Turbine Inlet Non-Uniformities and Unsteady Mechanisms CHIVES MASSACHUSETTS INSTITUTE OF TECHNOLOLGY JUN 23 2015 LIBRARIES by Devon Jedamski Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2015 Massachusetts Institute of Technology 2015. All rights reserved. Signature redacted Department of Aeronautics and Astronautics Certified by. Certified by. Signature redacted May 26, 2015 Edward M. Greitzer H.N. Slater Professor of Aeronautics and Astronautics Signature redacted Thesis Supervisor .. .............. . Choon S. Tan Accepted by .... Senior Signature redacted Research Engineer Thesis Supervisor Paulo C. Lozano Associate Professor of Aeronautics and Astronautics Chair, Graduate Program Committee Author ..
Transcript
Turbine Inlet Non-Uniformities
and Unsteady Mechanisms
CHIVESMASSACHUSETTS INSTITUTE
OF TECHNOLOLGY
JUN 23 2015
LIBRARIESby
Devon Jedamski
Submitted to the Department of Aeronautics and Astronauticsin partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
Massachusetts Institute of Technology 2015. All rights reserved.
Signature redactedDepartment of Aeronautics and Astronautics
Certified by.
Certified by.
Signature redacted May 26, 2015
Edward M. GreitzerH.N. Slater Professor of Aeronautics and Astronautics
Paulo C. LozanoAssociate Professor of Aeronautics and Astronautics
Chair, Graduate Program Committee
Author
..
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Turbine Inlet Non-Uniformities
and Unsteady Mechanisms
by
Devon Jedamski
Submitted to the Department of Aeronautics and Astronauticson May 26, 2015, in partial fulfillment of the
requirements for the degree ofMaster of Science in Aeronautics and Astronautics
Abstract
The effect of axial turbine stage inlet non-uniformities are examined through twomodel problems: wake attenuation and hot streak processing. In the first, two-dimensional calculations (RANS and URANS) are used to identify the mechanismscontributing to upstream stator wake attenuation through a turbine blade row. Fora representative turbine rotor, pitch and time-averaged wake attenuation by 74%percent is demonstrated at one quarter chord downstream of the trailing edge. Nearthe pressure surface, the wake stagnation pressure increases by up to 42% above thefreestream stagnation pressure. The mechanisms identified are a localized reduction inflow-through time for wake fluid near the pressure surface, compared to the freestream,and an unsteady pressure field (Op/&t) in the rotor reference frame that increases workextraction in the freestream relative to wake fluid. For the second model problem,three-dimensional calculations (RANS and URANS) identify a difference in turbineefficiency sensitivity to thermal distortion between a geometry with no tip gap anda geometry with a finite tip gap. The turbine with a tip clearance is 2.5 times lesssensitive, in terms of efficiency decrease, to an inlet hot streak. For the tip gap andno tip gap geometries, the efficiency drops by 0.75% and 1.86% respectively for apeak temperature non-uniformity equal to 0.6 times the combustor temperature rise.The difference in efficiency decrease, due to hot streak, between the two geometries islinked to a reduction in tip leakage mixing losses caused by changes in relative rotorinlet flow angle with and without hot streak.
Thesis Supervisor: Edward M. GreitzerTitle: H.N. Slater Professor of Aeronautics and Astronautics
Thesis Supervisor: Choon S. TanTitle: Senior Research Engineer
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Acknowledgments
"Trust in the Lord with all your heart, and lean not on your own understanding. In
all your ways acknowledge Him, and He shall direct your paths."
- Proverbs 3:5-6
The following research was conducted with the generous support of the Rolls-
Royce Whittle Fellowship. The work represents a close collaboration between the
MIT Gas Turbine Laboratory and the Turbine Aerodynamics group at Rolls-Royce
Corporation in Indianapolis.
This work could not have been possible without the support and guidance of
my advisors, Professor Greitzer and Dr. Choon Tan. I would also like to thank
Arthur Huang, a previous Rolls-Royce Whittle Fellow, for his direction and insightful
feedback throughout my first year at MIT.
