SIMULATION OF GAS TURBINES OPERATING IN OFF-DESIGN CONDITION

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1 SIMULAION OF GAS URBINES OPERAING IN OFF-DESIGN CONDIION Analdo Walte: Univesity of Campinas Dept. of Enegy DE/FEM/Unicamp P.O. Box ZIP code Bazil Abstact. In many counties themal powe plants based on gas tubines have been the main option fo new investment into the electic system due to thei elatively high efficiency and low capital cost. Cogeneation systems based on gas tubines have also been an impotant option fo the electic industy. Feasibility studies of powe plants based on gas tubine should conside the effect of atmospheic conditions and pat-load opeation on the machine pefomance. Doing this, an off-design pocedue is equied. A G off-design simulation pocedue is descibed in this pape. Ruston RM was used to validate the simulation pocedue that, geneal sense, pesents deviations lowe than 2.5% in compaison to manufactue s data. Key wods. Gas tubines; simulation. 1. INRODUCION Gas tubines maket has isen continuously duing last two decades. In many counties combined cycles ae the main option fo centalized powe secto expansion. On the othe hand, distibuted powe geneation has played a vey impotant ole as well and, in this categoy, cogeneation plants based on gas tubines have been a choice of pefeence. Gas tubine pefomance at ISO basis (buning a efeence fuel, as natual gas, at 15ºC, 1 atm, and 60% elative humidity), is an infomation always povided by machine manufactues. Nevetheless, a G fequently opeates unde an off-design condition as, fo instance, at pat load o unde diffeent atmospheic conditions, and in these conditions changes of pefomance can be damatic. A good pediction of G off-design pefomance is essential fo accuate technical and economic assessments. Off-design simulation of gas tubines equies a special pocedue. his pape pesents the basics of G off-design simulation, highlighting the impact ove the esults of some paametes evaluation, such as (i) new compesso pessue atio, (ii) coected compesso ai mass flow and (iii) coection of compesso efficiency. wo diffeent off-design situations ae analyzed: (i) G opeation unde vaiable ambient tempeatue, and (ii) pat load G opeation at ISO basis. 2. GAS URBINE OFF-DESIGN SIMULAION PROCEDURE A gas tubine off-design simulation pocedue evolves two steps. he fist one is a tuning phase, while the second is the simulation itself unde an off-design condition. he tuning step coesponds to the evaluation of unknown G paametes, usually not povided by

2 manufactues, suchlike compesso and tubine efficiencies, G fiing (maximum) tempeatue, pessue and themal losses and cooling ai faction. uning pocedue equies both an appopiate set of equations modeling enegy convesion inside the machine and the knowledge of some G opeational and pefomance paametes (tubine inlet tempeatue, themal efficiency, gas exhaust tempeatue, etc.) to check tuning adequacy. his shall be done fo a well-known opeation condition, as G full load opeation at ISO basis, fo which basic data ae pesented at the open liteatue. In pedicting machine off-design pefomance a special pocedue that uses the ISO known solution (modeling and setup paametes) as the stat point is applied. Vis-à-vis the basic modeling, additional functions ae equied to pedicted evising of some G paametes. Responding to ambient tempeatue vaiation o G de-ating (eduction of maximum gas tempeatue) a G can pesent substantial changes in compesso pessue atio, compesso ai mass flow and opeational efficiencies of both compesso and expande. he machine consideed in this pape is the fist vesion of fome Ruston RM model, an industial machine, single-shaft, pecusoy of cuent ABB Alstom yphoon, fo which a detailed pefomance map was available (Gas ubine Wold, 1987). Gas tubine manufactues geneally pesent off-design data on thei poducts in tems of pefomance paametes at diffeent ambient tempeatues (Desidei, 1994), but detailed infomation on pat load ae not usual. he pefomance map was detemined fo the following hypothesis: intake and exhaust losses equal to 10 and 20 mba, espectively, altenato efficiency 97% and gea box efficiency 98.2%. his map defines a efeence of compaison fo off-design cases that coespond to vaying ambient tempeatue and pat load opeation at ISO basis. Basic pefomance data of Ruston RM at ISO basis ae pesented in able 1 while off-design pefomance cuves ae pesented in Figues 1 and 2. able 1 also pesents estimated paametes duing tuning phase that vanish eos vis-à-vis declaed ISO ated pefomance. able 1. Ruston RM pefomance paametes at ISO basis and estimated paametes at tuning Manufactue pefomance paametes Gas tubine powe 3789 MW G themal efficiency 29.84% ubine inlet temp. I ºC ubine exhaust temp. E 500ºC Compesso pessue atio 12.8 Exhaust gas mass flow kg/s Estimated and imputed paametes Compesso isentopic effic. 83.0% Expande isentopic efficiency 87.69% Cooling ai faction 18.06% G maximum tempeatue ºC Compesso inlet flow 16.6 kg/s Fuel flow (LHV MJ/kg) kg/s Combusto pessue dop 5.5 dp/p Combusto efficiency 99% 3. G Modeling and Off-Design Equations he set of equations modeling enegy convesion within the main components of a gas tubine (compesso, combustion chambe and expande) ae not pesented hee. Basically, compesso and expande equations ae defined fo polytopic pocesses of known efficiencies allowing the evaluation of gas outlet tempeatue and the powe evolved with the compession and the expansion. Compesso equations ae functions of the inlet paametes (ai tempeatue, pessue and mass flow), the compesso pessue atio and the isentopic

