Theory and Applica>on of Gas Turbine Systems

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1 Theory and Applica>on of Gas Turbine Systems Part I: Ideal Sha- Power Cycles Munich Summer School at University of Applied Sciences Prof. Kim A. Shollenberger

2 Outline for Theory of Gas Turbine Systems Introduc6on I. Ideal Sha- Power Cycles II. Actual ShaB Power cycles III. Centrifugal Flow Compressors IV. Axial and Radial Flow Turbines V. Combus>on Systems VI. Performance Predic>on

3 References 1. Moran, M J and HN Shappiro, Fundamentals of Engineering Thermodynamics, 8 th edi>on, John Wiley & Sons, Munson, BR, Young, DF, and TF Okiishi, Fundamentals of Fluid Mechanics, 7 th edi>on, John Wiley & Sons, Inc., SaravanamuZoo, HIH, Rogers, GFC, Cohen, H, and P Straznicky, Gas Turbine Theory, 6 th edi>on, Pren>ce Hall (Pearson Educa>on LTD), Boyce, MP, Gas Turbine Engineering Handbook, 4 rd edi>on, Elsevier (BuZerworth Heinemann), 2012.

4 Basic Nomenclature c p specific heat at constant pressure c v Ė g h k!m p specific heat at constant volume energy rate gravitation acceleration specific enthalpy specific heats ratio mass flowrate pressure!q s T v V V!W z ρ heat transfer rate specific entropy temperature specific volume velocity volume work rate elevation density

5 Introduc>on to Gas Turbines Used to produce mechanical power by expanding a high energy gas across a turbine without reciproca>ng members (such as a piston/cylinder assembly), thus they have the following advantages: High power produc=on for their size and weight High reliability due to reduced rubbing members, few balancing problems, and low lubrica>ng oil consump>on Simple u>liza>on of mul=ple fuels

6 History of Water/Steam Turbines First turbines used water as the working fluid to produce hydro-electric power; s>ll a significant contributor to world s energy resources Steam turbines introduced around 1900; widely used for electricity genera>on (current units can have over 1 GW of shab power and 40% efficiency) Steam turbines were also widely used for marine propulsion up un>l mid 1970 s (when more efficient diesel engines took over) except for nuclearpowered aircrab carriers and submarines

7 Disadvantages of Steam Turbines Produc>on of high-pressure high-temperature steam requires bulky and expensive steam genera>ng equipment Hot gases produced in boiler or nuclear reactor core can never reach the turbine; instead an intermediate fluid, typically steam, flows through the turbine Satura>on temperature of steam, even at high pressures, limits maximum thermal efficiency theore>cally possible

8 History of Gas Turbines Serious development began in the 1940 s; mainly on turbojet engine for aircrab propulsion Significant use for other fields, including electrical power produc>on, began in the 1950 s Wide use today (current units can have over 0.5 GW of shab power and 45% efficiency) has been driven by improving two main performance limi>ng factors: Component efficiencies through aerodynamics research High temperature materials developed through advances in metallurgy

9 Gas Turbine Cycles Two main classifica>ons: 1. ShaC Power Cycles used for land based electric power genera>on, marine propulsion, mechanical drive systems, process heat, compressed air, etc. 2. AircraC Propulsion Cycles where performance depends on forward speed and al>tude This course will focus on shab power cycles.

10 ShaB Power Cycles Two main configura>ons: a. Open to the atmosphere Most common for power genera>on and engines Heat addi>on typically in a combus>on chamber b. Closed loop Found in nuclear power plants Heat addi>on and heat rejec>on done by heat exchangers at constant pressure

11 Open ShaB Power Cycle

12 Open ShaB Power Cycle Opera>on 1. Fresh air is drawn into the compressor where both its pressure and temperature are increased 2. Fuel is mixed with compressed air at an appropriate fuel/air ra>o and ignited in the combus=on chamber to produce high energy gases 3. Combus>on products are expanded across a turbine to a lower pressure and temperature which produces shac power that is used to operate the compressor and generate electricity

13 Closed ShaB Power Cycle Replace combus>on chamber with heat exchanger and close loop by adding a second heat exchanger

14 Ideal Condi>ons for Gas Turbines Assume the following: 1. Compression and expansion processes are reversible and adiaba>c, thus isentropic 2. Kine>c energy and poten>al energy changes for gas are negligible 3. Pressure losses for gas are negligible 4. Ideal gas with constant proper>es and composi>on at constant mass flowrate (steady opera>on) 5. Complete heat transfer (temperature rise on cold side equals temperature drop on hot side)

15 Ideal Gas Power Cycle (Also Called Brayton or Joule Cycle) Named aber an American engineer, George Brayton, who proposed the cycle for a reciproca>ng oil burning engine around 1870 Process 1-2: isentropic compression (compressor) Process 2-3: constant pressure heat addi>on Process 3-4: isentropic expansion (turbine) Process 4-1: constant pressure heat rejec>on NOTE: For ideal cycle that assumes constant working fluid, open and closed cycles are the same.

