ࡱ>     FV#`j.bjbj\.\. >D>Dl?4GGGhPHJ1L\R@@R@R@RSSS$ϐh7SSSSS@R@R?t?t?tS@R@R?tS?t?tVy@z@RL KG#f 4z ,01@zTݓo$ݓzݓz( S/S?t=S ISXSSSsXSSS1SSSS+1D1  REAKTIVNI PROPULZORI  OSNOVNI POJMOVI I SPOZNAJE REACTIVE PROPULSORS  BASIC CONCEPTS AND COMPREHENSION Miroslav Sambolek, Brodarski institut, Zagreb Sa~etak: U radu se sustavno prikazuje najopenitija teorija reaktivnih propulzora - RP, njihova svojstva, razli ite vrste takvih propulzora i njihovi dijelovi te veli ine o kojima im ovisi stupanj korisnosti. Polazei od najosnovnijih zakona fizike gradi se jednostavni, pregledni/ matemati ki model ovih propulzora, nu~nih za pogonjenje brodova i zrakoplova. Naglaaena je posebnost RP u odnosu na ostale propulzore, koje se radi odreenosti mo~e nazivati aktivnima, te sli nost njihova na ina rada s na inom pretvorbe toplinske energije u mehani ku, koja je opisana Drugim glavnim stavkom termodinamike. Radi jednostavnosti izvoenja i bolje preglednosti promatra se izolirani propulzor. Procijenjeni su raznovrsni gubitci snage, razmotreni su bezdimenzijski parametri koji karakteriziraju optereenje propulzora, te su definirani stupnjevi korisnosti RP. Prikazana je originalna tablica koja sadr~i potpuni sustav relacija va~nih za opisivanje djelovanja RP. Klju ne rije i: propulzori, reaktivna propulzija, Summary: The most general theory of reactive propulsors  RP, their characteristics, various types, principal parts of them and quantities on which their efficiency depends, are rewieved. Starting from elementary physical laws the simple and transparent mathematical model of RP, indispensable in ship's and airplane's propulsion, is constructed. It is pointed out the peculiarity of RP in comparison to other types of propulsors, which in sake of unambiguousness are called active. Some analogy of RP's way of action with the process of transformation of heat energy to mechanical work, as described by Second law of thermodynamics, is accentuated too. For the sake of simplicity of the derivation and clearer insight the isolated RP is considered. The different sources of energy losses are judged, the nondimensional parameters of RP loading are reviewed and efficiencies are defined. There is presented the original table consisting full set of formulas which are necessary to describe the functioning of RP. Key words: propulsor, reactive propulsion, UVOD Ovim se lankom ~eli podsjetiti na neke odavno dobro poznate injenice o teorijama djelovanja propulzora [2], ali uvesti i nove pojmove. Pita li se zaato treba ponovo govoriti o ne emu poznatome, mo~e se odgovoriti da se to, ato je poznato, ~eli prikazati na druga iji, novi na in. Cilj je dati sa~eti, lako razumljivi, i fizi ki o igledni prikaz koji e pomoi da se bolje shvate i do~ive, da postanu bli~i, pojmovi o na inu rada reaktivnih propulzora - RP. No osim toga ovdje se uvode i neke nove funkcije, pojmovi, formule i prikazi, koji se posebno odnose na na in definiranja optereenja propulzora, te na odreivanje stupnja korisnosti. Na po etku evo objaanjenja nekih osnovnih pojmova o reaktivnim propulzorima. Reaktivni propulzori - RP, su nu~ni kada se ~eli na neko tijelo djelovati odreenom silom (naj eae jednakom otporu medija koji ga okru~uje, zrak ili voda, s namjerom da bi se tijelo gibalo jednolikom brzinom), a pri tome se ne mo~e ostvariti mehani ku silu izmeu tijela koje se giba i tijela  to je gotovo uvijek Zemlja  u odnosu