Prediction of fuel gas pressure requirement for ALSTOM heavy duty gas turbines
Tua Högnäs June 2005 Thesis for degree of Master of Science Division of Heat and Power Engineering Lund Institute of Technology
ii
Abstract Within the ongoing development of Alstom’s latest heavy-duty gas turbine, the motivation for this
thesis is the need for a fuel gas pressure prediction software. The key challenge in the development of
such a software is finding the model that predicts the pressure drop over the burner hardware. This
model has to predict fuel pressure for over-critical and under-critical flow over the entire load range
with high accuracy. Old models are inadequate for predicting pressure drops at critical conditions.
Four main fuel pressure prediction models are presented in this work.
The Kv-model is a model where a pressure drop is attributable to a flow resistor and it contains one
hardware parameter. By introducing a second hardware parameter the model is refined to work also
for over-critical flow conditions.
The outflow model is a model in which the fuel pressure drop can be calculated as being only due to
the discharge through a nozzle.
The two stage-model is a model, which combines the Kv-model, and the outflow model in order to
offer a more sophisticated version. It contains the two hardware parameters from the models
described above. Four variants of this model are herewith investigated, in which these parameters are
considered either constant, Reynolds number-dependent or dependent of critical flow effects.
Finally, by means of a nominalization of the variables, a polynomial fitting method, using the least
squares procedure, provides the so-called polynomial model. Polynomials of second and fourth order
are considered.
In order to perform a structured and systematic selection between the different models, three design
criteria were defined: accuracy, simplicity and physicality. It is shown that a modified version of the Kv-
model, in which the burner hardware is treated a pure flow resistor, is the best compromise between
these design criteria. This model will predict fuel pressures with a high accuracy over the entire load
range of the engine and also predict well for diluted gases.
This thesis also contains an application of the finalised fuel pressure prediction software. Boundary
limits of the operation of the burner hardware are found, based on defined fuel pressure limits.
iii
Acknowledgements
I have had the great opportunity to do this master thesis at Alstom Technology Centre in Dättwil,
Switzerland. I would like to thank my supervisor at Alstom, William Anderson, for all his help, creativity
and expertise. I would like to thank Andreas Brautsch for all his support, encouragement and many
good ideas. My deepest thanks also go to Associate Professor Mohsen Assadi, my supervisor at Lund
Institute of Technology. I am also grateful to all my colleagues at Alstom who have made my stay here
a very pleasant one and who have provided an inspiring working atmosphere. Finally I want to thank
Eduardo for encouraging me throughout my engineering studies.
Tua Högnäs
Dättwil, June 16, 2005
iv
Table of contents
Subscript ................................................................................................................................... v 1 Introduction .......................................................................................................................1
1.1 Background ...............................................................................................................1 1.2 Objectives..................................................................................................................2 1.3 Limitations of this thesis ............................................................................................2 1.4 Method ......................................................................................................................2
2 Elementary gas turbine theory ..........................................................................................3 3 Description of the ALSTOM gas turbine GT26 .................................................................5
3.1 Combustor operation concept and burner hardware configuration...........................5 3.2 Fuel gas system ........................................................................................................8
4 Fuel gas pressure prediction.............................................................................................9 4.1 Necessity of accurate gas pressure prediction .........................................................9 4.2 Pressure drop calculations........................................................................................9
4.2.1 Critical flow ......................................................................................................10 4.3 Prediction of fuel pressure drop over the pilot lance...............................................11
4.3.1 Data normalization and selection ....................................................................11 4.3.2 Kv-model .........................................................................................................14 4.3.3 Outflow Model .................................................................................................18 4.3.4 Two-Stage Model ............................................................................................20 4.3.5 Polynomial.......................................................................................................23
4.4 Evaluation................................................................................................................24 4.4.1 Kv-model with constant kv*..............................................................................26 4.4.2 Kv-model with separate kv*-values for under- and over-critical flow ...............27 4.4.3 Outflow model .................................................................................................29 4.4.4 Two-stage model with constant kv* and .......................................................30 4.4.5 Two-stage model with separate kv*-values for under- and over-critical flow...31 4.4.6 Two-stage model with kv* as a function of the Reynolds number ...................32 4.4.7 Two-stage model with kv* as a function of the Reynolds number and itemized pressure losses over the lance .......................................................................................33 4.4.8 Polynomial of 2nd order ....................................................................................34 4.4.9 Polynomial of 4th order ....................................................................................35
4.5 Effects of dilution.....................................................................................................36 5 Boundary conditions for the fuel lance LoLa8.5..............................................................37 6 Discussion and conclusions ............................................................................................39 References..............................................................................................................................40 Appendix A..............................................................................................................................41
v
Nomenclature
A : Area [m2]
p : Pressure [Pa]
z : Height [m]
d : Pipe diameter [m]
w : Flow velocity [m/s]
ρ : Gas density [kg/m3]
ζ : Flow resistance number [-]
Ar : Area of the flow resistance [m2]
Aeff : Effective area [m2]
Kv : Flow number [m/s]
*
vk : kv*-value [m2]
.
m : Mass flow through lance
[kg/s]
fgp : Absolute fuel gas pressure after control valve [Pa]
combp : Absolute combustion pressure [Pa]
0p : Total pressure [Pa]
0p : Critical pressure [Pa]
fgT : Fuel gas temperature [K]
γ : Isentropic coefficient=Cp/Cv [-]
R : Specific gas constant [J/kgK]
Ψ : Psi-function [-]
s : Width of lance channel = router-rinner [m]
l : Length of lance [m] λ : Friction factor [-] � : Discharge coefficient [-]
Subscript
i : upstream
a : downstream
1
1 Introduction
1.1 Background
Gas turbines transfer kinetic and thermal energy of a gas into mechanical energy and are used for
power generation, mechanical drive and aircraft propulsion. It is a technology that has been
developing since the 1930’s. The power output of gas turbines ranges from a few kilowatts to
hundreds of megawatts.
Traditionally, gas turbines for power generation have been used for peak loading, when the possibility
of start-up and shut-down on demand is essential. More recently as cycle efficiencies have improved,
there has been an increased usage also for base load operation, especially in combined cycle mode,
where the waste heat is recovered in a steam cycle to produce additional electricity. There is also a
growing market of cogeneration power plants that produce power and heat simultaneously, which is
especially suitable for applications where both power and heat is needed, such as the paper industry.
Gas turbines can operate on both gaseous and liquid fuels, though gaseous fuel is the fuel of choice
due to environmental concerns, lower installation and maintenance costs. However, in particular
heavy-duty gas turbines often have dual fuel capability, which means that they can switch to operation
on other fuels, such as diesel oil, during peaks of natural gas prices.
Gas turbines with high pressure ratio compressors need to be supplied with fuel gas above the post-
compressor pressure. The system that leads the gas to the combustion chambers contains various
components, such as filters and control valves, which cause pressure losses. It is important to be able
to correctly calculate the required fuel pressure at offering, design and execution of a gas turbine
power plant. During the offering of a new project the calculated fuel pressure defines the configuration
of the fuel gas supply system. This can, for example, have impact on the decision on whether or not a
fuel gas compressor will be needed, or if pre-heating of the gas can be applied. During the design of
gas turbines a sufficiently accurate fuel gas pressure calculation can help in the definition of hardware
modifications.
The motivation behind this thesis is a contribution to the continuous development of Alstom’s latest
heavy-duty gas turbine GT26 in pursuit of optimising its operation. This engine is equipped with high
performance, low emissions combustion technology that aims to deliver improved levels of
performance and efficiency at a competitive emissions level (NOx, CO and UHC1). One of the key
elements of the combustor part of the GT26 is a new generation of combustion hardware, the staged
premix combustor. For gas turbines in general it is difficult to achieve low emissions over the entire
load range. In burner hardware based on the staged combustion concept, the fuel is injected in two or
more steps. By varying the so-called stage ratio, the ratio of fuel injected in one of the stages over the
total fuel mass flow, it is possible to reach lower levels of NOx through control of the flame
1 Unburned hydrocarbons
2
temperature and the combustion efficiency. The GT26 has two fuel injection lines, which are
permanently in operation. During the starting of the gas turbine a large quantity of the fuel gas mass
flow is being distributed through one of the fuel gas lines, which leads to critical flow conditions in this
supply line.
1.2 Objectives
This master thesis focuses on the fuel gas pressure requirement of the GT26, taking all of the above-
mentioned influences into account. The key challenge is the critical flow conditions during start-up
which will lead to the generation of a new set of equations compared to the current fuel pressure
prediction tool.
Due to new market demands high accuracy of the predicted fuel pressure requirement is not only
needed at base load, but over the entire load range. Another motivation is a new operation mode of
the engine, known as the sliding operation concept, where the load is a function of the available fuel
gas supply pressure. This prevents a plant shut down during times of low fuel gas pressure.
1.3 Limitations of this thesis
The experiments lie outside the scope of this thesis, though experimental data is the base for the
computational work.
1.4 Method
For this task a literature study has been made. Based on experimental data different models have
been tested and evaluated. Most work has been carried out in Excel. Programming has been done in
the program Visual Basic.
3
2 Elementary gas turbine theory One of the most efficient cycles for conversion of thermal energy to mechanical energy, on which gas
turbines operate, is the Brayton cycle2. The essential components of such a cycle are the compressor,
the combustion chamber and the turbine. The heat is supplied and rejected from the cycle at constant
pressure, therefore this cycle is also known as constant pressure cycle (Figure 1).
Figure 1. Enthalpy-entropy diagram for the ideal Brayton cycle.
The thermal efficiency of this cycle is, making the assumption that the working gas is perfect, is given
in eq. (1) [13].
23
141TT
TT
−−−=η
(1)
If the compression and expansion are considered isentropic, the following relation between pressure
ratio r and the cycle temperatures may be used to find the efficiency from eq. (1) as a function of only
pressure ratio and as presented in eq. (3) [13].
4
3/)1(
1
2
T
Tr
T
T == − γγ
(2)
γγ
η/)1(
11
−
−=r
(3)
2 This thermodynamic cycle was first proposed by George Brayton in 1870. It is also known as the
Joule cycle.
4
The work output
)()( 1243 TTCTTCW pp −−−= (4)
will increase with increasing turbine inlet temperature. This is limited by metallurgical limits as well as
restrictions of emissions.
The pressure of the fuel supplied to the gas turbine should be greater than the post compressor
pressure. A pressure difference is needed in order of creating the flow of the fuel into the burner. This
flow has to be high enough to assure sufficient mixing of air and fuel, which avoids high emissions,
and to move the flame away from the burner. Pressure losses are created in filters, valves, piping
etcetera. Sometimes the available onsite fuel gas pressure is sufficiently high. In other cases a fuel
gas compressor is required.
5
3 Description of the ALSTOM gas turbine GT26
3.1 Combustor operation concept and burner hardware configuration
The ALSTOM GT26 gas turbine (Figure 2, Table 1) is a sequential combustion turbine for the 50Hz
market. The advantage of a sequential combustion cycle (Figure 3) is an increased work output
without an increase in turbine inlet temperature, which raises emission levels.
Table 1. Technical data of the GT26 at base load condition. [1]
Load output 240 MW
Efficiency 38.2 %
Compressor ratio 30 -
Exhaust mass flow 545 Kg/s
Exhaust temperature 610 °C
Shaft speed 3000 Rpm
NOx emissions <15 ppm
Number of compressor stages 22 -
Number of turbine stages 5 -
Number of EV burners 26 -
Number of SEV burners 26 -
Figure 2. Cross-section of the GT26, with indication of its main components.
1) EV burner, 2) EV combustor, 3) SEV lance, 4) SEV combustor. [1]
6
Figure 3. Enthalpy-entropy diagram for a reheat cycle
The sequential combustion is split into an EV and a SEV combustor. The compressed air from the
combustor is heated up in the first combustion chamber, the EV combustor. EV is an abbreviation for
environmental vortex. These burners have the benefit of low NOx emission. The air expands through
the first turbine stage and is then led to the second combustion chamber, the SEV, or sequential
environmental vortex, combustor. The remaining fuel is added and the air-fuel mixture self-ignited.
Once again the turbine inlet temperature reaches its maximum before the gas expands through the
four-stage low-pressure turbine.
The 26 EV burners are placed in an annular arrangement. They are dual burner, meaning that they
can operate on both liquid and gaseous fuels. They have the shape of two half cones placed offset
sideways so that two slots are formed along the sides (Figure 4). It is through these gaps that the
combustion air enters.
Figure 4. The shape of the burner can be described as two half-cones slightly offset sideways in a way that the two gaps between the half-cones function as inlets for the combustion air. In the centre of the burner the pilot lance is located [9].
7
The lance, named LoLa8.53, is located in the centre of the burner. It has four fuel injection nozzles on
its cylindrical surface. The nozzle for oil operation is located at the end of the lance.
With the staged premix combustion concept the fuel gas enters the burners in two stages. Stage one
refers to the fuel lance, located in the centre of the burner. This stage is referred to as pilot. Stage two
refers to holes located in the surface of the burner where premixed air and fuel enters (Figure 5). This
stage is referred to as premix. According to the operation concept of the gas turbine GT26 both stages
are in continuous operation from ignition to base load. The load of the engine is directly linked to the
stage one ratio, which is the ratio of stage one fuel gas mass flow over total gas mass flow. Since one
of the drawbacks of lean premixed combustion is propensity to combustion instabilities, such as lean
blow out and pulsations, the stage one ratio is adjusted as to avoid these phenomena. Combustion
pulsations are caused by variations in pressure and the heat release rate [10]. It is of great importance
to avoid pulsations, as they shorten the lifetime of the hardware. Lean blow out refers to the loss of
flame that occurs when the fuel/air ratio is either too small to sustain combustion.
Figure 5. Cross-section view of the EV burner and lance: the two-stage concept [11].
Figure 6. Position of EV lance and EV burner [2].
3 LoLa stands for Long Lance.
8
3.2 Fuel gas system
The total fuel gas system stretches from the pipeline to the burners and includes piping and various
components. The configuration of the fuel gas system varies depending on site-specific conditions,
such as available minimum fuel gas supply pressure and ambient temperature and may or may not
include the components shown in Figure 7, such as pre-heaters and fuel gas compressors. The
pressure calculated by the pressure prediction tool is the pressure upstream of the strainer.
Figure 7. Schematic overview of the fuel gas supply system
9
4 Fuel gas pressure prediction
4.1 Necessity of accurate gas pressure prediction
It is essential at design, offering and execution of a power plant to be able to accurately predict the
fuel gas pressure. At the design phase, accurate fuel pressure calculation is indispensable. New
hardware must be validated to confirm that the required fuel pressure does not exceed the defined
limits. At the offering of a project input parameters are collected including available fuel gas pressure
on site, available gas temperature at boundary limit of the plant, fuel gas composition, minimal and
maximal ambient temperature. Data for the performance of the engine, for example the combustor
pressures and fuel mass flows, is calculated based on the collected input parameters. The required
fuel gas pressure is then calculated and the set-up of the fuel gas system can be determined. During
the execution of a power plant some data might need revision and the fuel gas pressure calculation
then needs to be repeated.
An accurate and valid fuel gas pressure requirement avoids any over- or undersized installation of fuel
gas compressors, which is a key risk to the sales of gas turbines. In average, gas compressors require
an investment of 2.3 M€, as well as an auxiliary power consumption of 1.5 MW. [7]
4.2 Pressure drop calculations
For the pressure drop calculations the assumption is made that the gas is ideal and the cooling of the
air through throttling, known as Joule-Thompson effect [14], is neglected. Bernoulli’s equation yields
that the total hydraulic head is constant along any streamline:
constant2
1 2 =++ pgzwp ρ (5)
or, with subscript 1 and 2 identifying conditions upstream and downstream respectively:
22
2
2211
2
112
1
2
1gzpwpgzpwp ++=++ ρρ (6)
Expressing the velocity in mass flow and neglecting the last term gives
ρρ 2
2
22
2
12
1
2
1
A
mp
A
mp
&&+=+
(7)
By adding the corrective flow number and defining the density by the pressure upstream, Bernoulli’s
equation takes the following form.
ζ⋅⋅⋅=∆2
2.
12
1
A
m
p
RTp
(8)
The fuel pressure is predicted by calculating in counter flow direction, starting from the combustion
chamber pressure and subtracting pressure losses along the line. [6]
10
For calculation of the pressure loss over a component eq. (8) is rewritten according to the following
steps to remove dependence of p1 on the right-hand side.
2
22
22
2
2
2212
1
2
1
2
1
+
⋅=
+−⋅
pA
mRTppppζ
(9)
2
22
22
212
1
2
1
2
1
+
⋅=
−⋅
pA
mRTppζ
(10)
2
2
22
2
2212
1
2
1
2
1
2
1
2
1pp
AmRTppp −
+
⋅=−−
⋅ ζ
(11)
2
2
22
2
2
12
2
1pp
AmRTp −+
⋅=∆
⋅ ζ
(12)
or, with the denotation of the flow number Kv:
})4{(5.0 2
5.0
2
2
2 pTRK
mpp
v
−⋅⋅
⋅+⋅=∆
⋅
(13)
Numerical values of and the cross section area are given for each component. Over the piping the
mass flow’s dependence of is negligible. [5] It is assumed that the piping pressure loss coefficient
is constant and equal to 0.02. The elbow number is equal to 0.3. The piping pressure loss coefficient
is calculated according to the following equation: [4]
elbow
piping
piping
elbowelbow
piping
pipingn
d
Ln
d
L⋅+⋅=⋅+⋅= 3.002.0ζλζ
( 14 )
For the control valves the pressure drop is calculated as a fraction of the absolute downstream
pressure, which is equal to the minimum pressure drop that ensures a reproducible and stable mass
flow. [12]
4.2.1 Critical flow
A pressure difference between a backpressure, pi and a receiver pressure pa, generates a flow. The
flow is compressible when the compressibility of the fluid must be taken into account. This is usually
the case when the flow is critical, i.e. the Mach number4 is equal to, or exceeds, one.
The equation of continuity [15] states that
awAm ρ⋅⋅=.
(15)
For ideal fluids a reversible, adiabatic process, which is isentropic, obeys eq. (16) below.
4 The Mach number is the ratio of the speed of the fluid to the speed of sound in the medium in case.
11
=
⋅γ
ρa
ap1
Constant
γ
ρρ/1
=⇒i
a
iap
p
(16)
In a flow through an orifice there is a pressure ratio at which the velocity reaches the speed of sound,
in other words, becomes critical. [15]
1
0 1
2 −∗
+=
γγ
γp
p
(17)
If this pressure ratio decreases below its critical value the velocity does not increase further and the
flow is said to be choked. However, it should be stressed that it is only the velocity that is choked and
constant. The mass flow, which according to eq. (15) is a function of velocity as well as density and
orifice area, is still allowed to increase as pi increases. It will, in other words increase linearly with pi,
even with pressure ratios below the critical one. The flow will also increase linearly with increase of the
area, which should be considered if critical flow occurs by a valve. For the case of the fuel lance, the
critical flow occurs at the injection holes, which lead gas to the burner to the burner. The area of these
holes is constant. The receiver pressure, which is the combustion pressure, is changing, which is why
the mass flow may increase even after the velocity of the gas reaches its critical value. It is critical flow
effects that make the old pressure obsolete.
4.3 Prediction of fuel pressure drop over the pilot lance
For prediction of the pressure drop over the fuel lance a more detailed study is needed. The
motivation for selecting a new algorithm is that the current Alstom model is unable to predict the fuel
pressure for both under and over-critical flow. The old model may be fitted as to predict critical flow or
to predict under critical flow, but cannot be fitted in a way as to work for both flow conditions. This is
not required for older hardware, since the flow is under-critical for the entire load range. The flow
through the fuel lance named LoLa8.5 is, however, critical under idle operation5.
4.3.1 Data normalization and selection
The evaluation of the different models is based on engine tests from the Alstom test facilities in Birr,
Switzerland and from tests performed at atmospheric conditions with air as fluid rather than fuel gas. A
selection of data is needed in order to remove unreliable data from the evaluation. It is difficult to
select the data based on a plot of pressure drop over mass flow, since the pressure drop is also
influenced by combustion pressure, fuel gas temperature and gas constant (Figure 8). By normalizing
the data to these factors, according to eq. (18) presented below, all the data sets can be compared in
one plot, and the selection process is simplified.
5 Idle is the operation mode when the gas turbine only produces enough power to spin itself around.
12
=
⋅⋅∆
combfgcomb p
mf
RTp
p.
(18)
The data that does not follow function f is considered unreliable and is not used in the evaluation. As
can be seen in Figure 9, two test runs from Birr, numbered 571 and 577, are therefore excluded. In
these two test runs, unlike in the others, modular lances were used. These have been subjected to
various modifications, such as closing of old injection nozzles and drilling of new nozzles. These
lances appear to have a different behaviour. Some individual data points were also excluded. Five test
engine test runs and twenty-five atmospheric test runs were selected for the evaluation. This is a very
good base for the evaluation. The data covers the entire load range and amount to about 3000
measurements.
Figure 8. Experimental data
13
0
0.002
0.004
0.006
0.008
0.01
0.012
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
m'/pcomb
delt
ap
/(p
co
mb
*T*R
) 699
587su
571
584
585
577
587
atmospheric tests
Figure 9. Normalized experimental data
14
4.3.2 Kv-model
4.3.2.1 Constant kv*
The present, for Alstom internal, algorithm for calculation treats the lance as a pure flow resistor,
similar to a valve.
The pressure drop as a function of fuel flow is in that case given by [5]:
2
2
2
2
2 m 2
1
AV
2
A w
2 p
⋅=
⋅==∆ ζζζ
(19)
Substituting the gas density in eq. (19) results in:
2
1
1
221 m 2p
T R
Ap-p p
•==∆ ζ
(20)
To remove the ambiguity in the selection of the area A, it is more common to use the flow number KV,
which is defined as the volume flow of water through the flow resistor at a pressure drop over the flow
resistor of 1 [3]. Inserting Kv as volume flow in eq. (20) results in:
2
V2 K
2
Abar 1 ∆p == with ρ = ρwater = 1 kg/dm
3 (21)
The flow resistance number and flow area A can thus be converted into the Kv-number, which is no
longer dimensionless, but has by definition the dimension of a volume flow [m3/s]. Conversion can be
obtained from eq. (21) as follows:
2
2
2v
32v
2 s
m
K
200
1000kg/m K
2bar
A=
⋅= (22)
A 2
10K v = (23)
When the area A is inserted in [m
2], eq. (23) directly gives the Kv-value in [m
3/s].
The pressure drop as a function of mass flow and Kv can be derived from eq. (22) and (23).
2
2
2
v
2
s
m100
K
m p ⋅=∆
•
(24)
The mass flow as function of Kv is therefore:
0.1s/m pKm v ⋅∆=⋅
(25)
15
Within Alstom another convention, which omits the conversion factor 0.1s/m, is used. The flow number
is based on the following equation for the mass flow:
pkm *
v ∆=⋅
(26)
and will here be denoted as kV*. It can be simply converted to Kv:
kV*
= 0.1 Kv s/m (27)
The flow number kV*
has the unit [m2], which can also be expressed as [kg/s/((N/m
2)*kg/m
3))
1/2] to
reflect the units, which are usually inserted in eq. (26).
For the use of flow numbers it is crucial to distinguish between the two definitions, since there is a
factor of 10 difference in-between. Which definition applies, can be easily read by the unit: Kv has the
unit of a volume flow, like [m3/s] and eq. (25) applies; kV
* has the unit [m
2] and eq. (26) applies. kV
* is
also referred to as flow number “FN” and may have different units, all based consistently on eq. (26).
4.3.2.2 kv* dependency of critical flow effects
In Figure 8 the experimental data, plotted as pressure loss over fuel gas mass flow, forms two
branches. A closer examination shows that the upper branch can be said to represent the pressure
loss at over-critical flow and the lower branch can be said to represent the pressure loss at under-
critical flow. This suggests that a model that takes into consideration critical flow effects would offer a
better accuracy. A modified kv model, with separate hardware parameters for critical and non-critical
flow could be a solution. The switch-over between critical and non-critical flow is determined by the
critical pressure ratio, given in eq. (28).
1
0 1
2 −∗
+=
γγ
γp
p
(28)
p* is the back pressure and p0 is the stagnation pressure upstream. If the assumption is made that the
stagnation pressure equals the total pressure, the flow is said to be critical when the ratio
fg
comb
p
p is
smaller than the critical pressure ratio. This criterion is however not adequate for the calculation
process since the fuel gas pressure, pfg, is the output of the calculation and is not initially available. By
plotting the combustor pressure against fuel gas mass flow and indicating where the flow is critical, a
clear limit of critical flow can be seen in Figure 10. Thus these two parameters may serve as a critical
flow condition.
16
0
5
10
15
20
25
30
35
0 1 2 3 4 5
fuel gas mass flow [kg/s]
co
mb
us
tor
pre
ss
ure
[b
ar]
non-critical
critical
Figure 10. Combustor pressure versus fuel gas mass flow with indication of critical flow.
Using experimental data, a limit is found above which the flow is critical (Figure 11). It is found that the
limit above which the flow is critical is:
0.1588
.
>comb
fg
p
mkg/s/bar
(29)
Figure 11. Combustion pressure versus the ratio mass flow combustion pressure
The pressure drop over the lance is calculated according to the equations presented below.
17
0.1588
.
>comb
fg
p
m =>
−
+=−
•
comb
critv
combcombfg pRTk
mppp
2
*
_
2 42
1
(30)
0.1588
.
<comb
fg
p
m =>
−
+=−
−
•
comb
critnonv
combcombfg pRTk
mppp
2
*
_
2 42
1
(31)
This model has been programmed in Visual Basic and the code may be found in Appendix A.
18
4.3.3 Outflow Model
4.3.3.1 Constant µ
The fuel pressure drop over the lance can be calculated as being a pressure drop due to only the
discharge through the nozzles. The fuel mass flow is determined according to eq. (32) by the size of
the outflow holes, i.e. the area Aa, and the pressure drop inside the lance, which is pf - pi. If this
pressure drop is neglected in a first approximation, the fuel mass flow as a function of inlet and outlet
pressure can be described by an outflow function for a compressible gas according to ref [3]:
)p,(p p 2 Am 211aµ=•
(32)
The outflow coefficient µ is used to characterise the reduction of the geometric nozzle area to an
effective area, defined as
Aeff = µ Aa (33)
is calculated according to the equation below for non-critical flow.
( )
−
=
+γ
γγ
γγ
1
1
2
2
1
2ia
p
p
p
p
1- )p,(p
(34)
and the gas density is calculated according to the ideal gas law.
1
1
RT
p= (35)
When the flow becomes critical the flow chokes, i.e. the velocity does not increase with decreasing
pressure ratio. is then constant and calculated according to eq. (36).
( ) 1-1
2
1
1
γγ
γγ −
+
=
(36)
Substituting the gas density in (36) results in:
RT
2p Am
i
iaµ=•
(37)
The effective area, in eq. (33) is specified for Alstom lances [8] and must be met by the supplier. This
specified area should be lower than the geometric area for gas fuel path of the standard EV fuel lance,
reflecting a significant pressure loss before or close to the exit. This pressure loss is reflected by a
rather low discharge coefficient (µ = 0.6). This coefficient is usually not smaller than 0.8 for cylindrical
exit hole types, like those of the EV fuel lance [3]. Thus an existing pressure drop upstream of the
outflow nozzle is included in that coefficient to describe the complete fuel lance. The outflow function
according to eq. (37) will therefore not necessarily be the best-possible description for the pressure
drop as function of mass flow.
19
4.3.3.2 µ as a function of pressure ratio
In most literature the effective area and thus µ are considered to be constant. This assumption may be
questioned. As the flow changes due to changed pressure ratio it is reasonable to believe that also the
effective area changes due to the changes in separation of the flow (Figure 12).
Figure 12. Effective areas for different flows
By plotting µ as a function of pressure ratio according to eq. (37), (34) and (36) this hypothesis is
strengthened. µ could be described as a polynomial of first degree, or one could consider a piecewise
function, where µ is described by an exponential function at one interval and then by a polynomial of
first degree. This hypothesis was not further evaluated in this master thesis, as it was discarded due to
its complexity.
Figure 13. with indication of how it may be approximated by a piecewice function of pressure ratio.
20
4.3.4 Two-Stage Model
nozzle exit
with area Aa
flow resisitor with
area Ar and
resistance value ζ
pf Tf pi Ti pa Ta
Figure 14. A schematic view of the fuel lance
A more advanced description of the mass flow through an EV fuel lance can be obtained by combining
the flow resistance, eq. (26), and outflow function, eq. (37). In such a calculation, a part of the
pressure drop in the lance is attributed to the flow resistance upstream the nozzle (Figure 14). After
subtraction of this pressure drop, the mass flow can be obtained by the outflow function (37). The
pressure pi for this calculation is no longer the fuel supply pressure at the interface of the fuel
distribution system (henceforth in this master thesis denoted FDS) and the EV lance, but the
calculated value after the pressure drop inside the lance. This approach can be handled
mathematically by a backwards calculation of the pressure pi based on the combustion pressure and
the fuel mass flow. This calculation can be done analytically by inverting the outflow function. Inserting
eq. (36) into eq. (37) and isolating terms of pI, one obtains the following equation:
γγ
γγ
γµκ
−−
−
=−122
22)(2
)1(
a
i
a
i
ap
p
p
p
pA
RTm& (38)
The left-hand side completely without dependence on pI, one can solve for pI by use of a symbolic
algebra solver, such as Mathematica. Doing this and selecting the physically meaningful root, one
finds the pressure, pI, upstream of the fuel nozzle as a function of the mass flow to be:
( ) a
a
a
ai p
pA
RTm
pA
RTm
pmp
γγ
γγ
γµγ
γµγ +−
−
−
−
−++−=
1
22
2
22
2
1
)(2
1
)(2
)1(411
2),(&
&
& (39)
After pi is calculated with eq. (39), the fuel gas supply pressure pf in Figure 15 can be calculated by the
following backwards calculation formula (37) and (24), which are based on the flow resistance eq. (21)
and eq. (26), respectively. Note that now, because of the two-stage approach, pf is the inlet pressure
and pi is the outlet pressure after the flow resistor. In the one stage model pf was the inlet pressure
and pa the outlet pressure.
21
−
+=−
•
iiif pRTA
mppp
2
24
2
1 ζ
(40)
−
+=−
•
i
v
iif pRTk
mppp
2
*
24
2
1
(41)
The pressure drop inside the lance is then described by an additional ζ- or kv*- value.
For all the versions of the two-stage models presented here, the pressure drop is calculated
separately for the piping upstream the control valve, the FDS and the lance itself. Only the pressure
loss over the lance is calculated with the two-stage model. The pressure loss for the piping and the
fuel distribution system are calculated according to eq. (10) and eq. (26).
4.3.4.1 Constant hardware parameters, kv* and
In its most simple form the two stage model has two constant parameters, kv*and .
4.3.4.2 kv* dependency of critical flow effects Just as for the kv-model it can be suggested that the two-stage model would benefit from having
separate kv*-values for critical and non-critical flow.
4.3.4.3 kv* dependency on Reynolds number
A function can be derived using fluid mechanics equations that give the kv*-value as a function of the
Reynolds number. The geometry of the lance is simplified so that the cross-section is considered
constant over its entire length. For an annular cross-section the pressure drop is calculated according
to eq.(42) [3].
2
25.1
2w
s
lp ⋅⋅
+
⋅⋅=∆ ρλ
(42)
is a function of the Reynolds number and flow regime. [3] The flow through the lance is considered
always to be fully turbulent.
41
Re
427,0=λ
(43)
22
By combining eq. (26), eq. (42) and eq. (43), kv* as a function of the Reynolds number can be derived.
2
2
2
2.
.
*
5.12
4
combcomb
v
ppA
m
s
l
RTmk
−
+
+⋅
=
ρλ
(44)
4.3.4.4 kv* dependency on Reynolds number and itemized lance component pressure losses
A more detailed and more physically accurate model of the lance takes into consideration that the
cross-section of the lance is not the same over its entire length. The part upstream the outlet has an
annular cross-section. Upstream this part the geometry of the lance may be approximated as a hollow,
circular cross-section.
Figure 15. Schematic view of the lance with two flow resistors.
The kv*-value for the channel part of the lance is given by eq. (44). The pressure drop over the hollow
part is given by eq. (45) below. [3]
2
2w
d
lp ⋅⋅⋅=∆ ρλ (45)
A first intermediate pressure pi1 is calculated according to the two stage model with the kv*-value as a
function of the Reynolds number according to eq. (44). A second intermediate pressure is calculated
according to eq. (45). Hydraulically smooth surfaces are assumed throughout.
23
4.3.5 Polynomial
By using the same function that was used for the selection of the data, eq. (18), a polynomial can be
fitted, using the least square’s method. This is a highly unphysical model, and should only be
considered as a last approach to achieve desired accuracy.
4.3.5.1 2nd-order
A second order polynomial has the benefit of few extra parameters. It should also be noted that kv*, is
a parabolic function, so there exists a possibility of finding a physical interpretation of the parameters
a, b and c.
2
⋅++=
⋅⋅
combcomb p
mc
p
mbaf
(46)
4.3.5.2 Higher order
For higher order polynomials no physical interpretation of the parameters can be found. The accuracy
can however be improved. A fourth order polynomial has been evaluated.
432
⋅+
⋅+
⋅++=
⋅⋅⋅⋅
combcombcombcomb p
me
p
md
p
mc
p
mbaf
(47)
24
4.4 Evaluation
The models are ranked on a scale from 1 to 5 for three factors: accuracy, simplicity and physicality.
These ratings are presented in radar charts with three axes for the three criteria. The ranking is
visualised in radar chart, see Figure 16 below. The triangular area that is formed in this calculated and
may serve as a measurement of each model’s appropriateness (Table 3).
0
1
2
3
4
5
physicality
simplicityaccuracy
Figure 16. Example of radar chart with the decision criteria on the three axes.
The area formed by the rating may serve as a measurement of the model’s appropriateness.
The accuracy ranking is estimated by calculating the maximum absolute deviation from measured
data at idle operation and at base load. The parameters for each model, with exception of the
polynomial model, have been fitted as to minimize the sum of absolute deviation from measured data
at idle and at base load. These two points in the load range were chosen since this is where the
pressure requirement is the highest. The fitting is not done as to minimize the maximum error,
because of the unreliability of the data.
The simplicity is ranked based on the numbers of parameters and the complexity of the calculation
process.
The ranking of the physicality gives an indication on how reasonable each model is in a physical
sense. This might seem as a secondary criterion, but is important for calculation of the uncertainty of
the estimated pressure.
The errors of the prediction of the models are presented in Table 2. In Table 3 the ranking of the
models for physicality, accuracy and simplicity is presented along with the calculated area of the chart.
25
Table 2. Maximum deviation from measured data at idle and at base load operation [bar] base load Idle
Kv 2.01 1.46
Kv, critical/non-critical 0.33 1.53
Outflow 3.97 2.33
Two-stage, 2 constant parameters 0.83 1.79
Two-stage, critical/non-critical 0.44 1.81
Two-stage, kv=f(Re) 4.40 2.75
Two-stage, kv=f(Re), itemized lance losses 3.61 2.20
Polynomial 2nd
order 1.39 3.71
Polynomial 4th order 0.42 1.87
Table 3. Models ranked for accuracy, simplicity and physicality
26
4.4.1 Kv-model with constant kv*
kv*=0.000432
0.000
5.000
10.000
15.000
20.000
25.000
30.000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
mass flow [kg/s]
de
lta
p [
ba
r]
kv
delta p
Figure 17. Measured pressure drop over fuel gas mass flow and calculated pressure drop according to the kv-model with one kv*-value.
Figure 18. Measured pressure requirement over load and estimated pressure requirement by the kv-model with one kv*-value.
kv* * 24 burners= 0.00049276
0
5
10
15
20
25
30
35
40
45
50
0 50 100 150 200 250 300 350
load [MW]
p a
fter
CV
[b
ar]
measured pressure requirement
pressure requirement estimatedby Kv- model wit separate Kvs forunder- and over-critical flow
27
Figure 19. Radar chart for kv-model
4.4.2 Kv-model with separate kv*-values for under- and over-critical flow
Figure 20. Measured pressure drop over fuel gas mass flow and calculated pressure drop according to the kv-model with separate kv*-values for under- and over-critical flow.
