Analysis of a Combined Regenerative and Reheat Gas Turbine Cycle using MATLAB
1Mohammed
1
Jasim Mohammed 2Dr. Mohammad Tariq
Research Scholar, Department of Mechanical Engineering, SSET, SHIATS-DU, Naini,
Allahabad, India
1
Assistant Professor, Department of Mechanical Engineering, SSET, SHIATS-DU, Naini,
Allahabad, India
ABSTRACT
In recent development of gas turbine cycles, new software for calculating thermal efficiency and
power output of a reheat and regenerative cycles are applied. There are one compressor and one
turbine used in regeneration gas turbine cycle and one compressor and two turbines are used in
reheat cycle. In the combined cycle, one compressor and two turbines (high pressure and low
pressure respectively) is using in the present work. The temperature after reheating assumes to be
reaching at the same temperature of HPT inlet. In the present work, a more sophisticated method
is developed from the earlier work and is used to calculate the various parameters of a combined
gas turbine cycle. The combination of the reheat and regenerative cycle has been taken in the
present work and the thermodynamic analysis has been performed using MATLAB 10 software.
The parameters taken in the well defined range for overall pressure ratio, turbine inlet
temperatures and ambient temperature. The cycle performs the analysis for various regenerative
effectiveness and it is found that the thermal efficiency has been increases on increasing the
regenerative effectiveness. Also found that the heat required in the burner decreases for higher
regenerative effectiveness.
Keywords: Gas Turbine, Regenerative Effectiveness, Reheat cycle, Thermal Efficiency.
1. Introduction
gas turbine, you need to be schooled in
1.1 Gas turbines theory
various topics. To define the compressor and
Gas turbines can be divided into important
the turbine, you need to use aerodynamics.
categories. There are industrial gas turbines
To get an efficient combustion, knowledge
and there are jet engine gas turbines. Both
on thermodynamics is required. Finally, to
types of gas turbines have a short but
make sure the engine survives the big
interesting background. When designing a
temperature differences and high forces, you
must be familiar with material sciences. A
Then the effects of oxygen utilization, fuel
gas turbine cycle is modeled to investigate
utilization,
the
efficiencies of the gas turbine components
effects
of
parameters
important
and
on the system performance of the RHE cycle
temperature (CIT), turbine inlet temperature
and the EGR cycle were discussed in detail.
(TIT) and pressure ratio (PR) on the overall
The effect of turbine efficiency on the
cycle performance and CO2 emissions [5].
system efficiency was more obvious than the
The reheat process is replaced by processes
effect of the compressor and recuperator
of heating the expanded gases while passing
efficiencies
through different turbine stator blades. Small
components. It was also indicated that
amount of combusted gases is utilized to
improving the
flow inside such blades for heating and
efficiencies for the RHE cycle increased
mixing with the expanded gases [2]. A
system efficiency higher than that for the
computational
the
EGR cycle [17]. The majority of the
performance of different gas turbine plants
Western world’s naval fleets already use
is presented in this paper. The work includes
gas-turbine engines for propulsion and
the effect of relative humidity, ambient inlet
electric power generation. The General
air temperature and types of fuels on gas
Electric LM2500 gas turbines used to power
turbine plants. Investigation also covers
ships have a simple-cycle thermal efficiency
economic analysis and effect of fuels on
of 37 percent. The General Electric WR-21
emissions [9]. The performance of actual
gas turbines equipped with intercooling and
cycles being used in gas turbines is
regeneration have a thermal efficiency of 43
discussed. A general overview of combined-
percent and produce21.6 MW (29040 hp).
cycle plants is provided [13].
