Lecture 42: Brayton cyclecc.sjtu.edu.cn/Upload/20160505155549814.pdf · 1.1 Thermodynamics I Lecture 42: Brayton cycle Yong Li Shanghai Jiao Tong University Institute of Refrigeration

1.1

Thermodynamics I

Lecture 42: Brayton cycle

Yong Li

Shanghai Jiao Tong University

Institute of Refrigeration and Cryogenics

800 Dong Chuan Road Shanghai, 200240, P. R. China

Email : [email protected]

Phone: 86-21-34206056; Fax: 86-21-34206056

1.2

Brayton Cycle

Open Brayton cycle Closed Brayton cycle

Gas-cooled

nuclear reactor

1.3

Ideal Brayton Cycle

Description

Process Closed cycle Open cycle

12 Isentropic compression Isentropic compression

23 Constant pressure heat input Heat librated from fuel

during combustion process

34 Isentropic expansion Isentropic expansion

41 Constant pressure heat Enthalpy difference between

rejection exhaust products and intake air

P-v diagram T-s diagram

1.4

Continue Brayton Cycle

V

p

1

2

4

3

qin

qout

s

T

1

2 4

3

s1=s2 s3=s4

qin

qout

V2 V3 V4 V1

Ideal Brayton Cycle

1.5


Comparison with vapor power cycle:

» lighter and more compact (air vs. water

density)

high power output-to-weight ratio

» lower pressure ratios, higher volume based on

gas vs. liquid compression

» lower efficiencies based on non-isothermal heat

addition and heat rejection

Typical applications:

» Aircraft propulsion

» Power plant for marine,

space, etc.

» Stationary peaking

power plant

» Ground transportation ??

1.6


Comparison with Otto and Diesel cycles:

4 1: constant pressure vs. constant volume

process (both Otto and Diesel cycles)

2 3: constant pressure vs. constant volume process (Otto cycle only)

» In general, pressure rise much smaller for turbo-machinery than

for reciprocating devices

Otto cycle Brayton cycle

Diesel cycle

1.7


inQ

Heat Exchanger

Turbine cycleW

1

2 3

4

Comp

Heat Exchanger

outQ

C 2 1

3 4T

W h hbwr

h hW

T3 4

Wh h

m C

2 1

Wh h

m and

in3 2

Qh h

m out

4 1

Qh h

m and

1st law, energy balances, for each component:

For gas turbine, bwr typically 40~80%

For vapor cycle, bwr 1~2%

Back Work Ratio:

1.8


Thermal efficiency:

in out outnet T Cth

in in in in

q q qw w w1

q q q q

closed cycle, SSSF, anFor d KE PE 0

out 4 1th

in 3 2

q h h1 1

q h h

constant specific heFor ats:

p 4 1

th

p 3 2

c (T T )1

c (T T )

4

11

32

2

T1

TT1

TT 1T

1.9


Continue thermal efficiency: pk

v

cFor an isentropic process : pv constant, with k

c

k k

1 1 2 2For process 1 2 : p v p v k

1 1k

k k11 2 1 2 2 1 2

kk

2 1 2 1 1 2 12

2

RT

pv p T p p T p

v p T p p T pRT

p

1 k k 1 k 1

k k k k k2 1 2 2 2 2

1 2 1 1 1 1

T p p p p p

T p p p p p

k 1 k 1

k k4 4 1

3 3 2

T p pAlso, using same analysis:

T p p

1.10

Continue Brayton Cycle thermal efficiency

k 1 k 1

k k2 1 2 4

1 2 1 3

p p T TThen, 1

p p T T

4 3 1th

1 2 2

T T T1

T T T

2p

1

pressurep

Define :o rratip

th k 1

kp

11

r

4

11th

32

2

T1

TT1

TT 1T

1.11


Thermal efficiency versus rp (air k=1.4):

th k 1

kp

11

r

1.12


For isentropic process of an ideal gas with varying specific heats:

2 r2

1 r1

p p (T)

p p (T) 4 r4

3 r3

p p (T)

p p (T)

4 1 2 3Also, since p p and p p :

1 4 r4 r1

2 3 r3 r2

p p p (T) p (T)

p p p (T) p (T)

r

o

where p is the relative pressus (T)

ere defined as xpR

1.13


Trade off between efficiency and power:

V

p

1 4

s

T

1

2

4

3

2 3

4’

4’

2’

3’

2’ 3’

Upper temperature limit

Which cycle has greater efficiency?

Which cycle has greater work output?

1.14


Note: Cycle B will require smaller device to produce

the same work output as cycle A. Need to

consider this for transport application!

Task: Maximize work output, i.e., find optimal T2 that

maximizes work output for given T1 and T3. T

s 1

2

4

3

2’

3’

T1

T3

4’

Limiting Cases:

1.) T2 = T3 wnet = 0

th = max

2.) T2 = T1 wnet = 0

th = 0

1.15


maximize work output:

net T C in outw w w q q

For constant specific heats:

net p 3 2 p 4 1w c (T T ) c (T T )

netFor maximum w :net 3

p

2 2

dw dT0 c

dT dT 4 1

2 2

dT dT1

dT dT

4 3

1 2

T TNow recall:

T T 1 3

4

2

T TT

T 4 1 3

2

2 2

dT T T

dT T

net 4 1 3

2

2 2 2

dw dT T T0 1 1

dT dT T

2 1 3T T T

For non-constant specific heats: use air tables!

1.16


Irreversibilities of Brayton cycles:

Deviation of actual gas-turbine

cycles from idealized ones:

s 2s 1C

a 2a 1

w h h

w h h

Note:

T2a > T2s if p2a = p2s

T4 > T4s if p4a = p4s

irreversibilities change

mechanical energy to thermal

energy through friction.

a 3 4aT

s 3 4s

w h h

w h h

1.17


Continue irreversibilities of Brayton cycles:

Example:

T1 = 22oC, p1 = 0.95 bars, rp = p2/p1 = 6, T3 = 1100 K

wC/wT

Ideal 0.38 0.44

C = 0.82 and T = 0.85 0.23 0.62

Notes:

» The overall efficiency is reduced by 40%!

» Gas turbine performance is very sensitive to turbine and

compressor efficiencies!

1.18

Example: Ideal Brayton Cycle

Known: rp = 10, state 1: p1 =100 kPa, volumetric

flow rate 5 m3/s, T1 =300 K, T3 =1400 K

Find: bwr, ηth and wnet

Assumptions: 1) Air-Standard assumptions. 2)

ΔKE=ΔPE =0. 3)Variable cp 4) ΔP =0 in HX, 5)

isentropic efficiency=1

Analysis:

The results with constant k and

ηt = ηc = 80% (Text Example 9.6)

η= 24.9%

bwr=61.8%

Wcycle=1254 kW

Lecture 42: Brayton cyclecc.sjtu.edu.cn/Upload/20160505155549814.pdf · 1.1 Thermodynamics I Lecture 42: Brayton cycle Yong Li Shanghai Jiao Tong University Institute of Refrigeration

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