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Brush Seal Temperature
Distribution Analysis
Yahya Dogu
Department of Mechanical Engineering,
Kirikkale University,
Yahsihan, Kirikkale 71451, Turkey
e-mail: [email protected]
Mahmut F. Aksit
Faculty of Engineering and Natural Sciences,
Sabanci University,
Tuzla, Istanbul 34956, Turkey
e-mail: [email protected]
Brush seals are designed to survive transient rotor rubs. Inherent brush seal flexibility
reduces frictional heat generation. However, high surface speeds combined with thin
rotor sections may result in local hot spots. Considering large surface area and accelerated oxidation rates, frictional heat at bristle tips is another major concern especially in
challenging high-temperature applications. This study investigates temperature distribution in a brush seal as a function of frictional heat generation at bristle tips. The twodimensional axisymmetric computational fluid dynamics (CFD) analysis includes the
permeable bristle pack as a porous medium allowing fluid flow throughout the bristle
matrix. In addition to effective flow resistance coefficients, isotropic effective thermal
conductivity as a function of temperature is defined for the bristle pack. Employing a fin
approach for a single bristle, a theoretical analysis has been developed after outlining
the brush seal heat transfer mechanism. Theoretical and CFD analysis results are compared. To ensure coverage for various seal designs and operating conditions, several
frictional heat input cases corresponding to different seal stiffness values have been
studied. Frictional heat generation is outlined to introduce a practical heat flux input into
the analysis model. Effect of seal stiffness on nominal bristle tip temperature has been
evaluated. Analyses show a steep temperature rise close to bristle tips that diminishes
further away. Heat flux conducted through the bristles dissipates into the flow by a strong
convection at the fence-height region. 关DOI: 10.1115/1.2135817兴
Proven performance of brush seal applications in rotating machinery over the past two decades has led to extensive research on
extending brush seal usage to more challenging locations subject
to elevated pressure load, temperature, rotor speed, and transient
rotor-stator closure. Backed by numerous experimental data, modeling and analysis efforts have identified various physical phenomena underlying seal dynamic behavior. From the beginning,
design tools have been developed in the light of these experimental and analytical findings. Leakage and life are defined as the two
main performance parameters of brush seals.
The brush seal is designed to work in contact with the rotor.
Typically, the seal is installed with some assembly interference,
which is expected to reach a line-to-line condition at steady-state
operation after some initial wear-in/break-in period. However, it is
common for brush seals to wear beyond line-to-line condition due
to transient rotor excursions or bristle blow-down caused by a
radial pressure distribution.
Friction between bristle tips and the rotor causes heat generation and wear, which are strongly related to each other. Seal life
and leakage are directly dominated by the amount of wear. Heat
generation and the resulting temperature significantly affect the
bristle wear mechanism and mechanical properties.
Blow-down is favorable to achieve steady leakage performance.
It helps maintain bristle-rotor contact and eliminate seal clearance.
On the other hand, blow-down enhances seal contact force by
pushing the bristles toward the rotor and results in increased heat
generation and wear.
During operation, hot spots may form at the bristle tips and
local temperatures may reach the bristle melting point. Hightemperature exposure degrades mechanical properties; therefore,
bristle tips wear out at an accelerated rate. In addition, a local
To whom correspondence should be addressed.
Contributed by the International Gas Turbine Institute 共IGTI兲 of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript
received August 30, 2005; final manuscript received September 6, 2005. IGTI Review Chair: K. C. Hall. Paper presented at the ASME Turbo Expo 2005: Land, Sea,
and Air, Reno, NV, June 6–9, 2005, Paper No. GT2005-69120.
temperature increase over a thin rotor section may lead to rotor
instability problems. As a result, the level of temperature increase
will dictate limits of brush seal applications.
From the beginning of brush seal usage, heat generation has
been stated as a significant parameter; nevertheless, less attention
has been paid to thermal issues. Only a few studies have appeared
in the literature, in spite of the significance of the issue.
In one of the pioneering brush seal publications, Gorelov et al.
关1兴 showed that with the decrease of airflow rate, there is a
marked heating of the brush. At the same time, very little airflow
is sufficient for cooling at low-pressure differentials.
Hendricks et al. 关2兴 were the first to consider the frictional heat
flux by employing a formula as products of spring force, surface
speed, and interface coefficient. They calculated increasing heat
flux as a function of interference.
Owen et al. 关3兴 developed a formula to calculate the heat generation; however, their analysis requires the rotor surface temperature as an input. It was assumed that heat was conducted toward
bristles and dissipated to the airflow. They also measured temperature under the rotor rim by utilizing infrared detectors. Temperature readings were taken with 20 s time intervals, which is a very
short duration to reach maximum frictional heat generation and
steady-state conditions. They calculated the rotor temperature
field using a finite element model.
Chew and Guardino 关4兴 developed a computational model for
flow between the bristle tips and the rotor to calculate tip force,
wear, and temperature. The model included heat conduction and
heat generation due to contact friction.
Demiroglu 关5兴 developed a closed-form equation to calculate
heat generation. He measured the temperature field over the rotor
rim and fence-height region using an infrared thermography technique. The heat flux was calculated in a finite element model for
the rotor by matching the measured temperature distribution.
Apart from research with gaseous working fluids, Aksit et al.
关6兴 studied the temperature rise in oil brush seal applications.
Their findings indicated that oil temperature levels at high speeds
were due to shear thinning.
The extent of bristle and rotor temperature rise is one of the
primary concerns in brush seal applications. Bristles are subjected
Journal of Engineering for Gas Turbines and Power
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Fig. 1 Schematic of brush seal heat transfer
to excessive bending stress at the backing plate corner due to
high-pressure load at fence height. High-temperature exposure in
the fence-height region decreases bristle mechanical strength leading to premature bristle failure. Except Demiroglu’s 关5兴 thermal
camera measurements, there has been no study showing the temperature distribution in the bristle pack.
