Chate NUCLEAR REACOR CONCEPS AND HERMODYNAMIC CYCLES M. Ragheb 6//06. INRODUCION Nuclea fission eactos shae the same basic design concet in that they have a coe in which the fission chain eaction oceeds. hey diffe fom fossil fuel owe lants in that they ae closed systems, athe than oen systems. In oen systems, the oducts of combustion with thei associated ollutants ae disesed and diluted in the atmoshee, since thei amounts ae so lage that containing them is not ossible. Nuclea owe lants geneate small amounts of fission oducts that ae contained within the system fo late disosal. Being adioactive, thei elease fom the eacto coe is evented with incooation into the design of multile baies and engineeed safety featues. he fission enegy is thee initially the kinetic enegy of the fission oducts of some fissile element fuel in the coe. Often a fetile mateial is also esent which can be bed into a fissile mateial though neuton tansmutations. his kinetic enegy is lost to the suounding stuctue in the fom of heat. A coolant is bought in to extact the heat. he coolant can also act as a modeato educing the enegy of the fast fission neutons enegy fom its aveage value of MeV to the themal equilibium enegy of 0.05 ev, whee the obability of fissioning the fissile element is damatically inceased. A neuton eflecto suounds the coe. he heat fom the coolant is moved to a heat tansfe cycle whee eventually electicity o ocess heat fo othe alications such as desalination, hydogen oduction, o distict heat, is oduced. Safety systems ae incooated into the design to ovide safety to the oeatos and membes of the ublic unde all foeseen conditions.. ENERGY CONVERSION PRINCIPLES, FLOW SYSEMS ASSYMERIES A fist basic incile of enegy convesion o extaction fom the envionment can be simly enunciated as: A coollay is that: Enegy can only be extacted fom a flow system. he enegy flow is fom a high enegy stoage esevoi to a low enegy sink. In hydoelectic owe geneation, the otential enegy of wate blocked behind a dam, a watefall o a dam on a ive o steam cannot be extacted unless it is allowed to flow. In this case
only a at of it can be extacted by a wate tubine. In a heat engine, the heat enegy cannot be extacted fom a totally insulated esevoi. Only when it is allowed to flow fom a high temeatue esevoi at which heat is added, to a low temeatue esevoi whee it is ejected to the envionment, can a faction of this enegy be extacted by a heat engine. In geothemal enegy oduction the diffeential temeatue dee undegound close to the magma and the Eath suface allows fo an enegy flow oducing steam to dive a steam tubine. In Ocean hemal Enegy oduction (OEC) the coole temeatue dee in the ocean comaed with the wame temeatue at the suface allows fo the boiling of a low boiling-oint woking substance such as ammonia (NH) at the suface and then its condensation at the coole deth esulting in a flow system. Ocean tidal owe geneation deends on the flow of wate stoed at a eiod of high tide behind a dam to flow out of stoage at a eiod of low tide. Ocean wave oduction uses the diffeence in the kinetic enegy content in waves fom cest to bottom geneated by wind flow on the suface of the wate. otally blocking a wind steam does not allow efficient enegy extaction. Only by allowing the wind steam to flow fom a high seed egion to a low seed egion can enegy be extacted by a wind enegy convete. A second incile can be stated as: Only asymmeties in a hydaulic, kinetic, themodynamic o aeodynamic system allow the extaction of a otion of the available enegy in the system. Ingenious devices, concetualized by ingenious eole, take advantage of natually existing asymmeties. Altenatively, ingenious atificial configuations o situations favoing the ceation of these asymmeties ae ceated so as to extact enegy fom the envionment. A thid incile is that: he existence of a flow system necessitates that only a faction of the available enegy can be extacted at an efficiency chaacteistic of the enegy extaction ocess, with the est etuned back to the envionment. In themodynamics, the ideal heat cycle efficiency is exessed by the Canot cycle efficiency. In a wind steam, the ideal aeodynamic cycle efficiency is exessed by Betz s efficiency equation [].. MAIN REACOR CONCEPS he owe geneated within the coe is ootional to the neuton density, o the numbe of neutons e unit volume and thei seed. he owe of the eacto can be contolled though managing the neuton density by moving ods of neuton absobing mateial like cadmium o boon, into o out of the coe. When these contol ods ae fully inseted, the chain eaction is stoed. Altenatively, a fuel od moved into o out of the coe, o a otion of a eflecto dislaced, would have the same contol effect.
Diffeent eacto concets can be consideed by choosing a comatible set of fuel, coolant, modeato and safety and contol stategies. hee exist seveal fission eacto concets that constitute the esent geneation of nuclea fission owe lants. able shows some of these main concets egading thei coe volume and thei owe density defined as: MWth q''' Ef f [ ] () m whee: Ef is the enegy elease e fission event = 00 [MeV / fission] =.x0 - [Watt.sec / fission], f is the macoscoic fission coss section in [cm - ], is the aveage neuton flux in [neutons / (cm.sec)]. Highe owe densities ae associated with smalle coe sizes and volumes. Small coe volumes ae favoable fom a caital cost esective, meaning that fewe mateials will have to be manufactued fo constucting the coe. Howeve, highe owe densities equie stingent heat tansfe systems and highe levels of needed oeational safety. he design enginees always ty to achieve a comomise between the cost and the desied level of safety. ye able. Powe densities and coe volumes in fission owe eactos. Descition Coe Aveage Powe Density [MWth/m ] Coe Volume [m ] PWR Pessuized Wate Reacto, HO 75.0 40.0 BWR Boiling Wate Reacto, HO 50.0 60.0 HGR High temeatue Gas-cooled Reacto, Gahite modeated, He cooled 7.0 48.6 GCFR LMFBR Gas Cooled Fast Reacto, He cooled, Fast neuton Beede Liquid Metal Fast Beede Reacto, Na cooled, Fast neuton Beede able. Powe data fo fission owe eactos. 80.0 0.7 50.0 5.7 Pimay ubine Oveall Powe coolant exit temeatue themal ye Level Pimay coolant temeatue and essue efficiency MWe and essue o C/atm o C/atm [ecent] PWR,00 Pessuized HO HO HO
0/58 84/68 BWR,00 Boiling HO HO 86/7 HO 8/67 AGR 600 Advanced Gas-cooled CO HO Reacto, Gahite 648/40 58/6 modeated, CO cooled HGR,00 High temeatue Gascooled Reacto, Gahite modeated, He cooled LMFBR,000 Liquid Metal Fast Beede Reacto, Na cooled, Fast neuton Beede GCFBR,000 Gas cooled Fast Beede Reacto, He cooled He 778/48 Na 65/0 He 568/4 HO 50/66 HO 58/69 HO 50/80 4 4 8 4 6 able. Fuel data fo fission owe eactos. Fuel loading ye [tonnes] heavy metal PWR 0 UO BWR 47 UO AGR 0 UO HGR 9 UC-hO LMFBR 9 PuO-UO GCFBR 8 PuC-UO Fissile enichment [ecent] Dischage bunu [MW.day/t onne heavy metal] Fuel Rating [kw/kg heavy metal] Fissile ating [MW/kg fissile ating] Powe density [kw/lite] Convesion, Beeding atio.,500 7.50 9.0 0.60.7 7,500 5.0 56.0 0.70. 8,000 0.54.7 0.50 4. 98,000 77.90 8.4 0.65.5 67,000 6.00 80.0.7.7 7,000 9 0.7 59.0.9.4 MULIPLE BARRIERS DESIGN CONCEP Undelying nuclea fission eactos designs is thei lage inventoy of fission oducts and the concen that an accident might exose the oulation aound the eacto site to hazadous levels of adiation. It is not ossible fo a owe lant to disese these substances with the exlosive foce of a weaon device, since they ae designed diffeently. he concen is that an accident might elease a hazadous amount of adioactive elements to the envionment.