The regeneration also reduces the exhaust
Two cycle schemes of recuperative heat
temperature from 600°C to350°C. Air is
exchanger
gas
compressed to 3 atm before it enters the
described
intercooler. Compared to steam-turbine and
according to the air reheating method. The
diesel propulsion systems, the gas turbine
system performance with operating pressure,
offers greater power for a given size and
turbine inlet temperature and fuel cell load
weight, high reliability, long life, and more
were studied based on the simulation results.
convenient operation. The engine start-up
study
(RHE)
(EGR)
compressor
temperature
inlet
recirculated
like
operating
operating
to
and
assess
exhaust
were
among
gas
the
gas
turbine
turbine component
time has been reduced from 4 h required for
gas turbine, the dual pressure reformer can
a typical steam propulsion system to less
give a further benefit, as far as an accurate
than 2 min for a gas turbine. Many modern
optimization of the steam management is
marine propulsion systems use gas turbines
performed [4]. A regenerative gas turbine
together with diesel engines because of the
engine, with isothermal heat addition,
high fuel consumption of simple-cycle gas-
working under the frame of a Brayton cycle
turbine engines. In combined diesel and gas-
has been analyzed. With the purpose of
turbine systems, diesel is used to provide for
having a more efficient small-sized gas
efficient low-power and cruise operation,
turbine engine, the optimization has been
and gas turbine is used when high speeds are
carried out numerically using the maximum
needed. In gas-turbine power plants, the
power (MP) and maximum power density
ratio of the compressor work to the turbine
(MPD) method [18].
work, called the back work ratio, is very
high. Usually more than one-half of the
1.2 The Regenerative Cycle
turbine work output is used to drive the
The
compressor. The situation is even worse
prominent in these days of tight fuel
when the isentropic efficiencies of the
reserves and high fuel costs. The amount of
compressor and the turbine are low. This is
fuel needed can be reduced by the use of a
quite in contrast to steam power plants,
regenerator in which the hot turbine exhaust
where the back work ratio is only a few
gas is used to preheat the air between the
percent. This is not surprising, however,
compressor and the combustion chamber.
since a liquid is compressed in steam power
The regenerator increases the temperature of
plants instead of a gas, and the steady-flow
the air entering the burner, thus reducing the
work is proportional to the specific volume
fuel-to-air ratio and increasing the thermal
of the working fluid. Two solutions are
efficiency.
proposed for the heat recovery scheme: a
1.3 Reheat Cycle
first reformer has a single pressure level
In the reheat gas turbine cycle, there are two
while the second has two in order to match
turbines used namely; high pressure turbine
the different pressures of the combustors.
(HPT) and low pressure turbine (LPT). The
While the single pressure scheme gives good
gases first expand in the high pressure
performance with respect to the stand alone
turbine and then in low pressure turbine. The
regenerative
cycle
is
becoming
temperature after expansion in the HPT
becomes low and then further head added in
the second combustor to increase the
temperature before expansion in the LPT.
Generally the temperature after expansion in
the HPT has to be increases up to the same
temperature of HPT inlet temperature. The
pressure of expansion in the turbine has
been taken as the root mean square value of
the overall pressure for optimum results.
Figure 2 T-s representation of combined
regenerative and reheat cycle
1.4 Reheat and Regenerative Cycle
There are one compressor and one turbine
2. Materials and Methodology
used in regeneration gas turbine cycle. In the
2.1Analysis of the Ideal Cycle
reheat or recuperation cycle, one compressor
The Brayton cycle in its ideal form consists
and two turbine is using in the present work.
of two isobaric processes and two isentropic
Fig 1 and fig 2 represents the combined
processes. The two isobaric processes
effect of reheating and regeneration of a gas
consist of the combustor system of the gas
turbine cycle.
