Strojni{ki vestnik 48(2002)10, Journal of Mechanical Engineering 48(2002)10, ISSN ISSN UDK : :621

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1 Strojni{ki vestnik 48(2002)10, Journal of Mechanical Engineering 48(2002)10, ISSN ISSN UDK : : UDC : : Mrki} Pregleni M.: znanstveni Analiza arametrov ~lanek (1.02) reverzibilne - An Anlysis of the Parameters Preview of Reversible scientific aer (1.02) Analiza arametrov reverzibilne ~ralne francisove turbine An Analysis of the Parameters of Reversible Francis-Tye Pum Turbines Milo Mrki} Pri rojektiranju reverzibilnih hidroelektrarn (RE) mora imeti rojektant na voljo èim bolj odrobne odatke o arametrih hidravliènih strojev, ki bodo v hidroelektrarno vgrajeni. Ta ogoj je še osebej omemben, kadar gre za reverzibilne èralno-turbinske agregate, saj morajo le-ti otimalno ustrezati režimu obratovanja v obeh smereh retoka (èralni in turbinski režim), da bi bila lahko vgrajena moè agregata otimalno izrabljena, tako ri olnjenju kakor tudi ri raznjenju zgornje akumulacije, in to v skladu z zahtevami elektroenergetskega sistema. Ko se rojektant loti rojektiranja RE, izbere o nomenklaturi ustrezen ti turbine, otem a uoštevajoè slošne karakteristike in nomenklaturne diagrame doloèa osnovne arametre reverzibilne èralke turbine (). Glede na to, da je nomenklatura omanjkljiva in da obstajajo slošne karakteristike samo za omejeno število tiov, je rimerno v zaèetni fazi rojekta najrej definirati osnovne arametre, v rvem koraku na temelju secifiène vrtilne frekvence. V risevku je odanih nekaj rezultatov študij razoložljive tehniène literature kakor tudi rezultatov teoretiènega dela, modelnih reiskav in reiskav v dejanskih razmerah, ki so bile ob sodelovanju avtorja risevka oravljene na Katedri za izkorišèanje vodnih virov v Moskvi (Inštitut MISI) Strojniški vestnik. Vse ravice ridržane. (Kljuène besede: rojektiranje hidroelektrarn, turbine francis, èralke reverzibilne, analize arameterske) When designing uming reservoir hydroelectric ower stations the designer must have available detailed data on the arameters of the hydraulic machines that will be installed in the ower lant. This is articularly imortant when reversible uming-turbine units are installed, since they must best suit the working mode in both directions of the flow (uming and turbine mode) so that the installed ower of the unit is best utilized in the case of filling as well as emtying the ustream reservoir in accordance with the requirements of the ublic electric ower system. When the lanning engineer starts to roject, according to the nomenclature he chooses the aroriate tye of turbine and then determines the basic arameters for the reversible um-turbine () by using universal characteristics or grahical nomenclature. Since the nomenclature still does not exist and the universal characteristics only exist for a limited number of tyes it is aroriate at the initial stage of the design to define the basic arameters of the, initially according to the secific number of revolutions. In the work in this context some results of the study of available technical literature as well as the results of theoretical works are given. The results of model researches and researches in real conditions which were erformed in exloitation of water ower university deartment in Moscow (institute MISI), with articiation of the author are also resented Journal of Mechanical Engineering. All rights reserved. (Keywords: hydroelectric ower stations, Francis turbines, reversible um turbines, arameter analysis) 1 OSNOVNE KARAKTERISTIKE DELOVNEGA PROCESA Reverzibilni hidravlièni stroj francisovega tia ima znaèilnosti, ki se kažejo ri razliki njihovih osnovnih geometrijskih arametrov in obratovalnih karakteristik glede na klasiène èralke in turbine. 1 BASIC CARACTERISTICS OF WORKING PROCESS TEORY A reversible hydraulic machine of the Francis tye has some secific features whose basic geometrical arameters and oerating characteristics differ from the conventional um and turbine. stran 528

