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Similar a Thermodynamics of axial compressor and turbine - 3rd December 2009
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Thermodynamics of axial compressor and turbine - 3rd December 2009
- 1. Gas Turbine Axial Compressors andCompressors and Turbines Thermodynamics calculationsThermodynamics calculations 3rd December 2009 Prepared by: Cheah CangTo Supervised by: James Richard Bryan
- 2. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Objectives of this discussion: a) Overview of Brayton cycle. b) Is to provide the insight of prediction on thermodynamics performances of gas turbine axial compressor and turbine. c) Note when considering the fundamentals of axial compressor and turbine design, it should be emphasized that successful compressor / turbine design is very much an art, and all the major engine manufacturers have developed a body of knowledge which is kept proprietary for competitive reasons. 2Thermodynamics of axial compressor a body of knowledge which is kept proprietary for competitive reasons.
- 3. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Overview of Brayton cycle The Brayton cycle was first proposed by George Brayton for use in the reciprocating oil-burning engine that he developed around 1870. Today, it isreciprocating oil-burning engine that he developed around 1870. Today, it is used for gas turbines only where both the compression and expansion processes take place in rotating machinery. Picture taken from Wikipedia 1 to 2: Isentropic air compression1 to 2: Isentropic air compression 2 to 3: Isobaric (constant pressure) heat addition 3 to 4: Isentropic expansion of heated air 3Thermodynamics of axial compressor 4 to 1: Isobaric heat rejection (for closed-cycle)
- 4. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine With input parameters: a) air mass flow ratea) air mass flow rate b) compressor compression ratio (note turbine expansion ratio is proportional per Brayton’s P-v diagram discussed earlier) c) inlet temperaturec) inlet temperature d) polytropic efficiency Basically, there are two parameters needed to be evaluated: a) shaft power requires to perform compression work b) temperature rises at compressor outlet 4Thermodynamics of axial compressor
- 5. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Formula for gas power Power (kJ/s = kW) = mass flow rate (kg/s) x specific heat capacity at constant pressurePower (kJ/s = kW) = mass flow rate (kg/s) x specific heat capacity at constant pressure (kJ/kg.K) x delta temperature (K) Known / given: mass flow rate To find:To find: a) specific heat capacity at constant pressure, Cp b) delta temperature = T_out – T_in (note: Inlet temperature, T_in is given)b) delta temperature = T_out – T_in (note: Inlet temperature, T_in is given) 5Thermodynamics of axial compressor
- 6. Specific heat capacity at constant pressure, Cp is a function of temperature. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Specific heat capacity at constant pressure, Cp is a function of temperature. What should the temperature be? Inlet temperature or outlet temperature? The answer is mean temperature, i.e. T_mean = (T_in + T_out)/2 should be used in order to evaluate Cp. But, how do we calculate T_mean since T_out is an unknown parameter.But, how do we calculate T_mean since T_out is an unknown parameter. This problem can be solved by iteration method, i.e. take T_mean = T_in (i.e. without T_out) for the first pass of iteration loop until values of T_out converge. A0 0.992313 A1 0.236688 A2 -1.852148 A3 6.083152 A4 -8.893933 A5 7.097112 A6 -3.234725 A7 0.794571 A8 -0.081873A8 -0.081873 8765432 1000 8 1000 7 1000 6 1000 5 1000 4 1000 3 1000 2 1000 10 ×+ ×+ ×+ ×+ ×+ ×+ ×+×+= meanmeanmeanmeanmeanmeanmeanmean p T A T A T A T A T A T A T A T AAC 6Thermodynamics of axial compressor
- 7. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Outlet temperature, T_out is a function of: a) pressure ratioa) pressure ratio b) gama = Specific gas constant / (Specific gas constant – specific heat capacity at constant pressure) c) inlet temperaturec) inlet temperature d) isentropic efficiency of compressor it is defined on following page inTratiopressure × − − γ γ 1_ 1 in isentropic in out TT + = η 7Thermodynamics of axial compressor b) gama = Specific heat capacity at constant pressure / (Specific heat capacity at constant pressure - Specific gas constant)
