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83
Calibration of porous medium models for brush seals
A O Pugachev∗ and P Helm
Institute of Energy Systems, Technische Universität München, Garching, Germany
The manuscript was received on 19 May 2008 and was accepted after revision for publication on 3 September 2008.
DOI: 10.1243/09576509JPE641
Abstract: One of the theoretical approaches to modelling brush seals is based on the porous
medium models. In this approach, influence of the brush on the flow is defined by a set of resistance coefficients. Although these coefficients can be estimated, the brush seal model needs to
be calibrated against the measurements. This work analyses calibration procedures with respect
to extrapolation of the theoretical results on different brush seals and operating conditions. Two
sealing configurations and two bristle packs are studied experimentally and theoretically. Computational fluid dynamics predictions and measurements of leakage, axial pressure, and brush
clearance are presented. The efficiency of calibration procedures is also discussed.
Keywords: leakage, porosity, bristle pack, computational fluid dynamics
1
INTRODUCTION
Originally proposed for aircraft engine applications
[1, 2], brush seals are one of the innovative dynamic
sealing concepts that have great potential as alternatives to the conventional labyrinth seals in steam
turbines. Figure 1 shows a brush seal that consists
of fine metallic or ceramic bristles closely packed
between front and backing plates. Bristles are inclined
to circumferential direction at a lay angle of 45◦ . Brush
seal designs differ in bristle pack properties (material, diameter and length of bristles, packing density,
and pack thickness) and geometry of front and backing plates. They can be designed as contact seals with
zero or negative radial clearance and with a small cold
clearance. Generally, brush seals provide significantly
better leakage performance compared with labyrinths.
Compliant bristle pack can compensate for radial
clearance variation during transient, operating, and
off-design conditions with controllable wear by eliminating immediate damage. Primary concerns when
using brush seals can be costs of fabrication, uncontrollable wear, heat generation because of friction
between a rotor and bristles, and rotordynamic performance. Moreover, other factors should be considered
∗ Corresponding
author: Institute of Energy Systems, Technische
Universität München, Boltzmannstrasse 15, Garching 85747,
Germany. email: [email protected]
JPE641 © IMechE 2009
during the design process [3] due to complex aerodynamical and mechanical interaction of the bristle pack
with stator and rotor.
Computational fluid dynamics (CFD) techniques
have been used for brush seal modelling in many
studies. Braun and Kudriavtsev [4] solved the twodimensional Navier–Stokes equations for pin arrays
representing an idealized brush seal in order to gain an
understanding of the local characteristics of the flow.
Later, more comprehensive models have been developed, in which the mechanical behaviour of bristles
was taken into account [5]. Such an approach combines detailed CFD simulation resolving flow structure
through the bristles with finite-element analysis to
determine bristle deformations due to aerodynamic
forces. The whole iteration procedure is computationally very expensive, which allows only a small number
of bristles to be considered during simulations.
A simple and widely used approach to the brush
seal flow calculation is based on the porous medium
models. In this approach, a bristle pack is treated as
an anisotropic continuous porous region with defined
resistance to the flow. These models depend greatly on
heuristic information and require adjustment (calibration) to improve correlation with the measurements
quantitatively. More detailed description and a brief
overview of the porous medium models are presented
in the corresponding section.
In this article, experimental results on leakage, axial
pressure, and radial clearance are presented for four
combinations of brush and labyrinth seals. Theoretical
Proc. IMechE Vol. 223 Part A: J. Power and Energy
84
A O Pugachev and P Helm
Fig. 1
Brush seal
results on sensitivity of calibration procedures based
on variation of bristle pack thickness and brush clearance are discussed. The results can be used to develop
a more general calibration procedure that requires less
experimental data and is more accurate for diverse
bristle packs.