turbine and the gas side of the HRSG. The
two isentropic processes represent the
compression
(Compressor)
and
the
expansion (Turbine Expander) processes in
the gas turbine. A simplified application of
the first law of thermodynamics to the airstandard
Figure 1 Schematic of combined
regenerative and reheat cycle
Brayton
cycle
(assuming
no
changes in kinetic and potential energy) has
the following relationships:
Work of compressor
WC = ṁa (h2 − h1 )
(1)
Work of high pressure turbine
Whpt = (ṁa + ṁf )(h3 − h4 )
Work of low pressure turbine
(2)
W
Wlpt = (ṁg + ṁf2 )(h5 − h6 )
act
ηc = (LHV)η
b
Total work output
As shown in fig 1, air enters the compressor
Wcyc = Whpt + Wlpt − Wc
(3)
at a state defined by T1 and P1. The
Net turbine work is given by
compressor exit pressure, P2, is given by:
Wnet = Whpt + Wlpt
p2 = rp × p1
Heat added to combustor 1 and combustor 2
given as follows;
Q2,3 = ṁf × LHVfuel = (ṁa + ṁf )(h3 ) −
ṁa (h2 )
(4)
Q4,5 = ṁf × LHVfuel = (ṁa + ṁf )(h5 ) −
ṁf (h4 )
rp is the compressor pressure ratio. The
ideal compressor discharge temperature, T2s
is given by the isentropic relation
T2′ = T1 × rp [k]
The
compressor
isentropic
efficiency,
defined as the ratio of the compressor
Total heat input is given by;
isentropic work to the actual compressor
Qtot = Q2,3 + Q4,5
work with both starting at the same initial
Thus, the overall thermal cycle efficiency is
ηth = Wnet /Qtot
(5)
state and ending at the same pressure level,
may be written as:
Assuming the compressor efficiency is (ηc )
and the turbine efficiency is (ηt ), then the
ɳc =
isentropic work
actual work
=
h2 −h1
h2′ −h1
=
T2 −T1
T2′ −T1
actual compressor work and the actual
Here the steady-flow energy equation has
turbine work is given by:
been applied to obtain expressions for the
Wca =
ṁa (h2 −h1 )
work
(6)
ηc
(7)
Thus, the actual total output work is
(8)
temperature from 2 to 3 is
h
−h
b
irreversible
adiabatic
isentropic compressor in the numerator.
Actual compressor discharge temperature is
given as
The actual fuel required to raise the
3a
2a
ṁf = (LHV)η
an
compressor in the denominator and for an
Wta = (ṁa + ṁf )(h3 − h4 )ηt
Wact = Wta − Wca
for
(9)
Thus, the overall adiabatic thermal cycle
T2′ = T1 +
T2 −T1
ηc
[k]
The work needed by the compressor, Wc:
WC = Cp (T2′ − T1 ) =
Cp (T2 −T1 )
ηc
kJ
⁄kg
efficiency can be calculated from the
After leaving the compressor at an elevated
following equation:
pressure and temperature, the air then enters
the
combustion
chamber,
where
it
completely oxidizes a liquid or a gaseous
m°f,b
FAR =
m°a
fuel injected under pressure.
Pressure and temperature at exhaust of
γa−1
pe γa
2.3 Turbine
T2 = T1 ( p )
i
andηc is
In this equation Te is the turbine inlet
combustion efficiency.
i
Pi
.LCVf −Cpg . Te
temperature of HP compressor, ηb is the
p
pe = pi ( pe )
Pe
b
temperature, Ti is stagnation or total exit
compressor by relation;
where
Cpg .Te −Cpa . Ti
=η
Turbine produces power to drive engine
is the pressure ratio of compressor
compressor due to expansion of gas stream.
polytrophic
The efficiency of gas turbine is taken care
efficiency
of
the
compressor.
by considering polytropic efficiency of
Wc = h2 − h1
turbine.
