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ABSTRACT
Loss mechanisms in a scallop shrouded transonic power
generation turbine blade passage at realistic engine conditions have
been identified through a series of large-scale (typically 12 million
finite volumes) simulations. All simulations are run with second-
order discretization and viscous sublayer resolution, and they include
the effects of viscous dissipation. The mesh (y+ near unity on all
surfaces) is highly refined in the tip clearance region, casing recesses,
and shroud region in order to fully capture complex interdependent
flow physics and the associated losses.
Aerodynamic losses, in order of their relative importance, are a
result of the following: separation around the tip, recesses, and
shroud; tip vortex creation; downstream mixing losses, localized
shocks on the airfoil; and the passage vortex emanating from under
the shroud. A number of helical lateral flows were established near
the upper shroud surfaces as a result of lateral pressure gradients on
the scalloped shroud. It was found that the tip leakage and passage
losses increased approximately linearly with increasing tip clearance,
both with and without the effect of the relative casing motion. For
each tip clearance studied, scrubbing slightly reduced the tip leakage,
but the overall production of entropy was increased by more than
50%. Also the overall passage mass flow rate, for a given inlet total
pressure to exit static pressure ratio, increased almost linearly with
increasing tip clearance. In addition, it was also found that there was
slight positive and negative lift on the shroud, depending on the tip
clearance. At the lowest tip clearance of 20 mils there was a negative
lift on the shroud. In the 200-mil tip clearance case there was a
positive lift on the shroud. The relative motion of the casing
contributed positively to the lift at every tip clearance, affecting more
at the lowest tip clearance where the casing is closest to the blade tip.
Lastly, it was found that the computed entropy generation for the
stationary 80-mils case using the SKE turbulence model was close to
that of the 80-mils scrubbing case using the RKE turbulence model.
In light of the proposed mechanisms and their relative contributions,
suggested design considerations are posed.
NOMENCLATURE
CP crossflow plane
LE airfoil or shroud leading edge
Ma Mach number
M-M mid-meridional cutting plane for post-processing
P pressure [Pa]; mass-weighted, area-averaged when in
context of a crossflow plane
PS airfoil pressure surface
RKE realizable k- turbulence model
RSM differential Reynolds stress turbulence model
s entropy [J/kg/K]
SKE standard k- turbulence model
SS airfoil suction surface
T static temperature [K]
TE airfoil or shroud trailing edge
u velocity magnitude [m/s], area-averaged when shown in
brackets
Wsshear work done on the fluid by the casing motion [J/s]
x streamwise direction as shown in Figure 1
y lateral direction as shown in Figure 1
y+dimensionless distance from wall
z spanwise direction as shown in Figure 1
Subscripts
ext generated through external exchange
Inlet at the inlet plane
int generated through internal means
S static quantity
T total quantity
x quantity on plane of constant x-coordinate
Copyright © 2004 by ASME
IMECE2004-59116
TRANSONIC PASSAGE TURBINE BLADE TIP CLEARANCE WITH SCALLOPED
SHROUD: PART II – LOSSES WITH AND WITHOUT SCRUBBING EFFECTS IN
ENGINE CONFIGURATION
Wayne S. Strasser Gregory M. Feldman F. Casey Wilkins James H. Leylek
Advanced Computational Research Laboratory
Department of Mechanical Engineering
Clemson University
Clemson, SC 29634
1
INTRODUCTION
This work is part of a unified, focused three-part study of a
scallop shrouded turbine blade. Part I by Feldman et al. [1] sets the
basis for the computational methodology, gridding techniques, and
experi-mental validation for the present work as well as future work.
Part III by Wilkins et al. [2] represents a continuation of this work as
the effects on local heat transfer coefficients caused by the flow
features described in Part I and in the present work are carefully
studied. The computational domain and grid in this part are similar to
those in Part I (details discussed in the upcoming “MODEL” section),
while exactly the same grids and domains are used for this part and
Part III.
For tabulated summaries of the findings from decades of
computational and experimental papers on tip-related losses, see
Strasser [3]. According to Yaras and Sjolander [4] blade tip flow
leakage studies date back to 1926. Although idealized tip gaps have
been explored computationally from Wadia and Booth [5] in 1982 to
Willinger and Haselbacher [6] in 2000, most experimental and
computational studies have shown that the flow across the gap is not
simply two-dimensional flow normal to the chord line. Bindon [7],
for example, proposed complex flow mechanisms of the tip flow
through even a flat gap. He shows how the flow through the gap
exhibits strong chordwise dependence and that losses increase in the
chordwise direction as the flow crossing through a given axial chord
location interacts with fluid entering the gap at an upstream axial
chord location. Reduction of tip-related losses has been extensively
studied. The concept of a separation bubble, vena contracta, and tip
vortex are well recognized. In general, it has been found that the
relative leakage flow increases linearly with increasing tip clearance.
Reduction of the gap discharge coefficient tends to reduce the net loss
of motive fluid through the gap as well as the reentry losses. In some
studies the resulting mixing losses in the gap (after the intense
separation) reduced the total stage efficiency. Making the gap entry a
smoother transition so that the direction change can be negotiated by
the flow (raising the discharge coefficient and removing the
separation bubble) is an alternative. Here, leakage flow reentry
losses are increased. It is apparent upon examination of the mixed
results that one must consider the overall stage efficiency along with
downstream losses and not just a single component of the loss
contribution (such as tip clearance mixing losses). An excellent
summary of the balance needed in considering total efficiency is
given by Harvey and Ramsden [8].