2 st P MG Sl. 1. Shema reverzibilne hidroelektrarne Fig. 1. Working lan of the reversible hydro ower station Predvsem je treba vedeti, da sta adec vode reverzibilne hidroelektrarne (RE) v turbinskem režimu ( t ) in višina RE v èralnem režimu ( ) razlièna (sl. 1). V turbinskem režimu je adec vode doloèen kot: In articualr, it is necessary to realise that the fall of the reversible hydroelectric ower lant in the turbine working mode ( t ) and the head in the um working ( ) mode are different (Fig. 1). In the turbine working mode the fall is defined as follows. t st -ht (1), v èralnem režimu a višina kot: and the head in the um working mode is defined as: st + h (2), ri èemer so: where: st - hidrostatièni adec vode (višina) st is the water head h t, h - hidravliène izgube. idravliène izgube ri turbinskem obratovanju (h t ) niso enake izgubam v èralnem režimu (h ) obratovanja, ker sta retoka v enem in drugem režimu v osnovi razlièna in ker tudi koeficienti lokalnih izgub v dovodnem in odvodnem sistemu niso enaki v turbinski in èralni smeri retoka vode (sl. 3). Eulerjeva enaèba za hidravlièni reverzibilni stroj ima obliko: - za turbinski režim h t, h are the hydraulic losses The hydraulic losses during turbine oeration (h t ) are not the same as the losses in the um working mode (h ) because in rincile the two flows in the first and second modes are different, and also because the coefficients of the local losses in the conduit and in the outflow system are not identical in the turbine direction and in the um direction of the water flow (Fig. 3). Euler s equation for a reversible hydraulic machine has the following form: - for the turbine working mode u1 c0 cos a0 - u2 c3 cos a w 3 t( G-G 1 2) DG t wt ht g t 2ð g t 2ð g t (3), - za èralni režim - for the um working mode g 2 ð g 2 ð g h u1 c0 cos a0 - u2 c3 cos a3 w( G1-G2) DG w (4), ri èemer je: where: G 2ð r cu - obtok (cirkulacija), G 2ð r cu is the circulation ð n w - kotna hitrost. 30 Indeks 1 se nanaša na vhod v delovno kolo, indeks 2 a na izhod iz delovnega kolesa v turbinskem režimu. Ustrezajoèi trikotniki hitrosti za ð n w is the angular seed 30 The index 1 refers to the inlet to the working wheel and the index 2 refers to the outlet from the working wheel in the turbine working mode. Figure 1 stran 529

3 èralni in turbinski režim so rikazani na sliki 2. Èrte vhodnih (0-0) in izhodnih (3-3) ovršin delovnega odroèja kolesa so glede na èrte vhodnih (1-1) in izhodnih (2-2) robov loatic omaknjene, da bi se izognili vlivu konènega števila loatic na retok vhodnih in izhodnih rerezov (sl. 2.). shows the relevant triangles of the seeds in the um and turbine working modes. The contours of the inut (0-0) and oututs (3-3) working area surfaces are shifted with resect to the contours of the inut (1-1) and outut (2-2) edges of the moving blades to avoid influence at definitive numbers of blades on the flow in inut and outut cross sections (Fig. 2.). èralni režim um regime turbinski režim turbine regime Sl. 2. Osnovni geometrijski arametri francisovega tia in trikotniki hitrosti v èralnem in turbinskem režimu Fig. 2. Basic geometrical arameters of the reversible um - turbine of Francis tye and triangles of seeds in the um and turbine working modes Èe veljemo oznaki: G-G 1 2 DG oziroma G -G DG, dobita enaèbi (3) in (4) obliko: 1 2 If the terms G-G 1 2 DG and G1-G 2 DG are introduced, equations (3) and (4) assume the following form : oziroma razmerje: Èe redostavimo, da so izgube višine v turbinskem in èralnem režimu enake in znašajo h t h 0,05 st, otem je skladno z (1) in (2): DG t wt 2ð g t ht 2 ð g DG w h and/or the ratio : DG w DG w h h t t t t 0,95 ; 1,05 t st st (3') (4') (5). If it is assumed that the head losses in the turbine and the um working modes are identical and amount to h t h 0.05 st, the following alies in accordance with (1) and (2): stran 530

4 2 ODVISNOST OSNOVNI PARAMETROV OD SPECIFIÈNE VRTILNE FREKVENCE 2 DEPENDENCE OF BASIC PARAMETERS ON SPECIFIC NUMBER OF REVOLUTIONS Glede na to, da v obratovanjih RE ni mogoèe doseèi enako velike stonje izkoristka, je ugodneje imeti veèjo stonjo izkoristka v turbinskem režimu obratovanja kakor v èralnem režimu (sl. 3), saj je cena vršne elektriène energije nekajkrat veèja od cene elektriène energije v obdobjih najmanjše obremenitve elektroenergetskega sistema (sl. 4). Predostavimo, da sta h t 0, 93 in h 0, 90, ti dve vrednosti vstavimo v enaèbo (5), dobimo: Na odlagi analize (5 ) lahko ovzamemo, da moramo ri definiranju obratovalnih karakteristik reverzibilne èralne turbine uoštevati naslednji redostavki: 1. Èe redostavimo, da je razlika obtoka (cirkulacije) na vstou in izstou iz delovnega kolesa v turbinskem in èralnem režimu enaka, to je D G D Gt, otem mora biti vrtilna frekvenca v èralnem režimu veèje od vrtilne frekvence v turbinskem režimu ( 1, 3 wt). V raksi omeni to uorabo dvohitrostnih generatorjev (MG), ki imajo dve vrtilni frekvenci, vendar v nasrotnih smereh. Pri tem je treba ri rehodu iz enega v drugi režim obratovanja zamenjati število arov olov, ki so trenutno v obratovanju. Pomanjkljivost te rešitve je, da se cena generatorja, elektriènih aaratov, sistema avtomatike in zašèite v tem rimeru oveèa za 25 do 30 % ob hkratnem zmanjšanju stonje izkoristka generatorja (sl. 1). 