0-S-PP-Chap6

ME # 804466-4

Power Plants

Dr. Kamel Mohamed Guedri

Mechanical Engineering Department, The College of Engineering and Islamic Architecture,

Umm Al-Qura University, Room 1091

[email protected]

1

Gas-turbine Power Cycles

Chapter 3

2

3

Brayton Cycle: Ideal Cycle for Gas-Turbine Engines

Gas turbines usually operate on an open cycle (Fig. 6-1).

Air at ambient conditions is drawn into the compressor, where its

temperature and pressure are raised. The high pressure air proceeds into the

combustion chamber, where the fuel is burned at constant pressure.

The high-temperature gases then

enter the turbine where they

expand to atmospheric pressure

while producing power output.

Some of the output power is used

to drive the compressor.

The exhaust gases leaving the

turbine are thrown out (not re-

circulated), causing the cycle to be classified as an open cycle.

(Fig. 6-1

4

The open gas-turbine cycle can

be modelled as a closed cycle,

using the air-standard

assumptions (Fig. 6-2).

The compression and expansion

processes remain the same, but

the combustion process is

replaced by a constant-pressure

heat addition process from an

external source.

The exhaust process is replaced

by a constant-pressure heat

rejection process to the ambient

air.

Closed Cycle Model

(Fig. 6-2

5

The ideal cycle that the working fluid

undergoes in the closed loop is the

Brayton cycle. It is made up of four

internally reversible processes:

1-2 Isentropic compression;

2-3 Constant-pressure heat addition;

3-4 Isentropic expansion;

4-1 Constant-pressure heat rejection.

The T-s and P-v diagrams of an ideal

Brayton cycle are shown in Fig. 6-3.

Note: All four processes of the Brayton

cycle are executed in steady-flow devices

thus, they should be analyzed as steady-

flow processes.

The Brayton Cycle

(Fig. 6-3

6

Both Rankine and Brayton Cycles

(Two isobaric processes)

+ (Two isentropic processes)

Two phase : Rankine cycle Steam Power Plant

Single phase : Brayton cycle Gas Turbine

7

Thermal Efficiency

The energy balance for a steady-flow process

can be expressed, on a unitmass basis, as

The heat transfers to and from the working fluid

are:

The thermal efficiency of the ideal Brayton cycle,

is the pressure ratio. where

Constant specific heats

Example 6.1

In an air-standard Brayton cycle the air enters the compressor

at 0.1 MPa, 15C. The pressure leaving the compressor is 1.0

MPa, and the maximum temperature in the cycle is 1000C.

Determine

1. The pressure and temperature at each point in the cycle\

2. The compressor work, turbine work, and cycle efficiency

Solution of Example 6.1

For each of the control volumes analyzed, the model is ideal gas

with constant specific heat, value at 300 K, and each process is

SSSF with no kinetic or potential energy changes.

Control volume: Compressor

Inlet state: P1, T1 known; state fixed.

Exit state: P2 known.

2 1

2 1

1

2 2

1 1

c

k

k

w h h

s s

T P

T P

Control volume: Turbine

Inlet state: P3, T3 known; state fixed.

Exit state: P4 known.

1

2

1

2

2 1 2 1

1.932

556.8

269.5 /

k

k

c p

P

P

T K

w h h C T T kJ kg

3 4

3 4

1

3 3

4 4

t

k

k

w h h

s s

T P

T P

Control volume: High-temperature heat exchange

Inlet state: state 2 fixed.

Exit state: State 3 fixed.

1

3

4

4

3 4 3 4

1.932

710.8

664.7 /

395.2 /

k

k

t p

net t c

P

P

T K

w h h C T T kJ kg

w w w kJ kg

3 2 3 2 819.3 /H pq h h C T T kJ kg

Control volume: Low-temperature heat exchange.

Inlet state: state 4 fixed.

Exit state: State 1 fixed.

4 1 4 1 424.1 /

48.2%

L p

netth

H

q h h C T T kJ kg

w

q

13

Problem

A stationary gas-turbine power plant operates on a simple

ideal Brayton cycle with air as the working fluid. The air enters

the compressor at 95 kPa and 290 K and the turbine at 760

kPa and 1100 K. Heat is transferred to air at a rate of 35,000

kJ/s.

Determine the power delivered by this plant:

(a) assuming constant specific heats at room temperature,

and

(b) accounting for the variation of specific heats with

temperature.

Ideal and Actual Gas-Turbine (Brayton) Cycles

14

The thermal efficiency of an ideal

Brayton cycle depends on the pressure

ratio, rp of the gas turbine and the

specific heat ratio, k of the working

fluid.

The thermal efficiency increases with

both of these parameters, which is also

the case for actual gas turbines.

A plot of thermal efficiency versus the

pressure ratio is shown in Fig. 6-4, for

the case of k =1.4.

