ANALYSIS OF THE IMPACT OF MASS FLOW EXTRACTION ON THE
CHANGE OF PARAMETERS IN A LABYRINTH SEAL USING THE
STODOLA METHOD
Paweł Kaszowski, Marek Dzida
Gdańsk University of Technology
Ul. Narutowicza 11/12, 80-233 Gdańsk, Poland
Phone: +48 58 347 1842,
e-mail: pawkaszo1@pg.gda.pl
dzida@pg.gda.pl
Abstract
Labyrinth seals are an important element of a steam turbine set design. The use of diagnostic
extraction makes it possible to control the operation of a seal by providing information on the
thermodynamic parameters along the length of the seal. Diagnostic extraction has a considerable
impact on the change of the parameters, the amount of the extracted mass. This article describes
the dependence of pressure in the clearance downstream of the extraction and in the chamber in
which the extraction point is located, on the amount of the extracted steam. Relation between
pressure and nominal seal clearance is discussed, which enables the control of the seal operation.
The calculations of the seal operation parameters were performed using a method proposed by
Stodola.
Keywords: labyrinth seals, Fanno curve, diagnostic extraction, Stodola
1. Introduction
Clearances between the elements of the rotor and the frame are associated with the leaks of
the working medium. The resultant losses may be reduced using labyrinth seals that contain a
number of cross-section constrictions where the flow rate significantly increases. The kinetic
energy of the stream flowing out of a constriction is converted into heat as a result of whirls
taking place in the chamber between the constrictions. The seal design should ensure that the
flow rate upstream of the next clearance is completely decelerated.
A diagram of a labyrinth seal is given in Figure 1. When analysing flow through such a seal
it should be assumed that isentropic expansion takes place in each clearance, while in the
chamber kinetic energy is converted into heat as a result of an isobaric process. Generally, it is
assumed that the process of kinetic energy conversion into heat is adiabatic, with no heat
exchange between the stream and the seal walls.
Fig. 1 Labyrinth seal diagram
2. Stodola method
The labyrinth seal calculation method proposed by Stodola is described below.
The rate at which the working medium flows out of a clearance is expressed as follows:
c = �2hs (1)
where h s – isentropic enthalpy reduction in the analysed clearance.
Assuming that the flow constriction in each clearance is identical and that it is a steady
flow, the equation of continuity for the given case looks as follows:
𝑚𝑚𝑛𝑛 𝑣𝑣 = 𝐴𝐴𝐴𝐴 (2)
In equation (2) A stands for an effective cross-section expressed with the following formula:
𝐴𝐴 =∝ 𝐴𝐴𝑛𝑛 (3)
where:
𝐴𝐴𝑛𝑛 = 𝜋𝜋𝜋𝜋𝜋𝜋 (4)
𝐴𝐴𝑛𝑛 stands for a geometrical cross-section, while α is the liquid flow coefficient of
contraction.
Considering experimental and computational data, an average coefficient of contraction
amounts to:
α≈0,8 [6]
Combined equations (1) and (2) result in:
mn c �2hs (5)
= = = const
A v v
Equation (5) on an i – s diagram is represented by a Fanno curve that constitutes the
geometric locus of the end points of all expansion lines in constrictions, as shown in Figure 2.
The diagram shows thermodynamic changes taking place during a liquid flow through a
labyrinth seal. There is a change reflecting the isentropic enthalpy reduction during a liquid
flow through a seal clearance between points 1 1 and 2 1 , and a change in isobaric expansion
during the outflow of the liquid from the seal clearance between points 2 1 and 1 2 .