2. V rimeru enake vrtilne frekvence ( w wt) je treba zagotoviti ogoj D 1, 3 D Gt. To je mogoèe doseèi samo s redostavko, da je remer delovnega kolesa v èralnem režimu veèji od remera delovnega kolesa v turbinskem režimu. Za rešitev tega roblema je uorabljenih veè konstrukcijskih rešitev reverzibilnih hidravliènih strojev z dvema delovnima kolesoma (èralnim in turbinskim), ki se s osebnimi naravami vkljuèujeta v en ali drug režim obratovanja. Primeri take rešitve so reverzibilne èralne turbine Isogyre (Švica), one (ÈSSR) in druge. Znane so tudi konstrukcijske rešitve s samo enim vgrajenim delovnim kolesom, katerega remer se sreminja glede na vrsto obratovanja. Vse te rešitve a so dokaj zaletene, zato ridejo v oštev samo za agregate manjših moèi. V svetovni raksi gradnje reverzibilnih agregatov velikih moèi revladuje uoraba As an identical degree of efficiency cannot be reached with reversible hydroelectric ower lants in both working modes (Fig. 3.) it is more convenient to have a higher degree of efficiency in the turbine working mode than in the um working mode since the rice of eak electric ower is several times higher than the rice of electric ower during the eriod of least loading of the ublic electric ower system, i.e. the rice of free energy in the ublic electric ower system (at the time when the reversible ower lant oerates in the um working mode) Fig. 4. If it is assumed accordingly that h t 0, 93 and h 0,90 and if these values are entered into equation (5), the following is obtained: 1, 05 1, 3 (5') After analyzing equation (5') we come to the conclusion that for defining the oerating characteristics of the reversible um-turbine the following assumtions must be taken into account: 1. If it is assumed that the difference of circulation at the entry into and the exit from the working wheel in the turbine and um working mode is identical, i.e. D G D Gt, then the number of revolutions in the um working mode must be greater than the number of revolutions in the turbine working mode ( 1, 3 wt). In ractice this imoses the use of two-seed generators (MG), having two rotating seeds in oosite directions. When switching from one to the other working mode it is necessary to change the number of ole airs currently in oeration. A disadvantage of this solution is that in this case the rice of the generator, the electrical equiment and the automatic control system and rotection is increased by %, whereas the degree of efficiency of the generator is reduced (Fig. 1.). 2. In the case of an identical number of revolutions ( w wt) it is necessary to ensure the condition D 1, 3 D Gt. This can only be reached with the assumtion that the diameter of the working wheel in the um working mode is greater than the diameter of the working wheel in the turbine working mode. In order to solve this roblem in ractice several design solutions for reversible hydraulic machines with two working wheels (um and turbine working wheel), activated in one or other oerating mode by secial devices, are used. Examles of such a solution are the reversible um-turbines Isogyre (Switzerland) and one (Czechoslovakia). In addition, design solutions with one incororated working wheel, whose diameter changes with resect to the working mode, are well known. owever, all these solutions are rather comlicated, and so they can only be considered for low-ower generating units. In most arts of the world, when building reversible ower-generation units, the revailing D G w D G w 0,90 0,93 0,95 t t st stran 531

5 generatorjev z eno hitrostjo z izbiro rimerne konstrukcijske rešitve delovnega kolesa hidravliènega reverzibilnega stroja z visokimi energijskimi lastnostmi v turbinskem in èralnem režimu obratovanja (zaradi ravilne izbire rofila loatic delovnega kolesa in loatic vodilnika). Toda iz navedenih razlogov tudi v tem rimeru ni mogoèe doseèi otimalnih karakteristik èralnega im turbinskega režima. To je razvidno s slike 3, na kateri so v koordinatah Q - redstavljene tiiène delovne karakteristike èralke - turbine, ri èemer ima retok v èralnem režimu negativni redznak. Posebno konstrukcijo je razvil rof. Krivèenko [6]. Ta ima zaradi uèinka delno omiènih loatic delovnega kolesa skoraj otimalno vrtljivo rešetko delovnih loatic v turbinskem in èralnem režimu. concet is the use of one-seed generators with the selection of a comromise design solution of the working wheel of the hydraulic reversible machine with highower roerties in the turbine and um working mode (as a consequence of the correct selection of the contour of the working wheel blades and flow device blades). owever, for the above reasons it is also not ossible in this case to achieve the otimum characteristics