na kojega se (ono) giba. Meutim, ako se spomenuta mehani ka sila ipak mo~e ostvariti rabe se aktivni propulzori, primjerice kota  na cesti ili tra nici. Ali, naravno, i vozilima koja se gibaju povrainom drugih nebeskih tijela (Mjesec, Mars) nije nu~na primjena reaktivnih propulzora. Osnovna je zna ajka reaktivnog propulzora da on aktivnom silom djeluje na neku kona nu masu  naj eae fluid kojega uzima iz okoline, odnosno kod raketnih propulzora na masu koja je ukrcana na vozilo  tako da se poriv T, sila kojom propulzor djeluje na tijelo/vozilo na koje je ugraen, ostvaruje kao reaktivna sila ubrzavane mase. Premda se ponekad RP primjenjuju samo zato da se stvori potrebna sila (npr. odsukivanje broda), ipak naj eae propulzor goni/tjera vozilo brzinom VA. Tako RP pri gibanju vrai rad, razvija korisnu snagu poriva PT. Za pogon potrebnu snagu PD propulzor dobiva od pogonskog stroja; prema tome je RP pretvornik (transformator) dovedene snage PD u korisnu snagu PT. Iznimno va~an pokazatelj uspjeanosti RP je stupanj korisnosti O= PT/PD, koji se naziva stupanj korisnosti izoliranog propulzora. Stupanj korisnosti RP se bitno  kvalitativno, a ne samo kvantitativno - razlikuje od stupnja korisnosti mehani kih, aktivnih propulzora, kao, primjerice, ve spomenutog kota a na krutoj podlozi. Razlika je u tome ato je za djelovanje RP nu~no  izgubiti odreenu snagu. Po tome kao pretvornik energije RP pokazuje izvjesnu sli nost s toplinskim strojevima, koji takoer pri pretvorbi toplinske energije u mehani ki rad uvijek moraju neki dio toplinske energije predati toplinskom spremniku ni~e temperature [6].  Slika 1 Prikaz brzina strujanja i poriva na slo~enom RP koji se sastoji od aktivnog dijela 1 i pasivnih dijelova 2; elipsa prikazuje cjelokupni propulzor Fig. 1 Presentation of the flowing velocities and thrust developed on RP consisting of active part 1, and passive parts 2; the ellipse encircles the complete propulsor Ovdje e se govoriti samo o brodskim RP koji ubrzavaju dio vode kroz koju se gibaju, pri emu neki dio mase vode protje e kroz propulzor. RP mogu biti jednostavni, oni imaju samo jedan dio, i slo~eni, koji imaju viae dijelova na kojima se stvara poriv. Na slici 1. shematski je elipsom, koja obuhvaa i aktivne i pasivne dijelove, predo en cjelokupni propulzor. Granice kontrolnog volumena su tako daleko od RP da je svugdje na njima tlak jednak tlaku neporemeene vode. Dijelovi propulzora koji ostvaruju poriv mogu biti aktivni i pasivni. Aktivni su oni koji prenose dovedenu snagu na vodu, oni razvijaju poriv TA, dok se pasivnima ne dovodi snaga, ali strujanje vode i na njima stvara silu uzgona, koja ima neku, od nule razli itu, komponentu u smjeru poriva jednaku TP. Tako za ukupni poriv RP vrijedi: T = TA + TP Obi ni brodski vijak je primjer jednostavnog propulzora, koji ima jedan aktivni dio; vijak u Kortovoj sapnici je slo~eni RP kojemu je aktivni dio vijak, a sapnica pasivni dio; RP kojega ini par suosnih, suprotnovrteih vijaka je slo~eni propulzor koji ima dva aktivna dijela. Vanjsku struju propulzora ini voda koja struji oko ili kroz RP, ali joj se ne mijenja energija, dok je unutarnja struja sastavljena od vode koja je pri strujanju kroz aktivni dio propulzora primila energiju. Dio unutarnje struje iza propulzora zove se mlaz. Gotovo da nema primjera pogonjenja (propulzije) broda gdje su RP i trup broda tako udaljeni, da prakti ki ne postoji njihovo meudjelovanje/interakcija, osim mogue kod izvanbrodskog Z prigona s vrlo dugom  nogom . Ipak, u ovom se radu  radi jednostavnosti i bolje preglednosti  to meudjelovanje zanemaruje, i promatra se izolirani propulzor, ili kako se ka~e propulzor u uvjetima neograni ene vode ( open water condition ). 