aqukethe 40, 50, 60, 80, 100, 120, 160, 200, 240, kanye nezithombe ezingu-280.Kutholwe usayizi wesampula wezithombe ezingu-240 ukunikeza imiphumela enesilinganiso sesikhathi esizinzile uma kubhekwa ukuthi isithombe ngasinye siqukethe amafreyimu amabili.
Njengoba ukugeleza ku-flocculator kunesiphithiphithi, iwindi elincane lokuphenywa kanye nenani elikhulu lezinhlayiya liyadingeka ukuze kuxazululwe izakhiwo ezincane eziyaluzayo.Ukuphindaphinda okuningana kokunciphisa usayizi kusetshenziswa kanye ne-algorithm yokuhlanganisa ukuze kuqinisekiswe ukunemba.Usayizi wokuqala wewindi lokuvota wamaphikseli angu-48×48 onokugqagqana okungu-50% kanye nenqubo eyodwa yokujwayela kwalandelwa usayizi wokugcina wewindi lokuvota wamaphikseli angu-32×32 onokugqagqana okungu-100% kanye nezinqubo ezimbili zokuzivumelanisa nezimo.Ngaphezu kwalokho, ama-sphere angenalutho engilazi asetshenziswa njengezinhlayiya zembewu ekugelezeni, okuvumele okungenani izinhlayiya eziyi-10 ngefasitela ngalinye lokuvota.Ukurekhoda kwe-PIV kuqalwa umthombo wokucupha ku-Programmable Timing Unit (PTU), enesibopho sokusebenzisa nokuvumelanisa umthombo we-laser nekhamera.
Iphakheji yezohwebo ye-CFD ANSYS Fluent v 19.1 yasetshenziselwa ukuthuthukisa imodeli ye-3D nokuxazulula izibalo zokugeleza eziyisisekelo.
Kusetshenziswa i-ANSYS-Fluent, imodeli ye-3D ye-paddle flocculator yesikali selabhorethri yadalwa.Imodeli yenziwe ngendlela yebhokisi elingunxande, elinamasondo amabili okugwedla abekwe eksisi evundlile, njengemodeli yaselabhorethri.Imodeli ngaphandle kwe-freeboard ingu-108 cm ukuphakama, 118 cm ububanzi no-138 cm ubude.Indiza eyisilinda evundlile yengezwe eduze kwe-mixer.Ukukhiqizwa kwendiza eyi-cylindrical kufanele kuqalise ukuzungezisa kwayo yonke i-mixer phakathi nesigaba sokufaka futhi kulingise inkambu yokugeleza ejikelezayo ngaphakathi kwe-flocculator, njengoba kuboniswe ku-Fig. 3a.
I-3D ANSYS-umdwebo wejiyomethri eshelelayo kanye nemodeli, i-ANSYS-flocculator body mesh endizeni yentshisakalo, umdwebo we-ANSYS oshelelayo endizeni enentshisekelo kukho.
I-geometry yemodeli iqukethe izifunda ezimbili, ngasinye esiwuketshezi.Lokhu kufinyelelwa kusetshenziswa umsebenzi wokususa onengqondo.Okokuqala khipha isilinda (kuhlanganise ne-mixer) ebhokisini ukumela uketshezi.Bese ususa i-mixer kusilinda, okuholela ezintweni ezimbili: i-mixer kanye noketshezi.Ekugcineni, kusetshenziswe isixhumi esibonakalayo esishelelayo phakathi kwezindawo ezimbili: isikhombimsebenzisi se-cylinder-cylinder kanye nesixhumi esibonakalayo se-cylinder-mixer (Fig. 3a).
