Chapter and. FIGURE 9 36 The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities.

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1 Chapter 9 The thermal efficiency could alo be determined from where h th q out q out h h kj>kg Dicuion Under the cold-air-tard aumption (contant pecific heat value at room temperature), the thermal efficiency would be, from Eq. 9 7, h th,brayton r k >k p 0.8. >. 8 which i ufficiently cloe to the value obtained by accounting for the variation of pecific heat with temperature. Deviation of Actual Ga-Turbine Cycle from Idealized One The actual ga-turbine cycle differ from the ideal Brayton cycle on everal account. For one thing, ome preure drop during the heat-addition heatrejection procee i inevitable. More importantly, the actual work input to the compreor i more, the actual work output from the turbine i le becaue of irreveribilitie. The deviation of actual compreor turbine behavior from the idealized ientropic behavior can be accurately accounted for by utilizing the ientropic efficiencie of the turbine compreor a h C w w a h h h a h (9 9) h T w a h h a (9 0) w h h where tate a a are the actual exit tate of the compreor the turbine, repectively, are the correponding tate for the ientropic cae, a illutrated in Fig The effect of the turbine compreor efficiencie on the thermal efficiency of the ga-turbine engine i illutrated below with an example. T a Preure drop during heat addition a Preure drop during heat rejection FIGURE 9 6 The deviation of an actual ga-turbine cycle from the ideal Brayton cycle a a reult of irreveribilitie. EXAMPLE 9 6 An Actual Ga-Turbine Cycle Auming a compreor efficiency of 80 percent a turbine efficiency of 8 percent, determine (a) the back work ratio, (b) the thermal efficiency, (c) the turbine exit temperature of the ga-turbine cycle dicued in Example 9. Solution The Brayton cycle dicued in Example 9 i reconidered. For pecified turbine compreor efficiencie, the back work ratio, the thermal efficiency, the turbine exit temperature are to be determined.

2 Thermodynamic T, K a q out a FIGURE 9 7 T- diagram of the ga-turbine cycle dicued in Example 9 6. Analyi (a) The T- diagram of the cycle i hown in Fig The actual compreor work turbine work are determined by uing the definition of compreor turbine efficiencie, Eq : Compreor: Turbine: Thu, w comp,in w.6 kj>kg 0.0 kj>kg h C 0.80 w turb,out h T w kj>kg.6 kj>kg r bw w comp,in 0.0 kj>kg 0.9 w turb,out.6 kj>kg That i, the compreor i now conuming 9. percent of the work produced by the turbine (up from 0. percent). Thi increae i due to the irreveribilitie that occur within the compreor the turbine. (b) In thi cae, air leave the compreor at a higher temperature enthalpy, which are determined to be Thu, w comp,in h a h S h a h w comp,in h th w net That i, the irreveribilitie occurring within the turbine compreor caued the thermal efficiency of the ga turbine cycle to drop from.6 to 6.6 percent. Thi example how how enitive the performance of a ga-turbine power plant i to the efficiencie of the compreor the turbine. In fact, ga-turbine efficiencie did not reach competitive value until ignificant improvement were made in the deign of ga turbine compreor. (c) The air temperature at the turbine exit i determined from an energy balance on the turbine: Then, from Table A 7, kj>kg T a 98 K h h a kj>kg w net w out w in kj>kg 0. kj>kg 0.66 or 6.6% kj>kg w turb,out h h a S h a h w turb,out T a 8 K kj>kg Dicuion The temperature at turbine exit i coniderably higher than that at the compreor exit (T a 98 K), which ugget the ue of regeneration to reduce fuel cot.