The engineers of the Rolls-Royce Turbine Aerodynamics group have been an im-
mense help. In particular, Jon Ebacher, Eugene Clemens, Ed Turner, Chong Cha,
and Steve Mazur provided assistance throughout the entirety of this thesis that was
invaluable to its completion. Steve Mazur laid the framework for the beginning of
my research and was always willing to assist with valuable discussions and direction.
In addition, Tyler Gillen and the members of the Rolls-Royce Methods group, Todd
Simons, Kurt Weber, and Moujin Zhang were always willing to help in implementing
HYDRA for my research.
To Mom and Dad, I would not be here today without your love, support, and sac-
rifice. I would also like to thank Derek and Katie. You are the best siblings I could
have asked for; never let me forget to stay humble. Finally, and most importantly, I
would like to thank my wife, Christiana, who has been my biggest supporter through-
out graduate school. You are kind, loving, and most importantly, you've taught me
to find joy in all seasons.
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Contents
1 Introduction
1.1 Background . . . . . . . . . .
1.1.1 Wake Attenuation . . .
1.1.2 Hot Streak Processing
1.2 Research Questions . . . . . .
1.3 Methodology . . . . . . . . .
1.3.1 Wake Attenuation. . .
1.3.2 Hot Streak Processing
1.4 Contributions . . . . . . . . .
1.5 Organization of Thesis . . .
2 Wake Kinematics: Kelvin's Theorem and
2.1 Introduction . . . . . . . . . . . . . . . .
2.2 Background . . . . . . . . . . . . . . . .
2.3 Kelvin's Theorem . . . . . . . . . . . . .
2.4 Computational Methodology . . . . . . .
2.4.1 Blade Design Specification . . . .
2.4.2 Boundary Conditions and Mesh .
2.5 R esults. . . . . . . . . . . . . . . . . . .
2.5.1 Wake Attenuation Metric . . . .
2.5.2 Attenuation Quantification
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Wake
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25
27
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30
31
31
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32
Convection
32
3 Assessing Wake Attenuation in a Turbine Blade Row 37
S Entropy production within a control volume (= f a dV)
15
t
T
T
TG
U
U
V
AV
W
(x, r, 0)
(x, y, z)
y +
Ratio of specific heats
Circulation (f w dA)
Wake thickness
Difference or change
Wake strength (1 - umax/Umin)
Isentropic efficiency
Dynamic viscosity
Loss coefficient
Density
Work coefficient (Aht/U 2 )
Flow coefficient (UX/U)
Radian frequency (27f)
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Time
(1) Blade passing time
(2) Static temperature
(3) Time of periodicity
Stagnation (or "total") temperature (T + U 2/2 c,)
Tip gap
Velocity magnitude
Velocity components in cartesian coordinates
Blade translational speed
Volume
Wake velocity defect
Pitch
Polar coordinates
Cartesian coordinates
Non-dimensional wall cell distance
Symbols
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/1
p
pI
Vorticity
Blade rotational speed
Subscripts
fs
main
max
min
irr
1
S
t
th
tip
V
w
(x, y, z)
0
0, 1, 2, etc.
Free stream average
Quantity representative of mainstream
Maximum value
Minimum value
Denotes an irreversible process
Denotes quantity due to laminar process
Denotes process at constant entropy
(1) Stagnation quantities
(2) Denotes quantity due to turbulent process
Thermal component
Quantity representative of tip-gap
Viscous component
Wake average
Components in x, y, z directions
Reference station
Station numbers
Superscripts
( )'- (e.g. ft)
aa
A
M
wa
Perturbation quantity
Mean or background flow variable
Availability average
Area average
Mass average
Work average
17
w
Q
Mixed out averageX
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Chapter 1
Introduction
Inlet non-uniformities to a turbine stage have the potential to either increase or
decrease stage performance. This thesis examines two model problems in the context
of inlet non-uniformity processing. The first is wake attenuation in a turbine blade
row. The second is the effect of a hot streak on turbine stage performance and the
aerodynamic mechanisms that influence stage efficiency sensitivity to hot streak.