Ukuhlanganiswa kwamamodeli akhiwe kuqediwe ukuze kuhlangatshezwane nezidingo zamamodeli esiphithiphithi azosetshenziswa ukwenza ukulingisa kwezinombolo.Kusetshenziswe i-mesh engakhiwe enezendlalelo ezinwetshiwe eduze nendawo eqinile.Dala izendlalelo zokunweba zazo zonke izindonga ngezinga lokukhula elingu-1.2 ukuze uqinisekise ukuthi amaphethini okugeleza ayinkimbinkimbi ayathathwa, ngogqinsi yisendlalelo sokuqala esingu-\(7\mathrm{ x {10}^{-4}\) m ukuze uqinisekise ukuthi \ ( {\umbhalo {y))^{+}\le 1.0\).Usayizi womzimba ulungiswa kusetshenziswa indlela yokufaka i-tetrahedron.Usayizi wohlangothi lwangaphambili wezindawo ezimbili zokusebenzelana ezinosayizi we-elementi engu-2.5 × \({10}^{-3}\) m uyakhiwa, futhi usayizi wangaphambili wokuhlanganisa ongu-9 × \({10}^{-3}\ ) m isetshenziswa.I-mesh ekhiqiziwe yokuqala yayihlanganisa izici ze-2144409 (Fig. 3b).
Imodeli yesiphithiphithi ye-k–ε enamapharamitha amabili yakhethwa njengemodeli yesisekelo sokuqala.Ukulingisa ngokunembile ukugeleza okujikelezayo ngaphakathi kwe-flocculator, imodeli ebiza kakhulu ngekhompyutha yakhethwa.Ukugeleza okunyakazayo okunyakazayo ngaphakathi kwe-flocculator kwaphenywa ngezinombolo kusetshenziswa amamodeli amabili e-CFD: SST k–ω51 kanye ne-IDDES52.Imiphumela yawo womabili amamodeli yaqhathaniswa nemiphumela yokuhlola ye-PIV ukuze kuqinisekiswe amamodeli.Okokuqala, imodeli ye-SST k-ω turbulence iyimodeli ye-viscosity enezixazululi ezimbili yezinhlelo zokusebenza ze-fluid dynamics.Lena imodeli eyingxube ehlanganisa amamodeli e-Wilcox k-ω kanye ne-k-ε.Umsebenzi wokuhlanganisa wenza imodeli ye-Wilcox isebenze eduze nodonga kanye nemodeli ye-k-ε ekugelezeni okuzayo.Lokhu kuqinisekisa ukuthi imodeli efanele isetshenziswa kuyo yonke inkambu yokugeleza.Ibikezela ngokunembile ukuhlukana kokugeleza ngenxa ye-gradients yokucindezela okubi.Okwesibili, kukhethwe indlela ye-Advanced Deferred Eddy Simulation (IDDES), esetshenziswa kabanzi kumodeli yomuntu ngamunye ye-Eddy Simulation (DES) enemodeli ye-SST k-ω Rans (Reynolds-Averaged Navier-Stokes) .I-IDDES iyinhlanganisela ye-RANS-LES (i-eddy simulation enkulu) ehlinzeka ngemodeli yokulingisa evumelana nezimo futhi esebenziseka kalula (i-SRS).Isekelwe kumodeli ye-LES yokuxazulula ama-eddies amakhulu futhi ibuyele ku-SST k-ω ukuze ilingise ama-eddies esikali esincane.Ukuhlaziywa kwezibalo kwemiphumela evela ekufanisweni kwe-SST k–ω kanye ne-IDDES kwaqhathaniswa nemiphumela ye-PIV ukuze kuqinisekiswe imodeli.