of the um and turbine working mode. This can be seen in Figure 3, showing in coordinates Q the tyical working characteristics of the umturbine where the flow in the um working mode has a negative sign. A secial structure of was develoed by Prof. Krivchenko, who has a nearly otimal rotation grating of the working blade in the turbine and um modes, on the basis of the effect at artly moveable mobile blades of the working wheel (1). Sl. 3. Tiiène delovne karakteristike francisove v obeh režimih obratovanja Fig. 3. Tyical oerating characteristics of the Francis reversible um-turbine in both working modes Na sliki 3 je karakteristika èralnega režima rikazana za rimer nsremenljivega odrtja vodilnika (a 0 ), kakor je to na RE obièajno. Srememba a 0 malo vliva na vrednost retoka, moè in stonje izkoristka, odstoanje od otimalne vrednosti a 0 a ovzroèa ojav recejšnjih utriov tlaka v retoènem rostoru turbine. Za turbinski režim so odane krivulje nesremenljivih odrtij vodilnika a 0 in stonje izkoristka do h 0, to je do režima obega turbine. Poveèanje višine z namenom rehajanja delovnega odroèja na odroèje otimalnega izkoristka turbine omeni hkrati rehod na odroèje zelo majhnih retokov in nizkih stoenj izkoristka v rimeru èralnega režima (sl. 3). Nomenklatura reverzibilnih èralnih turbin je omanjkljiva, obstajajo a glavne univerzalne karakteristike za zelo omejeno število tiov. Toda, glede na to, da se dandanes rojektira vrsta RE za zelo širok as višin od 100 do 1200 metrov, se okaže otreba o doloèanju osnovnih arametrov èralnih turbin, v odvisnosti od teh arametrov a tudi otreba o doloèanju samih RE. Na današnji stonji raziskav lahko izbiro reverzibilnih èralnih turbin oravljamo na temelju In addition, Figure 3 shows the characteristic um working mode for the case of a constant cross section of the flow device (a 0 ), as is usual for reversible hydroelectric ower lants, since the change a 0 only slightly influences the value of the flow, the ower and the degree of efficiency, and the deviation from the otimum value a 0 results in considerable fluctuations of the ressure in the turbine flow sace. For the turbine working mode the isoclines of constant cross section of the flow device a 0 and of the degree of efficiency u to h 0 i.e. u to the turbine over seed are given. The increase of the head, aimed at the working area assing into the range of otimum efficiency of the turbine, simultaneously imlies assing into the range of very small flows and low degrees of efficiency in the case of the um working mode (Fig. 3). The arts lists of reversible um-turbines are not yet available, whereas the rincial universal characteristics for a very limited number of tyes are available. owever, considering the fact that nowadays the tye of reversible hydroelectric ower lants for a very wide range of heads from 100 to 1200 m is designed, the need for determining the basic arameters of the um-turbines and, deending on those arameters, the need for determining the reversible hydroelectric ower lant itself are imosed. At today s level of research the selection of reversible um-turbines can be made on the basis of stran 532

6 turbinski režim turbine regime TURBINE REGIME èralni režim PUMP REGIME um regime h f(q11) Q11 Q11 sistematizacije in analize statistiènih odatkov sedanjih RE, ki so že v obratovanju ali a so v fazi rojektiranja oziroma gradnje. Na inštitutu MISI v Moskvi, na Katedri za izkorišèanje vodne moèi, je bila od vodstvom rof. Aršenevskega in ob sodelovanju avtorja tega risevka oravljena analiza veè ko 40 reverzibilnih agregatov razliènih zahodnih izdelovalcev. Ob tej riložnosti je bila ugotovljena naslednja odvisnost secifiène vrtilne frekvence francisovih reverzibilnih èralnih turbin v turbinskem režimu: Sl. 4. Glavna slošna karakteristika Fig. 4. Main universal characteristic of (1) the systematization and analysis of statistical data from the reversible hydroelectric ower lants that are already in oeration, being designed, or being built. At the MISI institute in Moscow, in the Deartment of Utilization of Water Power, an analysis of more than 40 reversible ower generation units from different Western manufactures was made under the leadershi of Professor Arshenevski, in cooeration with the author of this aer. On that occasion the following deendence of the secific number of revolutions of the Francis reversible umturbines in the turbine working mode was found: n 1,36 P 1212 ns tmax tmax t max (6), ri èemer so: where n - vrtilna frekvenca, min -1 n is the rated number of revolutions (min -1 ) P - najveèja moè, kw P is the maximum ower (kw) t - najveèji turbinski adec RE, m. Z analizo odatkov [1] se dobi naslednja t is the maximum turbine fall on the reversible hydroelectric ower lant (m) If these facts are rocessed (1) the following enaèba: ratio is obtained: Analiza arametrov reverzibilnih hidravliènih strojev nekaterih RE v nekdanji ZSSR in v ZDA je okazala, da obstaja tendenca oveèanja secifiène vrtilne frekvence, zato je bolj n s (6'). 0,4 t max owever, an analysis of the arameters of reversible hydraulic machines on some reversible hydroelectric ower lants in the former USSR and the USA showed that there is a tendency towards an stran 533

