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Efficiency of a Rankine Cycle

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Efficiency of a Rankine Cycle

Introduction
 

Consider a Rankine cycle with

 

• 

a condenser temperature of 380 K,

• 

a compressor output pressure of 3.5 MPa

• 

and a boiler temperature of 900 K

 

 

Calculate the thermal efficiency of the cycle, and visualize the cycle on a temperature-entropy chart.

 

> 

restart; with(ThermophysicalData); with(Units[Standard]); with(plots)

Condenser
 
> 

T__1 := 380*Unit('K')
> 

P__1 := Property(pressure, temperature = T__1, Q = 0, water)

128.8530538*Units:-Unit(kPa)

 (2.1)
> 

s__1 := Property(entropy, temperature = T__1, Q = 0, water)

1.383949980*Units:-Unit(kJ/(kg*K))

 (2.2)
> 

h__1 := Property(massspecificenthalpy, temperature = T__1, Q = 0, water)

448.0920826*Units:-Unit(kJ/kg)

 (2.3)
> 

v__1 := 1/Property(density, temperature = T__1, Q = 0, water)

0.1048957566e-2*Units:-Unit(m^3/kg)

 (2.4)

Compressor
 

Assuming isentropic operation

> 

P__2 := 3.5*Unit('MPa')
> 

s__2 := s__1
> 

T__2 := Property(temperature, pressure = P__2, S = s__2, water)

380.2497332*Units:-Unit(K)

 (3.1)
> 

h__2 := Property(enthalpy, pressure = P__2, S = s__2, water)

451.6256349*Units:-Unit(kJ/kg)

 (3.2)
> 

v__2 := 1/Property(density, pressure = P__2, S = s__2, water)

0.1047395909e-2*Units:-Unit(m^3/kg)

 (3.3)

Work done to compress liquid for an isentopic process, assuming negligible changes in specific volume. This term will be small compared to the turbine work

> 

W__compressor := v__1*(P__2-P__1)

3.536190095*Units:-Unit(kJ/kg)

 (3.4)

Boiler
 

Assuming isobaric opertion

> 

T__3 := 900*Unit('K')
> 

P__3 := P__2
> 

h__3 := Property(enthalpy, pressure = P__3, temperature = T__3, water)

3740.306762*Units:-Unit(kJ/kg)

 (4.1)
> 

s__3 := Property(entropy, pressure = P__3, temperature = T__3, water)

7.504961955*Units:-Unit(kJ/(kg*K))

 (4.2)

Boiler heat duty

> 

Q__b := h__3-h__2

3288.681127*Units:-Unit(kJ/kg)

 (4.3)

Turbine
 

Assuming isentropic expansion

> 

s__4 := s__3
> 

T__4 := Property(temperature, pressure = P__1, S = s__3, water)

425.5018567*Units:-Unit(K)

 (5.1)
> 

h__4 := Property(enthalpy, pressure = P__1, S = s__3, water)

2779.193714*Units:-Unit(kJ/kg)

 (5.2)

Hence the condenser heat duty

> 

Q__c := h__4-h__1

2331.101631*Units:-Unit(kJ/kg)

 (5.3)

Work extracted in turbine

> 

W__turbine := h__4-h__3

-961.1130480*Units:-Unit(kJ/kg)

 (5.4)

Efficiency
 
> 

eta := -(W__turbine-W__compressor)/Q__b

.2933240411

 (6.1)

Plotting the Cycle
 
> 

pathThickness := 3; pathColor := ColorTools:-Color("RGB", [68*(1/255), 108*(1/255), 179/255])
> 

p23 := plot([0.1e-2*Property(S, T = t, pressure = P__3/Unit('Pa'), water), t, t = T__2/Unit('K') .. T__3/Unit('K')], color = pathColor, thickness = pathThickness)
> 

p34 := plot(`~`[`~`[convert]]([[0.1e-2*s__4, T__3], [0.1e-2*s__4, T__4]], unit_free), color = pathColor, thickness = pathThickness)
> 

p41_1 := plot([0.1e-2*Property(S, T = t, P = P__1/Unit('Pa'), water), t, t = T__1/Unit('K') .. T__4/Unit('K')], color = pathColor, thickness = pathThickness, useunits)

p41_2 := pointplot(`~`[`~`[convert]]([[0.1e-2*s__1, T__1], [0.1e-2*Property(S, T = T__1, Q = 1, water), T__1]], unit_free), color = pathColor, thickness = pathThickness, connect = true)
Code to generate temperature-entropy plot for water
> 

display(TS_plot, p23, p34, p41_1, p41_2, labels = ["Entropy (kJ/kg)", "Temperature (K)"], labeldirections = [horizontal, vertical], labelfont = [Calibri], size = [1000, 600], axesfont = [Calibri], title = "Rankine Cycle using Water", titlefont = [Calibri, 20], view = [0 .. 12, 300 .. 1100])

 
> 

NULL
> 

``