1. OSNOVNI ZAKONI FIZIKE VA}NI ZA OBJA`NJENJE DJELOVANJA REAKTIVNIH PROPULZORA Osnovne odnose izmeu veli ina va~nih za prou avanje RP mo~e se dobiti primjenjujui neke temeljne prirodne zakone, pri emu e se promatrati zbivanja unutar kontrolnog volumena, dalje KV, omeenog kontrolnim plohama, tj. unutar kona nih kapljevitih ili plinovitih tijela omeenih geometrijskim plohama [3], [4], [9]. Prvo e se primijeniti na elo klasi ne fizike o odr~anju mase. Pretpostavlja se neviskozna tekuina gustoe , i gibanje nekoga openitoga propulzora brzinom VA. Pri tome je jednak (nema ni izvora ni ponora tekuine) protok mase M (kg/sec) kroz sve presjeke unutarnje struje propulzora, brzina struje na ulazu u KV je VA, a na izlazu VA+UA". Izlazni presjek unutarnje struje RP ima ploatinu A", a ulazni A-". Onda se jednad~ba kontinuiteta, jer se vodu smatra nestla ivom mo~e ovako napisati:  EMBED Equation.DSMT4  (1) Na elo o odr~anju energije omoguuje primjenu I. stavka termodinamike na zatvoreni KV koji uklju uje dovoljno veliki volumen vode u okoliau RP kojemu se dobavlja mehani ka snaga PD. Korisna snaga poriva  EMBED Equation.DSMT4  je umno~ak brzine gibanja propulzora VA u odnosu na okolnu vodu i sile poriva T. Ta se snaga, u ovom modelu izoliranoga RP, iznosi iz kontrolnog volumena ili ako se smatra da je pojava stacionarna, onda iz KV mora istjecati energija. Prema tome brzina prirasta energije u KV iznosi P=PD-PT. Openito, bilo kakav RP, a posebno brodski vijak, vodi u KV predaje za poriv ne iskoriatenu snagu P koja mo~e imati mnoge raznolike oblike, od kojih je najva~nija kineti ka energija translacije mlaza. Brzina translacije mlaza openito nije svugdje jednaka, ali e se nadalje, opet radi jednostavnosti, pretpostavljati stalnom, nepromjenljivom po presijeku. Za razliku od drugih oblika gibanja vode iza RP ovo je gibanje nu~no za stvaranje poriva, pa se ni u jednom modelu RP, bez obzira koliko je pojednostavljen, ne smije zanemariti. Snaga gubitaka uslijed kineti ke energije translacije mlaza ozna uje se PAL, pri emu se indeks odnosi na engleski  axial loss , a iznosi:  EMBED Equation.DSMT4  (2) Ukupno dovedena mehani ka snaga PD vea je od snage PJ = PT + PAL koju bi trebalo dovesti RP, a koja se zove snaga mlaza, kada bi postojali samo nu~ni gubitci. Brodski vijak, kao jednostavni propulzor, uvijek stvara i kineti ku energiju rotacije mlaza, jednaku PRL ( rotational loss ). Taj se gubitak, u slo~enom RP koji uz vijak ima i statorsko kolo, mo~e barem djelomi no iskoristiti, pri emu treba napomenuti da postojanje rotacijskog gubitka nije nu~no za djelovanje RP. Nadalje se u KV susree gubitak snage, koji je ovdje uvjetno nazvan ireverzibilnim gubitkom PIL, koji se sastoji od a)kineti ke energije kaoti nog, turbulentnog gibanja PTL i b)mehani ke snage pretvorene u toplinu, disipacije mehani ke energije PDL, tako da je PIL=PTL+PDL. Mogue nije na odmet objasniti razlog zbog kojih je autor ubrojio i gubitke uslijed turbulentnosti strujanja u ireverzibilne gubitke, kojima  naravno - po svojem termodinami kom karakteru disipacija imanentno pripada. Dobro je poznata  