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Yan2009-LabSeals-Modeling.pdf
Xin Yan
Jun Li
e-mail: [email protected]
Liming Song
Zhenping Feng
Institute of Turbomachinery,
School of Energy and Power Engineering,
Xi’an Jiaotong University,
Xi’an 710049, P. R. China
1
Investigations on the Discharge
and Total Temperature Increase
Characteristics of the Labyrinth
Seals With Honeycomb and
Smooth Lands
The viscous work generated by the rotating components of a seal not only represents a
direct loss of power but also causes an increase in the total temperature of fluid (windage
effect). In order to study the discharge and total temperature increase characteristics of
the stepped labyrinth seals with smooth and honeycomb lands, 3D Reynolds-averaged
Navier–Stokes solutions from CFX is used in this work. At first, the influences of the inlet
preswirl, leakage flow rate, and rotational speed on the total temperature increase in the
convergent and divergent stepped labyrinth seals with smooth and honeycomb lands are
conducted. The obtained 3D numerical results are well in agreement with the referenced
experimental data. It shows that the utilized numerical approach has sufficient precision
to predict the total temperature increase in seals. Then, a range of pressure ratios and
four sizes of sealing clearance are performed to investigate the effects of sealing clearances and pressure ratio impact on the discharge and total temperature increase of the
stepped labyrinth seals with honeycomb and smooth liners. 关DOI: 10.1115/1.3068320兴
Introduction
Nowadays, the increasing demands of performance and fuel
efficiencies for the gas turbine engine lead to an increase in core
flow temperature. In order to protect the turbine airfoil from thermal stress fields created by exposure to the combustion gases,
more and more advanced cooling technologies are introduced by
the researchers. However, achievements of enhancing cooling for
the gas turbine engine will encounter the windage heating effect in
seals. In the internal cooling air system, seals serve the purpose of
metering the cooling air to prevent hot air ingress. The viscous
work generated by the rotating components, the so-called windage
heating effect, will induce an increase in the total temperature of
the fluid. It degrades the cooling quality and in turn necessitates
increasing the quantities of cooling flow extracted from the main
gas path. Neglect of such effect will decrease the lifetime of
blades working in a high temperature environment. Second, the
cooling air is contaminated by the labyrinth seal leakage flow and
then passes into the blades or interstage cavities for the purpose of
cooling. The heat transfer characteristics in the next gas path are
directly affected by the former outlet temperature and exit swirl.
As a result, cooling air temperature is the most important information for a gas turbine designer or researcher to evaluate the
cooling quality of the components and quantity of the cooling
flow. Hence it is crucial to study the total temperature increase
characteristic in the seal.
There are many factors that can affect windage effect. One of
these factors is the inlet preswirl. The positive preswirl will decrease the total temperature difference between seal inlet and outlet 关1–3兴. Another factor is the swirl development in the seal
chamber. Moreover, for interstage seals, the exit swirl can change
the incidence angle of the main flow into the downstream blades,
Contributed by the International Gas Turbine Institute of ASME for publication in
the JOURNAL OF TURBOMACHINERY. Manuscript received August 21, 2008; final manuscript received September 1, 2008; published online July 2, 2009. Review conducted
by David Wisler. Paper presented at the ASME Turbo Expo 2008 Land, Sea and Air
共GT2008兲, Berlin, Germany, June 9–13, 2008.
Journal of Turbomachinery
thereby generating stage loss 关4兴. Empirical results as well as
theoretical analysis have shown that other factors, such as pressure ratio, seal geometry, rotational speed, and thermodynamic
parameters, may impact the discharge characteristics 关5–7兴 and
temperature distributions 关8兴 of a seal. Many simple correlation
equations based on the experimental data were derived and used
to predict the performance of the seal. However, these equations
require empirical corrections to have the prediction match the experimental results. And different researchers may choose different
correction factors for different seals 关1兴. Therefore, it is hard to
decide the factors for every new design. Recently, the progress of
computer and computational fluid dynamics 共CFD兲 technologies
makes it possible to utilize a numerical simulation to predict the
performance of rotating seals. And it is also convenient to obtain
the correction factors directly if the validity of the numerical
method has been demonstrated.
