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Effects of tip-gap size on the tip-leakage ow in a turbomachinery cascade Effects of tip-gap size on the tip-leakage ow in a turbomachinery cascade
Donghyun You
a
Center for Turbulence Research, Stanford University, Stanford, California 94305
Meng Wang
Department of Aerospace and Mechanical Engineering, University of Notre Dame,
Notre Dame, Indiana 46556
Parviz Moin
Center for Turbulence Research, Stanford University, Stanford, California 94305
Rajat Mittal
Department of Mechanical and Aerospace Engineering, George Washington University,
Washington, D.C. 20052
Received 23 May 2006; accepted 15 August 2006; published online 5 October 2006
The effects of tip-gap size on the tip-leakage vortical structures and velocity and pressure elds are
investigated using large-eddy simulation, with the objective of providing guidelines for controlling
tip-leakage cavitation and viscous losses associated with the tip-leakage ow. The effects of tip-gap
size on the generation and evolution of the end-wall vortical structures are discussed by
investigating their evolutionary trajectories and the mean velocity eld. The tip-leakage jet and
tip-leakage vortex are found to produce signicant mean velocity gradients, leading to the
production of vorticity and turbulent kinetic energy. Inside the cascade passage, the peak streamwise
velocity decit and magnitudes of vorticity and turbulent kinetic energy in the tip-leakage vortex are
reduced as the tip-gap size decreases. The present analysis indicates that the mechanisms for the
generation of vorticity and turbulent kinetic energy are mostly unchanged by the tip-gap size
variation. However, larger tip-gap sizes are found to be more inductive to tip-leakage cavitation
judged by the levels of negative mean pressure and pressure uctuations. � 2006 American Institute
of Physics. DOI:
10.1063/1.2354544
I. INTRODUCTION
The radial clearance between a rotor-blade tip and casing
wall in a turbomachine is indispensable for its operation.
However, its existence has been a major source of unfavor-
able ow phenomena. Complicated vortical structures are
generated by the tip-clearance ow and its interactions with
the end-wall boundary layer, the blade wake, and neighbor-
ing blade. The tip-clearance vortical structures often induce
rotating instabilities and blockage in the ow passage which
result in severe performance loss and subsequent stall of
axial compressors.
1,2
In a transonic compressor, interaction
between passage shock and tip-clearance ow is implicated
in the degradation of efciency as well as vibrations and
noise generation
3
while tip-leakage cavitation is induced by
the low pressure events in the vicinity and downstream of the
tip gap of liquid pumps.
48
These issues have motivated a
number of experimental and computational investigations
where a reduction of the tip-clearance ow related detrimen-
tal effects was attempted through the change of tip-gap
size.
414
In axial compressors, it has been reported that an in-
crease of tip gap between the blade tip and casing wall also
increases the size of the tip-leakage vortex and shifts the
origin of the vortex further downstream with an increased
angle between the path of the tip-leakage vortex center and
that of the blade wake.
9,10
Storer and Cumpsty
11
employed a
compressor cascade with a variety of tip-gap sizes and
showed a nonlinear relation of total pressure loss with the
tip-gap size, while the size of tip-leakage vortex varied lin-
early with tip-gap height. Later experimental studies by
Zierke et al.
4
and Zierke and Straka
5
in a high-Reynolds-
number pump facility showed that the size of the rotor tip
gap signicantly inuences the evolution of the tip-leakage
vortex and resultant cavitation.
The effects of tip-gap size on the tip-leakage cavitation
in a rotating hydraulic pump were examined more exten-
sively by Farrell and Billet
6
who found that the cavitation
inception indices increase with decreasing tip-gap sizes.
They also found a minimum in the cavitation inception index
when the ratio of tip-gap size to the maximum tip thickness
is in the range of 0.1 0.2. Experiments performed by Boulon
et al.
7
in a setup with a stationary end-wall showed decreased
cavitation inception indices with decreasing tip-gap sizes.
Similar observations were reported by Gopalan et al.
8
Al-
though the gross effects of tip-gap size on the tip-leakage
ow have been known for sometime, the quantitative effects
on the dynamics of the tip-leakage vortical structures, tip-
leakage cavitation, and performance loss associated with the
tip-leakage ow are poorly understood.