Parameters Affecting Thermal

Efficiency

(Fig. 6-4

15

The early gas turbines (1940s to 1959s) found only limited use despite their

versatility and their ability to burn a variety of fuels, because its thermal

efficiency was only about 17%. Efforts to improve the cycle efficiency are

concentrated in three areas:

1. Increasing the turbine inlet (or firing) temperatures.

The turbine inlet temperatures have increased steadily from about 540C

(1000F) in the 1940s to 1425C (2600F) and even higher today.

2. Increasing the efficiencies of turbo-machinery components (turbines,

compressors).

The advent of computers and advanced techniques for computer-aided

design made it possible to design these components aerodynamically

with minimal losses.

3. Adding modifications to the basic cycle (intercooling, regeneration or

recuperation, and reheating).

The simple-cycle efficiencies of early gas turbines were practically

doubled by incorporating intercooling, regeneration (or recuperation), and

reheating.

Improvements of Gas Turbines Performance

16

Actual Gas-Turbine Cycles

Some pressure drop occurs during the heat-

addition and heat rejection processes.

The actual work input to the compressor is

more, and the actual work output from the

turbine is less, because of irreversibilities.

Deviation of actual compressor and

turbine behavior from the idealized

isentropic behavior can be accounted

for by utilizing isentropic efficiencies

of the turbine and compressor.

Turbine:

Compressor:

(Fig. 6-5

Example 6.2

Example 6.3

22

Problem

A simple Brayton cycle using air as the working fluid has a pressure

ratio of 8. The minimum and maximum temperatures in the cycle are

310 K and 1160 K, respectively. Assuming an isentropic efficiency of 75

percent for the compressor and 82 percent for the turbine, determine:

(a) the air temperature at the turbine exit,

(b) the net work output, and

(c) the thermal efficiency.

Assume variable specific heats conditions.


23

Problem

Air enters the compressor of a gas-turbine engine at 300 K and 100

kPa, where it is compressed to 700 kPa and 580 K. Heat is transferred

to air in the amount of 950 kJ/kg before it enters the turbine.

For a turbine efficiency of 86 percent, determine:

(a) the fraction of turbine work output used to drive the

compressor,

(b) the thermal efficiency.

Assume:

(a) variable specific heats for air.

(b) constant specific heats at 300 K.


24

Brayton Cycle With Regeneration Temperature of the exhaust gas leaving the turbine

is higher than the temperature of the air leaving the

compressor.

The air leaving the compressor can be heated by

the hot exhaust gases in a counter-flow heat

exchanger (a regenerator or recuperator) a process called regeneration (Fig. 6-6 & Fig. 6-4).

The thermal efficiency of the Brayton cycle

increases due to regeneration since less fuel is

used for the same work output.

Note:

The use of a regenerator is

recommended only when the

turbine exhaust temperature is

higher than the compressor

exit temperature.

(Fig. 6-6

(Fig. 6-7

25

Effectiveness of the regenerator,

Effectiveness under cold-air standard assumptions,

Thermal efficiency under cold-air standard assumptions,

Effectiveness of the Regenerator

Assuming the regenerator is well insulated and changes in kinetic and

potential energies are negligible, the actual and maximum heat transfers

from the exhaust gases to the air can be expressed as

(Fig. 6-7

Example 6.4

28

Problem

Air enters the compressor of a regenerative gas-turbine engine

at 300 K and 100 kPa, where it is compressed to 800 kPa and

580 K. The regenerator has an effectiveness of 72 percent, and

the air enters the turbine at 1200 K.

For a turbine efficiency of 86 percent, determine:

(a) the amount of heat transfer in the regenerator, and

(b) the thermal efficiency.

Assume variable specific heats for air.

Answers: (a) 152.5 kJ/kg, (b) 36.0 percent

Brayton Cycles with Regeneration

29

Problem

The 7FA gas turbine manufactured by General Electric is reported

to have an efficiency of 35.9 percent in the simple-cycle mode and

to produce 159 MW of net power. The pressure ratio is 14.7 and

the turbine inlet temperature is 1288C. The mass flow rate

through the turbine is 1,536,000 kg/h.

Taking the ambient conditions to be 20C and 100 kPa, determine:

(a) the isentropic efficiency of the turbine and the compressor,

(b) the thermal efficiency of this gas turbine if a regenerator

with an effectiveness of 80 percent is added.

Assume constant specific heats at 300 K.


30

Problem

A Brayton cycle with regeneration using air as the working

fluid has a pressure ratio of 7. The minimum and maximum

temperatures in the cycle are 310 and 1150 K respectively.

Assuming an isentropic efficiency of 75 percent for the

compressor and 82 percent for the turbine and an

effectiveness of 65 percent for the regenerator, determine:

(a) the air temperature at the turbine exit,

(b) the net work output, and

(c) the thermal efficiency.

Answers: (a) 783 K, (b) 108.1 kJ/kg, (c) 22.5 percent


31

Thermal efficiency of Brayton cycle with regeneration depends on:

a) ratio of the minimum to maximum temperatures, and

b) the pressure ratio.

Regeneration is most effective at lower pressure ratios and small minimum-to-maximum temperature ratios.