7 rimeren naslednji izraz: increase in the secific number of revolutions, therefore the following relation is more aroriate: n (6''). s 0.4 t max Zanimivo je rimerjati secifièno vrtilno It is interesting to make a comarison of the secific frekvenco obièajnih turbin ( n st ) in reverzibilnih number of revolutions of a conventional turbine ( n st ) and èralnih turbin ( n s ). Za klasiène E s francisovimi that of reversible um-turbines ( n s ). For conventional turbinami lahko ta arameter izrazimo kot funkcijo hydroelectric ower lants with Francis turbines this imenskega adca [3]: arameter can be exressed as a function of the rated fall: 2300 nst (7). ot Za klasiène E velja razmerje: On the other hand, the following ratio alies for conventional hydroelectric ower lants: ot Èe vzamemo srednjo vrednost ot/max 0,88, dobi enaèba (7) obliko: Razmerje med secifièno vrtilno frekvenco reverzibilnih in klasiènih francisovih turbin tako izraèunamo z enaèbo: nst Na odlagi tmax in P lahko o enaèbi (6) doloèimo vrtilno frekvenco turbine: Dobljeno vrednost zaokrožimo na najbližjo sinhrono vrtilno frekvenco. Na sliki 5 so odani rezultati analize odvisnosti glavnih izmer delovnih koles nekaterih že izvedenih reverzibilnih èralnih turbin () ri tmax od secifiène vrtilne frekvence n s. Odvisnost enotske vrtilne frekvence n11 f( n s ) lahko na temelju izvedene analize rioroèimo v obliki: max n 0,78-0,95 n st s If the mean value ot/max 0.88 is adoted, equation (7) assumes the following form: 2070 (8). max The ratio of the secific number of revolutions of the reversible and conventional Francis turbines gives the following relation: 0,58 t n t max (9). As tmax, and P are known, the number of turbine revolutions can be determined according to equation (6): 0.5 max (10). P The value obtained is aroximated to the nearest synchronous number of revolutions. Figure 5 gives the results of the analysis of deendence of the main working wheel dimensions of some reversible um-turbines already in oeration, with tmax on the secific number of revolutions n s. The deendence n11 f( n s ) can be recommended in the following form on the basis of the analysis carried out: n ,05 n s (11). V tem rimeru bo remer delovnega kolesa: In this case the working wheel diameter will be: n D ( , 05 ns ) P tmax 11 tmax n 1040 tmax (12). Èe dobljeno vrednost D 1 zaokrožimo na višjo vrednost do 0,1 m, moramo reveriti, ali smo dobili najveèjo višino v èralnem režimu. Iz teorije èralk je oznano razmerje [5]: If the obtained value D 1 is aroximated to a higher value of u to 0.1 m it is necessary to check whether the maximum head in the um working mode has been obtained. The following ratio is known from the theory of ums: 2 æð ö (13), è ø u K D n max K ç 2 g 2 g 60 stran 534

8 nsrt Sl. 5. Odvisnost izmer delovnega kolesa od n s [2] Fig. 5. Deendence of working wheel dimensions on n s [2] ri èemer je K0,8-0,9, iz tega izhaja: where K , therefore: 2 2 ( 0, , ) - n D max 1 (14). od: Tako dobimo remer D 1, ki ne sme biti manjši Thus the diameter D 1 is obtained, which must not be smaller than: Obdelava statistiènih odatkov že izdelanih reverzibilnih hidravliènih strojev je rieljala do izkustvene odvisnosti enotnega retoka Q 11 (l/s) ri obratovanju v turbinskem režimu ri tmax v obliki [2]: D 1 ( 89-95) max (15). n The rocessing of statistical data on reversible hydraulic machines that are already built has led to the exerimental deendence of the unit flow Q 11 (l/s) in the case of maximum oeration in the turbine working mode in the following form [2]: ( ) 2 Q11 0, 008-0, 012 n s (16). Po drugi strani a lahko vrednost Q 11 doloèimo o enaèbi za secifièno vrtilno frekvenco [2]: On the other hand, the value Q 11 can be determined according to the equation for the secific number of revolutions: n 3, 65 n Q h s (17), ri èemer ima Q 11 mero m 3 /s. Èe vzamemo vrednost h 0,9, dobimo ovezavo: where Q 11 has the dimension m 3 /s. If the value h 0.9 is assumed, the following relation is obtained: ( ) 1.8 Q11 0, 029-0, 032 n s (18). Glede na to je remer delovnega kolesa uoštevajoè (11) in (16): 1,166 D Premer delovnega kolesa se lahko izraèuna tudi iz enaèbe za moè in enotski retok Q 11 z uoštevanjem enaèb (16) in (18): 1 3/4 ns So the diameter of the working wheel considering (16) and (11) is: n11 P (19). tmax On the otherr hand, from the equation for the ower and unit flow Q 11 and by taking into account the relation (16) and (18) it is also ossible to calculate the diameter of the working wheel: stran 535

