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EGR 334 Thermodynamics Chapter 9: Sections 5-6

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EGR 334 ThermodynamicsChapter 9: Sections 5-6

Lecture 35:

Gas Turbine modeling with the Brayton Cycle

Quiz Today?

- 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

B

C

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

p

.

.

4

1

1’

.

.

3

2’

2

v

A

D

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).

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

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

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

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.

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

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:

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

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:

Example (9.38):

- Wcycle, in Btu/lb.
- Qout, in Btu/lb.
- The thermal eff.
- The cut off ratio

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:

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.

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

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.

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.

Sec 9.3 : Air-Standard Diesel Cycle

- Gas Turbine Analysis

Effect of Compressor pressure on efficiency.

with

Max T3 is approximately 1700 K

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

- The thermal efficiency
- The net power developed.

But need the mass flow rate.