kaskada postupnog smanjivanja na po etku velikih vrtloga u turbulentnom strujanju, prema sve manjima i manjima, dok se u kona nici turbulentnost ne svede na gibanje molekula, ato je, naravno, toplinski gubitak, tj. poveanje unutarnje energije tekuine. Ako si dopustimo izlet u podru je znanstvene fantastike mogli bi zamisliti kako bi se u nekim drugim mjerilima linearnih dimenzija i vremena - neka siuana razumna bia, koja mnogo br~e ~ive - moglo iskoristiti neki vrlo mali, kratkovje ni vrtlog, kao ato vjetrenja ama iskoriatavamo vjetar, vrtlo~no strujanje velikih atmosferskih vrtloga. Sada se mo~e pisati zakon odr~anja energije, odnosno  u uvjetima ustaljenog strujanja - snage:  EMBED Equation.DSMT4  (3) Pokusom se snaga PD dade lako odrediti, ne samo na modelu, ve i na brodu, dok je snagu PT na vijku u naravi, za razliku od modela teako odrediti jer je poriv veli ina koju nije jednostavno mjeriti. 2. NA ELO ODR}ANJA KOLI INE GIBANJA Kombinacija Drugoga i Treega Newtonovog zakona izra~ena u obliku u kojemu se mo~e zgodno primijeniti na strujanje fluida naziva se stavak o impulsu, ili integralni Eulerov teorem, koji je izveden iz na ela odr~anja koli ine gibanja. Za primjenu ovoga teorema potrebno je prikladno definirati kontrolni volumen KV; uzevai da je on tako velik da su tlakovi na zatvorenoj plohi koja ga obuhvaa svugdje jednaki i ograni ivai se samo na komponente sila u pravcu gibanja propulzora dobiva se slijedei izraz u kojemu je poriv izra~en pomou veli ina u beskona no udaljenom presjeku mlaza odnosno veli ina na disku:  EMBED Equation.DSMT4  (4) Va~no je naglasiti da napisana formula vrijedi kako za jednostavni, tako i za slo~eni propulzor, pri emu se poriv stvara na svim dijelovima slo~enog propulzora. Meutim, na jednostavnom propulzoru, koji se zamialja u obliku propulzorskog diska, itav poriv T djeluje samo na disk, pa se sila poriva mo~e dobiti pomou razlike tlakova na stra~njoj p2 i prednjoj strani p1 diska, a koje se odreuje dvokratnom primjenom Bernoullijevog teorema (integrala ili jednad~be).  EMBED Equation.DSMT4  (5) I Bernoullijev je teorem izveden iz zakona o o uvanju koli ine gibanja, pa je va~no da se ne primjenjuje na isti dio strujanja kao i Eulerov teorem, tj. od jedne do druge beskona nosti, ve od diska do pozitivne, odnosno drugi puta do negativne beskona nosti. Naime, uzastopna uporaba u biti iste zakonitosti, ali razli ito izra~ene ne mo~e dovesti do dobro definiranog modela  jedna jednad~ba nedostaje. Usporedba dva izraza za poriv, (4) i (5) pokazuje da je u primjeru jednostavnog RP brzina strujanja kroz disk jednaka  EMBED Equation.DSMT4 , ato zna i da je aksijalna komponenta na disku inducirane brzine jednaka polovini brzine inducirane u beskona no dalekom presjeku mlaza. To je sadr~aj u teoriji RP esto primjenjivanog teorema Froudea - Finsterwaldera, [1] i [2]. 3. RAZNI NA INI DEFINIRANJA OPTEREENJA PROPULZORA Stupanj korisnosti propulzora, o kojem e se joa govoriti, ponajprije i prete~ito ovisi o njegovu optereenju. Pored uobi ajenog i openito primjenjivanog koeficijenta optereenja vijke porivom,  EMBED Equation.DSMT4 , ovdje se spominju i neki drugi koeficijenti optereenja; radi se o optereenju momentom i snagom, te o druga ijem na inu definiranja koeficijenta, tj. obzirom na  EMBED Equation.DSMT4  ploatinu beskona no dalekog presjeka mlaza. To je va~no da bi se moglo prou avati i druge tipove propulzora, a