1
1. INTRODUCTION
Tip clearance is an essential feature in the rotating machine in
order to allow for the relative motion between the blade tip and
casing, prevent the mechanical friction between them, and provide
a suitable space for centrifugal and thermal expansions. On the
other hand, as a result of the pressure difference between the
pressure and suction sides, the tip clearance provides a path for
flow escape from the former to the latter. In addition, the blade tip
has a possibility to be burn-out or worn-out due to high heat
transfer rate there. Incidentally, the tip clearance accounts for up to
one third of the total losses in a blade row.1)
So far many researchers have studied the tip leakage flow
problem experimentally and analytically. Sjolander2) reviewed
secondary and tip-clearance flows in axial turbines as well as their
interactions. Recently, Bunker3) made a concise, informative
review of turbine blade functional, design, and durability issues.
Above all, passive control of the leakage flow has been the main
subject for many researches. Azad et al.4)
studied the effect of
squealer tip geometry arrangement on heat transfer and static
pressure distributions. Their results show that a squealer on the
suction side provides better performance than that on the pressure
side or along the mid camberline. Kwak et al.5)
used the same test
rig to study the effects of the same squealer tip arrangement on the
tip and neighboring regions. Prakash et al.6) made a CFD analysis
for two improved blade tip geometries with different squealers.
They found that the inclined shelf case can reduce leakage and
improve efficiency. Recently Mischo et al.7)
proposed an improved
design of a conventional recessed blade tip for a highly loaded
axial turbine rotor blade. The overall efficiency improvement was
0.2% in experiment and 0.38% in CFD.
In numerical studies, Moore and Tilton8) used a potential flow
model as well as a mixed model to simulate the flow in the tip
clearance of a linear turbine rotor blade cascade, the results of
which gave better agreement with experiment. In addition, Moore
et al.9) used a 2-D, laminar flow model to investigate the effects of
Reynolds number and Mach number on the flow through a flat tip
clearance. Ameri and Steinthorsson10,11) used a 3-D, RANS model
with an algebraic turbulence model to predict the heat transfer rate
on the tip of shrouded/unshrouded turbine rotors of SSME (Space
Shuttle Main Engine). Yang et al.12) applied three different
turbulence models (standard high Re k-ε, RNG k-ε, and Reynolds
stress model) to heat transfer prediction, and analyzed the heat
transfer of the 1st stage high-pressure turbine rotor blade of General
Electric-Energy Efficient Engine13) (GE-E3).
In the present paper a new blade tip shape, triple squealer, is
proposed. This new shape is based on the conventional double
squealer, and a third squealer is added along the blade camber line.
Four cases for GDS ratio (the ratio of groove depth to span):
0.75%, 1.5%, 2.25%, and 3%, which correspond to 50%, 100%,
150%, and 200% of the tip to span ratio, respectively, were
selected to examine the effect of GDS ratio on the performance of
the triple squealer. For comparison the flat tip case (baseline case),
and the double squealer case were also calculated.
2. MODEL EMPLOYED IN THIS STUDY
Figures 1(a)-1(c) show schematic of three tip shapes used in this
study. The tip nomenclature is depicted in Fig. 1(d).
Calculation was performed for a three times scaled-up model in
the same way as Yang et al.12) This scaled-up model has an axial
cord of 86.1 mm (Cx = 86.1), and a span of 122 mm (h = 122);
therefore the aspect ratio is AR = 1.4. The blade model is
two-dimensional with a same profile in the span direction. The tip
clearance, t, is constant for all computations, which is 1.5% of the
blade span (t = 0.015h), and the squealer thickness is b = 2.3mm.
A Triple Squealer For Axial Flow Turbines
By Mohamed El-Ghandour,*
M. K. Ibrahim,**
Koichi Mori**
and Yoshiaki Nakamura**
* Graduate student, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
(Tel : +81-52-789-3396; E-mail: [email protected]) **
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Abstract: In this paper a new blade tip shape, triple squealer, has been proposed. This shape is based on the conventional double
squealer, and the cavity on the tip surface is divided into two parts by using a third squealer along the blade camber line. Four
cases for the ratio of groove depth to span (GDS ratio): 0.75%, 1.5%, 2.25%, and 3%, which correspond to 50%, 100%, 150%, and
200% of the tip clearance to span ratio, respectively, were taken up to investigate the effects of the GDS ratio on the flow field and
losses. The flat tip case (baseline case) and the double squealer case were also calculated for comparison. The in-house,
unstructured, 3D, Navier-Stokes, finite volume, multiblock code with DES (Detached Eddy Simulation) as turbulence model was
used to calculate the flow field. It was found from calculated results that reduction in the mass flow rate of leakage flow in the case
of a triple squealer with a GDS ratio of 1.5% is 8 times that for the double squealer case.