This study presents analytical and numerical investigations of
brush seal temperature distribution after providing an outline for
the seal heat transfer mechanism. The full flow and temperature
field solution has been obtained using a two-dimensional axisymmetric computational fluid dynamics 共CFD兲 model. The CFD
model employs a bulk porous medium approach with defined flow
resistance coefficients 关7兴 and a thermal conductivity for permeable bristle pack. Thermal conductivities of all sections 共air,
bristle, and front and backing plates兲 are considered as a function
of temperature since temperature variation is high in the problem
domain. After evaluating brush seal heat transfer mechanisms and
possible frictional heat generation levels, a wide range of frictional heat generation is considered to ensure coverage of all practical heat flux inputs in the model. Frictional heat generation is
calculated using overall brush pack stiffness. Temperature fields
have been identified as a function of seal heat flux input values. To
serve as a benchmark, a theoretical analysis has been developed
employing a simple fin approach. Analytical results have been
compared to the CFD model. The investigation covers various
pressure loads representing a range of brush seal operational
Outline of Brush Seal Heat Transfer Mechanism
Brush seals are located between high- and low-pressure cavities. Frictional heat generation between the bristle tips and rotor
surface occurs during line-to-line or interference operations. Highspeed sliding with bristle-rotor interface produces frictional heat
as a function of the tip force, sliding velocity, and friction coefficient. Coupled effects of initial build interference and blow-down
produce large bristle tip forces, which may result in excessive
frictional heat.
Frictional heat generation at the bristle-rotor interface can be
treated as an area of a circumferential heat source all around the
rotor and across the bristle pack thickness. As a result of this heat
flux input, the temperature rises around heat source region. As
illustrated in Figs. 1 and 2, frictional heat is dissipated primarily
through surrounding materials, by conduction through the rotor
and bristles and by convection to the fluid from both the rotor and
bristle surfaces. Examination of heat transfer mechanisms leads to
several heat transfer paths as shown in Fig. 1.
The frictional heat at the bristle-rotor interface is, primarily,
conducted through the rotor and bristles, which are marked as
numbers 1 and 2, respectively, and convectively transferred to the
surrounding fluid 共3 and 4兲. In addition, once the temperature rise
reaches up to backing plate, additional heat transfer paths are
introduced, as illustrated in Figs. 1 and 2. There will be conduction transfer to backing plate 5a through line bristle contacts and
Fig. 2 Schematic of brush seal heat partition mechanism
600 / Vol. 128, JULY 2006
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convection to inward radial flow between backing plate and bristle
5b. The heat will also convectively transferred from backing plate
to downstream air 6 as listed below:
Conduction into rotor 1
Conduction into bristles 2
Convection from rotor 3 关=3a + 3b + 3c兴
Convection from bristles 4
Conduction and convection between bristles and backing
plate 5 关=5a + 5b兴
6. Convection from backing plate 6
The heat conduction through the rotor at the interface 1 is dissipated to the rotor surroundings by convection. Rotor convection
occurs by means of several surfaces 3; rotor surfaces subject to
the fluid flow among randomly distributed bristles 3a, rotor surfaces at up- and downstream sides of the bristle pack 3b, and
surfaces below the thin rotor rim 3c.
The voids among the bristles are very small as the bristle pack
compacts under pressure load. The convection surface among
bristles over the rotor is practically negligible; however, high fluid
velocity formed by axial leakage flow and rotor speed may yield a
sizeable amount of heat convection. There is also convection over
the rotor surfaces subject to up- and downstream flows. Convection from these surfaces is driven again by axial flow and rotor
speed. The rotor also dissipates heat to the surroundings below its
thin rim.
The dominant heat transfer mechanism is driven by the leakage
flow forming a cross flow around bristles as well as the inward
radial flow near the backing plate. The heat conducted through
bristles is convectively transferred to the leakage flow 4. Most of
the generated frictional heat is carried away by leakage flow in the
fence-height section. Each bristle 共or entire bristle pack if treated
as a bulk兲 acts as a fin carrying the base heat to fluid flow. The
leakage flow is heated up by convection from both the rotor and
bristle surfaces. Examination of flow field shows that upstream
flow smoothly approaches the seal and penetrates into the bristle
pack over the entire upstream face 关7兴. In the upper region supported by backing plate, the penetrating fluid accumulates near the
backing plate as it flows toward the rotor. The inward radial flow
merges with the axial flow in the fence-height region and discharges downstream. The leakage flow through the fence-height
section carries the heat conducted by the bristles downstream.
In reality, the heat transfer mechanism is three-dimensional and
a conjugate form of conduction and convection. In order to calculate the bristle temperature distribution, a full solution of the flow
and temperature fields through randomly formed voids among
bristles is required in addition to solving conduction along
bristles. It is very difficult to obtain a closed-form analytical solution for such a complicated geometry. It is also not an easy task
to employ CFD codes to solve three-dimensional Navier-Stokes
and energy equations for the real brush geometry. One way to
simplify this otherwise complicated problem is to neglect circumferential temperature variations. Tangentially uniform heat generation assumption means a concentric and uniform seal interference
with uniform seal and rotor material properties. However, temperature varies in both radial and axial directions.
The present study considers fluid and heat flow within the upand downstream cavities and the bristle pack, in addition to front
and backing plates, and omits the rotor. The two-dimensional 共2D兲
axisymmetric CFD analysis involves a bulk porous-medium approach applied to the permeable bristle pack. Because of solidfluid friction, the flow within the bristle pack is subject to additional resistance forces, which are defined throughout a calibration
procedure 关7兴. The temperature-dependent thermal conductivity of
the solid bristle material is also defined for the porous bristle pack
filled by the sealing fluid. This approach overcomes the difficulty
of dealing with an undefined flow path and related complicated
formulations in order to obtain a full solution for flow and temperature fields within the bristle pack.
