Numerical benchmarking of tip vortex breakdown in axial turbines
by
Eunice Allen-Bradley
An Engineering Project Progress Report Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
David Tew, Project Advisor
_________________________________________
Ernesto Guitierrez-Miravete, Project Advisor
Rensselaer Polytechnic Institute
Hartford, CT
February 2009
(For Graduation May 2009)
TABLE OF CONTENTS
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
ACKNOWLEDGMENT ................................................................................................... v
ABSTRACT ..................................................................................................................... vi
NOMENCLATURE …………………………………………………………………....vii
1. INTRODUCTION …………………………………………………………………… 1
2. METHODOLOGY …………………………………………………………………... 2
3. RESULTS & DISCUSSION ………………………………………………………… 7
4. FUTURE WORK & CONCLUSIONS …………………………………………….. 12
5. REFERENCES ………………………………………………………………………13
ii
LIST OF TABLES
Table 2.1 – TVB Airfoil Design Conditions
iii
LIST OF FIGURES
Figure 2.1 -- Improper definition of vortex breakdown
Figure 2.2 -- Definition of vortex breakdown
Figure 2.3 -- Example of tip vortex where vortex breakdown is unclear
Figure 2.4 -- Example of tip vortex where vortex breakdown is clear
Figure 2.5 -- Example of tip vortex where no breakdown is clear
Figure 2.6 -- Surface streamlines for vortex breakdown & stable vortex
Figure 2.7 -- Surface streamlines where vortex breakdown is unclear
Figure 3.1 -- Pressure loss trend to Mach number at various tip clearances
Figure 3.2 -- Pressure loss trend to tip clearance at various exit Mach numbers
Figure 3.3 -- Pressure loss trend to Mach number at various tip clearances
Figure 3.4 -- Pressure loss trend to tip clearance at various exit Mach numbers
Figure 3.5 -- Grid topology for CFD domain
Figure 3.6 -- Pressure loss trend to tip clearance for various grid densities
iv
ACKNOWLEDGMENT
The author with acknowledge the contributions and guidance given by following from
Pratt & Whitney East Hartford: Andrew Aggarwala, Timothy Nash, Anil Prasad,
Thomas Praisner, & Richard Gacek.
v
ABSTRACT
The scope of the current study is to benchmark turbine blade performance in the
event of blade passage vortex breakdown with the use of a standard Reynolds-Averaged
Navier-Stokes (RANS) computational fluid dynamics (CFD) code. The ultimate goal of
the present work is to determine a range of conditions where the CFD does and does not
predict tip vortex breakdown for testing in a turbine cascade rig. It is well known that
tip leakage loss has a large impact on the efficiency of turbomachines. There have been
numerous studies that have explored minimizing the tip leakage loss with various flow
control methods. There have also been many studies to measure tip leakage flow and the
resulting tip vortex that is generated in the flowfield. The tip vortex encounters a strong
adverse pressure gradient within the blade passage, and on occasion, causes the vortex to
burst (or breakdown). Although there has been much study of vortex breakdown on
external airfoils, there has been relatively limited investigation of tip vortex breakdown
in turbomachines. It is unclear if the current design tools are adequate for predicting tip
vortex breakdown in axial turbines.
Preliminary results of the study have developed performance curves based on
varying boundary conditions.
For several simulations, tip vortex breakdown was
predicted with the CFD tool with the original airfoil. However, when the grid was
increased for these simulations, tip vortex breakdown was not predicted. Another option
for consideration is to model a larger pitch of the study airfoil to achieve vortex
breakdown.
When vortex breakdown is achieved (and confirmed with the grid
sensitivity study), further simulations varying other boundary conditions will be run for
their influence on the vortex behavior. Further confirmation of vortex breakdown will
be demonstrated with changes in turbulence models. With the use of flow visualization
tools, the predicted flow field will be examined and commented on.
vi
NOMENCLATURE
BX
Axial Chord
H
Cascade Span

Flow Angle
M
Mach number
Subscripts
1
Inlet condition
2
Exit condition
vii
1. Introduction
It is well known that tip leakage loss has a large impact on the efficiency of
turbomachines. There have been numerous studies that have explored minimizing the
tip leakage loss with various flow control methods. There have also been many studies
to measure tip leakage flow and the resulting tip vortex that is generated in the flowfield.
