Renewable Energy 29 (2003) 529547

www.elsevier.com/locate/renene

Computed eects of tip clearance on

performance of impulse turbine for wave
energy conversion
A. Thakker
, T.S. Dhanasekaran
Wave Energy Research Team, Department of Mechanical and Aeronautical Engineering,
University of Limerick, Limerick, Ireland
Received 3 June 2003; accepted 10 September 2003

Abstract
This paper depicts numerical analysis on Impulse turbine with xed guide vanes for wave
energy conversion. From the previous investigations, it is found that one of the reasons for
the mismatch between computed and experimental data is due to neglecting tip clearance effect. Hence, a 3-D model with tip clearance has been generated to predict the internal ow
and performance of the turbine. As a result, it is found that the comparison between computed and experimental data is good, quantitatively and qualitatively. Computation has
been carried out for various tip clearances to understand the physics of tip leakage ow and
eect of tip clearance on performance of such unconventional turbine. It is predicted that
the turbine with 0.25% tip clearance performs almost similar to the case of without tip clearance for the entire ow coecients. The designed value of 1% tip clearance has been validated numerically and computed that the eciency of the turbine has been reduced around
4%, due to tip clearance ow at higher ow coecients.
# 2003 Elsevier Ltd. All rights reserved.
Keywords: Wave energy; Impulse turbine; CFD; Tip clearance ow

1. Introduction
For the last two decades, scientists have been investigating and dening dierent
methods for power extraction from wave motion. These devices utilize the principle
of an oscillating water column (OWC). OWC-based wave energy power plants

Corresponding author. Tel.: +353-61-202223; fax: +353-61-202944.

E-mail address: ajit.thakker@ul.ie (A. Thakker).

0960-1481/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2003.09.007

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A. Thakker, T.S. Dhanasekaran / Renewable Energy 29 (2003) 529547

Nomenclature
ACL
b
CT
CA
Hs
H

lr
m
Q
rR
Ts
UR
T
va
z

axial chord length

height of blade
torque coecient
input power coecient
signicant wave height
non-dimensional wave height
chord length of rotor blade
area ratio
ow rate
mid span radius
mean time period
circumferential velocity at rR
torque generated
axial ow velocity
number of rotor blades

Greek symbols
dp
total pressure drop across the rotor
g
eciency of turbine

g
mean turbine eciency under irregular ow condition
gmax
maximum turbine eciency under steady ow condition
/
ow coecient
q
density of air
r
solidity
c
hub-to-tip ratio
x
angular velocity
e
percentage of computational error

convert wave energy into low-pressure pneumatic power in the form of bidirectional airow. Self-rectifying air turbines (which are capable of operating unidirectionally in bidirectional airow) are used to extract mechanical shaft power,
which is further converted into electrical power by a generator. Two dierent turbines are currently in use around the world for wave energy power generation,
Wells turbine, introduced by Dr. A. A. Wells in 1976 and Impulse turbine with
self-pitch controlled guide vanes by Kim et al. [1]. Both these turbines are currently
in operation in dierent power plants in Europe, Canada, Australia and Asia on an
experimental, as well as a commercial basis. The present work deals with the Impulse turbine. A 1.0-m diameter Impulse turbine with self-pitch controlled guide
vanes was designed, fabricated and is being operated by National Institute of Tech-

