A gas turbine as part of a cogeneration plant delivers power at constant shaft
speed and hot exhaust gas at optimum heat recovery steam boiler inlet temperature
from the combustion of a gas or liquid fuel. Main components of a typical single-shaft
gas turbine are as indicated in Fig. 1. The corresponding
process diagram is given in Fig. 2. The air from the atmosphere
is first compressed (process 1-2) to high pressure in the compressor. The compressed
air is then mixed with fuel and burned (process 2-3) in the combustion
chamber. The hot gas then expands through the turbine (process 3-4) resulting
in rotation work on the turbine shaft. In an industrial gas turbine, the shaft
is connected to a generator shaft through a speed reduction gear box.
In general, gas turbines have fast starting characteristics. The improved dynamic
load characteristic has made them the preferred choice for industrial applications.
In the state of the art designs they are equipped with variable geometry compressors
which allow wider surge and stall margins in part load applications. Topic of
concern is a gas turbine working in synchronous with another gas turbine to
provide the required load demand and at the same time delivering high temperature
gas to a heat recovery steam generator.
During starting and for speeds lower than about 65% of the design speed, the
Inlet Guide Vanes (IGVs) and Variable Stator Vanes (VSVs) are at minimum opening
position; at a speed of about 98%, they open fully with the opening starting
at around 65% of design speed. The latter region is identified as a variable
geometry region where the IGVs and VSVs are manipulated to vary the air flow
||Process diagram for a single-shaft gas turbine
In a cogeneration design, the gas turbine is also expected to deliver high
temperature exhaust gas. For loads higher than 50% of the rated value this requirement
is achieved by a temperature controller. In this region, IGVs and VSVs are manipulated
to vary the air flow rate into the compressor as per the load demand. Fuel flow
is also varied to keep temperature at the inlet of the third stage of the gas
turbine (T5) to the required set point. For a load demand lower than
50%, the gas turbine is on speed and load control. During this period the variable
geometry (θIGV) is at fully open position and the state can
be considered as fixed geometry region. Figure 3 shows plots
of main parameters in their normalized form-each divided by their maximum value.
Dynamic studies of a gas turbine require thermodynamic models of the gas turbine
components as well as details of the control system. Overall performance map
instead of component performance maps are usually provided by the manufacture
that made it difficult to proceed with the dynamic studies. For a variable geometry
compressor, it is not practical to provide performance maps corresponding to
the whole working region of the IGV and VSV settings. In energy and exergy focused
parametric studies, compressor and turbine efficiencies may be assumed constant
(Abam et al., 2011; Mahmoudi
et al., 2009) which neglects the effect of IGV. In power plant stability
studies, the simplest approach yet is to use empirical models to describe the
thermodynamic part (Rowen, 1983; Zhang
and So, 2000). In the study of Kakimoto and Baba (2003),
the pressure ratio in the compressor and turbine are described as a function
of design pressure ratio and air flow rate while the efficiencies are assumed
constant. The effect of rotational speed on the pressure ratio was latter included
in the models by Suzaki et al. (2000).
||Actual Operating schedule for a Single-shaft Gas Turbine Generator
from Univeriti Teknologi PETRONAS GDC Plant
An alternative approach is to use a scaling method for fixed geometry compressors
and turbines (Gaudet, 2008) with extrapolation techniques
applied at lower speeds. Stage-stacking techniques based on generalized stage
performance curves are another widely used method (Kim
et al., 2001). Recent techniques from computational intelligence-neural
network (Zayandehroodi et al., 2010) and fuzzy
logic (Radaideh, 2003) are also getting frequent use
in the area of thermal plants. They can be applied to capture thermodynamic
characteristics of the system over the whole operating region. In dynamic studies,
a model needs to be simple to consume short calculation time and good enough
to accommodate variable operating conditions. It must also allow the study of
change in parameters like compressor inlet temperature, efficiency of the compressor,
efficiency of the turbine etc.
The objective of this study is to develop compressor and turbine maps for a
5.2 MW rated industrial gas turbine whose design specifications are partially
known. The research proposes the use of scaling method in the fixed geometry
regions and stage-stacking method in the variable geometry region. Generalized
stage and overall component performance curves from literature are used in presenting
the performance characteristics. The reference map for compressors is selected
after preliminary tests on the suitability of three different generalized maps.
It is hoped that the resulting maps will be suitable enough to perform steady
state performance and dynamic studies.