Journal of Engineering for Gas Turbines and Power
Another difficulty arises from the fact that the amount of frictional heat generation varies with respect to several parameters:
interference, blow-down, material pair, surface speed, friction coefficient, etc. In addition, partitioning of total heat generation between the rotor and bristles is a complicated problem, and there
has been no established procedure.
The main concern in this study is to determine temperature
distribution and maximum temperature through the bristle pack
for various heat flux inputs. Therefore, a wide range of heat flux
rates are studied to cover possible heat-generation cases that can
be practically achieved in common applications. A detailed discussion and outline of the calculation procedure for the frictional
heat generation is presented below.
Frictional Heat Generation
Frictional work due to rotor rub at the bristle tips can be calculated from the product of frictional force and sliding velocity.
Assuming all the frictional work is converted into heat, the total
frictional heat generation at the bristle-rotor interface is stated as
Q = ␮ F bV
where ␮ is the interface friction coefficient, Fb is the normal force
acting at bristle tips, and V is the rotor surface speed.
Although this frictional power relation is very simple, determining the defining factors proves difficult. In a typical design
problem, sliding velocity is known. Because many interacting factors from seal design to operating pressure affect the bristle tip
force, determining the friction coefficient at the bristle-rotor interface is quite difficult. There is a range of reported friction coefficient values from 0.08 to 0.47 under various test conditions
关8–12兴. A cobalt alloy, Haynes 25, is a common industry standard
bristle material. For the common Haynes 25-Inco 718 and Haynes
25-ChromeCarbide pairs, Fellenstein and DellaCorte 关8兴 and Fellenstein et al. 关9,10兴 reported friction coefficient values of 0.25–
0.47. Crudgington and Bowsher 关12兴 obtained steady friction coefficient readings of 0.28 when running against stainless steel. In
the present thermal study, the approach is to analyze a range of
heat input cases rather than calculating thermal distribution of any
specific design or rotor material. Therefore, a representative friction coefficient of 0.3 is considered for all cases.
Determining bristle tip force is much more complicated because
it is a function of many parameters: geometry, interference level,
flow and pressure field, blow-down, material, seal stiffness, etc.
Brush deflection coupled with pressure loads and interbristle interactions becomes very complicated in nature and does not lend
itself to an accurate analytical formulation. Starting with Flower
关13兴, simple beam theory has been used in many analyses to calculate bristle tip forces. Hendricks et al. 关2兴 presented a comprehensive analytical model including mechanical, aerodynamic, and
pressure loads. The loads calculated from a bulk flow model were
applied on beams representing the bristles to calculate their deflection in both the axial and radial directions. The model addressed interbristle interactions through propped points, however,
did not fully capture frictional coupling, lateral support, and torsional effects. Modi 关14兴 used results from linear elasticity as
initial guess for the large deformation solutions. However, the
model did not include backing plate friction. Later, some researchers 关15–18兴 combined porous media flow models with beam
theory to estimate bristle loads. More recently nonlinear beam
solutions have also been implemented in bristle force analyses
关19,20兴. On the other hand, other groups of researchers used detailed finite-element-based numerical models to calculate bristle
forces 关12,21–23兴. Recently, Demiroglu 关5兴 has developed an empirical expression covering a variety of parameters.
Selecting the correct bristle tip force value to define the right
range of heat flux values for practical applications is difficult with
so many different approaches to find the beam forces. Therefore,
an approach based on overall seal stiffness 关12,23–27兴 is chosen
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Table 1 Limits of operational variables considered for defining heat flux analysis domain
Stiffness 共Ks兲
Speed 共V兲
Interference 共⌬r兲
0.2 psi/ mil
54.3 kPa/ mm
40 ft/ s
12 m / s
4 mil
0.102 mm
4 psi/ mil
1085.8 kPa/ mm
984 ft/ s
300 m / s
30 mil
0.762 mm
for the frictional heat generation calculations. Stiffness values calculated through the beam theory does not reflect stiffness experienced during actual rotor incursions. Published experimental data
indicate that typical seal stiffness without pressure load may vary
from 54.3 kPa/ mm 共0.2 psi/ mil兲 关12兴 to 230.7 kPa/ mm
共0.85 psi/ mil兲 关23兴. Brush seals are known to experience strong
friction pressure coupling. Chupp et al. 关26兴 reported a two- to
threefold increase, whereas Short et al. 关27兴 reported up to a sixfold increase in the overall seal stiffness with increasing pressure
loads. The aim in the presented study is to cover common applications ranging from mild to severe heat-generation cases. Therefore, a general seal stiffness range from 54.3 kPa/ mm
共0.2 psi/ mil兲 共to represent a soft seal with light pressure load兲 to
1085.8 kPa/ mm 共4 psi/ mil兲 共hard seal with large pressure load兲 is
employed to obtain heat input estimates.
Seal stiffness Ks is defined by measuring contact pressure per
unit radial interference/deflection ⌬r 关12,23–27兴. Contact pressure
at bristle tips is calculated by multiplying the seal stiffness by the
bristle deflection as follows:
Pc = Ks⌬r
Then, frictional heat flux per unit contact area can be calculated as
q f = ␮ P cV
In order to identify the limits of the frictional heat flux that may
exist in common applications, extreme ranges of seal stiffness,
surface speed, and radial rotor interference are considered, as
listed in Table 1. Using mild and severe condition parameters,
minimum and maximum heat-generation values are calculated as
q fmin = 20 kW/ m2 and q fmax = 74,464 kW/ m2. A difficulty arises
from the unknown heat rates transferred into the rotor and bristles.
If half of the generated heat is assumed to be transferred to the
bristles while other half is conducted through rotor, then the problem domain is identified as q fmin = 10 kW/ m2 and q fmax
= 37,232 kW/ m2. For the sake of simplicity, five heat flux cases
with q f = 10, 100, 1000, 5000, and 10,000 kW/ m2 have been analyzed in this work. In terms of investigating the temperature distribution as a function of the heat flux, the assumption of a 50-50
heat portioning by the rotor and bristles becomes insignificant
since a wide range of heat flux values are covered in the scope of
the investigation.
