CHAPTER 2 GAS POWER CYCLES

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1 CHAER GA OWER CYCLE Gas power cycle are power producin cycles with as as workin fluid that does not undero any phase chane unlike apor power cycles where workin fluid underoes phase chane. arious as power cycles are:-. Joule or Brayton cycle. Otto cycle. Diesel cycle INRODUCION O BRAYON CYCLE Brayton cycle is the air standard cycle for a closed cycle as turbine power plant. Here air is first compressed reversibly and adiabatically, heat is added to it reversibly at constant pressure, air expands in the turbine reversibly and adiabatically, and heat is then rejected from air reversibly at constant pressure to brin it to the initial state. he as turbine power plant is started by rotatin the compressor turbine assembly by a startin motor. When the compressor develops enouh power to support combustion of fuel in the combustion chamber, the hot ases then themselves drive the as turbine, and the plant becomes self sustainin. he compressor is driven by turbine and so it is coupled to turbine shaft. If the compressed workin fluid is expanded directly into turbine (assumin no losses in either component) net work obtained is zero. Net work can be obtained by addin heat to the workin fluid in between compression and expansion so that temperature of workin fluid is increased after compression. o et hiher temperature of workin fluid a combustion chamber is required where combustion of air and fuel takes place ivin temperature rise to the workin fluid. Cycle involvin constant volume heat addition has hiher thermal efficiency but posses mechanical difficulties requirin valves to isolate the combustion chamber from compressor and turbine. Constant pressure heat addition is acceptable as valves are not required. When as turbine is used as power plant entire expansion of as takes place in turbine and enerator mounted on turbine shaft enerates electricity. However as turbines when used in jet enines, the as expands in turbine partially so that power output is just enouh to drive compressors and accessories. he rest of as expansion takes place in nozzle to produce hih velocity jet for propulsion of aircraft in opposite direction of jet. Gas turbine plants are of two types:-. Open cycle as turbine plants. Closed cycle as turbine plants OEN CYCLE GA URBINE LAN An open cycle as turbine plant in shown in Fi.. Fresh air from atmosphere is the workin fluid used in open cycle as turbine plants. Air is compressed in compressor and enery is added by combustion of fuel in the workin fluid itself. Combustion products than expands throuh the turbine and finally exhausted to atmosphere and no recirculation of workin fluid takes place.

2 Combustion chamber Fuel b c Combustion b c Compressor a Air Fiure : Open cycle as turbine plant d roducts of combustion (exhaust) urbine Air Compression a Expansion d CLOED CYCLE GA URBINE LAN Air or some other as be used as workin fluid which is repeatedly circulated throuh the system (like steam power plants) and fuel combustion cannot take place in workin fluid. If fuel is burnt directly in the circulatin air, the oxyen will soon deplete and combustion will fail. Heat is added separately throuh a heat exchaner from an external source and heat must be rejected throuh another heat exchaner with a coolin medium enerally called precooler. Closed cycle as turbine plant is shown in Fiure. Q W C Compressor Heat exchaner W C Heat exchaner W = W - W net C urbine p p =c p=c Q W W C p=c (c) Fiure : Closed cycle as turbine Q

3 Air is not necessarily required as workin fluid unlike open cycle as turbine plants as workin fluid is not required to support combustion in closed cycle as turbine plants. Gases of hiher density are enerally preferable as workin fluid. Hiher density of the workin fluid reduces the size of the system. Hiher values of c p and n facilitates increase in the work of compression as well as turbine output. It may be noted that net output of the cycle will always increase with hih values of c v and n. Helium with n =.66 can be used to increase the thermal efficiency. In closed system cycle systems low quality cheaper fuels are enerally used since combustion takes place outside the system and therefore corrosive combustion products do not enter turbine blades. A closed is dependent system as it depends on coolin water which must be provided for the precoolers. his eliminates the use of this system as an aeronautical enine. It is best suited for marine propulsion where provision of coolin water is not a problem. A closed cycle as turbine plant is used in a as cooled nuclear reactor plant, where source is a hih temperature as cooled reactor supplyin heat from the nuclear fission directly to the workin fluid (a as). However closed cycle as turbine plants have bulky heat exchaners. Also it is quite difficult to make system leak proof. Back work ratio r w urbine w urbine bw Compressor work rbw urbine work Work ratio r r W W W Compressor Efficiency of simple as turbine cycle = Q = Fiure Q R