3 efficiency. Convesely, expande equations ae function of tubine inlet paametes (tempeatue I and pessue IP), expande pessue atio (diffeent fom compesso pessue atio due to pessue losses at the combustion chambe) and the isentopic efficiency. Powe output [kw] powe efficiency Ambient tempeatue [C] hemal efficiency [%] Figue 1. Ruston RM powe output and themal efficiency as function of ambient tempeatue Powe outuput [kw] powe efficiency Load [%] hemal efficiency [%] Figue 2. Ruston RM pat load powe output and themal efficiency 15ºC he fuel input is calculated though an enegy balance at the combustion chambe, imposing that a specified maximum gas tempeatue should be veified. he maximum gas tempeatue is even evaluated as function of the known I o just specified to contol G powe output. Fo a given gas tubine, the compesso pessue atio is only known fo the efeence ISO case. As long as atmospheic popeties change o de-ating is imposed, compesso pessue atio vaies. An essential featue of a G off-design pocedue is its ability in

4 evaluating new compesso pessue atio. Doing this it is assumed that the flow at the inlet to the gas tubine expande is always choked. his is a vey easonable assumption fo a wide ange of G opeation conditions (Cohen et al, 1996). he mass flow equation fo choked flow of an ideal gas Eq. (1) - is used to calculate the new pessue atio. m = pa * Mol γ 2 R 1 γ + γ + 1 γ 1 (1) whee m is the gas mass flow, p is the total pessue, A* is the citical aea whee the flow is choked, Mol is the gas molecula weight, is the gas tempeatue (absolute), R is the univesal gas constant and γ is the atio of specific heats of the gas. All popeties ae evaluated at the gas tubine expande inlet section. Equation (1) should be fist applied to the efeence case, allowing the evaluation of A* that is set constant heeafte. A second impotant featue of an off-design pocedue is the coect evaluation of compesso ai mass flow. In the simulation model hee pesented, two diffeent situations should be identified: (i) when the compesso opeates with ai inlet popeties equal to the ISO case (15ºC, 1 atm), but with diffeent pessue atio due to G de-ating (o lowe LHV fuel), and (ii) when just ai inlet popeties change. An industial single-shaft gas tubine, as the one consideed hee, always opeates ove the same compesso unning-line if it is connected to electic gid (changes in G otation ae not possible) and, in addition, if atmospheic popeties ae kept constant. Running-line (RL) is defined by the compesso speed N and the ai tempeatue at the compesso entance; a unning-line 100, o 100%, means that the compesso opeates at its nominal speed being the inlet ai at the compesso design tempeatue (in geneal, 15ºC). Changing inlet ai tempeatue, but keeping the compesso velocity, the new unning line can be evaluated by Eq. (2). RL = 100 (2) A compesso unning-line can define how inlet ai mass flow vaies with pessue atio, but compesso maps and, consequently, thei unning-lines - ae geneally not known fo a given gas tubine model. he pocedue hee poposed is just conside a geneic unning-line; the effect upon the simulation esults of thee diffeent unning lines, taken fom geneic compesso maps, ae then analyzed. he unning-lines consideed ae pesented in Figue 3, elating compesso pessue atio to its educed ai mass flow - RMF. Fo all thee cuves, RMF = coesponds to compesso opeation at 15ºC, 1 atm, when inlet ai flow is 16.6 kg/s and compessing pessue atio is RMF is defined accoding to Eq. (3): m RMF = p (3) Fo a defined compesso unning-line, once the new compesso pessue atio is known (fom Eq. 1) it is then possible to evaluate the coected ai flow. he code used do this though a simple function elating the compesso educed mass flow (RMF) to its pessue