In an axial compressor, there is consensus that wake fluid receives more work
than freestream fluid due to a longer flow-through time for wake particles. The
unsteady, reversible work transfer to the wake decreases wake mixing losses and thus
increases component efficiency. Various descriptions of the phenomenon and of the
mechanism have appeared in the literature 18, 17, 18]. In contrast, there is not
consensus concerning the different amounts of work extracted from the freestream
and wake fluid that pass through a turbine blade row. This thesis addresses that
issue.
There has been exploration of hot streak migration in the context of blade cooling
and thermal loads [16, 11]. Flow structures such as the "positive jet" induce circum-
ferential migration of the hot streak and increase the heat load on the pressure surface
of the first stage rotor 110]. The swirling flow in the rotor can create a radial pres-
sure gradient leading to radial migration of the hot streak toward the rotor tip [11].
Questions still remain however, regarding the effect of hot streak on stage efficiency.
Addressing this issue is the objective of this thesis.
19
The thesis does the following:
" Identifies two mechanisms for wake attenuation: a pitchwise variation in flow-
through time of the wake particles compared to the freestream and an unsteady
pressure in the relative coordinate system that increases local freestream work
extraction.
" Relates wake deformation to downstream wake stagnation pressure 18] to quan-
tify the effect of the first mechanism.
" Identifies and explains the relationship between turbine efficiency sensitivity to
inlet hot streak magnitude and turbine tip leakage flow.
" Examines and compares existing efficiency definitions and presents a suggested
efficiency metric for flows with hot streaks and large thermal dissipation.
1.1 Background
1.1.1 Wake Attenuation
Viscous mixing of upstream wakes represents a substantial portion of losses in tur-
bomachinery. Hall et al. report wake mixing losses representing 20% and 13% of the
profile loss for a baseline compressor and uncooled turbine stage respectively, at peak
efficiency conditions [5]. For a steady flow at uniform pressure, wake attenuation is
achieved by an irreversible mixing process. When the decrease in wake depth occurs
reversibly, without mixing, it is referred to as reversible attenuation or wake recovery.
Irreversible wake mixing losses may be reduced by reversible attenuation of the wake
downstream of the blade row before full mixing of the wake occurs, as shown in [17].
For steady flow, attenuation of the velocity defect has been shown by Denton 13] to
be produced by favorable pressure gradients in a contraction. Attenuation of a stag-
nation pressure defect by unsteady mechanisms is described by Greitzer et al. 141 and
Smith [17]. The focus of the this thesis is reversible wake attenuation by unsteady
mechanisms and differential work transfer.
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Reversible attenuation results in reduced mixing losses and improved component
performance. Figure 1-1 shows rotor wake depth plotted versus distance through
the compressor stator at a peak pressure rise condition [201. The "viscous" only
curve indicates viscous mixing (irreversible attenuation) at uniform pressure. The
two lines labeled "stretching only" and "viscous + stretching" represent reversible
wake attenuation alone and reversible and irreversible wake attenuation combined.
Laser anemometer measurements are shown by the crosses. The curve including
both viscous and reversible attenuation has a smaller viscous component than the
"viscous only" line, because the smaller viscous mixing is reduced by the reversible
wake attenuation.
Figure 1-1 illustrates the means by which a compressor wake may be attenuated.
Initially the wake fluid has a lower stagnation pressure than the freestream. If the
wake fluid receives more work than the freestream as it travels through the passage,
the stagnation pressure defect decreases. Similarly, for a turbine, if less work were
extracted from the wake fluid than the freestream fluid, the wake defect would be
decreased.
vlscous only NS
Si hs n -stretching only
0.2 -viscous+stretchingW
0 20 40 so so 100 2io
% Stator Axial Chard
Figure 1-1: Compressor rotor wake evolution through a stator passage at peak pres-sure rise condition; lines present analysis, symbols present data [201.
