Lecture 15 & 16

BRAYTON CYCLE: The Ideal Cycle For

Gas Turbines (Ch-9)

Thermodynamics - II

Zia Ud Din

2

BRAYTON CYCLE: THE IDEAL CYCLE FOR

GAS-TURBINE ENGINES

An open-cycle gas-turbine engine. A closed-cycle gas-turbine engine.

1) Air as an ideal gas is the working fluid.

2) The combustion process is replaced by a constant-pressure heat-addition

process from an external source, and the exhaust process is replaced by a

constant-pressure heat-rejection process to the ambient air.

1-2 Isentropic compression (in a compressor)

2-3 Constant-pressure heat addition

3-4 Isentropic expansion (in a turbine)

4-1 Constant-pressure heat rejection

Areas on T-s Diagram

2-3-a-b-2 = Heat Addition

1-4-a-b-1= Heat Rejection

Areas on P-v Diagram

1-2-a-b-1 = Work Input

3-4-b-a-3 = Work Done

1-2 Isentropic compression (in a compressor)

2-3 Constant-pressure heat addition

3-4 Isentropic expansion (in a turbine)

4-1 Constant-pressure heat rejection

Air-Standard BRAYTON Cycle:(Constant Pressure Cycle)

Back Work Ratio for Cycle: Thermal Efficiency:

Using Control Volume mass & energy rate balance:

12

1 2

Wh h

m

233 2

Qh h

m

411 4

Qh h

m

34

3 4

Wh h

m

Air-Standard BRAYTON Cycle Analysis:(Constant Pressure Cycle)

η is the ratio of network of cycle to Qin:

When air table data are used to conduct an

analysis involving ideal Brayton Cycle the

following relationship apply for isentropic

processes 1-2 and 3-4

(for variable specific heats)

Where, p4/p3 = p1/p2

Air-Standard BRAYTON Cycle Analysis:(Considering variable specific heats)

On constant specific heats basis, following expressions used for

isentropic processes

On a cold air-standard basis, Thermal

efficiency is:

Eq. 9.23

Eq. 9.24

Air-Standard BRAYTON Cycle Analysis:(Considering constant specific heats)

Thermal efficiency of the ideal Brayton

cycle is a function of pressure ratio

across the compressor

Air-Standard BRAYTON Cycle Analysis:(Considering constant specific heats)

Thermal

efficiency of the

ideal Brayton

cycle as a

function of the

pressure ratio.

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For fixed values of Tmin and Tmax, the net

work of the Brayton cycle first increases

with the pressure ratio, then reaches a

maximum at rp = (Tmax/Tmin)k/[2(k - 1)], and

finally decreases.

The fraction of the turbine work

used to drive the compressor is

called the back work ratio.

The two major application areas of gas-

turbine engines are aircraft propulsion

and electric power generation.

The highest temperature in the cycle is

limited by the maximum temperature that

the turbine blades can withstand. This

also limits the pressure ratios that can be

used in the cycle.

The air in gas turbines supplies the

necessary oxidant for the combustion of

the fuel, and it serves as a coolant to

keep the temperature of various

components within safe limits. An air–fuel

ratio of 50 or above is not uncommon.

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Deviation of Actual Gas-Turbine Cycles from

Idealized Ones

The deviation of an actual gas-

turbine cycle from the ideal

Brayton cycle as a result of

irreversibilities.

Reasons: Irreversibilities in turbine and compressors, pressure

drops, heat losses

Isentropic efficiencies of the

compressor and turbine

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Example 9-5

11

Example 9-5

12

Example 9-5

13

Example 9-5

14

Example 9-6

15

Example 9-6

16

Example 9-6

17

Example 9-6