The effect of scrubbing is also of great interest. It does not
appear in the rotating shrouded bladerow computational studies of
Peters et al. [9] and Wallis et al. [10] that the effect of scrubbing was
isolated. Bindon and Morphis [11] showed that the outer passage
vortex is enhanced by the casing relative motion, reducing the
pressure differential driving force for tip leakage. Wadia and Booth
[5] and Farokhi [12] also proposed through 2-D studies that leakage
flow rate will be reduced by rotational effects. Scrubbing effect
studies agree that the relative motion of the casing reduces the flow
of leakage gas through the gap.
The primary value of the open literature to the present research
is the general trends established and range of reasonable values that
can be expected. The general understanding of the flow physics of a
scallop shrouded turbine bladerow at real engine conditions (as
defined by the sponsor) has not been clearly established in the open
literature. The effects of tip clearance variation in conjunction with
relative casing motion at realistic engine conditions have not been
explored. None of the shrouded blade studies dealt with a relative
casing speed greater than one-thirteenth of that in the present study or
at transonic Mach numbers in the passage. Very few of the open
literature studies dealt with shrouded blades, while none dealt with
scalloped shroud designs. Shrouded blade studies are expected to
show different results than those involving unshrouded blades in that
the passage vortex is below the shroud instead of near the casing.
Also, the tip leakage flow orientation relative to the passage flow of
shrouded blades is different than that of unshrouded blades. Lastly,
flow separation around the shrouds adds to losses for shrouded
geometries. Scalloped shrouds are unique in that pitchwise pressure
gradients develop in the tip clearance region as a result of shroud
curvature. Peters et al. [9] and Wallis et al. [10] studied shrouded
geometries computationally, but the flow was not transonic nor was
the shroud scalloped. Of the few computational studies that included
a shrouded blade, it is unclear the level of resolution employed for the
surfaces of the shroud and tip, but few studies involved grids much
over 1 million cells. The need exists for higher grid fidelity in order
to resolve the viscous sublayers imbedded in turbulent boundary
layers present in a transonic turbine blade passage flow. For
example, the benefits of grid resolution are clearly discussed by
Gupta et al. [13] in 2003, who demonstrated that the sensitivity of the
tip region flows to grid resolution is enhanced with increasing grid
resolution. In other words, until regions of high gradients are
sufficiently resolved, the ability to detect computational results
improvements due to incremental grid enhancements is diminished.
The overall objective of the present research is to study losses in
a shrouded turbine bladerow at real engine conditions, including
realistic engine speed, Mach number, and inlet Reynolds number.
The primary goal is to study the aerodynamic losses associated with
tip leakage and scallop shroud-related flow phenomena and to
identify the particular physics mechanisms contributing to these
losses. The combined effects of tip clearance variation (20 to 200
mils) and relative casing motion are also investigated. In addition,
the relative performance of some popular turbulence models will be
evaluated.
MODEL
The present study involves 3-D, steady, transonic, and turbulent
flow of air through an infinitely repeating turbine blade cascade,
including the effects of viscous dissipation. For a complete
discussion of gridding techniques, models, equations, solution
techniques, and experimental validation, see Part I by Feldman et al.
[1]. Note specifically that the gridding techniques displayed in
Figure 2 of Part I were employed for the present work. In addition,
see Strasser [3] for the reasons and methods regarding the attention
given to cell shape, growth, and placement on surfaces and in
volumes. All boundary conditions, including turbulence properties
and casing speed (5.2 times the average inlet velocity), were set to
realistic engine conditions as defined by the sponsor.
The test rig shown in Figure 1 (a), which was computationally
studied by Feldman et al. [14], is designed to represent two passages
in an engine configuration and is discussed in detail in Part I of this
paper. The goal of the present study is to match real engine
conditions, so the modeled domain had to be modified. The span and
pitch were maintained, but the entire geometry was clipped along
lateral planes so that passage was repeating. The tailboards, tailboard
gaps, and shroud cracks were removed. The end result is a truly
infinite cascade representation of a turbine bladerow with the original
airfoil, shroud, and knife-edge in tact. Figures 1 (b) shows the blade-
to-blade view of the modified, periodic domain.