- 8. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Isentropic efficiency of compressor is a function of: a) pressure ratioa) pressure ratio b) gama c) polytropic efficiency 1_ 1 − − ratiopressure γ γ 1_ 1 − = − ratiopressure isentropic γ γ η 1_ − × polytropic ratiopressure ηγ 8Thermodynamics of axial compressor
- 9. 1−γ TURBO GROUP – Thermodynamics of Axial Compressor and Turbine 1_ 1_ 1 1 − − = × − − polytropic ratiopressure ratiopressure isentropic ηγ γ γ γ η 1_ −ratiopressure Isentropic efficiency of compressor falls as pressure ratio is increased for the same polytropic efficiency. 9Thermodynamics of axial compressor
- 10. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine In the previous slide, we learned that isentropic efficiency of compressor falls as compression ratio increases. But why GT manufacturers are building high pressure ratio machines (e.gBut why GT manufacturers are building high pressure ratio machines (e.g LMS100, compression ratio of 40:1)? Reasons are:Reasons are: a) Isentropic efficiency of turbine increases as expansion ratio increases. b) Higher OVERALL (combination of compressors, combustors, diffusers, turbineb) Higher OVERALL (combination of compressors, combustors, diffusers, turbine expanders, etc) efficiency. Overall efficiency means net shaft output power divided by fuel input power. Compression work is taking energy from the fuel, in contrast turbine is extracting work from it. Turbine work is defined by:contrast turbine is extracting work from it. Turbine work is defined by: ∆××= • TCpmPower turbineturbine −××=∆ − γ γ 1_ _ 1 1 ratioExpansion EffTT turbineisentropicinturbine 10Thermodynamics of axial compressor _ ratioExpansion
- 11. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine In order to maintain maximum temperature drop across turbine, it is necessary to have higher expansion ratio, this means the pressure shall be kept high at turbine inlet and low at turbine outlet. This leads to the reason why high powerturbine inlet and low at turbine outlet. This leads to the reason why high power rating GT requires high compression ratio. Although it is true that a higher T_in (combustion outlet temperature) will improve efficiency (refer Brayton cycle), for the purposes of this discussion T_in is assumed constant since all turbinethe purposes of this discussion T_in is assumed constant since all turbine manufacturers have similar combustor outlet temperatures to maximize efficiency. c) Mismatch (in term of air density) between compressor and turbine affecting overall GT efficiency occurs on high compression ratio machine at high ambientoverall GT efficiency occurs on high compression ratio machine at high ambient temperature. This effect can be clearly seen when comparing temperature de- rate curves between low pressure ratio industrial gas turbines versus high pressure ratio aero-derivative gas turbines. However, the topic is out of scope ofpressure ratio aero-derivative gas turbines. However, the topic is out of scope of this discussion. 11Thermodynamics of axial compressor
- 12. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine −××=∆ − γ γ 1_ _ 1 1 ratioExpansion EffTT turbineisentropicinturbine Delta T across turbine vs expansion ratio 800 γ _ ratioExpansion 700 750 800 DeltaTemperature(K) 600 650 DeltaTemperature(K) 500 550 DeltaTemperature(K) 400 450 0 5 10 15 20 25 30 35 40 Expansion ratio 12Thermodynamics of axial compressor Expansion ratio
- 13. • TURBO GROUP – Thermodynamics of Axial Compressor and Turbine turbineturbine TCpmPower ∆××= • Turbine power output vs expansion ratio 90000 95000 80000 85000 Turbineshaftpower(kW) 70000 75000 Turbineshaftpower(kW) 55000 60000 65000 Turbineshaftpower(kW) 50000 55000 0 5 10 15 20 25 30 35 40 Expansion ratio 13Thermodynamics of axial compressor
- 14. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine 2.00 Specific work output vs pressure ratio T3/T1 = 2 T3/T1 = 3 T3/T1 = 4 T3/T1 = 5 1.50 T_in)] T3/T1 = 5 1.00 Specificworkoutput[W/(Cp*T_in 0.50 Specificworkoutput[W/( 0.00 0 5 10 15 20 25 30 -0.50 Pressure ratio 14Thermodynamics of axial compressor