Fig. 2 Change in a labyrinth seal, 1 1 , 1 2 , 1 3 – states upstream of clearances, 2 1 , 2 2 , 2 3 – states
downstream of the seal clearance
The Fanno curve may be established in the following manner. Assuming that the effective
dimensions of clearance A cross-section are known. Assuming that the value of leak 𝑚𝑚𝑛𝑛 is
known using formula (5)
𝑐𝑐 𝑚𝑚𝑛𝑛
= = 𝐾𝐾 (6)
𝑣𝑣 𝐴𝐴
the following is determined:
�2ℎ𝑠𝑠 (7)
𝑣𝑣 =
𝐾𝐾
Starting from the first clearance, knowing the initial state in point 1 1 (p 1 ,v 1 ) upstream of
the seal, such value of h 1 is selected using the trial method that it satisfies equation
�2ℎ1 (8)
𝑣𝑣21 =
𝐾𝐾
That way point 2 1 and pressure downstream of the first clearance are determined. The state
upstream of the second clearance 1 2 is expressed using values 𝑖𝑖1,2 = 𝑖𝑖1 , 𝑝𝑝1,2 = 𝑝𝑝2,1 . Further
points are determined using the given formula. In practice such a procedure would be tedious,
which is why Stodola provided simple, approximate formulas. In case of a large number of fins
𝑧𝑧 ≫ 1 the pressure drop in the clearance ∆𝑝𝑝 is small, therefore enthalpy reduction may be
calculated using formula
ℎ𝑠𝑠 = 𝑣𝑣∆𝑝𝑝 (9)
hence
𝑐𝑐 = �2𝑣𝑣∆𝑝𝑝 (10)
for the states upstream of clearances
𝜅𝜅
𝑖𝑖 = 𝑝𝑝𝑝𝑝 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (11)
𝜅𝜅 − 1
Using this dependence for any given clearance the following is correct:
𝑝𝑝𝑖𝑖 𝑣𝑣𝑖𝑖 = 𝑝𝑝1 𝑣𝑣1 (12)
If the following is assumed:
𝜅𝜅 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
considering equation (10) and equation (11) in formula (5) the following is obtained
𝑚𝑚𝑛𝑛 ∆𝑝𝑝
= �2 𝑜𝑜𝑜𝑜
𝐴𝐴 𝑣𝑣
𝑚𝑚𝑛𝑛 2 ∆𝑝𝑝 𝑝𝑝∆𝑝𝑝 (13)
� � =2 =2
𝐴𝐴 𝑣𝑣 𝑝𝑝𝑝𝑝
𝑝𝑝1 𝑣𝑣1 𝑚𝑚𝑛𝑛 2
𝑝𝑝∆𝑝𝑝 = � �
2 𝐴𝐴
expression (13) is true for any clearance.
The 𝑝𝑝∆𝑝𝑝 product is identical for each clearance; by summing up equation (13) for all of the
clearances the following is obtained:
𝑝𝑝1 𝑣𝑣1 𝑚𝑚𝑛𝑛 2
� 𝑝𝑝∆𝑝𝑝 = 𝑧𝑧 � � (14)
2 𝐴𝐴
If drop ∆𝑝𝑝 is small, the summation sign may be replaced with integration
𝑝𝑝1
𝑝𝑝1 2 − 𝑝𝑝2 2 𝑧𝑧𝑝𝑝1 𝑣𝑣1 𝑚𝑚𝑛𝑛 2
� 𝑝𝑝𝑝𝑝𝑝𝑝 = = � � (15)
2 2 𝐴𝐴
𝑝𝑝2
In this case expression (14) enables the calculation of leak 𝑚𝑚𝑛𝑛 with the assumed number of
teeth z
𝑝𝑝1 2 − 𝑝𝑝2 2 1 𝑝𝑝1 𝑝𝑝2 2
𝑚𝑚𝑛𝑛 = 𝐴𝐴� = 𝛼𝛼𝐴𝐴𝑛𝑛 � �1 − � � � (16)
𝑧𝑧𝑝𝑝1 𝑣𝑣1 √𝑧𝑧 𝑣𝑣1 𝑝𝑝1
Leak 𝑚𝑚𝑛𝑛 is proportional to the reciprocal of the z seal number root
1
𝑚𝑚𝑛𝑛 ~ (17)
√𝑧𝑧
Formula (16) may be simplified
𝑝𝑝1
𝑚𝑚𝑛𝑛 = 𝐴𝐴𝑛𝑛 𝛷𝛷𝑠𝑠 � (18)
𝑣𝑣1
where
1 𝑝𝑝2 2
𝛷𝛷𝑠𝑠 = 𝛼𝛼� �1 − � � � (19)
𝑧𝑧 𝑝𝑝1
Using property (16) it is possible to solve a reverse problem where the size of leak 𝑚𝑚𝑛𝑛 is
assumed by searching for the number of constrictions of a flow through the seal.