GAS TURBINE THERMODYNAMIC MODEL
In the simulation of a gas turbine the compressor and turbine are represented
by performance maps. For a given inlet
conditions and inlet fuel flow
thermodynamic equations are applied to estimate properties of the working fluid
at following state points. For the compressor, the temperature at the outlet
(T2) and work input requirement ,
respectively are calculated by:
where, h is enthalpy, PRc and ηc are pressure ratio
and efficiency, respectively, of the compressor corresponding to the given mass
flow rate. The two values are read from specific compressor maps usually described
as PRc = f (mair, N) and ηc = f (PRc,
N). Where, N is the compressor shaft speed.
The compressed air from the compressor is mixed with fuel and burned in the
combustion chamber before it expands through the turbine. The temperature at
the outlet of the combustion chamber (T3') can be estimated using
combustion charts (Razak, 2007) or by an iterative approach.
The energy balance around the combustor is expressed as:
where, h is the enthalpy, LHV is lower heating value of the fuel and FAR is
the fuel to air ratio.
There is a pressure loss in the compressor due to the chamber resisting air
flow, high level of turbulence required for combustion and heat addition. This
pressure loss is considered in the model applying the following equation:
where, PLF is the pressure loss factor; M23' is the dimensionless
flow; K1 and K2 are constants for the cold loss and hot
loss of the combustor, respectively. Then from the pressure loss and inlet pressure:
The hot gas temperature leaving the turbine (T4) and the power transferred
to the turbine shaft are expressed as:
where, h is enthalpy of the hot gas; ηt = f1 (PRt,
N) and PRt are isentropic efficiency and pressure ratio, respectively,
of the turbine. The pressure at the outlet of the turbine P4 is limited
to less than 105.825 kPa. Using this value, the pressure ratio is calculated
and used in (mair+mf) = f2 (PRt,
N) to check if the mass balance is satisfied.
The following is assumed for the electric power at the generator terminal:
where, ηm and ηele are mechanical efficiency
and electrical efficiency, respectively.
In the first step of performance map calculation, Eq. 1-8
are applied iteratively to determine estimated design point parameters. At each
state point variation of specific heats with temperatures are taken into consideration.
Most of the time, Heat Rate (HR), Lower Heating Value (LHV) of the fuel and
exhaust flow rate
are provided. In that case, the following equations are applied to obtain the
fuel flow rate and air mass flow rate, respectively:
Once the component design parameters are determined, scaling and stage-stacking
methods are applied to generate the performance maps. Off-design analysis is
just solving the same set of Eq. 1-8 satisfying
the matching conditions-conservation of mass and power.
Scaling method: For a compressor, there are three available performance
calculation techniques: scaling method, stage-stacking method and blade element
method (Johnsen and Bullock, 1965). Among the three,
scaling method is the easiest. But the inherent simplicity has the drawback
of demanding a suitable reference map. Besides, it is not suitable for studying
variable geometry compressors from the point of view of understanding the stage
interaction inside the compressor. Scaling method is good enough if the interest
of the analyst is to understand the compressor as a black box. This is true
for the case of fixed geometry compressors. As will be demonstrated in the results
and discussion section, the accuracy of the method is largely dependent on the
shapes of the reference maps. Scaling method overlooks compressibility effect.
Modified versions of the scaling method have been suggested recently (Kong
and Ki, 2007; Kong et al., 2003). The main
idea in the scaling method is that performance map of a compressor can be generated
if the design conditions
are known. The basic equations for the scaling method are:
Mass flow rate:
where, PRmap, des and PRmap are design pressure ratio
and off-design pressure ratio for the reference map ;
are design mass flow rate and off-design mass flow rate for the reference map;
ηisen, des and ηisen, map are design efficiency
and off-design efficiency, respectively, of the reference map. For generating
the compressor performance maps using the scaling method, multi-stage compressor
maps from three different sources (Converse and Giffin, 1984;
Johnsen and Bullock, 1965; Saravanamuttoo
and MacIsaac, 1983) will be considered. The first set of maps were used
to study a two-spool industrial gas turbine (Zhu and Saravanamuttoo,
For turbines, the easiest method is to assume that the turbine is choked and
the corresponding efficiency is constant. If that is not good enough, Stodola
ellipse equation (Dixon, 2005) or one-dimensional nozzle
equation (Ordys et al., 1994) may be applied. The
third option is to use Ainley and Mathieson (1951) method.
This method, however, requires geometric data which is hardly available. In
this paper, scaling method that demands relatively little information at design
point is considered.
Stage-stacking method: In the stage stacking method, generalized stage
performance curves are used in order to develop overall compressor performance.