Heat Transfer Analysis Employing Fin Approach
A bristle acts like a fin attached to the rotor surface as shown in
Fig. 3. The heat flux is applied at the base representing the frictional heat generation at bristle-rotor interface. The heat is conducted within the bristle and convectively transferred to airflow.
The heat conduction through the bristle can be assumed as onedimensional in the radial direction because of its high conductivity and small diameter. The Biot number 共Bi= hd / 2kb兲, which is
the ratio of convection and conduction heat transfer, is much less
than unity for the tiny bristle.
Although bristles subjected to cross flow in the fence-height
region are well represented with the simple fin approach, the heat
transfer mechanism becomes more complicated at the outer sections. Packed against the backing plate under pressure load,
602 / Vol. 128, JULY 2006
Fig. 3 Schematic of bristle heat transfer as an infinitely long
bristles may form numerous interbristle and bristle-backing plate
line contacts. The fin heat transfer approach yields a closed-form
solution for calculating the temperature distribution along each
individual bristle.
By employing the energy equation for the differential element
共Fig. 3兲 and combining it with the Fourier conduction law for a
single bristle, the heat transfer equation becomes 关28兴
d 2␪
− m 2␪ = 0
dy ⬘2
where y ⬘ denotes the radial distance from the rotor surface along
the bristle axis and ␪ is the normalized temperature defined as ␪
= T − T⬁. The fluid temperature is taken as equal to the upstream
inlet temperature, T⬁ = Tu. The term m2 for the cylindrical bristle
stands for
m2 =
kbA kb␲d2/4 kbd
The bristle diameter is denoted as d, and h is the convective heat
transfer coefficient around the bristle. Bristle perimeter for convectional area is denoted with p, and bristle cross-sectional area
for conduction is shown as A. Equation 共4兲 is derived assuming
constant bristle thermal conductivity.
Two boundary conditions are required for the solution of the
second-order linear differential equation to obtain the temperature
distribution along the bristle. The first boundary condition is applied at the base of the fin at the bristle-rotor interface, where the
frictional heat generation is introduced as heat flux. The second
boundary condition is defined using an infinitely long fin approach, which is the case for a highly convective surrounding.
Because of high convective heat transfer, the bristle temperature
exponentially approaches the surrounding fluid temperature when
moving away from the bristle-rotor interface. These applied
boundary conditions can be stated as
y ⬘ = 0 Þ q f = − kb
冏冉 冊冏
dy ⬘
y⬘ → ⬁ Þ ␪ = 0
y ⬘=0
The solution of the differential equation for conduction in the
bristle under these prescribed boundary conditions yields the temperature distribution along the bristle as follows:
␪共y ⬘兲 =
q f −my⬘
Substituting y ⬘ = 0, a closed-form solution for the maximum temperature on rotor surface can be obtained as
兩Tmax兩y⬘=0 =
+ T⬁ .
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Fig. 5 Brush seal CFD model domain
Fig. 4 Bristle layout for calculation of convective heat transfer
V1 =
4.1 Convective Heat Transfer Coefficient Within Bristle
Pack. Equations 共7兲 and 共8兲 require the convective heat transfer
coefficient around the bristle as an input. The convection coefficient is set by the flow-through voids among randomly packed
bristle matrix.
When the flow field within the bristle pack is considered, cross
flow among bristles and inward radial flow over the backing plate
are the two main flow types in addition to tangential flow due to
rotor rotation. The cross flow is very effective at the fence-height
section, where the fin approach is well applicable. For a simplified
analysis, the convective heat transfer coefficient can be calculated
by employing the approximation of following flow types as illustrated in Fig. 4:
V2 =
Nud =
= C Rem
d Pr
For cross flow around a bank of aligned/staggered tubes,
Nud =
= C1 Red,max
Details and calculations of the parameters in Eqs. 共9兲 and 共10兲
are available in most heat transfer textbooks 关28兴. The convective
heat transfer coefficient h is calculated using total leakage obtained from CFD analysis and experimental data. All leakage is
assumed to cross flow among bristles at the fence-height section.
First, the average flow velocity VFH through the fence-height
opening is obtained using the continuity equation
ṁ = ␳VFHAflow Þ VFH =
␳␲关共r + hFH兲2 − r2兴
where r is rotor radius and hFH is the fence height, which is the
distance between rotor surface and backing-plate inner edge.
Bristle spacing is needed to calculate flow velocity for Re.
Bristles are randomly compacted under a pressure load and touch
each other at many locations. For a representative calculation,
interbristle space is taken as one-tenth of the bristle diameter
关4,23兴, which is 0.102 mm 共0.004 in.兲. The effective flow area is
calculated by taking the interbristle space between two neighboring bristles and multiplying this value by the total number of
bristles per row along the seal circumference. When the total leakage rate is applied to this effective area, the flow velocity is calculated. For configuration of cylinder row in cross flow 共type 1兲,
the flow velocity is defined with the following relation:
Journal of Engineering for Gas Turbines and Power
ST − d
For staggered tube configuration,
冋 冉 冊册
if SD = SL2 +
ÞV3 =
The Nusselt number correlations for these kinds of flows are very
well established 关28兴. For cross flow around cylinders,
This procedure has been repeated for both aligned 共type 2兲 and
staggered 共type 3兲 bristle configurations 共Fig. 4兲, which involve
different spacing relations 关28兴. The flow velocity is calculated as
follows: For aligned bristle configuration,
1. cross flow over cylinders
2. cross flow through bank of aligned tubes
3. cross flow through bank of staggered tubes
where Red =
d 2␲r
10 11d/10
2 1/2
ST + d
2共SD − d兲
otherwise Þ V3 = V2
For 70 kPa 共10.2 psi兲 pressure load, the total leakage rate is
calculated as 0.003 kg/ s using the CFD model. Based on this
average flow rate, the flow velocity has been calculated as
24.1 m / s for a single row of bristles in cross flow and 23.7 m / s
for aligned/staggered tube banks with the bristle spacing values
discussed above. These flow velocities are used in Re calculations.