2
EXPERIMENTAL INVESTIGATION
Experimental investigations on brush seals have been
carried out on the static test rig at the Institute
of Energy Systems, Technische Universität München,
Germany (Fig. 2). The Jeffcott rotor has a diameter of
179.98 mm and its shaft is supported by two ball bearings at its ends. A variable-speed direct-current motor
drives the test rotor up to 12 000 r/min. A compressor supplies air to the test rig at the maximum inflow
pressure of 1.0 MPa. Compressed air is injected at the
centre of the assembly into the swirl vane to generate an inlet preswirl nearly independent of the inflow
pressure. The preswirl value can be set between 80
and 300 m/s. The air divided into two flows passes axially through the twin test sealing configurations. The
detailed description of the test rig could be found in
references [6] and [7].
The sealing configuration has a modular structure
and is assembled from a series of interchangeable
rings. Figure 3 presents a cross-section of the typical seal used in this study. A sealing ring refers to
either brush seal or labyrinth seal. According to the
notion used in this work, the seal shown in Fig. 3 is
referred to as a BSS seal – a brush seal set upstream
of two labyrinth teeth. Four sealing configurations are
studied: two different seal designs with two different bristle packs. The two designs are brush seal at
the upstream followed by two sealing teeth (Fig. 3)
and brush seal placed downstream of two sealing
teeth (SSB). Each sealing configuration is tested with
two different bristle packs, B2 and B3, with metallic
(cobalt-based alloy) bristles. The bristle packs differ
in bristle diameter and packing density. All configurations tested are summarized in Table 1. The bristle
pack B2 consists of a larger amount of finer bristles compared with B3. Another feature of the tested
brush seals is a front plate design. Brush seals usually have a massive front plate that protects the
Fig. 2 Test rig
Proc. IMechE Vol. 223 Part A: J. Power and Energy
JPE641 © IMechE 2009
Calibration of porous medium models
Fig. 3
BSS sealing configuration
Table 1 Tested sealing configurations
BSS B2
N (bristles/mm)
d (mm)
bb (mm)
200
0.07
1.98
SSB B2
BSS B3
SSB B3
50
0.15
clearance is 0.31 mm. More detailed description of the
optical measurements could be found in reference [6].
3
CFD MODELLING OF BRUSH SEALS
3.1
bristle pack from the upstream. Brush seals considered in this work have practically no front plate
(Fig. 1).
A combination of labyrinth and brush seals provides some advantages. The brush seal offers better
leakage performance and requires less space than
the labyrinth seal. The leakage through brush seals
is considerably less than that through conventional
labyrinth seals. In real applications, brush seals are
often built into existing labyrinth seals replacing one
or several seal teeth, as in the case of the test seals
presented in this work. The labyrinth seals in turn are
low-cost sealing elements and could be used to control
the magnitude of pressure drop across the brush.
Static air pressure is measured in all chambers of
the sealing configuration. Pressure values in chambers were averaged over ten measurement positions
across the circumference. The leakage through the left
and right sealing configurations is calculated from the
total leakage in the test rig. Inlet pressure takes values from 0.1 to 1.0 MPa. Separate measurements have
been carried out to estimate the magnitudes of radial
clearance in the brush seals at different pressure differentials. The brush radial clearance was determined
from the optical measurements in the SSB configuration on a digital camera at the zero rotor speed. A
simple image processing provides an estimation of
radial clearance with the root mean square deviation
of 10 per cent of cold clearance value of 0.21 mm. Tooth
JPE641 © IMechE 2009
85
Porous medium model
A porous medium approach is considered in this work
to model the bristle pack. This approach allows avoiding full resolving of individual bristles. It makes the
whole CFD model of the seal simpler. The bristle pack
of the brush seal is treated as a porous structure. The
basic characteristic of the porous medium is porosity
ε – the ratio of the volume of voids to the total volume
(voids and solids). For the bundle of cylinders, porosity
is represented as
ε =1−
πd 2 N
4bb cos ϕ
(1)
In this formula, there is only one parameter that
may greatly depend on operating mode. This parameter is the bristle pack thickness bb and it depends
on the pressure drop across the seal due to the compliant nature of the bristle pack. The porosity of the
tested brush seals for the initial bristle pack thickness (manufacture’s value) is 0.42 and 0.34 for brushes
B2 and B3, respectively. The theoretical closest packing of bristles may be estimated from the geometrical
considerations [8]
√ dN
3d
min
bb = d +
−1
(2)
2
cos ϕ
Minimum values of bb for B2 and B3 are equal to 1.21
and 1.40 mm with porosities of 0.1 and 0.11, respectively. However, as several theoretical studies have
shown [8, 9], the bristle pack thickness does not reach
Proc. IMechE Vol. 223 Part A: J. Power and Energy
86
A O Pugachev and P Helm
Table 2
Minimal pack thickness and porosity of investigated bristle packs
Minimal pack thickness (mm)
Porosity (–)
viscous resistances in different directions
an = az = 80C,
B2
B3
1.21
0.10–0.42
1.40
0.11–0.34
bn = bz = 1.16D,
(1 − ε)2
ε3 d 2
1−ε
D= 3
ε d
as = 32εC, C =
bs = 0,
(4)
its theoretical minimum value even at high pressure
differentials. Porosity ranges of the bristle packs are
summarized in Table 2. The bristle pack B3 is less compliant than B2. For the same pack thickness, B3 is less
porous compared with B2.