𝛼𝛼𝐴𝐴𝑛𝑛 2 𝑝𝑝2 2 𝑝𝑝1
𝑧𝑧 = � � �1 − � � � (20)
𝑚𝑚𝑛𝑛 𝑝𝑝1 𝑣𝑣1
The problem presented in this way can sometimes be more difficult to solve, in case of
minor leaks 𝑚𝑚𝑛𝑛 leading to a large number of teeth z.
Fig. 3 Expansion curve for a labyrinth seal
An increase in specific volume along the Fanno curve results in a constant increase in
velocity and enthalpy reduction in the subsequent clearances, as shown in Figure 2. Critical
velocity c=a may be reached in the ultimate clearance, therefore further expansion to ultimate
pressure 𝑝𝑝2 takes place downstream of the clearance, Figure 3. In such a case the described
procedure is applied until and including the penultimate clearance. Critical pressure occurs in
the ultimate clearance.
3. Calculations
The amount of steam extracted as a result of diagnostic extraction (Fig. 4) has a significant
impact on the pressure distribution in a labyrinth seal and the enthalpy change curve (Fanno
curve). For this purpose calculations were performed that show the dependence of differential
pressure of a labyrinth without diagnostic extraction ∆𝑚𝑚0 = 0.0 𝑘𝑘𝑘𝑘/𝑠𝑠 and a labyrinth with
mass extraction that amounts to, respectively:
− ∆𝑚𝑚1 = 0.2 𝑘𝑘𝑘𝑘/𝑠𝑠
− ∆𝑚𝑚2 = 0.4 𝑘𝑘𝑘𝑘/𝑠𝑠
− ∆𝑚𝑚3 = 0.6 𝑘𝑘𝑘𝑘/𝑠𝑠
Fig. 4 Diagram of a labyrinth seal with diagnostic extraction
Parameters of operation of a high pressure (HP) turbine interframe seal listed in Table 1 were
assumed for the calculations.
Table 1. Parameters of an HP turbine interframe seal
Pressure upstream of seal 𝑝𝑝1 MPa 9.861
Steam temperature 𝑡𝑡1 °C 522.5
upstream of seal
Enthalpy upstream of seal ℎ1 kJ/kg 3433
Steam pressure 𝑝𝑝2 MPa 4.204
downstream of seal
Steam flow through seal 𝑚𝑚𝑛𝑛 kg/s 2.228
Shaft diameter 𝑑𝑑 mm 475
Nominal seal clearance 𝑠𝑠𝑛𝑛 mm 1.0
Number of seal teeth 𝑧𝑧 80
Further analysis is based on a labyrinth seal calculation method proposed by Stodola. In
accordance with this method, a mass flow through a labyrinth is determined with the following
formula:
1 𝑝𝑝1 𝑝𝑝 2
𝑚𝑚𝑛𝑛 = 𝛼𝛼𝐴𝐴𝑛𝑛 � �1 − � 2 � �
√𝑧𝑧 𝑣𝑣1 𝑝𝑝1 (21)
It is proportional to the reciprocal of the z seal teeth number root in accordance with the
following dependence:
1
𝑚𝑚𝑛𝑛 ~
√𝑧𝑧 (22)
Expression (21) was used to derive a formula for the coefficient of contraction of a flow
through the clearance of a labyrinth seal:
𝑚𝑚𝑛𝑛 √𝑧𝑧
𝛼𝛼 =
𝑝𝑝 𝑝𝑝 2 (23)
𝐴𝐴𝑛𝑛 �𝑣𝑣1 �1 − �𝑝𝑝2 � �
1 1
where:
𝑚𝑚𝑛𝑛 − mass flow through the seal,
𝛼𝛼 − flow coefficient of contraction,
𝐴𝐴𝑛𝑛 − clearance effective cross-section,
𝑧𝑧 − number of the seal teeth,
𝑝𝑝1 − pressure upstream of the seal,
𝑝𝑝2 − pressure downstream of the seal,
𝑣𝑣1 − specific volume of steam.