5 atio. It should be noticed that ai flow coection and the evaluation of new compesso pessue atio is always an inteactive pocedue. Pessue atio C1 C3 C2 2,70 2,72 2,74 2,76 2,78 2,80 2,82 Reduced mass flow (RMF) Figue 3. Consideed unning-lines fo thee diffeent compesso maps Changes in ambient tempeatue coespond to the second off-design case. As seen befoe, in this situation the compesso no longe opeates ove the same known unning-line, and a new pocedue is equied to adjust ai mass flow. Fo a constant-speed compesso, constant volumetic ai flow equation could be used once its vanes ae completely opened. o bette fit to the ai flow changes, the poposed equation (Eq. 4) incopoates a flow coection popotional to the deviation of inlet ai tempeatue. Rigoously, coection facto CF must be evaluated fo each gas tubine. he subscipt efes to a efeence condition, e.g., the ai mass flow at ISO basis. m = m p p 1 + CF (4) he thid coection that should be done to the basic set of equations coesponds to the compesso efficiency adjustment as fa as pessue atio changes. he fist option hee pesented is based on the assumption that compesso isentopic efficiency vaies with pessue atio while polytopic efficiency is essentially kept constant (Cohen et al, 1996). Equation (5) shows the elation between isentopic (γ i ) and polytopic (β) efficiency as function of compesso pessue atio (PR): γ 1 γ 1 γ γβ ηi = PR 1 PR 1 (5) In applying Eq. (5) it is fist necessay to evaluate polytopic efficiency fo the efeence solution (ISO), consideing a given tuning value of isentopic efficiency (see able 1). Based on this equation the isentopic efficiency inceases as fa as pessue atio dops; this tendency is just coheent fo not high flowed G compesso, paticulaly when eductions on

6 compesso pessue atio ae caused by eductions on inlet ai flow (Ragland, 1998) (e.g., when ambient ai tempeatue ises). Altenatively, exclusively fo off-design cases that coespond to changes of ambient tempeatue Eq. (6) could be used to adjust compesso isentopic efficiency. his equation is based on GateCycle softwae (GateCycle, 1998) and imposes a coection as function of unning-line changes. Evaluating new RL value, Eq. (2) can be used. As in Eq. (4), the subscipt efes to a efeence condition, e.g., the compesso efficiency at RL (ISO basis). Again, if possible, coection facto ECF should be evaluated fo each gas tubine modeling. η i = η i 2 1 RL RL ECF RL (6) Finally, as an altenative to Eq. (5) an option was defined to coect compesso isentopic efficiency fo cases in which the unning-line is constant but the pessue atio changes (off-design with G de-ating, fo instance). In this case, a geneic polynomial function on PR was defined based on the shape of geneic efficiency cuves available at the liteatue (Cohen et al, 1996). Fo the unning-line that coesponds to ISO basis opeation, its maximum value is 0.83 (see able 1) at PR = OFF-DESIGN SIMULAION RESULS AND DISCUSSION o validate the poposed code fo off-design situations Ruston RM was simulated consideing vaiations of ambient tempeatue and G pat load opeation at ISO basis. In the fist case, compesso pessue atio and compesso efficiency change just in esponse to the alteation of compesso ai flow. In the 0-40ºC ange it is supposed that no G contol opeation, such as de-ating o closing inlet guide vanes, is applied. he diffeence between simulated cases 1 and 2, as summaized in able 2, is the function used to coect compesso pessue atio. Coection facto CF used in Eq. (4) was evaluated as the aveage value between those that allow eo minimization in each simulation case vis-à-vis manufactue declaed powe output in the whole ange of tempeatues. able 2. Summay of simulated off-design cases Off-design case Case Equations used Pessue atio Ai flow Compesso effic. Ambient tempeatue 1 Equation 1 Equation 4 (CF = ) Equation 5 Ambient tempeatue 2 Equation 1 Equation 4 (CF = ) Eq. 6 (ECF=0.20) Pat load 3 Equation 1 Running-line C3 Polynomial Pat load 4 Equation 1 Running-line C2 Equation 5 Pat load 5 Equation 1 Running-line C3 Equation 5 Pedicted manufactue esults of powe output and themal efficiency pesented in Figue 1 wee used as basis of compaison. Simulation eos vis-à-vis these pedicted esults ae shown in Figues 4 and 5. Geneal sense, powe output and themal efficiency esults in all ange of tempeatues fit well with pedicted values as the maximum eo is neve lage than 2.5%; simulation eos bellow 3% ae always consideed acceptable. Case 1, in which Eq. (5) is used to coect compesso efficiency, oveestimates powe output and efficiency, while