Key Words: Triple squealer, Tip clearance, Axial Flow Turbine, CFD.
2
b b t
h =
12
2 m
m
zw
= 1
23
.97 m
m
d
b
0.951.051.151.251.351.45-0.2 0 0.2 0.4 0.6 0.8 1 1.2
x/Cx
Pre
ssu
re r
atio p
to/p
s
Yang et al. (2002) present CFD
(a) Flat (b) Double squealer
(c) Triple squealer
Fig. 1. Schematic of three tip geometries.
3. COMPUTATIONAL METHOD
The numerical solver used here is the in-house code developed by
our laboratory. This code uses an unstructured, finite volume,
multiblock solver for the 3-D compressible Reynolds-Averaged
Navier-Stokes equations. Primitive variables on each side of a cell
interface are interpolated by using the 3rd-order MUSCL scheme
with van Albada limiter, and inviscid numerical fluxes at the cell
interface are calculated by using Roe's approximate Riemann
solver. For viscous numerical fluxes the 2nd-order central
differencing is applied. The solution is advanced in time by
LUSGS. For more details, the reader is referred to Kitamura et
al.14)
In this study this numerical code was modified for
turbomachinery simulation by adding inlet boundary conditions
regarding the total pressure and the total temperature, and periodic
boundary conditions regarding turbine blade cascade, as well as a
subroutine to calculate the turbulent viscosity of DES based on the
Spalart-Allmaras one equation turbulence model.15) As for
boundary conditions, at the inlet plane a total pressure of 129.96
kPa (pto = 129.96 kPa), a total temperature of 300 K, and a flow
angle of 32 deg were given, while at the exit plane a static pressure
of 108.3 kPa was applied. The no-slip and adiabatic boundary
conditions were imposed at the wall. The periodic boundary
condition was employed in the pitch direction.
The grid was first generated as a structured multiblock grid by
using the commercial software Gridgen, and then modified to an
unstructured grid. Figure 2(a) shows a 3-D view of the grid used in
this study. The computational domain, shown in Fig. 2(b), is a
single pitch of the GE-E3 (the 1st stage rotor blade row). The
number of blocks and grid cells in the computational domain
varies with the tip geometry. For example, there are 507,009 grid
cells distributed in 53 blocks for the triple squealer case with a
GDS ratio of 1.5%. The grid was clustered close to the blade and
endwall surfaces. The first cell was located at 5x10-6 m from the
wall which corresponds to Y+ =1.47.
(a) 3-D grid view (b) Computational domain
Fig. 2. Grid and computational region
4. RESULTS AND DISCUSSION
Figure 3 shows the pressure distribution along the blade surface
in the case of a flat tip with a clearance to span ratio of 1.5%, along
with the numerical results of Yang et al.12) for validation. The
vertical axis is the pressure ratio, pt,o/ps, where pt,o is the total
pressure at the inlet, and ps the static pressure on the wall. The both
results show reasonable agreement, except for some differences on
the suction side and near the trailing edge, which considered to be
due to the difference in the turbulence model and grid topology
used.
Fig. 3. Pressure distribution along the blade surface at midspan
section (z/h = 0.5)(flat tip case)
4.1. Flat Tip Case
The flow field and losses associated with the flat tip case will be
described here, which is used as the baseline in this study. Figure 4
shows contours of the pressure ratio on the blade tip and on the
pressure side.