16 Brayton Cycle heat exchanger turbine compressor heat exchanger Pressure (p) Specific Volume (v) Diagram Temperature (T) - Entropy (s) Diagram

17 1 st Law of Thermodynamics For control volume (CV) with inlet at (1) and outlet at (2): de cv dt = Q! cv W! " cv +!m $ h 1 h 2 # For steady state and where changes in kine>c energy (KE) and poten>al energy (PE) negligible: 0 = Q! cv W! cv +!m ( h 1 h 2 ) ( ) + V 1 2 V 2 2 NOTE: Sign conven>on is heat transfer into the CV and work out of the CV are posi>ve, thus nega>ve sign above 2 ( ) + g z 1 z 2 % ' &

18 1 st Law of Thermodynamics Analysis Process 1 st Law Analysis Descrip6on Symbols 1-2!W 12 =!m ( h 1 h 2 ) compressor work rate in!w c =! W heat addi>on 3-4!Q 23 =!m h 3 h 2 ( )!W 34 =!m ( h 3 h 4 )!Q 41 =!m h 1 h 4 ( ) turbine work rate out 4-1 heat rejec>on!q in =! Q 23!W t =! W 34!Q out =! Q 41

19 Brayton Cycle Analysis Net work rate for cycle:!w cycle = W! 12 + W! 34 = W! c + W! t =!m ( h 1 h 2 + h 3 h 4 ) Net heat transfer for cycle:!q cycle = Q! 23 + Q! 41 = Q! in Q! out =!m ( h 3 h 2 + h 1 h 4 ) NOTE: As expected for a closed cycle:!w cycle =! Q cycle

20 Process Defini>ons Back Work Ra=o ra>o of compressor work input to turbine work output bwr =! W c!m!w t!m =!W 12!W 34 = h 2 h 1 h 3 h 4 Compressor Pressure Ra=o ra>o of the exit and inlet pressures for the compressor r p = p 2 p 2 = p 3 p 1 p 1 NOTE: For Brayton cycle p 4

21 Cycle Performance Thermal efficiency - desired power or work rate output divided by required heat input η th =! W cycle!m!q in!m =! Q 23 +! Q 41!Q 23 =1! Q out!q in η th =1 h 4 h 1 h 3 h 2 NOTE: By the 2 nd Law of Thermodynamics power cycle must reject heat to produce work, thus η th < 1.

22 Cold Air-Standard Analysis For ideal gas with constant specific heats: h 1 h 2 = c p ( T 1 T 2 ) Use isentropic rela>onship for Process 1-2 and 3-4: T 2! = p 2 # T 1 " p 1 $ & % ( k 1) k ( k 1) k = r p T 4! = p 4 # T 3 " p 3 $ & % ( k 1) k = 1 ( ) = T 1 k r p k 1 T 2

23 Cold Air-Standard Analysis for Cycle Specific Work Output Recall cycle work rate from earlier:!w cycle =!m h 1 h 2 + h 3 h 4!W cycle = " 1 r p!m c p T # 1 ( ) =!m c p T 1 1 T 2 * $ ( k 1) k $ % + T 3 T 1 " & 1 #& 1 r p k 1 ( ) ( ) k $ ' %' " # T 1 % " '+T 3 1 T 4 $ & # T 3 % + '- &, Calculate op>mum r p for maximum using W! cycle r p = 0: ( k 1) r k p, opt = T 3 T 1

24 Brayton Cycle Net Work Rate For fixed T 1 = T min and T 3 = T max, net work rate first increases with pressure ra>o, reaches maximum at r p, opt, and then decreases.