7 case 2 undeestimates both paametes beyond 15ºC. As the diffeence between the two cases is just how compesso efficiency is coected, it should be concluded that actual compesso efficiency is, appoximately, an intemediate value between these two evaluations. Pat load opeation of Ruston RM at ISO basis was simulated consideing continuos deating. Combination of thee unning-line cuves and two diffeent pocedues to evaluate compesso efficiency gives the numbe of cases simulated. Nevetheless, consideing the accuacy of simulation esults on themal efficiency and on E as well, just the thee best cases ae hee pesented. hese cases ae defined accoding to the infomation shown in able 2. Pedicted manufactue esults of themal efficiency pesented in Figue 2 wee used as basis of compaison. Simulation eos vis-à-vis these pedicted esults ae shown in Figues 6, while eos on E ae pesented in Figue 7. Fo all non epoted cases eos ae slightly lage than those that coespond to case 3. Fom the point of view of efficiency, simulation esults can be consideed good, but fom the point of view of E, and especially fo lowe loads, evaluation is just acceptable. Simulations 4 and 5 give bette esults, but the use of Eq. (5) to adjust compesso efficiency is questionable in this case as isentopic efficiency continuously incease with eduction of pessue atio. he use of a polynomial function to adjust compesso efficiency is moe coheent, but this function should be defined with moe pecision. On the othe hand, the use of unning-lines seems to be easonable, at least to give the ight tendency to ai flow coection. Howeve, it is not possible to peviously know which unning-line will fit bette in each case. Eo on powe output [%] 1,5 1,0 0,5 0,0-0,5-1,0-1,5-2,0-2,5-3,0 case Ambient tempeatue [C] case 2 Figue 4. Simulation eos on powe output Pat load off-design simulation deviates moe fom tuning solution than the case that coesponds to changes in ambient tempeatue. In this sense, the model could be futhe impoved in some aspects, especially on the estimation of cooling ai coection, coection of expande isentopic efficiency and evaluation of I in esponse to G de-ating.

8 Eo on themal eff. [%] 1,5 1,0 0,5 0,0-0,5-1,0-1,5-2,0 case case 2 Ambient tempeatue [C] Figue 5. Simulation eos on themal efficiency Eo on themal eff. [%] 0,0 50-0, ,0-1,5 case 4-2,0 case 5-2,5-3,0 case 3 Load [%] Figue 6. Pat load opeation simulation eos on themal efficiency Eo on E [%] 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 case 3 case 4 case Load [%] Figue 7. Pat load opeation simulation eo on E

9 5. CONCLUSIONS he code pesented in this pape leads to quite easonable esults on off-design G simulation. Deviations egad manufactue pefomance data ae lage as fa is off-design condition fom ISO point, i.e. highe ambient tempeatue and lowe G load. Nevetheless, fo the majoity of conditions simulated, eos ae lowe than 3%, that is the acceptable eo in a commecial softwae. Acknowledgments he code pesented in this pape was patially developed duing a post-doctoal season at the National Renewable Enegy Laboatoy - NREL, Golden, USA, fom he autho is gateful to Fundação de Ampao à Pesquisa do Estado de São Paulo - FAPESP - fo the financial suppot eceived at that time. REFERENCES Cohen H, Roges G and Saavanamuttoo H., 1996, Gas ubine heoy, Essex, Longman Goup Limited. Desidei U., 1994, Pefomance analysis of gas tubines opeating at diffeent atmospheic conditions, Poceedings of ASME Cogen ubo Powe 94, Octobe, Potland, pp GateCycle, 1998, Uses Manual of GateCycle fo Windows, Ente Softwae, Palo Alto, USA. Gas ubine Wold, 1987, Ruston woking on a pai of small high efficiency engines, Gas ubine Wold, Vol. 17, n. 3, pp Ragland,.L., 1998, Industial gas tubine pefomance upates: tips, ticks, and taps, Jounal of Engineeing fo Gas ubine and Powe, Vol. 120, Octobe, pp

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