3 Chapter 9 6 Regenerator Heat Combution chamber Compreor Turbine w net FIGURE 9 8 A ga-turbine engine with regenerator. 9 9 THE BRAYTON CYCLE WITH REGENERATION In ga-turbine engine, the temperature of the exhaut ga leaving the turbine i often coniderably higher than the temperature of the air leaving the compreor. Therefore, the high-preure air leaving the compreor can be heated by tranferring heat to it from the hot exhaut gae in a counter-flow heat exchanger, which i alo known a a regenerator or a recuperator. A ketch of the ga-turbine engine utilizing a regenerator the T- diagram of the new cycle are hown in Fig , repectively. The thermal efficiency of the Brayton cycle increae a a reult of regeneration ince the portion of energy of the exhaut gae that i normally rejected to the urrounding i now ued to preheat the air entering the combution chamber. Thi, in turn, decreae the heat input (thu fuel) requirement for the ame net work output. Note, however, that the ue of a regenerator i recommended only when the turbine exhaut temperature i higher than the compreor exit temperature. Otherwie, heat will flow in the revere direction (to the exhaut gae), decreaing the efficiency. Thi ituation i encountered in ga-turbine engine operating at very high preure ratio. The highet temperature occurring within the regenerator i T, the temperature of the exhaut gae leaving the turbine entering the regenerator. Under no condition can the air be preheated in the regenerator to a temperature above thi value. Air normally leave the regenerator at a lower temperature, T. In the limiting (ideal) cae, the air exit the regenerator at the inlet temperature of the exhaut gae T. Auming the regenerator to be well inulated any change in kinetic potential energie to be negligible, the actual maximum heat tranfer from the exhaut gae to the air can be expreed a q regen,act h h q regen,max h h h h (9 ) (9 ) The extent to which a regenerator approache an ideal regenerator i called the effectivene ` i defined a T q regen ' Regeneration 6 q out q aved = q regen FIGURE 9 9 T- diagram of a Brayton cycle with regeneration. P q regen,act q regen,max h h h h (9 )

4 6 Thermodynamic η th,brayton With regeneration Without regeneration T /T = 0. T /T = 0. T /T = Preure ratio, r p FIGURE 9 0 Thermal efficiency of the ideal Brayton cycle with without regeneration. When the cold-air-tard aumption are utilized, it reduce to P T T T T (9 ) A regenerator with a higher effectivene obviouly ave a greater amount of fuel ince it preheat the air to a higher temperature prior to combution. However, achieving a higher effectivene require the ue of a larger regenerator, which carrie a higher price tag caue a larger preure drop. Therefore, the ue of a regenerator with a very high effectivene cannot be jutified economically unle the aving from the fuel cot exceed the additional expene involved. The effectivene of mot regenerator ued in practice i below 0.8. Under the cold-air-tard aumption, the thermal efficiency of an ideal Brayton cycle with regeneration i h th,regen a T T br p k >k (9 ) Therefore, the thermal efficiency of an ideal Brayton cycle with regeneration depend on the ratio of the minimum to maximum temperature a well a the preure ratio. The thermal efficiency i plotted in Fig. 9 0 for variou preure ratio minimum-to-maximum temperature ratio. Thi figure how that regeneration i mot effective at lower preure ratio low minimum-to-maximum temperature ratio. EXAMPLE 9 7 Actual Ga-Turbine Cycle with Regeneration T, K a a q regen = q aved FIGURE 9 T- diagram of the regenerative Brayton cycle decribed in Example 9 7. Determine the thermal efficiency of the ga-turbine decribed in Example 9 6 if a regenerator having an effectivene of 80 percent i intalled. Solution The ga-turbine dicued in Example 9 6 i equipped with a regenerator. For a pecified effectivene, the thermal efficiency i to be determined. Analyi The T- diagram of the cycle i hown in Fig. 9. We firt determine the enthalpy of the air at the exit of the regenerator, uing the definition of effectivene: Thu, P h h a h a h a 0.80 h 60.9 kj>kg kj>kg S h 8.7 kj>kg h h kj>kg kj>kg Thi repreent a aving of 0.0 kj/kg from the heat input requirement. The addition of a regenerator (aumed to be frictionle) doe not affect the net work output. Thu, h th w net 0. kj>kg 0.69 or 6.9% kj>kg