Imodeli yesiphithiphithi ye-k–ε enamapharamitha amabili yakhethwa njengemodeli yesisekelo sokuqala.Ukulingisa ngokunembile ukugeleza okujikelezayo ngaphakathi kwe-flocculator, imodeli ebiza kakhulu ngekhompyutha yakhethwa.Ukugeleza okunyakazayo okunyakazayo ngaphakathi kwe-flocculator kwaphenywa ngezinombolo kusetshenziswa amamodeli amabili e-CFD: SST k–ω51 kanye ne-IDDES52.Imiphumela yawo womabili amamodeli yaqhathaniswa nemiphumela yokuhlola ye-PIV ukuze kuqinisekiswe amamodeli.Okokuqala, imodeli ye-SST k-ω turbulence iyimodeli ye-viscosity enezixazululi ezimbili yezinhlelo zokusebenza ze-fluid dynamics.Lena imodeli eyingxube ehlanganisa amamodeli e-Wilcox k-ω kanye ne-k-ε.Umsebenzi wokuhlanganisa wenza imodeli ye-Wilcox isebenze eduze nodonga kanye nemodeli ye-k-ε ekugelezeni okuzayo.Lokhu kuqinisekisa ukuthi imodeli efanele isetshenziswa kuyo yonke inkambu yokugeleza.Ibikezela ngokunembile ukuhlukana kokugeleza ngenxa ye-gradients yokucindezela okubi.Okwesibili, kukhethwe indlela ye-Advanced Deferred Eddy Simulation (IDDES), esetshenziswa kabanzi kumodeli yomuntu ngamunye ye-Eddy Simulation (DES) enemodeli ye-SST k-ω Rans (Reynolds-Averaged Navier-Stokes) .I-IDDES iyinhlanganisela ye-RANS-LES (i-eddy simulation enkulu) ehlinzeka ngemodeli yokulingisa evumelana nezimo futhi esebenziseka kalula (i-SRS).Isekelwe kumodeli ye-LES yokuxazulula ama-eddies amakhulu futhi ibuyele ku-SST k-ω ukuze ilingise ama-eddies esikali esincane.Ukuhlaziywa kwezibalo kwemiphumela evela ekufanisweni kwe-SST k–ω kanye ne-IDDES kwaqhathaniswa nemiphumela ye-PIV ukuze kuqinisekiswe imodeli.
Sebenzisa isixazululi sesikhashana esisekelwe kungcindezi futhi usebenzise amandla adonsela phansi esiqondisweni sika-Y.Ukuzungezisa kufinyelelwa ngokunikeza ukunyakaza kwe-mesh kusixhumi, lapho imvelaphi ye-eksisi yokuzungezisa iphakathi nendawo ye-eksisi evundlile futhi isiqondiso se-eksisi ejikelezayo siku-Z.Isixhumi esibonakalayo semeshi sidalelwe zombili izixhumi ezibonakalayo zejometri, okuholela emaphethelweni amabili ebhokisi abophayo.Njengendlela yokuhlola, isivinini sokujikeleza sihambisana nokuphenduka oku-3 no-4.
Izimo zomngcele wezindonga ze-mixer kanye ne-flocculator zibekwe odongeni, futhi ukuvulwa okuphezulu kwe-flocculator kubekwe yi-outlet nge-zero gauge pressure (Fig. 3c).ISIkimu sokuxhumana se-pressure-velocity ESULULA, ukuhlukanisa isikhala segradient semisebenzi ye-oda lesibili nawo wonke amapharamitha asekelwe ezintweni eziyisikwele esincane.Umbandela wokuhlangana wawo wonke okuguquguqukayo okugeleza yinsalela enesilinganiso esingu-1 x \({10}^{-3}\).Inombolo enkulu yokuphindaphinda ngesinyathelo sesikhathi ngasinye ngu-20, futhi usayizi wesinyathelo sesikhathi uhambisana nokuzungezisa okungu-0.5°.Isixazululo siyahlangana ekuphindaphindweni kwesi-8 kumodeli ye-SST k–ω futhi ekuphindaphindweni kwe-12 kusetshenziswa i-IDDES.Ngaphezu kwalokho, inani lezinyathelo zesikhathi libalwe ukuze umxube enze okungenani ama-revolution angu-12.Sebenzisa isampula yedatha yezibalo zesikhathi ngemva kokuzungezisa okungu-3, okuvumela ukujwayela kokugeleza, okufana nenqubo yokuhlola.Ukuqhathanisa okukhiphayo kwezihibe zesivinini ku-revolution ngayinye kunikeza imiphumela efanayo ncamashi yama-revolution amane okugcina, okubonisa ukuthi isimo esizinzile sifinyelelwe.Ama-revs engeziwe awazange athuthukise ijubane elimaphakathi.