In the present paper, in order to investigate how these factors,
such as pressure ratio and sealing clearance, affect the windage
heating and discharge behavior, numerical investigations are performed to calculate the total temperature increase and leakage rate
in the stepped labyrinth seals configured with smooth and honeycomb lands. First of all, the computed windage heating numbers
and detailed velocity profiles within the seal chambers are compared with the obtained experimental data. After the accuracy and
reliability of the utilized numerical method have been demonstrated, the influence of pressure ratios and sealing clearance sizes
on the leakage flow and windage heating is investigated in detail.
2
Literature Review
The research on windage heating effect was initially performed
by using the experimental methods. Based on the experimental
data, simple correlations were derived and used to predict the
windage loss for other seals. The first experimental data for the
windage heating was reported by Stocker et al. 关9兴. They measured the power losses of the straight-through and stepped labyrinth seals. The experiment conducted by Tipton et al. 关10兴 in the
Copyright © 2009 by ASME
OCTOBER 2009, Vol. 131 / 041009-1
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Fig. 1 Stepped labyrinth seal geometry
test seal rig shows that the temperature increase can reach up to
19.4 K and is influenced by the pressure ratio, rotor speed, and
sealing clearance.
McGreehan and Ko 关3兴 presented a correlation based on the
energy conservation law and wall shear stress expressions to predict the total temperature increase with different inlet preswirl
ratio, mass flow rate, and rotational speed. But it requires empirical correction to have the predictions match the experimental results.
Millward and Edwards 关11兴 measured the windage heating
power in various seals with a plain liner and derived a simple
correlation 共Eq. 共1兲兲 for windage power prediction in labyrinth
seals with smooth and honeycomb lands. However, the credibility
of the predictions for plain liner seals in their experiments was
within ⫾25%, and the worst value can reach up to +40%. Moreover, this correlation was not suitable for the seal with inlet preswirl,
H = Cms · ␲X␳␻3Rm4
Cms = 6 ⫻ 10−5
冋 册
Cw
Re
0.55
· n−0.65
HHC = 1.15H
共1兲
Denecke et al. 关4兴 reported that the discharge behavior, windage
heating, and exit swirl velocity can be uniquely defined by several
dimensionless numbers in Eq. 共2兲 from dimensional analysis and
scaling methods. They utilized experiments 关1兴 to measure the
windage heating in the labyrinth seals with smooth and honeycomb stators. They also measured the tangential velocity at two
special positions in the seal chamber using the laser Doppler velocimeter 共LDV兲 method. Besides these investigations, they calculated the windage heating number for a labyrinth seal with a
smooth stator by using the CFD commercial software FLUENT.
They used a 2D axis-symmetric geometry model to investigate the
total temperature difference in the smooth configuration. Their
numerical results did not show good agreement with the experiment data in most cases, and they did not calculate the windage
heating number of the honeycomb configuration. So, the main
objective of the present work is to utilize a 3D numerical method
to investigate the windage heating effect and discharge behavior
in the labyrinth seals with smooth and honeycomb lands based on
the experimental work 关1兴,
冦 冧
CD
␴
Kout
= f共⌸,Rex,M U,Kin,geometry, ␬,Pr兲
CD =
Q̇id =
冑
⌸=
3
ṁ
ṁid
2␬
·
R共␬ − 1兲
冉
=
ṁ冑Ttotal,in
Q̇id · Pin · A
冋冉 冊 冉 冊 册
1
⌸
2/␬
−
␬−1 2 2
Pin
Kin Mu
· 1+
2
pout
1
⌸
冊
共␬+1兲/␬
−␬/共␬−1兲
共2兲
Numerical Approach
3.1 Computational Model. In this work, the computational
geometrical parameters of the convergent and divergent stepped
labyrinth seals with smooth and honeycomb lands are obtained
from Ref. 关1兴. The stepped labyrinth seal geometry with smooth
and honeycomb configurations is defined in Fig. 1. It features four
straight knives for convergent or divergent steps 共depending on
the flow direction兲 on the rotor. The cell width of the honeycomb
configuration is 1.59 mm 共1/16 in.兲, and the cell depth is 4.2 mm.
Also, each seal has a tip thickness of 0.4 mm.
3.2 Numerical Method. Since the flow in stepped labyrinth
seals with smooth and honeycomb lands is typically threedimensional turbulence due to their structures and flow conditions
and since there exists high relative rotating speed, it is necessary
to solve 3D Reynolds-averaged Navier–Stokes 共RANS兲 equations
to analyze their flow patterns and predict their total temperature
increase.