Porous medium models describe the relation
between pressure gradient and velocity for the fluid
flow through the porous structure. At low Reynolds
numbers where viscous resistance is dominant, this
pressure drop depends linearly on the flow velocity
(Darcy’s law). To eliminate deviations at high velocities, Darcy’s law was extended taking into account
a quadratic term that represents an inertial contribution to the momentum balance [10].
Bristle packs of brush seals have strong anisotropic
structure. The flow resistance is obviously smaller in
the direction along the bristle (streamwise direction s)
than in the directions normal to the bristles (axial z
and circumferential n directions). Thus, the porous
medium equation in terms of linear and quadratic
resistance for the three anisotropic directions (n, z,
and s) in the bristle pack can be represented as
−
∂p
= ai μvi + bi ρ|vi |vi
∂xi
(3)
Considering the three directions in the bristle pack,
the resistance equation is determined by three viscous or linear resistance coefficients a and three
inertial or quadratic coefficients b. If an isotropic, onedimensional porous medium model is considered,
there are only two unknown resistance coefficients.
In this case, one can directly calibrate these coefficients based on two operating points [11]. Otherwise,
additional models for the resistance coefficients are
required.
In the case of isotropic structure, the viscous resistance a may be obtained from the semi-empirical
Carman–Kozeny theory for solid matrices [10]. Ergun
[12] extended this theory and constructed an empirical correlation for the non-Darcy coefficient b for
packed beds on the basis of large amount of experimental data.
The model by Ergun was adopted by several authors
for the brush seal applications and modified to
account for anisotropy and match experimental observations. Chew et al. [13, 14] have modified viscous
and inertial resistance in the streamwise direction;
as is reduced by an empirical factor and bs is set to
zero. Recently, Pröstler [8] has proposed another factor for as by introducing a non-linear relation between
Proc. IMechE Vol. 223 Part A: J. Power and Energy
The coefficients defined in equation (4) are used
in this study. A comparison of the models of Ergun
et al. applied to brush seals has shown that the leakage predictions with equation (4) lie between values
obtained with the model by Ergun and modification
by Chew [15]. The resistance coefficients are larger
in the modification by Pröstler compared with Chew’s
expressions at the same bristle pack thickness, i.e. the
medium is less porous.
3.2
Calibration procedure
As mentioned earlier, porous medium models are
based on empirical information. Sources of uncertainty during operation are bristle pack thickness and
radial clearance between bristle pack and rotor (the
latter only in the case of non-zero cold clearance).
Therefore, theoretical model for a particular brush seal
needs to be calibrated. Calibration means that the
seal operating characteristics (leakage and/or pressure drop) should be adjusted to experimental data for
one or more operational points (inlet pressures), i.e.
the greatest lack of available porous medium models.
However, fortunately, the calibration only at one pressure drop could be sufficient to provide reasonable
predictions of leakage performance.
