Lecture note   gas turbine cycle
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  • 1. •1/10/2013 •1 GAS TURBINE CYCLES Introduction Chapter Objective • To carry out first law analysis on a gas turbine plant in which the working fluid is assumed as a perfect gas. How a Gas Turbine Works? • It is a heat engine in which a pressurized hot gas spins a gas turbine, thus producing mechanical work. • This pressurized gas produced by burning fuels such as propane, natural gas, kerosene or jet fuel. • The heat that comes from burning fuel expands air, and the high speed rush of this hot air spins the turbine. •1-Oct-13 •Gas Turbine Cycle •2
  • 2. •1/10/2013 •2 Gas Turbine Combined Cycle •1-Oct-13 •Gas Turbine Cycle •3 The Use of Gas Turbine Gas turbine plants are widely used in the following engineering fields: 1. Aircraft propulsion system 2. Electric power generation 3. Marine vehicle propulsion 4. Combined-cycle power plant (with steam power plant) •1-Oct-13 •Gas Turbine Cycle •4
  • 3. •1/10/2013 •3 Aircraft engine •1-Oct-13 •Gas Turbine Cycle •5 Front view of the aircraft engine Aircraft engine sketch Gas Turbine Animation •1-Oct-13 •Gas Turbine Cycle •6 Gas Turbine Animation.mp4
  • 4. •1/10/2013 •4 Note: The processes taking place in an actual gas turbine plant are complicated. To carry out thermodynamics study on the system, we will develop a simplified model of the system. •1-Oct-13 •Gas Turbine Cycle •7 Types of Gas Turbine Cycles There are two types of gas turbine cycle: Brayton/Joule Cycle and Atkinson Cycle. Brayton Cycle Heat added and rejected is at constant pressure. Atkinson Cycle 1.Heat added at constant volume, therefore a. It needs valve to control gas flow to ascertain constant volume b. Complicated 2.Heat rejected at constant pressure 3.Not popular 4.Out of the SKMM2423 scope. •1-Oct-13 •Gas Turbine Cycle •8
  • 5. •1/10/2013 •5 Brayton Cycle • It is an ideal and closed type cycle. • It is used as a reference cycle, where actual cycle can be compared with this cycle. • The working fluid is merely air. • The basic components comprise of air compressor, heat exchanger and gas turbine. •1-Oct-13 •Gas Turbine Cycle •9 Brayton/Closed Cycle The cycle comprises of 4 internal reversible processes. • Process 1-2: isentropic compression • Process 2-3: isobaric heat addition • Process 3-4: isentropic expansion • Process 4-1: isobaric heat rejection •1-Oct-13 •Gas Turbine Cycle •10 1 3 4 2
  • 6. •1/10/2013 •6 Cycle Analysis - Thermal Efficiency By using steady flow energy equation (sfee), this closed ideal cycle can be analyzed as follows, ( ) ( ) ( ) ( )1212 4334 1441 2323 TTcww TTcww TTcqq TTcqq pcom ptur pout pin −== −== −== −== •1-Oct-13 •Gas Turbine Cycle •11 Brayton/Closed Cycle 2 4 1 3 i.e. ( ) ( )23 14 11 TTc TTc q q q qq q w wwqqw p p in out in outin in net th compturoutinnet −/ −/ −=−= − == −=−= η •1-Oct-13 •Gas Turbine Cycle •12 ( ) ( )23 14 1 TT TT th − − −=η (1) First law of thermodynamic states, net heat received by any cyclic device is the same with the net work produced, i.e., Brayton/Closed Cycle
  • 7. •1/10/2013 •7 γ γ 1 4 3 4 3 −       = p p T T 32 pp = 14 pp = •1-Oct-13 •Gas Turbine Cycle •13 γ γ 1 1 2 1 2 −       = p p T T But, for isentropic processes, and Because and Therefore, pr p p p p == 4 3 1 2 (2) 1 3 4 2 Brayton/Closed Cycle 2 4 1 3 ratiopressure=pr ( )4.1airratioheatspecific === v p c c γ γ γ 1 43 − ⋅= prTT •1-Oct-13 •Gas Turbine Cycle •14 Where, So, and andγ γ 1 12 − ⋅= prTT 2 4 1 3 Brayton/Closed Cycle
  • 8. •1/10/2013 •8 •1-Oct-13 •Gas Turbine Cycle •15 Therefore, (3)γ γ 1 4 3 1 2 − == pr T T T T 2 4 1 3 Brayton/Closed Cycle ( ) ( ) γ γ 1 1423 − −=− prTTTT •1-Oct-13 •Gas Turbine Cycle •16 So, or ( ) ( ) γ γ 1 23 14 1 − = − − prTT TT Brayton/Closed Cycle 2 4 1 3
