Brayton cycle (Gas Cycle)-Introduction

Gas-turbine cycles (types)
• Direct open: Used in jet aircraft
• Indirect open: Suitable where environmental concerns
prevent the air from receiving heat directly.
Direct open Indirect open

Gas-turbine cycles (types)
Direct closed Indirect closed
• Direct & Indirect closed: Best suited for heat transfer
from nuclear-reactors compared to open type.

Let's take a closer look at the effect of the
pressure ratio on the net work done.
w w w
C T T C T T
C T T T C T T T
C T
r
C T r
net turb comp
p p
p p
p
p
k k p p
k k
 
   
   
   


( ) ( )
( / ) ( / )
( ) ( )
( )/
( )/
3 4 2 1
3 4 3 1 2 1
3 1 1
1
1 1
1
1
1
For fixed values of Tmin and Tmax, the net work of the Brayton cycle first increases with the
pressure ratio, then reaches a maximum at rp=(Tmax/Tmin)k/[2(k-1)], and finally decreases. What
happens to th and wnet as the pressure ratio rp is increased? Consider the T-s diagram
for the cycle and note that the area enclosed by the cycle represents the net work
done.
Brayton Cycle: Max Net Work

Note that the net work is zero when
/( 1)
3
1
1
k k
p p
T
r and r
T

 
   
 
For fixed T3 and T1, the pressure ratio that makes the work a maximum is obtained
from:
dw
dr
net
p
 0
This is easier to do if we let X = rp
(k-1)/k
w C T
X
C T X
net p p
   
3 1
1
1
1
( ) ( )
dw
dX
C T X C T
net
p p
     

3
2
1
0 1 1 0 0
[ ( ) ] [ ]
Solving for X ,

Then, the rp that makes the work a maximum for the constant property case and fixed T3 and
T1 is
For the ideal Brayton cycle, the following results are true.
• When rp = rp,max work, T4 = T2
• When rp < rp,max work, T4 > T2
• When rp > rp,max work, T4 < T2
For the same procedure, this gives a value of T2 as:
And since , then
2
/
1
3
1
2 )
( T
T
T 
k
k
p
r
T
T
T
T
/
)
1
(
4
3
1
2 /
/



4
2 T
T 

0 2 4 6 8 10 12 14 16 18 20 22
120
140
160
180
200
220
240
260
280
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Pratio
w
net
kJ/kg

th,Brayton
T1 = 22C
P1 = 95 kPa
T3 = 1100 K
t = c = 100%
rp,max
The following is a plot of net work per unit mass and the efficiency as a function of the
pressure ratio.
k
r
th
p
th




th is independent of
temperatures.

The pressure ratio across the compressor ( rp,c ) would be greater
than the pressure ratio across the turbine ( rp,t ).
Non-ideal Brayton Cycle

The net power of the cycle, for constant specific heats,


























 

k
k
p
C
k
k
p
T
p
net
r
r
T
T
T
c
m
W /
)
1
(
/
)
1
(
1
3
1
1
1




Non-ideal Brayton Cycle
]
)
(
)
[(
)]
(
)
[( 1
2
4
3
1
2
4
3
C
s
T
s
p
p
net
T
T
T
T
c
m
T
T
T
T
c
m
W









 


in
net
th
Q
W




and in terms of the min and max temperatures and pressure ratio,
The heat added in the cycle, for constant specific heats, is given by







 






C
k
k
p
p
in
p
r
T
T
T
c
m
T
T
c
m
Q

1
)
(
)
(
/
)
1
(
1
1
3
2
3



The efficiency of the cycle can then be obtained by dividing the
above two equations,

For the Brayton cycle, the turbine exhaust temperature is greater than the compressor
exit temperature. Therefore, a heat exchanger can be placed between the hot gases
leaving the turbine and the cooler gases leaving the compressor. This heat exchanger
is called a regenerator or recuperator. The sketch of the regenerative Brayton cycle is
shown below.
Regenerative Brayton Cycle