In actual compressor process the work
T3
required by the compressor for unite mass
T4
P3
(ɤ−1)
ɤ
= (P )
4
flow rate is given by the following equation
Wt = ηt Cpg (T3 − T4 )
Wc = Cpa (T2′ − T1 )
The turbine power output is then ma
[kJ/kg]
(1+FAR) Wt, where, as seen earlier, ma(1+
FAR) is the mass flow rate of combustion
2.2 Combustion chamber
The
combustion
process
raises
the
gas flowing through the turbine.
combustion gas temperature to the turbine
The cycle thermal efficiency is the ratio of
inlet temperature T3. One of the goals of
the network to the heat supplied to the
combustion chamber design is to minimize
heater:
the pressure loss from the compressor to the
ηt = Q net =
W
add
Cpg (T3 −T′ 4 ) − Cpa (T2′ −T1 )
Cpg (TIT)−Cpa (T2′ )
turbine. Ideally, then, P3= P2, as assumed by
2.4 Regeneration Effect
the Air Standard analysis. The rate of heat
In a simple gas turbine cycle the turbine exit
released by the combustion process may
temperature is nearly always appreciably
then be expressed as:
higher than the temperature of the air
°
Qadd = m a (1 + FAR)Cpg (T3 − T2 )
leaving the compressor. Obviously, the fuel
Where FAR is the mass fuel-air ratio and
requirement can be reduced by the use of a
calculated by equation:
regenerator in which the hot turbine exhaust
gas preheats the air between the compressor
and the combustion chamber. In an ideal
3600
AFR . Wnet
SFC =
case the flow through the regenerator is at
constant
pressure.
The
regenerator
effectiveness is given by the following
relationship:
ɳreg =
T3 − T2
T5 − T2
Fuel to air ratio is given by
1
AFR
Thermal efficiency is given by
AFR =
η
Wnet
Qadd
th =
Thus, the overall efficiency for this system's
cycle can be written as
ɳRcyc =
2.5 Analysis gas turbine cycle with
(T4 −T5 )−(T2 −T1 )
(T4 −T3 )
reheating
…
Increasing the effectiveness of a regenerator
calls for more heat transfer surface area,
which increases the cost, the pressure drop,
The compressor efficiency ( ηc ), the turbine
( ηt ),
and
effectiveness
of
regenerator (heat exchanger) are considered
in this study.
These parameters in terms of temperature
are defined as:
T ′ 2 − T1
ηC =
T2 − T1
T3 − T4
ηt =
T3 − T ′ 4
′
εrc =
T 2 − T1
T2 − T1
basic cycle is to increase the specific work
output and cycle efficiency. The specific
work output from the cycle can be increased
and the space requirements of the unit.
efficiency
The very purpose of any modification in the
by including reheater and carrying out the
expansion in two stages. The work output of
the reheat (reheating is done to its original
temperature T5= T3). The turbine work
increases as the vertical distance between a
pair of pressure line increases with as
increase in entropy as:
(T5 − T6 ) > (T3 − T4 )
Pi
P1
=
P2
Pi
The pressure ratio of compression is given
by
P2
Pi P2
= × = R pc1 × R pc2
P1
P1 Pi
Power output is given by
R pc =
P = m′a × Wnet
Where the R pc1 and R pc2 are the pressure
Air to fuel ratio is given by
ratio of expansion-I and expansion-II.
AFR =
LCVf
Qadd
Specific fuel consumption
The net specific work output of the cycle is
given by:
Wnet = Whpt + Wlpt − Wc
inlet temperatures (TIT) for various ambient
Whpt = Cp (T3 − T4 )
temperatures. Heat sully to the combustor
Wlpt = Cp (T5 − T6 )
increases on increasing the turbine inlet
WC = Cp (T2 − T1 )
temperatures. Fig 4 shows the variation of
Net work with TIT for various overall
Wnet = Cp [(T3 − T4 ) + (T5 − T6 ) − (T2
pressure ratios. Net work increases on
− T1 )]
The best pressure Pi, where reheating is
increasing the TIT for a given OPR.
carried out for maximum specific work
output can be obtained by equation:
600
550
Pi = √P1 P2
OPR=10
OPR=20
OPR=30
OPR=40
500
3. Results and Discussion
This paper presents the results of the
Net Work
450
Tamb=300K
REGEFF=0.85
400
350
300
250
combined cycle in the form of graphs for
200
150
various parameters. The software developed
1000
1100
in MATLAB 10 for the thermodynamic
1200
1300
1400
1500
Turbin Inlet Temperature
calculations of the cycle and then graphs
Fig 4 Variation of Net work vs TIT
have been plotted in menu driven software
‘Origin 6.1’.