9 Bodimo ozorni na koeficiente v števcu enaèbe (15). To so vrednosti n 11 v èralnem režimu za max, kjer je n11 t > n11, saj je tmax < max. Ob znani vrednosti D 1 lahko izhodni remer delovnega kolesa (v turbinskem režimu) D 2, višino dovodnega aarata B 1 in celotno višino delovnega kolesa B 2 (sl. 2) doloèimo o diagramu na sliki 5. D 1 P 9,81 Q h 11 (20). Let us look at the coefficients in the numerator of equation (15). These are the values n 11 in the um working mode for max, where n 11t > n 11, because of tmax < max. Since we know the value D 1 the outlet diameter of the working wheel D 2 (with resect to the turbine working mode), the head of the flow device B 1 and the total head of the working wheel B 2 (Fig. 2) can be determined according to the grahics in Figure 5. 3 DOLOÈITEV SESALNE VIŠINE Eden izmed najomembnejših arametrov, ki odloèujoèe vliva tudi na zasnovo RE, je lega delovnega kolesa reverzibilnega stroja glede na najmanjšo koto vode v sodnji akumulaciji oziroma sesalna višina reverzibilnih hidravliènih strojev. Za RE je znaèilno, da je treba sesalno višino doloèiti izhajajoè iz ogojev obratovanja v èralnem režimu. Koeficient kavitacije je v tem režimu veèji kakor v turbinskem režimu. Tako je na rimer za Kijevske RE kavitacijski koeficient v otimalnem turbinskem obratovanju s T 0,12 v èralnem a s P 0,33. To je razlog, da je èralka v rimeru trojnih agregatov vedno vgrajena od turbino. Po drugi strani a je vgradnja delovnega kolesa na globinah 20 do 50 m ali veè odvisna od zasnove odzemeljske ali olodzemeljske strojnice RE, kar ima za osledico oveèanje 3 DETERMINATION OF TE INTAKE ALTITUDE One of the most imortant arameters that also decisively influences the concet of reversible hydroelectric ower lants is the altitude osition of the working wheel of the reversible machine in relation to the minimum level of the downstream reservoir and/ or the suction height of the reversible hydraulic machines. It is characteristic of reversible hydroelectric owers lants that it is necessary to determine the suction height starting from the oerating condition in the um working mode, taking into account that the cavitations coefficient is greater in this working mode than in the turbine working mode. In this way for the of the Kiev REPP the coefficient of cavitations in the otimum turbine regime s T 0.12 in the turbine working mode and s P 0.33 in the um working mode. On the other hand, the requirement for the installation of the working wheel at m deths or more, conditions the concet of an underground or semiunderground owerhouse of the reversible hydroelectric P nsrt Sl. 6. Vrednosti s v odvisnosti od in n srt [3] Fig. 6. Values of s as a function of and n srt [3] stran 536

10 dolžine odvodnih sistemov. Ti sistemi so zaradi recejšnjih nihanj nivoja vode v sodnji akumulaciji ogosto izvedeni od tlakom [4]. Èe analiziramo odatke že zgrajenih RE in RE v fazi rojektiranja, oazimo, da sesalna višina v mnogoèem rekaša vrednosti, ki jih sreèujemo ri obièajnih turbinah z enako vrtilno frekvenco. V reglednici 1 so rikazane sesalne višine nekaterih že izvedenih in karakteristiènih RE [3]. Preglednica 1 Table 1 RE Reversible hydroelectric ower lant Vianden Krauchan Numaara Katrua-Pon. Država Country Luksemburg Luxemburg Velika Britanija Great Britain Jaonska Jaan Belgija Belgium Sesalna višina Suction height (m) V rvem ribližku lahko sesalno višino doloèimo o diagramu na sliki 6. Analitièna enaèba za izraèun sesalne višine je: ower lant, which results in the increase of the length of outflow systems which are frequently designed ressurized due to considerable fluctuation of the water level in the downstream reservoir [4]. If the data on the reversible hydroelectric ower lants already constructed or under construction are analyzed it can be seen that the suction height, in many asects, exceeds the values occurring on the conventional turbines with an identical number of secific revolutions. Table 1 shows the suction heights of some characteristic reversible hydroelectric ower lants already constructed [3]. Èralna višina ead (m) Pretok v èralni smeri Flow rate at uming (m 3 /s) Vrtilna frekvneca Number of revolutions (min -1 ) - 26, ,1 333,30-45, ,6 500,00-55, ,0 375,00-20, ,0 300,00 The suction