4 W Q Q Q Q Q Q net s R R s s s cp h h h h c p r p where r p is the pressure ratio. r p r p r p Graph showin variation of efficiency with pressure ratio Fiure shows the variation of efficiency with pressure ratio r r p p When rp, 0 Fiure Optimum pressure ratio for maximum work out for constant minimum and maximum temperatures. r

5 w w w net compressor turbine w h h h h net w c net p p net r where r is the pressure ratio. r p p wnet cp ince (minimum temperature) and (maximum temperature) are fixed therefore differentiatin w with and equatin it to zero dw d 0 0 opt net r max ropt min Fiure 5 5

6 w c net p wnet cp max wnet cp max Graph showin variation of net work with pressure ratio Fiure 6 shows the variation of net work with pressure ratio r r max opt r max min opt max r min max (r p) opt (r p) max Fiure 6 Our aim is to achieve hih efficiency for any thermodynamic cycle. In Brayton cycle efficiency is directly proportional to pressure ratio. hall we o on increasin pressure ratio to achieve hiher thermal efficiency of as turbine power plants? he answer is no. Obviously hiher efficiency is achieved at hiher pressure ratios but increase in efficiency is marinal beyond a certain increase in pressure ratio. he hihest temperature in the cycle occurs at the end of combustion process (state ) and it is limited by the maximum temperature that the turbine can withstand. his also limits the pressure ratios that can be used in a cycle. For a fixed turbine inlet temperature the net work output per cycle increases with pressure ratio, reaches a maximum and then starts to decrease. hus a compromise should be made between the pressure ratio (thermal efficiency) and the net work output per cycle. With less work output per cycle, a larer mass flow rate (thus a larer system) is needed to maintain the same power output, which is not economical. W net W max max 000 K r =5 p r p=8. W net.max r = p min 00 K Fiure 7 6

7 DEIAION OF ACUAL GA URBINE CYCLE FROM IDEALIZED BRAYON CYCLE he actual as turbine cycle differs from Brayton cycle on several rounds. ome pressure drop occurs durin heat addition and heat rejection process which is inevitable. Moreover compression and expansion process are not isentropic process. Actual work input to compressor is more and the actual work output from turbine is less due to irreversibilities. Also variation in mass flow rate and variable specific heat of workin fluid are taken into system. ressure drop durin heat addition s a a ressure drop durin heat rejection Fiure 8 Efficiency of compressor ` 5 - Actual compression -s Isentropic compression Fiure 9 Isentropic work done c Actual work done hs h s c h h 7

8 Efficiency of turbine - Actual expansion -s Isentropic expansion 5 h h s s Fiure 0 Actual work obtained Isentropic work obtained h h Effect of varyin mass flow rate m mass flow rate of air a m mass flow rate of fuel f f fuel air ratio m m m turbine as flow rate m m a f f a mf m ma ma f ma he compressor handles a mass flow rate of m a taken from atmosphere and sends it to combustion chamber where a fuel flow rate of m f is added. Due to this turbine as flow rate m is reater than compressor air flow rate m by (+ f ) where f is fuel air ratio by mass. Applyin enery conservation across the combustion chamber m f h m h m C. a a f m f h h m f C. a a a 8

9 Effect of variable specific heat he specific heat of air is independent of pressure within the operatin limits of as turbine. However it varies considerably with temperature. p air c =.005 kj/kk at 00 K p air c =. kj/kk at 000 K Also specific heat of product of combustion is different from specific heat of air. Mechanical losses In most of the as turbines ower required to drive the compressor is transmitted directly from turbine without any intermediate earin. Any loss that occurs is therefore due to bearin friction and windae. hus loss is equal to 0% of the power necessary to drive compressor. W c kj/k of air C pa mech Loss due to incomplete combustion It is taken into account the performance calculation by dividin the theoretical amount of fuel required by combustion (0.98 enerally) and it effects only cycle and not work output. Equatin heat supplied to the heat required to raise the temperature of as to we have m C m m c m c f combustion f a p a pa MODIFICAION O HE BAIC CYCLE Gas turbine was developed in 90s. he earliest as turbine built had an efficiency of about 7%. A considerable improvement in as turbine efficiency was achieved by incorporatin reeneration, reheatin and intercoolin. Reeneration he temperature of exhaust leavin the as turbine is hiher than the temperature of air leavin the compressor. he hih pressure air at the exit of compressor is heated from the hot exhaust ases in a counter flow heat exchaner, also known as reenerator or recuperator. he thermal efficiency of Brayton cycle increases since exhaust enery that is normally rejected to atmosphere is used to preheat the air enterin the combustion chamber. his decreases the requirement of heat to be added in the combustion chamber. a a Heat 9 5

