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EGR 334 Thermodynamics Chapter 9: Sections 7-8 Lecture 36: Reheat and Intercooling of Gas Turbine Systems Quiz Today? Today’s main concepts: • Be able to explain the concept and purpose of using reheat in a gas turbine. • Be able to explain the concept and purpose of using intercooling in a gas turbine system. • Be able draw and explain Brayton cycles with reheat and intercooling. Reading Assignment: Read Chapter 10 Homework Assignment: Problem 9:80 Sec 9.5 : Modeling Gas Turbine Power Plants Last time: Introduced to the Gas Turbine Power Plant Working fluid is air Heat transfer from an external source (assumes there is no reaction) Process 1 – 2 : Isentropic compression of air (compressor). Process 2 – 3 : Constant pressure heat transfer to the air from an external source (combustion) Process 3 – 4 : Isentropic expansion (through turbine) Process 4 – 1 : Completes cycle by a constant volume pressure in which heat is rejected from the air 3 4 How a Jet Engine Works: http://www.youtube.com/watch?NR=1&f eature=endscreen&v=ON0sVe1yeOk Jet Engine Power Station Gas Turbine Images from: http://library.thinkquest.org/C006011/english/sites/gasturbine.php3?v=2 5 Possible Enhancements to the Brayton Cycle: 1) Use of Regenerator to preheat combustion air. 2) Reheating air between successive turbine stages. 3) Intercooling of air between successive compressor stages. 6 Brayton Cycle with Regeneration: The exhaust air out of the turbine contains significant waste heat that would normally be discarded to the atmosphere. Use of regenerator can make use of this heat that would be discarded to preheat the air on its way to the combustor, allowing the burned fuel to be used more efficiently. Sec 9.8 : Regenerative Gas Turbines with Reheat and Intercooling To limit the temperature of the gas entering the turbine, air is provided in excess to the primary combustion chamber. The excess air limits the temperature of the combustion process by providing a heat sink for the heat produced during combustion. Q Combustion m rxn c P T Q Combustion m rxn c P T m inert c P T This has the added advantage of having the second turbine run at lower pressure. Processes 2-3, a-b, and 4-1 occur isobarically. 7 Sec 9.8 : Regenerative Gas Turbines with Reheat and Intercooling Improved efficiency may also be achieved by decreasing the work required for the compressors. It is not practice to achieve such cooling within a compressor. Consequently, the compressor is spit with a heat-exchanger in between. 8 Sec 9.8 : Regenerative Gas Turbines with Reheat and Intercooling Putting all three enhancements together, the diagram show a process combining regeneration, reheat, and intercooling. 9 10 Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, 300 K. The air is compressed stages to 900 to4 State 1 in two 2 kPa, 3 with intercooling c d a b 300 K between the stages at a pressure of 300 kPa. The turbine inlet 300the expansion 300occurs in two 1480stages, with 1420reheat temperatureTis(K)1480 K and P (kPa) the stages 100 at300 300 of900 900 The300 300 100 to 1420 K between a pressure 300 kPa. compressor and turbine stage Prefficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine h (kJ/kg) (a) The volumetric flow rate entering the cycle. (b) The thermal efficiency of the cycle. (c) The back work ratio. 11 Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine (a) of StateThe thermal 1 efficiency 2 3 c d 4 a b the cycle. (b) work ratio. 300 T (K)The back300 1480 1420 p (kPa) 100 300 300 900 900 pr 1.3860 1.3860 568.8 h (kJ/kg) 300.19 300.19 1611.79 300 300 100 478.0 1539.44 Find state a, Process 1 – a is Isentropic compression 300 1 . 3860 4 . 158 p1 100 Using the isentropic compressor efficiency: From the table haS = 411.26 kJ/kg h1 p ra S p r 1 h a h1 h aS h1 h aS h a h1 300 . 19 pa 411 . 26 300 . 19 0 . 84 432 . 42 kJ kg 12 Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine (a) of bthe cycle. StateThe thermal 1 efficiency 2 3 c d 4 a (b) work ratio. T (K)The back300 300 1480 1420 P (kPa) 100 300 pr 1.3860 h (kJ/kg) 300.19 300 432.42 900 900 1.3860 568.8 300.19 1611.79 300 300 100 478.0 1539.44 Find state a, Process b – 2 is Isentropic compression p2 900 p r 2 S p rb 1 . 3860 4 . 158 pb 300 Using the isentropic compressor efficiency: From the table h2S = 411.26 kJ/kg hb h 2 hb h 2 S h 2 hb h 2 S hb 300 . 19 411 . 26 300 . 19 0 . 84 432 . 