Air properties are evaluated at upstream conditions except for
density, which is calculated using the ideal gas equation at average
pressure of up- and downstream sides.
The convective heat transfer coefficients are calculated for
brush seal representative parameters using various Nu correlations
for cross flow around cylinders and through the bank of aligned
and staggered tubes. The resulting h values from different correlations are fairly comparable 共ranging between 1400 and
2200 W / m2 ° C for the range of parameters considered兲, and h is
evaluated for the approximation of cross flow around a cylinder.
The thermal conductivity of bristle material is taken as a constant
in the fin analysis. The CFD analysis and analytical solutions are
compared in the Results and Discussion section.
It should also be noted that convective heat transfer coefficient
within bristle pack varies with respect to leakage rate and interbristle spacing that are primarily dictated by pressure load. In
order to identify effects of these two parameters, the h coefficient
is also evaluated for a range of the parameters as presented in Sec.
CFD Model
A representative brush seal CFD model domain is selected as
shown in Figs. 5 and 6. The model is built in two-dimensional
axisymmetric coordinates with a domain consisting of the up- and
downstream cavities, the bristle pack, and the front and backing
plates. In order to ensure fully developed flow conditions, the upand downstream cavities are axially extended. The rotor surface is
included in the model as a solid boundary. Other than the porous
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Fig. 7 Sample meshing
Dogu 关7兴. For the porous bristle pack, fluid flow is subject to
additional resistance forces due to fluid friction at solid bristle
surfaces other than inertial and viscous forces as given in Eq. 共16兲.
Among the many transport models for porous media, the following non-Darcian equation has been employed for the brush seal
Fig. 6 Typical brush seal dimensions used in CFD model
bristle pack and the front and backing plates, solid sections are
omitted in the present investigation by using an adiabatic boundary assumption. As discussed above, since the primary concern of
the present analysis is to determine bristle temperature, the heat
transfer to the rotor is not included in the model. Meanwhile,
considering possible effects of backing plate thermal conductivity
on bristle temperature patterns under low-pressure loads with
minimal leakage flow, the backing plate is also included in the
The Newtonian airflow is assumed to be compressible, complying with the ideal gas law 共P = ␳RT兲 and turbulent following
k − ␧ turbulence model. The Navier-Stokes and energy equations
for steady flow through the model domain can then be written in
Cartesian tensor notation as Continuity equation
共␳u j兲 = 0
Momentum equation
⳵ 共 ␳ u iu j 兲
⳵ ui ⳵ u j
⳵ xi ⳵ x j
⳵ x j ⳵ xi
冊册 冉
⳵ 2 ⳵ uk
⳵ xi 3 ⳵ xk
Energy equation
冉 冊
⳵ 共␳u jcT兲
⳵xj ⳵xj ⳵xj
冊 冉 冊
⳵ ui ⳵ ui ⳵ u j
2 ⳵ uk
− ␮
3 ⳵ xk
⳵ x j ⳵ x j ⳵ xi
The energy flow within the solid front and backing plates is conduction heat transfer, defined as
冉 冊
The bristle pack is considered to be a porous medium in the
model by applying a bulk porous medium approach, as defined by
604 / Vol. 128, JULY 2006
= 共␣i兩ui兩 + ␤i兲ui
where ␣ and ␤ represent effective inertial and viscous flow resistance throughout the bristle pack. Frictional forces for the porous
bristle pack, described on the right-hand side of Eq. 共19兲, are
added to the right-hand side of the momentum equation 共Eq. 共16兲兲.
However, as in the case for a compact bristle pack under pressure
load, inertial and viscous forces in Eq. 共16兲 for a highly resistive
porous medium become negligibly small relative to frictional
forces because of fluid-solid interaction 共Eq. 共19兲兲. Therefore, Eq.
共19兲 stands alone for flow transport in the porous bristle pack for
the present bulk porous medium approach.
Flow resistance coefficients ␣ and ␤ are functions of many
parameters: geometric configuration, operating conditions, and
bristle-pack dynamic issues. To account for all these parameters in
a balanced manner, these flow-resistance coefficients are calculated using experimental data 关15,18兴. For a comprehensive calculation, axial pressure on rotor and radial pressure on backing
plate are used in addition to leakage flow. The bulk porousmedium approach employed incorporates of all the parameters in
a balanced manner in matching the experimental data. Details of
calibration procedure are presented by Dogu 关7兴.
The energy equation 共Eq. 共17兲兲 is also valid for the porous
bristle pack with the supplied temperature-dependent thermal conductivity for the bristle pack evaluated for the bristle material.
Together with other properties, air conductivity is also defined as
a function of temperature. Sutherland law is employed for
temperature-dependent air viscosity. The conduction heat transfer
equation 共Eq. 共18兲兲 within the solid front and backing plates is
also solved using temperature-dependent thermal conductivity of
plate materials.
A typical brush seal geometry is shown in Fig. 6. Dimensions
are representative of a brush seal as given by Demiroglu 关5兴. The
bristle diameter is 0.102 mm 共0.004 in.兲 with a lay angle of 45
The solution domain is finely meshed to ensure a mesh independent solution. The typical meshing is plotted in the brush seal
region in Fig. 7. A single mesh thickness is considered in the
tangential direction at an angle, which is selected to conserve a
moderate aspect ratio for meshes in that direction. In a 2D axisymmetric model, in order to take into account the effect of tangential velocity due to the rotor speed, mesh boundaries are cyclically matched in the tangential direction forming pairs of
geometrically and physically identical boundaries. By means of
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cyclic matching for flow repetition on identical faces, the size of
computational domain and associated computing time is reduced
in the 2D axisymmetric model.