ne samo slobodne vijke, osobito da bi se moglo usporeivati vijke s mlaznim propulzorima. Optereenje RP odreuje gornju granicu stupnja korisnosti propulzora O, koju nikada nije mogue prijei, a mo~e se definirati na viae na ina. Vrlo jednostavan, ali fizi ki vrlo utemeljen i razumljiv parametar optereenja je omjer/kvocijent aksijalne komponente inducirane brzine u mlazu u beskona noj udaljenosti iza propulzora i brzine dostrujavanja:  EMBED Equation.DSMT4 . (6) Slijedea, dobro poznata mogunost definiranja optereenja je pomou koeficijenta optereenja porivom; pri tome se mo~e kao karakteristi nu ploatinu uzeti hidrauli ka ploatina RP, a to je ploatina aktivnog dijela propulzora, pa se dobiva:  EMBED Equation.DSMT4 , (7) gdje je za obi ni brodski vijak  EMBED Equation.DSf d f >`ͻ߬ߚ߈߈߈vvvvd]V hh9 hhFKK"hhW0J5OJQJ\^J"hhR0J5OJQJ\^J"hh\0J5OJQJ\^J"hhR-0J5OJQJ\^Jhnw0J5OJQJ\^J"hhQC0J5OJQJ\^J"hhFKK0J5OJQJ\^J"hh90J5OJQJ\^Jh(Q0J5OJQJ\^Jf0 2 D  ~ #**~- $xa$gd({/ $xa$gdxgd=Zxgd=Z $xa$gd=Z-h.dlerst9?ON_bʸʸʦʦpppppp"hhR0J5OJQJ\^J"hhPC\0J5OJQJ\^J"hh50J5OJQJ\^J"hh0J5OJQJ\^J"hh70J5OJQJ\^J"hhR-0J5OJQJ\^J"hhFKK0J5OJQJ\^J"hhc$0J5OJQJ\^J%24LNbd$24D .ʸʸʸʸvvc%hhW0J56OJQJ\^Jh90J5OJQJ\^J"hhW0J5OJQJ\^J"hhPv0J5OJQJ\^JhYg0J5OJQJ\^J"hh_0J5OJQJ\^J"hh#\0J5OJQJ\^J"hhc$0J5OJQJ\^J"hh90J5OJQJ\^J".0Fr 0~ "@rtܸܦܦܦp^p^Kp%hhD0J56OJQJ\^J"hhT0J5OJQJ\^J"hhD0J5OJQJ\^J"hhhf0J5OJQJ\^J"hh/0J5OJQJ\^J"hhPv0J5OJQJ\^J"hh_Ge0J5OJQJ\^J"hh)L0J5OJQJ\^J"hh_0J5OJQJ\^J"hh$:30J5OJQJ\^J$:NZn FHT\^dfrt"ʷܥܥo\%hh;j0J56OJQJ\^J"hh$:30J5OJQJ\^J"hhUy0J5OJQJ\^J"hh;j0J5OJQJ\^J"hh)L0J5OJQJ\^J%hhT0J56OJQJ\^J"hhT0J5OJQJ\^J"hhD0J5OJQJ\^J"hhr0J5OJQJ\^J$"LNvx ! !!,!!""""" 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hhl\5CJOJQJUV\^JaJ+jhhl\0J5OJQJU\^J"hh`r0J5OJQJ\^J"hhl\0J5OJQJ\^J"hh0J5OJQJ\^J"hh_0J5OJQJ\^J"hhl\0J5OJQJ\^J"hh 0J5OJQJ\^J"hh(I0J5OJQJ\^J"hhv0J5OJQJ\^JdgjjRkrVs:uuDd >0V $xa$gdsxgds $xa$gd=Z $xa$gdJ $xa$gdAxgd=Zxgdiii|iiiijjjjjRkllѿ|jZH2+jhh`r0J5OJQJU\^J"hhYF0J5OJQJ\^JhhA0JOJQJ\^J"hh_0J5OJQJ\^JhYg0J5OJQJ\^J%hhF0J56OJQJ\^Jhk20J5OJQJ\^J"hhF0J5OJQJ\^J"hhl\0J5OJQJ\^J+jhhl\0J5OJQJU\^J/jw2hhl\0J5EHOJQJU\^Jlm m mmmmn6n:nBnXnZnnnnnn p"p8p>pӻkP8k/j8hh*&0J5EHOJQJU\^J5jG hh*&5CJOJQJUV\^JaJ+jhh*&0J5OJQJU\^J"hh*&0J5OJQJ\^J"hhYF0J5OJQJ\^J+jhh`r0J5OJQJU\^J/j6hh`r0J5EHOJQJU\^J5j0G hh`r5CJOJQJUV\^JaJ"hh`r0J5OJQJ\^J>p@pPppppppppppqqrrrrss s"s&sVsZsܶ܏y^Fy/j;hhYF0J5EHOJQJU\^J5jKG hhYF5CJOJQJUV\^JaJ+jhhYF0J5OJQJU\^J"hh{=0J5OJQJ\^J(hh*&0J56H*OJQJ\^J%hh*&0J56OJQJ\^J%hhYF0J56OJQJ\^J"hh*&0J5OJQJ\^J"hhYF0J5OJQJ\^JZs\ss"t>t@t:u*OJQJ\^JMT4 . Ako se pak uzme ploatina presjeka mlaza u beskona nosti A", ato je vrlo pogodno ako se ~eli usporediti vijke s mlaznim propulzorima, jer je A" vrlo pribli~no jednak ploatini sapnice mlaznog propulzora, dolazi se do slijedeega izraza, koji nije obuhvaen popisom simbola ITTC-a:  EMBED Equation.DSMT4  (8) Manje se susree, ali je uklju ena u popisu simbola ITTC-a, veli ina zvana koeficijent optereenja snagom:  EMBED Equation.DSMT4 . (9) Modificirani koeficijent optereenja vijka snagom, izra~en pomou ploatine presjeka mlaza u beskona nosti, definiran je ovako:  EMBED Equation.DSMT4  (10) U Tablici 1 sustavno su prikazani svi ovdje spomenuti bezdimenzijski parametri kojima se izra~ava optereenje reaktivnih propulzora, kao i formule pomou kojih se od jednoga poznatog parametra mo~e doi do drugih, tra~enih. 4. STUPNJEVI KORISNOSTI REKTIVNOG PROPULZORA U stvarnim uvjetima propulzoru se isporu uje dovedena snaga PD, dok bi isti propulzor u uvjetima kada nema drugih gubitaka osim neizbje~ivih, troaio manju snagu koja se naziva snaga mlaza i ozna ena je simbolom PJ. Snaga mlaza jednaka je zbroju korisne snage poriva PT i neizbje~ive snage gubitaka PAL uslijed kineti ke energije mlaza.  