5 Chapter 9 7 Dicuion Note that the thermal efficiency of the ga turbine ha gone up from 6.6 to 6.9 percent a a reult of intalling a regenerator that help to recuperate ome of the thermal energy of the exhaut gae. 9 0 THE BRAYTON CYCLE WITH INTERCOOLING, REHEATING, AND REGENERATION The net work of a ga-turbine cycle i the difference between the turbine work output the compreor work input, it can be increaed by either decreaing the compreor work or increaing the turbine work, or both. It wa hown in Chap. 7 that the work required to compre a ga between two pecified preure can be decreaed by carrying out the compreion proce in tage cooling the ga in between (Fig. 9 ) that i, uing multitage compreion with intercooling. A the number of tage i increaed, the compreion proce become nearly iothermal at the compreor inlet temperature, the compreion work decreae. Likewie, the work output of a turbine operating between two preure level can be increaed by exping the ga in tage reheating it in between that i, utilizing multitage expanion with reheating. Thi i accomplihed without raiing the maximum temperature in the cycle. A the number of tage i increaed, the expanion proce become nearly iothermal. The foregoing argument i baed on a imple principle: The teady-flow compreion or expanion work i proportional to the pecific volume of the fluid. Therefore, the pecific volume of the working fluid hould be a low a poible during a compreion proce a high a poible during an expanion proce. Thi i preciely what intercooling reheating accomplih. Combution in ga turbine typically occur at four time the amount of air needed for complete combution to avoid exceive temperature. Therefore, the exhaut gae are rich in oxygen, reheating can be accomplihed by imply praying additional fuel into the exhaut gae between two expanion tate. The working fluid leave the compreor at a lower temperature, the turbine at a higher temperature, when intercooling reheating are utilized. Thi make regeneration more attractive ince a greater potential for regeneration exit. Alo, the gae leaving the compreor can be heated to a higher temperature before they enter the combution chamber becaue of the higher temperature of the turbine exhaut. A chematic of the phyical arrangement the T- diagram of an ideal two-tage ga-turbine cycle with intercooling, reheating, regeneration are hown in Fig The ga enter the firt tage of the compreor at tate, i compreed ientropically to an intermediate preure P,i cooled at contant preure to tate (T T ), i compreed in the econd tage ientropically to the final preure P. At tate the ga enter the regenerator, where it i heated to T at contant preure. In an ideal regenerator, the ga leave the regenerator at the temperature of the turbine exhaut, that i, T T 9. The primary heat addition (or combution) proce take P P P D B Iothermal proce path Polytropic proce path INTERACTIVE TUTORIAL SEE TUTORIAL CH. 9, SEC. ON THE DVD. C Work aved a a reult of intercooling A Intercooling FIGURE 9 Comparion of work input to a ingle-tage compreor (AC) a two-tage compreor with intercooling (ABD). v

6 8 Thermodynamic 0 Regenerator Combution chamber Reheater Compreor I Compreor II Turbine I Turbine II w net Intercooler FIGURE 9 A ga-turbine engine with two-tage compreion with intercooling, two-tage expanion with reheating, regeneration. T q regen q regen = q aved q out place between tate 6. The ga enter the firt tage of the turbine at tate 6 exp ientropically to tate 7, where it enter the reheater. It i reheated at contant preure to tate 8 (T 8 T 6 ), where it enter the econd tage of the turbine. The ga exit the turbine at tate 9 enter the regenerator, where it i cooled to tate 0 at contant preure. The cycle i completed by cooling the ga to the initial tate (or purging the exhaut gae). It wa hown in Chap. 7 that the work input to a two-tage compreor i minimized when equal preure ratio are maintained acro each tage. It can be hown that thi procedure alo maximize the turbine work output. Thu, for bet performance we have P P P P P 6 P 7 P 8 P 9 (9 6) FIGURE 9 T- diagram of an ideal ga-turbine cycle with intercooling, reheating, regeneration. In the analyi of the actual ga-turbine cycle, the irreveribilitie that are preent within the compreor, the turbine, the regenerator a well a the preure drop in the heat exchanger hould be taken into conideration. The back work ratio of a ga-turbine cycle improve a a reult of intercooling reheating. However, thi doe not mean that the thermal efficiency alo improve. The fact i, intercooling reheating alway decreae the thermal efficiency unle they are accompanied by regeneration. Thi i becaue intercooling decreae the average temperature at which heat i added, reheating increae the average temperature at which heat i rejected. Thi i alo apparent from Fig. 9. Therefore, in gaturbine power plant, intercooling reheating are alway ued in conjunction with regeneration.

