© Strojni{ki vestnik 48(2002)10,528-540 © Journal of Mechanical Engineering 48(2002)10,528-540 ISSN 0039-2480 ISSN 0039-2480 UDK 621.311.21:621.224.24:621.224.7 UDC 621.311.21:621.224.24:621.224.7 Pregleni znanstveni ~lanek (1.02) Preview scientific paper (1.02) Analiza parametrov reverzibilne ~rpalne francisove turbine An Analysis of the Parameters of Reversible Francis-Type Pump Turbines Milo Mrki} Pri projektiranju reverzibilnih hidroelektrarn (RHE) mora imeti projektant na voljo čim bolj podrobne podatke o parametrih hidravličnih strojev, ki bodo v hidroelektrarno vgrajeni. Ta pogoj je se posebej pomemben, kadar gre za reverzibilne črpalno-turbinske agregate, saj morajo le-ti optimalno ustrezati režimu obratovanja v obeh smereh pretoka (črpalni in turbinski režim), da bi bila lahko vgrajena moč agregata optimalno izrabljena, tako pri polnjenju kakor tudi pri praznjenju zgornje akumulacije, in to v skladu z zahtevami elektroenergetskega sistema. Ko se projektant loti projektiranja RHE, izbere po nomenklaturi ustrezen tip turbine, potem pa -upoštevajoč splošne karakteristike in nomenklaturne diagrame - določa osnovne parametre reverzibilne črpalke - turbine (RPT). Glede na to, da je nomenklatura RPT pomanjkljiva in da obstajajo splošne karakteristike samo za omejeno število tipov, je primerno v začetni fazi projekta najprej definirati osnovne parametre RPT, v prvem koraku na temelju specifične vrtilne frekvence. V prispevku je podanih nekaj rezultatov študij razpoložljive tehnične literature kakor tudi rezultatov teoretičnega dela, modelnih preiskav in preiskav v dejanskih razmerah, ki so bile ob sodelovanju avtorja prispevka opravljene na Katedri za izkoriščanje vodnih virov v Moskvi (Institut MISI). © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: projektiranje hidroelektrarn, turbine francis, črpalke reverzibilne, analize parameters) When designing pumping reservoir hydroelectric power stations the designer must have available detailed data on the parameters of the hydraulic machines that will be installed in the power plant. This is particularly important when reversible pumping-turbine units are installed, since they must best suit the working mode in both directions of the flow (pumping and turbine mode) so that the installed power of the unit is best utilized in the case of filling as well as emptying the upstream reservoir in accordance with the requirements of the public electric power system. When the planning engineer starts to project, according to the nomenclature he chooses the appropriate type of turbine and then determines the basic parameters for the reversible pump-turbine (RPT) by using universal characteristics or graphical nomenclature. Since the RPT nomenclature still does not exist and the universal characteristics only exist for a limited number of types it is appropriate at the initial stage of the design to define the basic parameters of the RPT, initially according to the specific 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 performed in “exploitation of water power” university department in Moscow (institute MISI), with participation of the author are also presented. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: hydroelectric power stations, Francis turbines, reversible pump turbines, parameter analysis) 1 OSNOVNE KARAKTERISTKE DELOVNEGA PROCESA RPT Reverzibilni hidravlični stroj francisovega tipa ima značilnosti, ki se kažejo pri razliki njihovih osnovnih geometrijskih parametrov in obratovalnih karakteristik glede na klasične črpalke in turbine. 1 BASIC CHARACTERISTICS OF WORKING PROCESS RPT THEORY A reversible hydraulic machine of the Francis type has some specific features whose basic geometrical parameters and operating characteristics differ from the conventional pump and turbine. 0 BnnBjfokJ][p)l]Olf|ifrSO | | ^SsFÜWEIK | stran 528 Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible ¦ ¦ ¦ I •!•!