10 Reenerator 5 Heat a C.C C Fiure he exhaust as temperature is the maximum possible temperature to which air can be preheated in reenerator. However air normally leaves the reenerator at a lower temperature a. Effectiveness ( ) of a reenerator can be defined as the ratio of actual heat ain to the maximum possible heat ain in reenerator. Q h h Q h h actual a a maximum Effects of reeneration. No chane in compressor and turbine work is seen. herefore there is no chane in net work obtained from the system.. Decrease in heat supply to the workin fluid in combustion chamber due to preheatin.. Efficiency of the plant increases due to decrease in heat supplied. Reeneration can be utilized only when exhaust as temperature ( ) is hiher than compressor exit temperature ( ). Otherwise heat will flow in reverse direction decreasin the efficiency. his situation is encountered in as turbines operatin at very hih temperatures. Reheatin he net work output of the as turbine plant workin between two pressure levels can be increased by expandin the as in two staes and reheatin it in between. he ases underoes partial expansion in turbine and is then aain reheated in combustion chamber before final expansion in turbine to atmospheric pressure. ressure lines are diverin lines and therefore h h is reater than h h ' 5 6. his results in increased turbine work output. erfect reheatin is said to occur when exit temperature of ases from both the combustion chambers are equal i.e. = 5. Wok output from perfect reheatin will be maximum when 6 0

11 C.C C.C 5 C 5 6 Fiure 6 W W WC Qin Effects of reeneration. No chane in compressor work.. Increase in turbine work.. Increase in net work output.. cope of reeneration improves since turbine exhaust to atmosphere is at hiher temperature in case of reheatin when compared to simple Brayton cycle arranement h 6 h '. 5. Heat addition increases by an amount (h 5 h ) when compared to equivalent simple Brayton cycle without reheatin. 6. Heat supplied to the system as well as net work obtained from the system increases. herefore the efficiency of the system may increase or decrease. However a sliht decrease in efficiency is noted practically. he net work done is more with reheat compared to ideal cycle. he efficiency with which the heat is added to as in combustion chamber at lower pressure is lower than the efficiency when this heat is added to as in combustion chamber at hiher pressure. Also mean temperature of heat addition increases by reheatin as in reeneration. But mean temperature of heat rejection is also increased. hus the thermal efficiency of Reheat cycle is slihtly less than simple as turbine cycle. Intercoolin he net work output of the as turbine plant workin between two pressure levels can be increased by decreasin the work input to compressor. his is done by carryin out the compression in staes and coolin in between that is usin multistae compression with intercoolin. he as underoes partial compression in compressor followed by coolin in an intercooler before final compression to pressure of combustion chamber in second compressor. ressure lines are diverin lines and therefore ( h h ) is less than ( h h ). his results in decrease in work input to compressor.

12 C Intercooler C.C 5 C 6 5 avin of work 6 Fiure Effects of intercoolin. Decrease in compressor work input.. No chane in turbine work.. Increase in net work output.. cope of reeneration improves since compressor exit temperature of as is less in case of intercoolin when compared to simple Brayton cycle arranement ( > ). 5. Heat addition increases by an amount h h when compared to equivalent simple Brayton cycle without reheatin. 6. Heat supplied to the system as well as net work obtained from the system increases. herefore the efficiency of the system may increase or decrease. However decrease in efficiency is noted practically. Mean temperature of heat addition decreases where as mean temperature of heat addition increase which decreases the efficiency of intercooled cycle. Advantae of increase in thermal efficiency and net work output can be obtained by usin reeneration alon with reheatin and intercoolin. hus desiners of practical as turbine plants prefer only reheatin and reeneration. ADANAGE AND DIADANAGE OF GA URBINE OER RECIROCAING ENGINE Advantaes. Better mechanical efficiency due to absence of numerous slidin or bearin members.. Better Balancin due to absence of reciprocatin masses.. Hih operational speeds can be obtained in rotary compressors.