Isinyathelo sesikhathi sichazwa maqondana nesivinini sokujikeleza, 3 rpm noma 4 rpm.Isinyathelo sesikhathi sicwengisiswa kuze kufike isikhathi esidingekayo ukuze ujikeleze i-mixer ngo-0.5 °.Lokhu kuvela ukuthi kwanele, njengoba isisombululo sihlangana kalula, njengoba kuchazwe esigabeni esandulele.Ngakho, zonke izibalo zezinombolo zawo womabili amamodeli esiphithiphithi zenziwe kusetshenziswa isinyathelo sesikhathi esilungisiwe sika-0.02 \(\stackrel{\mathrm{-}}{7}\) ngo-3 rpm, 0.0208 \(\stackrel{\mathrm{-} {3}\) 4 rpm.Ngesinyathelo sesikhathi sokwenza ngcono esinikeziwe, inombolo ye-Courant yeseli ihlezi ingaphansi kuka-1.0.
Ukuze uhlole ukuncika kwemodeli ye-mesh, imiphumela iqale yatholwa kusetshenziswa i-2.14M mesh yoqobo kwase kuba i-2.88M mesh ecwengisisiwe.Ukulungiswa kwegridi kufinyelelwa ngokunciphisa usayizi weseli womzimba we-mixer ukusuka ku-9 × \({10}^{-3}\) m ukuya ku-7 × \({10}^{-3}\) m.Kumameshi asekuqaleni nacwengisisiwe amamodeli amabili esiphithiphithi, amanani amaphakathi amamojula wesivinini ezindaweni ezahlukahlukene ezungeze i-blade aqhathaniswe.Umehluko wamaphesenti phakathi kwemiphumela ngu-1.73% wemodeli ye-SST k–ω kanye no-3.51% wemodeli ye-IDDES.I-IDDES ibonisa umehluko wamaphesenti aphezulu ngoba iyimodeli eyingxube ye-RANS-LES.Lo mehluko uthathwe njengokungabalulekile, ngakho-ke ukulingisa kwenziwa kusetshenziswa inetha langempela elinezinto eziyizigidi ezingu-2.14 kanye nesinyathelo sesikhathi sokuzungezisa esingu-0.5°.
Ukukhiqizwa kabusha kwemiphumela yokuhlola kwahlolwa ngokwenza ucwaningo ngalunye kweziyisithupha okwesibili nokuqhathanisa imiphumela.Qhathanisa amanani esivinini maphakathi ne-blade ochungechungeni olubili lokuhlolwa.Umehluko omaphakathi wamaphesenti phakathi kwamaqembu amabili okuhlola wawungu-3.1%.Uhlelo lwe-PIV luphinde lwalinganiswa ngokuzimela ekuhlolweni ngakunye.Qhathanisa isivinini esibalwe ngokuhlaziya phakathi nendawo yeblade ngayinye nesivinini se-PIV endaweni efanayo.Lesi siqhathaniso sibonisa umehluko ngephutha lephesenti eliphezulu elingu-6.5% leblade 1.
Ngaphambi kokulinganisa i-slip factor, kuyadingeka ukuqonda ngokwesayensi umqondo wokushelela ku-flocculator ye-paddle, okudinga ukutadisha ukwakheka kokugeleza okuzungeze ama-paddles we-flocculator.Ngokomqondo, i-slip coefficient yakhelwe ekwakhiweni kwama-paddle flocculators ukuze kubhekwe ijubane lama-blades ahlobene namanzi.Izincwadi zincoma ukuthi leli jubane libe ngu-75% wejubane le-blade, ngakho-ke amadizayini amaningi ngokuvamile asebenzisa u-ak ka-0.25 ukuze aphendule ngalokhu kulungiswa.Lokhu kudinga ukusetshenziswa kwemigqa yesivinini etholwe ekuhlolweni kwe-PIV ukuze kuqondwe ngokugcwele inkambu yesivinini sokugeleza nokufunda lesi siliphu.I-Blade 1 iyinsingo engaphakathi kakhulu eseduze ne-shaft, i-blade 3 iyi-blade engaphandle, kanti i-blade 2 iyinsingo ephakathi.
