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ME 200 L34Gas Turbine Power Generation and Aircraft Propulsion

Self Study Assignment 9.6Today’s Class 9.11

Kim See’s Office ME Gatewood Wing Room 2172 Examination 3 grades, Quiz 5 grades are available Blackboard and Examinations

and Quizzes can be picked up all of this week from Gatewood Room 2172

Material not picked up this week may be recycled!

https://engineering.purdue.edu/ME200/ThermoMentor© Program

Spring 2014 MWF 1030-1120 AMJ. P. Gore

gore@purdue.eduGatewood Wing 3166, 765 494 0061

Office Hours: MWF 1130-1230TAs: Robert Kapaku rkapaku@purdue.edu

Dong Han han193@purdue.edu

2

Outline• Brayton Cycle (with Improved Performance)

– Brayton Cycle for land based power generation and for aircraft propulsion (9.6; 9.11)

– Reheating- land based power generation: will mention but leave for you to explore (9.7)

– Regeneration - will mention but leave for you to explore (9.8)

– Combined Regeneration and Reheating, Cogeneration - will mention but leave for you to self-study (9.9, 9.10)

– Aircraft Propulsion (9.11) Will cover today including using Quiz 6.

3

InletState

Component

a Diffuser

1 Compressor

2 Combustor

3 Turbine

4 Nozzle

2 21 1 12 2a a ah V / h V / ;V V

2 2 2 21 1 2 2 2 1 2 12 2 0cW / m h V / h V / ;V V ;h h

2 2 2 24 4 3 3 3 4 3 42 2 0TW / m h V / h V / ;V V ;h h

2 2 2 24 4 5 5 5 4 4 5 5 42 2h V / h V / ;V V ;h h ;V V

2 2 2 22 2 3 3 3 2 3 22 2 0cQ / m h V / h V / ;V V ;h h

Aircraft Propulsion (9.11) : Quiz 6.

Air Standard Brayton Cycle

1

2 3

4

1

2 3

4

Thermal Efficiency

back work ratio

Compressor Pressure Ratio and Brayton Cycle Performance

The Brayton cycle thermal efficiency increases as the compressor pressure ratio increases

60

hth

(%

)

2 4 6 8 10

CompressorPressure Ratio

𝜼=(𝑻 𝟑−𝑻𝟒 )− (𝑻𝟐−𝑻 𝟏 )

(𝑻𝟑−𝑻𝟐)=

(𝑻𝟑−𝑻𝟐 )− (𝑻 𝟒−𝑻 𝟏 )(𝑻𝟑−𝑻 𝟐)

=𝟏−(𝑻𝟒−𝑻𝟏 )(𝑻𝟑−𝑻𝟐 )

=𝟏−𝑻 𝟏𝑻 𝟐

(𝑻𝟒𝑻𝟏

−𝟏)

(𝑻𝟑𝑻𝟐

−𝟏)

¿𝒄𝑷 (𝑻𝟑−𝑻𝟒 )−𝒄𝑷 (𝑻𝟐−𝑻 𝟏 )

𝒄𝑷 (𝑻 𝟑−𝑻𝟐)

𝟏−𝑻𝟏𝑻𝟐

=𝟏−𝟏

(𝒑𝟐𝒑𝟏 )𝒌−𝟏𝒌

See Figure 9.12

6

Gas Turbine Example ProblemGiven: Heat supplied by the boiler = 5.2x108 Btu/h, Pressure ratio = P2/P1=P3/P4=12, Tmin = T1 = 520oR, Tmax = T3= 2800oR

1

2 3

4

Find: Thermal efficiency: EtaTh, mdotair (lb/hr), wdot

cycle(Btu/hr)

If the turbine and the compressor are not isentropic but operate with 𝜼T , 𝜼C find the impact on the work of the cycle, heat input and thermal efficiency

𝜼C = 0.86 (Chosen in class based on student input); 𝜼T =0.91 chosen to be higher than Compressor efficiency since turbine efficiency matters more and companies mustimprove it sooner. Steps: (1) Identify and number all states and start a table of propertiesfor the states. (2) Recognize that compressor efficiency and turbine efficiencylead to additional state definitions (2s, 2a in place of 2 and 4s and 4a in place of 4).