7 If the number of compreion expanion tage i increaed, the ideal ga-turbine cycle with intercooling, reheating, regeneration approache the Ericon cycle, a illutrated in Fig. 9, the thermal efficiency approache the theoretical limit (the Carnot efficiency). However, the contribution of each additional tage to the thermal efficiency i le le, the ue of more than two or three tage cannot be jutified economically. T T H,avg Chapter 9 9 P = cont. P = cont. EXAMPLE 9 8 A Ga Turbine with Reheating Intercooling T L,avg An ideal ga-turbine cycle with two tage of compreion two tage of expanion ha an overall preure ratio of 8. Air enter each tage of the compreor at 00 K each tage of the turbine at 00 K. Determine the back work ratio the thermal efficiency of thi ga-turbine cycle, auming (a) no regenerator (b) an ideal regenerator with 00 percent effectivene. Compare the reult with thoe obtained in Example 9. Solution An ideal ga-turbine cycle with two tage of compreion two tage of expanion i conidered. The back work ratio the thermal efficiency of the cycle are to be determined for the cae of no regeneration maximum regeneration. Aumption Steady operating condition exit. The air-tard aumption are applicable. Kinetic potential energy change are negligible. Analyi The T- diagram of the ideal ga-turbine cycle decribed i hown in Fig We note that the cycle involve two tage of expanion, two tage of compreion, regeneration. For two-tage compreion expanion, the work input i minimized the work output i maximized when both tage of the compreor the turbine have the ame preure ratio. Thu, P P P P 8.8 P 6 P 7 P 8 P Air enter each tage of the compreor at the ame temperature, each tage ha the ame ientropic efficiency (00 percent in thi cae). Therefore, the temperature ( enthalpy) of the air at the exit of each compreion tage will be the ame. A imilar argument can be given for the turbine. Thu, At inlet: T T, h h T 6 T 8, h 6 h 8 At exit: T T, h h T 7 T 9, h 7 h 9 Under thee condition, the work input to each tage of the compreor will be the ame, o will the work output from each tage of the turbine. (a) In the abence of any regeneration, the back work ratio the thermal efficiency are determined by uing data from Table A 7 a follow: T 00 K S h 00.9 kj>kg P r.86 P r P P P r S T 0. K h 0. kj>kg FIGURE 9 A the number of compreion expanion tage increae, the gaturbine cycle with intercooling, reheating, regeneration approache the Ericon cycle. T, K q primary q out q reheat FIGURE 9 6 T- diagram of the ga-turbine cycle dicued in Example