Copyright © 2004 by ASME
2
x = Streamwise direction
y = Lateral direction
Casing
recess
Scalloped
shroud
Tip / Knife-edge
Tailboards
z = Spanwise direction
(a)
x = Streamwise direction
y = Lateral direction
Casing
recess
Scalloped
shroud
Tip / Knife-edge
Tailboards
z = Spanwise direction
(a)
Figure 1 (a): Test rig discussed in Part I of this paper
Periodic
boundaries
(b)
Periodic
boundaries
(b)
Figure 1 (b): Repeating model representing the “engine
configuration” for present work
z = Spanwise direction
x = Streamwise direction
Airfoil
Casing
Symmetry
plane
Tip clearance
y = Lateral direction
Casing
recesses
Knife-edge
20 Mils 80 Mils 200 Mils
z = Spanwise direction
x = Streamwise direction
Airfoil
Casing
Symmetry
plane
Tip clearance
y = Lateral direction
Casing
recesses
Knife-edge
20 Mils 80 Mils 200 Mils
Figure 1 (c): Span and tip clearances studied in Parts II and III
As shown in Figure 1, the x-coordinate is the streamwise
direction, the y-coordinate is the lateral (blade-to-blade) direction,
and the z-coordinate is the spanwise direction. The inlet plane of the
domain at x = 0 is 1.4 chord lengths upstream of the leading edge
(LE) plane of the airfoil cascade and is treated as a total pressure
inlet. The exit plane is 1.8 chord lengths downstream of the trailing
edge (TE) plane and is treated as a pressure outlet. The casing,
shroud, airfoil, and knife-edge surfaces were set as no-slip walls. The
lowest spanwise plane of the domain (passing through z = 0, as
shown in Figure 1 (c)) is set to be a symmetry plane, since no flow is
expected to move normal to this plane. The symmetry plane location
is the same as the “Hub” shown in Figure 1 (A) in Part I of this paper.
The domain is set such that it repeats infinitely along y, the blade-to-
blade direction. The mid-meridional (M-M) plane, which will be used
to show some results, cuts the knife-edge through the middle at a
constant y-axis location. It cuts the geometry along the machine axis,
but the flow is not aligned with the machine axis; therefore, flow
streamlines cross the M-M plane.
Three tip gap clearances are to be studied in the present
research: 20mils, 82mils (same as the test rig), and 195 mils.
Throughout the rest of this paper, these gaps will be referred to in
nominal terms, i.e. 20, 80, and 200 mils. The gap aspect ratios are
4.0, 1.1, and 0.57, respectively. A typical tip clearance region grid is
shown in Figure 2.
83 cells span the gap
Casing
Knife-edge
83 cells span the gap
Casing
Knife-edge
Figure 2: Tip clearance grid sample from the 200-mils case
RESULTS
All the infinitely repeating, shrouded, transonic turbine
bladerow results presented in this section represent fully-converged,
grid-independent solutions. Results of the present research will be
interpreted based on the following discussion of entropy and total
pressure. Entropy creation processes affect system total pressure
through the steady-state relation,
(1)
where entropy is the combination of internally-generated entropy, sint,
and of that which is due to heat exchange through bounding surfaces,
sext. All external sources of entropy are ignored in this study, since all
of the bounding surfaces in the present study are adiabatic. In the
Copyright © 2004 by ASME
3
absence of work input or heat transfer, any process that creates
entropy internally will produce a drop in total pressure, or the ability
to perform work. Also, if work is done on the system, as in relative
casing motion, the effect of the work may somewhat offset the effect
of the internal entropy generation in reducing the total pressure.
Denton [15] lists the sources of internal entropy to be viscous effects
in boundary layers, viscous effects in mixing processes, and shock
waves.
Sample Results and Key Flow Features
To provide an idea of the general flow in the bulk of the
passage, Figure 3 is given to show Mach number contours on the
symmetry plane. At design point there does not appear to be any
separated flow along the PS or SS of the airfoil until the TE is
reached. There are two supersonic flow areas, a localized bubble on
the PS at the TE, and a relatively large bubble along the SS. In both
cases, there are weak local shocks downstream of both the SS and PS
supersonic bubbles.
1.2
0.0
0.8
0.6
0.4
0.2
1.0
80 Mils, Stationary
Ma
1.2
0.0
0.8
0.6
0.4
0.2
1.0
80 Mils, Stationary
Ma
Figure 3: Mach number contours on symmetry plane
80 Mils, Stationary
3.8
0
Inlet
V
u
Inlet
u
u
1st Recess 2nd Recess Casing
Airfoil
80 Mils, Stationary
3.8
0
Inlet
V
u
Inlet
u
u
1st Recess 2nd Recess Casing
Airfoil
Figure 4: Streamlines released from inlet showing passage vortex
Figure 4 shows an isometric view of streamlines released from
the inlet for the 80-mils stationary case. Shown is the passage vortex
as documented in the open literature and which was discussed in the
“Secondary Flow Structure” section and illustrated in Figure 7 in Part
I by Feldman et al. [1]. Low momentum fluid just under the shroud
is forced to migrate from the PS to the SS of the airfoil as it responds
to the lateral pressure gradient established under the shroud. Because
of the migration of fluid under the shroud, fluid particles in the
boundary layer on the PS migrate radially outward toward the shroud.
Those particles in the boundary layer on the SS migrate radially
inward toward the pitchline. The effect of the passage vortex is felt
even down to the pitchline at 50% immersion. Most of the
streamlines released from highest spanwise location of the inlet
circulate in the first recess and move under the shroud and get swept
into the passage vortex. Figure 5 is offered to show the effect of the
passage vortex on a crossflow plane downstream from the airfoil.
The view provided is aft looking forward to a reference plane 1
downstream of the airfoil TE plane. There is a large loss pocket
along the casing at the top of the figure from the leakage flow, but the
interesting feature is the loss pocket that is below that, seemingly
unrelated. Streamlines were traced upstream in reverse from that
pocket and were found to originate in the passage vortex.