  • 9. •1/10/2013 •9 ( ) ( ) γ γ η 1 23 14 1 11 − −= − − −= p th rTT TT •1-Oct-13 •Gas Turbine Cycle •17 So, (4) Brayton/Closed Cycle 2 1 1 T T th −=η ( ) ( ) 2 1 2 3 2 1 4 1 23 14 1 1 T T T T T T T T TT TT =       −       − = − − •1-Oct-13 •Gas Turbine Cycle •18 Also, Therefore, (5) Note: Only valid for ideal closed cycle. Brayton/Closed Cycle
  • 10. •1/10/2013 •10 ( ) ( ) ( )43 1243 34 1234 TTc TTcTTc w ww w w w p pp turbine net r − −−− = − == •1-Oct-13 •Gas Turbine Cycle •19 Cycle Analysis - Work Ratio, wr, Brayton/Closed Cycle 2 4 1 3 ( ) ( )43 12 1 TT TT wr − − −= •1-Oct-13 •Gas Turbine Cycle •20 Cycle Analysis - Work Ratio, wr, ie., Brayton/Closed Cycle 2 4 1 3
  • 11. •1/10/2013 •11       −       − −=           −       − −= − −− − − 1 .1 1 1 1 1 1 1 3 11 1 13 1 1 γ γ γ γ γ γ γ γ γ γ p pp p p r rT rrT r T rT w γ γ 1 12 . − = prTT •1-Oct-13 •Gas Turbine Cycle •21 We know that, and γ γ 1 3 4 − = pr T T Therefore, Brayton/Closed Cycle γ γ 1 3 1 .1 − −= pr r T T w •1-Oct-13 •Gas Turbine Cycle •22 or, (6) Brayton/Closed Cycle
  • 12. •1/10/2013 •12 Modifications of Brayton Gas Turbine Cycle Brayton/Joule Cycle (Closed & Ideal) Open Cycle Basic Two-Stage Expansion Two-Stage Compression with Intercooler Two-Stage Compression + Two-Stage Expansion + Reheating Basic + Two-Stage Expansion + Two-Stage Compression + Reheating + The Use Of Heat Exchanger •1-Oct-13 •Gas Turbine Cycle •23 Basic Gas Turbine •1-Oct-13 •Gas Turbine Cycle •24 Basic Components The basic components of a gas turbine plant working on an open cycle. The plant comprises of: 1. Air compressor (centrifugal or axial-flow type) 2. Combustion chamber 3. Gas turbine
  • 13. •1/10/2013 •13 •1-Oct-13 •Gas Turbine Cycle •25 Basic Gas Turbine p2 2 ’ ’ Basic Gas Turbine •1-Oct-13 •Gas Turbine Cycle •26 Process Description 1-2: Compression process Atmospheric air at pressure p1 and temperature T1 is induced and compressed adiabatically to higher pressure p2 and temperature T2. The process is not reversible, thus, not isentropic. 2-3: Combustion process Fuel is injected into the air stream. The mixture of air and fuel is burned at constant pressure inside a combustion chamber (CC), thus producing hot combustion gases. p2 2 ’ ’
  • 14. •1/10/2013 •14 •1-Oct-13 •Gas Turbine Cycle •27 Process Description 3-4: Expansion process The hot combustion gases expands through the gas turbine. The process is assumed adiabatic but not reversible, thus, not isentropic. Mechanical work is produced by the turbine. Part of this work is used to drive the compressor. The air exiting the turbine is exhausted to atmosphere. New fresh air is induced into the compressor and the processes are repeated. p2 2 ’ ’ Basic Gas Turbine •1-Oct-13 •Gas Turbine Cycle •28 Energy Analysis • The steady-flow energy equation (SFEE) is applied to each component of the gas turbine plant. • Neglecting the change in the kinetic and potential energy of the working fluid, we have, work to drive the compressor: (7) p2 2 ’ ’ Basic Gas Turbine ( )' 12 .C paw c T T= −
  • 15. •1/10/2013 •15 •1-Oct-13 •Gas Turbine Cycle •29 Heat added to the compressed air (8) Work produced by the turbine (9) Note: The turbine is connected to the compressor via a common shaft. Thus, part of the work produced by the turbine is used to drive the compressor. p2 2 ’ ’ Basic Gas Turbine ( )'3 2 .CC pgq c T T= − ( )'3 4 .T pgw c T T= − •1-Oct-13 •Gas Turbine Cycle •30 Properties of Working Fluid The air and combustion gases are assumed to have the following properties: For air: cpa = 1.005 kJ/kg.K, γa = 1.4 For gas: cpg = 1.110 kJ/kg.K, γg = 1.33 Basic Gas Turbine