Diffeent eacto systems designs shae the same concet fo the containment of adioactive eleases. o make cetain that the adioactive mateials, incially the fission oducts ae etained within the eacto system; they ae suounded by a seies of hysical baies as shown in able 4. o each the envionment, the adioactive fission oducts would have to enetate all these baies in succession. hese baies ae imaily at of the lant's design fo nomal oeation. able 4. Multile baies concet to contain fission oducts in nuclea owe lants. Baie o Laye Function. Ceamic fuel ellets A faction of the gaseous and volatile fission oducts can be eleased fom the oous ceamic fuel ellets.. Metal fuel cladding Contains the fission oducts eleased fom the fission ocess. Less than 0.5 ecent of the tubes develo inhole sized leaks though which fission oducts would escae, ove the lifetime of the fuel.. Reacto vessel and iing. he 8-0 inch thick steel vessel and 4-inch thick steel iing contain the eacto coolant. A otion of the coolant is continuously assed though filteing tas keeing the coolant activity at a low level. 4. Concete shield Plant oeatos and equiment ae otected fom coe adiation by biological concete shields 7-0 feet thick. 5. Containment stuctue he entie nuclea island is enclosed to otect fom the outside elements such as huicanes o tonado winds. Any elease of adioactivity in case of eacto cooling wate ie leakage o utue is quenched by a containment say system. High essue and low-essue coolant um ovide cooling in case of a eacto imay coolant loss. 6. Exclusion aea A designated aea aound each lant seaates the lant fom the ublic. Entance is esticted. 7. Plant seaation distance Plants ae sited at a distance fom oulation centes..5 ENGINEERED SAFEY FEAURES (ESFs) AND DEFENSE IN DEPH DESIGN PRINCIPLE Successive Engineeed Safety Featues (ESFs) ae a at of a nuclea owe lant design to otect against thee tyes of occuences:. Equiment failues.. Human Eo.. Sevee natual events.
Figue. Engineeed Safety Featues fo the PWR Concet. Any sudden incease in owe level is counteed and limited by hysical self-egulating ocesses such as the negative temeatue coefficients of eactivity. he ESFs fo the PWR concet ae shown in Fig.. hese include:. he contol ods, to shut down the chain eaction.. he containment vessel and its say system, to quench any steam eleased into the containment.. he accumulato tanks containing a suly of wate unde nitogen essue fo emegency cooling. 4. A esidual heat emoval system heat exchange. 5. A High Pessue Coolant Injection system, HPCI. 6. A Low Pessue Coolant Injection system, LPCI. 7. A boon injection tank to shut down the chain eaction in case the contol ods ae not caable of being inseted into the coe. 8. An exta suly of cooling wate in the efueling stoage tank.
Figue. Engineeed Safety Featues fo the BWR Concet. he ESFs fo the Boiling Wate Reacto (BWR) concet ae also shown in Fig.. It shaes simila comonents with the PWR ESFs, and include:. he contol ods, to shut down the chain eaction.. he containment-say system, to quench any steam eleased unde abnomal conditions.. he essue suession ool to condense any steam leaking into the containment vessel. 4. A esidual heat emoval system heat exchange. 5. A High Pessue Coolant Injection system, HPCI. 6. A Low Pessue Coolant Injection system, LPCI. 7. A boon injection tank to shut down the chain eaction in case the contol ods ae not caable of being inseted into the coe. 8. An exta suly of cooling wate in the condensate stoage tank. 9. An intenal coe-say system. he system is designed to oeate with wide magins of stability, so that it will toleate a boad sectum of malfunctions and eos. Only tested, oven mateials ae used in constuction, and they assembled and tested with stict quality assuance citeia. Instuments and contols ae edundant, with one system substituting fo anothe so that oeatos at all times ae awae of, and can egulate eacto conditions. he assumtion is made that the equiment will fail and that oeatos will make eos. he eacto thus has built into it extensive systems to monito temeatue, essue, wate levels in the coe, and othe asects of oeation beaing on safety. he sensos ae linked to automatic contol systems that adjust o shut down the eacto if edetemined levels ae exceeded. he contol mechanisms ae designed to be fail safe: that is the malfunction of any comonent in the netwok activates the oveall system. Mechanisms ae designed to be edundant and indeendent: if one fails, anothe is available to efom the same otective action. he system is designed fo accidents mitigation, a safety measue shaed with the aeosace industy.
