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Ideal Brayton Cycle

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Ideal Brayton Cycle

Introduction

Consider this ideal Brayton cycle.

 

 

 

The compressor inlet temperature and pressure is 300 °C and 101 kPa, the compression ratio is 8, and the combuster outlet temperature is 1300 °C. The compressor and turbine are isentropic, and combustion is isobaric.

 

What is the thermal efficiency of the system?

Parameters

> 

with(ThermophysicalData):

 

Compressor Inlet Temperature

> 

Tmin := Units:-Standard:-`*`(300, Unit('degC')):

 

Compressor Exit Temperature

> 

Tmax := Units:-Standard:-`*`(1300, Units:-Standard:-Unit('degC')):

 

Compressor inlet pressure

> 

Pmin := Units:-Standard:-`*`(101, Units:-Standard:-Unit('kPa')):

 

Compressor pressure ratio

> 

r := 8:

Compressor Inlet

> 

P1 := Pmin:

> 

T1 := Tmin:

> 

h1 := Property(enthalpy, temperature = T1, pressure = P1, air)

705272.9614*Units:-Unit(('J')/('kg'))

> 

s1 := ThermophysicalData:-Property(entropy, temperature = T1, pressure = P1, air)

4547.480132*Units:-Unit(('J')/(('kg')*('K')))

Combustor Inlet

> 

s2 := s1:

> 

P2 := Units:-Standard:-`*`(r, P1):

> 

T2 := ThermophysicalData:-Property(temperature, pressure = P2, entropy = s2, air)

991.5856803*Units:-Unit('K')

> 

h2 := ThermophysicalData:-Property(enthalpy, temperature = T2, pressure = P2, air)

1163321.097*Units:-Unit(('J')/('kg'))

Turbine Inlet

> 

P3 := P2:

> 

T3 := Tmax:

> 

h3 := ThermophysicalData:-Property(enthalpy, temperature = T3, pressure = P3, air);

1851847.268*Units:-Unit(('J')/('kg'))

> 

s3 := ThermophysicalData:-Property(entropy, T = T3, P = P3, air);

5092.509817*Units:-Unit(('J')/(('kg')*('K')))

Turbine Exit

> 

P4 := P1:

> 

s4 := s3:

> 

T4 := ThermophysicalData:-Property(temperature, pressure = P4, entropy = s4, air)

947.0939895*Units:-Unit('K')

> 

h4 := ThermophysicalData:-Property(enthalpy, temperature = T4, pressure = P4, air);

1112422.426*Units:-Unit(('J')/('kg'))

Thermal Efficiency

> 

eta := Units:-Standard:-`+`(1, Units:-Standard:-`-`(Units:-Standard:-`*`(Units:-Standard:-`+`(h4, Units:-Standard:-`-`(h1)), Units:-Standard:-`/`(Units:-Standard:-`+`(h3, Units:-Standard:-`-`(h2))))))

.4086652304

>