25 Cold Air-Standard Analysis for Back Work Ra>o Recall from earlier: bwr = h h 2 1 = c p T 2 T 1 h 3 h 4 c p T 3 T 4 ( ) ( ) = T T 1 ( T ) T 4 ( T 3 T 4 1) bwr = T 1 = T 2 = T 1 ( k 1) k r p T 4 T 3 T 3 NOTE: Minimize compressor versus turbine work by decreasing compressor temperatures (T 1 and T 2 ) and increasing turbine temperatures (T 3 and T 4 )

26 Cold-Air Standard Analysis Recall from earlier: for Thermal Efficiency η th =1 h h 4 1 =1 c T T p 4 1 h 3 h 2 c p T 3 T 2 η th =1 T 1 T 2 =1 T 4 T 3 =1 ( ) ( ) =1 T T 1 ( T ) T 2 ( T 3 T 2 1) NOTE: Efficiency increases with pressure ra>o. 1 ( ) k r p k 1

27 Example #1 Air enters the compressor of an ideal gas turbine system at 100 kpa and 27 C. The pressure ra>o is 5 and the maximum temperature is 867 C. For your calcula>ons use the cold-air standard and list any addi>onal assump>ons. a. Sketch the T-s diagram for this cycle. b. Calculate the thermal efficiency. c. Calculate the back work ra>o. d. Calculate the specific work output.

28 Brayton Cycle Performance k = 1.4, T 1 = 300 K, T 3 = 1000 K 80% 0.8 Thermal Efficiency 60% 40% 20% 0% typical pressure ratios for gas- 0.2 turbine engines Specific Work Output Pressure Ratio

29 Notes on Brayton Cycle Effect of pressure ra=o on efficiency can be observed by considering areas on T-s diagram Maximum temperature (T 3 ) limited by turbine blades (approximately 1750 K) oben called the metallurgical limit Minimum temperature (T 1 ) usually ambient (approximately 300 K), thus not considered an independent variable Tradeoff between op>mum thermal efficiency and maximum work output

30 Improving Gas Turbine Performance 1. Regenera=on - use turbine exhaust to preheat air entering combustor 2. Reheat - reheat turbine exhaust and add addi>onal turbine(s) 3. Intercooling - cool compressor exhaust and add addi>onal compressor(s)

31 Regenera>ve Gas Turbine

32 Brayton Cycle with Regnera>on

33 Brayton Cycle with Regenera>on Turbine exhaust at State (4) is used to preheat air from State (2) to State (x) before entering combustor Reduces heat addi>on: Reduces heat rejec>on:!q in =! Q x3 <! Q 23!Q out =! Q y1 <! Q 41 Addi>onal heat exchanger increases capital costs Can increase thermal efficiency at lower r p ( ) + ( h 3 h 4 ) ( ) W η th =! cycle!m!q in!m = W! 12 + W! 34 = h h 1 2!Q x3 h 3 h x

34 Regenerator Performance Regenerator Effec=veness ra>o of actual to maximum theore>cal enthalpy increase η reg = actual heat transfer maximum heat transfer = h x h 2 h 4 h 2 Ideal Regenerator for a heat exchanger with infinite area: η reg = 100%, T x = T 4, T y = T 2, and!q 2 x =! Q 4 y NOTE: Specific work output and bwr are unchanged.

35 Brayton Cycle with Regenera>on Thermal Efficiency For cold air-standard analysis: ( ) + ( h 3 h 4 ) ( ) η th = h h 1 2 h 3 h x For an ideal regenerator: ( ) + ( T 4 T x ) ( ) =1 T T 2 1 T 3 T x η th =1 T 1 T T T 3 1 T 4 T 3 " η th =1 T % 1 $ # & T 3 ( ) ( ) =1 " T 1 $ # T 3 ( k 1)/k 'r p % " ' T 2 $ & # T 1 NOTE: % ' & For r p = 1, η th equals Carnot efficiency

36 Example #2 Air enters the compressor of an ideal gas turbine system at 100 kpa and 27 C with ideal regenera=on. The pressure ra>o is 5 and the maximum temperature is 867 C. For your calcula>ons use the cold-air standard and list any addi>onal assump>ons. a. Sketch the T-s diagram for this cycle. b. Calculate the thermal efficiency. c. Calculate the back work ra>o. d. Calculate the specific work output.