, o F 500 Rankine, Steam ubine cycle Bayton, Gas ubine cycle 000 Sueheate Reheate Heat Addition ubine ubine Exansion Evaoato Recueato Addition 500 Economize Recueato Rejection Comesso Feed Heates Heat Rejection 0 S Figue. Comaison of the Gas ubine Bayton Cycle to the Rankine, Joule o Steam Cycle on a emeatue-entoy S Diagam. he most sevee hyothetical accidents ae assumed, eflecting combinations of highly imobable failues occuing all at the same time. hese design basis accidents include such emotely cedible events as the sudden ejection of the most citical contol od, a beak in a steam line, a Loss of Coolant Accident (LOCA) and othe events. Extenal events ae assumed such as a 00 miles/hou tonado o huicane, the most sevee eathquake in the seismic egion and the obable maximum flood. o conside these events does not imly that they ae likely to occu, but fo each of these incidents, the designe ovides divese and edundant safeguads in the fom of the Engineeed Safety Featues..6 HERMAL POWER CYCLES Most owe eacto designs use the Steam, o Rankine cycle as shown in Fig.. he newe osective designs take advantage of new develoments in tubine technology such as magnetic beaings, and use the Bayton, Joule o Gas ubine cycle shown in Fig.. With the use of the Bayton gas tubine cycle, the gaseous coolant such as helium coolant is enclosed in a single cicuit moving fom the comesso to the tubine. he ossibility of its deessuization o leakage is minimized, and it is not eactive with gahite like steam would be. he designs can oeate at highe temeatues and offe a high value of the themal efficiency aound 40 ecent, comaed with the 0 ecent value fo light wate eactos. he high
temeatues offe the ossibility of ocess heat geneation and use in industial ocesses such as high temeatue wate electolysis fo the oduction of hydogen fo futue non-fossil tansotation fuel sulies. RANKINE OR SEAM URBINE CYCLE he Rankine o steam cycle system is the most widely used cycle in nuclea and fossil owe lants, dating back to the Watt s steam engine used in boiles and steam locomotives fom the beginning of the industial evolution. It uses a liquid that evaoates in a steam geneato when heated and exands to oduce wo k, such as otating a tubine o iston, which when connected to the shaft of a geneato, oduces electicity. he exhaust vao leaving the tubine condenses in a condense and the liquid is umed back to the steam geneato to be evaoated again. he woking fluid most commonly used is wate, though othe liquids such as ammonia o mecuy can also be used. he Rankine cycle design is used by most commecial electic owe lants. BRAYON, JOULE OR GAS URBINE CYCLE he Bayton o gas tubine cycle is suggested fo new nuclea owe lants since it allows oeation at highe temeatues, hence highe cycle efficiencies. It incooates a tubine and a comesso on the same shaft connected to an electical geneato and uses a gas as the woking medium. hee exist oen cycle and closed cycle Bayton systems. he gas tubine is a common examle of the oen cycle Bayton system. Ai is dawn into a comesso, heated and exanded though a tubine, and exhausted into the atmoshee. Nuclea owe lants use the closed cycle Bayton system whee a gas, such as steam, H, CO o He. he gas in the closed cycle system gives u some of its heat in a heat exchange afte it leaves the tubine. It then etuns to the comesso to continue the cycle again. SIRLING CYCLE he Stiling cycle is also called an extenal combustion engine diffes fom the Rankine cycle in that it uses a gas, such as ai, helium, o hydogen, instead of a liquid, as its woking fluid. he extenal souce of enegy could be fom a adioisotoe, heat um fom a fission eacto, concentated sunlight, biomass, o fossil fuels. he extenal heat is ovided to one cylinde. his causes the gas to altenately exand and contact, moving a dislace iston back and foth between a heated and an unheated cylinde. DISSOCIAING GASES CYCLE Dissociating gases which dissociate uon heating and ecombine uon cooling can be used in nuclea owe lants to consideably educe the weight of the heat exchange and otating machiney. Such a eaction can occu in nitogen tetoxide: NO4 NO ()
he doubling of the numbe of molecules in the woking gas fom n to n, doubles the amount of wok e unit mass in the ideal gas equation: PV nr () he esulting doubling of the wok done e unit mass of the woking fluid allows the use of smalle size and weight tubines, comessos and heat exchanges. As oosed by Ragheb and Hadwidge, if used in the oulsion system of a nuclea submaine, it can incease its owe to weight atio and consequently its attainable seed by 0 ecent fo the same eacto owe. he weight eduction makes it also suitable fo sace owe alications. Othe gases such as aluminum chloide and aluminum bomide can be used. Dissociating gas 4 able 5. Candidate dissociating gas systems. Incease facto in gas constant hemal elease fom eaction [Kcal/mole] emeatue Range o C N O NO.7 5-70 NO NO O.5 7.0 40-850 Al B AlB 0.0 00-,400 6 Al Cl AlCl 9.8 00-,00 6 Al I AlI 6.4 0-.00 6 NOB NO B.5-5-500 NOCl NO Cl.5-5-900 AlCl6 4 Al( liquid ) 6AlCl 6 6.8 670-,00 AlB6 4 Al( liquid ) 6AlB 6 8.4 670-,400 AlI6 4 Al( liquid ) 6AlI 6 96.4 670-,00 HgCl Hg( liquid ) HgCl 70.4 80-700 HgB Hg( liquid ) HgB 6.7 50-700 SnCl Sn( liquid ) SnCl 8.6-4 SnB Sn( liquid ) SnB 65. - 4 Ga Cl GaCl 0.0 0-,000 6 Ga B GaB 8.5 50-,00 6 Ga I GaI.0 50-,00 6 GaCl6 4 Ga( liquid ) 6GaCl 6 58.8 00-,000 able 6. Chaacteistics of diffeent tubines using steam and dissociating gases.
HO Steam ubine Woking Fluid HO AlCl6 Steam Gas ubine ubine AlB6 Gas ubine Outut, MWe 500 00 555 40 Pessue, tubine inlet, ata 40 40 80 80 emeatue, tubine inlet, o C 580 580 600 750 Pessue, tubine exhaust, ata 0.05 0.05 5 5 Mass flow ate, metic tonne/h,495 880 7,900,900 ubine evolutions, m,000,000,000,000 Numbe of exhausts 4 4 otal numbe of tubine stages 4 9 6 Mean diamete of last stage, m.550.480.8 0.95 Height of last stage blade, m.050 0.960 0.495 0.50 Intenal efficiency High essue cylinde - 80.0 89.9 90.0 Intemediate essue cylinde - 89.5 - - Low essue cylinde - 8.0 - - Numbe of tubine shafts ubine length, m 9.. 9.0 7.6 Weight of tubine, metic tonnes 964 690 55 90 Powe to weight atio, [MWe/Metic tonne] 0.5 0.4 0.09.78 he damatic advantage of using dissociating gases is a educed size and weight in the tubo machiney. A 500 MWe steam tubine would measue. metes in length comaed with just 9 metes fo a 555 MWe AlCl6 tubine. his is associated with an incease by a facto of 0.09/0.5 = 9.4 in the owe to weight atio. he educed weight in the othe associated heat tansfe equiment makes dissociating gases a omising choice fo sace, naval oulsion, sace alications, as well as cental station alications. KALINA CYCLE he Kalina cycle can be used in nuclea owe alications inceasing the efficiency u to 0 ecent. It is simle in design and can use eadily available, off the shelf comonents. It is simila to the Rankine cycle excet that it heats two fluids, such as a mixtue of ammonia and wate, instead of one. he dual comonent vao consisting fo instance of 70 ecent ammonia and 0 ecent wate is diected to a distillation subsystem which ceates thee additional mixtues. One is a 40/60 mixtue, which can be comletely condensed against a nomal cooling souce. Afte condensing, it is umed to a highe essue, whee it is mixed with a ich vao oduced duing the distillation ocess. his eceates the 70/0 woking fluid. he elevated essue comletely condenses the woking fluid and etuns it to the heat exchange to comlete the cycle. he mixtue's comosition vaies thoughout the cycle with the advantages of vaiable temeatue boiling and condensation, and a high level of ecueation. Its main use has been so fa in geothemal heat extaction.
.7 ENROPY AND HE EMPERAURE-ENROPY -S DIAGRAM Fo an intenally evesible ocess the change in entoy is elated to the absolute temeatue and change in heat tansfeed as: o: dq ds (4) S S S dq (5) whee: dq = Heat tansfeed in [BU/lbm] o [kjoules / kg] = emeatue in degees Rankine [ o R = 460 + o F] o kelvins [K = 7 + o C] S = Entoy in [BU / (lbm. o R)] o [kjoules / (kg.k)] Fom Eqn. 5, we can deduce that: Q ds (6) A emeatue-entoy o -S diagam shown in Fig. 4 o themodynamic tables can thus be used to calculate the heat Q..8 HE MOLLIER CHAR: ENHALPY-ENROPY DIAGRAM A fluid ossesses stoed intenal enegy u [kj/kg] due to the intenal otential and kinetic enegy of its molecules. hat fluid assing though a system s bounday ossesses an enegy quantity enteing o leaving the system denoted as flow enegy:
Figue 4. emeatue-entoy, o -S diagam fo wate in SI units.