Interestingly, the enhancement of local heat transfer coefficients by
the passage vortex is shown in Figure 4 of Part III by Wilkins et al.
[2].
Loss pocket
1.0
0.3680 Mils, Stationary
InletT,
P
T
P
Tip gap losses
Viewing plane
Viewing angle
Knife-edge and
scalloped shroud
Loss pocket
1.0
0.3680 Mils, Stationary
InletT,
P
T
P
Tip gap losses
Viewing plane
Viewing angle
Knife-edge and
scalloped shroud
Figure 5: Total pressure loss on reference plane
Another well-documented flow feature is the tip vortex. The
production of the tip vortex is shown clearly in Figure 6 (blade-to-
blade direction looking radially inward) for the 200-mils stationary
computational case. When vorticity-laden flow leaving the tip
clearance region is reoriented downstream of the knife-edge, it rolls
up into a vortex. Also found was the fact that most of the tip vortex
is made up of leakage flow from the gap, which is consistent with the
open literature. Note from Part I by Feldman et al. [1] that the
present geometric configuration involves a flow field with less loss
penalty caused by the meeting of the tip vortex with the main passage
flow. In these studies the knife-edge prevents the tip leakage flow
from being as far under-turned as in most of the open literature
studies.
There are a number of secondary flows, other than the tip vortex
and passage vortex, in the passage caused by a combination of
Copyright © 2004 by ASME
4
separations and/or pressure gradients along surfaces. There is
stagnation under the LE of the shroud and the separation above the
shroud LE as the flow moves into the area above the shroud and into
Tip vortex
200 Mils, Stationary
3.8
0
Inlet
V
u
Flow
Tip vortex
200 Mils, Stationary
3.8
0
Inlet
V
u
Flow
Figure 6: Streamlines released from gap showing leakage vortex
Shroud LE
Separation
Stagnation 80 Mils, Stationary
1.0
0.36
InletT,
P
T
P
Shroud LE
Separation
Stagnation 80 Mils, Stationary
1.0
0.36
InletT,
P
T
P
Figure 7: Flow separation and stagnation at shroud LE on M-M
Shroud TE
80 Mils, Stationary
1.0
0.36
InletT,
P
T
P
Shroud TE
80 Mils, Stationary
1.0
0.36
InletT,
P
T
P
Figure 8: Flow separation and mixing behind shroud TE and
knife-edge on M-M
3.8
0
Inlet
u
u
Inlet
u
u
80 Mils, Stationary
Flow
3.8
0
Inlet
u
u
Inlet
u
u
80 Mils, Stationary
Flow
Figure 9: Streamlines released above shroud LE showing
complex helical flow pattern above shroud
the tip gap shown in Figure 7. Also, there is a counter rotating vortex
pair downstream of the shroud TE made up of fluid circulating
behind the knife-edge and flow separating behind the shroud TE as
illustrated in Figure 8.
There is a multitude of distinguished flow features within these
separations as a result of lateral shroud pressure gradients caused by
shroud scallop curvature. These include helical flows (with relative
motion in the blade-to-blade direction) occurring downstream of both
casing recesses, above the shroud LE, behind the knife-edge, and at
the shroud TE. These flows input vorticity into the flowfield. In
addition, there is a lateral pressure gradient established in the tip gap
by the flow variation from the scalloped shroud, causing a helical
flow in the tip clearance separation bubble (not shown). Separation
bubble variation creates differing flow reattachment points laterally
along the tip for the 80 and 20-mils cases, but no reattachment
occurred for the 200-mils cases. Feldman et al. [1] noted that for the
80-mils stationary test rig CFD study, reattachment was more
pronounced where the scalloped edge dips in streamwise closer to the
knife-edge. A sample of the complex flow patterns near the shroud is
shown in Figure 9. Also note the culmination of flows that
Copyright © 2004 by ASME
5
eventually end up in the tip vortex as shown in Figure 9. The essence
of the complexity of the tip vortex is well-captured by Feldman et al.
[1] who stated, “…the tip vortex is made up of several low
momentum fluid layers, all with different flow orientations and
vorticity alignment.” In addition, Wilkins et al. [2] show the impact
of these lateral flows on local heat transfer on the top surface of the
shroud in Figure 2 of Part III.
Case Comparisons
Seven cases (Table 1) will be compared both quantitatively and
qualitatively in this section. Figure 10 depicts the effect of tip
clearance on normalized tip leakage. Normalized tip leakage is
defined as the percentage of mass flow through the tip clearance
region compared to the total passage mass flow. The approximately
linear relationship that was found in the open literature is exhibited
here as well. The value of 7% at nominally 200 mils is in the range
of that found by in an experimental study by Dishart and Moore [16].
They showed 5.7% tip leakage for a very different tip gap geometry
with incompressible flow. The value of around 3% for the nominally
80 mils case is comparable to that found by a computational study of
Tallman and Lakshminarayana [17]. They found a leakage of 2.3%
at 73 mils for a very different geometry and incompressible flow.
Their study also showed 6.2% at 183 mils, which falls within close
range of the present linear relationship.