height can be determined according to figure 6 as a first aroximation. The analytical exression for the calculation of the intake altitude is: Ñ& s hus - ks s 900 (21), ri èemer so: where: Ñ & h us - absolutna kota vgradnje delovnega kolesa, - hidravliène izgube v odvodnem sistemu od Ñ & is the absolute elevation of the installation of the working wheel ritiskom, h us is the hydraulic loss in the ressurized outflow system s - koeficient kavitacije v èralnem režimu, s is the cavitations coefficient in the um working mode - èralna višina RE, is the head of the reversible hydroelectric ower lant ks - koeficient rezerve. Glede na to, da obstaja zelo majhno število ks is the coefficient of reserve As there are only a small number of universal modelnih univerzalnih karakteristik reverzibilnih hidravliènih strojev, ki vsebujejo odatke o koeficientu kavitacije, koeficienta kavitacije ni mogoèe definirati na naèin, kakor je to obièajno ri obièajnih turbinah. Zato ostaja možnost uorabe emiriènih enaèb. Iz teorije èralk je znana enaèba Rudneva za kritièni koeficient kavitacije èralk v otimalnem režimu obratovanja, in sicer v odvisnosti od vrtilne frekvence [6]: characteristics for the model of reversible hydraulic machines and, esecially with information about the coefficient of cavitations, the cavitations coefficient cannot be defined in the usual way for conventional turbines. Therefore, the ossibility for using on exerimental equation remains. Rudnev s equation for the critical coefficient of the um cavitations in the otimum working mode deending on the secific number of revolutions is known from the theory of ums [6]: s n 4/3 / A ; A (22), ri èemer je koeficient A odvisen od konstrukcijske izvedbe delovnega kolesa in n s, A4700 ri n s 110; A6300 ri n s 180 [8]. Nekaj veèjo vrednost where the coefficient A deends on the structural design of the working wheel and n s, A4700 at n s 110; A6300 at n s 180 [8]. A somewhat higher stran 537

11 koeficienta kavitacije dobimo, èe uorabimo enaèbo: value of the cavitations coefficient is obtained if the following equation is used: s n 4/3 / 4000 (23). Koeficient rezerve ks definiramo analogno kakor ri doloèanju sesalne višine turbine. Predvsem moramo uoštevati možne naake ri ovzemanju modelnih kavitacijskih karakteristik, rav tako a tudi odstoanja, ki so osledica dejstva, da ne moremo zagotoviti oolne geometrijske in dinamiène odobnosti modela in dejanskega stroja. V rimeru kalanovih turbin obièajno jemljemo koeficient ks 1,1; ri francisovih turbinah za adce do 250 m je ks 1,15 do 1,2, za adce rek 250 m a se ta koeficient ne uošteva, to je ks 1,0. Ker za reverzibilne hidravliène stroje do sedaj še ni na voljo dovolj odatkov za njihovo nomenklaturo, se vrednost tega koeficienta jemlje analogno nomenklaturi obièajnih hidravliènih turbin velikih moèi: ks 1,1 do 1,15 [2]. Jaonski strokovnjaki rioroèajo enaèbo (23) v obliki [3]: The reserve coefficient ks is defined analogously to the determination of the turbine suction height. In articular, it is necessary to take into consideration the mistakes in obtaining the model cavitations characteristic as well as the deviation resulting from the fact that it is not ossible to ensure comlete geometrical and dynamic equality of the model and the actual machine. For the case of Kalans turbines the coefficient ks 1.1 is usually assumed; in the case of Francis turbines for 250 m falls the coefficient ks , whereas for falls over 250 m that coefficient is not taken into account, i.e. ks 1.0. For the time being, sufficient data are not available for arts lists of the reversible hydraulic machines, the value of that coefficient is taken in the same way as the arts lists of conventional hydraulic turbines of high owers: ks [2]. Jaanese exerts recommend equation (23) in the following form [3]: ( ) 4/3 4/3 n Q ns s /3 4/3 n Q ns n Q ns kjer velja: ns 3, 65 considering relation: ns 3, 65 3/4, that is s 3/4 in s, kjer je Q, srednji retok v èralnem režimu. where Q is the mean flow rate in the um working mode. V obmoèju èralnih višin do 100 m se In the range of falls of u to 100 m the value of the vrednosti dejanskih sesalnih višin veèine RE actual suction height on most reversible hydroelectric dobro ujemajo z vrednostmi, o enaèbi (24). S ower lants coincides well with the value obtained from oveèanjem èralne višine se vrednost S o enaèbi equation (24). With an increase of the water head, however, (24) zmanjša. Zato je treba enaèbo (24) oraviti the value s according to equation (24) decreases. takole [2]: Therefore, a correction must be entered in the water head and the following equation is obtained [2]: 4/3 ns s 10 - (25) ,94 max (24), M S glede na (24) according to (24) 600 M 400 M 200 M glede na (25) according to (25) 0 n Q Fig. 7. Primerjava teoretiènih in raktiènih vrednosti s [3] Fig. 7. Comarison between s from theoretical and ractical values [3] stran 538