Smith has explained this effect using Kelvin's theorem' [17] for an inviscid wake.
'Kelvin's theorem states that for an inviscid and barotropic flow with conservative body forces,the circulation around a fluid contour is constant in time.
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This analysis captures the effect well for a compressor, and Van Zante et al. iden-
tify it as the dominant mechanism in reversible wake attenuation [20]. As a wake
segment passes through a blade row, the wake segment changes through end-to-end
stretching of the wake segments. If we assume the wake segments remains linear and
are uniformly stretched, Kelvin's theorem implies that stretching of the wake along
the centerline direction means a consequent decrease in the wake velocity defect and
thus the mixing losses. This is seen in Figure 1-2 where segment AB is stretched so
that CD > AB as it passes through the compressor rotor.
Fixed Incoming Wake
B
\U
\ C
D 'Moving Rotor Fixed "Avenue"Streamlines\ Along Which
Wakes Proceed
Figure 1-2: Chopping and stretching of an incoming wake [181
1.1.2 Hot Streak Processing
Hot streak processing in high pressure turbines is an active research area and a sum-
mary of the findings and related fluid mechanics are presented below.
A hot streak is defined, for purposes of this thesis, as a temperature non-uniformity
at the combustor-turbine interface caused by discrete fuel injectors in the combustor.
It has been observed that there is a decrease in stage efficiency in high pressure
turbines when subjected to a hot streak, but at the present the cause is still not clear.
Several mechanisms for migration of turbine hot streaks have been presented.
These include radial migration of the hot streak, baroclinic torque, inlet swirl, and tip
flow ingestion [16, 111. Circumferential migration mechanisms include what is known
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as the segregation effect or the Kerrebrock-Mikolajczak effect [101, which has been
used to explain the increased heat load seen on the pressure surface. The increased
heat load at the tip has been ascribed to radial migration, however, the link with
aerodynamic performance is not yet clear. The dominant effect isolated in this thesis
is the relative flow angle variation and subsequent blade loading imposed by the hot
streak at the rotor.
1.2 Research Questions
The aim of this work is to quantify the impact of turbine inlet non-uniformities
on stage performance. The specific topics are stagnation pressure defects from up-
stream stator wakes and stagnation temperature non-uniformities from combustor
hot streaks. The research questions are:
e Are stator wakes attenuated through a turbine rotor row?
e How does wake evolution differ between turbine and compressor blade rows?
e How does a hot streak at the combustor-turbine interface change the high pres-
sure turbine stage efficiency with and without the presence of a tip gap?
9 Are mixing plane calculations sufficient to predict the variation in stage effi-
ciency with inlet hot streak strength?
1.3 Methodology
1.3.1 Wake Attenuation
To answer the first two research questions, two types of two-dimensional calculations
have been used. The first utilizes RANS CFD for an isolated rotor to illustrate
the convection of tracer particles, a surrogate for the vorticity in the wake which is
convected by a background steady flow. The second is an unsteady simulation of a
moving blade row with a stagnation pressure non-uniformity at the inlet. This set of
23
calculations captures the same effect, but at a higher fidelity, to give insight into the
mechanisms of reversible wake attenuation.
Results from the steady calculations show reversible attenuation is possible, de-
spite compression of the wake segment, and quantify the magnitude for a represen-
tative turbine geometry. A reversible attenuation of 46% is found from the steady
background flow calculations. The unsteady calculations show reversible wake at-
tenuation of 74% one quarter chord downstream of the trailing edge for the same
geometry.
1.3.2 Hot Streak Processing
To answer the third and fourth research questions, we have analyzed two geometries
to determine the dependence of turbine efficiency sensitivity to hot streaks for a
stage with a tip clearance and a stage without tip gap. Both RANS and URANS
calculations for a vane-rotor first stage high pressure turbine geometry were used to
characterize the sensitivity of the stage efficiency to hot streaks for the two geometries.