We define the regenerator effectiveness regen as the ratio of the heat transferred to
the compressor gases in the regenerator to the maximum possible heat transfer to
the compressor gases.
q h h
q h h h h
q
q
h h
h h
regen act
regen
regen
regen act
regen
,
, max '
,
, max
 
   
 


5 2
5 2 4 2
5 2
4 2


For ideal gases using the assumption of constant specific heats, the regenerator
effectiveness becomes
5 2
4 2
regen
T T
T T




Using the closed cycle analysis and treating the heat addition and heat rejection as
steady-flow processes, the regenerative cycle thermal efficiency is
Notice that the heat transfer occurring within the regenerator is not included in the
efficiency calculation because this energy is not heat transferred across the cycle
boundary.
The effectiveness of most regenerators in practice is below 0.85.
5
3
1
6
, 1
1
h
h
h
h
q
q
in
out
regen
th







Note: Under cold air standard
assumptions, the thermal
efficiency of an ideal Brayton
cycle with (ideal) regeneration is

The following shows a plot of the regenerative (Ideal) Brayton cycle efficiency as a
function of the pressure ratio and minimum to maximum temperature ratio, T1/T3.
Shows that regeneration is most effective at lower pressure ratios and low minimum
to maximum temperature ratios.

A regenerative gas-turbine power plant operating on an actual Brayton cycle
has a pressure ratio of 8. The gas temperature is 300 K at the compressor
inlet and 1300 K at the turbine inlet. If the regenerator has an effectiveness
of 80%, with the compressor and turbine efficiencies at 80% and 85%,
respectively; determine the
(a) compressor and turbine exit temperatures.
(b) back work ratio.
(c) cycle thermal efficiency.
(d) heat transfer in the regenerator.
Regenerative Brayton Cycle (Example)

Assignment # 5
1. In the preceding example, what was the temperature
drop experienced in the regenerator by the turbine
exhaust line?
2. Under cold air standard assumptions, the thermal
efficiency of an ideal Brayton cycle with (ideal) regeneration
is
Derive this equation.

Intercooling and reheating are two important ways to improve the performance of the
Brayton cycle with regeneration.
Brayton Cycle (Other Improvements)

When using multistage compression, cooling the working fluid between the stages
will reduce the amount of compressor work required. The compressor work is
reduced because cooling the working fluid reduces the average specific volume of
the fluid and thus reduces the amount of work on the fluid to achieve the given
pressure rise.
Brayton Cycle with Intercooling
P PP
2 1 4

or, the pressure ratios across the two compressors are
equal.
When the temperature rises are equal, the pressure
ratios are equal because
)
1
/(
1
2










n
n
p
T
T
r
For two-stage compression, let’s assume that intercooling takes place at constant
pressure and the gases can be cooled to the inlet temperature for the compressor,
such that P3 = P2 and T3 = T1. Then the intermediate pressure at which intercooling
should take place to minimize the compressor work, in this case is given by:
2
4
1
2
P
P
P
P

3
4
P
P

(n = k for ideal compression)

Intercooling is almost always used with regeneration. During intercooling, the
compressor final exit temperature is reduced; therefore, more heat must be supplied
in the heat addition process to achieve the maximum temperature of the cycle.
Regeneration can make up part of the required heat transfer.
Brayton Cycle with Intercooling
And the general expression for the pressure ratio per stage is given by
c
N
c
tot
p
c
stage
p r
r ,
,
,
, 
where Nc is the number of compressor sections (there are 2 in this case).
rp,stage,c is the pressure ratio per stage (P2 / P1 in this case) and
rp,tot,c is the overall pressure ratio (P4 / P1 in this case).

When using multistage expansion through two or more turbines, reheating
between stages will increase the net work done (it also increases the average
temperature of heat rejection). The regenerative Brayton cycle with reheating was
shown above.
The optimum intermediate pressure for reheating is the one that maximizes the
turbine work. Following the development given above for intercooling and assuming
reheating to the high-pressure turbine inlet temperature in a constant pressure
steady-flow process, we can show the optimum reheat pressure to be
P P P
7 6 9

or the pressure ratios across the two turbines are equal.
P
P
P
P
P
P
6
7
7
9
8
9
 
Brayton Cycle with Reheating
Similarly, the general expression for the pressure ratio per turbine stage is given by
T
N
T
tot
p
T
stage
p r
r ,
,
,
, 
where NT is the number of turbine sections (there are 2 in this case).