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531

nology at Vizhinjam, a site near Thiruvanandapuram, which is a city on the west

coast of India [2]. The guide vanes pitch at the wave frequency. Such moving
parts lead to maintenance and operating life problems and increased cost and
hence the performance of the turbine with xed turbine has been investigated by
Maeda et al. [3].
There are few reports presented on the numerical analysis on Impulse turbine
and Wells turbine. An optimal installation angle of the Impulse turbine has been
investigated by numerical and experimental analysis (Kim et al. [4]). The performance of the Impulse turbine with unstructured grids and various turbulence
models has been studied by Thakker et al. [5]. CFD analysis on CA9 Wells turbine
has been made to validate the performance of the turbine and to analysis
aerodynamics characteristics [6]. In all the earlier studies, tip clearance has not
been incorporated in the numerical model. The tip leakage ow is one of the most
prevalent and inuential features of the ow through turbomachine rotors. In addition, the tip leakage ow is a phenomenon that is dicult to measure in most
turbomachines. Computed eects of solidity on Wells turbine performance with tip
clearance have been investigated by Watterson and Raghunathan [7]. The predicted
eect of solidity on the turbine pressure drop, torque and eciency agreed qualitatively and quantitatively with the experimental data. Few authors [811] have been
investigated the eect of tip clearance on the performance of Wells turbine
experimentally and numerically with CFD codes and found that the turbine is very
sensitive to tip clearance when compared to a conventional turbine. They have
concluded that the decrease in tip clearance advances the stall but increases the
cyclic eciency as a result of reduced leakage losses. Also it has been proved that
the turbine with a relatively large tip clearance could operate over a much
wider range of ow rate range of ow rate without stalling. To investigate the effect of blade sweep on the performance of the Wells turbine, numerical investigation was carried out under steady ow condition with a fully 3-D NavierStokes
code for two kinds of blades, NACA 0020 and CA9 by Kim et al. [12]. Extensive
work has been performed in the realm of tip clearance studies on conventional
turbine [1315].
This paper describes the use of CFD method to investigate the eect of tip clearance on performance of Impulse turbine, which is working under bidirectional airow for wave energy conversion. The method employs structured grids, which
allow inclusion of such features as the blade tip and casing treatments. The 3-D
CFD model has been generated with tip clearance to validate the computed results
with experimental data. The study has shown that the numerical method is able to
predict with reasonable accuracy; the variations of pressure drop across the turbine
rotor, torque and eciency with ow coecient, and the eect of tip clearance. An
optimum tip clearance has been suggested where the eect of tip clearance is
almost negligible. Furthermore, the design tip clearance (1 mm) has been validated
numerically. In addition, the performance of Impulse turbine with various tip
clearances has been computed under irregular wave condition by using numerical
simulation technique.

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2. Review of experimental apparatus

A schematic layout of the experimental rig of Wave Energy Research Team at
University of Limerick is shown in Fig. 1. It consists of a bell mouth entry, 0.6 m
test section with a hub-tip ratio of 0.6, drive and transmission section, a plenum
chamber with honeycomb section, a calibrated nozzle and a centrifugal fan. Air is
drawn into the bell mouth shaped open end, it passes through the turbine and then
enters the plenum chamber. In the chamber, the ow is conditioned and all swirls/
vortices are removed prior to passing through a calibrated nozzle and is nally
exhausting at the fan outlet. Using a valve at fan exit controls the ow rate. Details
of the test rig calibration can be found from Thakker et al. [6]. The turbine was
mounted on a shaft in a cylindrical annular duct, with a blade tip clearance of 1
mm. The shaft is coupled to a motor/generator via a torque meter. The two guide
vanes were mounted on the up-stream and down-stream hubs of the rig. The turbine was tested by keeping a constant axial velocity of 8.49 m/s. Data was collected by varying the rotational speed from 1250 to 125 rpm, thus giving a ow
coecient range of 0.27 to 2.7 under unidirectional steady ow conditions. The Reynolds number based on the blade chord length was 0:74  105 at peak eciency.
The specication of the turbine is listed in Table 1.
The overall performance of the turbine was evaluated by the turbine angular velocity x. Torque generated T, ow rate Q and total pressure drop dp across the rotor.
The results are expressed in the form of torque coecient CT, input power coecient
CA and eciency g in terms of ow coecient /. The denitions are given below
CT T=fqv2a UR2 blr zrR =2g

CA dpQ=fqVa2 UR2 blr zva =2g

Fig. 1. Schematic diagram of the test rig.

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533

Table 1
Specication of the turbine
Parameter
Blade prole
Number of blades
Tip diameter
Chord length
Pitch
Blade inlet angle
Guide vanes prole: Plate type
Pitch
Chord length
Number of guide vanes
Guide vanes inlet/outlet angle

Symbol

H=T 0:6

z
D
lr
Sr
c

30
598.0 mm
100.0 mm
50.0 mm
v
60

Sg
lg
g
h

58.0 mm
131.0 mm
26
v
30

/ va =UR

g Tx=dpQ CT =CA /

3. Computational uid dynamics analysis

3.1. Governing equations
Gambit 2.0 and FLUENT V6 were used for meshing and analyzing the problems, respectively. FLUENT V6 solves the NavierStokes equations for conversion of mass and momentum (Eqs. (5)(8)). Additional conservations of k and e
equations are solved for turbulence closure. Governing NavierStokes transport
equations are:
MASS
@ qu @ qv @ qw