  • 16. •1/10/2013 •16 •1-Oct-13 •Gas Turbine Cycle •31 Isentropic Efficiency The compression and expansion processes are not isentropic. The isentropic efficiency of the compressor and the turbine is defined as follows, Compressor: (10) Turbine: (11) p2 2 ’ ’ Basic Gas Turbine ( ) ( )' 2 1 , 12 is C T T T T η − = − ( ) ( ) '3 4 , 3 4 is T T T T T η − = − γ γγ γ 1 1 1 1 2 12 − − =      = prT p p TT γ γ γ γ 1 1 3 1 3 4 34 −         =      = − pr T p p TT •1-Oct-13 •Gas Turbine Cycle •32 Isentropic Process The isentropic process between path 1-2 is And the isentropic process between path 3-4 is where the values of γ for air and gas are different. Basic Gas Turbine
  • 17. •1/10/2013 •17 •1-Oct-13 •Gas Turbine Cycle •33 Thermal efficiency Thermal efficiency of the basic gas turbine cycle is Cycle Performance The performance of the basic gas turbine cycle is measured by the following criteria: (12) p2 2 ’ ’ Basic Gas Turbine ( ) ( ) ( ) ' ' ' 3 14 2 3 2 net T C th in CC pg pa th pg w w w q q c T T c T T c T T η η − = = − − − = − •1-Oct-13 •Gas Turbine Cycle •34 Work ratio The work ratio of the plant is (13) p2 2 ’ ’ Cycle Performance The performance of the basic gas turbine cycle is measured by the following criteria: Basic Gas Turbine ( ) ( ) ' ' 12 3 4 1 1 net T C C r T T T pa r pg W w w w w W w w c T T w c T T − = = = − − = − −
  • 18. •1/10/2013 •18 Assumptions The following assumptions are made on the simplified model of the gas turbine plant: 1. The mass of fuel injected into the air is ignored since the air fuel ratio is usually large. 2. The mass flow rate of the working fluid is considered constant. fag mmm /+= •1-Oct-13 •Gas Turbine Cycle •35 Basic Gas Turbine Example 1 A gas turbine has an overall pressure ratio of 5/1 and a maximum cycle temperature of 550oC. The turbine drives a compressor and an electric generator, the mechanical efficiency of the drive being 97%. The ambient temperature is 20oC and the isentropic efficiencies of the compressor and turbine are 0.8, and 0.83 respectively. Calculate the power output in kilowatts for an air flow of 15 kg/s. Calculate also the thermal efficiency and the work ratio. Neglect changes in kinetic energy, and the loss of pressure in the combustion chamber. Please use the following assumptions: for air, cp = 1.005 kJ/kg and γ = 1.4, for gas, cp = 1.15 kJ/kg and γ = 1.333. •1-Oct-13 •Gas Turbine Cycle •36
  • 19. •1/10/2013 •19 •1-Oct-13 •Gas Turbine Cycle •37 Basic Gas Turbine p2 2 ’ ’ Two-Stage Expansion Process • It is more practical to expand the hot gases in two turbine stages. • The high-pressure (HP) turbine is solely used to drive the compressor. • The low-pressure (LP) turbine produces net power output. •1-Oct-13 •Gas Turbine Cycle •38
  • 20. •1/10/2013 •20 •1-Oct-13 •Gas Turbine Cycle •39 Two-Stage Expansion Process 2 2’ 4 4’ 5 5’ •1-Oct-13 •Gas Turbine Cycle •40 Energy Analysis Neglecting changes in the kinetic and potential energy of the working fluid, Compressor Work The high-pressure turbine is dedicatedly used to drive the compressor, therefore Work required to drive the air compressor = Work produced by the high-pressure (HP) turbine Two-Stage Expansion Process
  • 21. •1/10/2013 •21 •1-Oct-13 •Gas Turbine Cycle •41 Energy Analysis i.e. wC = wT,hp or (14) where cpa and cpg are specifics heats at constant pressure for the air and hot gases respectively. Two-Stage Expansion Process ( ) ( )2' 1 3 4'. .pa pgc T T c T T− = − •1-Oct-13 •Gas Turbine Cycle •42 Note: Given the value of T1, maximum cycle temperature T3 and the overall pressure ratio, (p2/p1), eq. (14) can be used to determine the temperature T4 at the inlet to the low-pressure (LP) turbine and the pressure ratio (p2/p4) across the high-pressure (HP) turbine. Two-Stage Expansion Process 2 2 ’ 4 4’ 5 5 ’