A multiblock structured grid is generated for the computational
case. Figure 2 gives the impression of the computational grids for
two seals and corresponding boundary condition definitions. In
Fig. 2共a兲, the mesh generation of the honeycomb labyrinth seal is
shown. In the honeycomb land case, two honeycomb cells are
used in the circumferential direction and periodic boundary definition. Figure 2共b兲 shows the mesh and boundary definitions for
the smooth labyrinth seal.
In order to study the flow and heat transfer characteristics for
the convergent and divergent stepped labyrinth seals with smooth
and honeycomb lands, the commercial finite volume code CFX
关12兴 is used. This software solves the compressible time-averaged
RANS equations. And a second order high resolution discretization scheme is used. The turbulence characteristics of the flow are
modeled by the standard k-␧ equations. The scalable logarithmic
wall function is used to describe the near wall velocity. The y +
criterion is met over almost the entire wall region. The boundary
conditions and numerical methods are listed in Table 1. The total
temperature 共300 K兲 and mass flow rate or the total temperature
and total pressure are given at the inlet. The outlet static pressure
041009-2 / Vol. 131, OCTOBER 2009
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Transactions of the ASME
Table 2 Windage heating numbers ␴ of the labyrinth seal with
smooth land
Grid number
CFD
Expt.
94,000
142,000
250,000
0.38
0.39
0.39
0.38
The discharge behavior can affect the windage heating and
swirl within the seal, as Scherer 关13兴 found from numerical simulations. In that study, an effective pressure ratio ⌸ is used instead
of ␲ to account for the influence of the inlet preswirl on the
leakage 关14兴.
3.4 Grid Independence Analysis. Before comparisons are
made to the experiment, a mesh independence study is performed
to determine how fine a mesh density is necessary to capture the
flow physics.
The axial Reynolds number Rex was kept at 10,000, and a circumferential Mach number Mu was 0.31. Then the windage heating number of the stepped labyrinth seal with smooth land was
derived with 94,000, 142,000, and 250,000 nodes separately, as
shown in Table 2. The differences between the CFD value and
experimental data are about 0%, 2.6%, and 2.6%. In order to
balance the calculation accuracy and simulation time, a 142,000
node mesh is employed in the present numerical study for the
smooth labyrinth seal, while for the labyrinth seal with the honeycomb land case, the node number in the chamber part is increased to 289,000 because the flow field becomes more complex
than that of smooth configuration. And 244,000 nodes are generated in the honeycomb part.
4
Fig. 2 Calculated
definition
seal
mesh
and
boundary
condition
is 200,000 Pa. The desired convergent target of each simulation is
that the root mean square 共rms兲 residuals of the momentum and
mass equations, energy equation, and turbulence equations reach
共or even lower than兲 10−6.
3.3 Windage Heating. In the adiabatic flow condition, the
total temperature increase due to the internal losses in labyrinth
seals is described as windage heating H using
H = ṁ · C p · ⌬Ttotal
共3兲
The windage heating number ␴ is defined as
␴ = 2C p⌬Ttotal/U2
共4兲
Table 1 Conditions and numerical methods
Average rotor radius
Inlet total temperature
Outlet static pressure
Discretization scheme
Computational method
Turbulence model
Fluid
Wall properties
Journal of Turbomachinery
0.253 m
300 K
200,000 Pa
High resolution
Time marching method
k-␧, scalable log wall function
Air 共ideal gas兲
Adiabatic smooth surface
Results and Discussions
To demonstrate the accuracy and reliability of the present numerical approach, the effects of different rotational speeds, leakage flow rates, and two kinds of inlet swirl on the total temperature increase in convergent and divergent stepped labyrinth seals
are calculated and compared with the experimental data. Then, the
influence of the pressure ratio and sealing clearance on the discharge and total temperature increase in convergent stepped labyrinth seals with smooth and honeycomb lands is investigated and
discussed in detail.
4.1 Windage
Heating
and
Numerical
Method
Demonstration. The uncertainties for the windage heating varied
from 2% to 30% in extreme cases, e.g., Re= 20,000 and Mu
= 0.3, and yielded 10.2% as an average value, mentioned in Ref.