Tamb=280K
Tamb=290K
Tamb=300K
Tamb=310K
Tamb=320K
Tamb=330K
1000
Total Heat Input
900
Thermal Efficiency
1100
OPR=20
REGEF=0.85
800
700
0.50
0.48
0.46
0.44
0.42
0.40
0.38
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
Tamb=300K
REGEFF=0.85
OPR=10
OPR=20
OPR=30
OPR=40
1000
600
1100
1200
1300
1400
1500
Turbine Inlet Temperature
500
1000
1100
1200
1300
1400
1500
Turbine Inlet Temperature
Fig 5 Variation of Thermal efficiency vs
TIT
Fig 3 Variation of Head input vs TIT
Fig 5 shows the variation of Thermal
Figure 3 represents the variations of heat
efficiency with TIT for different OPR. It
supply to the combustor at different turbine
seems from the figure that the thermal
efficiency increases on increasing the TIT
while
the
network
output
increases
for a given value of OPR. Fig 6 shows the
continuously. Fig 13 shows the variation of
variation of Work ratio with TIT. Work ratio
mass of fuel required in the combustor one
decreases ion increasing the TIT and it is
and two with TIT. It has been observed that
minimum for minimum OPR. Fig 7 shows
the fuel required in the first combustor is
the variation of Air rate with TIT and it is
more as compared to the second combustor.
observed that the air rate decreases on
This is due to fact that the temperature is
increasing the TIT for a given value of OPR.
well above after expansion in HPT.
Fig 8 represents the variation of specific fuel
4.0
decreases on increasing the TIT. The rate of
3.5
decrease is less at higher values of TIT. Fig
9 shows the variation of Net power with
Work Ratio
consumption (SFC) with TIT. The SFC
OPR=10
OPR=20
OPR=30
OPR=40
Tamb=300K
REGEFF=0.85
3.0
2.5
TIT. The net power increases on increasing
2.0
the TIT. Fig 10 represents the variation of
1.5
heat input with TIT. The heat addition to the
1000
1100
1200
1300
1400
1500
Turbine Inlet Temperature
burner is decreases on increasing the
regenerative effectiveness. Overall heat
Fig 6 Variation of Work ratio vs TIT
input increases on increasing the turbine
20
inlet temperature. Fig 11 represents the
18
variation of heat input in the burner at
OPR=10
OPR=20
OPR=30
OPR=40
16
observed that the heat input decreases on
increasing the ambient temperature. At
Air Rate
14
various ambient temperatures. It has been
Tamb=300K
REGEFF=0.85
12
10
8
6
higher regenerative effectiveness, the heat
4
1000
input is minimum. Fig 12 shows the
variation of Net work and thermal efficiency
with TIT. The thermal efficiency and net
work both increases on increasing the TIT
but after reaching an optimum value; the
rate of increase is low for thermal efficiency
1100
1200
1300
1400
Turbine Inlet Temperature
Fig 7 Variation of Air rate vs TIT
1500
655
0.46
650
0.44
Specific Fuel Consumption
0.38
0.36
640
Tamb=300K
REGEFF=0.85
635
Heat input to combustor
OPR=10
OPR=20
OPR=30
OPR=40
0.40
REGEFF=0.75
REGEFF=0.80
REGEFF=0.85
REGEFF=0.90
REGEFF=0.95
TIT=1400K
OPR=20
645
0.42
0.34
0.32
0.30
0.28
0.26
630
625
620
615
610
605
600
0.24
595
0.22
590
0.20
585
580
0.18
1000
1100
1200
1300
1400
280
1500
290
300
310
320
330
Ambient Temperature (K)
Turbine Inlet Temperature
Fig 11 Variation of Heat input vs ambient
Fig 8 Variation of SFC vs TIT
temperature
550
Net Power Output (kW)
450
0.55
Tamb=300K