An ideal gas-turbine with two stages of compression and two stages of
expansion cycle has an overall pressure ratio of 8. Air enters each stage of
the compressor at 300 K and each stage of the turbine at 1300 K. Determine
the back work ratio and thermal efficiency assuming (a) no regenerator (b)
an ideal regenerator with 100% effectiveness.
Consider ideal compressors and turbines and no pressure losses.
Regenerative Brayton Cycle (Example)

FIGURE.
Combined gas–vapor
cycle.

Combined cycle power plants are those which have both gas and steam turbines
supplying power. A summary of some of its advantages/disadvantages is as follows:
Efficiencies exceeding 50% can be attained.
Suitable for Cogeneration.
Increased complexity
Combined Cycles (Advantages)

In the figure below, the topping cycle is a gas-turbine cycle that has a
pressure ratio of 8. Air enters the compressor at 300 K and the turbine at
1300 K. The isentropic efficiency of the compressor is 80% and that of the
gas-turbine is 85%. The bottoming cycle is a simple ideal Rankine cycle
operating between the pressure limits of 7 MPa & 5 kPa. Steam is heated in
a heat exchanger by the exhaust gases to a temperature of 500 °C. The
exhaust gases leave the heat exchanger at 450 K. Determine (a) the ratio of
the mass flow rates of the steam and the combustion gases and (b) the
thermal efficiency of the combined cycle.
Combined Gas-Steam Power Cycle (Example)

FIGURE.
Mercury–water binary
vapor cycle.

Advantages/disadvantages of binary-vapor cycles are as follows:
Efficiencies exceeding 50% can be attained.
Mercury has a high critical temperature (898 °C) compared to water (374 °C).
Not economically attractive due to high initial cost and competition offered by
combined gas-steam power plant.
Mercury is toxic.
Combined Cycles (Advantages)

Introduction
Ideal Jet Propulsion Cycle

• Aircraft gas turbines operate on an open
cycle called the jet-propulsion cycle.
• Power produced in the turbine is just
sufficient to drive the compressor and the
auxiliary equipment (Wnet = 0).
• Higher pressure ratios involved (10 to 25)
• Irreversibilities of all devices should be
considered in actual cycle analysis.
Gas Turbine Jet Propulsion (Summary)

 The ideal cycle for modern gas-turbine engines is the
Brayton cycle, which is made up of following processes:
Process 1-2 Isentropic deceleration through Diffuser.
Process 2-3 Isentropic compression through compressor.
Process 3-4 Constant-pressure heat addition in Combustor.
Process 4-5 Isentropic expansion through Turbine.
Process 5-6 Isentropic expansion through Nozzle.

Net thrust developed by the engine is
The power developed from the thrust of the engine is called the propulsive
power ( ), which is the propulsive force (thrust) times the distance this force
acts on the aircraft per unit time.
The propulsive efficiency is the ratio of propulsive power produced to propel
the aircraft to the total heat transfer rate to the working fluid.
)
( inlet
exit V
V
m
F 
 
aircraft
inlet
exit
aircraft
P V
V
V
m
FV
W )
( 

 

P
W

in
P
P
Q
W




It is a measure of how efficiently the thermal energy released during the
combustion process is converted to propulsive energy.

A turbojet aircraft flies with a velocity of 259 m/s at an altitude where the
air is at 34.5 kPa and -40 °C. The compressor has a pressure ratio of 10
and the temperature of the gases at the turbine inlet is 1100 °C. Air enters
the compressor at a rate of 45.36 kg/s. Using cold-air-standard
assumptions, determine (a) the temperature and pressure of the gases at
the turbine exit, (b) the velocity of the gases at the nozzle exit, and (c)
the propulsive efficiency of the cycle.
Ideal Jet Propulsion Cycle (Example)
T, °C
1093
-40

Brayton cycle (Gas Cycle)-Introduction

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Brayton cycle (Gas Cycle)-Introduction