A comparison of efficiency definitions is also presented to show the importance
of selecting a proper efficiency metric. Viscous dissipation in the rotor is used to
quantify loss sources and highlight tip leakage flow mixing as a dominant effect in
setting stage efficiency sensitivity to inlet hot streak.
1.4 Contributions
The contributions of this thesis are:
9 It is shown that there can be reversible wake attenuation in a turbine. The
process is different than for a compressor because, velocity gradients normal
to the wake orientation deform the wake. An inviscid attenuation of 74% has
been demonstrated for a representative geometry. It is also shown that the
wake can increase in stagnation pressure relative to the freestream near the
pressure surface if the wake is turned such that the velocity defect vector points
24
downstream.
" Wake segments in a turbine are not purely stretched or compressed as can
be approximated for a compressor. Bowing and turning of the segments can
reorient the velocity defect from pointing upstream to downstream, decreasing
or increasing the wake flow-through time compared to the freestream. The
unsteady pressure field in the relative coordinate system can also provide work
extraction from the wake relative to the freestream in the passage.
" The calculated efficiency sensitivity to inlet hot streak for a rotor with a tip
clearance is similar for steady CFD with a mixing plane and unsteady CFD
with phase-lag boundary conditions.
" For the turbine geometry examined, a turbine rotor with a 2% clearance is
roughly twice as sensitive to hot streaks than the same rotor with no tip gap.
The difference in hot streak sensitivity is attributed to a reduction in tip leakage
mass flow and thus tip leakage mixing losses, compared to the rotor operating
without a hot streak.
" A turbine performance efficiency definition is proposed for evaluating turbine
efficiency sensitivity to hot streaks. The efficiency definition utilizes a work-
averaged inlet condition and mixed-out exit condition to conserve enthalpy flux
and work output between the original three-dimensional unsteady flow field and
the averages.
1.5 Organization of Thesis
The remainder of this thesis is separated into two primary sections to address the
preceding research questions; Chapters 2 through 4 address wake attenuation and
Chapters 5 and 6 address hot streak processing. Chapter 2 describes a model used
to highlight the change in wake flow-through time relative to freestream. Chapter
3 shows, with unsteady CFD, that reversible attenuation is possible by two inviscid
25
mechanisms. Chapter 4 shows where each mechanism contributes to wake attenua-
tion. Chapter 5 describes the approach and design of computations for the hot streak
research questions. Chapter 6 evaluates the effect of inlet hot streak on the turbine
stage and highlights tip leakage flow as the cause of the difference in stage perfor-
mance sensitivity to inlet hot streak for the two geometries. Finally, Chapter 7 gives
a summary, conclusions, and recommendations for future work.
26
Chapter 2
Wake Kinematics: Kelvin's Theorem
and Wake Convection
2.1 Introduction
In this chapter, wake convection by a steady background flow is used as a qualitative
tool to interpret wake attenuation and the differences between turbine and compressor
wake evolution. We extend work by Joslyn, Caspar, and Dring f8J to determination of
the downstream stagnation pressure distribution in the wake, using Kelvin's theorem
and the wake geometry. The results show a reversible attenuation of the wake by 46%
which is associated with the first of two mechanisms to be described.
The analysis in this chapter is based on thin wakes with small velocity defect which
are convected by a steady background flow. In contrast to previous approximations
of the wake as a single linear segment, we use a distribution of infinitesimal control
volumes along the wake to calculate the distribution of wake quantities downstream
of the turbine. The analysis is useful to explain results in subsequent chapters and
to identify the importance of wake segment turning in the wake attenuation process.
27
2.2 Background
For a compressor blade row, a streamtube expands as it passes through the row. If
we approximate the wake as a linear segment with uniform velocity defect, Kelvin's
theorem can be stated as in Equation 2.1 where L denotes the segment length and AV
denotes the wake velocity defect. In a compressor, wake stretching typically occurs
because of both streamtube expansion and blade circulation, leading to end-to-end
stretching of the wake, described as
=o A <1 (2.1)LcO A V
where 0 denotes a station far upstream, and oc denotes far downstream, of the rotor.