The pressure distribution in the spanwise direction (the
z-direction) is almost two-dimensional except for small deviations
seen near the tip; other cases also show the same trend. This
feature was previously noted experimentally by Sjolander and
Cx=86.1 mm
S = 91.5 m
m
(d) Nomenclature and dimension of tip
configuration
casing
Blade cross-section
h
=122 mm z w
=123.97 mm ≈ ≈
Cx/4 Cx/4
y x o
x
Y
Z
X
Suction side
Pressure side
3
Amrud16)
and numerically by Yang et al.12)
On the tip surface,
there is a low static pressure region which covers about one third
of the tip area. This indicates a rapid leakage flow passing from the
pressure side toward the suction side, which is an undesirable
effect from the view point of efficiency and lossess. The maximum
pressure ratio is pt,o/ps = 1.4, which is located close to the pressure
squealer at x/Cx = 0.47. The average value of the pressure ratio on
the tip surface is pt,o/ps = 1.245 in the flat tip case.
Fig. 4. Pressure ratio contours on pressure side and on tip surface
(flat tip case)
Fig. 5. Velocity Vectors in a plane with x/Cx = 0.5
Figure 5 shows velocity vectors in the clearance in the
cross-section with x/Cx = 0.5. It is confirmed that a large amount
of flow goes through the tip clearance. In this case, the overall
mass flow rate in the passage was MF = 1.052 kg/s.
Fig. 6. Velocity vectors at mid-tip (z-h)/c = 0.5
Figure 6 shows velocity vectors in a plane with (z-h)/c = 0.5
which is inside the clearance and parallel to the tip surface. It is
clear from this figure that the flow is turned upward and
accelerated after entering the tip side edge. Even after it passes the
tip region, the flow maintains its direction and magnitude over
some distance. This feature of flow direction can also be confirmed
from the streamlines shown in Fig. 7.
Fig. 7. Streamlines at mid-tip (z-h)/c = 0.5
The leakage flow velocity magnitude is 2~3 times as large as the
inlet velocity at the trailing and the leading edges, while it is 3~4
times as large in the mid-chord region.
Fig. 8. Streamlines at mid-span z/h = 0.5
For comparison, the streamlines at the mid-span plane with z/h =
0.5 are depicted in Fig. 8. We can see a large difference between
Figs. 7 and 8. This suggests the tip flow might deteriorate the
turbine performance.
Fig. 9. Secondary velocity vectors in a plane with x = 0.5Cx The secondary velocity vectors in the middle cross-section: x/Cx
Low pressure
region High pressure
region
PS SS
Pressure side
Tip
Casing
x
Y
SS
Casing
Tip clearance
Leakage vortex
Y
X
4
= 0.5 are depicted in Fig. 9. It represents the deviation from the
potential flow. This secondary flow field was estimated, for every
point in the domain, by subtracting the corresponding mid span
velocity vector from the local velocity vector. The figure shows
clearly the leakage vortex lies close to the suction surface. It shows
also that the leakage flow increases the three-dimensionality to the
flow field. The leakage flow mixing with the main flow is not
confined to the vicinity to the blade suction side but spreads into
the main flow passage which reduced the main flow area and force
the main stream to change its path.
4.2. Triple Squealer Case
Fig. 10. Pressure ratio contours on the blade pressure side and tip
for triple squealer tip with GDS ratio of 1.5%
The pressure ratio, pt,o/ps, distribution on the triple squealer tip
with a GDS ratio of 1.5% is depicted in Fig. 10. The pressure
distribution on the blade tip has been changed dramatically. The
high pressure ratio region at the mid chord is reduced considerably,
except in a small region at the middle of the suction side squealer,
and a quite uniform flow pattern are noticed at the pressure side
squealer. The low pressure ratio region near the leading edge is
expanded and shifted away from the suction side towards the
pressure side and is confined to the second cavity (close to the
suction side). There are also a relatively high velocity spot at the
middle of the middle squealer.
Figure 11 shows the component of velocity (vy, vz) on a
cross-section (x= 0.5Cx), for triple squealer tip with a GDS ratio of
1.5%. This figure explains the philosophy behind introducing this
particular shape, as by introducing more resistance to the flow path
in the cross tip direction, this will force the flow to change its
direction to a less resistance route, turning with the main stream. In
the triple squealer shape the leakage flow suffers from two
successive sudden expansion followed by a sudden contraction.
The leakage flow is first roll against the suction side squealer, then
it expands in the first cavity and losses some of its momentum,
then it crosses over the middle squealer, then it expands again in
the second cavity and losses another momentum, then it crosses
over the suction side squealer and finally exits from the tip region
and mixes with the main stream. The flow in both cavities is
backward flow with different strength. It seems that the flow near
the casing is not affects so much by the squealers.