  • 22. •1/10/2013 •22 •1-Oct-13 •Gas Turbine Cycle •43 Net work output The low-pressure turbine produces the net work output for the plant, thus, (15) Two-Stage Expansion Process 2 2 ’ 4 4’ 5 5 ’ ( ) , 4' 5'. net T lp net pg w w w c T T = = − A gas turbine unit takes in air at 17oC and 1.01 bar with an overall pressure ratio 8:1 and a maximum cycle temperature of 650oC. The compressor is driven by the high-pressure (HP) turbine and the low-pressure (LP) turbine drives a separate power shaft. The isentropic efficiencies of the compressor, the HP turbine and the LP turbine are 0.8, 0.85 and 0.83 respectively and the mechanical efficiency of both shafts is 0.95. Calculate the: a) pressure and temperature at the inlet of LP turbine, b) net power output for each kg/s mass flow rate, c) work ratio of the plant, and d) thermal efficiency of the cycle. •1-Oct-13 •Gas Turbine Cycle •44 Example 2
  • 23. •1/10/2013 •23 •1-Oct-13 •Gas Turbine Cycle •45 Two-Stage Expansion Process 2 2’ 4 4’ 5 5’ Two-Stage Compression Process •1-Oct-13 •Gas Turbine Cycle •46
  • 24. •1/10/2013 •24 Two-Stage Compression Process •1-Oct-13 •Gas Turbine Cycle •47 • In real gas turbine plant, the compression process is carried out in more than one stage. • An intercooler is used between each stage. 4 4’ A A’ 6’ 6 2 2’ •1-Oct-13 •Gas Turbine Cycle •48 Reasons • The work required to drive the compressor can be reduced. • Since the work output of the low-pressure (LP) turbine is unchanged, the work ratio of the plant is increased. Analysis of the Cycle The work required to drive compressor with inter-cooling, (16) Two-Stage Compression Process ( ) ( ), 2' 1 4' 3. .C ic pa paw c T T c T T= − + −∑
  • 25. •1/10/2013 •25 ( ) ( )'2'1'2 .. TTcTTcw ApapaC −+−=∑ ( ) ( )'2'3'4 .. TTcTTc Apapa −<− ∑ ∑< CicC ww , •1-Oct-13 •Gas Turbine Cycle •49 The work required to drive compressor without intercooling, Since the pressure lines on the T-s diagram diverge to the right, Therefore, the compressor work input with intercooling is less than the work input without intercooling, i.e. Two-Stage Compression Process 4 4’ A A’ 6’ 6 2 2’ 3 4 1 2 p p p p = 13 TT = •1-Oct-13 •Gas Turbine Cycle •50 Minimum Compressor Work The work input with intercooling, ΣwC,ic will be MINIMUM when: 1. The pressure ratio in each stage is equal, i.e. 2. The intercooling process is complete, i.e. the temperature of the air entering between the stages the high-pressure (HP) and the low- pressure (LP) stage is the same, i.e. Two-Stage Compression Process 4 4’ A A’ 6’ 6 2 2’
  • 26. •1/10/2013 •26 T CT r w ww w − = •1-Oct-13 •Gas Turbine Cycle •51 Advantage Two-stage compression with inter- cooling between the stages reduces the work required to drive the compressor. Recall, Since wC is reduced while wT remains unchanged, the work ratio of the plant increased. Two-Stage Compression Process 4 4’ A A’ 6’ 6 2 2’ ( )'45, . TTcq pgicCC −= ( )'5. ApgCC TTcq −= •1-Oct-13 •Gas Turbine Cycle •52 Disadvantage The heat added to the air during combustion with 2-stage compression and inter-cooling is and that without 2-stage & inter-cooling is From T-s diagram, (T5 – T4’) > (T5 – TA’). Therefore the heat added to the air increases with 2-stage compression with inter-cooling. Thus, thermal efficiency of the cycle decreases. 4 4’ A A’ 6’ 6 2 2’ Two-Stage Compression Process
  • 27. •1/10/2013 •27 '4'2 31 TT TT ≠ ≠ 3 4 1 2 p p p p = 3 4 1 2 p p p p ≠ •1-Oct-13 •Gas Turbine Cycle •53 Comparison Between Complete & Incomplete Inter-cooling T1 = T3 T2’ = T4’ s T 1 2 2’ 3 4 4’ 6 5 6’ T s 1 2 2’ 3 4 4’ 6 5 6’ Two-Stage Compression Process A gas turbine unit has a pressure ratio of 10/1 and a maximum temperature of 700oC. The compression process is carried out in 2 stages and inter-cooling is used between the stages. The isentropic efficiencies of the compressors and the turbine are 0.82 and 0.85 respectively. The air enters the compressor at 15oC at the rate 15 kg/s. Calculate, a) the power output of an electric generator geared to the turbine; b) the work ratio; c) the thermal efficiency. Assume the conditions for minimum compressor works •1-Oct-13 •Gas Turbine Cycle •54 Example 3