EMBED Equation.DSMT4 . (11) Treba razlikovati idealni stupanj korisnosti propulzora, kojega nazivaju i stupanj korisnosti mlaza  EMBED Equation.DSMT4 , (12) od realnog stupnja korisnosti O izoliranoga propulzora kod kojega se povrh neizbje~ivog gubitka kineti ke energije aksijalne brzine mlaza PAL, pojavljuju i svi ostali razni gubitci. Taj se realni stupanj korisnosti mo~e u obliku umnoaka ovako prikazati:  EMBED Equation.DSMT4 . (13) Omjer snage mlaza i RP dovedene snage naziva se hidrauli ki stupanj korisnosti  EMBED Equation.DSMT4 . (14) Stupanj korisnosti izoliranog propulzora je stvarna, izmjeriva fizi ka veli ina, koju se mo~e razmjerno lako odrediti pokusom slobodne vo~nje modela propulzora u bazenu. Za razliku od njega, nedosti~an idealni stupanj korisnosti mlaza  EMBED Equation.DSMT4  je veli ina koju treba procijeniti, u okviru neke teorije, odnosno nekog matemati kog modela RP, tako da se predvidi gubitak snage PAL. Kao ato je ve uvodno spomenuto, stupanj korisnosti RP se bitno, kvalitativno, razlikuje od stupnja korisnosti aktivnih mehani kih propulzora, kao npr., kota a lokomotive ili dizalice na tra nicama, odnosno automobilskog pneumatika na asfaltu. Ta bitna razlika u odnosu na aktivni propulzor sastoji se u tome ato je za djelovanje RP nu~no  izgubiti odreeni dio snage dovedene RP. Po tome kao pretvornik energije RP pokazuje izvjesnu sli nost s toplinskim strojevima, koji takoer pri pretvorbi toplinske energije u mehani ki rad uvijek moraju neki dio toplinske energije predati toplinskom spremniku ni~e temperature. Na Slici 2 geometrijski je pokazana ovisnost stupnja korisnosti mlaza, definiranog jednad~bom (12), pri emu je koriatena u Tablici 1 dana ovisnost stupnja korisnosti mlaza TJ o  EMBED Equation.DSMT4 ; arafirani pravokutnici predo uju isti poriv T koji se zahtijeva od RP; stupanj korisnosti je jednak kvocijentu ploatine praznoga pravokutnika i dvostruko obrubljenoga pravokutnika  Slika 2 Slikovni prikaz ovisnosti stupnja korisnosti mlaza TJ o protoku mase M, koji je, pri istoj brzini pritjecanja VA, razmjeran ploatini hidrauli kog presjeka propulzora A0. Figure 2 Graphical presentation of the dependence of the jet efficiency TJ on mass flow M, which is at same inflow velocity VA, proportional to the area of RP hydraulic section A0. 5. VEZA IZMEU KARAKTERISTI NIH PARAMETARA REAKTIVNIH PROPULZORA Ovdje e se prikazati neke esto koriatene relacije koje se primjenjuju kako bi se predvidio stupanj korisnosti RP kada je poznat samo vrlo ograni eni broj podataka. Dobro je poznata i esto koriatena formula Rusa Vet inkina [1], koja izra~ava idealni stupanj korisnosti vij anog propulzora pomou koeficijenta optereenja vijka porivom (7), a glasi:  EMBED Equation.DSMT4 . (15) I pomou koeficijenta optereenja propulzora snagom koji je dan izrazom (9) mo~e se izra unati idealni stupanj korisnosti; ova nova formula, koja se mo~e smatrati pandanom ranije napisane formule Vet inkina, ali je bitno slo~enijeg oblika, glasi:  EMBED Equation.DSMT4 . (16) Zbog svoje glomaznosti nije prikladna za neposredno izra unavanje, ali se mo~e ucrtati u