L4-Gas Turbine Systems SSR

GAS POWER SYSTEMObjective: Study Gas Power Plants

in which working fluid is always a gas

Gas turbines

Internal combustion engines: spark-ignition and compression-ignition

Internal Combustion Engines

Engine Terminology

Air-Standard Cycles: Otto, Diesel and Dual Cycles

ME 306 Applied Thermodynamics

Gas Turbine Power Plants

Modelling gas turbine power plants

Air-Standard Brayton cycle

Improving performance using

Regeneration, reheating and intercooling

Gas turbines for aircraft propulsion

Combined gas turbine – vapour power cycle

Ericsson and Sterling cycles 1

GAS TURBINE POWER PLANTS

• Lighter than Vapour Power Plants

• Compact as Compared to Vapour Power Plants

• Higher Power-Output-to-Weight-Ratio

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• Simple Cycle based GTPP have Lower Efficiency

• 15 to 18%

• Regenerative Cycle based GTPP have Higher Efficiency

• 25 to 42%

GAS TURBINE POWER PLANTS

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OPEN SYSTEM CLOSED SYSTEM

CYCLE ANALYSISTURBINE

COMPRESSOR

HEAT INPUT

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HEAT REJECTED

Thermal Efficiency

Back work ratio (bwr)

higher compared to VPS

NUMERICAL PROBLEM

Air enters the compressor of an ideal air-standard Brayton cycle

at 100 kPa, 300 K, with a volumetric flow rate of 5 m3/s. The

compressor pressure ratio is 9. The turbine inlet temperature is

1500 K. Determine (a) the thermal efficiency of the cycle, (b) the

back work ratio, (c) the net power developed, in kW.

ASSUMPTIONS:

1. Each component is analyzed as a control volume at steady state.

ME 306 Applied Thermodynamics 5Moran and Shapiro (2006)

1. Each component is analyzed as a control volume at steady state.

2. The turbine and compressor processes are isentropic.

3. There are no pressure drops for flow through the heat exchangers.

4. Kinetic and potential energy effects are negligible.

5. The working fluid is air modeled as an ideal gas.

6. Specific heat is assumed to be constant.

'

0( )

( )

Tp

T

c Ts T dT

T= ∫

EFFECT OF PRESSURE RATIO

( ) ( )3 4 2 1 4 1

3 2 3 2

1T T T T T T

T T T Tη

− − − −= = −

− − ( )( 1) /

11

pRγ γ

η−

= −

ME 306 Applied Thermodynamics 6Moran and Shapiro (2006)

CONDITION FOR MAXIMUM WORK OUTPUT

( ) ( )3 4 2 1p

Wc T T T T

m= − − − �

�

γ

Differentiate and equate it to zero

ME 306 Applied Thermodynamics 7Moran and Shapiro (2006)

2( 1)3

1

p

TR

T

γ

γ − =

2 4 1 3T T TT= =

Regenerative Gas Turbines

ME 306 Applied Thermodynamics 8Moran and Shapiro (2006)

Regenerator effectiveness around 60-80%

Gas Turbines with Reheat

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Moran and Shapiro 2006

Gas Turbines with Intercooling

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Moran and Shapiro 2006

Regenerative gas turbine with intercooling and reheat

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Gas Turbines for Aircraft Propulsion

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Combined Gas Turbine–Vapor Power Cycle

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Other Cycles

Ericsson Cycle

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Stirling Cycle

Condition for minimum workIf the inlet state and the exit pressure are specified for a two-stage compressor operating at

steady state, show that the minimum total work input is required when the pressure ratio is

the same across each stage. Use a cold air-standard analysis assuming that each

compression process is isentropic, there is no pressure drop through the intercooler, and

the temperature at the inlet to each compressor stage is the same. Kinetic and potential

energy effects can be ignored.

1. The compressor stages and intercooler are analyzed

as control volumes at steady state.

2. The compression processes are isentropic.

ME 306 Applied Thermodynamics 15Moran and Shapiro (2006)

2. The compression processes are isentropic.

3. There is no pressure drop for flow through the

intercooler.

4. The temperature at the inlet to both compressor stages

is the same.

5. Kinetic and potential energy effects are negligible.

6. The working fluid is air modeled as an ideal gas.

7. The specific heat cp and the specific heat ratio k are

constant.

Numerical ProblemAir enters the compressor at 100 kPa, 300K and is compressed to 1000 kPa. The temperature

at the inlet to the first turbine stage is 1400 K. The expansion takes place isentropically in two

stages, with reheat to 1400 K between the stages at a constant pressure of 300 kPa. A

regenerator having an effectiveness of 70% is also incorporated in the cycle. Determine the

thermal efficiency. Consider an isentropic efficiency of 85% for each turbine.

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Numerical Problem

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 5.807 kg/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 back work

ratio, (c) the net power developed, in kW.

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Air enters a turbojet engine at 0.8 bar, 240�K, and an inlet velocity of 1000 km/h (278 m/s).

The pressure ratio across the compressor is 8. The turbine inlet temperature is 1200�K and

the pressure at the nozzle exit is 0.8 bar. The work developed by the turbine equals the

compressor work input. The diffuser, compressor, turbine, and nozzle processes are

isentropic, and there is no pressure drop for flow through the combustor. For operation at

steady state, determine the velocity at the nozzle exit and the pressure at each principal

state. Neglect kinetic energy at the exit of all components except the nozzle and neglect

potential energy throughout.

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Moran and Shapiro (2006)