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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]


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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.



7/8

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.



8/8

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.

References

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