The porous medium model in equation (4) for a particular bristle pack is fully determined by its bristle
pack thickness; there is only one unknown variable
during the operation. Variation of the lay angle can be
neglected. Thus, the natural way to calibrate the model
is to vary bb between its initial cold value and theoretical closest packing from equation (2). In this case,
one keeps the leakage through the clearance constant
and affects the leakage through the bristle pack. Brush
seals operating with non-zero radial clearance could
also be calibrated by varying s. Brush radial clearance
is constrained by the cold and zero clearance. One of
the aims of this work is to compare these two possibilities and to show which procedure is preferable.
The calibration procedure could be also based on
variation of both parameters (pack thickness and
radial clearance). Further complications of calibration procedures are also possible, e.g. by dividing the
bristle pack into a number of regions with different
coefficients [16, 17].
Generally, results of calibration are resistance coefficients of porous medium model and/or brush clearance. These results are used later to calculate brush
seal performance for the whole operating range.
JPE641 © IMechE 2009
Calibration of porous medium models
87
Bristle pack thickness variation is used as a primary
calibration procedure in this work. Calibration of the
theoretical model is carried out for four sealing configurations at a single pressure differential from the
middle of the operating range. During calibration, the
value of the bristle pack thickness is changed proportionally to the weighted value of leakage. A realistic
value of brush radial clearance is estimated from the
optical measurements (discussed subsequently).
3.3
CFD modelling
Numerical calculations are performed by using ANSYS
CFX 11. A three-dimensional hexahedral grid with
one cell in the circumferential direction that represents a 0.2◦ slice is generated in ANSYS ICEM CFD
11. Total pressure and temperature are set on the inlet
boundary and static pressure on the outlet boundary.
Periodic boundary conditions are applied on the slice
faces. The rotor surface is modelled as a rotating wall
and the porosity region as a subdomain with defined
momentum losses. The dimensions of the porosity
region are not defined strictly by geometry primitives
during the mesh generation, but they are defined by
algebraic expressions in the preprocessing of the CFD
analysis. Two functions are introduced into the model:
one for the brush radial clearance and the other for the
bristle pack axial thickness. The function returns 1 for
a particular node if the node lies within the porosity
region, otherwise it returns 0. According to the value,
the momentum loss model is either switched on or
off. The nodes with the function value 1 represent
the porous medium region. The algebraic definition
of the bristle pack allows the automation of the calibration process and parametric studies (e.g. clearance
and thickness variation in the brush seal), because the
computational grid has to be generated only once.
A disadvantage of such approach is that the grid in
the bristle region must be extremely fine to capture
possible changes in the dimensions of the porous
medium, which in turn slows down convergence of
calculations.
4
RESULTS AND DISCUSSION
To obtain better predictions with the theoretical
model, the experimental data for brush radial clearance are used for calibration. The clearance values
have been estimated from the optical measurements
at different pressure drops in SSB sealing configuration. Figure 4 shows the optical measurement results at
pressurizing and depressurizing conditions. The pressure drop shown on the horizontal axis corresponds to
the whole sealing assembly. Both bristle packs observe
similar behaviour with the distinction that the blowdown effect is not as strong for B3 as it is for B2. This is
due to the higher stiffness and, therefore, smaller radial
JPE641 © IMechE 2009
Fig. 4
Measured rotor brush clearance versus pressure
drop for SSB
bending of bristles in B3. The bristle pack B2 reaches
a zero clearance with increasing pressure, whereas the
minimum clearance of B3 is ∼40 per cent of its cold
clearance. The near constant radial clearance is settled
already by relatively moderate pressure differentials
(0.2 MPa for B2 and 0.4 MPa for B3). It means that the
thickness of the bristle pack could play an important
role in leakage control.
Experimental results also show a hysteresis effect,
which is a typical characteristic of brush seals
and could have a great influence on seal leakage
performance. A depressurization leads to smaller
clearance values, i.e. smaller mass flowrates. The
clearance values at pressurizing conditions are used
for calibration.