>. . J I/J Sl. 1. Shema reverzibilne hidroelektrarne Fig. 1. Working plan of the reversible hydro power station Predvsem je treba vedeti, da sta padec vode In particualr, it is necessary to realise that the reverzibilne hidroelektrarne (RHE) v turbinskem fall of the reversible hydroelectric power plant in the režimu (H) in višina RHE v črpalnem režimu (H) turbine working mode (H) and the head in the pump različna (sl. 1). p working (H) mode are different (Fig. 1). V turbinskem režimu je padec vode določen In the turbine working mode the fall is defined kot: as follows. Ht=Hst-ht (1), v črpalnem režimu pa višina kot: Hp=Hst+hp and the head in the pump working mode is defined as: (2), pri čemer so: H - hidrostatični padec vode (višina) h , h - hidravlične izgube. p Hidravlične izgube pri turbinskem obratovanju (ht) niso enake izgubam v črpalnem (h) are not the same as the losses in the pump working where: Hst is the water head ht , hp are the hydraulic losses The hydraulic losses during turbine operation režimu (h ) obratovanja, ker sta pretoka v enem in drugem režimu v osnovi različna in ker tudi koeficienti lokalnih izgub v dovodnem in odvodnem sistemu niso enaki v turbinski in črpalni smeri pretoka vode (sl. 3). Eulerjeva enačba za hidravlični reverzibilni stroj ima obliko: - za turbinski režim mode (h) because in principle 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 pump direction of the water flow (Fig. 3). Euler's equation for a reversible hydraulic machine has the following form: - for the turbine working mode ht u1-c0-cos a0 - u2 ¦ c3 • cos a3wt ( G1-G2 DGt-wt - za črpalni režim hp g-Ht g-Hp 2-n-g-Ht 2-n-g-Ht - for the pump working mode _______________________= 2-n-g-Hp = 2-n-g-Hp u1-c0-cos a0-u2-c3-cos a3 wp(G1-G2) DGp-wp pri čemer je: where: G = 2-n-r-cu- obtok (cirkulacija), G = 2 • n ¦ r ¦ cu is the circulation (3), (4), iz-n iz-n w= - kotna hitrost. w= is the angular speed Indeks 1 se nanaša na vhod v delovno kolo, The index 1 refers to the inlet to the working indeks 2 pa na izhod iz delovnega kolesa v wheel and the index 2 refers to the outlet from the turbinskem režimu. Ustrezajoči trikotniki hitrosti za working wheel in the turbine working mode. Figure 1 gfin^OtJJIMISCSD 02-10 stran 529 |^BSSITIMIGC Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible črpalni in turbinski režim so prikazani na sliki 2. Črte vhodnih (0-0) in izhodnih (3-3) površin delovnega področja kolesa so glede na črte vhodnih (1-1) in izhodnih (2-2) robov lopatic pomaknjene, da bi se izognili vplivu končnega števila lopatic na pretok vhodnih in izhodnih prerezov (sl. 2.). črpalni režim pump regime shows the relevant triangles of the speeds in the pump and turbine working modes. The contours of the input (0-0) and outputs (3-3) working area surfaces are shifted with respect to the contours of the input (1-1) and output (2-2) edges of the moving blades to avoid influence at definitive numbers of blades on the flow in input and output cross sections (Fig. 2.). \ turbinski režim i turbine regime Sl. 2. Osnovni geometrijski parametri RPT francisovega tipa in trikotniki hitrosti v črpalnem in turbinskem režimu Fig. 2. Basic geometrical parameters of the reversible pump - turbine of Francis type and triangles of speeds in the pump and turbine working modes Če vpeljemo oznaki: G1 -G2 = DG oziroma G1 - G2 = DGp, dobita enačbi (3) in (4) obliko: If the terms G1 -G2 = DG and G1 -G2 = DGp are introduced, equations (3) and (4) assume the following form : DGt-wt=2-n-g-Ht-ht 2-n-g-Hp DGp-wp hp oziroma razmerje: and/or the ratio : DGp-wp = Hp DGt wt h-ht-Ht (3') (4') (5). Če predpostavimo, da so izgube višine v If it is assumed that the head losses in the turbinskem in črpalnem režimu enake in znašajo turbine and the pump working modes are identical h =hp=0,05 • Ht , potem je skladno z (1) in (2): o ht =hp=0.05 • Ht, the following applies in accordance with (1) and (2): Ht=0,95-Hst ; H =1,05-Hst 02-10 grin^SfcflMISDSD I ^BSfiTTMlliC | stran 530 Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible 2 ODVISNOST OSNOVNIH PARAMETROV RPT OD SPECIFIČNE VRTILNE FREKVENCE Glede na to, da v obratovanjih RHE ni mogoče doseči enako velike stopnje izkoristka, je ugodneje imeti večjo stopnjo izkoristka v turbinskem režimu obratovanja kakor v črpalnem režimu (sl. 3), saj je cena vršne električne energije nekajkrat večja od cene električne energije v obdobjih najmanjše obremenitve elektroenergetskega sistema (sl. 4). Predpostavimo, da sta ht = 0,93 in hp = 0,90, ti dve vrednosti vstavimo v enačbo (5), dobimo: 2 DEPENDENCE OF BASIC RPT PARAMETERS ON SPECIFIC NUMBER OF REVOLUTIONS As an identical degree of efficiency cannot be reached with