Figue 5. Mollie, Enthaly-Entoy, o H-S diagam fo wate in SI units. P Flow Enegy=PV= ρ (7)
whee: P is the essue of the fluid V is the secific volume of the substance ρ is the density of the substance. Because it often haens in flow oblems, the sum of the flow enegy and intenal enegy, using Joule s constant J, is designated as the enthaly h: PV h=u+ J [kj/kg] (8) o obtain the values of the enthaly, the themodynamic tables o the Mollie Chat o Enthaly- Entoy diagam shown in Fig. 5 ae used..9 CARNO CYCLE EFFICIENCY A themodynamic cycle is defined as a seies of ocesses duing which a substance stats in a cetain state and etuns to its initial state. Heat is added to the substance as Qa and heat is extacted at a heat sink as Q. A heat engine such as a tubine geneates wok as Wtubine, and the fluid is ciculated though the system using a um o a comesso as Wum. In owe oduction, the oveall themal efficiency is defined as: th W Q W Net Wok Outut Heat Inut net a tubine a W Q Qa Q Q a um (9) he Canot Cycle is an idealized owe oduction ocess. It is the most efficient cycle that is conceivable and can be used as the standad of comaison fo all othe heat engines. It consists of fou evesible ocesses, as shown in Fig. 6 fo an idealized Boiling Wate Reacto (BWR):. Isothemal heat addition at the absolute temeatue a, fom oint to oint.. Isothemal heat ejection at the absolute temeatue, fom oint to oint 4.. Isentoic o constant entoy exansion in a tubine fom oint 4 to oint. 4. Isentoic o constant comession in a um o comesso fom oint 4 to oint. Consideing that the heat addition and ejection can be exessed in tems of the change in entoy as:
Q. S a a Q. S (0) In this case the oveall themal efficiency can be deduced by substituting fom Eqn. 0 into Eqn. 9 as: Canot a. S. S S a a a a () Steam Electical Geneato ubine Reacto Coe Qa Heat Addition Condense Reacto Coolant Reciculation Pum 4 Q Heat Rejection
, K Qa 0 4 Q S S Figue 6. Canot Cycle efficiency fo an idealized BWR system. he Canot Cycle efficiency is less than unity. It inceases as the diffeence between the heat addition temeatue and the heat ejection temeatue is inceased. hus inceasing the heat addition temeatue and deceasing the heat ejection temeatue becomes an objective of any heat engine design. hee is limited contol on the heat ejection medium such as ai in a cooling towe, o a body of wate such as a ond, lake, ive o the ocean. Inceasing the heat addition temeatue becomes the majo engineeing objective, justifying the use high temeatue mateials such as ceamics such as uanium dioxide (UO), o uanium cabide (UC) as nuclea eacto fuels. he ue limit is eached accoding to the maximum temeatue that mateials can safely withstand without deteioation in thei mechanical oeties. It also deends on ou ability to design efficient cooling systems that use mateials at high temeatues without a loss of thei mechanical oeties o befoe catastohic failue, melting o vaoization. In nuclea alications, this suggests fo instance the use of gahite as a modeato mateial in gas cooled eactos instead of wate in light wate eactos. his is associated with an incease in the oveall themal efficiency fom about ecent in light wate eactos to about 40 ecent is gas-cooled eactos..0 HE REVERSIBLE SAURAED SEAM RANKINE CYCLE he intenally evesible Rankine cycle fo an idealized Pessuized Wate Reacto (PWR) is shown on the -S diagam in Fig. 7. he satuated steam at oint exands to oint whee it is condensed to oint then umed to oint B. hee heat is added in the feed wate heate fom oint B to oint 4, whee it entes in the heat exchange at 4. Heat is then added in he heat exchange fom oint 4 to oint. Notice that even though the heat addition in the coe is at a temeatue A, the woking medium is actually eceiving the heat at a temeatue.
Figue 7. Rankine evesible satuated Steam Cycle fo a PWR system. he oveall themal efficiency in tems of the enthaly of this cycle becomes; Rankine W tubine ( h h ) ( hb h) h h W Q a B um () Nomally fo a liquid coolant the uming wok is negligible, thus: hb h () Substituting fom Eqn. into Eqn. 0 we get: Rankine h h h h (5)
. USING HE MOLLIER CHAR o obtain values of the enthaly using the Mollie Chat the following aoach can be followed as shown in Fig. 8. Figue 8. Use of the Mollie Chat.. If the steam essue and the steam temeatue t ae known, this detemines oint on the diagam.. If the steam quality x at exhaust and the steam essue at exhaust ae known, then oint can be located on the chat.. Following the P = constant line we can get oint on the satuated liquid line, so that we can estimate the efficiency fom Eqn... MAXIMIZING HE EFFICIENCY OF HE RANKINE CYCLE Seveal aoaches esent themselves fo inceasing the themal efficiency of the Rankine cycle. As shown in Fig. 9 the efeence themal efficiency is given by: W net th QA aea 4 aea 56
Qa Qa Wok W net P 4 Q P 4 6 6 5 S Figue 9. Enhancing the efficiency of the Rankine cycle though loweing of the condense essue.. Loweing the condense essue as shown in Fig. 0 leads to a new value of the themal efficiency: aea '4' th aea '56' his clealy leads to an enhanced themal efficiency.. Raising the heat exchange essue as shown in Fig. 0 leads to the new value of the themal efficiency: aea ''4' th aea ''5'6 In this case the new efficiency may be lage o lowe than the initial efficiency.
P 4 P 4 4 6 5 5 S Figue 0. Enhancing efficiency of the Rankine steam cycle though aising the heat exchange essue. 650 F 7 4 4 6 5 7 S Figue. Enhancing efficiency of the Rankine steam cycle using sueheat.. he use with sueheat with a temeatue limitation. Accoding to Fig. the themal efficiency becomes: aea ''74' th aea ''77'6 Again in this case the new efficiency may be lage o smalle than the initial efficiency.
he advantage of the use of sueheating is that we obtain a highe quality steam at the tubine at oint 4 instead of oint 4. Only if thee is not a limitation on the heat addition temeatue should we exect that; th th. HE WO SAGE REGENERAIVE RANKINE CYCLE We conside a essuized wate eacto steam cycle whee the steam exiting the steam geneato entes the tubine and is atially exanded. As it exands, the steam is bled to heat the wate in two feed wate heates befoe it eentes the steam geneato. ubine Geneato Steam geneato PWR 4 Condense 0 Feed wate heate 9 8 7 5 6 Figue. wo stage Pessuized Wate Reacto Rankine cycle with egeneation. he condensate fom the fist heate is fed back though a steam ta to the evious heate and then to the hot well of the condense. he emaining steam is used to dive the electical geneato then is fed to the condense and its hot well.