  • 28. •1/10/2013 •28 Two-Stage Compression Process •1-Oct-13 •Gas Turbine Cycle •55 Two-Stage Expansion & Reheating •1-Oct-13 •Gas Turbine Cycle •56 With 2-stage expansion, the gas exiting the high-pressure (HP) turbine can be reheated in a second combustion chamber, before expanding the low- pressure (LP) turbine. 2 2’ 4’ 4 A A’ 6
  • 29. •1/10/2013 •29 ( )''4, . ApgLPt TTcw −= •1-Oct-13 •Gas Turbine Cycle •57 Analysis of the cycle Neglecting any mechanical losses, the work produced by the low-pressure (LP) turbine WITH reheating, (17) and the work produces WITHOUT reheating, 2 2’ 4’ 4 A A’ 6 Two-Stage Expansion & Reheating ( ), , 5 6'.t LP rh pgw c T T= − ( ) ( )''4'65 ATTTT −>− •1-Oct-13 •Gas Turbine Cycle •58 Analysis of the cycle Hence, reheating between the turbine stages increases the work output of the low-pressure (LP) turbine. The constant pressure lines diverge to the right on the T-s diagram, so Two-Stage Expansion & Reheating 2 2’ 4’ 4 A A’ 6
  • 30. •1/10/2013 •30 ∑∑ ∑ −= − = t c t ct r w w w ww w 1 •1-Oct-13 •Gas Turbine Cycle •59 Advantage The work ratio of the plant is given by The total turbine work, Σwt increases with reheating between the turbine stages. Therefore the work ratio of the plant increases. Two-Stage Expansion & Reheating 2 2’ 4’ 4 A A’ 6 •1-Oct-13 •Gas Turbine Cycle •60 cpg(T5 – T4’) is the additional heat added to the working fluid in the second combustion chamber. Clearly, reheating between the turbine stages increases the amount of heat supplied in the combustion chambers. This causes the thermal efficiency of the plant to decrease. Disadvantage The heat added to the working fluid in the combustion chambers, (18) Two-Stage Expansion & Reheating 2 2 ’ 4 ’ 4 A A’ 6( ) ( )3 2' 5 4'CC pg pgq c T T c T T= − + −∑
  • 31. •1/10/2013 •31 A gas turbine unit is used in a marine ship consists of a compressor, two combustion chambers and two stages of turbines. The compressor is driven by the high-pressure (HP) turbine and the low-pressure (LP) turbine drives the ship rotor. The overall pressure ratio is 10:1. The atmosphere air enters the compressor at 1.01 bar and 30oC with the rate of 20 kg/s. The gas enters the HP turbine at 900oC and enters the LP turbine at 700oC. The mechanical efficiency for both shafts is 90%. The isentropic efficiency for both turbines is 85%. The power received by the rotor is 2590 kW. a) Show the plant components arrangement and all the processes on a T-s diagram, b) Calculate the intermediate pressure between the HP turbine and LP turbine, c) Calculate the compressor power, d) Calculate the isentropic efficiency of the compressor, e) Thermal efficiency of the cycle. •1-Oct-13 •Gas Turbine Cycle •61 Example 4 •1-Oct-13 •Gas Turbine Cycle •62 Two-Stage Expansion & Reheating
  • 32. •1/10/2013 •32 A gas turbine power plant consists of 2-stages compressor and 2- stages turbine. The high-pressure and low-pressure compressor are driven by the high-pressure (HP) turbine and the low-pressure (LP) turbine drives a separate power shaft. The low-pressure compressor takes in air at 100 kPa and 27oC with the mass flow rate of 5.80 kg/s. The compressors have equal pressure ratios and inter-cooling is complete between stages. The temperature of the gases at entry to the HP turbine is 1327oC and the gases are reheated to 1127oC at 300 kPa after expansion in the first turbine. The overall pressure ratio is 10. The isentropic efficiency of each compressor stage and each turbine stage is 80 %. Calculate; a) net power output (kW), b) work ratio of the plant, c) thermal efficiency of the cycle. Sketch the schematic diagram of the plant and all the processes on a T-s diagram. •1-Oct-13 •Gas Turbine Cycle •63 Example 5 •1-Oct-13 •Gas Turbine Cycle •64 HP C CC LP T Exhaust Net power output 8’ 4’ 3 HP T 5 CC 6’ 7 4 4 ’ 2 ‘ ‘ ‘ Two Stage Compression & Two Stage Expansion
