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Thermal Efficiency of the combined (binary) cycle

Author: Valery Ochkov (http://twt.mpei.ac.ru/ochkov/v_ochkov.htm)

Introduction
 

The figure shows the scheme of a simplest ideal combined (binary) cycle, i.e. steam turbine (6-7) cycle with use of superheated water steam. At this plant the boiler (6-9) burner is replaced with gas turbine unit (Brayton cycle: 1-4) equipped with air compressor (1-2), combustion chamber (2-3), gas turbine (3-4) and one more electric generator.

> 

restartwith(ThermophysicalData)with(Units[Standard])

 

Calculations
 

Steam turbine cycle
 

Input data:

> 

t_6 := Units:-Standard:-`*`(480, Unit('degC')); 1; p_6 := Units:-Standard:-`*`(9, Unit('MPa')); 1; p_7 := Units:-Standard:-`*`(4.76, Unit('kPa'))

480*Units:-Unit('`°C`')

9*Units:-Unit('MPa')

4.76*Units:-Unit('kPa')

 

Specific entropy of fresh (live) steam (the turbine inlet):

> 

s_6 := Property(entropy, pressure = p_6, temperature = t_6, water)

6.593467590*Units:-Unit(kJ/(kg*K))

Specific enthalpy of fresh (live) steam (the turbine inlet):

> 

h_6 := ThermophysicalData:-Property(enthalpy, pressure = p_6, temperature = t_6, water)

3336.426849*Units:-Unit(kJ/kg)

Outlet steam specific entropy from the turbine (an ideal process of the steam extension)

> 

s_7 := s_6:

Dryness of steam in outlet of the turbine:

> 

x_7 := ThermophysicalData:-Property(Q, P = p_7, entropy = s_7, water)

.7712559666

Outlet wet steam temperature from the turbine

> 

t_7 := ThermophysicalData:-Property(temperature, pressure = p_7, Q = 1, water); -1; Units:-Standard:-`+`(t_7, Units:-Standard:-`-`(Units:-Standard:-`*`(273.15, Units:-Standard:-Unit('K'))))

32.0015827*Units:-Unit(`°C`)

Outlet wet steam specific enthalpy from of the  turbine:

> 

h_7 := ThermophysicalData:-Property(enthalpy, T = t_7, Q = x_7, water)

2004.437563*Units:-Unit(kJ/kg)

Specific work of steam in the turbine:

> 

w_st := Units:-Standard:-`+`(h_6, Units:-Standard:-`-`(h_7))

1331.989286*Units:-Unit(kJ/kg)

Specific enthalpy of water at saturated line at temperature in the condenser

> 

hw_7 := ThermophysicalData:-Property(enthalpy, T = t_7, Q = 0, water)

134.1008689*Units:-Unit(kJ/kg)

Specific entropy of water at saturated line at temperature in the condenser

> 

sw_7 := ThermophysicalData:-Property(entropy, T = t_7, Q = 0, water)

.4642623028*Units:-Unit(kJ/(kg*K))

 

Specific enthalpy of condensate

> 

h_8 := hw_7:

Pressure of feed water

> 

p_9 := p_6:

Specific entropy of feed water (an ideal process in the pump):

> 

s_9 := sw_7:

Temperature of feed water:

> 

t_9 := ThermophysicalData:-Property(temperature, pressure = p_9, entropy = s_9, water); -1; Units:-Standard:-`+`(t_9, Units:-Standard:-`-`(Units:-Standard:-`*`(273.15, Units:-Standard:-Unit('K'))))

32.2161406*Units:-Unit(`°C`)

Specific enthalpy of feed water:

> 

h_9 := ThermophysicalData:-Property(enthalpy, pressure = p_9, temperature = t_9, water)

143.1237785*Units:-Unit(kJ/kg)

Specific useful work of the feed pump:

> 

w_p := Units:-Standard:-`+`(h_9, Units:-Standard:-`-`(hw_7))

9.022909600*Units:-Unit(kJ/kg)

Specific heat supplied to the boiler:

> 

q_b := Units:-Standard:-`+`(h_6, Units:-Standard:-`-`(h_9))

3193.303070*Units:-Unit(kJ/kg)

Hence the thermal efficiency of the steam turbine cycle:

> 

`η_tst` := Units:-Standard:-`*`(Units:-Standard:-`+`(w_st, Units:-Standard:-`-`(w_p)), Units:-Standard:-`/`(q_b))

.4142940231

Gas turbine cycle
 

Input data:

> 

t_1 := Units:-Standard:-`*`(15, Units:-Standard:-Unit('degC')); 1; p_1 := Units:-Standard:-`*`(.1, Units:-Standard:-Unit('MPa')); 1; p_2 := Units:-Standard:-Unit('MPa'); 1; t_3 := Units:-Standard:-`*`(1100, Units:-Standard:-Unit('degC')); 1; t_5 := Units:-Standard:-`*`(130, Units:-Standard:-Unit('degC'))

15*Units:-Unit('`°C`')

.1*Units:-Unit('MPa')