Conservation equations describing the mass, momentum, and
energy transfer within the fluid are discretized by the finite volume method. Upwind differencing discretization schemes are employed for all flow variables except density, for which a central
differencing scheme is used. The resulting form of the discretealgebraic finite-volume equations is implicitly solved employing
the well-known SIMPLE solution algorithm.
tionship with respect to temperature. The temperaturedependent thermal conductivity for the widely used bristle
material Haynes 25 is
kb共W/m ° C兲 = 8.84 + 0.02 T共°C兲
valid for temperatures from 0 to 1000°C 关5兴. This equation
gives the thermal conductivity of bristle material itself.
However, the bristles are treated as a porous medium in the
model. When considering packed bristle matrix under pressure load, the bristles are randomly distributed within the
pack. They touch at many points with small voids remaining. In order to consider the effect of voids and contact
resistance, bristle pack thermal conductivity could be evaluated by decreasing its magnitude depending on the porosity
and thermal contact resistance. Because there is no interruption to heat flow along the bristle axis, bristle conductivity
can be used in the radial direction omitting the voids among
bristles. However, in the rotor axial direction, the intermittent bristle-bristle line contacts and voids forming among
bristles make calculation of heat transfer much more complicated. Unfortunately, there is no available thermal data to
estimate the unisotropic thermal conductivity. Therefore, in
the model, the isotropic-effective conductivity of the porous
bristle pack is assumed to be equal to the thermal conductivity of bristle material as a starting point. The heat flow
within the bristle matrix in the rotor axis direction is dominated by conduction through intermittent bristle contacts and
flow convection through voids between the bristles. When
evaluating heat conduction in the axial direction, depending
on the magnitude of convection among bristles, the total
axial heat conductance of bristle matrix could be higher or
lower than the bristle material thermal conductivity. As the
axial conductance of bristle pack gets smaller, the bristle
pack would be subject to higher axial temperature gradient.
10. The front and backing plate material is taken as common
stainless steel of AISI 304 whose temperature-dependent
thermal conductivity is defined as 关28兴
Boundary Conditions and CFD Model Specifications.
1. Pressure boundary conditions are applied at up- and downstream faces of the model domain. A representative pressure
load of 70 kPa 共10.2 psi兲 is chosen. In addition, the analysis
is extended to cover effect of several pressure loads as 200,
350, and 700 kPa 共29.0, 50.8, and 101.5 psi兲. Downstream
pressure is kept constant at atmospheric pressure of 100 kPa.
2. Temperature at the upstream inlet is imposed at 20°C. In
addition, in order to accurately involve the swirl effect, a
linear variation of the tangential velocity is prescribed at the
upstream face. It is mainly equal to rotor surface speed at the
rotor and zero at the stator.
3. No-slip and impenetration boundaries are imposed for all
solid walls, surfaces of the rotor and stator and the front and
backing plates.
4. At fluid-solid interface for front and backing plate surfaces,
conjugate heat transfer is applied to take full account of
convection over the surface and conduction through the
wall. In addition to defining a single temperature at the wall,
the imposed boundary condition equates the convection heat
flux over the surface to the conduction heat flux through the
wall. In fact, details of the thermal mechanism, where
bristles have intermittent line contacts on the backing plate
surface with some air gaps in between, cannot be fully represented. The tiny voids among the bristles and backing
plate are not considered in the porous medium treatment.
Voids are random and too small to fill with micromeshes.
However, the porous model includes a porous brush pack in
contact with the solid conductive backing plate, allowing a
radial inward flow to develop over the backing plate, while
modeling the heat transfer between the porous pack, inward
radial flow, and the backing plate. The model aims to simulate random conduction and convection zones, which may be
present between the bristles and the backing plate to some
5. Stator and rotor surfaces except the bristle-rotor interface are
assumed to be adiabatic.
6. Heat flux is determined at bristle-rotor interface. A 50-50
heat portioning is assumed, and only half of the frictional
heat is applied to the bristle tips. The heat flux values are
varied over a practical, wide range as outlined in frictional
heat generation discussed above. The aim is to determine the
bristle temperature profile for various representative heat inputs. Heat flux is assumed to be uniformly distributed over
the bristle pack thickness. However, it should be noted that
blow-down is not uniform in the axial direction over the
bristle pack that causes nonuniform heat generation. Nevertheless, this distribution is not yet fully established.
7. Rotor surface speed is defined as the tangential velocity for
the rotor wall. Rotor speed is chosen at 3000 rpm, which
yields a rotor surface speed of 20.34 m / s for all of the presented analysis cases.
8. Mesh faces in the tangential direction are cyclically matched
to consider the tangential flow velocity due to rotor speed.
The flow properties, such as velocity components, pressure,
and temperature, are identically matched at corresponding
meshes on cyclic boundaries.
9. Bristle thermal conductivity is found to follow a linear relaJournal of Engineering for Gas Turbines and Power
k p共W/m ° C兲 = 13.68 + 0.015 T共°C兲
11. Air thermal conductivity is also defined as a function of
temperature 关28兴. The viscosity is calculated as a function
of temperature complying the Sutherland law defined as
␮0共T/T0兲3/2共T0 + S兲
where ␮0 = 1.716⫻ 10−5 kg/ m s, S = 116 K, and T0 = 273 K.
12. In addition to use of calculated flow-resistance coefficients
in axial and radial directions 关7兴, tangential flow resistance
is assumed to be the arithmetic average of the radial and
axial flow resistances. This assumption is applied by considering the common 45 deg lay angle.
Results and Discussion
In all analysis cases, typical parameters are as follows: pressure
load is constant at 70 kPa; air inlet temperature is 20°C, rotor
surface speed is 20.34 m / s. The frictional heat generation is varied from 10 to 10,000 kW/ m2. A heat generation of 100 kW/ m2
is chosen as the baseline case. From CFD analysis, mass flow rate
under these conditions is calculated as 0.003 kg/ s, which is comparable to experimental data in the literature 关15,18兴.