Figure 12 depicts the contours of total pressure coefficient, Cpt, at
a plane x= 0.5 Cx. This figure indicates that the separation region
at the tip entrance is much less than that at the flat plate, which
indicates less flow entering the tip. This leads also to a smaller
boundary layer thickness in the region from the tip entrance till the
middle squealer for both near-tip and near-casing boundary layers.
On the other side, the flow field at remaining part suffers from a
mixing process which reduces the lossless flow thickness till it
totally vanished at the tip exit.
Fig. 11. Velocity vectors in a plane with x = 0.5Cx (triple squealer tip
with GDS ratio 1.5%)
Fig. 12. Total pressure in a plane with x = 0.5Cx (triple squealer tip with GDS
ratio 1.5%)
The streamlines of the flow close to the tip are depicted in Fig. 13.
By introducing the middle squealer the flow in the cavity is
divided into two parts; the near-tip flow in the first cavity (near the
pressure squealer), which rolls-up forming a vortex. This vortex
will be referred as “cavity vortex” throughout this paper. The
cavity vortex crosses the middle squealer, which explains the
existence of relatively high velocity region on the middle squealer.
Then it crosses the second cavity where it gradually entrained the
lossless flow and exits the tip between x = 0.48 and 0.62Cx which
explains the existence of the high velocity region on the suction
squealer. The near-tip flow in the second cavity is mainly parallel
to the suction squealer. This is because the middle squealer reduces
the effect of the cavity vortex and provides a safe channel for the
flow. Because this flow turning with the blade turning, it give work
to the blade, and contributes positively to increase the efficiency.
Fig. 13. 3d streamlines for triple squealer tip with GDS ratio of
1.5%.
x
Y
Z
x
z
y
SS
SS PS
PS
5
4.3. Comparison between Triple Squealer Cases
(a) GDS ratio 0.75% (b) GDS ratio 2.25% (c) GDS ratio 3%
Fig. 14. 3d streamlines for triple squealer tip
Figure 14 shows the streamlines passing adjacent to the tip for
triple squealer tip configuration for three values of GDS ratio:
0.75%, 2.25%, and 3%. Figure 14 indicates that the cavity vortex
size and shape are function of cavity depth. This vortex formation
is looks very similar to the leakage vortex. The possible reason for
this vortex formation is the vorticity generated from the velocity
gradient of the near-tip flow and the interaction between the
leakage flow from the suction side and the leakage flow from the
first part of the pressure side.
In the GDS ratio cases of 0.75% and 1.5%, the cavity vortex is
attached to the inner side of the pressure squealer. The cavity size
in the case of GDS ratio of 0.75% is slightly larger than that of
GDS ratio of 1.5%. This is attributed to the larger mass flow rate of
the leakage flow in the 0.75% GDS ratio case.
In the GDS ratio cases of 2.25% and 3%, the cavity vortex is
detached from the pressure squealer towards the middle squealer,
where it crosses the second cavity (near the suction squealer) quite
normal to the cumber line. Upon its exit from the tip it wraps
around the leakage vortex formed previously.
Figure 15 shows the component of velocity (vy, vz) in a
cross-section (x= 0.5Cx), for triple squealer tip , for three values of
the ratio GDS are considered: 0.75%, 2.25%, and 3%. This figure
indicates that the behavior in the tip clearance depends on the
cavity depth. For the cases of GDS ratio of 0.75% and 1.5% the
flow in the first cavity is one directional reverse flow, while for the
cases of GDS ratio of 2.25% and 3% the flow in the first cavity are
two opposite streams. For the triple squealer with GDS ratio of
1.5%, although there is a strong reverse flow in the cavity, the jet
like flow velocity increases which leads to a high velocity region
outside the suction side noticed in Figure 7.
Figure 16 depicts the total pressure coefficient, Cpt, at plane of x=
0.5 Cx for triple squealer, three values of the ratio GDS are
considered: 0.75%, 2.25%, and 3%. As was expected previously by
introducing the triple squealer the losses decreased except the triple
squealer with d= c, which experienced an increase in aerodynamic
losses. For the flat tip case Fig. 7, the velocity jet is accompanied
with a large boundary layer thickness, which explains the high Cpt
region near the tip. The shape of the mixing zone is elongated in
the leakage flow direction; this is because the flow issues from the
suction side have a large momentum. For the double and triple
squealer (GDS ratio of 1.5%) cases Fig. 10 and Fig. 13, there is a
strong interaction between the leakage flow and the fluid in the
cavity, which marked by high cpt value. While in the other cases,
triple squealer GDS ratio of 0.75%, 2.25%, and 3%, the interaction
strength is significantly reduced especially in the second cavity
(close to the suction side). Which inspire the research towards the
best design parameters of the cavities.