The tip vortex encounters a strong adverse pressure gradient within the blade passage,
and on occasion, causes the vortex to burst (or breakdown). Although there has been
much study of vortex breakdown on external airfoils, there has been relatively limited
investigation of tip vortex breakdown in turbomachines. It is unclear if the current
design tools are adequate for predicting tip vortex breakdown in axial turbines.
The above is just a place holder. The initial review of the literature gave guidance
for the many things to consider for the best way to achieve vortex breakdown with the
CFD simulations. After a thorough literature review, this section will include a record of
results and opinions from previous authors regarding tip leakage measurements in
cascade testing environments, and previous attempts to model tip leakage for cascade
geometries.
This section may also include opinions on how to quantify vortex
breakdown in several regimes.
1
2. Methodology
The plan was to take airfoil geometry from an existing and well known turbine
cascade facility and model tip gap in the CFD simulations. The desired features were
that the airfoil should be a low-camber airfoil, similar to the airfoil geometry found in
the tip region of turbine blades. Table 2.1 contains limited details of the study airfoil
geometry and describes the design boundary conditions:
Table 2.1 – Base Airfoil Design Conditions
Cascade Span (H)
2.4”
Axial Chord (BX)
1.0”
Inlet flow angle1)
63o
Exit flow anlge2)
26o
Exit Mach number (M2)
0.8
The boundary conditions were systematically varied until tip vortex breakdown was
achieved (tip clearance, pressure ratio, inlet flow angle, inlet boundary layer). Ideally,
we want to achieve vortex breakdown in the absence of airfoil stall due the boundary
conditions, so as to not contaminate the performance results. The option of increasing
the pitch of the cascade was also considered during the initial studies to achieve vortex
breakdown.
The CFD domain size was varied to determine the effectiveness of the vortex
breakdown prediction. Initially, the exit boundary of the simulation was located 0.5*BX
downstream of the airfoil trailing edge. It was found that as the exit boundary was
moved aft of the trailing edge, the tip vortex seem to stabilize, minimizing the behavior
of vortex breakdown.
Determination of Vortex Breakdown. During the course of the study, it was found
to be a challenge determining when the tip vortex breaks down. There needed to some
grounds rules that determined whether breakdown was achieved. During the initial set
of simulations, it was found that breakdown could be achieved with excessively large tip
clearances (>5% of axial chord). However, with the aid flow visualization software, it
2
was found that the tip vortex breakdown occurred AFT of the trailing edge due to the
amount of diffusion that occurs downstream of the blade passage (shown in the Figure
2.1 below).
Figure 2.1 -- Improper definition of vortex breakdown for current study.
Figure 2.2 shows the ideal features of a simulation that achieves a massive vortex
breakdown. Notice that several arrows on the streamlines visualizing the tip vortex
show the direction of the flow. The tip vortex clearly reverses on itself within the blade
passage.
Figure 2.2 -- Definition of vortex breakdown for the present work.
In some instances, it was difficult to determine if breakdown actually achieved due
the size of the tip vortex. This was a constant occurrence for simulations of lower exit
3
Mach numbers. For example, as shown in Figure 2.3 below, it is unclear if the vortex
has broken down. The size of the tip vortex is small, although several of the arrows
visualizing the vortex suggest that is, indeed, reversing on itself while still within the
blade passage.
Figure 2.3 -- Example of tip vortex where vortex breakdown is unclear.
Conversely, Figures 2.4 & 2.5 clearly shows the behavior of the tip vortex for the
given set of boundary conditions of the cascade. Figure 2.5 is an example of tip vortex
breakdown; Figure 2.6 is an example of a well contained tip vortex.
Figure 2.4 -- Example of tip vortex where vortex breakdown is clear.
4
Figure 2.5 -- Example of tip vortex where no breakdown is clear.
The issue of inducing vortex breakdown during testing was considered. Standard
measurements of loss employ the usage of kiel head probes or multi-hole probes that are
relatively large when compared to the region that will be measured. The presence of
these probes in the tip region may cause the tip vortex to breakdown. After several
discussions with several associates at the testing facility, it was suggested that using
surface streamlines would be an adequate method of confirming vortex breakdown. As
demonstrated in Figure 2.6, the suction surface streamlines have distinct characteristics
between a stable tip vortex and when the vortex breaks down (flow moves from right to
left in the figure).