In recent experiments performed at Virginia Tech, which
are also benchmarked in the present large eddy simulation
a
Author to whom correspondence should be addressed. Telephone:
1-650-
725-1821. Fax:
1-650-725-3525. Electronic mail: dyou@stanford.edu
PHYSICS OF FLUIDS 18, 105102 2006
1070-6631/2006/18 10 /105102/14/$23.00
� 2006 American Institute of Physics
18, 105102-1
Downloaded 25 Nov 2006 to 128.164.158.224. Redistribution subject to AIP license or copyright, see http://pof.aip.org/pof/copyright.jsp LES study, the effects of tip-gap size on the downstream
tip-leakage ow eld were examined.
12,13
Since the experi-
ments were performed in a wind tunnel, cavitation was not
an issue in those studies. Muthanna and Devenport
12
inves-
tigated the effects of tip-gap size on the cross-sectional struc-
ture of the tip-leakage vortex at about three axial chord C
a
lengths downstream from the trailing-edge by comparing the
mean ow and turbulence properties in the base tip-gap size
3.06% axial chord with those in the doubled and halved
tip-gap sizes. The vortex center, dened by the location of
peak streamwise vorticity, moved across the end-wall and the
pitchwise separation between the vortex and wake center in-
creased as the tip gap was increased. In general, the regions
of tip-leakage ow in terms of mean velocity, vorticity, and
turbulent kinetic energy were found to increase in size as the
tip gap size increased. However, the magnitudes of stream-
wise mean velocity decit and turbulent kinetic energy in the
downstream tip-leakage vortex appeared to be almost un-
changed by the tip-gap size variation. Wang and Devenport
13
performed experiments in the same conguration studied by
Muthanna and Devenport
12
but replaced the stationary end-
wall with a moving end-wall. Many of the characteristics of
the tip-leakage vortex including the mechanism that drives
the vortex were similar to those observed without end-wall
motion.
However, these studies
12,13
focused on the ow eld
downstream of the cascade passage and did not provide in-
formation regarding the effects of tip-gap size on the genera-
tion and evolution stages of the tip-leakage vortex and other
induced scraping or tip-separation vortices. In addition, the
previous experimental
12,13
and Reynolds-averaged Navier-
Stokes RANS computational studies
15,16
could not provide
information regarding the unsteady pressure eld in the cas-
cade passage region. Since the induced and tip-separation
vortices, as well as the tip-leakage vortex, can signicantly
inuence the tip-leakage cavitation phenomenon, detailed ef-
fects of tip-gap size on the vortical structures need to be
better understood. An understanding of the effects of tip-gap
size on the pressure eld in the vicinity of the tip gap is also
crucial in designing cavitation-control methodologies based
on the optimal tip-gap size or on modications of the blade
tip and end-wall.
In this study, the tip-leakage ow, particularly in regions
not studied experimentally,
13
is investigated using data ob-
tained by LES. In Refs. 14 and 17, the mean and turbulence
statistics, the vortex dynamics, and the space-time correla-
tions of velocity and pressure uctuations in a linear cascade
conguration with a tip-gap size of 3.06% axial chord were
computed, validated, and analyzed throughout the cascade
passage, inside the tip gap, and at several downstream loca-
tions. This paper deals with the effects of tip-gap size on the
tip-clearance ow dynamics with a particular emphasis on
understanding the effects of tip-gap size on the end-wall vor-
tex dynamics, mechanisms for viscous losses, and tip-
leakage cavitation.
Flow
congurations
and
grid
spacings
for
the
simulations are addressed in Sec. II. Results and discussion
of the effects of tip-gap size on various features of the tip-
clearance ow are given in Sec. III, followed by conclusions
in Sec. IV.
II. COMPUTATIONAL SETUP
A. Flow conguration
The numerical algorithms and their implementation are
described in Ref. 17 in detail. The three-dimensional, un-
steady, incompressible Navier-Stokes equations are solved
in a generalized coordinate system in conjunction with a
Lagrangian dynamic subgrid-scale SGS model.
18
The ow conguration and coordinate denitions are
schematically shown in Fig. 1. The present study is focused
on a linear cascade with a moving end-wall at the bottom of