Egr 334 thermodynamics chapter 9 sections 5 6
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EGR 334 Thermodynamics Chapter 9: Sections 5-6. Lecture 35: Gas Turbine modeling with the Brayton Cycle. Quiz Today?. Today’s main concepts:. Be able to recognize Dual and Brayton Cycles Understand what system may be modeled using Brayton Cycle.

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EGR 334 Thermodynamics Chapter 9: Sections 5-6

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Egr 334 thermodynamics chapter 9 sections 5 6

EGR 334 ThermodynamicsChapter 9: Sections 5-6

Lecture 35:

Gas Turbine modeling with the Brayton Cycle

Quiz Today?


Today s main concepts

Today’s main concepts:

  • Be able to recognize Dual and Brayton Cycles

  • Understand what system may be modeled using Brayton Cycle.

  • Be able to perform a 1st Law analysis of the Brayton Cycle and determine its thermal efficiency.

  • Be able to explain how regeneration may be applied to a Brayton Cycle model.

Reading Assignment:

Read Chapter 9, Sections 7-8

Homework Assignment:

Problems from Chap 9: 42, 47, 55


Ok quick matching quiz

OK….Quick Matching Quiz

B

C

a) Carnot b) Rankine c) Otto d) Diesel

p

.

.

4

1

1’

.

.

3

2’

2

v

A

D


Today you get to add two more cycles to your cycle repertoire dual cycle brayton cycle

Today you get to add two more cycles to your cycle repertoire.Dual Cycle Brayton cycle.

Used as a hybrid cycle which includes elements of both the Otto and Diesel cycles. Used to model internal combustion engines

Used as a model for gas turbines (such as jet engines).


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.4 : Air-Standard Duel Cycle

Neither the Otto or Diesel cycle describe the actual P-v diagrams of an engine

Heat addition occurs in two steps

  • 2 – 3 : Constant volume heat addition

  • 3 – 4 : Constant pressure heat addition (first part of power stroke)

Process 1 – 2 : Isentropic compression

Process 2 – 3 : Constant volume heat transfer

Process 3 – 4 : Constant pressure heat transfer

Process 4 – 5 : Isentropic expansion

Process 5 – 1 : Constant volume heat rejection

To set state 3: Use ideal gas law with V3 = V2.

and


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.4 : Air-Standard Duel Cycle

Dual Cycle analysis

process 1-2: s1 = s2

process 2-3: v2 = v3

process 3-4: p3 = p4

process 4-5: s4 = s5

process 5-1: v5 = v1


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38): The pressure and temperature at the beginning of compression in an air-standard dual cycle are 14 psi, 520°R. The compression ratio is 15 and the heat addition per unit mass is 800 Btu/lbm. At the end of the constant volume heat addition process the pressure is 1200 psi. Determine,

  • Wcycle, in BTU/lb.

  • Qout, in BTU/lb.

  • The thermal efficiency.

  • The cut off ratio


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

Given Information:

compression ratio, r = 15

Qin= Q23 + Q34 = 800 Btu

Qout = - Q51

Identify State Properties

State 1: p1 = 14 psi, T1 = 520 R

State 2: s2 = s1 v2 = v1/r

State 3: v3 = v2 and p3 = 1200 psiState 4: p4 = p3 = 1200 psi

State 5: s5 =s4 and v5 = v1

Use Table A22E to fill in many of the other properties.


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

  • State 1: given T = 520 R

  • look up u, h, vr, and pr

  • State 2: use r to find v2

  • and since 1-2 is isentropic

  • find vr2

  • then use Table A22E to look up T2, pr2, u2, and h2:

  • Pressure p2, can then be calculated using


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

  • State 3: given v3 = v2 and

  • p3 = 1200 psi, use ideal

  • gas law:

  • then use Table A22E to look up u3 and h3:


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

  • State 4: Knowing p4=p3 and the heat in:

  • Qin= 800 Btu/lb

  • use the 1st Law:

O

  • Use Table A-22E

  • to find T4 ,u4, pr4,

  • and v4r


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

  • State 5:

  • process 4-5 is also isentropic

  • Replace V’s using ideal gas.

  • Use Table A-22E to look up T5, u5, h5, and pr5 and then find p5:


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

  • Wcycle, in Btu/lb.

  • Qout, in Btu/lb.

  • The thermal eff.

  • The cut off ratio


Egr 334 thermodynamics chapter 9 sections 5 6

Example (9.38):

  • Wcycle, in Btu/lb.

  • Qout, in Btu/lb.

  • Thermal efficiency

  • The cut off ratio

Cut off ratio: from ideal gas equation at constant pressure:


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.5 : Modeling Gas Turbine Power Plants

Air-Standard analysis of Gas Turbine Power plants.

Gas power plants are lighter and more compact than vapor power plants.

Used in aircraft propulsion & marine power plants.


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.5 : Modeling Gas Turbine Power Plants

Air-Standard analysis:

Working fluid is air

Heat transfer from an external source (assumes there is no reaction)

Jet engine:

Suck (intake)

Squeeze (compressor)

Bang/Burn (combustion)

Blow (turbine/exhaust)

Heat Ex

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


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.5 : Modeling Gas Turbine Power Plants

Gas Turbine Analysis

process 1-2: s1 = s2

process 2-3: p2 = p3

process 3-4: s3 = s4

process 4-1: p4 = p1

  • For a gas turbine, the back work ratio is much larger than that in a steam cycle since vair>>vliquid

  • bwr for a gas turbine power cycle is typically 40-80% vs. 1-2% for a steam power cycle.


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.3 : Air-Standard Diesel Cycle

  • Gas Turbine Analysis

  • Given T1 & T3  use table to find h1 & h3 .

Find state 2.

Find state 4.

Compressor

pressure ratio:

For Cold-Air Standard analysis:

For state 2.

For state 4.


Egr 334 thermodynamics chapter 9 sections 5 6

Sec 9.3 : Air-Standard Diesel Cycle

  • Gas Turbine Analysis

Effect of Compressor pressure on efficiency.

with

Max T3 is approximately 1700 K


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 Btu/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate

  • The thermal efficiency

  • The back work ratio.

  • The net power developed.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate

  • The thermal efficiency

  • The back work ratio.

  • The net power developed.

  • Since we are given k=1.4, use a cold-air standard analysis.

  • Temperatures for states 1 and 3 are given.

For state 2.

For state 4.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate

  • The thermal efficiency

  • The back work ratio.

  • The net power developed.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example: Air enters the compressor of an ideal cold air-standard Brayton cycle at 500°R with an energy input of 3.4x106 BTU/hr. The compression ratio is 14 and the max T is 3000°R. For k=1.4 calculate

  • The thermal efficiency

  • The back work ratio.

  • The net power developed.

But need the mass flow rate.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine

  • The thermal efficiency

  • The net power developed.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine

  • The thermal efficiency

  • The net power developed.

  • Temperatures for states 1 and 3 are given. Relative pressure and enthalpy values from Table A-22E

Find state 2.

Find state 4.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine

  • The thermal efficiency

  • The net power developed.


Egr 334 thermodynamics chapter 9 sections 5 6

  • Example (9.43): The rate of heat addition to an air-standard Brayton cycle is 3.4x109 BTU/hr. The pressure ratio for the cycle is 14 and the minimum and maximum temperatures are 520°R and 3000°R, respectively. Determine

  • The thermal efficiency

  • The net power developed.

But need the mass flow rate.


End of slides for lecture 35

End of Slides for Lecture 35


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