关1兴. Figure 3 shows the relation between the windage heating
number and the circumferential Mach number in the convergent
stepped labyrinth seal with smooth land. Different circumferential
Mach numbers mean different rotational speeds. The present 3D
model is more agreeable with the experimental data at Rex
= 10,000 than the 2D axis-symmetric model, which was adopted
by Denecke et al. 关1兴. Additionally, the windage heating number
increases as the circumferential Mach number 共which indicates
the rotational speed兲 increases. This can be explained by the wall
shear stress increasing as the rotational speed increases.
Figure 4 shows the relation between the windage heating number and the circumferential Mach number in the divergent stepped
labyrinth seal with smooth land at two kinds of inlet swirl conditions. The present numerical results are well in agreement with
experimental data at Rex = 10,000. And the windage heating number decreases by about 25% in the case of Kin = 0.3 compared with
the no preswirl case. The obtained numerical results with the 3D
model show that the present method is able to analyze the windage heating effect in the convergent and divergent labyrinth seals
at different inlet swirls.
Figure 5 shows the relations between ␴ and Mu for the converOCTOBER 2009, Vol. 131 / 041009-3
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Fig. 3 ␴ versus Mu in the convergent labyrinth seal „Rex
= 10,000…
gent stepped labyrinth seal with 1/16 in. honeycomb cell land. It
gives the comparison between numerical data and experimental
data. The present CFD results are lower than that of the experiment data by about 8% at Rex = 10,000, and two lines are almost
parallel, indicating the reasonability of simulations. The CFD results show excellent agreement with the experimental one at Rex
= 20,000.
The above discussion shows that the numerical method has sufficient accuracy to simulate the total temperature difference in the
labyrinth seal. However, we do not know whether the simulated
flow field in the chamber is right or not. Therefore, two special
positions in the chamber were selected for the divergent flow in
the smooth configuration, as shown in Figs. 6 and 7. The swirl
velocity is plotted and compared with the LDV measurement 关1兴.
The results show that the calculated swirl velocity presented is in
agreement with the experimental data and better than the 2D axissymmetry one performed by Denecke et al. 关1兴. It can also be
deduced that the swirl velocity decreases along the axial direction,
and the difference in tangential velocity between Kin = 0.3 and
Kin = 0 increases along the axial direction.
Fig. 5
␴ versus Mu in the 1/16 in. honeycomb cell seal
effects of the pressure ratios and sealing clearances on the discharge and total temperature increase in the convergent stepped
labyrinth seals with smooth and 1/16 in. honeycomb cell lands are
conducted. Four sizes of sealing clearance for these two seal configurations are set to be 1.3 mm, 1.5 mm, 1.7 mm, and 1.9 mm.
Five different pressure ratios ranging from 1.1 to 1.9 are calculated in this study. And no inlet preswirl is considered in these
cases.
Figures 8 and 9 show the dependence of the leakage flow rate
on radial clearance and pressure ratio. For these two configurations, the increase in leakage rate is almost linearly proportional to
the clearance and pressure ratio, which corresponds to the study of
Schramm et al. 关5兴. The similarity between the two figures means
that radial clearance and pressure ratio have the same effect on the
leakage rate of two different configurations. However, the leakage
flow rate of the honeycomb configuration is a little larger 共⬇10%兲
than that of the smooth configuration at the same radial clearance
and pressure ratio.
Figures 10 and 11 illustrate the relations between the windage
power and leakage flow of honeycomb and smooth configurations.
The windage power increases as the leakage rate and clearance
4.2 Pressure Ratio and Sealing Clearance Effects. On the
basis of the demonstration of the present numerical approach, the
Fig. 4 ␴ versus Mu in the divergent labyrinth seal „Rex
= 10,000…
Fig. 6 Swirl velocity at x = 17.5 mm, divergent flow, smooth
configuration „Mu É 0.46, Rex = 10,000…
041009-4 / Vol. 131, OCTOBER 2009
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Fig. 7 Swirl velocity a x = 22.5 mm, divergent flow, smooth
configuration „Mu É 0.46, Rex = 10,000…
increase, which corresponds to the research reported by Millward
and Edwards 关11兴. As to the smooth configuration, the relations of
the windage power and leakage rate at C = 1.7 mm and C
= 1.9 mm nearly coincide with each other, which are different
from the honeycomb configuration. The calculated windage power
of the honeycomb configuration is a little higher than that of the
smooth one due to the damping effect of the honeycomb, but it
does not correspond to the +15% magnitude reported by Millward
and Edwards 关11兴.