Steps: (1) Identify and number all states and start a table of propertiesfor the states. (2) Recognize that compressor efficiency and turbine efficiencylead to additional state definitions (2s, 2a in place of 2 and 4s and 4a in place of 4).(3) Table A 22 E is to be referenced with the known states and knowledge of processdefinitions to find all properties necessary to calculate the work of compressor, work ofTurbine, heat added, heat rejected and resulting EtaTh, mdot

air (lb/hr), wdotcycle(Btu/hr)

State T, oR h, Btu/lbm Pr P, atm

1 520 124.27 1.2147 1

2s 1040 250.95 1.2147*12= 14.5764 or ~14.18 12

2a 1120 271.57 ~ 271.03 Pr not relevant 12

3 2800 732.33 702 12

4s 1520 374.47 702/12=58.5 ~ 58.78 1

4a 1650 406.67~409.13 Pr not relevant 1

22

1

34

4

Pr12 Pr 12*1.2147 14.5768 ~14.18

Pr

Pr12 Pr 702 /12 58.5 ~ 58.78

Pr

ss

ss

3 44 3 3 4

3 4

2 12 1 2 1

2 1

0.91 0.91( )

0.86 ( ) / 0.86

aT a s

s

sC a s

a

h hh h h h

h h

h hh h h h

h h

Answers3 4 2 1

3 2

( ) ( )/ / a a

T C H T C HThermala

h h h hW W Q w w q

h h

0.3817(732.33 409.13) (271.57 124.27) 323.2 147.3

732.33 271.57 460.76Thermal

8 63 2/ ( ) 5.2x10 (Btu / h)/323.2(Btu/lbm)=1.6x10 /am Q h h lbm hr

63 4 2 1

8

( ) ( ) 1.6x10 (323.2 147.3)

2.83*10 /

Cycle a aW m h h h h

Btu hr

Gas Turbine Power Plants

3. Compressor, combustion chamber, and turbine are treated as control volumes and mass, energy, and entropy balances are applied to each.4. The heat rejection process substitutes exhaust and fresh air admission.

1. Compression, heat addition and expansion are followed by exhaust of products and induction of fresh air. 2. The last two steps represent heat rejection.

1

2 3

4

1

2

3

4

Gas Turbine Power Plants

1

2 3

c4

1

2 3

4

Gas Turbine Power Plants

1

2 3

4

1

2 3

4

Thermal Efficiency

back work ratio

Compressor Pressure Ratio and Brayton Cycle Performance

►Consider compressor pressure

ratios p2/p1 and p2′/p1 yielding cycles:

1-2-3-4-1 to 1-2′-3′-4-1.

►TH greater in cycle 1-2′-3′-4-1, and both cycles have the same heat rejection, hence cycle 1-2′-3′-4-1 has inherently greater thermal efficiency.

The Brayton cycle thermal efficiency increases as the compressor pressure ratio increases

60

hth

(%

)2 4 6 8 10

CompressorPressure Ratio

13

Gas Turbine Example ProblemGiven: Heat supplied by the boiler = 5.2x108 Btu/h, Pressure ratio = P2/P1=P3/P4=12, Tmin = T1 = 520oR, Tmax = T3= 2800oR

1

2 3

4

State T, R h, Btu/lb Pr

1 520 124.27 1.2147

2 1047.5 252.84 14.5764 Pr2=Pr1*P2/P1

3 2800 732.33 702

4 1518 373.95 58.5 Pr4=Pr3/12

Find: Thermal efficiency: EtaTh, mdotair (lb/hr), wdot

cycle(Btu/hr)

Solution

Net power output is: