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Thermodynamic model of HPeIP leakage and IP turbine efficiency
Jian-qun Xu a, Gang Li a, Ling Li a,*, Ke-yi Zhou a, Yong-feng Shi b
a School of Energy and Environment, Southeast University, Nanjing 210096, Chinab Huadian Electric Power Research Institute, Hangzhou 310030, China
a r t i c l e i n f o
Article history:
Received 25 June 2010
Accepted 14 September 2010
Available online 19 September 2010
Keywords:
Steam turbine
Steam leakage
Temperature variation method
Numerical calculation method
Error analysis
IP turbine efficiency
a b s t r a c t
In this paper, temperature variation method and numerical calculation method are both presented for
the calculation of the HPe
IP steam leakage through midspan packing (N2 packing), which is called N2leakage for short, and an error analysis mathematical model about the impact of measured parameters
error on N2 leakage rate is established. The two methods have been both applied to a 600 MW super-
critical steam turbines N2 leakage rate estimation, and the results show that numerical calculation
method can estimate N2 leakage rate as accurately as temperature variation method, and the chief
parameters which affect the accuracy of N2 leakage rate are hot reheat temperature and IP turbine
exhaust temperature. Taking the leakage from HP turbine exhaust balance piston to IP turbine exhaust
zone (N1 leakage) quantity into account, which has great influence on N2 leakage calculation precision,
combined with N2 leakage, IP turbine efficiency is calculated exactly, and the result indicates that:
Compared to N1 leakage, N2 leakage is the main factor which affects the IP efficiency.
2010 Elsevier Ltd. All rights reserved.
1. Introduction
Steam turbine thermal performance parameters are the
important indexes to evaluate operation states and equipment
performance, among these parameters, turbine efficiency shows
the degree of turbine flow path aerodynamics perfection, and heat
rate expresses the steam turbines capacity of converting heat to
work. To obtain these parameters accurately is important for steam
turbine operation optimization, energy saving and technological
innovation. Generally, combined HPeIP casing steam turbine has
HPeIP leakage (N2 leakage in this paper) [1], which influences the
accuracy of efficiency and other performances, and the definition
can be seen in Fig. 1. For impulse steam turbine, N2 leakage mixes
with the main steam flow behind IP turbine first-stage; for reaction
steam turbine, which has no impeller and balance hole, N2 leakage
mixes with the main steam flow behind the stationary blades of IP
turbine first-stage.N2 leakage causes loss, because it cannot produce work in HP
turbine and stationary blades of IP turbine first-stage [2]. Mean-
while,without being reheated, theleakage will also reduce thecycle
efficiency. If N2 leakage is ignored in the thermal calculation, IP
turbine efficiency and heat rate of the unit will be greater than the
actual value, i.e. the leakage reduces the economy of the steam
turbine unit. As the application of steam seals is the most popular
meansusedin thesteam turbine toreducethe leakage,there is much
researchon its behavior, aiming to increase itsdurability andreduce
the leakage. Tong Seop Kim and Kyu Sang Cha [3] analyzed the
influence of configuration and clearance on the leakage behavior of
labyrinth seals. Jun Li, et al. [4] used the three-dimensional
Reynolds-averaged NaviereStokes (RANS) solutions from CFX to
investigate the leakage flow characteristics in the labyrinth honey-
comb seal of steam turbines. Luis San Andres, et al. [5] proved that
the hybrid brush seal (HBS) was more durable and reliable than
conventional brush seals, and allows reverse shaft rotation without
seal damage, and the result indicated that flow rate measurements
at room temperature 25 C had a leakage reduction of about 36%
compared with a first generation shoed-brush seal.
There are also some calculation methods, when N2 internal
packing is intact and the installation gap is under the limited level,
Martins formula can be applied to N2 leakage rate estimation, and
the result is almost equal to the actual leakage quantity, meetingthe requirements of engineering calculations. However, the seal
teeth are easy towear as the result of rotor deflection and vibration.
In this condition, Martins formula does not work well, with the
coefficient has changed. In addition, it is impossible to install a flow
orifice plate to measure the actual steam leakage quantity.
For some turbines with blowdown valves (BDV), which are
installed on the front of IP section, the N2 leakage quantity can be
calculated by blowdown method [6], and its impact on the effi-
ciency of IP turbine can be analyzed, while it is unfeasible to install
BDV just for this purpose for its high cost and security risks.
Currently, temperature variation method is usually used in the* Corresponding author.
E-mail address: [email protected] (L. Li).
Contents lists available at ScienceDirect
Applied Thermal Engineering
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p t h e r m e n g
1359-4311/$e see front matter 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.applthermaleng.2010.09.011
Applied Thermal Engineering 31 (2011) 311e318
mailto:[email protected]://www.sciencedirect.com/science/journal/13594311http://www.elsevier.com/locate/apthermenghttp://dx.doi.org/10.1016/j.applthermaleng.2010.09.011http://dx.doi.org/10.1016/j.applthermaleng.2010.09.011http://dx.doi.org/10.1016/j.applthermaleng.2010.09.011http://dx.doi.org/10.1016/j.applthermaleng.2010.09.011http://dx.doi.org/10.1016/j.applthermaleng.2010.09.011http://dx.doi.org/10.1016/j.applthermaleng.2010.09.011http://www.elsevier.com/locate/apthermenghttp://www.sciencedirect.com/science/journal/13594311mailto:[email protected]7/28/2019 Thermo Iop Lp
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calculation of N2 leakage [7], Caudill and Griebenow [8] explainedthe principles of the temperature variation method, and Ray Beebe
[9] demonstrated a case of practical application.
However, all the methods mentioned above does not analyze
the influence of the leakage on the IP turbine efficiency effectively,
so the author presented a new calculation method e numerical
calculation method [10], which cannot only calculate the leakage as
exactly as temperature variation method, but also can analyze the
influence of leakage on the IP turbine in detail. In order to improve
this method, the N2 leakage rate error analysis equations as the
further development of numerical calculation method are derived
in this paper.
Aiming to explain the numerical calculation method exactly,
the temperature variation method with its issues in application
and numerical calculation method are both concerned in thispaper. What is more, the impact of measured parameters (such as
pressure, temperature) error on the results of the leakage calcu-
lation is analyzed in detail. As there are N2 leakage and N1
leakage, the measured parameters are not the actual parameters
of IP turbine flow path, and the tested IP turbine efficiency is not
the actual value. In order to calculate the IP turbine efficiency
accurately [11], these two leakages must be taken into account
together. A supercritical 600 MW steam turbine is taken as anexample to illustrate the theory above.
2. Temperature variation method
2.1. Temperature variation method principles
The steam behind HP turbine first-stage leaks into IP turbine
through N2 internal packing actually, there is a little amount of
other steam flow, such as intercalated layer leakage between HP
inside and outside cylinder, and Warren Hopson [12,13] specified
these leakage. Since this paper is not a study on the influence of N2
leakage on steam flow in IP turbine first-stage, rotor cooling and
heat transfer, therefore, it is reasonable to approximately assume
that N2 leakage mixes with hot reheat steam at IP turbine inlet, andthe mixed steam flows through IP turbine flow path.
Several N2 leakage rates are assumed between design value and
maximum value, and IP turbine efficiency is calculated respectively
with each rate. IP turbine inlet parameters are the mixture
parameters, which is mixed by assumed N2 leakage and hot reheat
steam, and the outlet parameters are the IP turbine exhaust
measured parameters.
Nomenclature
Dh enthalpy drop, kJ/kg
x N2 leakage rate, %
hR hot reheat steam enthalpy, kJ/kg
hI HP turbine first-stage outlet enthalpy, kJ/kg
hc IP turbine exhaust enthalpy, kJ/kg
Dht ideal enthalpy drop, kJ/kg
hi IP turbine efficiency, %
Dx variable quantity of N2 leakage rate variation, %
DhI variable quantity of HP turbine first-stage outlet
enthalpy, kJ/kg
Dhc variable quantity of IP turbine exhaust enthalpy, kJ/kg
DhR variable quantity of hot reheat steam enthalpy, kJ/kg
D(Dht) variable quantity of ideal enthalpy drop, kJ/kg
k adiabatic exponent for steam
Rg gas constant for steam, kJ/(kg.K)
DT variable quantity of temperature, K
Dp variable quantity of pressure, MPa
p2 outlet steam pressure, MPa
T2 outlet steam temperature, K
p1 inlet steam pressure, MPa
T1 inlet steam temperature, K
cp specific heat at constant pressure, kJ/(kg.K)
agl N1 leakage quantity, kg
hgp HP turbine exhaust enthalpy, kJ/kg
a4 fourth extraction quantity (to deaerator and feedwater
pump turbine), kJ/kg
hzp enthalpy of steam in crossover pipe, kJ/kg
h4 fourth extraction enthalpy, kJ/kg
Subscripts
I HP turbine first-stage
1 inlet of steam turbine
2 outlet of turbine
Superscripts
0 the parameter is for the second test condition
fourth steam
extraction
Crossover pipe
between IP and LP
HP exhaust balance piston
HP exhaust
check valve
Equilibrium pipe
steam baffle
IP balance piston
Measurement
point
Measurement point of
HP exhaust zone
Measurement point
of IP exhaust
Equilibrium pipe
N2 leakage
N1 leakage
N1 leakage
Fig. 1. N1 leakage and N2 leakage.
J.-q. Xu et al. / Applied Thermal Engineering 31 (2011) 311e318312
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Then the relationship curve between N2 leakage rate and IP
turbine efficiency is depicted, which is named test 1. Corresponding
to the same IP turbine exhaust parameters, the IP turbine efficiency
is higher with the smaller assumed N2 leakage rate, because the
effective enthalpy drop increases, while the ideal enthalpy drop is
near constant. Therefore, N2 leakage rate vs IP turbine efficiency
curveis descending.Theremustbe a point in thecurvewhich means
the actual N2 leakage rate and IP turbine efficiency, but these two
parameters are both unknown, so the solution demands an addi-
tional condition keeping N2 leakage rated and IP turbine efficiency
equal to the test 1, i.e. theflow of HP and IP turbines remains nearly
unchanged in the other operating condition. That is, HP first-stage
pressure, hot reheat steam pressure and IP turbine exhaust pressure
should be almost equal to the corresponding pressure of test 1.
Only the change in main steam temperature or hot reheat steam
temperature satisfies this requirement. Forexample, reducethe hot
reheat steam temperature, then according to the measured IP
turbine exhaust parameters, use the same method mentioned
above, the relationship curve between N2 leakage rate and IP
turbine efficiency, test 2, can be depicted on the same graph with
test 1 curve. As the hot reheat steam temperature decreases, the N2
leakage quantity decreases, and the effective enthalpy drop
increases, but the ideal enthalpy drop increases slightly, thereforethe IP turbine efficiency raises up on a small scale, showing this N2
leakage rate has slight affection on IP turbine efficiency. Therefore,
the slope of test 2 is smaller than that of test 1, and then two curves
have an intersection, which indicates the same IP turbine efficiency
of the two test conditions, and shows the actual IP turbine effi-
ciency and true N2 leakage rate.
2.2. Temperature variation method practical application issues
(1) HP turbine first-stage temperature
Theenthalpy after theHPfirst-stageis used in theN2 leakage rate
calculation process. For the steam turbine unit with nozzle gov-
erning, if the valve position of each nozzle regulator is different,the HP turbine first-stage temperature distribution will be
uneven in the circumferential direction. So it is better to operate
with single valve,nozzle regulators fully open, or twoconditions
with same valveposition. Another advantageof doingso is that, if
HP turbine first-stage temperature measuring point is out of
control, the HP turbine first-stage steam temperature can be
calculated according to estimated stage efficiency, with the
systematic errors under the extent permitted.
(2) Temperature variation Extent and test load
As shown in Fig. 2, the angle between the two curves will be
smaller if the temperature difference between the two test
conditions is smaller. Then, even a small error of measured
parameters can lead to a larger error on the test results. As it isthe major problem that needs to be avoided, the two test
conditions temperature change should be as great as possible,
increasing the angle and IP turbine efficiency difference
produced by N2 leakage, and improving the N2 leakage test
accuracy. In N2 leakage test, there are several means to regulate
the steam temperature, among them, swing burner and regu-
lating gas baffle opening degree are the key means. In addition,
test load should be under the full capacity, for the boiler could
have enough room to regulate. At present, the recommended
temperature change range of the two tests is 30 e41.7 C.
(3) Tests stability
If the measured parameters of the two tests have the same
direction deviations and the amounts are similar, N2 leakage
rate will change slightly, or, N2 leakage rate will change greatly,
namely, the major factor that impacts N2 leakage rate is the
deviation direction of measured parameters of the two test
conditions.
3. Numerical calculation method
3.1. Numerical calculation method principles
Approximately, considering N2 leakage mixes with hot reheat
steam before IP turbine first-stage, the parameters of mixed steam
as IP turbine inlet parameters and the parameters of IP turbine
exhaust as outlet parameters as demonstrated [10], the actual
enthalpy drop Dh of steam in IP turbine is:
Dh xhI hc hR hc
1 x (1)
The IP turbine efficiency hi is:
hi xhI hc hR hc
Dht1 x(2)
where, x is the N2 leakage rate(N2 leakage quantity/IP turbine
admission quantity), hR is the hot reheat steam enthalpy, hI is the
HP turbine first-stage outlet enthalpy, hc is the IP turbine exhaust
enthalpy, Dht is the ideal enthalpy drop of the mixture of N2
leakage and hot reheat steam.
N2 leakage rate and IP turbine efficiency are both unknown in
equation (2), therefore, to gain simultaneous solution needs
another equation. In the condition that main steam temperature or
hot reheat steam temperature changed and the other parametersunchanged, N2 leakage and IP turbine efficiency are nearly
constant, for main steam flow and reheat steam flow unchanged
and pressure before and after separation seal and pressure before
each stage unchanged. Therefore, change main steam temperature
and hot reheat steam temperature, keep N2 leakage rate and IP
turbine efficiency unchanged, so another operation condition and
another IP turbine efficiency equation can be obtained:
hi x
h0I h0c
h0R h0c
Dh0t1 x
(3)
The superscript 0indicates that the parameter is for the second
test condition. Substitute equation (2) into equation (3) and elim-
inate hi, then N2 leakage rate x can be acquired.
0.89
0.895
0.9
0.905
0.91
0.915
0.92
0.925
0 0.01 0.02 0.03 0.04 0.05 0.06
N2 leakage rate
IPt
urbine
efficiency
Fig. 2. IP turbine efficiency vs N2 leakage rate.
J.-q. Xu et al. / Applied Thermal Engineering 31 (2011) 311e318 313
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x hR hcDh
0t
h0R h
0c
Dht
h0I h0c
Dht hI hcDh
0t
(4)
3.2. The error analysis equations based on numerical calculation
method
The enthalpy error and ideal enthalpy drop caused by measured
parameters deviation (temperature or pressure) influence the
accuracy of N2 leakage rate x, which are analyzed as follows:
1) x variation caused by the error of HP turbine first-stage
enthalpy hI
Dx
hR hcDh0t
h0R h
0c
Dht
h0I h0c
Dht hI hcDh0c
2 DhtDh0IDh0tDhI (5)
2) x variation caused by the error of IP turbine exhaust enthalpy hc
Dx
Dh0cDht DhcDh
0t
h0I h0c
Dht hI hcDh
0t
h0I h0c
Dht hI hcDh
0t
2
hR hcDh
0t
h0R h
0c
Dht
h0I h0c
Dht hI hcDh
0t
2 Dh0tDhcDhtDh0c (6)
3) x variation caused by the error of hot reheat steam enthalpy hR
Dx Dh0tDhR DhtDh
0R
h0I h
0c
Dht hI hcDh
0t
(7)
4) x variation caused by the error of ideal enthalpy drop Dht
In analysis of the influence of the measured parameters error on
steam enthalpy values and ideal enthalpy drop, the ideal gasformulas [14] are applied for approximate calculation. For ideal gas,
the temperature variation affects enthalpy and pressure variation
(temperature unchanged), and affects the ideal enthalpy drop (for
steam k 1.3, Rg 0.462) as follows:
Dh cpDT k
k 1RgDT (9)
DDht RgT0
p2p0
1=k 1p0Dp2 RgT0
p2p0
1=kp2
1
p20Dp0 (10)
With equations (9) and (10), enthalpy changeDh and ideal enthalpy
drop change D(Dht) which caused by temperature variation DTand
pressure variationD
p can be calculated, and the corresponding
change of N2 leakage rate can be calculated by substituting Dh, D
(Dht) into equations (5)e(8).
4. Calculation of a practical steam turbine
4.1. N2 leakage test
A 600 MW supercritical steam turbine, model N600-24.2/566/
566, whose N2 leakage rate design value is 1.20%, while the tested
value is 2.55% before overhaul, is conducted N2 leakage test after
overhaul.
The N2 leakage test is carrying out at 3VWO condition, and the
test conditions are: Test 1, keep main steam temperature rated and
reduce the hot reheat steam temperature; test 2, keep hot reheat
steam temperature rated and reduce the main steam temperature;
test 3, keep hot reheat steam and main steam temperature both
rated. Each test lasts for 2 h, and during the test the unit is keeping
well isolated. The measured parameters include: main steam
pressure and temperature, hot reheat steam pressure and
temperature, IP turbine exhaust pressure and temperature, HP
turbinefi
rs-stage pressure and temperature, atmospheric pressure.At the same time obtain the standard elevation of measuring
points.
After the abnormal data points are removed, average the
monitoring parameters of test 1 and 2. As N2 leakage test requires
higher stability of the test data of test 3, average its test data at the
most stable period. Then use the atmospheric pressure and stan-
dard elevation to amend average pressure to absolute pressure. The
relevant test data are arranged in Table 1.
4.2. N2 leakage rate calculation
Based on the temperature variation method and numerical
calculation method mentioned above, N2 leakage rates are esti-mated as follows.
(1) Temperature variation method
It is assumed that N2 leakage rates are 0%, 2% and 5% respec-tively, and IP turbine efficiency of each test is calculated, as shown
in Table 2.
According to the results, the relationship curve between N2
leakage rate and IP turbine efficiency is plotted (see Fig. 2). The
curves of the three tests cross at three points, so three N2 leakage
rates are available, that is, one N2 leakage rate is calculated by any
two of the three tests in combination, the results are shown in
Table 3. N2 leakage rate takes the result of combination 1,
x 1.669%.
(2) Numerical calculation method
For any combination of two tests in Table 1, N2 leakage rate is
iteratively calculated with formula (4). For thefi
rst iterative
Dx
h0R h0c
h0I h
0c
Dht hI hcDh
0t
hR hcDh0t
h0R h
0c
Dht
h0I h
0c
h0I h0c
Dht hI hcDh
0t
2 DDht
hR hc
h0I h0c
Dht hI hcDh
0t
hR hcDh0t
h0R h
0c
Dht
hI hc
h0I h0c
Dht hI hcDh
0t
2 DDh0t (8)
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calculation, Dht and Dh0t are assumed as the ideal enthalpy drop of
hot reheat steam, and in each subsequent iterative calculation DhtandDht are assumed as the ideal enthalpy drop of the mixed steam.
After 10 iterations, the change of x is less than 107, then it can be
said that x has been convergent, and the iteration is over, three N2
leakage rates are available, showing as Table 3. The N2 leakage rate
is x 1.655%.
As shown in Table 3, for a combination of any two tests in Table
1, N2 leakage rates estimated by temperature variation method and
numerical calculation method are almost identical. The N2 leakage
rate calculated by combination 1 is between combination 2 andcombination 3, and the difference is extremely small, indicating
great precision. N2 leakage rate is taken as the result calculated by
combination 1, because the denominator of error analysis formulas
of combination 1 are bigger than other combinations, and the same
measured parameters error will cause the smallest error on N2
leakage rate, that is, the N2 leakage rate of combination 1 has the
highest precision.
4.3. Error analysis
Take the N2 leakage rate 1.655% of combination 1 calculated by
numerical calculation method as the reference value, and analyze
the impact of measured parameters error on N2 leakage rate, underthe condition of one measured parameter changed, while other
parameters unchanged.
As can be seen from Table 2, the maximum arithmetic average
error of hot reheat pressure, hot reheat temperature, IP turbine
exhaust pressure, IP turbine exhaust temperature, HP turbine first-
stage pressure, HP turbine first-stage temperature of the three tests
are respectively 0.030 MPa, 2.738 C, 0.007 MPa, 2.081 C,
0.120 MPa, 1.265 C. The arithmetic average error is mainly caused
by the fluctuation of steam turbine operating condition, and the
measurement error is much smaller than the arithmetic average
error. It is assumed that the measurement error of test 1 is the
maximum arithmetic average error mentioned above, that is, the
relative error of hot reheat pressure, hot reheat temperature, IP
turbine exhaust pressure, IP turbine exhaust temperature, HP
turbine first-stage pressure and HP turbine first-stage temperature
are respectively 0.815%, 0.516%, 0.782%, 0.633%, 0.724%, 0.249%.
As follows, the ideal gas formula and IAPWS-IF67 are used to
analyze the change of steam enthalpy and ideal enthalpy drop
caused by measured parameters error (temperature and pressure),
and then the error analysis formulas are used to calculate the
deviation of N2 leakage rate.
(1) The ideal gas formulas
Apply equations (9) and (10) to calculate the change in the
corresponding enthalpy and ideal enthalpy drop caused by
measured parameters error, and then use the error analysis
formulas (5)e(8) to calculate the corresponding deviation of N2
leakage rate, results are shown in Table 4.
As the pressure deviation does not affect the enthalpy value
when use the ideal gas formulas, the Table 4 doesnt give the
influence offirst-stage pressure error on N2 leakage rate.
(2) IAPWS-IF67
IAPWS-IF67 is used to calculate the change of corresponding
enthalpy and ideal enthalpy drop caused by measured parameters
error. The error of hot reheat pressure, hot reheat temperature and
IP exhaust pressure affects not only the corresponding steam
enthalpy, but also affects the ideal enthalpy drop; while the error of
IP exhaust temperature, first-stage pressure and first-stage
temperature only affects the steam enthalpy. Therefore, N2 leakage
rate deviation caused by the measured parameters error above is
the sum of that caused by the error of steam enthalpy and ideal
enthalpy drop. Then error analysis formulas (5)e(8) can be used to
calculate the corresponding deviation of N2 leakage rate,results are
shown in Table 4.
According to Table 4, the deviations of N2 leakage rate calculated
by the ideal gas formulas and IAPWS-IF67 are almost equal, and the
difference of absolute value is less than 0.377%. Thus, in order to
facilitate the engineering application, the ideal gas formulas are
used to analyze N2 leakage rate deviation caused by measured
parameters error, with sufficient accuracy; in condition of other
parameters unchanged and only one parameter changed. The error
of hot reheat temperature and IP turbine exhaust temperature has
the greatest impact on N2 leakage rate, next, hot reheat pressure
and IP exhaust pressure, and measurement error of first-stage
parameters have the least impact on N2 leakage rate.
4.4. N1 leakage quantity and its impact on N2 leakage rate
accuracy
For some turbines, there is some N1 leakage (see Fig. 1). As the
measuring points of IP turbine exhaust are located at the crossover
pipe between IP and LP, the tested IP exhaust temperatures is less
than the actual temperature. Therefore, in order to obtain the real IPturbine exhaust temperature, N1 leakage quantity of test 3 is
calculated in this paper.
N1 leakage enters the exhaust pressure area by two routes after
completely mixed, that is, oneflows into the crossoverpipe, and the
other flows into the fourth extraction paragraphs, with the consid-
eration that the amount of these two routes are equal, and N1
leakage enthalpyhas thesame value of HPturbine exhaustenthalpy.
The parameters required for calculation are shown in Table 5.
According to mass conservation and energy conservation,
there are,
agl2
hgp a4 agl2 hzp a4h4 (11)
Table 2
Value of IP turbine efficiency.
N2 leakage rate 0% 2% 5%
IP efficiency/% Test 1 91.664 90.980 89.999
Test 2 92.070 90.897 89.206
Test 3 91.851 90.926 89.594
Table 3
Results of N2 leakage rates.
Calculation method Combination 1 Combination 2 Combination 3
Temperature variation 1.669% 1.815% 1.522%
Numerical calculation 1.655% 1.763% 1.543%
Table 1
Test Data of N2 leakage test.
Parameters Test 1 Test 2 Test 3
Main steam pressure (MPa) 23.564 22.922 23.617
Main steam temperature (C) 558.351 529.790 561.255
Hot reheat pressure (MPa) 3.682 3.745 3.772
Hot reheat temperature ( C) 531.085 564.097 567.721
IP exhaust pressure (MPa) 0.895 0.915 0.922
IP exhaust temperature (
C) 328.714 355.107 358.556First-stage pressure (MPa) 16.574 16.166 16.630
First-stage temperature (C) 508.710 478.301 508.344
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where, agl is the N1 leakage quantity, hgp is the HP turbine exhaust
enthalpy, a4 is the fourth extraction quantity (to deaerator and
feedwater pump turbine), hzp is the enthalpy of steam in crossover
pipe, h4 is the fourth extraction enthalpy. The N1 leakage quantity
calculated by equation (11) is 8.729 t/h.
The leakage quantity from HP exhaust steam balance piston to
crossover pipe is 4.365 t/h (half of N1 leakage quantity). It is
assumed that IP turbine exhaust pressure remains same before and
after steam mixing, then obtain the actual IP turbine exhaust steam
temperature of test 3, which is 358.895 C, 0.338 C higher than the
measured temperature. Similarly, N1 leakage of test 1 and 2 are
8.845 t/h and 8.398 t/h, and the actual IP exhaust temperature of
test 1 and 2 are 328.959 C and 355.539 C, 0.246 C and 0.432 C
higher than the measured temperature.
Combine the actual IP turbine exhaust temperature obtained
here with the parameters in Table 1, to calculate N2 leakage rates by
using the two methods, results are showed in Table 6, and N2
leakage rate-IP turbine efficiency curves, according to temperature
variation method, are shown in Fig. 3.Basedon thecalculation above,it is obvious that N1 leakageaffects
N2 leakage rate accuracy greatly. Although, in the three tests, N1
leakage quantity remains almost the same, but N1 leakage enthalpy
and IP exhaust enthalpy between any two tests have large discrep-
ancy, that is, IP exhaust temperature of the three tests are all greater
than the value without leakage, but the increment between each test
is great, so N1 leakage has a great impact on N2 leakage rate.
5. Check of IP turbine efficiency
5.1. IP turbine efficiency calculation
The thermodynamic process line of IP turbine is shown in Fig. 4.
IP turbine inlet and outlet measured parameters of test 3 are given
in Table 1, and measured IP turbine efficiency is 91.849%, with the
thermal process line 2e3. Impact of Steam leakage on IP thermal
process is shown in Fig. 4: point 1, actual IP turbine inlet point
considering the impact of N2 leakage; point 2, measured parame-
ters of IP turbine inlet (hot reheat) point; point 3, measured IP
turbine outlet point; point 4, actual IP turbine outlet points
(IP turbine exhaust).
Based on the steam leakage quantity calculated above, the actual
IP turbine efficiency of test 3 can be calculated as follows.
(1) Consider N2 leakage only
N2 leakage rate takes the value 1.334%, which calculated by
temperature variation method in Section 4.4. At this point, the
steam enthalpy of IP turbine inlet is 3597.235 kJ/kg, inlet steam
temperature is 566.053 C, the outlet parameter is the measured
value, and the corresponding thermal process line is 1e3, as
a result, the IP turbine efficiency is 91.096%, 0.753% lower than the
measured value.
(2) Consider N1 leakage only
Table 4
Impact of measured parameters error on the results of N2 leakage according to ideal gas property formulas IAPWS-IF67 (reference value of N2 leakage rate is 1.655%).
Measured parameters Hot reheat
pressure
Hot reheat
temperature
IP exhaust
pressure
IP exhaust
temperature
First-stage
pressure
First-stage
temperature
Relative error of measured parameters/% 0.815 0.516 0.782 0.633 0.249 0.724
Change in N2 leakage rate (ideal gas)/% 1.362 3.561 1.245 2.751 0 0.027
Change in N2 leakage rate (IAPWS-IF67)/% 1.571 3.264 1.409 3.128 0.018 0.043
Absolute value of difference of N2 leakage rate
change/%
0.209 0.297 0.164 0.377 0.018 0.016
Table 5
Data used to calculate N1 leakage quantity.
Parameters Unit HP exhaust zone Fourth steam extraction Crossover pipe
Pressure Mpa 4.058 0.963 0.922
Temperature C 305.595 356.514 358.556
Enthalpy kJ/kg 2975.988 3173.029 3178.096
Fl ow rate t/ h e 174.098 1239.959
Table 6
Results of N2 leakage rates (according to the actual IP turbine exhaust temperature).
Calculation method Combination 1 Combination 2 Combination 3
Temperature variation 1.334% 1.399% 1.267%
Numerical calculation 1.321% 1.404% 1.237%
0.885
0.89
0.895
0.9
0.905
0.91
0.915
0.92
0.925
0 0.01 0.02 0.03 0.04 0.05 0.06
N2 leakage rate
IPt
urbine
efficiency
Fig. 3. N2 leakage rate vs IP turbine efficiency (according to the actual IP exhaust
temperature).
Fig. 4. IP turbine thermodynamic process.
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At this point, the steam enthalpy of IP turbine outlet is
3178.810 kJ/kg, outlet steam temperature is 358.895 C, the inlet
parameter is the measured value, and the corresponding thermal
process line is 2e4, thence the IP turbine efficiency is 91.694%,
0.155% lower than the measured value.
(3) Consider the two leakages
At this condition, the steam enthalpy of IP inlet is 3597.235 kJ/
kg, inlet steam temperature is 566.053 C, the steam enthalpy of IP
turbine outlet is 3178.810 kJ/kg, outlet steam temperature is
358.895 C, and the corresponding thermal process line is 1e4, so
the IP turbine efficiency is 91.075%, 0.774% lower than the
measured value.
In order to compare the impact of the two steam leakages on IP
turbine efficiency under different operation conditions, calculation
is done on the basis of the steam turbine design data (see Fig. 5).
That is, load operation condition from 30% to 100%: as consider the
impact of N2 leakage, IP turbine efficiency is 0.253%e
0.636% lower
than the measuredvalue; taking N1 leakage into account, IP turbine
efficiency is 0.089%e0.187% lower than the measured value; IP
turbine efficiency is 0.341%e0.823% lower than the measured
value, considering the impact of both two leakages.
5.2. The expression of IP turbine efficiency deviation
The expression of IP turbine efficiency is defined by:
hi Dh
Dht
h1 h2h1 h1t
T1 T2
T1
1
p2p1
k1k
! 1 T2T11
p2p1
k1k
(12)
where, subscript 1 indicates IP turbine inlet, and 2 indicates IPturbine outlet.
N2 leakage and N1 leakage affect IP turbine inlet and outlet
temperatures. As the leakage quantity compared to the main steam
flow rate is small, it is assumed that the pressure of IP inlet and
outlet are not affected. The deviation of IP turbine efficiency can be
calculated approximately by the formula as follows:
Dhi 1
1
p2p1
k1k
"T2T21DT1
1
T1DT2
#(13)
According to equation (13): Steam leakage affects the IP turbine
efficiency through the influence of IP turbine inlet and outlet
temperatures; for the same inlet and outlet temperature variation
DT1 and DT2, outlet temperature variation affects IP turbine effi-
ciencygreater than that of inlet temperature. In the condition of the
same quantity of N2 leakage and N1 leakage, the IP turbine inlet
temperature variation DT1
is greater than the outlet temperature
variation DT2, mainly because only half of N1 leakage entering the
crossover pipe between IP and LP. Therefore, N2 leakage has
a greater impact on IP turbine efficiency.
6. Conclusions
(1) Due to the installation gap bias and the N2 packing seal friction
during operation, N2 leakage is often greater than the design
value, which affects the steam turbine economy. The actual
leakage rate of the 600 MW unit in this paper used to be about
2.13 times of the design value, while after overhaul the N2
leakage rate is close to the design value, and N1 leakage
quantity reaches to the design value, showing the good effectsof overhaul.
(2) The N2 leakage test theory of temperature variation method
and the issues should be noticed in practical application are
discussed in this paper, owning the actual operation guiding
significance.
(3) As can be seen from the calculations above, the N2 leakage
rates calculated by numerical calculation and temperature
variation method are almost identical, indicating that the
numerical calculations method also can estimate N2 leakage
rate successfully, and can be used to simplify on-line calcula-
tion, achieving real-time monitoring of N2 leakage rate.
(4) The error analysis shows that the most influential parameters
on the accuracy of N2 leakage rate are hot reheat steam
temperature and IP exhaust steam temperature, so it is criticalto ensure the temperature measurement accuracy in the test.
(5) The application of ideal gas formula or IAPWS-IF67 for the
analysis of N2 variation caused by measured parameters error
nearly has the same accuracy. To facilitate the analysis and
engineering application, can apply the ideal gas formula to
analyze the impact of measured parameters (temperature and
pressure) error on N2 leakage rate.
(6) In order to estimate N2 leakage more accurately, IP exhaust
temperature measuring points must be ranked in the final
stage of IP turbine, or calculate N1 leakage quantity and then
find the exact IP exhaust temperature, as the N1 leakage affects
the test accuracy of N2 leakage rate greatly.
(7) With the same leakage quantity, N2 leakage has greater impact
on IP effi
ciency than N1 leakage.
The impact of N1 and N2 leakage on IP turbine efficiency under different operation conditions
90.000%
90.500%
91.000%
91.500%
92.000%
92.500%
100% 75% 50% 40% 30%
load
IP
turbine
efficiency
tested IP turbine efficiency
IP turbine efficiency,considering N1
leakage
IP turbine efficiency,considering N2
leakage
IP turbine efficiency,considering the
two leakages
Fig. 5. Impact of N1 leakage and N2 leakage on IP turbine efficiency under different operation conditions.
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Acknowledgements
The tests in this paper were finished with the help of the
researcher Xiao-ling Zhu, who helped us to do these tests exactly,
and provided us a lot of valuable experience.
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