  • 33. •1/10/2013 •33 The Use of a Heat Exchanger •1-Oct-13 •Gas Turbine Cycle •65 The Use of a Heat Exchanger •1-Oct-13 •Gas Turbine Cycle •66 • The gases exiting the low-pressure (LP) turbine is still has a high temperature. • The heat energy contained in the exhaust gases can be utilized for improving the thermal efficiency of the cycle. • One scheme is by using a heat exchanger unit to preheat the air leaving the compressor, before it enters the combustion chamber. Net power output ’ ’ Ideal heat exchanger
  • 34. •1/10/2013 •34 6'2 TT = '53 TT = •1-Oct-13 •Gas Turbine Cycle •67 Ideal vs Actual Temperatures In an ideal cycle, temperatures and In an actual cycle, temperatures '53 TT <6'2 TT < and The finite temperature difference is required, between the compressed air and the exhaust gases, for the heat transfer process to take place. The Use of a Heat Exchanger ’ ’ •1-Oct-13 •Gas Turbine Cycle •68 Advantage of Heat Exchanger When the compressed air is preheated before entering the combustion chamber, the amount of heat qCC required to raise the temperature of the working fluid from T2’ to T4, is reduced. Heat only required to raise the temperature of the air from T3 to T4. This leads to saving in fuel consumption and hence the operating cost of the plant. Assuming that net work output of the plant remains unchanged, the thermal efficiency of the cycle increases by using the heat exchanger. Actual heat exchanger ’ ’ The Use of a Heat Exchanger
  • 35. •1/10/2013 •35 •1-Oct-13 •Gas Turbine Cycle •69 Heat Energy Balance Assuming the heat exchanger is well insulated (no heat loss), we have Heat transferred FROM the exhaust gases = Heat transferred TO the compressed air i.e. (19) The Use of a Heat Exchanger ( ) ( )5' 6 3 2'g pg a pam c T T m c T T− = − differenceretemperatuavailableMaximum airtheofriseeTemperatur =hetr •1-Oct-13 •Gas Turbine Cycle •70 Heat Exchanger Performance The performance of the heat exchanger is measured by it’s thermal ratio, defined as, (20) i.e. The Use of a Heat Exchanger ( ) ( ) 3 2 ' 5 ' 2 ' he T T tr T T − = −
  • 36. •1/10/2013 •36 •1-Oct-13 •Gas Turbine Cycle •71 Heat Exchanger Performance Without heat exchanger : With heat exchanger : (21) (22) Actual heat exchanger ’ ’ The Use of a Heat Exchanger ( )4 2'in pgq c T T= − ( )4 3in pgq c T T= − •1-Oct-13 •Gas Turbine Cycle •72 Conditions for Use To use the heat exchanger, there must be a sufficiently large temperature difference between the exhaust gases and the compressed air. The use of heat exchanger will not be feasible when the temperature of the exhaust gases is lower than the temperature of the compressed air leaving the compressor. The Use of a Heat Exchanger
  • 37. •1/10/2013 •37 •1-Oct-13 •Gas Turbine Cycle •73 You are required to carry out an energy audit on a gas turbine plant. In this plant the high pressure turbine (HPT) drives a compressor and the low pressure turbine (LPT) drives an electric generator (EG). Atmospheric air, after being compressed, enters a first combustion chamber (CC1) and the hot gas is then expanded in the HPT. The gas is reheated in a second combustion chamber (CC2) before it is expanded in the LPT. Based on the true measurements made, followings are the data recorded by your Technical Assistant: o output power of generator, 1080 kW; o mass flow-rate of air, 6.85 kg/s; o compressor pressure