The rearrangement of formula (21) provided an expression for the value of pressure 𝑝𝑝𝑥𝑥 in the n
clearance of the seal:
𝑚𝑚12 𝑝𝑝1 𝑧𝑧1 𝑣𝑣1
𝑝𝑝𝑥𝑥 = �𝑝𝑝12 − (24)
𝛼𝛼𝐴𝐴𝑛𝑛
4. Results
The coefficient of flow contraction calculated using equation (3) equals 𝛼𝛼 = 0.904. The
value of pressure in clearance 𝑧𝑧70 = 70 is 𝑝𝑝70 = 52.48 𝑏𝑏𝑏𝑏𝑏𝑏. Pressure in this clearance was
chosen because diagnostic extraction was used downstream of the 70th tooth of the seal.
Pressure value in clearance 𝑧𝑧 = 70 remains constant irrespective of whether there is diagnostic
extraction or not. A pressure change may be observed in the next clearance 𝑧𝑧 = 71 located
downstream of the mass extraction. Below is a list of pressure values in the clearance just
downstream of the diagnostic extraction for 𝑧𝑧 = 71 at different values of the extracted mass
∆𝑚𝑚, respectively for:
− 𝑝𝑝𝑥𝑥0 = 52.06 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚0 = 0.0𝑘𝑘𝑘𝑘/𝑠𝑠 (no extraction)
And for extraction values they amount to, respectively
− 𝑝𝑝𝑥𝑥1 = 52.09 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚1 = 0.2 𝑘𝑘𝑘𝑘/𝑠𝑠
− 𝑝𝑝𝑥𝑥2 = 52.13 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚2 = 0.4 𝑘𝑘𝑘𝑘/𝑠𝑠
− 𝑝𝑝𝑥𝑥3 = 52.17 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚3 = 0.6 𝑘𝑘𝑘𝑘/𝑠𝑠
The absolute differential pressure between clearance 𝑧𝑧 = 70 and 𝑧𝑧 = 71 for the analysed
clearance looks as follows:
− ∆𝑝𝑝0 = 0.42 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚0 = 0.0𝑘𝑘𝑘𝑘/𝑠𝑠 (no extraction)
− ∆𝑝𝑝1 = 0.39 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚1 = 0.2 𝑘𝑘𝑘𝑘/𝑠𝑠
− ∆𝑝𝑝2 = 0.35 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚2 = 0.4 𝑘𝑘𝑘𝑘/𝑠𝑠
− ∆𝑝𝑝3 = 0.31 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚3 = 0.6 𝑘𝑘𝑘𝑘/𝑠𝑠
The value of steam pressure in clearance 𝑧𝑧 = 71 downstream of the extraction point
increases proportionally to the increase in the value of steam ∆𝑚𝑚 extracted through the
diagnostic extraction point. The dependence of absolute differential pressure ∆𝑝𝑝𝑖𝑖 between
clearance 𝑧𝑧 = 70 and 𝑧𝑧 = 71 for a seal with and without extraction is shown in Figure 5.
0,43
∆𝑝𝑝_0
0,41
0,39 ∆𝑝𝑝_1
0,37
px [bar]
0,35 ∆𝑝𝑝_2
0,33
0,31 ∆𝑝𝑝_3
0,29
-0,1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7
∆m [kg/s]
Fig. 5 Dependence of pressure increase ∆𝑝𝑝𝑥𝑥 between a seal with and without extraction for
clearance 𝑧𝑧 = 71 for different values of mass extraction ∆𝑚𝑚.
∆𝑝𝑝0- no extraction, ∆𝑝𝑝1 for ∆𝑚𝑚1 = 0.2 𝑘𝑘𝑘𝑘/𝑠𝑠, ∆𝑝𝑝2 for ∆𝑚𝑚2 = 0.4 𝑘𝑘𝑘𝑘/𝑠𝑠, ∆𝑝𝑝3 for ∆𝑚𝑚3 = 0.6 𝑘𝑘𝑘𝑘/𝑠𝑠
The diagram shows that the change in pressure between the 70th and the 71st tooth of the
seal drops with an increase in the value of the steam jet extracted at the diagnostic extraction
point. The observed falling tendency is caused by the fact that the steam jet flowing through the
seal downstream of the extraction point is smaller than upstream of it, which with the assumed
isentropic expansion implies a smaller pressure drop in this clearance.
