Siemens SGT6-5000F(4) 150 MW power Gas Turbine

Gas turbine based power generation

hfCH4= 5.543×107 J / kg

Cycle Analysis

Across the burner.

τ f =hfCpT0

= 5.543×107

1005 × 298.15= 185

Power balance.

Divide by maCpT0

Work output coefficient.

= 1

Ideal Cycle.

τ cτ t = 1

The system is designed to take as much work as possible out of the turbine. The exit Mach number is very low and the exit pressure is very close to the ambient pressure.

Pt5 = Pte ≅ P0

π t = τ tγγ −1

For the ideal cycle the maximum work output coefficient occurs when

τ t =1τλ

and

Ideal Gas Turbine Power Generator.

f =τλ − τλ

τ f −τλ

Example, let

Gas Turbines for Power Generation

Capstone Turbine Corp - microturbine

Example from a previous midterm

ηoverall max =

τ λ 1− 1

ηpcτ λ( )ηpc

1+ηpc

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟− ηpcτ λ( )

11+ηpc −1

⎛⎝⎜

⎞⎠⎟

τ λ −τ x ηpcτ λ( )1

1+ηpc

ηoverall max ideal =

τ λ 1− 1

τ λ( )12

⎛

⎝⎜⎜

⎞

⎠⎟⎟− τ λ( )

12 −1⎛

⎝⎜⎞⎠⎟

τ λ − τ λ( )12

=4 1− 1

2⎛⎝⎜

⎞⎠⎟ − 2 −1( )

4 − 2= 1

2

In the ideal case with τ x = 1

In the real case with τ x = 1

ηoverall max real =

τ λ 1− 1

ηpcτ λ( )ηpc

1+ηpc

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟− ηpcτ λ( )

11+ηpc −1

⎛⎝⎜

⎞⎠⎟

τ λ −τ x ηpcτ λ( )1

1+ηpc

=

4 1− 1

3( )37

⎛

⎝⎜⎜

⎞

⎠⎟⎟− 3( )

47 −1⎛

⎝⎜⎞⎠⎟

4 − 3( )47

= 0.29561

In the real case the efficiency is only about 30% compared to 50% for the ideal case

τ x =1ηpc

= 43

In the real case with

The recuperator improves the efficiency of the real engine by 12%