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Brayton Cycle

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Brayton Cycle
Reading 9-8 → 9-10 Problems 9-78, 9-84, 9-108

Open Cycle Gas Turbine Engines

• after compression, air enters a combustion chamber into which fuel is injected • the resulting products of combustion expand and drive the turbine • combustion products are discharged to the atmosphere • compressor power requirements vary from 40-80% of the power output of the turbine (remainder is net power output), i.e. back work ratio = 0.4 → 0.8 • high power requirement is typical when gas is compressed because of the large specific volume of gases in comparison to that of liquids

Idealized Air Standard Brayton Cycle
• closed loop • constant pressure heat addition and rejection • ideal gas with constant specific heats

1

Brayton Cycle Efficiency
The Brayton cycle efficiency can be written as η = 1 − (rp )(1−k)/k where we define the pressure ratio as: P2 P1 P3 P4

rp =

=

2

Maximum Pressure Ratio
Given that the maximum and minimum temperature can be prescribed for the Brayton cycle, a change in the pressure ratio can result in a change in the work output from the cycle.

The maximum temperature in the cycle (T3 ) is limited by metallurgical conditions because the turbine blades cannot sustain temperatures above 1300 K. Higher temperatures (up to 1600 K can be obtained with ceramic turbine blades). The minimum temperature is set by the air temperature at the inlet to the engine.

3

Brayton Cycle with Reheat

• T3 is limited due to metallurgical constraints • excess air is extracted and fed into a second stage combustor and turbine • turbine outlet temperature is increased with reheat (T6 > T4 ), therefore potential for regeneration is enhanced • when reheat and regeneration are used together the thermal efficiency can increase significantly

4

Compression with Intercooling

• the work required to compress in a steady flow device can be reduced by compressing in stages • cooling the gas reduces the specific volume and in turn the work required for compression • by itself compression with intercooling does not provide a significant increase in the efficiency of a gas turbine because the temperature at the combustor inlet would require additional heat transfer to achieve the desired turbine inlet temperature • but the lower temperature at the compressor exit enhances the potential for regeneration i.e. a larger ΔT across the heat exchanger 5

Brayton Cycle with Regeneration

• a regenerator (heat exchanger) is used to reduce the fuel consumption to provide the required ˙ QH • the efficiency with a regenerator can be determined as: ˙ ˙ QL Wnet = 1− ˙ ˙ QH QH 6

η=

= 1− = 1− = 1− and

cp (T6 − T1 ) cp (T3 − T5 ) cp (T6 − T1 ) cp (T3 − T5 ) cp (T2 − T1 ) cp (T3 − T4 )

⇒ (f or a real regenerator) ⇒ (f or an ideal regenerator)

η =1−

Tmin Tmax

(rp )(k−1)/k

• for a given Tmin/Tmax , the use of a regenerator above a certain rp will result in a reduction of η with an ideal regenerator

without a regenerator

better with a regenerator

better without a regenerator

T1 / T3 = 0.2 T1 / T3 = 0.25 T1 / T3 = 0.3

r p, cr

rp

7

Regenerator Effectiveness
˙ h5 − h2 h5 − h2 T5 − T2 Qreg,actual = = = ˙ reg,ideal h5 − h2 h4 − h2 T4 − T2 Q

=

Typical values of effectiveness are ≤ 0.7

Repeated intercooling, reheating and regeneration will provide a system that approximates the TL . Ericsson Cycle which has Carnot efficiency η = 1 − TH

Brayton Cycle With Intercooling, Reheating and Regeneration

8

T
Tmax QH
7s

Q H, R
9s

Q reg Q reg
4s 2s

Tmin

QL Q L, I

s
Compressor and Turbine Efficiencies
Isentropic Efficiencies (1) ηcomp = h2,s − h1 h2 − h1 h3 − h4 h3 − h4,s Wnet QH = cp (T2,s − T1 ) cp (T2 − T1 ) cp (T3 − T4 ) cp (T3 − T4,s ) QL QH cp (T4 − T1 ) cp (T3 − T2 )

(2)

ηturb =

=

(3)

ηcycle =

=

QH − QL QH

=1−

=1−

Given the turbine and compressor efficiencies and the maximum (T3 ) and the minimum (T1 ) temperatures in the process, find the cycle efficiency (ηcycle ). (4) Calculate T2s from the isentropic relationship, T2,s T1 = P2 P1
(k−1)/k

.

Get T2 from (1). (5) (6) Do the same for T4 using (2) and the isentropic relationship. substitute T2 and T4 in (3) to find the cycle efficiency.

9

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