28
kv*crit= 0.0004488, kv* non-crit= 0.0004928
0
5
10
15
20
25
30
35
40
45
50
0 50 100 150 200 250 300 350
load [MW]
p a
fter
CV
[b
ar]
measured pressurerequirement
pressure requirementestimated by Kv- model witseparate Kvs for under- andover-critical flow
Figure 21. Measured pressure requirement over fuel gas mass flow and the pressure requirement estimated by the kv-model with separate kv*-values for under- and over-critical flow.
Figure 22. Radar chart for the kv-model with separate kv*-values for under- and over-critical flow.
29
4.4.3 Outflow model
Figure 23. Measured pressure requirement over load and estimated pressure requirement by the outflow model.
Figure 24. Radar chart for the outflow model.
30
4.4.4 Two-stage model with constant kv* and
It should be noted that for the best fitting of the two-stage model with two constant parameters, is
greater than one. This is according to the definition of , not possible and contributes to a low rating in
the physicality criteria.
Figure 25. Measured pressure requirement over load and estimated pressure requirement by the two-stage model with two constant hardware parameters.
0
1
2
3
4
5
physicality
simplicityaccuracy
Figure 26. Radar chart for the two-stage model with two constant hardware parameters.
31
4.4.5 Two-stage model with separate kv*-values for under- and over-critical flow
Figure 27. Measured pressure requirement over load and estimated pressure requirement by the two-stage model with separate kv*-values for under- and over-critical flow.
Figure 28. Radar chart for the two-stage model with separate kv*-values for under- and over-critical flow
32
4.4.6 Two-stage model with kv* as a function of the Reynolds number
Figure 29. Measured pressure requirement over load and estimated pressure requirement by the two-stage model with kv* as a function of the Reynolds number.
Figure 30. Radar chart for the two-stage model with kv* as a function of the Reynolds number
33
4.4.7 Two-stage model with kv* as a function of the Reynolds number and itemized pressure losses over the lance
Figure 31. Measured pressure requirement over load and estimated pressure requirement by the two-stage model with kv*-value as a function of the Reynolds number.
0
1
2
3
4
5physicality
simplicityaccuracy
Figure 32 Radar chart for the two-stage model with kv*-value as a function of the Reynolds number
34
4.4.8 Polynomial of 2nd order
Figure 33. Measured pressure drop over fuel gas mass flow and pressure drop estimated by the 2nd
order polynomial model.
0
1
2
3
4
5physicality
simplicityaccuracy
Figure 34. Radar chart for the 2nd
order polynomial model
35
4.4.9 Polynomial of 4th order
Figure 35. Measured pressure drop over fuel gas mass flow and pressure drop estimated by the 4th
order polynomial model.
0
1
2
3
4
5physicality
simplicityaccuracy
Figure 36. Radar chart for the 4th order polynomial model
36
4.5 Effects of dilution
Based on high pressure tests and evaluation was made with the aim to see if the effect of dilution
would have an impact of the accuracy of the model. Two different gases were tested. A low quality
gas, referred to as L-gas, with a lower heating value of 40.7 MJ/kg and a high quality gas, H-gas, with
a lower heating value of 49.9 MJ/kg. As is showed in Figure 37, the accuracy is not affected
significantly.
Figure 37. Measured and predicted fuel pressures for diluted fuel gases.
37
5 Boundary conditions for the fuel lance LoLa8.5
One application of an accurate fuel pressure prediction software tool is to find limits for the operation
of the burner hardware. A burner operation concept is defined which defines an interval of stage one
ratio for the load range. Three limits of stage one ratio are given, a nominal limit, a maximum limit and
a minimum limit (Figure 38). These allowable variations are limited by pulsations and lean blow out as
described in chapter 3.1. Another restriction states that the highest fuel gas pressure should occur at
base load as to avoid over dimensioned fuel gas compressors. The fuel gas system has a pressure
limit set to 60 bar. An analysis carried out taking into consideration these criteria further limits the
stage one ratio.
The highest pressure requirement during the load-up of the engine does not occur at maximum stage
one ratio but at the point just before the stage one ratio is switched down to the constant value it
keeps as the engine loads up to base load (Figure 38). This point is denoted as start-up interlock. The
pressure requirement is shown to be the highest at this point and at base load.
The fuel pressure requirements at base load and start-up interlock are calculated and compared. If the
pressure of start-up interlock for the limits of allowable staging ratio defined exceed the pressure
requirement at base load, the limits of allowable stage one ratio are further restricted. This analysis is
carried out for gases of two different heating values, 35MJ/kg and 50MJ/kg.
The worst-case scenario is identified and occurs when the ambient temperature is lowest
(-15°C) and the lower heating value is 35MJ/kg. This case sets the limits of the operation.
Figure 38. Fuel Gas Pressure Requirement for EV at fuel gas block entry
(LHV=35MJ/kg, Tamb=-15°C, Tfg =150°C)
35.00
40.00
45.00
50.00
55.00
60.00
65.00
0 50000 100000 150000 200000 250000 300000 350000GT Gross Power [kW]
Fu
el G
as
Pre
ss
ure
Re
qu
ire
me
nt
at
FG
B e
ntr
y
[ba
r]
maximum stage 1 ratio
nominal stage 1 ratio
minimum stage 1 ratio
38
It should be noted that, as can be seen in Figure 38, the highest stage one ratio does not always
correspond to the highest fuel pressure. As illustrated in Figure 39 and Figure 40, there is a point of
stage one ratio at which the highest pressure, or so-called leading pressure, is the pressure in the pilot
line.
Figure 39. Stage one and stage two pressures versus stage one ratio at start-up interlock.
Figure 40. Stage one and stage two pressure as a function of stage one ratio at base load.
The result from this analysis is presented in Figure 41. It is shown that for gases of lower heating
values of 35MJ/kg, the stage ratio at the point of start-up interlock must be lower than the nominal
value presented in the burner operation concept. For higher quality gases (50MJ/kg) the burner can be
operated at nominal stage one ratio at start-up interlock, though never at maximum stage one ratio.
Figure 41. Limit of stage one ratio at the point of start-up interlock for three heating values and three stage one ratio at the point of base load.