Table 1: Simulation matrix
Nominal Grid Turbulence
Gap Cell Model: Casing Speed
Run Width Count 2nd Order, Normalized by
#(Mils) (Million)
Sublayer Resolved Inlet Velocity Goal
1 80 11.7 RKE 0 80-Mils Stationary
2 80 13.5 RKE 0 Confirm Grid Independence
3 80 11.7 RKE 5.2 80-Mils Scrubbing
4 80 11.7 SKE 0 Effect of Turbulence Model
5 80 11.7 RSM 0 Effect of Turbulence Model
6 20 13.3 RKE 0 20-Mils Stationary
7 20 13.3 RKE 5.2 20-Mils Scrubbing
8 200 12.5 RKE 0 200-Mils Stationary
9 200 12.5 RKE 5.2 200-Mils Scrubbing
Also, notice on Figure 10 that the relative motion of the casing
reduced the leakage flow for all three tip clearances tested, ranging
from a 2.9% drop at 200 mils to a 12% drop at 20 mils. This trend
corresponds to what was found in the literature survey. There are
three reasons for the drop. Firstly, the casing is moving in a direction
normal to the tip leakage flow. The no-slip casing motion forces the
flow near the casing to move in this direction also. For a given
driving force across the tip gap, the input of momentum into the fluid
in a direction normal to the flow direction will allow less leakage to
flow through the tip gap. Secondly, the boundary layer attached to
the moving casing, however thin, increases blockage to flow through
the tip. Thirdly, the tip vortex is moved closer to the knife trailing
edge (reducing the pressure driving force), its speed is increased, and
its angle relative to the knife-edge is increased by scrubbing. This is
physically analogous to what was found by McCarter et al. [18] who
showed that the scrubbing effect “confines” the tip vortex closer the
airfoil SS. Notice the larger relative drop in tip leakage at lower tip
clearance values due to the fact that the casing is closer to the knife-
edge and has a more dominant effect. The absolute value of the drop
is least at the lowest tip clearance since there is less leakage flow
available to be reduced by the casing motion.
0
1
2
3
4
5
6
7
8
0 50 100 150 200
Tip Clearance [Mils]
Normalized Tip Leakage [%]
Stationary Scrubbing
Figure 10: Tip leakage versus tip clearance
The loss of total pressure to the crossflow reference plane 1
downstream from the airfoil TE plane is shown in Figure 11. The
increase in total pressure loss with tip clearance is almost linear.
Notice the 80-mils case using the SKE model (based on Launder and
Spalding, [19]) is much higher than the others due to the well-known
spurious turbulence kinetic energy production and higher effective
viscosity. The results of the cases that include the relative motion of
the casing are all below the results of the stationary cases. This is a
coupled effect due to the increase in total pressure that the casing had
through the work term in Equation 1 as well as the reduced leakage
flow due to scrubbing. The total pressure loss from the said reference
plane to the outlet of the domain shows similar trends. The losses
increase with increasing tip clearance, and the 80-mils SKE case
losses are higher than the 80-mils RKE (based on Shih et al. [20])
case. As in Figure 10, the scrubbing case results are all lower than
for the stationary cases.
2.5
3.0
3.5
4.0
4.5
5.0
5.5
0 50 100 150 200
Tip Clearance [Mils]
Total Pressure Loss [%]
RKE Stationary RKE Scrubbing SKE Stationary
Figure 11: Total pressure loss from inlet to reference plane
versus tip clearance
In order to take into account the effect of work and loss
mechanisms, the internal entropy generation calculated using
Equation 1 (from the inlet to the outlet of the domain) is given in
Figure 12. As with total pressure loss, entropy generation increases
almost linearly with increasing tip clearance. In this figure, however,
Copyright © 2004 by ASME
6
the casing relative motion adds entropy through viscous wall effects.
Scrubbing increases entropy generation at every tip clearance by
more than 50%. Note that the 80-mils stationary SKE case has
almost as much internal entropy generation as in the 80-mils
scrubbing RKE case. In other words, using the SKE model produces
almost as much entropy (from unphysical kinetic energy production)
throughout the domain as the effect of a casing moving relative to the
tip at a speed 5.2 times the inlet velocity. Also (not shown), is the
nearly 2.0 % increase in calculated overall passage total pressure loss
as a result of using the SKE model.
When considering all six cases and the effects on the passage
vortex of varying tip clearance and casing motion, a number of
conclusions can be drawn. The area occupied by the passage vortex
is reduced, and its position is moved closer to underneath the shroud
(higher spanwise location) with increasing tip clearance. Of the fluid
particles traced from the highest spanwise location of the inlet (as in
Figure 4), increasing tip clearance allows more of the fluid to move
through the tip clearance region instead of getting caught up in the
passage vortex. Similar effects on the passage vortex can be seen by
the introduction of scrubbing. The relative casing motion lowers the
10
15
20
25
30
0 50 100 150 200
Tip Clearance [Mils]
Entropy Generation [J/kg/K]
RKE Stationary RKE Scrubbing SKE Stationary
Figure 12: Internal entropy generation versus tip clearance
passage vortex spanwise placement and widens its radius of rotation
(lower vorticity). In addition, it moves laterally away from the
airfoil. Fewer of the particles released at the top of the inlet plane
are captured into the passage vortex after the introduction of relative
casing motion. The weakening of the passage vortex retards the heat
transfer under the shroud as noted by Wilkins et al. [2].