0
@x
@y
@z

MOMENTUM

@ P @ sxx @ syx @ szx

divquu
@x
@x
@y
@z

@ P @ sxy @ syy @ szy

divqvu
@y
@x
@y
@z

@ P @ sxz @ syz @ szz

divqwu
@z
@x
@y
@z

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A. Thakker, T.S. Dhanasekaran / Renewable Energy 29 (2003) 529547

3.2. Solver parameter

The solver treats each cell in the domain as a nite volume with a node at its
center and the ow properties for the entire model are solved at each of these
nodes. In order to predict the ow properties at the edge of control volume, the
ow properties must be interpolated between two nodal points. The discretisation
scheme governs the accuracy of its interpolation by controlling the number of
terms in Taylor series used for the interpolation. The discretisation scheme found
to be the most accurate for the second order scheme; this scheme was the highest
order available in the code being used.
3.3. The mesh and the solver
The computational grid is visualized in Fig. 2, where only the grid lines attached
to the surfaces are shown. Here, the resolution of all the boundary layers is visible.
An enlarged view at tip clearance is shown in Fig. 3. The complex 3-dimensional
computational domain has been meshed with hexahedral elements. This has been
achieved by partitioning the entire geometry into meshable pieces and meshed by
mapping and submapping algorithms. The grids clustered near the hub, casing, and
tip was close enough to give appropriate y+ values. The mesh was checked for low
level of skewness and reasonable aspect ratio and volume change. The grid independence test has been carried out on the computational domain with 350,000,
400,000, and 450,000 cells (Fig. 4). The performance curves of turbine are seen to
be almost similar for the cases with cells 400,000 and 450,000. Hence the grid cells
400,000 have been utilized for all the numerical studies in the present investigation.
The computational domain extended to 8.5 chord length upstream and downsteam, it is restricted to one blade to blade and guide vane to guide vane passage
with periodic boundaries. Computation has been carried out for various tip
clearances; 0, 0.25, 1, 2, 4 and 6% of axial chord and for each case with various
ow coecients.

Fig. 2. Computational grid.

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535

Fig. 3. Grids at the tip region.

3.4. Boundary conditions

It was necessary to set up three uid zones using mixing plane technique. Three
zones are the upstream guide vane, the rotor and the downstream guide vane. Inow is set as mass ow inlet, outow is set as pressure outlet and periodic walls are
set as transitional to allow cascade eect on blade and guide vane to be simulated.
The uid at rotor is dened as a moving reference frame with the angular speed
equivalent to that of the blade. The ow is set as fully turbulent.

Fig. 4. Grid independence test.

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3.5. Near-wall modeling

Near-wall modeling has a great impact on quality of numerical solution as the
variables mainly change near to the wall. The non-equilibrium wall functions were
used, as they are capable of dealing with complex ows involving separations, reattachment or any other non-equilibrium eects and also severe pressure gradients.
The near-wall cells were assumed to consist of a viscous sublayer and an inertia
dominated layer.

4. Results and discussion

4.1. Validation of numerical procedure
The present numerical model has been validated with the experimental data with
1% tip clearance. Fig. 5ac show the comparison between computed and measured
values for input coecient, torque coecient and eciency against ow coecient,
respectively. From Fig. 5a, it can be observed that the computed values overpredict
the measured values at high ow coecients. But good agreement has been
reached between computed and measured CT values, Fig. 5b. Computed eciency
of turbine matches very well with experimental results, for the entire ow coefcient, except at very low coecients (Fig. 5c). This implies that the turbulence
model ke produces good results in the lower rotational speed of the turbine. Accuracy of the present computational model has been plotted as the percentage of
error, e on computed CT, CA and eciency deviated from experimental values
(Fig. 6). From the gure, it can be observed that the accuracy of computed results
varied with ow coecient. In particular, the error of CT and CA fall approximately 10 percentage points from the experimental value in the normal operating
coecients. At the two extreme ow coecients, the percentage of error is seen
considerably more due to the nature of ow which seems highly unsteady and
three-dimensional in the blade passages. As far as the computed eciency of the
turbine is concern, the error is almost zero. In particular, at peak eciency, where

Fig. 5. Comparison between computed and measured values. (a) Coecient of input; (b) Coecient of
torque; (c) Eciency.

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537

Fig. 6. Computational error on coecient of torque, coecient of input, and eciency of the turbine.

the ow through the blade passage is more favorable in generating torque, the
computed error is close to zero (Fig. 6).
4.2. Eect of tip clearance on the performance of the turbine under steady ow
conditions
Fig. 7ac shows the variations of CA, CT and eciency, respectively, for the
cases of 0, 0.25, 1, 2, 4 and 6% tip clearances. Fig. 7a shows that the input coefcient is almost the same for the tip clearances 0 to 1%, up to the value of ow coecient 1.0. The reason for this behavior is explained in the following section.
Beyond this ow coecient, the input coecient is increasing as tip clearance
increases. When the tip clearance increase from 1%, there is considerable eect due
to tip clearance throughout the operating range of turbine. It can be noted that the
value of CA keeps remains similar for the cases of 0% and 0.25% tip clearance. It is
evident that there is tremendous pressure drop across the turbine due to tip leakage
ow beyond 1% tip clearance. This eect has been reected in terms of torque converted by the blades (Fig. 7b). Hence the eciency of the turbine is almost the
same for the cases of 0% and 0.25 tip clearance (Fig. 7c). The eciency with 1% tip
clearance remains the same as in the above cases up to the value of ow coecient
about 1.0 and keeps reducing gradually beyond this value. Also it can be noted
that the eciency curve for the cases above 1% tip clearance is apparently sharp

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A. Thakker, T.S. Dhanasekaran / Renewable Energy 29 (2003) 529547

Fig. 7. Eect of tip clearance. (a) Coecient of input; (b) Coecient of torque; (c) Eciency.

compare to the other cases. The peak eciency of the turbine is shifted towards the
left hand side as the tip clearance increases.
Fig. 8 shows the distribution of maximum eciency with tip clearance ratio.
Here the eect of tip clearance of impulse turbine has been compared with the
Wells turbine [10], as both the turbines operate in bidirectional ow applications.
The maximum eciency of the Impulse turbine is almost constant up to 1% tip
clearance, after this value there is sudden decrease in eciency. The reason for this
behavior is explained by physics of ow in the following section. Beyond 4% tip
clearance there is no noticeable decrease in eciency. Hence it is validated that the
design value of 1% tip clearance is an optimum value. Even though both turbines
are very sensitive to the tip clearance compared to conventional turbine, the Impulse turbine is relatively less sensitive when compared to the Wells turbine (Fig. 8).

Fig. 8. Eect of tip clearance on max eciency of various turbines.

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539

For example, the Impulse turbine nds no eect due to tip clearance up to 1% tip
clearance. But in the case of the Wells turbine, there is a drop in eciency which
starts from the 0.6% tip clearance itself. Generally, both the turbines seem sensitive
in the range of tip clearance from 1 to 4 percentage points.
4.3. Flow physics and the eect of tip clearance height
Fig. 9af show the velocity contours at 96 percentage points of blade height for
the cases of 0, 0.25, 1, 2, 4 and 6% tip clearances, respectively, for the ow coecient
of 1.68. From the gures, while considering the lead edge region of the blade,
without tip clearance and 0.25% tip clearance show similar distribution and the
forward portion of the blade passage, which are typical of a stagnating or lowvelocity ow. This supports the contention that for the front part of the blade tip

Fig. 9. Velocity contours at various tip clearances. (a) 0% tip clearance; (b) 0.25% tip clearance; (c) 1%
tip clearance; (d) 2% tip clearance; (e) 4% tip clearance; (f) 6% tip clearance.

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clearance gap could be blocked by the inlet boundary layer (aerodynamically

closed) and therefore could be sustaining a horseshoe vortex system. In the cases
of relatively open 1% and above tip clearances, size of the horseshoe vortex is to
gradually reduce (Fig. 8cf).
The size and location of vortex released from tip clearance can be clearly captured from the above gures. Even though there is no tip leakage vortex formed in
case of without tip clearance, the ow separation from the suction surface can be
seen from Fig. 9a. In the case of 0.25% tip clearance, the vortex takes place after
approximately 50% of axial chord length (ACL) apart from suction surface of the
blade, Fig. 9b. In the case of low tip clearance, the trailing edge of the blade also
closed aerodynamically. But the ow leaks through the clearance from 65 to 70%
axial chord length. But in the cases of 1% and above tip clearances, (Fig. 9cf)
there is no aerodynamic lock seen in the trailing edge of the turbine, causing large
mass ow of air leak through the tip clearance. Hence tip leakage vortex size is
large when compared to the case of the 0.25% tip clearance. From the gures, it
can be observed that the vortex grows in size from the location of 60% axial chord
to downstream of the blade trailing edge. As the strength of leakage vortex increases from 1% tip clearance, it enhances the ow separation at the downstream guide
vanes (Fig. 9cf). This may be the reason for the sudden decrease in eciency of
the turbine beyond 1% tip clearance (Fig. 8). The interpretation of this is that the
pressure drop across the rotor plays an important role rather than torque in the efciency of the turbine.
To picture the growth of the tip leakage ow vortex, and its interaction with
separated ow from the suction side of the blade, distribution of total pressure coecient has been plotted at 90% of axial chord length for various tip clearances.
These contours have been plotted for two ow coecients of 0.67 and 1.68. These
ow coecients have been chosen as the eect of tip clearance seems signicantly
dierent in the above two ow coecients (Fig. 7c). Fig. 10ad shows the total
pressure contours for the cases of 0.25, 1, 4 and 6% tip clearance, respectively, for
the ow coecient of 1.68. From Fig. 10a, it can be noted that the tip leakage vortex is almost diused for the case of 0.25% tip clearance. In case of the 1% tip
clearance, the vortex has been shed fully and the size of vortex keeps growing as
tip clearance increases (Fig. 10bd). It can be seen very clearly that the vortex occupied nearly 10% of blade passage width for the case of 1% tip clearance and
nearly 40% in case of 6% tip clearance. So from the Fig. 9, it can be interpreted
that the tip leakage ow induces a signicant area of low-momentum uid.
At the ow coecient of 0.67, there is no considerable eect due to tip clearance
for the cases of 0.25 and 1% tip clearance (Fig. 11). Also, there is no visible vortex
seen due to tip clearance leakage ow in the above tip clearances. This may be due
to the high-pressure drop across the turbine, which occurs before 55% of ACL. As
the velocity of ow entering the tip clearance is low, it has less energy to create a
vortex. Hence the eciency of the turbine is same for the both tip clearances of
0.25 and 1%. But in case of higher tip clearances, as the mass ow through the tip
gap increases, a vortex has been shed but on a small scale. Hence there is reduction
in eciency of the turbine after 1% tip clearance in low ow coecient also. This

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541

Fig. 10. Total pressure contours at 90% ACL at / 1:68. (a) 0.25% tip clearance; (b) 1% tip clearance;
(c) 4% tip clearance; (d) 6% tip clearance.

trend reveals that the lower tip clearances (below 1% tip clearance) aects the turbine performance in the higher ow coecients only (after peak eciency). As the
tip clearance increases from 1%, it gradually advances the turbine performance in
the lower ow coecients. Static pressure distribution on the suction and pressure
side of the blade is shown in Figs. 12 and 13, respectively, for the ow coecient
1.68. There is considerable eect due to tip clearance in the static pressure distribution as seen throughout the blade length. However, the eect is more predominant after 65% of ACL. The low-pressure region at the mid portion of the suction
side of the blade has been shifted towards the hub of the blade due to tip leakage
ow (Fig. 12bd). On the other hand, static pressure distribution on the pressure
side is seen to be shifted upwards, as the blade passage ow is diverted through the
tip gap (Fig. 13ad).
Static pressure distribution on the tip surface of the blade for various tip clearances at the ow coecient 1.68 is shown in Fig. 14ad. The eective leakage area
through the tip surface can be clearly captured from the above gures. At low tip
clearance, the blade passage ow released through the suction surface eectively,
about 6570% due to aerodynamic lock in the blade leading and trailing edges.
Hence the vortex has been formed at negligible sizes and do not aect the main
ow signicantly (Fig. 10a). But in the case of 1% tip clearance, leakage takes
place from 60% ACL to the trailing edge of the blade and beyond 1% tip