(a)
(b)
Figure 2.6 -- Surface streamlines for vortex breakdown (left) & stable vortex (right) (a);
Overlay of 3D streamlines of tip vortices on surface streamlines (b)
5
Using the surface streamlines as guidance (see Figure 2.7 below), it was determined
that the simulation from Figure 2.3 does indeed predict vortex breakdown.
Figure 2.7 -- Example of tip vortex where vortex breakdown is unclear.
After numerous perturbations on the boundary conditions, it was discovered that tip
clearance and exit Mach number were the strongest drivers in achieving burst. With this
information, along with influence of the downstream boundary location and a clear
definition of what a tip vortex breakdown should look like, the cascade geometry was
modeled with a refined set of boundary conditions. The CFD domain for all simulations
extends from 1.0*BX upstream of the leading edge of the cascade to 1.5*BX downstream
of the trailing edge. The results of this modified study will be presented in the following
chapter.
6
3. Results & Discussion
Preliminary Results. Each simulation was run with the same amount of grid for the
same amount of time using a fully turbulent two-equation turbulence model (Modified
Wilcox k-). The metric used for performance analysis is the total pressure loss across
the entire computational domain. Figure 3.1 shows the relationship of pressure loss to
the range of exit Mach numbers at the cascade design inlet flow angle. The different
curves represent the tip clearances that were modeled for each simulation.
This
information is useful for benchmarking how much pressure loss is attributed to the
addition of the tip clearance to the cascade row.
1.20
TC 0.004"
TC 0.006"
1.00
TC 0.010"
TC 0.013"
D  Loss
0.80
0.60
0.40
0.20
0.00
0.50
0.60
0.70
0.80
0.90
1.00
1.10
Exit Mach Num ber
Figure 3.1 -- Pressure loss trend to Mach number at varying tip clearances
It has been well documented that relationship between airfoil performance and tip
clearance is linear, except for in the event of a tip vortex breakdown. Figure 3.2 is a
representation of the same information from Figure 3.1 to show the relationship of
pressure loss to tip clearance. Note that for all of the Mach lines represented (except for
the 0.6-M2 line), the curves are NOT linear.
7
1.20
1.00
M2 1.0
M2 0.8
M2 0.6
M2 0.9
M2 0.7
D Loss
0.80
0.60
0.40
0.20
0.00
0.000
0.005
0.010
0.015
Tip Clearance (in)
Figure 3.2 -- Pressure loss trend to tip clearance at vary exit Mach numbers.
Along the 0.7, 0.8, 0.9, & 1.0 Mach lines, the vortex breakdown is predicted with
the same tip clearances (0.004” & 0.006”), where it does not occur for tip clearances of
0.010” and above (limited to excessive values). These simulations were also run to an
exit Mach number of 1.2. Tip vortex breakdown was predicted for all those simulations;
however, the CFD also predicted that the airfoil stalls, so those simulations will not be
considered for testing.
Open Pitch Results. During the course of the initial study, while it was difficult to
achieve vortex breakdown, several of the boundary conditions were run for increased
pitch simulations. The pitch was increased by 14%, simulating a single airfoil removed
from the original cascade pack and remaining airfoils being redistributed in the same
space. A reduced, modified matrix was run on these open pitch simulations to achieve
vortex breakdown. Figures 3.3 & 3.4 are the performance trends of the open pitch
simulations.
8
1.60
1.40
TC 0.006"
TC 0.010"
TC 0.013"
TC 0.016"
D  Loss
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.50
0.60
0.70
0.80
0.90
1.00
1.10
Exit Mach Num ber
Figure 3.3 -- Pressure loss trend to tip clearance at vary exit Mach numbers.
1.60
1.40
M2 1.0
M2 0.8
M2 0.9
M2 0.6
D  Loss
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.000
0.005
0.010
0.015
0.020
Tip Clearance (in)
Figure 3.4 -- Pressure loss trend to tip clearance at vary exit Mach numbers.
Similar to the design pitch results, vortex breakdown was achieved with a tip gap of
0.006” at exit Mach numbers of 0.8, 0.9, and 1.0.