Based on a flow coefficient φ calculated at the inlet of a stage, pressure
ratio ψ and efficiency η are read from generalized curves and used
to estimate for outlet pressure and temperature of the stage. The total pressure
and temperature at the outlet of the preceding stage are considered as an input
to the following stage. The calculations are repeated covering all the stages
in the compressor. The properties at the outlet of the last stage will be considered
as the properties of the compressor. The relevant equations are as described
where, Ca is the stage inlet axial velocity, U is the tangential
blade speed, Tos is stage inlet air total temperature, ΔTos
is stage total temperature rise, Cp is specific heat at constant
pressure and γ is ratio of specific heats.
Stage-stacking procedure is suitable to develop performance maps for fixed
as well as variable geometry compressors. The first proposed stage stacking
method was based on the stage performance map of a single stage compressor or
fan. Latter it was improved by introducing generalized stage performance curves.
||Graph of stage normalized efficiency versus ratio between
temperature coefficient and flow coefficient (Howell
and Bonham, 1950)
||Plot of normalized pressure coefficient versus normalized
flow coefficient ψ* = fψ (φ*, SF) (Spina,
Ratios of each characteristic parameter (Eq. 14-17)
and the value of the same parameter at the point of maximum efficiency are used
to define a point on the generalized curves. Figure 4 shows
the generalized efficiency curve as developed by Howell
and Bonham (1950). The other curve required for stage-stacking calculation
is the ψ* verse φ* plot (Fig. 5). This was developed
by Muir (1988) assembling a number of openly published
stage data on pressure ratio. The concept of Shape Factor (SF) was then introduced
by Spina (2002) to obtain a number of generalized curves
covering all the data points calculated by Muir (1988).
The corresponding equation becomes:
The normalized isentropic efficiency and total temperature equations are given
In order to obtain stage characteristics of a given compressor the shape factor
is estimated by minimizing the sum of squares of errors between calculated and
given performance parameter, for instance compressor pressure ratio.
In a variable geometry compressor, IGVs and VSVs are adjusted to cope with
the variation of speed and gas turbine load. In that case, each new setting
of the blades results in a new stage characteristic. From velocity triangle
of a rotating compressor blade (Fig. 6a) and assuming constant
axial flow velocity and mean rotor speed and from equation of energy balance
for the rotor:
Assuming that the IGVs and VSVs are adjusted such that the relative flow angles
are constant and equal to the design point angles (Fig. 6b),
Eq. 20 can be written in a form suitable to find generalized
performance curves at off-design IGVs and VSVs setting:
The same set of assumptions leads to the conclusion that efficiency is constant.
This makes sense for the pressure losses across the rotor blades are at minimum
if the angle of incidence is adjusted such that the flow angle is unaffected.
The resulting equation between φ and ψ will be:
||Compressor blades: (a) velocity triangles (b) IGV setting
RESULTS AND DISCUSSION
The results from application of the proposed methods are presented here. The
first sets of maps are modeled by scaling method. As mentioned in the discussion
of the scaling method, data from three different sources will be used as reference
data. Fig. 7 shows the difference in the shapes of the three
selected reference maps. At the corrected design speed (N/Nd = 1),
the three maps seem overlapping in a certain region. For speeds other than the
design point, the maps are hardly close to each other. These set of maps are
chosen arbitrarily to see if random selection of a compressor map in a certain
application is acceptable at all the times.
The first axial compressor considered for testing the suitability of the three
reference maps is taken from (Budinger and Thomson, 1952).
The compressor is a 10 stage axial flow compressor with mass flow rate ,
pressure ratio PR4 = 12.4, efficiency ηd = 0.86 and
shaft speed Nd = 14000 rpm. The comparison between experimental data
of the compressor and the maps generated based on the three reference maps are
shown in Fig. 8. The scaled maps predicted different points
except for the few points closely predicted by Johnsens Map in the lower
The second axial compressor selected for examining the same set of reference
maps is obtained from (Geye et al., 1953) . The
compressor is designed for a mass flow rate of
, pressure ratio of PRd = 10.26, isentropic efficiency of ηd
= 0.86 and rotational speed of Nd = 13380 rpm. As presented in Fig.
9, at the design speed of the compressor, the prediction by the three reference
maps are somehow in agreement. For the off-design speed, the only reference
map that may be considered is the Johnsens map.