REGEFF=0.85
3
Net Work (x10 )
Thermal Efficiency
0.50
Net Work and Thermal Efficiency
OPR=10
OPR=20
OPR=30
OPR=40
500
400
350
300
250
200
0.45
0.40
0.35
Tamb=300K
OPR=20
ETAGEN=0.85
0.30
0.25
150
0.20
1000
1100
1200
1300
1400
1500
1000
Turbine Inlet Temperature
1100
1200
1300
1400
1500
Turbine Inlet Temperature (K)
Fig 9 Variation of Net power vs TIT
Fig 12 Variation of Net work and thermal
700
REGEFF=0.75
REGEFF=0.80
REGEFF=0.85
REGEFF=0.90
REGEFF=0.95
600
0.017
0.016
550
Mass of fuel in Combustor 1
Mass of fuel in Combustor 2
0.015
500
Mass of Fuel (kg/s)
Heat input to combustor
650
efficiency vs TIT
Tamb=300K
OPR=20
450
400
1000
1100
1200
1300
1400
Turbine Inlet Temperature (K)
1500
0.014
0.013
OPR=20
Tamb=300K
REGEFF=0.85
0.012
0.011
0.010
0.009
0.008
Fig 10 Variation of Heat input to TIT
1000
1100
1200
1300
1400
Turbine Inlet Temperature (K)
Fig 13 Variation of Mass of Fuel vs TIT
1500
from 75% to 95%, the efficiency of the
CC1 at OPR=10
CC2 at OPR=10
CC1 at OPR=20
CC2 at OPR=20
CC1 at OPR=30
CC2 at OPR=30
CC1 at OPR=40
CC2 at OPR=40
Mass of Fuel in Combustion Chambrer 1 and 2
0.018
0.016
0.014
regenerative
Tamb=300K
REGEFF=0.85
cycle
is
higher
than
its
counterpart in the simple cycle. The work
output per kg of air is about the same or
0.012
slightly less than that experienced with the
0.010
simple cycle. Increasing the pressure ratio
0.008
0.006
and the turbine firing temperature increases
0.004
the Brayton cycle efficiency. The increase in
0.002
0.000
1000
1100
1200
1300
1400
1500
the pressure ratio increases the overall
Turbine Inlet Temperature (K)
efficiency at a given firing temperature;
Fig 14 Variation of mass of fuel required in
the combustor 1 and 2 with TIT
beyond a certain value at any given firing
Figure 14 shows the variation of the mass of
fuel required in the combustor 1 and 2 at
various
OPR.
Figures
however, increasing the pressure ratio
show
the
improvement in cycle efficiency because of
heat recovery with respect to a simple opencycle gas turbine. Cycle efficiency drops
with an increasing pressure drop in the
regenerator. There are two types of heat
exchangers Regenerative and Recuperative.
The term ``regenerative heat exchanger'' is
used for a system in which the heat transfer
between two streams is affected by the
exposure of a third medium alternately to
the two flows. The heat flows successively
into and out of the third medium, which
undergoes a cyclic temperature. These types
of heat exchangers are widely used where
compactness is essential. For a regenerator
assumed to have an effectiveness varies
temperature can actually result in lowering
the overall cycle efficiency. It should also be
noted that the very high-pressure ratios tend
to reduce the operating range of the turbine
compressor.
This
causes
the
turbine
compressor to be much more intolerant to
dirt build up in the inlet air filter and on the
compressor blades and creates large drops in
cycle efficiency and performance. In some
cases, it can lead to compressor surge, which
in turn can lead to a flameout, or even
serious
damage
and
failure
of
the
compressor blades and the radial and thrust
bearings of the gas turbine.
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