37 Comparison of Thermal Efficiency for Brayton Cycle with Regenera>on 80% Thermal Efficiency 60% 40% 20% k = 1.4 T3 / T1 = 5 T3 / T1 = 4 T3 / T1 = 3 T3 / T1 = 2 Simple Cycle NOTE: Curves stop at simple cycle because addi>onal regenera>on heat transfer is not possible. 0% Pressure Ratio

38 Brayton Cycle with Reheat

39 Brayton Cycle with Reheat Excess air is used for combus>on because of temperature limits imposed by turbine blades Second turbine uses excess air and addi>onal fuel for more combus>on For ideal reheat (maximum work rate) for fixed r p and T 3 = T b, pressure ra>o across each stage can be shown to be equal where p a = p b = p i : r p = p 2 = p 3 p 1 p a 2 = p b p 4 2

40 Brayton Cycle with Reheat Specific Work Output For cold air-standard analysis:!w cycle =!m ( h 1 h 2 ) +!m ( h 3 h a ) +!m ( h b h 4 )!W cycle = 1 T 2!m c p T 1 T 1 + T 3 T 1 1 T a T 3 + T b 1 T 4 T 1 T b!w cycle = 1 r p!m c p T 1 ( k 1) k + T 3 2 p i T 1 p 3 ( k 1) k p 4 p i ( k 1) k

41 Brayton Cycle with Reheat Specific Work Output, cont. Determine p i for ideal reheat using! W cycle p i = 0 T 3 T 1 k 1 p i k p 3 1 k 1 p 3 k 1 p 4 k p i 1 k p 4 p i 2 = 0 p i p 3 1 k p i p 3 = p 4 p i 1 k p 4 p i p i = p 4 = r p p 3 p i!w cycle = 1 r p!m c p T 1 ( k 1) k + 2 T 3 T 1 1 r p k 1 1 ( ) ( 2 k)

42 Brayton Cycle with Reheat Specific Work Output, cont. Calculate op>mum r p for maximum using! W cycle r p = 0 r p 1 r p ( k 1) k + 2 T 3 T 1 r p 1 r p k 1 1 ( ) ( 2 k) = 0 k 1 1 r k p 2 T 3 k T 1 k 1 1 3k r p 2k ( ) 2 k ( ) = 0 3 ( k 1) ( 2k r ) p, opt = T 3 T 1

43 Brayton Cycle with Reheat Thermal Efficiency For cold air standard analysis: ( ) + ( h 3 h a ) + ( h b h 4 ) ( ) + ( h b h a ) η th = h h 1 2 h 3 h 2 For ideal reheat: =1 ( T 4 T 1 ) ( T 3 T 2 ) + T b T a ( ) η th =1 ( ) ( k 1)/ ( 2k 1 r ) p T 1 T 3 ( k 1 2 ( T 1 T 3 )r )/k k 1 p 1 r p ( )/ 2k ( )

44 Example #3 Air enters the compressor of an ideal gas turbine system at 100 kpa and 27 C with ideal reheat. The pressure ra>o is 5 and the maximum temperature is 867 C. For your calcula>ons use the cold-air standard and list any addi>onal assump>ons. a. Sketch the T-s diagram for this cycle. b. Calculate the thermal efficiency. c. Calculate the back work ra>o. d. Calculate the specific work output.

45 Comparison of Specific Work Output for Brayton Cycle with Reheat k = 1.4, T 1 = 300 K, T 3 = 1000 K Specific Work Output Reheat Cycle Simple Cycle Pressure Ratio

46 Comparison of Thermal Efficiency for Brayton Cycle with Reheat 80% Thermal Efficiency 60% 40% 20% 0% k = 1.4 Simple Cycle T3 / T1 = 20 T3 / T1 = 6 T3 / T1 = 4 T3 / T1 = Pressure Ratio

47 Brayton Cycle with Intercooling

48 Brayton Cycle with Intercooling Less work is required to compress a cool gas Compensates for low temperature limited by nature (examples: air or ocean temperature) Limited use in prac>ce because requires bulky equipment and huge amounts of cooling water For ideal intercooling (minimum work rate) for fixed r p and T 1 = T d, pressure ra>o across each stage can be shown to be equal where p a = p b = p i : r p = p 2 p 1 =! # " p c p 1 $ & % 2! = p 2 # " p d $ & % 2

49 Brayton Cycle with Intercooling Specific Work Output For cold air-standard analysis:!w cycle =!m ( h 1 h c ) +!m ( h d h 2 ) +!m ( h 3 h 4 )!W cycle " = 1 T c $!m c p T 1 # T 1 % '+ T " d 1 T 2 $ & T 1 # T d % '+ T " 3 1 T 4 $ & T 1 # T 3 % ' & For ideal intercooling: 3 ( k+1) ( 2k r ) p, opt = T 3 T 1!W cycle = 2 " 1 r p!m c p T # 1 ( k 1) ( 2 k) $ % + T 3 T 1 " & 1 #& 1 ( ) k r p k 1 $ ' %'