Interesting insights can also be gained about the effects of tip
clearance and casing motion on the tip vortex. The tip vortex is
moved further downstream with increasing tip clearance, increasing
its evolution angle relative to the knife-edge. This makes sense since
there is more relative leakage flow (higher leakage momentum) at
higher tip clearances. Also the tip vortex evolves at a higher velocity
at the higher tip clearances. The scrubbing effect moves the tip
vortex further upstream closer to the knife trailing edge, decreasing
its angle relative to the knife-edge. Along with the change in angle,
there appears to be less rotation in the tip vortex as a result of relative
casing motion. Also, the tip vortex evolves at a higher velocity by
the relative casing motion when compared to the stationary cases.
Despite these impacts on the tip vortex, there is little change in the
heat transfer at the shroud trailing surface as noted by Wilkins et al.
[2].
The effective positive and negative lift force on the shroud is
another key parameter in the design consideration of a turbine
bladerow. Ideally, the shroud should experience zero lift as it is not
intended to participate in lift generation. In this study it was found
that there is positive and negative lift force applied to the shroud/
knife-edge / tip combination during operation. The net force is
negative when the tip clearance is low and then increases almost
linearly to a positive lift at the highest tip clearance. In all runs, the
relative motion of the casing added upward force to the assembly as
viscous effects lowered the total and static pressure in recess regions.
It is only at a tip clearance of 80 mils that the force is almost neutral
(zero net lift) on the shroud. There are a number of reasons the lift
force changes with tip clearance. First of all, there is increased
leakage through the gap at higher tip clearances creating lower
pressure in the recess, gap, and knife trailing edge areas. A lower
pressure above this assembly increases the positive lift force effect on
the entire structure. Second, for a given driving potential, inlet total
pressure to exit static pressure ratio, increasing the tip clearance
allows a higher mass flow rate through the passage. Since the flow
stagnates underneath the shroud as previously discussed, a higher
passage flow produces a higher momentum under the shroud for a
positive lift effect. Third, the passage vortex strength diminishes
with increasing tip clearance; there should be less of a low-pressure
pocket caused by the vortex under the shroud at higher clearances.
This will have the effect of a less of downward force on the shroud at
higher tip clearances, making the net effect a greater positive lift.
Along these same lines, it is possible that the weakening of the
passage vortex due to scrubbing contributes to the higher shroud lift
for the scrubbing cases.
The next series of quantitative discussions pertain to the relative
contributions of various loss mechanisms to the total pressure loss
throughout the domain. The proposed mechanisms, shown in the
upcoming sections, include separation regions in and around the
shroud, knife-edge, and gap; local shocks on the airfoil; mixing
behind the trailing edge of the airfoil; tip vortex; and passage vortex.
There are 7 crossflow planes (CP) plus the inlet and outlet planes
used to calculate losses along the machine axis (streamwise direction)
from the inlet to the outlet. These planes slice through the entire
geometry at a given crossflow location. A separator plane is shown
parallel with the majority of the flow field, aligned with the
symmetry plane. Figure 13 shows the meridional view of these
dissection planes. A summary of the location of each calculation
plane and the major effects isolated between consecutive CPs is
provided in Table 2. Above the separator plane includes the effect of
the recesses, shroud, gap, and knife-edge. Below the line includes the
effects of the passage vortex, airfoil shocks, and airfoil wake.
CP1 CP2 (LE)
CP3 CP4
Separator plane
200 Mils, Moving
CP5 CP6 (TE) CP7
CP1 CP2 (LE)
CP3 CP4
Separator plane
200 Mils, Moving
CP5 CP6 (TE) CP7
Copyright © 2004 by ASME
7
Figure 13: Near-tip view of crossflow planes and separator plane
Table 2: Summary of crossflow planes
Major Incremental Major Incremental
Effects Above Effects Below
CP Location Separator Plane Separator Plane
1 First Recess
Casing viscous losses
up to first recess
Turbulent mixing
2 Airfoil LE
Separation and mixing
after first recess
Turbulent mixing
3 Gap Inlet
Separation and mixing
after second recess
Creation of passage
vortex
4 Gap Outlet
Separation and mixing
inside tip clearance
Continued passage
vortex development
5 Shroud TE
Separation and mixing
behind knife-edge
Continued passage
vortex development
6 Airfoil TE
Separation and mixing
behind shroud TE
Airfoil local weak
shocks
7 Reference Plane
Creation of tip vortex
Passage vortex wake
and airfoil wake
Figure 14 (a) shows the relative cumulative contributions to loss
at each CP along the machine axis (streamwise direction) of the
domain for the stationary cases, while Figure 14 (b) shows the
contributions for the scrubbing cases. The numbers next to the
vertical lines on the plots correspond to the identification of the CP
over which the total pressure is mass-weighted and area-averaged.
This plot does not include the separate effects above and below the
separator plane. The relative contribution is defined as the relative
total pressure loss from one CP to the next consecutive CP, i.e.
. To find the cumulative value, the result on
each CP is added to the previous. By summing these values
streamwise along the domain, the total will equal the total pressure
loss in the domain from the inlet to the outlet. From the close
inspection of Figure 14 (a) and (b) a number of remarks can be made.