(a) Triple squealer (GDS ratio of 0.75%)
(b) Triple squealer (GDS ratio 2.25%)
(c) Triple squealer (GDS ratio 3%)
Fig. 15. Velocity vectors in a plane with x = 0.5Cx (triple squealer case)
4.4. Comparison of mass flow rate
Figure 17 represents the integral of mass flow rate through the tip
region out of suction side for three kinds of tip configuration: flat,
double squealer, and triple squealer. For the triple squealer, four
values of the ratio of GDS are considered: 0.75%, 1.5%, 2.25%,
and 3%. The significance of mass flow rate the leakage are: less
leakage flow means more fluid will give work to the blade, less
losses in the tip region, less size of the leakage vortex, and less
blockage to the main stream.
It is clear from the figure that the variation of the mass flow rate
through the tip region is not in a linear relation with the variation in
cavity depth. By introducing the double squealer, the mass flow
rate of leakage flow through the suction side reduced by 2.32%
compared to the baseline case (flat tip). While for the triple
squealer it was 9.53%, 17%, 15.25%, and 15.69% for GDS ratio of
0.75%, 1.5%, 2.25%, and 3% respectively. The case of triple
squealer with d=c gives the highest reduction in mass flow rate
though the tip region. While that of d= 0.5c, gives the lowest
reduction between the triple squealer cases tested. The difference
in the mass flow rate through the triple squealer cases d=1.5 and 2c
is not significant. It is worth noting that the reduction in mass flow
rate through the tip region in the triple squealer case d=1c, is
double that for d=1.5c which is four times that of double squealer.
SS PS
SS PS
SS PS
6
(a) GDS ratio 0.75%
(b) GDS ratio 2.25%
(c) GDS ratio 3%
Fig. 16. Total pressure contours in a plane with x = 0.5Cx (triple squealer case)
Fig. 17. Integral of mass flow rate through the tip region.
5. CONCLUSION
A new tip clearance shape, triple squealer, has been proposed.
The new shape is based on the conventional double squealer by
dividing the cavity into two parts by using a third squealer along
the blade camber line. . Four cases for the ratio of groove depth to
span (GDS ratio): 0.75%, 1.5%, 2.25%, and 3%, which correspond
to 50%, 100%, 150%, and 200% of the tip clearance to span ratio,
respectively, were taken up to investigate the effects of the GDS
ratio on performance of the triple squealer. The following
concluding remarks can be deduced from this study:
-The flow in the triple squealer shape is strongly dependent on the
cavity depth,
-The triple squealer case of the GDS ratio = 1.5% gives the least
mass, with a reduction in the leakage flow 8 times that of double
squealer case,
-Both triple squealer GDS = 2.25% and GDS = 3% has no
significant difference in the mass flow rate of leakage flow through
the tip region,
- The variation of the mass flow rate through the tip region is not in
a linear relation with the variation in the cavity depth.
ACKNOWLEDGMENT
The first author is thankful to the Egyptian Government, Ministry
of Higher Education for providing him the scholarship to have Ph
D. This work was supported by a Grant-in-Aid for the 21st Century
COE Program “Frontiers of Computational Sciences” from
Ministry of Education, Culture, Sports, Science and Technology,
Japan. The authors would like to thank Prof Igor Men’shov for his
valuable advices and guidance during his stay and visit to Nagoya
University, and Mr. M. El-Gendi, Dr. M. Jones, Dr. Kitamura, and
Mr. Hirose for their discussion and support.
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SS PS
SS PS
SS PS
0.000.010.010.020.020.030.030.040.04Suction SidesM
ass f
low
rate
th
rough t
he t
ip r
egio
n
(kg/s
)
Flat tip
Dou
ble squealer
Triple squealer GDS = 0.75%
Triple squealer GDS = 1. 5%
Triple squealer GDS = 2.25%
Triple squealer GDS = 3%
0.02
0.016