- 15. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine 2.00 Specific work output vs pressure ratio T3/T1 = 2 T3/T1 = 3 T3/T1 = 4 1.50 T_in)] T3/T1 = 5 PR=17 1.00 Specificworkoutput[W/(Cp*T_in PR=17 Optimum pressure ratio for a 0.50 Specificworkoutput[W/( PR=11 Optimum pressure ratio for a given temperature ratio, T3/T1. 0.00 0 5 10 15 20 25 30 Specificworkoutput[W/( PR=7 PR=3 -0.50 Pressure ratio 15Thermodynamics of axial compressor Pressure ratio
- 16. OVERALL (combination of compressors, combustors, diffusers, turbine expanders, etc) efficiency TURBO GROUP – Thermodynamics of Axial Compressor and Turbine OVERALL (combination of compressors, combustors, diffusers, turbine expanders, etc) efficiency increases as compression ratio increases. Overall GT efficiency versus compression ratio OverallgasturbineefficiencyOverallgasturbineefficiencyOverallgasturbineefficiency ( )rationcompressiooverall _ln09979.007641.0 ×+=η ( )rationcompressiooverall _ln09979.007641.0 ×+=η Note: Overall GT efficiency is derived from machine manufacturers’ published heat rate.. Compression ratio Gas turbine heat rate data courtesy of James Bryan [GSGnet.net (2009)] 16Thermodynamics of axial compressor Compression ratio
- 17. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine GT thermal efficiency versus pressure ratio: comparison between Brayton and actual cycle 0.6 0.7 1 0.5 0.6 Brayton Actual γ γ η 1 1 2 1 1 − −= P P Brayton 0.4 0.3 ×+= 2 ln09979.007641.0 P P actualη 0.1 0.2 1P 0.0 0.1 17Thermodynamics of axial compressor 0 5 10 15 20 25 30 35 40
- 18. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine GT thermal efficiency versus pressure ratio: comparison between Brayton and actual cycle 0.6 0.7 0.5 0.6 Brayton Actual Reduction of thermal efficiency due to irreversible losses. 0.4 to irreversible losses. 0.3 0.1 0.2 0.0 0.1 18Thermodynamics of axial compressor 0 5 10 15 20 25 30 35 40
- 19. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine But, hang on a second…previous slide tells us overall GT efficiency goes up as compression ratio increases (or temperature drop across turbine increases ascompression ratio increases (or temperature drop across turbine increases as expansion ratio increases), then why GT manufacturer don’t produce high efficiency machine, let say more than 50% at the expense of high compression ratio?ratio? The reason behind this, at least what I have in mind is explained on the following pages. 19Thermodynamics of axial compressor
- 20. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Let us revisit “Delta temperature versus expansion ratio” curve presented earlier. Delta T across turbine vs expansion ratioDelta T across turbine vs expansion ratio 750 800 650 700 DeltaTemperature(K) 3 25 Temperature drop is more sensitive on expansion 550 600 DeltaTemperature(K) 65 Temperature drop is more sensitive on expansion ratio of low pressure range compared to high pressure range. It means rate of change of efficiency is decreasing with increasing expansion ratio. 450 500 3 From this point onwards, please be absolute clear that (don’t confuse): a) Overall GT efficiency increases as expansion ratio increases. b) Rate of change of overall GT efficiency decreases as expansion ratio increases. 400 0 5 10 15 20 25 30 35 40 Expansion ratio decreases as expansion ratio increases. 20Thermodynamics of axial compressor
- 21. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine In order to quantify sensitivity of efficiency as a function of expansion ratio, the following expression is derived: by differentiating the curve function described previously to obtain slope gradient. Rate of change of efficiency = delta temperature turbine / delta expansion ratioRate of change of efficiency = delta temperature turbine / delta expansion ratio −××=∆ 1 −××=∆ − γ γ 1_ _ 1 1 ratioExpansion EffTT turbineisentropicinturbine These are nearly constant ( )24812.0 _1 − −=∆ ratioExpansionT Gama = 1.33 (for turbine) 24812.1 _24812.0 − ×= ratioExpansion dT ( )24812.0 _1 − −=∆ ratioExpansionT ( ) 24812.1 _24812.0 _ − ×= ratioExpansion ratioExpansiond dT It is proposed that this new function is used as the basis for gas turbine performance prediction and comparison within a database environment. 21Thermodynamics of axial compressor performance prediction and comparison within a database environment.