In general, the losses at each CP decrease with decreasing tip
clearance, in both the stationary and scrubbing cases. Therefore, the
losses for the overall passage decrease with decreasing tip clearance.
Also, the incremental losses inside the tip clearance region (between
CP 4 and 5) are among the lowest of all the sources of loss, for all tip
clearances in both the stationary and scrubbing cases. The slope of
the loss line does make a shift, however, at the inlet of the tip gap and
-1
0
1
2
3
4
5
6
0.0 0.2 0.4 0.6 0.8 1.0
Normalized Streamwise Distance Through Domain
Cummulative Total Pressure Loss [%]
200 80 20
1
3
4
5
6
Stationary Cases
2
Inlet
Outlet
7
LE
TE
Gap
Figure 14 (a): Cumulative losses for stationary cases
-1
0
1
2
3
4
5
6
0.0 0.2 0.4 0.6 0.8 1.0
Normalized Streamwise Distance Through Domain
Cummulative Total Pressure Loss [%]
200 80 20
1
3
4
5
6
Scrubbing Cases
2
Inlet
Outlet
7
LE
TE
Gap
Figure 14 (b): Cumulative losses for scrubbing cases
appears to continue on a steeper trend until the leakage-related losses
are mixed out. This indicates that the tip clearance leakage flow sets
the stage for increased losses throughout the remainder of the
domain. Viewing Figure 14 (b) is made complicated by the fact that
the longer the distance between CPs, the more casing work is allowed
to inflate the total pressure near the casing. For example, notice the
results at CP 1 and CP 2 for the scrubbing cases. The input of casing
work more than balances (making the loss negative) the lost total
pressure caused by the wall viscous effects and first recess separation.
It is desired to categorize the domain losses into three regions:
those upstream of the airfoil LE plane, those losses between the
airfoil LE and TE planes, and those downstream of the airfoil TE
plane as shown in Figure 15. For all tip clearances with and without
the scrubbing effect, the majority of the losses occur between the
airfoil LE and TE planes. Those losses downstream of the airfoil TE
plane are much higher than those upstream of the airfoil LE plane.
Typically, the effects in each category decrease in magnitude with
decreasing tip clearance. Also, the casing work more than balances
(making the loss negative) the lost total pressure caused by the effects
upstream of the airfoil TE plane. Figure 8 in Part I of this paper by
Feldman et al. [1] quantifies these concepts for the CFD study of the
test rig and is to be compared to Figure 15 (a). The findings of that
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Upstream of LE Between LE and TE Downstream of TE
Total Pressure Loss [%]
200 80 20
Stationary Cases
Figure 15 (a): Grouped loss contributions for stationary cases
Copyright © 2004 by ASME
8
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Upstream of LE Between LE and TE Downstream of TE
Total Pressure Loss [%]
200 80 20
Scrubbing Cases
Figure 15 (b): Grouped loss contributions for scrubbing cases
work, in terms of relative magnitudes, were consistent with those of
this work. The two figures should not agree completely, because the
losses found in Part I include the effects of the hub, sidewalls,
tailboards, and a reflected shock and should be higher at every
measurement location.
Figure 16 displays many of the incremental contributions of
those loss mechanisms below (a) and above (b) the separator line for
the 200-mils stationary and scrubbing cases. The use of the separator
plane is not a convenience for the other tip-clearance cases as
discussed in [3]. The definition of relative losses is consistent with
that of the previous discussion. It can be concluded that:
1. The effects below the separator plane contribute less to total
pressure losses in the domain than those above the plane.
2. In the life of the passage vortex, its creation near the airfoil LE
appears to have the most dramatic reduction in total pressure.
3. Surprisingly, the shroud LE separation contributes very little to
total pressure loss as evidenced by the similar loss magnitude at
CPs 2 (first recess) and 3 (second recess plus shroud LE).
Along those same lines, losses downstream of the shroud TE are
almost insignificant (CP 6).
4. Below the separator, the mixing toward the outlet of the domain
is the largest contributor to the losses, followed by the local
airfoil shocks downstream of the supersonic bubbles on the SS
and PS.
5. Above the separator, the flow behind the knife-edge is the
largest contributor, followed by the tip leakage vortex creation.
6. At almost every CP above and below the separator plane, the
contributions for the scrubbing case are less than those of the
stationary case again due to the input of total pressure by casing
work.
Cases Not Covered
Neither case 2 nor 5 in Table 1was considered in the discussion
thus far. The purpose of case 5 was to use the differential RSM
turbulence model in order to overcome the known deficiencies of the
linear eddy viscosity models, including the inability of the linear eddy
viscosity models to directly capture curvature effects and turbulence
anisotropy. The employed RSM model is a blend of various
approaches in the literature and is discussed in [21]. As a result of
the stiffness of the differential RSM in use with a near-wall treatment
[21], a converged solution was not obtained.
The purpose of case 2 was to confirm grid independence
through gradient-based adaption. Cells were added in regions where
the gradient criteria (Laplacian of a variable times the cube root of
cell volume) were above prescribed thresholds. The total cell count
only increased by 15%, but the cell counts in near-tip and near-
shroud regions increased by 8x as a result of the gradient-based
approach. A series of surface monitors throughout the domain in
case 2 were practically identical to the same monitors throughout
case 1, so the grid was determined to already be grid-independent [3].