The windage heating number of the honeycomb configuration
in Fig. 12 was found to be 1–10% lower than that of the smooth
case 共Fig. 13 and Table 3兲. It can be explained by comparing the
leakage flow and windage power between them. The leakage rate
of the honeycomb is about 10% higher than that of the smooth
case, as shown in Figs. 8 and 9. And the windage power of these
two configurations is nearly the same. In addition, for both smooth
and honeycomb configurations, the windage heating number decreases as the pressure ratio and clearance increase, which is opposite to the windage heating power.
Fig. 8 Leakage flow versus ␲ of the honeycomb configuration
Journal of Turbomachinery
Fig. 9 Leakage flow versus ␲ of the smooth configuration
4.3 Comparison Between Different Configurations. Selecting the convergent flow arrangement, smooth configuration C
= 1.3 mm, n = 10,000 rpm, and ␲ = 1.1 case as a reference point,
the difference between the other case and the reference case can
be defined as
⌬1 =
␴ − ␴smooth,convergent
⫻ 100%
␴smooth,convergent
⌬2 =
H − Hsmooth,convergent
⫻ 100%
Hsmooth,convergent
⌬3 =
ṁ − ṁsmooth,convergent
ṁsmooth,convergent
⫻ 100%
共5兲
The percentage differences in windage heating number, windage
heating power, and leakage rate for both convergent and divergent
configurations with smooth land and honeycomb land at five different pressure ratios are listed in Table 3. Several conclusions can
Fig. 10 Windage power versus leakage flow of the honeycomb
configuration
OCTOBER 2009, Vol. 131 / 041009-5
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Fig. 11 Windage power versus leakage flow of the smooth
configuration
be deduced from this table.
At the same clearance and rotor speed, the windage heating
number decreases as the pressure ratio increases. But the windage
heating power and leakage rate increase as the pressure ratio
increases.
As to the same configuration 共smooth land or honeycomb land兲,
the windage heating number of the convergent arrangement is
larger than that of the divergent arrangement. It means that the
total temperature difference is smaller in the divergent arrangement. For the smooth configuration, the windage power of the
convergent arrangement is smaller than that of the divergent arrangement, but it is the opposite for the honeycomb configuration.
For both smooth and honeycomb configurations, the leakage rate
of the convergent flow is smaller than that of the divergent flow.
As to the same flow arrangement 共divergent or convergent兲, the
windage heating number of the smooth land is larger than that of
the honeycomb land. And the leakage rate of the smooth land is
smaller than that of the honeycomb land. For the convergent arrangement, the windage heating power of the smooth land is
smaller than that of the honeycomb land by about 2–10%. But the
Fig. 13
␴ versus ␲ in the smooth configuration
windage heating power of the smooth land is a littler larger than
that of the honeycomb land for the divergent arrangement.
4.4 Flow Fields. Figure 14 shows the velocity vectors and
static pressure contour distribution in the smooth configuration
with two sealing clearances at ␲ = 1.1. According to Figs. 14共a兲
and 14共b兲, the flow patterns are nearly similar. The fluid flows into
the seal and is accelerated through the gap. Then, it impinges
toward the step and causes the pressure to increase near the step
wall. In each chamber, the jet separates the flow into two counterrotating vortices, one is behind the knife with higher pressure, and
the other is behind the step with lower pressure. The size of the
former becomes larger as the clearance increases. And the shape
of the latter decides the incidence angle into the gap, which has a
lot of influence on the leakage.