A change in pressure in the chamber where the diagnostic extraction point is located can
also be observed. Equation (25) specifies the mass flow through a labyrinth seal:
𝑚𝑚70 = 𝑚𝑚71 + ∆𝑚𝑚
(25)
where:
𝑚𝑚70 − mass flow into a labyrinth with diagnostic extraction
𝑚𝑚71 − mass flow out of a labyrinth with diagnostic extraction
∆𝑚𝑚 − steam jet value at the diagnostic extraction point
Using formula (21) equations determining the leakages stream in the individual sections of a
labyrinth seal were established:
1 𝑝𝑝1 𝑝𝑝𝑖𝑖 2
𝑚𝑚70 = 𝛼𝛼𝐴𝐴𝑛𝑛 � �1 − � � � (26)
�𝑧𝑧70 𝑣𝑣1 𝑝𝑝1
and
1 𝑝𝑝𝑖𝑖 𝑝𝑝2 2
𝑚𝑚71 = 𝛼𝛼𝐴𝐴𝑛𝑛 � �1 − � � � (27)
√𝑧𝑧71 𝑣𝑣𝑖𝑖 𝑝𝑝𝑖𝑖
The consideration of equality 𝑝𝑝1 𝑣𝑣1 = 𝑝𝑝𝑖𝑖 𝑣𝑣𝑖𝑖 and the substitution of equation (26) and (27) for
formula (25) result in a 4-degree polynomial equation, the solution for which is the value of
pressure 𝑝𝑝𝑖𝑖 in the chamber downstream of the 70th tooth of the seal.
The following results are obtained:
− 𝑝𝑝𝑥𝑥0 = 52.55 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚0 = 0.0𝑘𝑘𝑘𝑘/𝑠𝑠 without diagnostic extraction
− 𝑝𝑝𝑥𝑥1 = 54.06 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚1 = 0.2 𝑘𝑘𝑘𝑘/𝑠𝑠
− 𝑝𝑝𝑥𝑥2 = 55.61 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚2 = 0.4 𝑘𝑘𝑘𝑘/𝑠𝑠
− 𝑝𝑝𝑥𝑥3 = 57.22 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚3 = 0.6 𝑘𝑘𝑘𝑘/𝑠𝑠
Figure 6 shows the dependence of the value of differential pressure 𝑝𝑝𝑖𝑖 in the chamber
where the diagnostic extraction point is located between a seal without extraction and a seal
with extraction, calculated using the following formula:
∆𝑝𝑝 = |𝑝𝑝𝑖𝑖 − 𝑝𝑝𝑖𝑖+1 |
(28)
That amount to, respectively:
− ∆𝑝𝑝1 = 1.51 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚1 = 0.2 𝑘𝑘𝑘𝑘/𝑠𝑠
− ∆𝑝𝑝2 = 3.09 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚2 = 0.4 𝑘𝑘𝑘𝑘/𝑠𝑠
− ∆𝑝𝑝3 = 4.67 𝑏𝑏𝑏𝑏𝑏𝑏, for ∆𝑚𝑚3 = 0.6 𝑘𝑘𝑘𝑘/𝑠𝑠
in the function of the extracted mass ∆𝑚𝑚𝑖𝑖 in the seal.
An increase in pressure in the chamber downstream of the 70th tooth of the seal, progressing
with the increase in the value of the extracted steam, can be observed in comparison with a seal
without extraction.
5
4,5
4
3,5
px [bar] 3
2,5
2
1,5
1
0,5
0
0,1 0,2 0,3 0,4 0,5 0,6 0,7
∆m [kg/s]
Fig. 6 Dependence of differential pressure ∆𝑝𝑝𝑥𝑥 in a chamber with diagnostic extraction on the
mass extraction value
When analysing the obtained results shown in the form of a diagram in Figures 6 and 7, an
increase in pressure 𝑝𝑝𝑖𝑖 in the chamber between the 70th and the 71st tooth of the seal where a
diagnostic extraction point is located may be observed that depends on the size of the extracted
mass. A rapid increase in the enthalpy value will be visible in the location of the diagnostic
extraction point in diagram ℎ − 𝑠𝑠 . In the remaining section, from the chamber with an
extraction point up to the end of the seal, the resistance of the flow through the clearances of the
seal for a decreased leak will be lower. This is proven by the occurrence of lower flow rate
values in clearances and smoother curves of a pressure drop in the enthalpy/entropy dependence
diagram.