- 22. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Rate of change of overall GT efficiency as a function of expansion ratio is now defined: ( ) 24812.1 _24812.0 _ − ×= ratioExpansion ratioExpansiond dT ( )ratioExpansiond dT _ ( )_ ratioExpansiond 0.12 This curve (dT/d[expansion ratio]) enables us to visualize how sensitive is overall GT efficiency as a function of expansion ratio. ( )ratioExpansiond _ 0.08 0.1 overall GT efficiency as a function of expansion ratio. LM 6000 Compression ratio = 28.1 LMS 100 Compression ratio = 40 0.06 0.08 0.04 0 0.02 0 10 20 30 40 50 60 22Thermodynamics of axial compressor 0 10 20 30 40 50 60 Expansion ratio
- 23. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Overall GT efficiency merely increased by 3.43%increased by 3.43% OverallGTefficiencyOverallGTefficiencyOverallGTefficiency 23Thermodynamics of axial compressor Compression ratio
- 24. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine It’s time to put all theories discussed in the previous section into practical work. Attempt the following example: Calculate the isentropic efficiency, outlet temperature and power input for a compressor (of gas turbine) of 20:1 pressure ratio, polytropic efficiency of 91.07%, with a mass flow of 100 kg/s and an inlet temperature of 35 deg. C. Also insert a parametric table to investigate the effects (on the outlet temperature and power input) of changing inlet temperature to 30 and 38 deg. C respectively.respectively. 24Thermodynamics of axial compressor
- 25. Input parameters TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Input parameters a) Compression ratio 20:1 b) Polytropic efficiency of 91.07% c) Mass flow of 100 kg/sc) Mass flow of 100 kg/s d) Inlet temperature of 35 deg. C. But, something is missing...inlet pressure? Then make assumption, machine is located at mean sea level, i.e. atmospheric pressure = 101325 pascal e) Inlet pressure = 101325 pascale) Inlet pressure = 101325 pascal Parameters pass 1 pass 2 pass 3 pass 4 pass 5 pass 6 pass 7 pass 8 pass 9 Unit Cp 1004.33 1039.11 1036.61 1036.78 1036.77 1036.77 1036.77 1036.77 1036.77 J/(kg.K) gama 1.4002 1.3817 1.3830 1.3829 1.3829 1.3829 1.3829 1.3829 1.3829 - T_out 788.16 764.59 766.21 766.10 766.10 766.10 766.10 766.10 766.10 K Outlet temperature is converging from 4th T_out 788.16 764.59 766.21 766.10 766.10 766.10 766.10 766.10 766.10 K T_mean 308.15 548.16 536.37 537.18 537.12 537.13 537.13 537.13 537.13 K Isentropic efficiency 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 - Outlet temperature is converging from 4th iteration onwards. 25Thermodynamics of axial compressor
- 26. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Parameters pass 1 pass 2 pass 3 pass 4 pass 5 pass 6 pass 7 pass 8 pass 9 Unit Cp 1004.33 1039.11 1036.61 1036.78 1036.77 1036.77 1036.77 1036.77 1036.77 J/(kg.K) gama 1.4002 1.3817 1.3830 1.3829 1.3829 1.3829 1.3829 1.3829 1.3829 -gama 1.4002 1.3817 1.3830 1.3829 1.3829 1.3829 1.3829 1.3829 1.3829 - T_out 788.16 764.59 766.21 766.10 766.10 766.10 766.10 766.10 766.10 K T_mean 308.15 548.16 536.37 537.18 537.12 537.13 537.13 537.13 537.13 K Isentropic efficiency 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 0.8694 - Outlet temperature, T_out = 766.10 K or 492.95 deg. C Shaft power = 100 (kg/s) x 1036.77 (J/kg.K) x [766.10 - 308.15] (K) = 100 x 1036.77 x 457.95= 100 x 1036.77 x 457.95 = 47478882.15 J/s = 47479 kW 26Thermodynamics of axial compressor
- 27. TURBO GROUP – Thermodynamics of Axial Compressor and Turbine Parametric table Effects on shaft power and outlet temperature as inlet temperature changes. T_in (C) Power (kW) T_out (deg.C) Isentropic efficiency 30 46749 481.65 0.8693 35 47479 492.95 0.8694 changes. 35 47479 492.95 0.8694 38 47917 499.71 0.8694 Shaft power vs inlet temperature Outlet temperature vs inlet temperature 47600 47800 48000 500.0 Outlettemperature(deg.C) 47000 47200 47400 Shaftpower(kW) 490.0 Outlettemperature(deg.C) 46600 46800 30 31 32 33 34 35 36 37 38 39 Inlet temperature (deg. C) 480.0 30 31 32 33 34 35 36 37 38 39 Inlet temperature (deg. C) Outlettemperature(deg.C) 27Thermodynamics of axial compressor Inlet temperature (deg. C) Inlet temperature (deg. C)