6.1 Leakage and Convective Heat Transfer Coefficient.
The mass flow rates for the four pressure loads are calculated as
illustrated in Fig. 8. The flow rate increases almost linearly with
respect to pressure load within the range considered. The convective heat transfer coefficient is also calculated with the increasing
mass flow rate as outlined in Sec. 4 using Eqs. 共9兲 and 共10兲.
Higher flow rates yielding higher velocities enhance the heat convection. The bristle spacing also varies with pressure loads. In
JULY 2006, Vol. 128 / 605
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Fig. 8 Convective heat transfer coefficient versus mass flow
rate/pressure load
order to evaluate the effect of bristle spacing on the heat convection, the h coefficient is calculated for three values of interbristle
space as d / 5 , d / 10 关4兴, and d / 20. The thinner gap between bristles
yields higher velocities and resulting higher h coefficients as plotted in Fig. 8. h is considered at bristle spacing of d / 10 in the
presented results for comparison purposes.
6.2 Contour Plots of Pressure, Temperature, and Velocity
Vectors. For a heat generation of 100 kW/ m2, pressure contours,
velocity vectors, and temperature contours are shown in Figs. 9,
10, and 11共a兲–11共d兲, especially focused near the fence height.
Pressure contour lines are plotted at 5 kPa intervals 共Fig. 9兲. Examination of pressure field shows that pressure drop mostly occurs around the fence region closer to the downstream side, as
commonly observed in brush seal applications. This type of pressure gradient has been attributed to discharging flow with a contributed effect of expansion.
A velocity vector plot is produced combining the radial and
axial velocity components, omitting the tangential velocity component 共Fig. 10兲. This velocity vector plot shows the excessive
inward radial flow over the backing plate. The contribution of
Fig. 9 Pressure contours „in kilopascal… for ⌬P = 70 kPa, qf
= 100 kW/ m2
606 / Vol. 128, JULY 2006
Fig. 10 Velocity vectors „in meters per second… for ⌬P
= 70 kPa, qf = 100 kW/ m2
inward flow on leakage is considerably higher than the direct axial
flow at the fence-height region. The inward flow merges with
axial flow at the fence region and discharges downstream. A small
recirculation forms underneath the backing plate. This is a typical
flow field formation for brush seal contact operation. The velocity
reaches 12.2 m / s just around the backing plate inner corner, while
the rotor surface speed is 20.34 m / s. Combined with the leakage,
the velocity used in convective heat transfer coefficient reasonably
matches with these velocities.
Temperature contours are shown in Fig. 11共a兲–11共d兲. The findings indicate that a maximum temperature is reached at the bristlerotor interface as a result of heat flux input. The temperature at the
bristle tips reaches to 54.4°C for the frictional heat input of
100 kW/ m2 共Fig. 11共a兲兲. The temperature exponentially decreases
to inlet air temperature in the radial direction. As a result of leakage flow at the fence height, the temperature variation is higher at
the fence-height region relative to the upper region. Another observation is that temperature drop over bristle pack thickness in
the axial direction is negligibly small. The uniform axial temperature distribution is attributed to the effective convective cooling
mechanism of leakage flow in addition to high bristle conductivity. Temperature is ⬃37.1° C at the fence-height line corresponding to the backing-plate inner edge. Once temperature rise reaches
to backing plate, it caries the heat by conduction toward downstream and dissipates heat to downstream air. As also plotted in
Fig. 11共b兲, more temperature rise and heat diffusion is observed
throughout the bristle pack for higher heat flux of 1000 kW/ m2.
Figures 11共c兲 and 11共d兲 show the temperature contours for heat
flux of 1000 kW/ m2 at higher pressure loads of 200 and 350 kPa,
respectively. When compared to Fig. 11共b兲, the temperature rise
reduces for increasing pressure loads as a result of increased leakage. More leakage flow caries more heat away from the bristle
pack. Another observation is that the magnitude of inward radial
flow over backing plate increases with pressure load. This accelerated flow also prevents heat diffusion further into the upper
region as seen in the temperature contours.
6.3 Radial Temperature Distribution. The radial temperature distribution at the middle section of the bristle pack is plotted
for various values of pressure loads and frictional heat inputs in
Fig. 12. The temperature in Fig. 12 is nondimensionalized with
respect to minimum and maximum temperature in the domain as
T* = 共T − Tmin兲 / 共Tmax − Tmin兲. The minimum temperature is equal to
inlet air temperature at 20°C for all cases. The radial position is
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Fig. 11 Temperature contours „in degrees Celsius…
also evaluated as a measure of distance from rotor surface y relative to total bristle free height hb, as y * = y / hb. Fence height corresponds to the value of y * = 0.114.
An analytical temperature distribution for a single bristle, as
given in Eq. 共7兲, is also included in Fig. 12. All the analytical
results fall onto same curve when plotted with respect to the nondimensional temperature and radial distance from rotor surface.
Radial temperature exponentially decreases down to inlet air
temperature. Most of the temperature drop occurs in the fenceheight region for smaller heat flux values. As also seen in temperature contour plots, the radial diffusion of temperature rise is
more distributed toward the bristle root with increasing heat flux.
CFD results are comparable to the fin analysis for smaller heat
flux values. The larger differences at higher heat flux values are
attributed to the effect of inward radial flow. It should also be
noted that the fin analysis and the CFD model utilize different
thermal approaches for the bristle matrix. The fin analysis is based
on a single-bristle case, assuming a constant convective heat
transfer coefficient. In the calculation of convective heat transfer
coefficient, all the leakage is assumed to flow through fenceheight section. This yields higher velocity that overestimates h,
resulting in a fast cooling mechanism and steep temperature drop
along the bristle. On the other hand, the CFD model employs a
bulk porous-medium approach that deals with mass, momentum,
Journal of Engineering for Gas Turbines and Power
and energy transfer in the bristle matrix. Therefore, differences in
temperature profiles are reasonable while both models gave a
similar trend.