Fig. 7 Fanno curve for a labyrinth seal without extraction (black) and with diagnostic
extraction (red)
Nominal seal clearance 𝑠𝑠𝑛𝑛 also affects the change in thermodynamic parameters in the seal,
especially pressure. Given fixed mass extraction amounting to ∆𝑚𝑚 = 0.4𝑘𝑘𝑘𝑘/𝑠𝑠, calculations
were performed aimed at finding the value of pressure in a chamber with diagnostic extraction
at the change of parameter 𝑠𝑠𝑛𝑛 . The difference between the resultant pressure values and the
pressure value for a seal without extraction is shown in Figure 8.
4,5 ∆𝑝𝑝_1
4
[bar]
3,5
3 ∆𝑝𝑝_2
2,5 ∆𝑝𝑝_3
2
0 1 2 3 4
sn
Fig. 8 Dependence of differential pressure in a chamber with and without diagnostic extraction
in function 𝑠𝑠𝑛𝑛 of nominal seal clearance for ∆𝑚𝑚 = 0.4𝑘𝑘𝑘𝑘/𝑠𝑠
On the basis of the obtained results it may be concluded that the change in differential
pressure ∆𝑝𝑝1 , ∆𝑝𝑝2 , ∆𝑝𝑝3 between a seal with and without extraction is related with increasing
nominal seal clearance and a reduction in the rate of mass flow through a labyrinth seal
associated with a change in the clearance height.
5. Final conclusions
Labyrinth seals are an important element of a steam turbine set design. The use of
diagnostic extraction makes it possible to control the operation of a seal by providing
information on the thermodynamic parameters along the length of the seal. Diagnostic
extraction has an impact on the change of the parameters, the amount of the extracted mass.
This article described the dependence of pressure in the clearance downstream of the extraction
and in the chamber in which the extraction point is located, on the amount of the extracted
steam. Relation between pressure and nominal seal clearance was discussed, which enables the
control of the seal operation. All the dependences were derived in accordance with the method
proposed by Stodola. The results of calculations given above clearly show that the
thermodynamic parameters in a labyrinth seal (in the location of a diagnostic extraction point to
be precise) depend on the amount of the extracted mass and nominal seal clearance. The
presented calculations are the first attempt at applying the Stodola method. Further analyses
will focus on confirming the obtained results using CFD modelling methods.
References
[1] Chmielniak T.; Turbiny cieplne: podstawy teoretyczne. Gliwice, Poland, Wydawnictwo
Politechniki Śląskiej 1998.
[2] Kaszowski P.; Analiza pracy uszczelnień labiryntowych z upustem, Master's dissertation.
Gdańsk University of Technology, Institute of Power Engineering and Industrial
Instrumentation, Gdańsk, Poland 2011 .
[3] Kaszowski P., Dzida M., Krzyślak P.; Calculations of labyrinth seals with and without
diagnostic extraction in fluid flow machines. Polish Maritime Research 4(80) 2013 Vol 20;
pp. 34-38
[4] Kosowski K.; Steam and gas turbines., Publishing house: PG Delft University, Gdańsk,
Poland 2007.
[5] Krzyślak P.; A method of diagnosing labyrinth seals in fluid-flow machines. Polish
Maritime Research 3(57) 2008 Vol 15.
[6] Perycz S.; Turbiny parowe i gazowe. Gdańsk, Poland, Wydawnictwo Politechniki
Gdańskiej 1988
[7] Szczeglajew A.; Turbiny Parowe. Publishing house: Energia, Moscow, Russia 1967
[8] Tipton D., Scott T., Vogel R.; Labyrinth Seal Analysis. Volume 3. Analitycal and
Experimental Development of a Design Model for Labyrinth Seals, General Motors Corp
Indianapolis Allison Gas Turbine Div 1998
[9] Trütnovsky K.; Berührungsfreie Dichtungen, Grundlagen und Anwendungen der Strömung
durch Spalte und Labirynthe. VDI – VERLAG bh DÜSSELDORF, Verlag des Vereins
Deutscher Ingeniuere 1964.
[10] Yucel U.; Leakage and swirl velocities in labyrinth seals.A thesis presented to the
Graduate and research committee of Leigh University in Candidacy of the Degree of
Master of Science; Lehigh University 1996