ratio, 6.3 and HPT pressure ratio, 2.9; o compressor inlet and outlet air temperatures, 20oC and 252oC; o HPT inlet and outlet gas temperatures, 701oC and 487oC; o LPT inlet and outlet gas temperatures, 631oC and 486oC. Example 6 •1-Oct-13 •Gas Turbine Cycle •74 Sketch all processes on a T-s diagram and determine the following values, for you to prepare the audit report: i. compressor isentropic efficiency; ii. HPT isentropic efficiency; iii. HPT/compressor mechanical efficiency; iv. LPT isentropic efficiency; v. LPT/EG mechanical efficiency; vi. plant thermal efficiency, and vii. in the same report, you are proposing that a heat exchanger with a thermal ratio of 0.78, be installed to preheat the compressed air by the exhaust gas. To support your proposal what are: (a) the percentage saving on heat supply by CC1, and (b) the new value of the plant thermal efficiency. Please use the following assumptions: for air, cp = 1.005 kJ/kg and γ = 1.4 for gas, cp = 1.15 kJ/kg and γ = 1.333 Example 6
  • 38. •1/10/2013 •38 A 5000 kW gas turbine generating set operates with two compressor stages with inter-cooling between stages; the overall pressure ratio is 9/1. A HP turbine is used to drive the compressors, and a LP turbine drives the generator. The temperature of the gases at entry to the HP turbine is 650°C and the gases are reheated to 650°C after expansion in the first turbine. The exhaust gases leaving the LP turbine are passed through a heat exchanger to heat the air leaving the HP stage compressor. The compressors have equal pressure ratios and inter-cooling is complete between stages. •1-Oct-13 •Gas Turbine Cycle •75 Example 7 The air inlet temperature to the unit is 15°C. The isentropic efficiency of each compressor stage is 0.8 and the isentropic efficiency of each turbine stage is 0.85; the heat exchanger thermal ratio is 0.75. A mechanical efficiency of 98% can be assumed for both the power shaft and the compressor turbine shaft. Neglecting all pressure losses and changes in kinetic energy, calculate: (i) the cycle efficiency; (ii) the work ratio; (iii) the mass flow rate. For air take cp = 1.005 kJ/kg.K and γ = 1.4, and for the gases in the combustion chamber and in the turbines and heat exchanger take cp = 1.15 kJ/kg.K and γ = 1.33. Neglect the mass of fuel. •1-Oct-13 •Gas Turbine Cycle •76 Example 7
  • 39. •1/10/2013 •39 In a gas turbine generating station the overall pressure ratio is 15/1. The compression is performed in three stages with pressure ratios of 3/1, 2.5/1 and 2/1 respectively. The air inlet temperature of the plant is 30oC and inter-cooling between stages reduces the temperature to 45oC. The high pressure (HP) turbine drives all the compressors and the low pressure (LP) turbine drives the generator. The gases leaving the LP turbine are passed through a heat exchanger which heats the air leaving the HP compressor to 250oC. The temperature at inlet to the HP turbine is 700oC, and reheating between turbine stages raises the temperature to 650oC. The isentropic efficiency of each compressor stage is 0.85, and the isentropic efficiency of each turbine is 0.88. Take the mechanical efficiency of each shaft as 98%. The air mass flow rate is 120 kg/s. •1-Oct-13 •Gas Turbine Cycle •77 Example 8 Neglecting pressure losses and changes in kinetic energy, and taking the specific heat of water as 4.19 kJ/kgK, calculate, i. The power output (kW) ii. The cycle efficiency iii. The mass flow rate of cooling water for the intercoolers if its temperature rise must not exceed 20 K iv. The heat exchanger thermal ratio. Assume that cp and γ may be taken as 1.005 kJ/kgK and 1.4 for air, and as 1.15 kJ/kgK and 1.33 for combustion and expansion processes. •1-Oct-13 •Gas Turbine Cycle •78 Example 8