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Fig. 11. Total pressure contours at 90% ACL at / 0:67. (a) 0.25% tip clearance; (b) 1% tip clearance;
(c) 4% tip clearance; (d) 6% tip clearance.

clearance, the leakage takes place through the entire tip surface of the blade. It creates the relatively large vortex and makes a considerable impact on the eciency of
the turbine.
4.4. Performance of the Impulse turbine with various tip clearances under irregular
ow conditions
The conditions faced by the turbine in an actual wave energy power plant are irregular and unsteady due to the random nature of the sea waves. So, the performance of 0.6 m, 0.6 H/T ratio Impulse turbine with various tip clearances have been
evaluated using numerical simulation techniques under such conditions. Considering quasi-steady ow conditions, typical turbine characteristics shown in the unidirectional CFD results for the said turbine were used for this simulation. The
numerical simulation techniques used by Inoue et al. [16] and Setoguchi et al. [17]
for the performance prediction of 0.3-m diameter Wells and Impulse turbines
under irregular ow conditions were adopted for these analyses. The numerical
technique has been further ne-turned by adding the compressibility eect in the
OWC device by Thakker et al. [18]. A simple OWC device geometry with width 10
m with a turbine duct area to air chamber area ratio, m 0:00181 was adopted for
the simulation as shown in Fig. 15.

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543

Fig. 12. Static pressure contours on suction side of turbine blade at / 1:68. (a) 0.25% tip clearance;
(b) 1% tip clearance; (c) 4% tip clearance; (d) 6% tip clearance.

The actual sea data based on the water surface elevation time history were used
to simulate irregular test wave provided by Irish Utility, Electricity Supply Board
of Ireland (ESBI). The test waves had a mean time period, Ts 6:5 s and a signicant wave height, Hs 2:091 m. For this simulation, 30 waves were used with a
total time span of 1 month. A plot of non-dimensional wave height, H
vs. nondimensional time, t
is shown in Fig. 16 for 164 s. The mean output Co and the
mean input coecient Ci can be dened, respectively [18] as follows:
o 1
C
t


 

2 va
2
K x
41 m

dt

CT /
x
r
1m
2
0


 

2 va
2
K x
41 m
va
dt

r
1m
2

10

t

t

and
i 1
C
t

CA /

It can be noted from the above two equations that the performance of the turbine can be calculated as a function of Kx
and va
, when torque coecient CT

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Fig. 13. Static pressure contours on pressure side of turbine blade at / 1:68. (a) 0.25% tip clearance;
(b) 1% tip clearance; (c) 4% tip clearance; (d) 6% tip clearance.

Fig. 14. Static pressure contours on tip surface of turbine blade at / 1:68. (a) 0.25% tip clearance; (b)
1% tip clearance; (c) 4% tip clearance; (d) 6% tip clearance.

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545

Fig. 15. Schematic layout of a simple OWC device.

Fig. 16. Test irregular ow.

(/), input coecient CA (/), solidity, r, hub-to-tip ratio, c and non-dimensional


, va
mTs va =Hs and x

xTs .
angular speed are specied. Where / va
=K x
The mean eciency of the turbine can be dened as

o C
 i:

gC

11

The mean eciency of Impulse turbine with various tip clearance under such irregular condition is shown in Fig. 17.

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Fig. 17. Simulated mean eciency of turbine under irregular ow condition.

5. Conclusion
The present computational model has been validated with experimental results
with reasonable accuracy and found to be suitable for further design analysis. It is
found that ke turbulence model can predict the performance of turbine in the low
rotational speed of turbine. The performance curves of the Impulse turbine with
various tip clearances have been arrived at numerically. The ow physics of the
blade passage ow interacting with tip leakage ow has been analyzed with the
computed results. It is investigated that the turbine is very sensitive to tip clearance
when compared to a conventional turbine. It is predicted that the turbine with
0.25% tip clearance performs almost similar to the case with no tip clearance for
the entire ow coecients. The designed value of 1% tip clearance has been validated numerically.
Acknowledgements
The authors would like to acknowledge the nancial support given by ESBI, Ireland and also by the Wave Energy Research Team, Department of Mechanical and
Aeronautical Engineering, University of Limerick.
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