50 Brayton Cycle with Intercooling Thermal Efficiency For cold air standard analysis: ( ) + ( h d h 2 ) + ( h 3 h 4 ) ( h 3 h 2 ) η th = h 1 h c ( ) + ( h c h d ) ( ) =1 T T 4 1 T 3 T 2 For ideal intercooling: ( ) r p k 1 η th =1 1 r ( k 1 )/k p + T 1 T 3 1 T 1 T 3 " # ( ) r p k 1 ( )/ 2k ( )/k ( ) 2$ %

51 Comparison of Specific Work Output for Brayton Cycle with Intercooling k = 1.4, T 1 = 300 K, T 3 = 1000 K Specific Work Output Intercooling Simple Cycle Pressure Ratio

52 Comparison of Thermal Efficiency for Brayton Cycle with Intercooling 80% Thermal Efficiency 60% 40% 20% 0% k = 1.4 Simple Cycle T3 / T1 = 20 T3 / T1 = 6 T3 / T1 = 4 T3 / T1 = Pressure Ratio

53 Gas Turbine with Regenera>on, Reheat, and Intercooling While reheat and intercooling alone increase work output, they also decrease thermal efficiency: For reheat, need extra heat for hea>ng between stages and heat rejec>on at higher temperatures For intercooling, need to heat up more aber compression However, reheat and intercooling increase the poten>al for regenera>on; combined, the overall effect can be an increase in the thermal efficiency

54 Gas Turbine with Regenera>on, Reheat, and Intercooling

55 Brayton Cycle with Regenera>on, Reheat, and Intercooling

56 Example #4 Air enters the first compressor stage of an ideal gas turbine system with ideal regenera>on, reheat, and intercooling at 100 kpa and 27 C. The pressure ra>o is 5 across both compressors and the maximum temperature is 867 C. For your calcula>ons use the cold-air standard and list any addi>onal assump>ons. a. Sketch the T-s diagram for this cycle. b. Calculate the thermal efficiency. c. Calculate the back work ra>o. d. Calculate the specific work output.

57 Ericson Cycle Ideal cycle for gas turbine engines with an efficiency equal to the Carnot efficiency Theore>cally accomplished in the limit where regenera>on is used with an infinite number of stages of reheat and intercooling

58 Combined Gas Turbine-Vapor Power Cycle Waste heat from gas turbine power cycle (topping cycle) is used as heat input for vapor power cycle, thus the thermal efficiency becomes: η th =! W g!m g +! W v!m v!q in,g!m g where subscript g is for the gas cycle and the subscript v is for the vapor cycle.

59 Combined Brayton-Ideal Vapor Power Cycle

60 Combined Brayton-Ideal Vapor Power Cycle Analysis 1 st Law CV analysis of heat exchanger between cycles (assume adiaba>c, negligible KE and PE) 0 =!m g ( h 8 h 9 ) +!m v ( h 2 h 3 )!m g!m v = ( h 8 h 9 ) ( h 3 h 2 ) Subs>tute into thermal efficiency and reduce to get: " η th = η th,g + h h % 8 9 $ # h 7 h 6 & 'η th,v NOTE: Thermal efficiency is typically much higher than thermal efficiency of gas cycle alone.

61 Combined Brayton-Ideal Vapor Power Cycle Analysis, Cont. For cold air standard: " η th = η th,g + T T % 8 9 $ # T 7 T 6 & 'η th,v Ideally, T 9 would be as low as possible such that T 9 = T 5, then (T 8 - T 9 ) would be approximately the same as (T 7 - T 6 ) and η th would be the sum of the two individual cycles In prac>ce, η th is generally higher than either cycle would have individually because of both high temperature heat addi>on and low temperature heat rejec>on Efficiencies of over 60% are currently obtained by modern combined plants today

62 Gas Turbines For AircraB Propulsion S>ll use Brayton cycle with the following changes: Diffuser de-accelerates incoming flow to zero velocity (incoming flow has significant KE) Nozzle accelerates exi>ng flow to significant KE Turbine work produced equals compressor work and minor aircrab power needs h 1 = h air + V 2 air 2 V 5 2 ( h 4 h 5 ) h 3 h 4 h 2 h 1

Theory and Applica>on of Gas Turbine Systems

Theory and Applica>on of Gas Turbine Systems Part II: Actual Sha. Power Cycles Munich Summer School at University of Applied Sciences Prof. Kim A. Shollenberger Actual Sha@ Power Cycles: Compressor and