reversible hydroelectric power plants 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 pump working mode since the price of peak electric power is several times higher than the price of electric power during the period of least loading of the public electric power system, i.e. the price of free energy in the public electric power system (at the time when the reversible power plant operates in the pump working mode) Fig. 4. If it is assumed accordingly that ht = 0,93 and hp = 0,90 and if these values are entered into equation (5), the following is obtained: DG 1,05-H DG-w 0,90• 0,93-0,95-H 1, 3 (5') Na podlagi analize (5') lahko povzamemo, da moramo pri definiranju obratovalnih karakteristik reverzibilne črpalne turbine upoštevati naslednji predpostavki: 1. Če predpostavimo, da je razlika obtoka (cirkulacije) na vstopu in izstopu iz delovnega kolesa v turbinskem in črpalnem režimu enaka, to je DG = DGt, potem mora biti vrtilna frekvenca v črpalnem režimu večje od vrtilne frekvence v turbinskem režimu (w @ 1,3 • wt). V praksi pomeni to uporabo dvohitrostnih generatorjev (MG), ki imajo dve vrtilni frekvenci, vendar v nasprotnih smereh. Pri tem je treba pri prehodu iz enega v drugi režim obratovanja zamenjati število parov polov, ki so trenutno v obratovanju. Pomanjkljivost te rešitve je, da se cena generatorja, električnih aparatov, sistema avtomatike in zaščite v tem primeru poveča za 25 do 30 % ob hkratnem zmanjšanju stopnje izkoristka generatorja (sl. 1). 2. V primeru enake vrtilne frekvence ( wp = wt) je treba zagotoviti pogoj DT @1,3DGt. To je mogoče doseči samo s predpostavko, da je premer delovnega kolesa v črpalnem režimu večji od premera delovnega kolesa v turbinskem režimu. Za rešitev tega problema je uporabljenih več konstrukcijskih rešitev reverzibilnih hidravličnih strojev z dvema delovnima kolesoma (črpalnim in turbinskim), ki se s posebnimi napravami vključujeta v en ali drug režim obratovanja. Primeri take rešitve so reverzibilne črpalne turbine Isogyre (Švica), Hone (ČSSR) in druge. Znane so tudi konstrukcijske rešitve s samo enim vgrajenim delovnim kolesom, katerega premer se spreminja glede na vrsto obratovanja. Vse te rešitve pa so dokaj zapletene, zato pridejo v poštev samo za agregate manjših moči. V svetovni praksi gradnje reverzibilnih agregatov velikih moči prevladuje uporaba After analyzing equation (5') we come to the conclusion that for defining the operating characteristics of the reversible pump-turbine the following assumptions 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 pump working mode is identical, i.e. DG = DGt, then the number of revolutions in the pump working mode must be greater than the number of revolutions in the turbine working mode (w @ 1,3 • wt). In practice this imposes the use of two-speed generators (MG), having two rotating speeds in opposite directions. When switching from one to the other working mode it is necessary to change the number of pole pairs currently in operation A disadvantage of this solution is that in this case the price of the generator, the electrical equipment and the automatic control system and protection is increased by 25-30 %, whereas the degree of efficiency of the generator is reduced (Fig. 1.). 2. In the case of an identical number of revolutions (wp = wt ) it is necessary to ensure the condition DTp @1,3- DGt. This can only be reached with the assumption that the diameter of the working wheel in the pump working mode is greater than the diameter of the working wheel in the turbine working mode. In order to solve this problem in practice several design solutions for reversible hydraulic machines with two working wheels (pump and turbine working wheel), activated in one or other operating mode by special devices, are used Examples of such a solution are the reversible pump-turbines Isogyre (Switzerland) and Hone (Czechoslovakia). In addition, design solutions with one incorporated working wheel, whose diameter changes with respect to the working mode, are well known. However, all these solutions are rather complicated and so they can only be considered for low-power generating units. In most parts of the world, when building reversible power-generation units, the prevailing Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible generatorjev z