Operating conditions at the calibration points and
results of calibration are summarized in Table 3. It can
be seen that the brush seal B3 possessing more stiffness undergoes compaction. The pack thickness of B3
tends to the theoretical minimal value. In contrast, the
bristle pack B2 undergoes mainly a blow-down effect
with only small changes in bristle pack thickness. The
calibration results show that for the sealing configuration BSS B2, the bristle pack thickness remains
unchangeable when compared with the initial thickness of 1.98 mm. Generally, SSB configuration shows
smaller values for bb and s, compared with BSS.
By using the calibration results from Table 3, leakage
performance of four sealing configurations tested is
calculated for the whole inlet pressure range. Figure 5
illustrates the experimental and theoretical results on
mass flowrate as a function of inlet pressure. In Fig. 5,
Table 3
Calibration points and results
Inlet pressure (MPa)
Mass flowrate (g/s)
Brush radial clearance (mm)
Bristle pack thickness (mm)
SSB B2
SSB B3
BSS B2
BSS B3
0.507
86.20
0.009
1.8
0.507
55.64
0.079
1.495
0.54
100.64
0.02
1.98
0.5
67.19
0.089
1.55
Proc. IMechE Vol. 223 Part A: J. Power and Energy
88
A O Pugachev and P Helm
Fig. 5
Leakage versus inlet pressure
the stems represent the calibration points. A comparison between different brushes shows that brush B3
reduces leakage remarkably better than B2 in both seal
designs, although B3 operates at higher clearances.
This is one more significant difference between both
brush seals. The leakage through a brush seal consists
of two parts, of which one flows through the clearance and the other through the bristles. One could
state that the leakage through the bristle is significantly smaller for B3. This decrease in bristle leakage
is obviously higher than the increase in the clearance
leakage caused by a larger clearance. This effect leads
to a smaller leakage for B3. The lower bristle leakage
is not surprising because the porosity of B3 is only
81 per cent of that of B2 under cold conditions. The
results also show that the leakage performance of SSB
configuration is slightly better than that of BSS. This
means that the influence of the position of the brush
seal (upstream or downstream) is insignificant for the
leakage performance.
Theoretical predictions based on equation (4) follow
the same tendency in leakage performance. Generally, the theory underestimates mass flowrates for
pressures below the calibration point and overestimates for pressures above the calibration point. The
difference increases at high pressures, although the
accordance is fairly good with one exception. BSS B3 at
high pressures demonstrates relatively large deviation
Proc. IMechE Vol. 223 Part A: J. Power and Energy
between the measurements and predictions. Unfortunately, there is a lack of experimental data in the
high-pressure range for B3. BSS B2 shows the smallest
deviation at all pressure conditions.
The difference between CFD and experimental
results could be explained by the pressure-dependent
clearance in the brush seal. Although the value of s for
calibration is taken from the optical measurements, it
is kept constant over the whole pressure range. Introducing an approximate relation for a brush clearance
(e.g. logarithmic function) into the theoretical model
could increase the accuracy of predictions [18]. This
has been confirmed for SSB sealing configuration.
Other concern of deviation between theory and experiments is with applicability of the Ergun porous model
and its modifications. The original Ergun’s equation
was derived for spherical particles with the porosity
near 0.4. This could explain a larger deviation for B3,
which has porosity <0.2 at operating conditions. In
this regard, other models proposed in the theory of
porous media (e.g. [10, 19]) could be more accurate
when applied to the brush seal applications.
From the experimental point of view, it should be
mentioned that the error in leakage measurements
was slightly higher at high pressure differentials due
to the averaging procedure. A double-flow design of
the test rig requires two identical test seal configurations. Experimental value of leakage across the seal is
determined on the basis of the total leakage of the test
rig. During measurements, unbalanced axial pressure
distributions were observed at high inflow pressures
for the brush seals being in operation for some time.
This indicates that brush seals were no more identical
at those points due to rub or other effects.
To investigate the sensitivity of mass flowrate on
brush seal operating parameters (i.e. the sensitivity of different calibration procedures), parametric
studies on variation bb and s have been carried out.