13 . urbines can be mode lihter than reciprocatin enines of similar output. 5. Cheaper fuel and even solid fuels (pulverized coal) can be used 6. ower plant of reater capacity than diesel enine can be built. 7. Lesser lubrication is required. 8. It can be used in jet propulsion units because of continuous exhaust at hih temperature and pressure. 9. he system is flexible and thus reheatin, reeneration and inter coolin arranements can be added to the increase efficiency and work output of the system. 0. Comparatively silent operation due to continous exhaust. Disadvantaes. Overall efficiency is much less then reciprocatin enines since 70% of the output of turbine is to fed to compressor.. Maximum temperature in as turbine cannot exceed 500 K because of material consideration of blade while reciprocatin enines can sustain a temperature of 000K. his hih temperature is permitted since piston and cylinder heads are subjected to this hih temperature only for a fraction of seconds.. Additional reduction ears are required due to hiher speeds as such hih speeds cant be utilized.. Difficulty in startin of as turbines. 5. It is sensitive to chane in compressor and turbine efficiency. 6. It has hih air rate so that open cycle is not suitable in marine applications. 7. oor port load efficiency. OO CYCLE Otto cycle is the air standard cycle in a four stroke I enine. Each stroke consists of 80 0 C of crankshaft rotation and hence a stroke thermodynamic cycle is completed in 70 0 C of crank rotation. Durin strokes there are 5 events to be completed viz. suction, compression, combustion, expansion and exhaust.. uction stroke uction stroke starts when piston is at top dead center and about to move downwards. Initially the inlet valve opens and exhausts valve closes and fresh chare of fuel and air mixture is drawn into cylinder due to suction created by motion of piston towards the bottom dead center.. Compression stroke he mixture which fills the entire cylinder volume is now compressed into clearance volume as piston moves from BDC to DC. hortly before the piston reaches DC, the mixture is inited with the help of spark plu located on cylinder head. Durin compression stroke, inlet and exhaust valve remains closed. In ideal conditions it is assumed that burnin takes place instantly when piston is at top dead center and burnin process is considered as heat addition at constant volume.

14 E. I..D.C.D.C B.D.C uction troke B.D.C Compression troke Fiure. Expansion stroke he hih pressure ases (produced as a result of combustion) force the piston down, which in turn forces the crankshaft to rotate, producin the useful work output durin expansion or power stroke. Durin expansion stroke both inlet and outlet value remains closed and the piston moves from DC to BDC.. Exhaust stroke At the end of expansion stroke the exhaust value opens and the inlet value remains closed. he pressure falls to atmospheric pressure as a part of burnt ases escape. he piston starts movin from BDC to DC and sweeps the burnt ases out from cylinder at constant pressure. -v diaram of an Otto cycle 0,5 0- uction - Compression - Constant volume heat addition Fiure 5

15 - Expansion -5 Constant volume heat rejection / Blow down (pressure falls to atmospheric conditions) 5-0 Exhaust Gasoline and CNG are most commonly used fuels in I enine. hey require spark for inition due to their hih self inition temperatures. Compression ratio C Clearance volume troke olume C = = - osition of piston head at DC Fiure 6 osition of piston heat at BDC he minimum volume formed in cylinder when the piston is at DC is called clearance volume. he volume displaced by the piston as it moves between DC and BDC is called displacement volume or stroke volume. Ratio of maximum volume formed in the cylinder ( s + c ) to the minimum volume ( c ) is called compression ratio (r) of the enine. Compression ratio is also known as volume ratio. s c s r c c 5

16 Efficiency of Air tandard Otto Cycle Q Q Q R Q R -Reversible Adiabatic compression -Constant volume heat addition - Reversible Adiabatic expansion - Constant olume heat rejection Wnet Qs QR QR Q Q Q s s s mc mc v v r Fiure 7 r where r is the compression ratio. 6

17 r otto r Efficiency of an air standard Otto Cycle is directly proportional to compression ratio. Mean effective pressure ( m ) Mean effective pressure is a constant hypothetical pressure which ives same work as the oriinal cycle. ( ) W net m (W ) net = - = Wnet Wnet W net m Wnet m...() Fiure 8 Hih net work output for a iven amount of heat supply is desirable to achieve hih efficiency. herefore hiher mean effective pressures are desirable. 7