eno hitrostjo z izbiro primerne konstrukcijske rešitve delovnega kolesa hidravličnega reverzibilnega stroja z visokimi energijskimi lastnostmi v turbinskem in črpalnem režimu obratovanja (zaradi pravilne izbire profila lopatic delovnega kolesa in lopatic vodilnika). Toda iz navedenih razlogov tudi v tem primeru ni mogoče doseči optimalnih karakteristik črpalnega im turbinskega režima. To je razvidno s slike 3, na kateri so v koordinatah Q - H predstavljene tipične delovne karakteristike črpalke - turbine, pri čemer ima pretok v črpalnem režimu negativni predznak. Posebno konstrukcijo je razvil prof. Krivčenko [6]. Ta ima zaradi učinka delno pomičnih lopatic delovnega kolesa skoraj optimalno vrtljivo rešetko delovnih lopatic v turbinskem in črpalnem režimu. concept is the use of one-speed generators with the selection of a compromise design solution of the working wheel of the hydraulic reversible machine with highpower properties in the turbine and pump working mode (as a consequence of the correct selection of the contour of the working wheel blades and flow device blades). However, for the above reasons it is also not possible in this case to achieve the optimum characteristics of the pump and turbine working mode. This can be seen in Figure 3, showing in coordinates Q – H the typical working characteristics of the pumpturbine where the flow in the pump working mode has a negative sign. A special structure of RPT was developed by Prof. Krivchenko, who has a nearly optimal rotation grating of the working blade in the turbine and pump modes, on the basis of the effect at partly moveable mobile blades of the working wheel (1). Sl. 3. Tipične delovne karakteristike francisove RPT v obeh režimih obratovanja Fig. 3. Typical operating characteristics of the Francis reversible pump-turbine in both working modes Na sliki 3 je karakteristika črpalnega režima prikazana za primer nspremenljivega odprtja vodilnika (a0), kakor je to na RHE običajno. Sprememba a0 malo vpliva na vrednost pretoka, moč in stopnje izkoristka, odstopanje od optimalne vrednosti a0 pa povzroča pojav precejšnjih utripov tlaka v pretočnem prostoru turbine. Za turbinski režim so podane krivulje nespremenljivih odprtij vodilnika a0 in stopnje izkoristka do h = 0, to je do režima pobega turbine. Povečanje višine z namenom prehajanja delovnega področja na področje optimalnega izkoristka turbine pomeni hkrati prehod na področje zelo majhnih pretokov in nizkih stopenj izkoristka v primeru črpalnega režima (sl. 3). Nomenklatura reverzibilnih črpalnih turbin je pomanjkljiva, obstajajo pa glavne univerzalne karakteristike za zelo omejeno število tipov. Toda, glede na to, da se dandanes projektira vrsta RHE za zelo širok pas višin od 100 do 1200 metrov, se pokaže potreba po določanju osnovnih parametrov črpalnih turbin, v odvisnosti od teh parametrov pa tudi potreba po določanju samih RHE. Na današnji stopnji raziskav lahko izbiro reverzibilnih črpalnih turbin opravljamo na temelju In addition, Figure 3 shows the characteristic pump working mode for the case of a constant cross section of the flow device (a0), as is usual for reversible hydroelectric power plants, since the change a0 only slightly influences the value of the flow, the power and the degree of efficiency, and the deviation from the optimum value a0 results in considerable fluctuations of the pressure in the turbine flow space. For the turbine working mode the isoclines of constant cross section of the flow device a0 and of the degree of efficiency up to h = 0 i.e. up to the turbine over speed are given. The increase of the head, aimed at the working area passing into the range of optimum efficiency of the turbine, simultaneously implies passing into the range of very small flows and low degrees of efficiency in the case of the pump working mode (Fig. 3). The parts lists of reversible pump-turbines are not yet available, whereas the principal universal characteristics for a very limited number of types are available. However, considering the fact that nowadays the type of reversible hydroelectric power plants for a very wide range of heads from 100 to 1200 m is designed, the need for determining the basic parameters of the pump-turbines and, depending on those parameters, the need for determining the reversible hydroelectric