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: mghandour@fluid.nuae.nagoya-u.ac.jp) **

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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[1] T. C. Booth, Importance of Tip Leakage Flow in Turbomachinery Design,

VKI Lecture Series, 1985, 1985-05.

[2] S. A. Sjolander, Secondary and Tip-Clearance Flows in Axial Turbines,

VKI Lecture Series, 1997, 1997-01.

[3] R. S. Bunker, “Axial Turbine Blade Tip: Function, Design, and

Durability,” AIAA J. of Propulsion and Power, Vol. 22, pp. 271-285,

2006.

[4] Gm. S. Azad, J. C. Han, R. S. Bunker, and C. P. Lee, “Effect of Squealer

Geometry Arrangement on a Gas Turbine Blade Tip Heat Transfer,”

ASME J. of Turbomachinery, Vol. 124, pp. 452-459, 2002.

[5] J. S. Kwak, J. Ahn, J. C. Han, C. P. Lee, R. S. Bunker, R. Boyle, and R

Gaugler, “Heat Transfer Coefficients on the Squealer Tip and Near

Squealer Tip Regions of a Gas Turbine Blade with Single or Double

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301-309, 1989.

[10] A. A. Ameri,a and E. Steinthorsson, Analysis of Gas Turbine Rotor Blade

Tip and Shrouded Heat transfer, NASA, CR-198541, 1996.

[11] A. A. Ameri,b and E. Steinthorsson, Prediction of Unshrouded Rotor

Blade Tip Heat transfer, NASA, CR-198542, 1996.

[12] H. Yang, S. Acharya, S. V. Ekkad, C. Parakash, and R. Bunker, “Flow

and Heat Transfer Predictions for a Flat Tip Turbine Blade”, Proceedings

of ASME TURBO EXPO, June 3-6, Amsterdam, The Netherlands, 2002.

[13] L. P. Timko, Energy Efficient Engine High Pressure Turbine Component

Test performance Report, NASA, CR-168289, 1984.

[14] K. Kitamura, I. Men'shov, and Y. Nakamura, “Shock/Shoch and

Shoch/Boundary-Layer Interactions in Two-Body Configurations,” 35th

AIAA Fluid Dynamics Conference and Exhibit 6-9, Toronto, Canada,

AIAA-2005-4893, June 2005.

[15] D. Li, I. Men'shov, and Y. Nakamura, “Detached-Eddy Simulation of

Three Airfoils with Different Stall Onset Mechanisms”, J. of Aircraft,

Vol. 43, pp. 1014-1021, 2006.

[16] S. A. Sjolander, and K. K. Amrud, “Effects of Tip Clearance on Blade

Loading in a Planar Cascade of Turbine Blades,” ASME J. of

Turbomachinery, Vol. 109, pp. 237-245, 1987

[17] J. Tallman, and B. Lakshminarayana, “Numerical Simulation Of Tip

Leakage Flows in Axial Flow Turbines, With Emphasis On Flow

Physics: Part I-Effect Of Tip Clearance Height,” ASME J. of

Turbomachinery, Vol. 123, pp. 314-323, 2001.

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