We can efom enegy and mass balances on the individual comonents of the system. In tems of the mass flow ates and the enthalies, the enteing enegy into the fist feedwate heate is: Q mh9 mh he exiting enegy is: Q mh0 mh Equating those two enegies we get: Q Q mh m h mh m h 9 0 (6) he quantities in this equation ae usually known excet fo the bleeding mass flow ate m which can be calculated fom: h h 0 9 m m h h (7) he enegy balance on the second feedwate heate and the hot well taken togethe yields: m h m h m m m h mh (8) ( ) 5 W 9 whee W is the total owe of the ums in the system. All quantities in this equation ae known excet fo the bleeding mass flow ate m which can be estimated fom: m m h h m h h h h ( 9 5) ( 5) Wum 5 (9) he owe geneated by the tubine can be witten as: W m( h h ) ( m m )( h h ) ( m m m )( h h ) (0) tubine 4 he net wok done is:
Wnet Wtubine Wum () he heat added in the heat exchange is: Q h h () a m( 0) It follows that the themal efficiency of the egeneative cycle is: Regeneative Wnet Qa Wtubine Wum m( h h0) m( h h ) ( m m )( h h ) ( m m m )( h h4 ) W m( h h ) 0 ().4 HE GAS URBINE OR BRAYON CYCLE INRODUCION he gas tubine o Bayton cycle is unde consideation fo futue nuclea owe lants. he highe achievable temeatues imly oeation at highe themal efficiency. In addition, high temeatue ocess heat that they ae caable of geneating would be useful in the oduction of hydogen as a caie of fission enegy. It has also been suggested that ai cooling can be used in location whee a shotage exists of wate fo cooling.
Qa Reacto Coe Comesso ubine Coole Geneato 4 Q Figue. he ideal diect gas tubine o Bayton cycle. P Qa Qa P=c S=c S=c 4 Q 4 P=c Q V S Figue 4. Bayton cycle PV and S diagams.
In the ideal Bayton cycle, a high essue, high temeatue gas such as helium undegoes an adiabatic and isentoic exansion though a tubine to a lowe essue and temeatue state. Afte exansion, heat is emoved fom the gas at constant essue in a coole. he gas is then comessed in a comesso adiabatically and isentoically, befoe enteing the eacto coe whee it eceives the heat inut at a constant essue. Figue 5. Oen cycle gas tubine and comesso set oducing 50 MWe at 50 ecent efficiency. Assuming that the otential and kinetic enegy losses ae negligible, the tubine wok is given by the gas enthaly change in the tubine: W h h (4) tubine 4 he comesso wok is: W h h (5) comesso he heat added to the gas is: Q h h (6) a he oveall themal efficiency of the ideal Bayton cycle in tems of enthalies becomes: Wnet W WC ( h h4 ) ( h h ) Q Q h h a a (7)
USE OF HE GAS ABLES If one needs to use the Gas ables, two indeendent themodynamics oeties at each state must be secified. he mateials and design limitations ae usually exessed in tems of the essue and temeatue values. Assuming a efect gas, the enthaly diffeences can be exessed in tems of temeatue diffeences. he wok done by the tubine can the witten as: W h h c c c 4 tubine 4 ( 4) ( ) gas secific heat at constant essue assumed constant (8) o =absolute temeatue in K. he exansion though the tubine is assumed to be isentoic and adiabatic. Fo such an exansion the efect gas law alies: PV c = c c c v constant v = secific heat at constant essue = secific heat at constant volume (9) able 7 shows the secific heat and γ fo some ossible otential gaseous coolants. able 7. Secific heat and γ fo gaseous coolants at 68 o F. Gas Secific heat, c γ [BU/(lbm. o F)] [c/cv] Hydogen, H.40.405 Helium, He.50.659 Cabon dioxide, CO 0.0.90 Ai 0.40.400 Nitogen, N 0.48.400 Fom Eqn. 0, we can wite: PV PV (0) 4 4 he ideal gas law, not to be confused with the efect gas law, is: PV nr ()
Fo n= it becomes: PV Fom the ideal gas law we can wite: R () PV R PV R 4 4 4 PV PV 4 4 4 () Fom Eqn. 8 we can wite: PV PV 4 4 V V P P 4 4 4 4 V P P V P4 P (4) Substituting fom Eqn. 5 into Eqn. 4 we get: ( ) 4 4 4 4 4 4 4 PV P P P P PV P P P P (5) he wok in the tubine can be ewitten fom Eqns. 8 and 6 as: ( ) tubine 4 P 4 ( ) P P W c ( ) c [ ] c [ ] P 4 (6) he comesso wok can similaly be witten as:
comesso ( ) ( ) W h h c c P c( ) c[ ] P c[ ] P P (7) he comesso essue atio is defined as: (8) In actual cycles, the tubine essue atio is less than in the comesso because of the essue losses in the heating and the cooling ocesses. Howeve, fo simlicity we can assume that those losses ae negligible with the essue atio in the tubine equal to the essue atio in the comesso: (9) 4 he ubine and comesso wok in the tubine and comesso in tem of the essue atio become: W tubine c [ ] (40) ( ) W comesso c [ ] (4) he net wok in the cycle becomes: W W W he heat addition to the cycle is: net tubine comesso c ( )[ ] (4) ( )
Q h h c (4) ( ) a hus the themal efficiency of the cycle is: c ( )[ ] ( ) Wnet [ ] ( ) Qa c( ) (44) he last esult shows that the ideal cycle themal efficiency deends only on the essue atio and not on the temeatue diffeences. In the actual cycle is, howeve, the efficiency is temeatue deendent. HE MAXIMUM HERMAL EFFICIENCY BRAYON CYCLE he mateial limitations imose an ue limit on the achievable ue temeatue. o attain maximum themal efficiency, one must exand the woking gas to the lowest ossible temeatue, and also comess the gas to the maximum ossible temeatue. he essue atio is given in this case by Eqn. 6 as: (45) Substituting in the exession fo the themal efficiency we get: [ ] ( ). (46) his eveals that the maximum themal efficiency Bayton cycle is nothing but a Canot cycle. Howeve, it is an unealizable goal since in this case the net wok e unit mass of the gas is zeo, and an infinite gas flow is needed fo a finite amount of wok. OPIMAL PRESSURE RAIO An imotant design consideation is to detemine the essue atio coesonding to otimal owe lant efomance. In this case we conside the exession fo the net wok fom Eqn. 9 and ewite it in tem of the maximum gas temeatue and minimum gas temeatue.