power plant itself are imposed. At today’s level of research the selection of reversible pump-turbines can be made on the basis of 0 tsyTTTsjföwjp^DgiccD | | ^[M^lTD^QDtrS | stran 532 Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible Sl. 4. Glavna splošna karakteristika RPT Fig. 4. Main universal characteristic of RPT (1) sistematizacije in analize statističnih podatkov sedanjih RHE, ki so že v obratovanju ali pa so v fazi projektiranja oziroma gradnje. Na inštitutu MISI v Moskvi, na Katedri za izkoriščanje vodne moči, je bila pod vodstvom prof. Aršenevskega in ob sodelovanju avtorja tega prispevka opravljena analiza več ko 40 reverzibilnih agregatov različnih zahodnih izdelovalcev. Ob tej priložnosti je bila ugotovljena naslednja odvisnost specifične vrtilne frekvence francisovih reverzibilnih črpalnih turbin v turbinskem režimu: the systematization and analysis of statistical data from the reversible hydroelectric power plants that are already in operation, being designed, or being built. At the MISI institute in Moscow, in the Department of Utilization of Water Power, an analysis of more than 40 reversible power generation units from different Western manufactures was made under the leadership of Professor Arshenevski, in cooperation with the author of this paper. On that occasion the following dependence of the specific number of revolutions of the Francis reversible pump-turbines in the turbine working mode was found: n•1,36-P 1212 H 4HH0. tmax S/-" tmax tm .4 max (6), pri čemer so: n - vrtilna frekvenca, min1 P - največja moč, kW H - največji turbinski padec RHE, m. enačba: Z analizo podatkov [1] se dobi naslednja where n is the rated number of revolutions (min-1) P is the maximum power (kW) Ht is the maximum turbine fall on the reversible hydroelectric power plant (m) If these facts are processed (1) the following ratio is obtained: 1000^1300 n= sRPT 0,4 H (6'). t max Analiza parametrov reverzibilnih hidravličnih strojev nekaterih RHE v nekdanji ZSSR in v ZDA je pokazala, da obstaja tendenca povečanja specifične vrtilne frekvence, zato je bolj However, an analysis of the parameters of reversible hydraulic machines on some reversible hydroelectric power plants in the former USSR and the USA showed that there is a tendency towards an I IgfinHŽslbJlIMlIgiCšD I stran 533 glTMDDC Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible primeren naslednji izraz: increase in the specific number of revolutions, therefore the following relation is more appropriate: ns = RPT 1200 + 1500 H (6''). Zanimivo je primerjati specifično vrtilno frekvenco običajnih turbin (nst) in reverzibilnih črpalnih turbin (ns ). Za klasične HE s francisovimi turbinami lahko ta parameter izrazimo kot funkcijo imenskega padca [3]: tmax It is interesting to make a comparison of the specific number of revolutions of a conventional turbine (nst ) and that of reversible pump-turbines (nsRPT ). For conventional hydroelectric power plants with Francis turbines this parameter can be expressed as a function of the rated fall: nst = 2300 H (7). opt Za klasične HE velja razmerje: On the other hand, the following ratio applies for conventional hydroelectric power plants: H opt H 0,78 - 0,95 max Če vzamemo srednjo vrednost Hop/Hmax = 0,88, dobi enačba (7) obliko: nst = Razmerje med specifično vrtilno frekvenco reverzibilnih in klasičnih francisovih turbin tako izračunamo z enačbo: If the mean value Hopt/Hmax = 0.88 is adopted, equation (7) assumes the following form: 2070 H (8). max The ratio of the specific number of revolutions of the reversible and conventional Francis turbines gives the following relation: n sRPT = 0,58H 0.1 n st t max (9). Na podlagi H in P lahko po enačbi (6) določimo vrtilno frekvenco turbine: n = 1040 Dobljeno vrednost zaokrožimo na najbližjo sinhrono vrtilno frekvenco. Na sliki 5 so podani rezultati analize odvisnosti glavnih izmer delovnih koles nekaterih že izvedenih reverzibilnih črpalnih turbin (RPT) pri H od specifične vrtilne frekvence ns . Odvisnost enotske RPT vrtilne frekvence n11 =f(ns ) lahko na temelju izvedene analize priporočimo v obliki: As Htmax, and P are known, the number of turbine revolutions can be determined according to equation (6): H0.5 tmax 4p (10). The value obtained is approximated to the nearest synchronous