Grid Sensitivity Study. Vortex breakdown was achieved for the base airfoil
design conditions with 0.004” & 0.006” tip clearance. To confirm these predictions, the
entire 0.8 exit Mach number line (shown in Figure 3.2) was put through a grid sensitivity
study. The amount of grid used as a standard for the computational domain is 798,111
cells total (using the O-H mesh topology shown in Figure 3.5).
9
(a)
(b)
Figure 3.5 -- Grid topology for CFD domain: (a) Top-down View, (b) Side View.
It is a full span simulation of the airfoil with 57 grid points on the each side of the airfoil
surface, 81 grid points across the pitch, and 65 radial grid points (49 points in core, 16 in
the tip gap). The grid was then reduced to 435,167 total cells (57 points on the airfoil,
33 radial points in the core), and increased to 1,996,535 (115 grid points across the pitch,
81 radial points in the core, 32 points in the tip gap).
Recall, it was stated that, in the absence of tip vortex break, the relationship of
performance is linear. Figure 3.6 below are the results of the initial grid study for exit
Mach number of 0.8 for the design pitch:
1.00
0.90
Coarse
Standard
0.80
Dense
D  Loss
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
Tip Clearance (in)
Figure 3.6 -- Pressure loss trend to tip clearance for various grid densities.
10
For both the dense and coarse grid lines, the relationship of loss to tip clearance is
linear; and indeed, the conditions were breakdown is predicted for the standard grid, it
was NOT predicted for the others. Also note that, for the conditions where breakdown is
NOT predicted (10 mil and 13 mil tip clearance), the losses are very similar between the
standard and the dense grid (suggesting grid independence for those conditions). It is
also very apparent that the coarse grid is insufficient for this study, with the CFD
predicting a less conservative performance of the cascade with tip clearance across the
exit Mach line.
11
4. Future Work & Conclusions
Due to the surprising results of the grid sensitivity study, further simulations will
need to be run to achieve vortex breakdown. In a previously unpublished study, when
tip vortex breakdown was predicted with the standard grid, it was also predicted with the
dense grid. However, the aforementioned study was conducted with turbine airfoil
geometry modeled in a rotating rig environment, as opposed to a cascade environment.
At present, there have been no conditions where vortex breakdown has not been
predicted with the standard grid and predicted with the dense grid. The grid sensitivity
study has not been conducted on the open pitch simulations that have achieved vortex
breakdown, so there is still room for opportunity.
The performance sensitivity studies will be extended to vary inlet flow angle for the
newly determined primary test matrix. During the initial studies to achieve vortex burst,
it was found that inlet flow angle had a secondary effect on the whether the vortex
breaks down. The study will explore the influence of inlet flow angle on the behavior of
the tip vortex in the event of breakdown. The influence of the inlet boundary will also
be studies for the matrix of cases. Recall, the current cases are run with a 16% boundary
layer thickness, and will be reduced for boundary layer effects. These future studies will
be conducted in no particular order.
Recall, the actual computational domain extends 1.5*Bx downstream of the trailing
edge. For further analysis of the results, the spanwise pressure loss will be calculated
0.5*Bx downstream of the trailing edge of the airfoil. This result, with the aid of the
flow visualizations, will help determine where the losses are incurred within
computational domain. Loss generation plots will also be created for the simulations in
the test matrix.
In conclusion, the current progress is that we seem have an adequate method of
showing the event of vortex breakdown (as defined by the scope of the current study)
due to test measurement limitations. The fear of inducing of vortex breakdown was
considered with the presence of any sort of measurement probe in the tip vortex core.
However, with the use of the flow visualization, the predicted surface streamlines show a
distinct difference in the tip region in the event of vortex breakdown than when it does
not occur.
12
5. References
Bindon, J.P., “The Measurement and Formation of Tip Clearance Loss,” ASME
Journal of Turbomachinery, Vol. 111, 1989, pp.257-263.
Booth, T.C., Dodge, P.R., and Hepworth, H.K., “Rotor-Tip Leakage Part 1 – Basic
Methodology,” ASME Journal of Turbomachinery, Vol. 104, 1982, pp. 154-159.
Chan, J.K.K, Yaras, M.I., and Sjolander, S.A., “Interaction Between Inlet Boundary
Layer, Tip-Leakage and Secondary Flows in a Low-Speed Turbine Cascade,” ASME
Paper No. 94-GT-250.