Imigqa yesivinini ku-blade 1 ibonisa ukugeleza okujikelezayo okuqondile eduze kwe-blade.Lawa maphethini okugeleza aphuma endaweni engakwesokudla kwe-blade, phakathi kwe-rotor ne-blade.Uma ubheka indawo ekhonjiswe ibhokisi elinamachashazi abomvu ku-Figure 4a, kuyathakazelisa ukukhomba enye ingxenye yokugeleza komjikelezo ngenhla kanye nokuzungeza i-blade.Ukubuka okugelezayo kukhombisa ukugeleza okuncane endaweni yokujikeleza kabusha.Lokhu kugeleza kusondela ukusuka kwesokudla se-blade ekuphakameni okungaba ngu-6 cm ukusuka ekugcineni kwe-blade, mhlawumbe ngenxa yethonya le-blade yokuqala yesandla eyandulela i-blade, ebonakalayo esithombeni.Ukubona ngeso lengqondo ukugeleza ku-4 rpm kukhombisa ukuziphatha okufanayo nesakhiwo, ngokusobala ngesivinini esiphezulu.
Inkambu yesivinini kanye namagrafu amanje ama-blades amathathu ngesivinini sokujikeleza okubili kwe-3 rpm kanye ne-4 rpm.Isivinini esiphezulu sesilinganiso sama-blades amathathu ku-3 rpm ngu-0.15 m/s, 0.20 m/s no-0.16 m/s ngokulandelana, kanti isivinini esiphezulu esimaphakathi ku-4 rpm ngu-0.15 m/s, 0.22 m/s no-0.22 m/ s, ngokulandelana.emashidini amathathu.
Olunye uhlobo lokugeleza kwe-helical lutholwe phakathi kwama-vanes 1 no-2. Inkambu ye-vector ibonisa ngokucacile ukuthi ukugeleza kwamanzi kuya phezulu ukusuka phansi kwe-vane 2, njengoba kuboniswa isiqondiso se-vector.Njengoba kuboniswa ibhokisi elinamachashazi ku-Fig. 4b, lawa ma-vector awayi phezulu aqonde phezulu ukusuka endaweni ye-blade, kodwa ajike aye kwesokudla bese ehla kancane kancane.Ebusweni be-blade 1, ama-vectors aphansi ahlukaniswa, asondela kuzo zombili izindwani futhi azungezwe ukusuka ekugelezeni kokujikeleza okwakhiwa phakathi kwawo.Isakhiwo esifanayo sokugeleza sinqunywe kuzo zombili izivinini zokuzungeza nge-amplitude ephakeme yesivinini engu-4 rpm.
Inkambu yesivinini ye-blade 3 ayenzi umnikelo obalulekile kusukela ku-vector yesivinini se-blade yangaphambili ehlanganisa ukugeleza ngezansi kwe-blade 3. Ukugeleza okuyinhloko ngaphansi kwe-blade 3 kungenxa yevector yesivinini esime mpo ekhuphuka namanzi.
Amavetha esivinini phezu kobuso bensingo 3 angahlukaniswa ngamaqembu amathathu, njengoba kuboniswe kumfanekiso 4c.Isethi yokuqala yileyo esemaphethelweni angakwesokudla we-blade.Isakhiwo sokugeleza kule ndawo siqonde kwesokudla naphezulu (okungukuthi sibheke ku-blade 2).Iqembu lesibili liphakathi nendawo.Ivetha yesivinini yalesi sikhundla iqondiswe ngqo phezulu, ngaphandle kokuchezuka futhi ngaphandle kokuzungezisa.Ukwehla kwevelocity kuye kwanqunywa ngokunyuka kobude ngaphezu kokuphela kweblade.Eqenjini lesithathu, elitholakala kwesokunxele se-blades, ukugeleza kuqondiswa ngokushesha ngakwesobunxele, okungukuthi odongeni lwe-flocculator.Ukugeleza okuningi okumelelwe i-velocity vector kuya phezulu, futhi ingxenye yokugeleza iyehla iye ngokuvundlile.