SUMMARY AND CONCLUSIONS
In summary, a high-fidelity computational study has been
performed to examine loss mechanisms in a steady transonic scallop
shrouded turbine bladerow. The effects of tip clearance, casing
relative motion, and turbulence model performance on passage
aerodynamics were investigated in the present work, while these
effects on heat transfer considerations is given in Part III by Wilkins
0.0
0.5
1.0
1.5
2.0
2.5
Airfoil LE +
Start of
Passage
Vortex
Continued
Vortex
Development
Continued
Vortex
Development
Most of Local
AF Shocks
Passage
Vortex + AF
Wake
Continued
Mixing in Bulk
Total Pressure Los s Contribution [%]
200-Mils Stationary 200-Mils Scrubbing
Lower CP3
Lower CP4
Lower CP5
Lower CP7
Lower Outlet
Below Separator
Lower CP6
Figure 16 (a): Loss contributions below separator plane
0
1
2
3
4
5
6
7
8
First
Recess up
to AF LE
Second
Recess +
Shroud LE
Inside Gap
Behind
Knife-edge
Most of the
Shroud TE
Tip Vortex +
Shroud TE
Continued
Mixing Near
Top
Total Pressure Los s Contribution [%]
200-Mils Stationary 200-Mils Scrubbing
Upper CP3
Upper CP5
Upper CP6
Upper CP7
Upper Outlet
Upper CP2
Above Separator
Upper CP4
Figure 16 (b): Loss contributions above separator plane
Copyright © 2004 by ASME
9
et al.[2]. There were seven large scale computations, typically 12
million finite volumes, run with second order discretization and
viscous sublayer resolution. Grid independence was established
through localized gradient adaption, and experimental validation was
demonstrated in Part I by Feldman et al. [1]. This is the first study of
this scale and resolution for a shrouded turbine bladerow at real
engine conditions found in the open literature. It was the only study
found for a scallop-shaped shroud or a shrouded blade at real engine
conditions. The following proposed mechanisms, arranged in
descending order on a mass-weighted area-averaged basis, are
responsible for aerodynamic losses throughout the modeled
computational repeating passage: Separation and mixing behind the
knife-edge; Production of tip vortex; Mixing out of these features
near the casing; Separation and mixing after the first or second casing
recess; Separation losses in the gap; Mixing out of airfoil wake;
Localized shocks on airfoil; Passage vortex creation; Separation
behind airfoil and passage vortex meeting PS flow at airfoil TE. It
must be noted that the effects of the mixing out of the tip leakage
flow are not distinguished from the knife trailing edge mixing losses
in this study. It is expected that very little mixing occurs in the gap
except in the 20-miles cases where the gap aspect ratio is high.
Also, it was found that with increasing tip clearance for a given
casing boundary condition, the total passage flow, relative flow lost
through the tip gap, aerodynamic losses and entropy generation in the
domain, and the net upward lift on the shroud increase almost
linearly. In addition, the passage vortex strength is diminished, and
its position is moved radially outward. The tip vortex is
strengthened, and its angle relative to the knife-edge is increased.
When relative motion of the casing is introduced, the relative
flow lost through the tip clearance region decreases slightly ranging
from a 2.9% drop at 200 mils to a 12% drop at 20 mils. Entropy
generation in the domain increases by more than 50%, and net lift on
the shroud slightly increases. In addition, the passage vortex strength
is diminished, and its position is moved radially inward. Lastly, the
angle of the tip vortex relative to that of the knife-edge is decreased.
It has been shown that CFD can be used to produce sound and
internally consistent results for this class of problems. As a result, it
can be expected that CFD can be fruitfully utilized as a parametric
evaluation tool to take the place of the generally-accepted build-and-
bust technique for design studies. In light of some of the findings
regarding the sources of losses, it should prove helpful if some design
improvements could be sought through further CFD evaluations:
Tip and knife-edge: The separation area downstream of the
knife-edge (after the gap separation) is the largest contribution to
losses. A more contoured trailing knife-edge may increase the
total stage efficiency as an optimum balance between discharge
coefficient and mixing losses is sought in the tip flow area.
Casing recesses: As the tip gap grows with engine age, the
minimum effective flow area in the gap may be around the same
magnitude as the area between the second recess and the top of
the shroud. It is helpful to keep in mind the study by Xiao and
Amano [22], who discussed that the minimum flow area governs
the leakage. The movement of the recesses closer to the shroud
in conjunction with an un-scalloped shroud would minimize the
available area for flow. Also, sharp recess corners might not be
the optimum balance between entropy generation and flow
deflection. Shroud scallop: A design with less curvature would
reduce the lateral pressure differentials established in the
tip/shroud area.
Shroud position: If the shroud left the airfoil PS at a given radial
position and met the SS at a lower radial position some of the
PS-to-SS flow would be deflected. Thickness variation or both
thickness and position variation should more dramatically
improve this.
Shroud tilt: The shroud could be tilted to offset the lifting effect.
ACKNOWLEDGMENTS
The authors would like to sincerely thank GE Power Systems
of Greenville, SC for their funding of this work.
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Copyright © 2004 by ASME
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Copyright © 2004 by ASME
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