Figure 6 presents mass flowrates versus brush clearance at calibration point. The mass flowrate is shown
relative to the maximal leakage of corresponding sealing configuration. The brush clearance is related to
Fig. 6
Effect of brush clearance variation for BSS
JPE641 © IMechE 2009
Calibration of porous medium models
the maximal value of 0.21 mm. It should be mentioned that the porosity is kept constant. Observing
this plot from the right to the left, it is seen that the
total leakage decreases due to the reduction of clearance mass flowrate. Decreasing brush clearance to
zero results in leakage reduction of nearly 20 and 50
per cent for B2 and B3, respectively. According to this
notable difference, one could state that the calibration
procedure based on clearance variation may have different effectiveness when applied to different brush
seals.
Figure 7 shows the effect of the bristle pack thickness variation on leakage. The pack thickness is related
to the value of 2.4 mm, which is ∼21 per cent more
than the manufacture’s value. The minimal thickness
corresponds to the values near the theoretical closest packing. Here, a similar behaviour for B2 and B3
is observed. The leakage reduction comes to about
40 per cent. Generally, variation in bb has a greater
influence on leakage than the variation in s. All this
makes the calibration procedure based on variation of
bb more preferable from the point of view of different
bristle packs.
Figure 8 shows the axial pressure distribution for
the brush seal B3 in SSB and BSS sealing configurations at calibration point. As expected, most of the
pressure drop occurs in the brush seal, either in BSS
Fig. 7
Effect of bristle pack thickness variation for BSS
Fig. 8
JPE641 © IMechE 2009
89
or in SSB configuration. Slightly higher pressure drop
is observed in the SSB configuration, which leads to
a slightly smaller leakage (Fig. 5). The theory overestimates axial pressures for both configurations. The
largest deviation occurs in the BSS configuration and
is equal to 25 per cent. Figure 9 shows contour plots
of pressure in the two bristle packs investigated. In B2,
there is a strong radial pressure gradient. It confirms
the fact that B2 operates under the blow-down conditions. In B3, the axial pressure gradient dominates
over the radial one.
Fig. 9
Pressure contours in B2 (top) and B3 (bottom)
Axial pressure distribution for the seals with the bristle pack B3
Proc. IMechE Vol. 223 Part A: J. Power and Energy
90
5
A O Pugachev and P Helm
CONCLUSION
This work investigates the brush seal modelling based
on a porous medium approach. A CFD modelling
is applied to four different sealing configurations,
including two types of brush seals with different bristle
diameters and packing densities to predict their leakage performance. The calibration results indicate that
varying bristle pack thickness is more effective even at
high values of free radial clearance in the brush seal.
The dependence of the mass flowrate on the thickness
of the bristle pack can be approximated, which could
simplify the calibration procedure for different brush
seals. Theoretical predictions for mass flowrate show
good correlation with experimental data. The estimation of the brush radial clearance from the optical
measurements shows that the brush seal B2 operates under blow-down effect in most cases, whereas
the brush seal B3 has a significant radial clearance.
Despite this, the leakage is considerably smaller for
the brush seal B3. This must be a consequence of
smaller porosity of B3, which compensates for the
higher clearance leakage by a smaller mass flowrate
through the bristle pack.
ACKNOWLEDGEMENTS
The second author would like to thank the German
Federal Ministry of Economics and Labour (BMWA),
the Bavarian Government and Bayerische Forschungsstiftung (BFS), and Siemens AG for the financial support of this work as a part of the research
programme ‘Power Plants for the 21st Century (KW21)’.
REFERENCES
1 Gorelov, G. M., Reznik, V. E., and Tsibizov, V. I. Experimental study on brush seal flow characteristics and
comparison with a labyrinth seal (in Russian). Izvestiya
VUZov, Aviatsionnaya Tekhnika, 1988, 31(N4), 43–46.
2 Ferguson, J. G. Brushes as high performance gas turbine seals. In the ASME Gas Turbine and Aeroengine
Congress and Exposition, Amsterdam, The Netherlands,
1988, ASME paper 88-GT-182.
3 Dinc, S., Demiroglu, M., Turnquist, N., Mortzheim, J.,
Goetze, G., Maupin, J., Hopkins, J., Wolfe, C., and
Florin, M. Fundamental design issues of brush seals for
industrial applications. ASME J. Turbomach., 2002, 124,
293–300.