Amamodeli amabili esiphithiphithi, i-SST k–ω ne-IDDES, asetshenziselwa ukwakha amaphrofayili esivinini esilinganiselwe sesikhathi sika-3 rpm no-4 rpm endizeni yobude be-blade.Njengoba kuboniswe kuMdwebo 5, ukuzinza kufinyelelwa ngokufinyelela ukufana okuphelele phakathi kwamakhontowusi esivinini adalwe ngokuzungezisa okune okulandelanayo.Ukwengeza, ama-contours we-velocity wesikhathi esilinganiselwe akhiqizwa yi-IDDES aboniswa ku-Fig. 6a, kuyilapho amaphrofayili esivinini esilinganiselwe akhiqizwa yi-SST k - ω aboniswa ku-Fig. 6a.6b.
Isebenzisa ama-IDDES kanye namalophu esivinini esilinganiso sesikhathi akhiqizwe i-SST k–ω, i-IDDES inengxenye ephezulu yamalophu esivinini.
Hlola ngokucophelela iphrofayili yesivinini edalwe nge-IDDES ngo-3 rpm njengoba kukhonjisiwe kuMfanekiso 7. I-mixer izungeza njengokuya kwewashi futhi ukugeleza kuxoxwa ngokuvumelana namanothi abonisiwe.
Emkhiwaneni.I-7 ingabonakala ukuthi ebusweni be-blade 3 ku-quadrant I-quadrant kukhona ukuhlukaniswa kokugeleza, ngoba ukugeleza akuvinjelwe ngenxa yokuba khona komgodi ongaphezulu.Ku-quadrant II akukho ukuhlukaniswa kokugeleza okubonwayo, ngoba ukugeleza kunqunyelwe ngokuphelele izindonga ze-flocculator.Ku-quadrant III, amanzi ajikeleza ngesivinini esiphansi kakhulu noma esiphansi kunama-quadrants angaphambilini.Amanzi aku-quadrants I no-II ayasuswa (okungukuthi ayaphendukiswa noma aphushwe) aye phansi ngesenzo somxube.Futhi ku-quadrant III, amanzi aphushwa ngaphandle ngama-blades we-agitator.Kusobala ukuthi ubuningi bamanzi kule ndawo bumelana nomkhono we-flocculator osondelayo.Ukugeleza kwe-rotary kule quadrant kuhlukaniswe ngokuphelele.Ku-quadrant IV, ukugeleza komoya okuningi okungaphezulu kwe-vane 3 kuqondiswe odongeni lwe-flocculator futhi kancane kancane kuncipha usayizi wayo njengoba ukuphakama kukhuphukela ekuvulekeni okuphezulu.
Ngaphezu kwalokho, indawo emaphakathi ihlanganisa amaphethini okugeleza ayinkimbinkimbi abusa amaquadrants III kanye ne-IV, njengoba kuboniswa ama-ellipse anamachashazi aluhlaza.Le ndawo ephawuliwe ayihlanganise lutho nokugeleza okujikelezayo ku-flocculator ye-paddle, njengoba ukunyakaza okuzungezayo kungabonakala.Lokhu kuphambene nama-quadrants I no-II lapho kukhona ukuhlukana okucacile phakathi kokugeleza kwangaphakathi nokugeleza okugcwele kokujikeleza.
Njengoba kuboniswe emkhiwaneni.6, uma kuqhathaniswa nemiphumela ye-IDDES ne-SST k-ω, umehluko omkhulu phakathi kwamakhonco esivinini ubukhulu besivinini ngokushesha ngaphansi kwe-blade 3. Imodeli ye-SST k-ω ibonisa ngokucacile ukuthi ukugeleza kwesivinini esiphezulu okunwetshiwe kuthwalwa yi-blade 3 uma kuqhathaniswa ne-IDDES.