Denton, J.D., “Loss Mechanisms in Turbomachines,” ASME Journal of
Turbomachinery, Vol.115, 1997, pp. 1-32.
Govardhan, M., Venkatrayulu, N., and Vishnubhotla, V.S., “Influence of Tip
Clearance on the Inter Blade and Exit Flow of a Turbine Rotor Cascade,” ASME Paper
No. 94-GT-359.
Hamik, M., and Willinger, R., “An Innovative Passive Tip-Leakage Control Method
for Axial Turbines: Linear Cascade Wind Tunnel Results,” ASME Paper No. GT200050056.
Mizuki, S., and Tsujita, H., “Numerical Calculation of Flow for Cascade with Tip
Clearance,” ASME Paper No. 94-GT-361.
Moore, J., and Tilton, J.S., “Tip Leakage Flow in a Linear Turbine Cascade,”
ASME Journal of Turbomachinery, Vol. 110, 1988, pp. 18-26.
Morphis, G., and Bindon, J.P., “The Effects of Relative Motion, Blade Edge Radius
and Gap Size on the Blade Tip Pressure Distribution in an Annular Turbine Cascade
with Clearance,” ASME Paper No. 88-GT-216.
13
Morphis, G., and Bindon, J.P., “The Performance of a Low Speed One and a Half
Stage Axial Turbine with Varying Rotor Tip Clearance and Tip Gap Geometry,” ASME
Paper No. 94-GT-481
Morphis, G., and Bindon, J.P., “The Flow in a Second Stage Nozzle of a Low Speed
Axial Turbine and Its Effect on Tip Clearance Loss Development,” ASME Paper No.
94-GT-145.
Schabowski, Z., and Hodson, H., “The Reduction of Over Tip Leakage Loss in
Unshrouded Axial Turbines using Winglets and Squealers,” ASME Paper No. GT200727623.
Shavalikul, A., and Camci, C., “A Comparative Analysis of Pressure Side
Extensions for Tip Leakage Control in Axial Turbines,” ASME Paper No. GT200850782.
Sjolander, S.A., and Amrud, K.K., “Effects of Tip Clearance on Blade Loading in a
Planar Cascade of Turbine Blades,” ASME Journal of Turbomachinery, Vol. 109, 1987,
pp. 237-245.
Sjolander, S.A., and Cao, D., “Measurements of the Flow in an Idealized Turbine
Tip Gap,” ASME Paper No. 94-GT-74.
Sondak, D. L., and Dorney, D. J., "Simulation of Vortex Shedding in a Turbine
Stage," ASME Journal of Turbomachinery, Vol. 121, 1999, pp. 428–435.
Tallman, J. and Lakshminarayana, B., “Numerical Simulation of Tip Leakage Flows
in Axial Flow Turbines, with Emphasis on Flow Physics – Part I: Effect of Tip
Clearance Height,” ASME Paper No. 2000-GT-0514.
14
Tallman, J. and Lakshminarayana, B., “Numerical Simulation of Tip Leakage Flows
in Axial Flow Turbines, with Emphasis on Flow Physics – Part II: Effect of Outer
Casing Relative Motion,” ASME Paper No. 2000-GT-0516.
Van Ness, D.K., Corke, T.C., and Morris, S.C., “Tip Clearance Flow Visualization
of a Turbine Blade Cascade with Active and Passive Flow Control,” ASME Paper No.
GT2008-50703.
Willinger, R. and Haselbacher, H., “On the Modeling of Tip Leakage Flow in Axial
Turbine Blade Rows,” ASME Paper No. 2000-GT-633.
Willinger, R. and Haselbacher, H., “Axial Turbine Tip-Leakage Losses at OffDesign Incidences,” ASME Paper No. GT2004-53039.
Yamamoto, A., “Endwall Flow/Loss Mechanisms in a Linear Turbine Cascade with
Blade Tip Clearance,” ASME Journal of Turbomachinery, Vol. 111, 1989, pp. 264-275.
Yaras, M.I., and Sjolander, S.A., “Effects of Simulated Rotation on Tip Leakage in
a Planar Cascade of Turbine Blades, Parts 1 and 2,” ASME Journal of Turbomachinery,
Vol. 114, 1992, pp. 652-667.
15