8 0 Thermodynamic T 6 00 K S h kj>kg P r P r7 P 7 P 6 P r S T K Then w comp,in w comp,in,i h h kj>kg w turb,out w turb,out,i h 6 h kj>kg Thu, A comparion of thee reult with thoe obtained in Example 9 (ingletage compreion expanion) reveal that multitage compreion with intercooling multitage expanion with reheating improve the back work ratio (it drop from 0. to 0. percent) but hurt the thermal efficiency (it drop from.6 to.8 percent). Therefore, intercooling reheating are not recommended in ga-turbine power plant unle they are accompanied by regeneration. (b) The addition of an ideal regenerator (no preure drop, 00 percent effectivene) doe not affect the compreor work the turbine work. Therefore, the net work output the back work ratio of an ideal ga-turbine cycle are identical whether there i a regenerator or not. A regenerator, however, reduce the heat input requirement by preheating the air leaving the compreor, uing the hot exhaut gae. In an ideal regenerator, the compreed air i heated to the turbine exit temperature T 9 before it enter the combution chamber. Thu, under the air-tard aumption, h h 7 h 9. The heat input the thermal efficiency in thi cae are w net w turb,out w comp,in kj>kg q primary q reheat h 6 h h 8 h kj>kg r bw w comp,in 08. kj>kg 0.0 or 0.% w turb,out 68.8 kj>kg h th w net q primary q reheat h 6 h h 8 h kj>kg Dicuion Note that the thermal efficiency almot double a a reult of regeneration compared to the no-regeneration cae. The overall effect of twotage compreion expanion with intercooling, reheating, regenerah th w net h 7 0. kj>kg 77.0 kj>kg 0.8 or.8%.0 kj>kg 77.0 kj>kg or 69.6% 68.8 kj>kg

9 Chapter 9 tion on the thermal efficiency i an increae of 6 percent. A the number of compreion expanion tage i increaed, the cycle will approach the Ericon cycle, the thermal efficiency will approach h th,ericon h th,carnot T L 00 K T H 00 K Adding a econd tage increae the thermal efficiency from.6 to 69.6 percent, an increae of 7 percentage point. Thi i a ignificant increae in efficiency, uually it i well worth the extra cot aociated with the econd tage. Adding more tage, however (no matter how many), can increae the efficiency an additional 7. percentage point at mot, uually cannot be jutified economically. 9 IDEAL JET-PROPULSION CYCLES Ga-turbine engine are widely ued to power aircraft becaue they are light compact have a high power-to-weight ratio. Aircraft ga turbine operate on an open cycle called a jet-propulion cycle. The ideal jetpropulion cycle differ from the imple ideal Brayton cycle in that the gae are not exped to the ambient preure in the turbine. Intead, they are exped to a preure uch that the power produced by the turbine i jut ufficient to drive the compreor the auxiliary equipment, uch a a mall generator hydraulic pump. That i, the net work output of a jetpropulion cycle i zero. The gae that exit the turbine at a relatively high preure are ubequently accelerated in a nozzle to provide the thrut to propel the aircraft (Fig. 9 7). Alo, aircraft ga turbine operate at higher preure ratio (typically between 0 ), the fluid pae through a diffuer firt, where it i decelerated it preure i increaed before it enter the compreor. Aircraft are propelled by accelerating a fluid in the oppoite direction to motion. Thi i accomplihed by either lightly accelerating a large ma of fluid ( propeller-driven engine) or greatly accelerating a mall ma of fluid ( jet or turbojet engine) or both (turboprop engine). A chematic of a turbojet engine the T- diagram of the ideal turbojet cycle are hown in Fig The preure of air rie lightly a it i decelerated in the diffuer. Air i compreed by the compreor. It i mixed with fuel in the combution chamber, where the mixture i burned at contant preure. The high-preure high-temperature combution gae partially exp in the turbine, producing enough power to drive the compreor other equipment. Finally, the gae exp in a nozzle to the ambient preure leave the engine at a high velocity. In the ideal cae, the turbine work i aumed to equal the compreor work. Alo, the procee in the diffuer, the compreor, the turbine, the nozzle are aumed to be ientropic. In the analyi of actual cycle, however, the irreveribilitie aociated with thee device hould be conidered. The effect of the irreveribilitie i to reduce the thrut that can be obtained from a turbojet engine. The thrut developed in a turbojet engine i the unbalanced force that i caued by the difference in the momentum of the low-velocity air entering the engine the high-velocity exhaut gae leaving the engine, it i Turbine Nozzle High T P V exit FIGURE 9 7 In jet engine, the high-temperature high-preure gae leaving the turbine are accelerated in a nozzle to provide thrut.