Proposed Stage 1 ratio at Start-up Interlock to achieve highest
pressure requirement at baseload conditions
35 50
LHV [MJ/kg]
Sta
ge
1 r
ati
o
MinimumStage 1 ratioat base load
NominalStage 1 ratioat base load
MaximumStage 1 ratioat base load
max
nom
min
39
6 Discussion and conclusions The motivation behind this thesis has been the need for a fuel gas prediction software that can be
used by different departments within Alstom. The key challenge in the development of such a software
was finding the algorithm that predicts the pressure drop over the burner hardware. Various solutions
has been presented in this thesis. The evaluation of these is based on experimental data from engine
tests. The selection of the best-suited model has been carried out using the three decision criteria of
simplicity, accuracy and physicality. It has been shown that the so-called Kv-algorithm is the most
suitable, i.e. the best compromise between the three design criteria. It has been shown that, based on
experimental data that the algorithm also predicts for flow of diluted gases with high accuracy. This is
an important characteristic of the model since there is an increasingly important market in Asia, where
the fuel gas, in general, is of lower is of lower quality.
This new algorithm is required for GT26, the engine in question, since it provides the needed flexibility
to predict pressure drop for both under- and over critical flow. The algorithm may be applied to other
engines with similar burner hardware, in which the flow becomes critical.
One important requirement for the new fuel pressure prediction software is that it offers high accuracy
over the entire load range since many costumers today park the engine at part load. The new
operation mode, known as the sliding operation concept, in which the load is a function of available
fuel gas pressure onsite, also requires accurate fuel pressure prediction over the entire load range.
As an example of application the finalised fuel pressure prediction software was used to find the
boundary conditions for the operation of the burner, in chapter 5. These boundary conditions limit the
operation of the hardware so that over-dimensioned fuel gas compressors are avoided and make sure
that the upper limit of fuel gas pressure of 60 bar is never reached.
As a future application, also within the development phase of the gas turbine, this finalised fuel
pressure prediction tool may be used to investigate how changing the hardware influences the fuel
pressure requirement.
40
References
[1] GT24/26 Gas Turbine – The solution for deregulated and merchant markets, 2002
[2] J. Duckers, GT26xx.x Part Specification: EV lance and burner, HTCT607909 Rev. A, 2004
[3] W. Bohl, Technische Stömungslehre, Vogel-Verlag, Würzburg 2002
[4] Z. Jurjevic, GT24/26 - Standard Gas Supply Pressure Requirement - Algorithm and Input Parameters, TN01/517
[5] A. Belzner, Design Rules – Pressure Drop Calculation and Component Sizing in Fuel Gas Supply Systems, HTCT606219, 2000
[6] W. Anderson, GT26xx.x and GT26xx.x with low Dp SEV fuel lance_: Standard Gas Supply Pressure Requirement - Algorithm and Input Parameters, TN04/3277, 2004
[7] W. Anderson, Fuel Pressure Reduction Project (GT26xx.x): Product Requirements Fuel gas calculation tools ‘Gascalc’ and ‘Gascalc_Load’ for GT26xx.x engines, HTCT608145
[8] P. Marlow, General Flow Test Procedure for Burners & Lances, HTCT650443
[9] Rudolf Lachner, Reduction of Stage 2 Fuel Pressure of the Advanced Burner (EV17i Epsilon with Staged LoLa): Investigation at Atmospheric Pressure Conditions, TN04/2185, 2004
[10] S. Tachiban, L. Zimmer, Y. Kurozawa, K. Suzuki,J. Shinjo, Y. Mizobuchi, S. Ogawa, Active control of combustion oscillations in a lean premixed combustor by secondary fuel injection, http://www.turbulence-control.gr.jp/PDF/symposium/FY2004/Tachibana.pdf, 2005-05-15
[11] Susanne Schell, GT26xx.x: Combustor Operation Concept with staged LoLa - status PDR 2004, HTCT607597 Rev. A
[12] GT13E2-Standard Gas Supply Pressure Requirements – Algorithm and Input Parameters, TN03/0991, 2003
[13] Saravanamuttoo, Rogers, Cohen, Gas Turbine Theory, 5th Edition, Pearson, 2001
[14] Çengel, Boles, Thermodynamics – an Engineering Approach, 4th Edition, McGraw Hill, 2002
[15] Duncan, Thom, Young, Mechanics of Fluids, 2nd
Edition, Arnold, 1975
41
Appendix A Calculation of the pressure drop over the lance:
Function dkvcrit(ByVal Temp As Double, ByVal CombPress As Double, ByVal Mass As
Double, ByVal kappa As Double, ByVal R As Double, ByVal KV_non_crit As Double, ByVal
KV_crit As Double) As Double
Dim dp_lance As Double Dim pkrit As Double Dim Psimax As Double
Temp = Temp + 273.15 CombPress = CombPress * 100000
If ((Mass / (CombPress / 100000)) > 0.158778159) Then dp_lance = (0.5 * ((CombPress ^ 2 + 4 * R * Temp * (Mass / KV_crit) ^ 2) ^ 0.5 -
CombPress))
Else dp_lance = (0.5 * ((CombPress ^ 2 + 4 * R * Temp * (Mass / KV_non_crit) ^ 2) ^ 0.5 -
CombPress))
End If dkvcrit = dp_lance / 100000
End Function
Calculation of the pressure drop over the fuel distribution system
Function dpFDS(ByVal Temp As Double, ByVal CombPress As Double, ByVal Mass As
Double, ByVal R As Double, ByVal Kv_FDS As Double) As Double
Temp = Temp + 273.15 CombPress = CombPress * 100000
dpFDS = (0.5 * ((CombPress ^ 2 + 4 * R * Temp * (Mass / Kv_FDS) ^ 2) ^ 0.5 - CombPress))
/ 100000
End Function
Calculation of the pressure drop over the piping after the control valve.
Function dppip(ByVal Temp As Double, ByVal Mass As Double, ByVal R As Double, ByVal
Zheta As Double, ByVal P_pilot_FDS As Double, ByVal Area As Double) As Double
Temp = Temp + 273.15 P_pilot_FDS = P_pilot_FDS * 100000
dppip = (0.5 * ((P_pilot_FDS ^ 2 + 2 * R * Temp * Zheta * (Mass / Area) ^ 2) ^ 0.5 -
P_pilot_FDS)) / 100000
End Function