12 S rimerjavo vrednosti S, dobljenih o enaèbah (24) in (25), z dejanskimi vrednostmi na že izdelanih RE ridemo do ugotovitve, da daje enaèba (25) dobre rezultate za èralne višine od 100 do 500 m. Iz te rimerjave je tudi oèitno, da se vrednost S z veèanjem èralne višine moèno oveèa. 4 SKLEP Reverzibilna hidroelektrarna (RE) je vsekakor uèinkovit vir vršne energije. Ta ti elektrarne zato že dalj èasa vzbuja oveèano zanimanje ri mnogih rojektantskih organizacijah, raziskovalcih in konstrukterjih. V risevku je odana analiza nekaterih vrašanj, ki se ojavijo ri rojektiranju tovrstnega tia hidroelektrarne. Podane so namreè osnovne teorije delovnega rocesa reverzibilnih èralnih turbin. Razen tega je odana tudi analiza osnovnih rešitev nekaterih že izvedenih francisovega tia. V nadaljevanju so obravnavana razmerja med arametri, ki se uorabljajo ri obièajnih èralkah in turbinah ter na odlagi le-teh oravljena analiza režimov, v katerih lahko obratuje tudi. Dognana je ovezava med osnovnimi arametri RTP francisovega tia in vrtilno frekvenco, oravljena a je tudi analiza sesalne višine v odvisnosti od secifiène vrtilne frekvence. By comaring the s values obtained according to equations (24) and (25) with the actual values on the reversible hydroelectric ower lants already constructed we find that equation (25) gives good results for the heads from 100 to 500 m, and is also recommendable for that range of falls. The comarison shows that the value s strongly increases with an increase of the head and becomes infinite. 4 CONCLUSION A reversible hydroelectric ower lant (REPP) is surely the most real and the most efficient source of uermost energy, and that is why many roject deartments, researchers and designers have, for a long time, shown great interest in this tye of ower lant. In this context, an analysis of some questions concerning the lanning of hydro-electric ower lants of such tye are given in this aer. Namely, basic theories of the working rocess of reversible um turbines are given and concetual solutions of some erformed RTP of the Francis tye are analyzed. Then, relations between arameters are given, which are alied to classical ums and turbines, and concerning that the regimes in which can be found are analyzed. A connection between basic arameters of of the Francis tye and a secific number of revolutions is established. An analysis of the intake altitude of sucking as a function of n s is made. hidravliène izgube v èralnem režimu hidravliène izgube v turbinskem režimu hidravliène izgube v odvodnem sistemu od ritiskom adec reverzibilne hidroelektrarne v èralnem režimu sesalna višina hidrostatièni adec (višina) adec reverzibilne hidroelektrarne v turbinskem režimu koeficient rezerve število vrtljajev secifièna vrtilna frekvenca najveèja moè srednji retok v èralnem režimu koeficient kavitacije v èralnem režimu kotna hitrost absolutna kota vgradnje delovnega kolesa 5 OZNAKE 5 SYMBOLS h h t h us s st t ks n n s P Q s w Ñ & hydraulic losses in um working mode hydraulic losses in turbine working mode hydraulic losses in ressurized outflow system head of the reversible hydraulic ower lant in um working mode suction height head head of reversible EPP in turbine working mode coefficient of reserve number of revolutions secific rotating seed maximum ower average flow in um working mode cavitation coefficient in um working mode angular seed elevation of installation of working wheel stran 539

13 6 LITERATURA 6 REFERENCES [1] Krivèenko, G.I. (1975) Gidromehanièeskie erehodnye rocessy v gidroenergetièeskih ustanovkah, Energija, Moskva. [2] Aršenevskij, N.N. (1977) Obratimiye gidromašiny gidroakumulirujušèih elektrostancij, Energija, Moskva. [3] Trudy Instituta MISI - Moskva. [4] Mrkiæ, M. (1985) Koncecije rešavanja RE, Magistarski rad, Mašinski fakultet Beograd. [5] Lomakin, A.A. (1966) Centrobežnye i osevye nasosy, Mašinostroenije, Moskva. [6] Krivèenko, G.I. (1970) Nasosy i gidroturbiny, Energija, Moskva. [7] Floriniskij, G.I. i dr. (1967) Nasosy i nasosnye stancii, Moskva. [8] Gidroelektrièeskie stancii: Pod redakcijej Gubina, Energija, Moskva, Naslov avtorjev: rof.dr. Milo Mrkiæ Univerzitet Crne Gore Mašinski fakultet Podgorica Cetinjski ut bb Podgorica, ZRJ milom@cg.ac.yu Authors Address: Prof. Dr. Milo Mrkiæ University of Montenegro Faculty of Mech. Eng. Podgorica Cetinjski ut bb Podgorica, ZRJ milom@cg.ac.yu Prejeto: Received: Srejeto: Acceted: stran 540