In addition to results for 70 kPa pressure load plotted in Fig.
12共a兲, Figs. 12共b兲–12共d兲 present the radial temperature for pressure loads of 200, 350, and 700 kPa including all five heat flux
cases. Temperature lines have the similar trend, as in the case of
70 kPa; however, the effects of increasing leakage and inward
radial flow are more pronounced for higher pressure loads. Temperature rise due to heat flux is getting trapped close to the fenceheight section for increasing pressure loads, especially for 700
6.4 Maximum Temperature. In Fig. 13, maximum temperatures are plotted with respect to heat flux input obtained from both
analytical solution 共Eq. 共8兲兲 and CFD model. Maximum temperature occurs at the bristle-rotor interface. For very high heat flux
input cases 共which are discussed in Sec. 4兲, results indicate maximum temperature values beyond 1000°C are possible. This confirms field observations of an orange flash of hot brush fragments
during engine start-up 关29兴. The magnitude of the maximum temperatures exponentially increases with increasing heat flux. Analytical and CFD results follow a similar increasing trend with heat
flux. Magnitude of the maximum temperature considerably deJULY 2006, Vol. 128 / 607
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Fig. 12 Radial temperature distribution at the middle of the bristle pack for various pressure loads and frictional heat generations: „a… ⌬P = 70 kPa, „b… ⌬P = 200 kPa, „c… ⌬P = 350 kPa, and „d… ⌬P = 700 kPa
creases with increasing pressure load due to higher convectional
cooling and heat removal capacity of increasing leakage flow.
Frictional heat in advanced brush seal applications is a major
concern. High bristle tip temperatures will cause accelerated oxidation rates even tip melting at extreme cases. Bristle temperature
near backing-plate corner is also critical to determine creep behavior of highly loaded seals operating at elevated temperatures.
Temperature measurement through the bristle pack has been an
Fig. 13 Maximum temperature for various pressure loads and
frictional heat generations
608 / Vol. 128, JULY 2006
open area of interest. More emphasis would be expected based on
experimental work using thermocouples among bristles.
In this study, after outlining the brush seal heat transfer mechanism, both fin heat transfer analysis and porous CFD model have
been employed to investigate the bristle temperature distribution.
The analytical solution has been developed by treating bristles as
fins. The CFD model is based on a bulk porous medium approach
for mass and heat transfer in the bristle pack. The study of brush
seal thermal analysis can be outlined as follows:
1. Brush seal heat transfer mechanism has been outlined.
2. Frictional heat generation has been calculated based on overall seal stiffness.
3. A closed-form solution has been obtained for the temperature distribution along the bristle using heat transfer relations developed for fins. The convective heat transfer coefficient within the bristle matrix has been evaluated by
employing various cross-flow correlations.
4. A bulk porous medium approach has been employed in the
thermal CFD analysis.
5. Temperature field in the bristle pack has been obtained with
respect to various frictional heat generation rates. A maximum temperature is reached at bristle tips, and this temperature exponentially decreases to air inlet temperature as
moved radially away from the rotor surface. Temperature is
almost uniform through the bristle pack in the axial direction
due to high conductivity and effective cooling of leakage
flow. Most of the radial temperature drop occurs in the
fence-height region.
6. The maximum temperature exponentially increases with the
frictional heat generation.
7. At higher heat flux rates, radial temperature rise along the
bristle pack tends to spread toward the bristle root.
8. For higher pressure loads, increasing leakage enhances the
convective cooling and heat removal capacity; therefore,
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less temperature rise is observed. In addition, temperature
rise is trapped closer to the fence-height section due to accelerated inward radial flow over the backing plate.
9. CFD model and fin analyses reasonably match field experience. The fin approach underestimates the bristle temperature relative to CFD analysis.
A ⫽
Aflow ⫽
Bi ⫽
c ⫽
C / C1 ⫽
d ⫽
Fb ⫽
h ⫽
hb ⫽
hFH ⫽
k , kb , k p ⫽
SL,T,D ⫽
T ⫽
T* ⫽
u ⫽
ui ⫽
V ⫽
x ⫽
y ⫽
y⬘ ⫽
bristle cross-sectional area 关=␲d2 / 4兴, m2
flow area, m2
Biot number 关=hd / 2kb兴
specific heat, J / kg° C
bristle diameter, m
normal bristle tip load, N
convective heat transfer coefficient, W / m2 ° C
bristle free height, m
fence height, m
thermal conductivity of air, bristle, front and
backing plate, W / m ° C
bristle pack stiffness, Pa/ mm
constant/group of terms 关共4h / kd兲0.5兴, 1 / m
mass flow rate, kg/ s
rotor speed, rpm
Nusselt number
bristle perimeter 关=␲d兴, m
static pressure, Pa
bristle contact load, Pa
Prandtl number
frictional heat flux, W / m2
total frictional heat generation, W
rotor radius, m
ideal gas constant, J / kg K
Reynolds number
bristle spacing, m
temperature, °C
nondimensional temperature 关共T − Tmin兲 / 共Tmax
− Tmin兲兴
spatial velocity component, m / s
superficial velocity, m / s
flow velocity and rotor surface speed, m / s
average velocity at fence-height section, m / s
spatial coordinate direction
radial distance from rotor surface, m
radial distance from rotor surface along bristle
normalized radial coordinate
bristle lay angle, deg
inertial and viscous flow resistance coefficient
interference, mm
friction coefficient at bristle-rotor interface and
dynamic viscosity, kg/ m s
kinematic viscosity, m2 / s
density, kg/ m3
normalized temperature 共=T − T⬁兲, °C
viscous dissipation term
i, j, k ⫽ spatial coordinate direction
u / d ⫽ up-downstream
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JULY 2006, Vol. 128 / 609
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