W c ( )[ ] net ( ) c [ ].[ ] ( ) ( ) ( ) ( ) ( ) c { [ ] [ ]} ( ) c { [ ] [ ]} ( ) ( ) c { [ ] [ ]} ( ) (47) Since: P P ( ) ( ) (48) Fo maximum net wok we take the deivative of the exession fo the net wok with esect to the essue atio fo constant temeatues, and equate it to zeo, yielding: ( ) dwnet d c { [ ] [ ]} d d ( ) d c { [ ] [ ]} ( ) ( ) d ( ) ( ) c [ ] ( ) ( ) ( ) ( ) c [ ] 0 ( ) (49) his esults in:
( ) [ ] 0 ( ) ( ) ( ) (50) Hence the otimal comession atio fo maximum net wok is:, ot ( ) (5) he atio deceases with inceasing γ. Consequently fo fixed maximum and ( ) minimum gas temeatues, the otimal essue atio fo monatomic gases such as helium is lowe than fo olyatomic gases such cabon dioxide. his esults in highe tubine exhaust essues, and lant sizes ae consequently educed with imoved economics fom the esective of the lant s caital cost. OPIMAL HERMAL EFFICIENCY OF BRAYON CYCLE 5 is: he themal efficiency coesonding to maximum net-wok becomes fom Eqns. 44 and
ot [ ] ( ), ot [ ] ( ) ( ) [ ] ( ) ( ) (5) he aeaance of the squae oot makes that exession diffeent fom the one fo the Canot cycle efficiency. OPIMAL GAS EMPERAURE AFER COMPRESSION It is of inteest to estimate the gas temeatue afte comession,. Fom Eqn. 4:, ot ( ) (5) Howeve, fom Eqn. 9: ( ) (54) Equating the last two equations yields: hus:, ot ( ) (55) (56)
his eveals that the gas temeatue afte comession fo otimal net wok is the geometic mean of the highest gas temeatue at tubine inlet and the lowest gas temeatue at comesso inlet. IMPROVING HE BRAYON CYCLE S EFFICIENCY Methods simila to those used to enhance the efficiency in the steam cycle can be used in the gas tubine cycle. Reheat is used to incease the wok outut. Regeneative heat exchange between the tubine exhaust gas and comesso outlet educes the heat inut. Intecooling between the comesso stages educes the comesso wok..5 SIRLING CYCLE, EXERNAL HEA ENGINE INRODUCION he Stiling cycle engine, also called an extenal-heat engine diffes fom the Rankine o steam cycle in that it uses a gas, such as ai, helium, o hydogen, instead of a liquid, as its woking fluid. Fission enegy using a heat ie o adioisotoe heat, ovide extenal heat to one cylinde. his causes the gas to altenately exand and contact, moving a dislace iston back and foth between a heated and an unheated cylinde. Figue 6. Fee iston Stiling cycle owe convete fo electical geneation. HISORY
In 86, D. Robet Stiling (790-878), a eache in Scotland obtained a atent fo his Heat Economize. He descibed how to use a owe iston in combination with a seaate dislace, linked togethe on the same shaft with ai as a woking fluid. He exlained how to use a egeneato o heat economize, which he laces between the hot and cold ends of the dislace cylinde. he cycle he descibed was of a closed natue, meaning that the woking fluid is not exchanged duing the cycle s oeation. he heat equied to dive the cycle is ovided fom the outside athe than fom an intenal combustion ocess. he intenal volumes consist of a hot aea fo heat addition and a cold one fo heat ejection. he two aeas ae seaated by an insulated iston. he volumes ae connected with a byass that kees the essue in the two volumes equal and encloses a egeneato o economize. he egeneato stoes some of the enegy when the hot ai is tansfeed fom the hot volume to the cold volume. he enegy is then tansfeed back to the cold ai when it etuns to the hot volume. his minimizes the heat ejected and hels maximize the themal efficiency of the cycle. he Fod Moto Comany and Phillis develoed in the 970s an automotive Steling engine that oweed the Fod oino model. he Steling cycle has been used fo geneating electical owe in emote locations. he ideal Stiling cycle consists of two isothemal o constant temeatue and two isochoic o constant volume ocesses. POWER CYCLE he engine consists of two istons one is a dislace iston, the othe a owe iston, and a egeneato. Using aoiate aeas and essues, the dislace dive od can become unloaded and act in a self-diving oeation. With the addition of a linea altenato as a load, electical owe can be geneated. With aoiate masses, sing ates and daming, o dynamic tuning, the convete can esonate as a fee iston Stiling convete. he ideal Stiling cycle consists of fou distinct ocesses: Pocess - is an isothemal comession ocess. Wok WC is done on the system, while an equal amount of heat QC is ejected by the system to the cooling medium at a constant temeatue C. Pocess - is a constant volume dislacement ocess. Heat QR is absobed by the woking gas fom the egeneato matix. Pocess -4 is an isothemal exansion ocess. Wok WH is done by the system, while an equal amount of heat QH is added to the system fom the heat souce at a constant temeatue E. Pocess 4- is a constant volume dislacement ocess. Heat QR is ejected by the woking gas to the egeneato matix.
QH P =c 4 QR QH QR =c QC QR V=c QC V4=c 4 QR S V Figue 7. PV diagam fo the Stiling cycle. Comession ocess - and exansion ocess -4 ae isothemal ocesses. Since the Stiling cycle is a closed cycle, each ocess can be analyzed seaately. he wok done fo each ocess can be detemined by integation of the aea unde the PV diagam. Fo the isothemal comession ocess - the wok done is: C C Q W PdV (57) Similaly the wok done and heat tansfe in the exansion ocess -4 is: H H 4 Q W PdV (58) Since the comession wok is negative, the net wok done e cycle is: the aea within the cycle diagam ---4-. hus: Wnet WH WC (59) he owe becomes the net wok done multilied by the cycle fequency f (Hz o cycles/second): P fw f ( W W ) (60) net H C
o get the heat inut duing the ocess - we use the enegy equation with W = 0: Q Q W mc ( ) (6) R H V and finally the themal efficiency is given by: W net th (6) QH Afte noted success in the 9 th centuy, the Stiling cycle was consideed imacticable and non cometitive with the intenal combustion engine. Recently new inteest in the cycle has aisen fo use with extenal heat souces such as sola concentatos, adioactive isotoes, o fission eactos equied with heat ies. In the theoetical cycle, the heat tansfe between the woking fluid and its suoundings is achieved isothemally as in the Canot cycle, and essue incease and decease at constant volume ae achieved by intenal heat tansfe between the two ocesses. An ideal egeneato with a 00 ecent effectiveness to achieve the heat tansfe fom ocess -4 to ocess -. With the aeas unde the lines -4 and - equal on the S diagam, the themal efficiency then is the same as that fo the Canot cycle between the temeatues and. his should be the case since the Canot cycle and Steling cycle ae both evesible cycles eceiving heat and ejecting heat at two identical temeatues, thus: Stiling W net Canot (6) QH An advantage of the Stiling cycle ove the Canot cycle is that the wok aea is lage fo the same change in secific volume. PRACICAL CYCLE In eal cycles, the achievable cycle efficiency is always lowe than the Canot cycle efficiency due to seveal easons. Continuous athe than discontinuous volume changes, temeatue losses at the hot and cold sufaces, imefect isothemal ocesses with the vey shot exansion and comession times, fiction and iston seals leakages, can educe the eal efficiency. Howeve this aticula engine design leaves a lage otential fo imovements and eseach to aoach the theoetical cycle efficiency. SPACE APPLICAIONS An effot to elace the cuently emloyed Radioisotoe hemoelectic Geneatos (RGs) with a adioisotoe heated 55 Watt(e) Stiling convete is undeway to ovide owe fo dee sace obes. he highe oveall themal efficiency of the Stiling cycle in excess of 5 ecent, will allow the eduction of the isotoe inventoy in cuent RGs.