The computed flow fields of the honeycomb configuration are
shown in Fig. 15. The pressure decreases along the chamber,
while the pressure along the axial direction does not always deTable 3 ␴,
= 10,000 rpm
H,
and
ṁ
Configuration
Flow
arrangement
Smooth land
Convergent
Divergent
Honeycomb land
Convergent
Divergent
Fig. 12
␴ versus ␲ in the honeycomb configuration
differences
at
C = 1.3 mm,
n
␲
⌬1
共%兲
⌬2
共%兲
⌬3
共%兲
1.1
1.3
1.5
1.7
1.9
1.1
1.3
1.5
1.7
1.9
0.0
⫺24.4
⫺34.2
⫺40.3
⫺45.0
⫺12.8
⫺33.5
⫺42.4
⫺47.9
⫺52.5
0.0
38.7
63.3
82.6
97.8
3.7
44.0
67.9
86.5
100.0
0.0
83.5
148.2
205.9
259.6
19.0
116.5
191.4
258.2
320.6
1.1
1.3
1.5
1.7
1.9
1.1
1.3
1.5
1.7
1.9
⫺8.7
⫺29.3
⫺36.8
⫺41.9
⫺45.6
⫺17.5
⫺39.1
⫺45.7
⫺50.7
⫺54.7
2.3
42.2
68.6
89.1
107.4
0.16
37.9
66.0
85.0
99.0
12.0
101.2
166.9
225.6
281.3
21.4
126.5
206.0
275.3
339.0
041009-6 / Vol. 131, OCTOBER 2009
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Transactions of the ASME
Fig. 14 Static pressure contours and velocity vector distribution of the stepped labyrinth seal with smooth land, convergent
flow
crease in the cells, and the pressure in the cell above the knife is
higher than that of the neighbors. Compared with the smooth case,
the vortices behind the step disappeared, and the one in the chamber almost occupies the whole chamber volume. Low speed fluid
is filled within the honeycomb cells in the form of vortices, which
push the chamber flow to the seal bottom, or it is pushed back into
the cells.
5
Conclusions
Based on the experimental data of Denecke et al. 关1兴, threedimensional RANS solution with the commercial CFD software
CFX is utilized to analyze the influence of the pressure ratios and
sealing clearances on the discharge and total temperature increase
in the convergent and divergent labyrinth seals with smooth and
honeycomb lands.
As to both smooth and honeycomb configurations with convergent arrangement, the computed windage heating number decreases with increasing pressure ratio and sealing clearance. But
the leakage flow rate and windage heating power follow the opposite trend with these two factors. The influence of the pressure
ratio on the leakage flow pattern is nearly negligible.
As to the same configuration 共smooth land or honeycomb land兲,
the windage heating number of the convergent configuration is
larger than that of the divergent configuration, and the leakage rate
of the convergent flow is smaller than the divergent flow arrangement. For the smooth configuration, the windage power of the
convergent arrangement is smaller than the divergent arrangement, but it is opposite for the honeycomb configuration.
As to the same flow arrangement 共divergent or convergent兲, the
windage heating number of the smooth land is larger than that of
the honeycomb land at the same sealing clearance and pressure
ratio. And the leakage flow rate of the honeycomb configuration is
higher than that of the smooth one due to the larger effective
sealing gap of the honeycomb. For the convergent arrangement,
the windage heating power of the seal with smooth land is smaller
than that of honeycomb land by about 2–10%, but it is opposite
for the divergent flow.
Journal of Turbomachinery
Fig. 15 Static pressure contours and velocity vector distribution of the stepped labyrinth seal with honeycomb land, convergent flow
Acknowledgment
The authors are grateful for Project No. 50506023 supported by
the National Natural Science Foundation and Program for New
Century Excellent Talents in University of China 共Project No.
NCET-07-0669兲. Additionally, the authors thank Dr. Denecke for
his kind help to provide us a lot of information, which was helpful
for the present numerical study.