number of revolutions. Figure 5 gives the results of the analysis of dependence of the main working wheel dimensions of some reversible pump-turbines already in operation, with Htmax on the specific number of revolutions nsRPT . The dependence n11 =f(nsRPT ) can be recommended in the following form on the basis of the analysis carried out: n11=82 + 0,05-ns (11). V tem primeru bo premer delovnega kolesa: In this case the working wheel diameter will be: D 1Ht max (82 + 0,05-nsRPT)7^Htm 1040-H0 (12). Če dobljeno vrednost D1 zaokrožimo na višjo vrednost do 0,1 m, moramo preveriti, ali smo dobili največjo višino v črpalnem režimu. Iz teorije črpalk je poznano razmerje [5]: If the obtained value D1 is approximated to a higher value of up to 0.1 m it is necessary to check whether the maximum head in the pump working mode has been obtained. The following ratio is known from the theory of pumps: H =K u12 = K (n'D^n 2g 2g{ 60 (13), 0 BnnBjfokJ][p)l]Olf|ifrSO | I^SIFÜWEI&I stran 534 Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible Sl. 5. Odvisnost izmer delovnega kolesa RPT od n [2] Fig. 5. Dependence of RPT working wheel dimensions s on ns [2] pri čemer je K=0,8 - 0,9, iz tega izhaja: where K=0.8-0.9, therefore: Hpmax =(0,000111- 0,000126)-n2-D12 (14). od: Tako dobimo premer D1 ki ne sme biti manjši Thus the diameter D1 is obtained, which must not be smaller than: D1 = (89 - 95)Hpm Obdelava statističnih podatkov že izdelanih reverzibilnih hidravličnih strojev je pripeljala do izkustvene odvisnosti enotnega pretoka Q11 (l/s) pri obratovanju v turbinskem režimu pri H v obliki [2]: n (15). The processing of statistical data on reversible hydraulic machines that are already built has led to the experimental dependence of the unit flow Q11 (l/s) in the case of maximum operation in the turbine working mode in the following form [2]: Q11 =(0,008 - 0,012)ns2RP (16). Po drugi strani pa lahko vrednost Q11 določimo po enačbi za specifično vrtilno frekvenco [2]: On the other hand, the value Q11 can be determined according to the equation for the specific number of revolutions: 3,65-n11-y]Q11-h (17), pri čemer ima Q11 mero m3/s. Če vzamemo vrednost h = 0,9, dobimo povezavo: where Q11 has the dimension m3/s. If the value h = 0.9 is assumed, the following relation is obtained: Q11 =(0,029 - 0,032)n1sR.8P (18). Glede na to je premer delovnega kolesa So the diameter of the working wheel upoštevajoč (11) in (16): considering (16) and (11) is: 1,166-n11-Vp D sRPT tmax (19). Premer delovnega kolesa se lahko izračuna tudi iz enačbe za moč in enotski pretok Q11 z upoštevanjem enačb (16) in (18): On the otherr hand, from the equation for the power and unit flow Q11 and by taking into account the relation (16) and (18) it is also possible to calculate the diameter of the working wheel: gfin^OtJJIMISCSD 02-10 stran 535 |^BSSIfTMlGC Mrki} M.: Analiza parametrov reverzibilne - An Anlysis of the Parameters of Reversible D1 = P 9,81 H Jh-Q11-h (20). Bodimo pozorni na koeficiente v števcu enačbe (15). To so vrednosti n11 v Črpalnem režimu za H kjer je n11t > n11p , saj je Htmax < Hpmax. Ob znani vrednosti D1 lahko izhodni premer delovnega kolesa (v turbinskem režimu) D2 , višino dovodnega aparata B1 in celotno višino delovnega kolesa B (sl. 2) določimo po diagramu na sliki 5. 3 DOLOČITEV SESALNE VIŠINE RPT Eden izmed najpomembnejših parametrov, ki odločujoče vpliva tudi na zasnovo RHE, je lega delovnega kolesa reverzibilnega stroja glede na najmanjšo koto vode v spodnji akumulaciji oziroma sesalna višina reverzibilnih hidravličnih strojev. Za RHE je značilno, da je treba sesalno višino določiti izhajajoč iz pogojev obratovanja v črpalnem režimu. Koeficient kavitacije je v tem režimu večji kakor v turbinskem režimu. Tako je na primer za RPT Kijevske RHE kavitacijski koeficient v optimalnem turbinskem obratovanju sT = 0,12 v črpalnem pa sP = 0,33. To je razlog, da je črpalka v primeru trojnih agregatov vedno vgrajena pod turbino. Po drugi strani pa je vgradnja delovnega kolesa na globinah 20 do 50 m ali več odvisna od zasnove podzemeljske ali polpodzemeljske strojnice RHE, kar ima za posledico povečanje Let us look at the coefficients in the numerator of equation (15). These are the values n11 in the pump working mode for Hpmax, where n11t >n11 p , because of Ht max