Conventional convective cooling cannot be used in sace. Instead adiative cooling using adiatos must be used, adding weight to osective sacecaft. he use of dissociating gases instead of He can significantly incease the owe to weight atio of the engine. Figue 8. Stiling cycle engine using adioisotoes as a heat souce fo sace alications, NASA Glenn Reseach Cente. Figue 9. Stiling engine oweed by a adio isotoe heat souce, NASA Glenn Reseach Cente. Wok was initiated by the National Aeonautics and Sace Administation (NASA) in its Civil Sace echnology Initiative (CSI) to develo a nuclea oweed Stiling engine to ovide electic owe geneation in futue Luna o Mas missions. Diffeent designs ae ossible to ealize a Stiling engine, some of them with otating cankshafts. Fo sace alications an engine oducing owe though linea motion is favoable. his is achieved with linea altenatos o evesibly oeated linea motos. he advantage hee
is that the engine does not oduce any toque which would have to be balanced in ode to event the whole sace fom otating in sace. he numbe of convetes is usually an even numbe so that the linea momentum oduced is balanced. he choice of two o fou convetes deends on the system s edundancy and secific owe needs of the alication. he entie unit would be hemetically sealed with stainless steel o Inconel 78 heate heads and flexue beaings that suot the istons with non contacting cleaance seals which ae used to ovide a maintenance fee system ove its exected lifetime of moe than 00,000 hous. Helium gas at chage essue of.5 MPa is used as a woking fluid fo its good heat tansfe oeties. he owe iston fequency is 8 Hz with a owe iston amlitude of less o equal to 6 mm. he mass of a 55 Watts(e) geneato is about 4 kgs. he design temeatues of the heating heads and cold end temeatues ae 650 and 60-0 o C esectively. he actual cold sink temeatue to which heat would be adiated in sace is consideed to be at 40 o C, which would vay though sace. he nominal themal heat inut is 5 Watts(th), esulting in a themal efficiency of: Watts( e) 55 W( e) th.4% Watts( th) 5 W( th). his value can be comaed to the ideal Canot cycle efficiency of the Stiling cycle as: Stiling cold 7 0 9 0.458 57.4% 7 650 9 hot he maximum owe outut is not just deendent on the temeatues of the hot and cold esevois, but is also limited by the maximum allowable stoke of the owe iston. Fo a given fequency, the stoke of the istons detemines the oduced voltage. o incease the owe ove a load of constant esistance, the voltage and the stoke must be inceased, which can only be achieved within the geometic limits..6 KALINA DUAL-FLUID ENGINE CYCLE INRODUCION he Kalina cycle engine, which is at least 0 ecent moe efficient than the othe heat engines, is simle in design. his new technology is simila to the Rankine cycle excet that it heats two fluids, such as an ammonia and wate mixtue, instead of just wate. Conventional equiment such as steam tubines can be used in the Kalina cycle. he molecula weight of ammonia NH and wate HO ae close at 7 and 8 esectively. Such a cycle can be alied to low temeatue nuclea owe lants that would be dedicated to fesh wate oduction. he closed system technology uses a mixtue of wate and ammonia athe than wate alone to suly the heat ecovey system fo electicity geneation in a owe lant. Because ammonia has a much lowe boiling oint than wate, the Kalina Cycle is able to begin sinning the steam
tubine at much lowe temeatues than tyically associated with the conventional steam boile and tubine systems. he lowe boiling oint of ammonia allows additional enegy to be obtained on the condense side of the steam tubine. Instead of being discaded as waste at the tubine exhaust, the dual comonent vao as 70 ecent ammonia and 0 ecent wate entes a distillation subsystem. his subsystem ceates thee additional mixtues. One is a 40/60 mixtue, which can be comletely condensed against nomal cooling souces. Afte condensing, it is umed to a highe essue, whee it is mixed with a ich vao oduced duing the distillation ocess. his eceates the 70/0 woking fluid. he elevated essue comletely condenses the woking fluid and etuns it to the heat exchange to comlete the cycle. he mixtue's comosition vaies thoughout the cycle. he advantages of this ocess include vaiable temeatue boiling and condensing, and a high level of ecueation. A Kalina cycle engine was built in 99, at the Enegy echnology Engineeing Cente in Canoga Pak, Califonia. he owe lant may also imove heat engine efficiency though bette themodynamic matching in the boile and distillation subsystem, and though ecueation of the heat fom the tubine exhaust. Data fom the oeating tials confimed the incile of the Kalina Cycle technology. he technology is cuently being used in geothemal owe lants. Figue 0. Flow diagam of a Kalina cycle using a high essue and low essue sections and a mixtue of two woking fluids. When the Kalina Cycle elaces the Rankine Cycle in any owe lant it educes entoy oduction significantly. In the case of liquid metal o helium cooled eactos, the mismatch between the oeties of wate and the eacto coolant causes vey lage entoy losses. he use of a mixtue as the woking fluid educes these losses and can incease the themal efficiency of the cycle by aoximately 0 ecent. he Kalina Cycle is the ceation of Alexande Kalina, meaning flowe in the Slavic languages, who came to the USA fom Russia.
Figue. Simlified Kalina cycle using exhaust gases to a boile. By ciculating the mixtue at diffeent comositions in diffeent ats of the cycle, condensation (absotion) can be done at slightly above atmosheic essue with a low concentation of ammonia, while heat inut is at a highe concentation fo otimum cycle efomance. EXERGY FLOW IN HE KALINA CYCLE he exhaust gases ente a boile at oint and exit at oint. he geneated ammoniawate vao mixtue is evaoated in the boile, exits at then is exanded in a tubine to geneate wok at 4. he tubine exhaust 5 is cooled in a distille at 6, a fist eheate at 7 and a second eheate at 8. It is then diluted with an ammonia oo liquid steam at oints 9 and 0, then condensed at in the absobe by the cooling wate flow fom to. he satuated liquid leaving the absobe is comessed at 4 to an intemediate essue and heated in a eheate at 5, anothe eheate at 7 and the distille at 8. he satuated mixtue is seaated into an ammonia-oo liquid at 9 which is cooled at 0, and then deessuized in a thottle. Ammonia ich vao at is cooled at and some of the oiginal condensate at 4 is added to the nealy ue ammonia vao to obtain an ammonia concentation of about 70 ecent in the woking fluid at 5.