dijagram. Prednost joj je ato se u nekoj ranijoj fazi osnivanja broda ve pribli~no poznaje snaga i brzina broda, tako da je CP mogue izra unati. Pomou koeficijenta optereenja vijka porivom, svedenoga na ploatinu presjeka mlaza u beskona noj udaljenosti od RP, formula (8), mo~e se prora unati idealni stupanj korisnosti ovom vrlo jednostavnom formulom:  EMBED Equation.DSMT4 . (17) Ovaj je izraz uobi ajen pri promatranju mlaznog propulzora, gdje se naziva koeficijent korisnosti mlaza, [8]. Kod mlaznog propulzora ploatina presjeka mlaza u beskona nosti prakti ki je jednaka ploatini izlaznog presjeka sapnice. Razlika je samo u koeficijentu kontrakcije, koji je kod dobro izvedenih sapnica gotovo jednak jedan. Kako za izolirani vijak (ne vijak u sapnici) vrijedi poznati teorem Froudea-Finsterwaldera, to se odnos meu ploatinama A0 i A" mo~e izraziti pomou omjera brzina, formula (6) A" = A0 (2+)/(2+2). (18) Sve funkcijske ovisnosti izmeu pojedinih ovdje promatranih bezdimenzijskih veli ina prikazane su u eksplicitnom obliku u Tablici 1, odnosno one, koje tra~e du~e izraze, na posebnom popisu. OVO JE MJESTO TABLICE, A ODMAH IZA NJE DOLAZE FORMULE KOJE NE STAJU U POLJA TABLICE Radi zornijeg shvaanja odnosa definiranih formulama u Tablici, nacrtano je viae dijagrama, koji prikazuju neke od va~nijih funkcijskih veza. Tako je u obliku dijagrama prikazana je ovisnost razli ito definiranih optereenja RP te (idealnog) stupnja korisnosti mlaza TJ o  - omjeru prirasta brzine i brzine dostrujavanja vode, Slika 3.  Slika 3 Ovisnost na razli ite na ine definiranoga koeficijenta optereenja i deseterostruke vrijednosti stupnja korisnosti TJ o relativnom prirastu brzine u beskona no dalekom presjeku mlaza RP Figure 3 Dependance of differently defined loading coefficients and tenfold value of efficiency TJ on relative increase of water flow velocity in infinitely distant section of RP jet Radi boljega uvida u odnose izmeu razno definiranih stupnjeva korisnosti Wageningenskih vijaka [5] pokazana je slika 4, koja se odnosi na vijak WB5.70 s omjerom uspona P/D=1.  Slika 4 Ovisnost stupnjeva korisnosti izoliranog vijka WB5.70 s P/D=1 o koeficijentu napredovanja J; stvarni (pokusom odreeni) stupanj korisnosti O, stupanj korisnosti mlaza TJ, (nekada nazivan idealni, teorijski) i hidrauli ki stupanj korisnosti JP Figure 4 Dependance of efficiencies of the propeller WB5.70, P/D=1 on advance coefficient J; (1) - open water efficiency (experimentaly determined) O, (2)- jet efficiency (formerly ideal efficiency) TJ and (3) - hydraulic efficiency JP Budui da se esto ve u ranoj fazi osnivanja broda poznaje snaga pogonskog stroja, brzina broda i koeficijent sustrujanja te promjer vijka, to se mo~e izra unati koeficijent optereenja snagom CP, kojega je definicija napisana u Tablici 1, a potom je jednostavno odrediti i idealni stupanj korisnosti TJ. Za vijke raznovrsne geometrije ispitane u Wageningenu pomou tamo dobivenih regresijskih formula izra unate su vrijednosti O stupnja korisnosti u uvjetima slobodne vo~nje i te su u obliku snopa krivulja, skupa s idealnim stupnjem korisnosti TJ nacrtane u dijagramu na Slici 5. Lako je uo iti da je razlika izmeu najveih u praksi postizivih vrijednosti O i apsolutno najvee, na elno mogue vrijednosti TJ gotovo neovisna o optereenju vijka i da iznosi oko 0,125.  