18 m W net...() Q s From equation () and () Qs mcv m Heat is supplied at constant volume mr m m since m r m heoretically efficiency of air standard Otto cycle is directly proportional to compression ratio. However actual variation of efficiency with compression ratio and adiabatic index of workin fluid is show in Fiure9. otto r=.67 r=. r=. 8 r Fiure 9 We observe that thermal efficiency curve flattens out startin with r of about 8. herefore increasin compression ratio beyond 8 has very little effect on efficiency. Also auto inition occurs at very hih compression ratio which is hihly undesirable. 8

19 DIEEL CYCLE 9

20 Diesel cycle is an air standard cycle in a stroke compression inition (CI) enine. he CI enine, first proposed by Rudolph diesel in 890s, is very similar to I enine, differin mainly in the method of initiatin combustion. In CI enines air is compressed durin air is compressed stroke. he temperature of air after compression must be hih enouh so that fuel sprayed into hot air burns spontaneously. he spark plu and carburetor (for mixin fuel and air) are replaced by fuel injector in diesel enines. Diesel enine operates at hiher compression ratios ( to ) so that hih temperature of air after compression supports the burnin of fuel. Fuel used is CI enine such as diesel has low self inition temperature which eliminates the use of spark plu. CI enines have hiher efficiency than I enines due to use of hiher compression ratios. Fuel injection starts at the end of compression stroke. he rate of injection is such that combustion maintains the pressure constant inspite of piston movement on its expansion stroke increasin the volume. herefore heat is assumed to be added at constant pressure. -v diaram of Diesel cycle 0-uction -Compression -Constant pressure heat addition -Expansion 0,5 5-0Exhaust Fiure 0 Efficiency of Air tandard Diesel Cycle Q -5Blow down (Constant volume heat rejection) Q =C =C QR =C Fiure -Reversible adiabatic compression -Constant pressure heat addition - Reversible adiabatic expansion - Constant pressure heat rejection Q R lope of constant volume lines is more than slope of constant pressure line on - diaram. 0

21 r (compression ratio) r c (cutt off ratio) rc re r r e (expansion ratio) W Q Q Q Q Q Q net s R R s s s mc mc r v p...() Re versible adibatic compression r...() Re versible adibatic expansion re r c rc rc r r r r rc r c...() c c From equation (), () and () rc rc r Effect of cut-off ratio on performance of diesel cycle

22 Q Q Q R Q R Fiure With the increase in cut-off ratio both heat supply and heat rejection increases but the rate of heat rejection is more because it occurs at constant volume and slope of constant volume line is reater than slope of constant pressure line. his efficiency decreases with increase in cutt off ratio. DUAL CYCLE he air standard diesel cycle does not simulate exactly the pressure volume variation in an actual CI enine, where the fuel injection is started before the end of compression stroke. A closer approximation is the limited pressure cycle in which some part of heat is added to air at constant volume, and the remainder at constant pressure. Q Q Fiure COMARION OF OO AND DIEEL CYCLE. ame compression ratio and same amount of heat addition Q Q R Q Q otto QR Q otto R otto s=c W W C E s=c 5 diesel diesel diesel Q R W C =C Q Q R =C =C =C =C Extra heat rejection in diesel cycle =C 5 W E

23 Fiure. ame compression ratio and same amount of heat rejection Q Q R QR Q otto R Q Q otto otto diesel diesel diesel Extra heat addition in Otto cycle =C =C =C Fiure 5

24 . ame maximum temperature and heat rejection Q Q R QR Q otto R Q Q otto diesel diesel diesel otto Extra amount of heat added in diesel cycle Conclusion Fiure 6 Otto cycle have hiher efficiency as compared to diesel cycle for same compression ratio. his can also be concluded by the formulas otto r rc diesel rc ince rc rc otto r diesel for same compression ratio For same maximum temperature and pressure and same amount of heat rejection,. his comparison is of reater sinificance, since Diesel cycle diesel otto would definitely have a hiher compression ratio then the Otto cycle.

(v) Cylinder volume It is the volume of a gas inside the cylinder when the piston is at Bottom Dead Centre (B.D.C) and is denoted by V.

(v) Cylinder volume It is the volume of a gas inside the cylinder when the piston is at Bottom Dead Centre (B.D.C) and is denoted by V. UNIT II GAS POWER CYCLES AIR STANDARD CYCLES Air standard cycles are used for comparison of thermal efficiencies of I.C engines. Engines working with air standard cycles are known as air standard engines.