he mixtue is then cooled at 6, condensed at 7 by the cooling wate at 8 and 9, comessed at 0, and sent to the boile though a egeneative feed wate heate at. he mass flow ciculating between the seaato and the absobe is about 4 times that though the tubine, thus, causing some additional condensate um wok. Howeve, this loo makes ossible the changes in comosition between the initial condensation in the absobe and the heat addition in the boile. By modifying the dew oint of the mixtue, the waste heat fom the tubine exhaust, which is lost in a Rankine cycle, can be used to dilute the ammonia wate vao with a steam of wate, thus, oducing a mixtue with a substantially lowe concentation of ammonia which allows condensation at a much highe temeatue. he themodynamic oeties of ue fluids and infomation about the deatue fom ideal solutions ae sufficient to deive the mixtue oeties. Stability, seconday eactions, and safety must be taken into consideation. COMPARISON OF HE KALINA AND SEAM CYCLES he Kalina cycle is a new concet in heat ecovey and owe geneation, which uses a mixtue of 70 ecent ammonia and 0 ecent wate as the woking fluid with the otential of significant efficiency gains ove the conventional Rankine cycle. Basically this concet is suitable fo medium to low gas temeatue heat ecovey systems with gas inlet temeatues in the ange of 400 to 000 o F, offeing moe gains, ove the Rankine cycle, as the gas temeatue deceases. Gas tubine based combined cycles using this concet have - ecent highe efficiency ove multi essue combined cycle lants using steam and wate as the woking fluid. In low gas temeatue heat ecovey systems such as diesel engine exhaust o fied heate exhaust, the enegy ecoveed fom the hot gas steam is moe significant and Kalina cycle outut inceases by 0-0 ecent. he main eason fo the imovement is that the boiling of ammonia wate mixtue occus ove a ange of temeatues, unlike steam and hence the amount of enegy ecoveed fom the gas steam is much highe. Consideing a 550 o F gas temeatue souce with a cold end fluid temeatue of 00 o F and 70/0 NH/HO mixtue at 500 sia, by vitue of its vaying boiling oint, is able to match o un aallel to the gas temeatue line while ecoveing enegy and hence the exit gas temeatue can be as low as 00 o F.
o F Kalina Rankine 600 500 400 00 Gas Wate Gas Steam 500 sia 00 00 70/0 HN /H O 500 sia Enegy Recovey [ecent] Figue. Comaison of the heat ecovey in the Kalina and Steam cycles. he steam-wate mixtue at 500 sia, on the othe hand, due to inch and aoach oint limitations and a constant boiling oint of 467 o F, cannot cool the gases below about 400 o F. Only about 5-0 ecent of the enegy is ecoveed, comaed with 00 ecent in the Kalina cycle. he condensation of ammonia-wate also occus ove a ange of temeatues and hence emits additional heat ecovey in the condensation system, unlike the Rankine cycle, whee the low end temeatue, affected by ambient conditions, limits the condense back essue and owe outut of the system. If the cooling wate temeatue is say 00 o F, less owe is geneated by the steam tubine comaed to say 40 o F cooling wate. he condense essue can be much highe in a Kalina cycle, and the cooling wate temeatues does not imact the owe outut of the tubine as in the Rankine cycle. he themo-hysical oeties of ammonia-wate mixtue can also be alteed by changing the concentation of ammonia. his hels to ecove enegy in the condensation system. Modifications to the condensing system ae also ossible by vaying the ammonia concentation and thus moe enegy can be ecoveed fom the exhaust gases. Exansion in the tubine oduces a satuated vao in the Kalina cycle comaed with wet steam in Rankine cycle, which equies otection of the tubine blades in the last few stages. Also due to the highe essue of vao and lowe secifc volume, the exhaust system size can be smalle comaed to steam. Fo examle the secific volume of a 70 ecent ammonia wate mixtue exhausting fom a tubine at its dew oint of 40 F is 5. ft / lb,while steam at its condensing temeatue of 70 F(satuation essue = 0.6 sia) has 868 ft /lb. hus the equiment size can be smalle with a Kalina system. EXERCISES
. Assuming that heat ejection occus at an ambient temeatue of 0 degees Celsius, fo the aveage heat addition temeatues a given below, comae the Canot cycle themal efficiencies of the following eacto concets:. PWR, 68 o C.. BWR, 64 o C.. CANDU, 4 o C. 4. HGR, 05 o C. 5. LMFBR, 5 o C.. A boiling wate eacto oduces satuated steam at,000 sia. he steam asses though a tubine and is exhausted at sia. he steam is condensed to a subcooling of o F and then umed back to the eacto essue. Comute the following aametes: a. Net wok e ound of fluid. b. Heat ejected e ound of fluid. c. Heat added by the eacto e ound of fluid. d. he tubine heat ate defined as: [(Heat ejected +Net tubine wok)/net tubine wok] in units of [BU/(kW.h)] e. Oveall hemal efficiency. You may use the following data: Fom the ASME Steam ables, satuated steam at,000 sia has an enthaly of h=9.9 [BU/lbm] At sia essue the fluid enthaly fom an isentoic exansion is 776 [BU/lbm] he isentoic uming wok is.96 [BU/lbm] he enthaly of the liquid at sia subcooled to o F is 66.7 [BU/lbm] [kw.h] = 4 [BU]. In the eceding oblem calculate the quantities of inteest fo a actical cycle with a tubine efficiency of 80 ecent and a um efficiency of 80 ecent. 4. Fo a 00 ecent egeneative effectiveness, ove that the Stiling cycle has a Canot cycle efficiency. 5. A Stiling cycle engine using a adioactive isotoe fo sace owe alications oeates at a hot end temeatue of 650 o C and ejects heat though a adiato to the vacuum of sace with a cold end temeatue at 0 o C. Calculate its ideal Stiling cycle efficiency. REFERENCES. Magdi Ragheb and Adam M. Ragheb (0). "Wind ubines heoy - he Betz Equation and Otimal Roto i Seed Ratio," Fundamental and Advanced oics in Wind Powe, Ru Caiveau (Ed.), ISBN: 978-95-07-508-, Inech, htt://www.intechoen.com/aticles/show/title/wind-tubines-theoy-the-betz-equation-andotimal-oto-ti-seed-atio. W. B. Cotell, "he ECCS Rule-Making Heaing," Nuclea Safety, Vol. 5, no., 974.. James H. Rust. Nuclea Powe Plant Engineeing, Haalson Publishing Comany, Buchanan, Geogia, 979. 4. B. I. Lomashev and V. B. Nesteenko, Gas tubines with Dissociating Woking Fluids, A. K. Kasin, ed., Dissociating Gases as Heat ansfe Media and Woking Fluids in Powe
Installations, Academy of Sciences, Beloussian SSR, Institute of Nuclea Powe, Nauka and ekhnica Pess, Minsk, 970. 5. V. B. Nesteenko, hemodynamic Schemes and Cycles of APS using he Dissociating Gases, A. K. Kasin, ed., Dissociating Gases as Heat ansfe Media and Woking Fluids in Powe Installations, Academy of Sciences, Beloussian SSR, Institute of Nuclea Powe, Nauka and ekhnica Pess, Minsk, 970. 6. Benad D. Wood, Alications of hemodynamics, Addison-Wesley Publishing Co., Reading, Massachussets, 98. 7. C. M. Hageaves, he Philis Stiling Engine, Elsevie Science, New Yok, 99. 8. Allan J. Ogan, hemodynamics and Gas Dynamics of the Stiling Cycle Machine, Univesity of Cambidge Pess, 99. 9. heodoe Finkelstein and Allan J. Ogan, Ai Engines, Ameican Society of Mechanical Enginees, 00. 0. Joel Weisman, Elements of Nuclea Reacto Design, Elsevie Scientific Publishing Comany, 977.. Kal Witz, Lectue Notes on Fast Reactos, Kenfoschungszentum Kalsuhe, Univesität Kaluhe, Gesellschaft fü Kenfoschung m.b.h., 97.