Slika 5 Dijagram ovisnosti stupnjeva korisnosti o koeficijentu optereenja propulzora snagom CP. Na vrhu je krivulja TJ, a ispod je snop krivulja koje odgovaraju stupnjevima korisnosti O za razne vrijednosti koeficijenta napredovanja J (od 0.4 do 1.0) Wageningenskih vijaka serija WB.3.35, WB.5.70 i WB.7.90 Figure 5 Graphical representation of differently defined efficiencies on power loading coefficient CP. On the top is JT, and below it is a bundle of curves coresponding to open water efficiencies O for different advance coefficients J of Wageningen propeller series WB.3.35, WB.5.70 and WB.7.90 Tablica 1 Funkcijske ovisnosti meu promatranim bezdimenzijskim veli inama Table 1 Functional relationship between relevant nondimensional quantities  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 EMBED Equation.DSMT4 CT"(CP") EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 Formule za Tablicu 1.  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4   EMBED Equation.DSMT4  ZAKLJU AK Izrazi dobiveni pomou osnovnih i najopenitijih fizi kih zakona, ne samo ato omoguuju shvaanje i razumijevanje, moglo bi se rei dobivanje osjeaja za sve ato se zbiva pri radu reaktivnih propulzora, ve daju i praksi korisne upute za svrsishodno projektiranje brodskih vijaka, kao i procjenu njihovog o ekivanog stupnja korisnosti. LITERATURA ARTJU`KOV, L. S., A KINADZE, A. `., RUSECKIJ, A. A., "Sudovye dvi~iteli", Sudostroenie, Leningrad, 1988. BASIN, A. M., MINIOVI , I. JA., "Teorija i ras et grebnyh vintov", Sudostroenie, Leningrad, 1963. BI 13 252 FANCEV, M.,  Mehanika fluida , posebni otisak iz Tehni ke enciklopedije JLZ, Zagreb, 1982. FEDJAEVSKIJ, K.K, VOJTKUNSKIJ, JA.I., FADDEEV, JU.I., "Gidromehanika", Sudostroenie, Leningrad, 1968. BI 2 205 ITTC 23rd QUALITY SYSTEMS GROUP,  International Towing Tank Conference  ITTC Symbols and Terminology List, Version 2002, 02 July 2002. LAMMEREN, W. P. A. van, TROOST, L., KONING, J. G.,  Resistance, Propulsion and Steering of Ships , Haarlem, Holland, 1948. SAMBOLEK, M., "Noviji razvoj brodskih propulzora", Zbornik radova IX. simpozija "Teorija i praksa brodogradnje" odr~anog u Dubrovniku 1990. SAMBOLEK, M., "O stupnju djelovanja propulzora", Zbornik radova III. simpozija "Teorija i praksa brodogradnje" odr~anog u Zagrebu 1978. SAMBOLEK, M., "On Jet propulsion Efficiency , Brodogradnja 45 (1997) 2, pp. 133/135 `A`IN, V. M., Gidromehanika, Vysaaja akola, Moskva, 1990. Popis upotrebljenih simbola A -"Ploatina presjeka unutarnje struje beskona no daleko ispred propulzoram2A0Ploatina presjeka aktivnog dijela RP; ploatina unutarnje struje na prolazu kroz propulzor m2A"Ploatina presjeka unutarnje struje beskona no daleko iza propulzoram2CPkoeficijent optereenja snagom1CP"koeficijent optereenja snagom definiran pomou ploatine mlaza A"CThkoeficijent optereenja porivom1CT"koeficijent optereenja porivom definiran pomou ploatine mlaza A"Mprotok masekg/sp"tlak u neporemeenoj beskona no rasprostrtoj tekuiniPaPALsnaga gubitaka kineti ke energije uslijed aksijalne brzine (translacije) mlazaWPDpropulzoru predana mehani ka snagakWPDLsnaga gubitaka uslijed disipacije mehani ke energije mlazaWPILsnaga gubitaka WPJsnaga mlazaWPRLsnaga gubitaka kineti ke energije rotacije mlazaWPTkorisna snaga porivakWPTLsnaga gubitaka uslijed turbulentnog gibanja tekuine/vode u mlazuWTukupni poriv reaktivnog propulzoraNTASuma poriva aktivnih dijelova RPNTPSuma poriva pasivnih dijelova 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