4 Braun, M. J. and Kudriavtsev, V. V. A numerical simulation of a brush seal section and some experimental
results. ASME J. Turbomach., 1995, 117, 190–202.
5 Lelli, D., Chew, J. W., and Cooper, P. Combined threedimensional fluid dynamics and mechanical modelling
of brush seals. ASME J. Turbomach., 2006, 128, 188–195.
6 Helm, P., Spliethoff, H., and Neef, M. Closing the clearance: measuring bristle blow down of brush seals. In the
Proc. IMechE Vol. 223 Part A: J. Power and Energy
7
8
9
10
11
12
13
14
15
16
17
18
19
19th International Conference on Fluid Sealing, Poitiers,
France, 2007.
Schettel, J., Deckner, M., Kwanka, K., Lüneburg, B., and
Nordmann, R. Rotordynamic coefficients of labseals for
turbines – comparing CFD results with experimental
data on a comb-grooved labyrinth. In the ASME Turbo
Expo, Reno-Tahoe, Nevada, USA, 2005, ASME paper
GT2005-68732.
Pröstler, S. Modellierung und numerische Berechnung
von Wellenabdichtungen in Bürstenbauart (in German).
Doctoral Thesis, University of Bochum, Germany, 2005.
Holle, G. F., Chupp, R. E., and Dowler, C. A. Brush
seal leakage correlations based on effective thickness. In
the 4th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-4,
Honolulu, USA, 1992.
Kaviany, M. Principles of heat transfer in porous media,
1995 (Springer-Verlag, New York).
Hendricks, R. C., Flower, R., and Howe, H. A brush
seal program modeling and developments. Int. J. Rotat.
Mach., 1998, 4(N2), 91–96.
Ergun, S. Fluid flow through packed columns. Chem.
Eng. Prog., 1952, 48, 89–94.
Chew, J. W., Lapworth, B. L., and Millener, P. J. Mathematical modeling of brush seals. Int. J. Heat Fluid Flow,
1995, 16, 493–500.
Chew, J. and Hogg, S. Porosity modeling of brush seals.
ASME J. Tribol., 1997, 119, 769–775.
Neef, M., Hepermann, F., Sürken, N., and Schettel, J.
Brush seal porosity modeling – applicability and limitations. In the 7th European Conference on Turbomachinery, Athens, Greece, 2007.
Chen, L. H., Wood, P. E., Jones, T. V., and Chew, J. W.
Detailed experimental studies of flow in large scale brush
seal model and a comparison with CFD predictions.
ASME J. Eng. Gas Turbines Power, 2000, 122, 672–679.
Dogu, Y. Investigation of brush seal flow characteristics
using bulk porous medium approach. ASME J. Eng. Gas
Turbines Power, 2005, 127, 136–144.
Pugachev, A. O., Deckner, M., Kwanka, K., Helm, P., and
Schettel, J. Rotordynamic coefficients of advanced gas
seals: measurements and CFD simulations. In the International Scientific Symposium on Hydrodynamic Theory
of Lubrications, Orel, Russia, 2006.
Wu, J., Yu, B., and Yun, M. A resistance model for
flow through porous media. Transp. Porous Media, 2008,
71(N3), 331–343.
APPENDIX
Notation
a
b
bb
d
h
hb
hf
N
viscous resistance (1/m2 )
inertial resistance (1/m)
bristle pack thickness (m)
bristle diameter (m)
bristle length (m)
backing plate clearance (m)
front plate clearance (m)
bristle packing density (bristles/m)
JPE641 © IMechE 2009
Calibration of porous medium models
p
s
v
x
pressure (Pa)
radial clearance (m)
velocity (m/s)
spatial coordinate (m)
ρ
φ
ε
μ
porosity (–)
dynamic viscosity (Pa s)
n, z
s
JPE641 © IMechE 2009
91
density (kg/m3 )
lay angle (◦ )
Subscripts
directions normal to bristles
bristle lengthwise direction
Proc. IMechE Vol. 223 Part A: J. Power and Energy
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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