Units:-Unit('MPa')

1100*Units:-Unit('`°C`')

130*Units:-Unit('`°C`')

Specific enthalpy of fresh air

> 

h_1 := ThermophysicalData:-Property(enthalpy, pressure = p_1, temperature = t_1, air)

414.3778321*Units:-Unit(kJ/kg)

Specific entropy of fresh air

> 

s_1 := ThermophysicalData:-Property(entropy, pressure = p_1, temperature = t_1, air)

3.849952078*Units:-Unit(kJ/(kg*K))

Outlet air specific entropy, temperature and spacific enthalpy from the compessor

> 

s_2 := s_1:
> 

t_2 := ThermophysicalData:-Property(temperature, pressure = p_2, entropy = s_2, air); -1; Units:-Standard:-`+`(t_2, Units:-Standard:-`-`(Units:-Standard:-`*`(273.15, Units:-Standard:-Unit('K'))))

279.4631181*Units:-Unit(`°C`)

> 

h_2 := ThermophysicalData:-Property(enthalpy, pressure = p_2, temperature = t_2, air)

683.6031240*Units:-Unit(kJ/kg)

Inlet gas pressure, specific entropy and specific enthalpy to  the gas turbine

> 

p_3 := p_2:
> 

s_3 := ThermophysicalData:-Property(entropy, pressure = p_3, temperature = t_3, air)

4.867024310*Units:-Unit(kJ/(kg*K))

> 

h_3 := ThermophysicalData:-Property(enthalpy, pressure = p_3, temperature = t_3, air)

1610.338970*Units:-Unit(kJ/kg)

Outlet gas pressure, specific entropy, temperature and specific enthalpy from the gas turbine

> 

p_4 := p_1:
> 

s_4 := s_3:
> 

t_4 := ThermophysicalData:-Property(temperature, pressure = p_4, entropy = s_4, air); -1; Units:-Standard:-`+`(t_4, Units:-Standard:-`-`(Units:-Standard:-`*`(273.15, Units:-Standard:-Unit('K'))))

498.0105159*Units:-Unit(`°C`)

> 

h_4 := ThermophysicalData:-Property(enthalpy, pressure = p_4, temperature = t_4, air)

916.8176736*Units:-Unit(kJ/kg)

Specific heat supplied to the combustion chamber:

> 

q_1 := Units:-Standard:-`+`(h_3, Units:-Standard:-`-`(h_2))

926.7358460*Units:-Unit(kJ/kg)

Specific work of the gas turbine

> 

w_gt := Units:-Standard:-`+`(h_3, Units:-Standard:-`-`(h_4))

693.5212964*Units:-Unit(kJ/kg)

Specific work of the air compressor

> 

w_c := Units:-Standard:-`+`(h_2, Units:-Standard:-`-`(h_1))

269.2252919*Units:-Unit(kJ/kg)

Hence the thermal efficiency of the gas turbine cycle:

> 

`η_tgt` := Units:-Standard:-`*`(Units:-Standard:-`+`(w_gt, Units:-Standard:-`-`(w_c)), Units:-Standard:-`/`(q_1))

.4578392067

Combined (binary) cycle
 

Outlet gas pressure and specific enthalpy from the steam boiler

> 

p_5 := p_4:
> 

h_5 := ThermophysicalData:-Property(enthalpy, pressure = p_5, temperature = t_5, air)

530.4505082*Units:-Unit(kJ/kg)

 

Ratio of gas and steam mass flow

> 

m := Units:-Standard:-`*`(Units:-Standard:-`+`(h_6, Units:-Standard:-`-`(h_9)), Units:-Standard:-`/`(Units:-Standard:-`+`(h_4, Units:-Standard:-`-`(h_5))))

8.264944217

Specific heat supplied to the combustion chamber:

> 

q_1 := Units:-Standard:-`*`(m, Units:-Standard:-`+`(h_3, Units:-Standard:-`-`(h_2)))

7659.420071*Units:-Unit(kJ/kg)

Specific work of the gas turbine cycle

> 

w_gtc := Units:-Standard:-`+`(Units:-Standard:-`+`(h_3, Units:-Standard:-`-`(h_4)), Units:-Standard:-`-`(Units:-Standard:-`+`(h_2, Units:-Standard:-`-`(h_1))))

424.2960045*Units:-Unit(kJ/kg)

Specific work of the steam turbine cycle

> 

w_stc := Units:-Standard:-`+`(Units:-Standard:-`+`(h_6, Units:-Standard:-`-`(h_7)), Units:-Standard:-`-`(Units:-Standard:-`+`(h_9, Units:-Standard:-`-`(h_8))))

1322.966376*Units:-Unit(kJ/kg)

 

Hence the thermal efficiency of the Combined (binary) cycle is higher than separate steam or gas turbine cycles:

> 

`η_tbc` := Units:-Standard:-`*`(Units:-Standard:-`+`(Units:-Standard:-`*`(m, w_gtc), w_stc), Units:-Standard:-`/`(q_1))

.6305632987

> 

NULL

``