The third test compressor map is a 16 stage compressor taken from Medeiros
et al. (1951).
||Normalized reference compressor performance maps
It has the design flow capacity of
and pressure ratio of PRd = 8.75 for a speed of Nd = 6100
rpm and efficiency ηd = 0.83. Similar to the previous compressors
the same set of reference compressors maps were applied to predict off-design
characteristics of the compressor. The resulting curves are depicted in Fig.
10. At 80% of the design speed, Saravanamuttos map seems predicting
the performance accurately.
||Performance maps of a 3-stage turbine: (a) Normalized efficiency
versus normalized pressure ratio (b) Normalized mass flow rate versus normalized
Except that, the rest of the predictions are far from being acceptable for
From the presented tests, it is observed that even for pressure ratios closer
to the reference map pressure ratio the resulting prediction may not be as accurate
as expected. Therefore, having this problem from the simplest technique known
and with the scant information available from manufactures catalogue, the task
of finding a suitable map using this method is too much of an out of option
procedure than other wise.
|| Design specification of solar gas turbine
The present work suggested scaling method for the fixed geometry region and
stage stacking method for the variable geometry region. The stage stacking method
is more involved as it follows a design procedure based on carefully decided
design parameters. However, as demonstrated latter, the accuracy is much better
than scaling method.
After studying the importance of choosing a geometrically suitable reference
map for predicting the performance of an axial compressor based on the scaling
method, the technique was applied to the components of a 5.2 MW Solar gas turbine.
Manufacturer supplied overall parameters as indicated in Table
1 are used for the calculations. To determine the missing design information
regarding the 12 stage axial flow compressor and the 3 stage turbine, Eq.
1-10 were solved in an iterative way with the objective
of minimizing sums of Squares of Relative Errors (SSRE) given by the following
where, P2a is design point compressor discharge pressure and
is the power at the generator terminal. The error is minimized varying isentropic
efficiencies of the compressor and turbine, respectively. The design point discharge
pressure is read from overall performance map of the gas turbine provided by
the manufacturer. Results of the optimization calculation are given in Table
From the optimized result, the turbine appeared to have exhaust gas flow rate
and a pressure ratio of Prd = 10 while the compressor is featured
by a mass flow rate of and
pressure ratio of PRd = 11. The performance maps developed based
on the calculated design values are portrayed in Fig. 11
||Performance maps of a 12-stage compressor: (a) Normalized
pressure ratio versus normalized mass flow rate (b) Efficiency versus normalized
mass flow rate
As a reference, a turbine map from Converse (1984) is
chosen for applying the scaling method attributed closer design pressure ratio
to the pressure ratio of the Solar Turbine.
||Stage inlet flow area of a 16-stage compressor (Muir,
||Plot of normalized pressure ratio versus normalized mass flow
rate for a 3-stage axial compressor (Kashiwabara et
In applying the stage-stacking method, Eq. 22 and 23
are first validated by experimental data taken from (Kim
et al., 2001). As indicated in Fig. 13, the results
from the two equations are in good agreement with the experimental data.
Stage-stacking method relies on geometric data. However, this information is
not available for proprietary reasons. In this paper, a general design procedure
with design conditions decided based on data from well established literature
are adapted. The following parameters are assumed for design point calculation.
||150 m sec-1
||Inlet flow angle
For validating the geometry calculation, actual dimensions for 16 stage axial
compressor taken from Muir (1988) is compared with the
geometry calculated using to the above input parameters. As indicated in Fig.
14, the real design and the calculation result match quite closely. The
stage-stacking method, before it is applied to the Solar Turbine, is also tested
by predicting off-design performance characteristics of a 3 stage axial flow
compressor taken from Kashiwabara et al. (1986).
As shown in Fig. 15, the calculated result agrees well with
the experimental data as compared to other similar work (Song
et al., 2000).
In this study, we have developed gas turbine component maps based on partially
known design information. At the start, three reference maps from different
sources have been tested to verify if random selection of reference maps could
be used for generating characteristic curves through scaling method. After testing
the reference maps by three other actual compressor maps, the scaling method
is applied to Solar Taurus 60s gas turbine whose overall design information
is partially known. Based on the cases tested, the following conclusions have
||Having partially known overall design information, the application
of scaling method requires care in the selection of the reference map. It
was observed that even for the case where the design pressure ratios of
the reference and the new compressor are closer, accurate off design point
performance prediction may not be granted
||As compared to the scaling method, the stage stacking method well matches
the experimental data. The only drawback to this method is the need for
design point calculation
The next task to the presented work is to test the generated performance maps
in actual overall performance prediction of the gas turbine generator.
The authors acknowledge the support by Universiti Teknologi PETRONAS for providing
all the resources sought by the research.