42 kJ kg 13 Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine (a) ofbbthe cycle. State StateThe thermal 11 efficiency 22 33 c dd 44 aa work ratio. 300 T(b) T(K) (K)The back 300 300 300 1480 1480 1420 1420 pp(kPa) (kPa) 100 100 300 300 300 300 900 900 1.3860 1.3860 900 900 568.8 568.8 300 300 300 300 ppr r 1.3860 1.3860 hh(kJ/kg) (kJ/kg) 300.19 300.19 432.42 432.42 300.19 300.19 432.42 432.42 1611.79 1611.79 1275.4 1539.44 1539.44 100 100 478.0 478.0 Find state a, Process 3 – c is Isentropic expansion 300 568 . 8 189 . 60 p3 900 Using the isentropic turbine efficiency: From the table hcS = 1201.5 kJ/kg h3 hc p rcS p r 3 pc h3 h cS hc h3 h3 h cS 1611 . 79 0 . 82 1611 . 79 1201 . 5 1275 . 4 kJ kg 14 Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine State 11 T (K) 300 300 p (kPa) 100 100 aa bb 22 300 300 300 300 300 300 900 900 1.3860 1.3860 33 c c d d 1480 1480 1420 1420 900 900 300 300 300 300 568.8 568.8 44 100 100 prr 1.3860 1.3860 478.0 478.0 h (kJ/kg) 300.19 300.19 432.42 432.42 300.19 300.19 432.42 432.42 1611.79 1611.79 1275.4 1275.4 1539.44 1539.44 1216.77 Find state a, Process d – 4 is Isentropic expansion 100 478 . 0 159 . 33 pd 300 Using the isentropic turbine efficiency: From the table h4S = 1145.94 kJ/kg h4 hd p r 4 S p rd p4 h 4 h dS h 4 h d h d h 4 S 1539 . 44 0 . 82 1539 . 44 1145 . 94 1216 . 77 kJ kg 15 Example (9.74): The compressor and turbine stage efficiencies are 84 and 82% respectively, The net power developed is 1.8 W. Determine State 1 2 3 c d 4 (a) The thermal efficiency a of b the cycle. (b) The back T (K) 300work ratio. 300 1480 1420 p (kPa) 100 300 pr 1.3860 h (kJ/kg) 300.19 300 900 900 1.3860 432.42 300.19 300 568.8 432.42 1611.79 1275.4 300 100 478.0 1539.44 1216.77 Determine the mass flow rate W cycle W T 1 W T 2 W C 1 W C 2 1 .8 kJ / s W cycle m W cycle m 394 . 6 h3 hc h d h 4 h a h1 h 2 hb kJ kg m W cycle 3 9 4 .6 kJ / kg 1 .8 kJ / s 3 9 4 .6 kJ / kg 4 .5 6 2 kg / s 16 Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, State 1 is compressed 2 d 4to a bin two stages 300 K. The air to 3900 kPa,cwith intercooling a pressure of 300 kPa. The turbine T 300 (K) K between 300 the stages at 300 1480 1420inlet temperature is 1480 K and the expansion occurs in two stages, with reheat p (kPa) 100 300 300 900 900 300 300 100 to 1420 K between the stages at a pressure of 300 kPa. The compressor and prturbine stage 1.3860 568.8 478.0 efficiencies 1.3860 are 84 and 82% respectively, The net power h developed (kJ/kg) 300.19 432.42 300.19 432.42 1611.79 1275.4 1539.44 1216.77 is 1.8 W. Determine (a) The volumetric flow rate. kg (b) The thermal efficiency of the cycle. m 4 . 562 s (c) The back work ratio. A V 1 A V 1 R T1 0 .2 8 7 0 kJ / kg K 3 0 0 K m 4 .5 6 2 kg / s 5 2 p (1 0 / m ) 1 3 .9 3 m s 3 17 Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, State 1 is compressed 2 d 4to a bin two stages 300 K. The air to 3900 kPa,cwith intercooling a pressure of 300 kPa. The turbine T 300 (K) K between 300 the stages at 300 1480 1420inlet temperature is 1480 K and the expansion occurs in two stages, with reheat p (kPa) 100 300 300 900 900 300 300 100 to 1420 K between the stages at a pressure of 300 kPa. The compressor and prturbine stage 1.3860 568.8 478.0 efficiencies 1.3860 are 84 and 82% respectively, The net power h developed (kJ/kg) 300.19 432.42 300.19 432.42 1611.79 1275.4 1539.44 1216.77 is 1.8 W. Determine (a) The volumetric flow rate. W cycle kg (b) The thermal efficiency of the cycle. m 4 . 562 Q (c) The back work ratio. in s kJ Q in m h3 h 2 h d h c 1443 . 41 kg W cycle 394 . 6 0 . 2734 Q in 1443 . 41 18 Example (9.74): Air enters the compressor of a gas turbine at 100 kPa, State 1 is compressed 2 d 4to a bin two stages 300 K. The air to 3900 kPa,cwith intercooling a pressure of 300 kPa. The turbine T 300 (K) K between 300 the stages at 300 1480 1420inlet temperature is 1480 K and the expansion occurs in two stages, with reheat p (kPa) 100 300 300 900 900 300 300 100 to 1420 K between the stages at a pressure of 300 kPa. The compressor and prturbine stage 1.3860 568.8 478.0 efficiencies 1.3860 are 84 and 82% respectively, The net power h developed (kJ/kg) 300.19 432.42 300.19 432.42 1611.79 1275.4 1539.44 1216.77 is 1.8 W. Determine (a) The volumetric flow rate. WC kg (b) The thermal efficiency of the cycle. b w r m 4 . 562 W T (c) The back work ratio. s h a h1 h 2 hb W C bwr h3 h c h d h 4 WT bwr 264 . 46 659 . 06 0 . 401 19 end of slides for Lecture 36