Nomenclature
a = 冑␬RTstatic,in
C
CD = ṁ / mid
Cp
H = C p · ṁ · ⌬T
K = Vt / U
ṁ
Mu = U / a
n
p
P
R
R = 287.2
Rm
Rex = ṁ / ␮m␲Rm
T
U = ␻ · Rm
X
Greek Letters
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
⫽
speed of sound 共m/s兲
sealing clearance 共mm兲
discharge coefficiency
specific heat capacity 共J / kg K兲
windage heating power 共kW兲
swirl ratio
mass flow rate 共kg/s兲
circumferential Mach number
rotor speed 共rpm兲
static pressure 共Pa兲
total pressure 共Pa兲
radial distance 共m兲
specific gas constant 共J / kg K兲
average rotor radius 共m兲
axial Reynolds number
temperature 共K兲
rotor circumferential velocity 共m/s兲
axial discharge along seal 共m兲
⌬ ⫽ difference
␬ ⫽ ratio of specific heats
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␮
␲ = Pin / pout
⌸
␳
␴ = 2Cp⌬Ttotal / U2
␻
Subscripts
HC
id
in/out
m
r/t/x
static/total
⫽
⫽
⫽
⫽
⫽
⫽
dynamic viscosity 共N s / m2兲
pressure ratio
effective pressure ratio
density 共kg/ m3兲
windage heating number
rotor angular velocity 共rad/s兲
关6兴
关7兴
关8兴
⫽
⫽
⫽
⫽
⫽
⫽
honeycomb
ideal
inlet/outlet condition
arithmetic average of the inlet and outlet
radial/tangential/axial direction
static/total value
References
关1兴 Denecke, J., Dullenkopf, K., Wittig, S., and Bauer, H.-J., 2005, “Experimental
Investigation of the Total Temperature Increase and Swirl Development in
Rotating Labyrinth Seals,” ASME Paper No. GT2005-68677.
关2兴 Peitsch, D., Friedl, W.-H., Dittmann, M., and Denecke, J., 2003, “Detailed
Investigation of the Flow Within the Secondary Air System in High Pressure
Turbines of Aero Engines,” ISABE Paper No. 2003-1038.
关3兴 McGreehan, W., and Ko, S., 1989, “Power Dissipation in Smooth and Honeycomb Labyrinth Seals,” ASME Paper No. 89-GT-220.
关4兴 Denecke, J., Färber, J., Dullenkopf, K., and Bauer, H.-J., 2005, “Dimensional
Analysis and Scaling of Rotating Seals,” ASME Paper No. GT2005-68676.
关5兴 Schramm, V., Willenborg, K., Kim, S., and Wittig, S., 2002, “Influence of a
关9兴
关10兴
关11兴
关12兴
关13兴
关14兴
Honeycomb Facing on the Flow Through a Stepped Labyrinth Seal,” ASME J.
Eng. Gas Turbines Power, 124, pp. 140–146.
Paolillo, R., Moore, S., Cloud, D., and Glahn, J. A., 2007, “Impact of Rotational Speed on the Discharge Characteristic of Stepped Labyrinth Seals,”
ASME Paper No. GT2007-28248.
Morrison, G. L., and Al-Ghasem, A., 2007, “Experimental and Computational
Analysis of a Gas Compressor Windback Seal,” ASME Paper No. GT200727986.
Willenborg, K., Schramm, V., Kim, S., and Wittig, S., 2002, “Influence of a
Honeycomb Facing on the Heat Transfer in a Stepped Labyrinth Seal,” ASME
J. Eng. Gas Turbines Power, 124, pp. 133–139.
Stocker, H., Cox, D., and Holle, G., 1977, “Aerodynamic Performance of
Conventional and Advanced Design Labyrinth Seals With Solid-Smooth,
Abradable and Honeycomb Lands,” NASA Report No. CR-135307.
Tipton, D., Scott, T., and Vogel, R., 1986, “Labyrinth Seal Analysis: Volume
III—Analytical and Experimental Development of Design Model for Labyrinth Seals,” Allision Gas Turbine Division, General Motors Corporation,
Technical Report No. AFWAL-TR-85-2103.
Millward, J., and Edwards, M., 1996, “Windage Heating of Air Passing
Through Labyrinth Seals,” ASME J. Turbomach., 118, pp. 414–419.
AEA Technology GmbH, 2004, CFX-TASCFLOW User Documentation, AEA
Technology, Software Ltd., Waterloo.
Scherer, T., Waschka, W., and Wittig, S., 1992, “Numerical Predicitions of
High-Speed Rotating Labyrinth Seal Performance: Influence of Rotating on
Power Dissipation and Temperature Rise,” ICHMT 1992 International Symposium on Heat Transfer in Turbomachinery, Athens, Greece, Vol. 26, pp. 1514–
1522.
Denecke, J., Dullenkopf, K., and Wittig, S., 2004, “Influence of Preswirl and
Rotation on Labyrinth Seal Leakage,” Proceedings of the Tenth International
Symposium on Transport Phenomena and Dynamics of Rotating Machinery
ISROMAC, HI, Paper No. ISROMAC10-2004-105.
041009-8 / Vol. 131, OCTOBER 2009
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