Factors Affecting Thermal Efficiency

(Fig. 6-8

32

Brayton Cycle With Intercooling, Reheating, & Regeneration

The net work output of a gas-turbine cycle can be

increased by either:

a) decreasing the compressor work, or

b) increasing the turbine work, or

c) both.

The compressor work input can be decreased by

carrying out the compression process in stages

and cooling the gas in between (Fig. 9-9), using

multistage compression with intercooling.

The work output of a turbine can be

increased by expanding the gas in stages and

reheating it in between, utilizing a multistage

expansion with reheating.

(Fig. 6-9

33

Physical arrangement of an ideal two-stage

gas-turbine cycle with intercooling, reheating,

and regeneration is shown in Fig. 9-10.

(Fig. 6-10

34

The work input to a two-stage compressor is minimized when equal

pressure ratios are maintained across each stage. This procedure also

maximizes the turbine work output.

Thus, for best performance we have,

Conditions for Best Performance

Intercooling and reheating always

decreases thermal efficiency unless

are accompanied by regeneration.

Therefore, in gas turbine power

plants, intercooling and reheating are

always used in conjunction with

regeneration.

(Fig. 6-11

35

Example 6.5 Brayton Cycle with Intercooling, Reheating, and Regeneration

A regenerative gas turbine with intercooling and reheat operates at steady state.

Air enters the compressor at 100 kPa, 300 K with a mass flow rate of

5.807kg/s. The pressure ratio across the two-stage compressor is 10.

The pressure ratio across the two-stage turbine is also 10. The

intercooler and reheater each operate at 300 kPa. At the inlets to the

turbine stages, the temperature is 1400 K. The temperature at the

inlet to the second compressor stage is 300 K. The isentropic

efficiency of each compressor and turbine stage is 80%. The

regenerator effectiveness is 80%.

Determine

a) The thermal efficiency

b) The net power developed (kW)

c) The back work ratio

36

Solution of Example 6.5 Step 1: Draw a diagram to represent the system

To better visualize what is happening during

the cycle we can draw a T-s process diagram.

37

Solution of Example 6.5 Step 2: Prepare a property table Step 3: State your assumptions

Assumptions:

1) ke, pe 0

2) air-standard assumptions are applicable

3) air is an ideal gas with constant specific

heats at room temperature

4) SSSF

38

Solution of Example 6.5 Step 4: Calculation

39


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47


48


Step 5: Concluding remarks and Discussion

49

Example 6.6

Consider an ideal gas-turbine cycle with two stages of

compression and two stages of expansion. The pressure ratio

across each stage of the compressor and turbine is 3. The air

enters each stage of the compressor at 300 K and each stage

of the turbine at 1200 K. Determine:

(a) the back work ratio, and

(b) the thermal efficiency of the cycle

assuming:

(I) no regenerator is used, and

(II) a regenerator with 75 percent effectiveness is used.

Use a variable specific heats assumption.

Brayton Cycle with Intercooling, Reheating, and Regeneration

50


51


52


53

Problem

Consider a regenerative gas-turbine power plant with two stages

of compression and two stages of expansion. The overall pressure

ratio of the cycle is 9. The air enters each stage of the compressor

at 300 K and each stage of the turbine at 1200 K.

Accounting for the variation of specific heats with temperature,

determine the minimum mass flow rate of air needed to develop

net power output of 110 MW.

Answer: 250 kg/s.

Brayton Cycle with Intercooling, Reheating, and Regeneration

Second-law Analysis of Gas Power Cycles

The exergy destruction for a closed system can be expressed as

A similar relation for steady-flow systems can be expressed, in rate form, as

On a unitmass basis, for a one-inlet, one-exit steady-flow device,

54

The ideal Otto, Diesel, and Brayton cycles may involve irreversibilities

external to the system. A second-law analysis of these cycles will reveal

where the largest irreversibilities occur and where to start the improvements.

Exergy

Destruction!

The exergy destruction of a cycle

is the sum of the exergy

destructions of the processes that

compose that cycle.

It depends on the magnitude of the

heat transfer with the high- and

low-temperature reservoirs

involved and on their

temperatures.

For a cycle that involves heat transfer

only with a source at TH and a sink at TL,

the exergy destruction becomes

Closed system,

Flow stream, 55

Exergy of

56

Problem

A gas-turbine power plant operates on the simple Brayton cycle

between the pressure limits of 100 and 700 kPa. Air enters the

compressor at 30C at a rate of 12.6 kg/s and leaves at 260C. A

diesel fuel with a heating value of 42,000 kJ/kg is burned in the

combustion chamber with an airfuel ratio of 60 and a combustion efficiency of 97 percent. Combustion gases leave the combustion

chamber and enter the turbine whose isentropic efficiency is 85

percent.

Treating the combustion gases as air and using constant specific

heats at 500C, determine:

(a) the isentropic efficiency of the compressor,

(b) the net power output and the back work ratio,

(c) the thermal efficiency, and

(d) the second-law efficiency.

Second-Law Analysis of Gas Power Cycles

The End

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