Omunye umehluko ungatholakala ku-quadrant III.Kusukela ku-IDDES, njengoba kushiwo ngaphambili, ukuhlukaniswa kokugeleza okujikelezayo phakathi kwezingalo ze-flocculator kwaphawulwa.Kodwa-ke, lesi sikhundla sithinteka kakhulu ukugeleza kwejubane eliphansi kusuka emagumbini nangaphakathi kwe-blade yokuqala.Kusukela ku-SST k–ω endaweni efanayo, imigqa yamakhonco ibonisa isivinini esiphakeme uma kuqhathaniswa ne-IDDES ngenxa yokuthi akukho ukugeleza okuhlanganayo okuvela kwezinye izifunda.
Ukuqonda ikhwalithi yezinkambu zevekhtha yesivinini kanye nemigqaliselo kuyadingeka ukuze kuqondwe kahle ukuziphatha nokugeleza kwesakhiwo.Uma kubhekwa ukuthi i-blade ngayinye inobubanzi obungu-5 cm, amaphuzu esivinini ayisikhombisa akhethiwe kuwo wonke ububanzi ukuze anikeze iphrofayili emele isivinini.Ukwengeza, ukuqonda okulinganiselwe kobukhulu besivinini njengomsebenzi wokuphakama ngaphezu kwendawo ye-blade kuyadingeka ngokuhlela iphrofayili yesivinini ngokuqondile phezu kwendawo ngayinye ye-blade kanye nebanga eliqhubekayo lika-2.5 cm ukuya phezulu lifinyelele ku-10 cm ubude.Bheka i-S1, i-S2 ne-S3 esithombeni ukuze uthole ulwazi olwengeziwe.Isithasiselo A. Umfanekiso we-8 ubonisa ukufana kokusabalalisa kwesivinini esiphezulu se-blade ngayinye (Y = 0.0) etholwe kusetshenziswa izivivinyo ze-PIV kanye nokuhlaziywa kwe-ANSYS-Fluent kusetshenziswa i-IDDES ne-SST k-ω.Womabili amamodeli ezinombolo enza kube nokwenzeka ukulingisa ngokunembile isakhiwo sokugeleza ebusweni bama-flocculator blades.
Ukusabalalisa kwesivinini i-PIV, i-IDDES ne-SST k–ω endaweni ye-blade.I-eksisi ka-x imele ububanzi beshidi ngalinye ngamamilimitha, nomsuka (0 mm) omele umngcele ongakwesokunxele weshidi kanye nesiphetho (50 mm) omele umngcele ongakwesokudla weshidi.
Kubonakala ngokucacile ukuthi ukusabalalisa kwejubane kwama-blades 2 no-3 kuboniswe ku-Fig.8 naku-Fig.8.I-S2 ne-S3 ku-Appendix A ibonisa amathrendi afanayo anobude, kuyilapho i-blade 1 ishintsha ngokuzimela.Amaphrofayili esivinini ama-blades 2 no-3 aqonde ngokuphelele futhi abe ne-amplitude efanayo ekuphakameni okungu-10 cm ukusuka ekugcineni kwensingo.Lokhu kusho ukuthi ukugeleza kuba okufanayo kuleli phuzu.Lokhu kubonakala ngokucacile emiphumeleni ye-PIV, ekhiqizwe kahle yi-IDDES.Ngaleso sikhathi, imiphumela ye-SST k–ω ibonisa umehluko othile, ikakhulukazi ku-4 rpm.
Kubalulekile ukuqaphela ukuthi i-blade 1 igcina isimo esifanayo sephrofayili yesivinini kuzo zonke izikhundla futhi ayijwayelekile ukuphakama, njengoba i-swirl eyakhiwe phakathi nendawo ye-mixer iqukethe i-blade yokuqala yazo zonke izingalo.Futhi, uma kuqhathaniswa ne-IDDES, amaphrofayili esivinini se-PIV blade 2 no-3 abonise amanani esivinini aphakeme kancane ezindaweni eziningi aze acishe alingane ku-10 cm ngaphezu kwendawo yeblade.
Isikhathi sokuthumela: Dec-27-2022