Figure 2-1 presents tracer particles convected by an inviscid, steady background
flow in a compressor. Upstream wake segments are absolute streamlines and each
line segment represents a snapshot of the wake as it convects through the blade
passages. Figure 2-1 illustrates wake segment stretching through the turbine blade
row as described in Equation 2.1.
Suppose now that we apply these arguments to a turbine blade row. Assuming
the wake remains straight with uniform stretching as before, we would conclude that
the wake segment is compressed, the wake defect is amplified, and that wake mixing
losses are increased. Figure 2-2 however shows that this viewpoint is too naive; the
wake segment end-to-end length decreases through the turbine blade row, but the
arc length of the wake segment increases. The explanation for wake attenuation in
a compressor thus cannot be directly extended to turbine blade rows because the
assumptions are not valid.
2.3 Kelvin's Theorem
Kelvin's theorem states that the circulation, F, of a material contour remains constant
in time for an inviscid, barotropic flow with conservative body forces. The circulation
around a closed material contour, N, is defined as
Figures 4-5 and 4-6 display the spatial dependence of the two mechanisms responsible
for reversible wake attenuation. The mechanism in Figure 4-5 (pressure fluctuations)
is primarily caused by blade loading changes from impingement of the wake on the
rotor. This is most apparent in the upstream section of the passage where wake
impingement on the suction surface occurs. A cartoon is shown in Figure 4-9 where
the wake impingement near the leading edge imposes a localized high pressure region.
The high pressure region convects downstream along the suction surface such that
fluid directly downstream of the impingement point experiences a ap/&t larger than
when the wake is not present. The wake is in front of the impingement point so less
work is extracted from the wake than the surrounding freestream fluid. Although
first identified by Meyer [131, this effect is described in-depth by Hodson and Dawes
16] for a wake in a turbine passage.
The second mechanism is variation in the axial velocity and hence in particle flow-
through time between the wake and freestream. This mechanism includes a weighting
factor of &p/&t which determines whether work extraction or addition occurs locally in
the passage. Figure 4-6 shows that this mechanism imposes attenuation upstream of
the pressure surface stagnation point and downstream of the trailing edge stagnation
point. Wake attenuation occurs in these regions due to the work addition occurring
53
- 5.0
0.0 0.5 1.0 0.0 0.5 1.0x/cX x/cX,
Figure 4-9: Description of unsteady Figure 4-10: Description of flow-throughpressure mechanism time mechanism
by p/&t and the longer residency time of wake particles in this region. Conversely,
work extraction occurs in the remainder of the passage. The weighting term, Op/Dt
causes work extraction in the main passage but, the shorter flow-through time of wake
fluid leads to a reduction in work extraction in the wake. This is shown in Figure
4-10 where the positive and negative regions denote work addition and extraction
respectively. The positive region of the wake segment, u ,g [+], denotes wake fluid
traveling faster than freestream fluid and the contrary for u', 8 [-]. These two regions
describe wake attenuation and amplification respectively in agreement with the result
shown in Figure 4-6.
54
Phigh
act~
U X +1
X " H +
Chapter 5
Effects of Hot Streaks on High
Pressure Turbine Efficiency
5.1 Introduction
In Chapters 5 and 6, we address a second subject: the effect of hot streaks on high
pressure turbine efficiency. Three topics are addressed. First, a method of time-
averaging is outlined that reduces flow time requirements by use of a finite impulse
response filter. Second, a generalized efficiency definition for unsteady non-uniform
flow is introduced. Third, the results are interrogated and show the efficiency of a
turbine with a tip clearance is 2.5 times less sensitive to inlet hot streak than the
same turbine with no tip gap.
5.2 Computational Methodology
The sensitivity of turbine efficiency to inlet hot streak magnitude is shortened herein
to hot streak sensitivity. Hot streak sensitivity is defined as 07r/(OTDF)'. It is
reported here for a given geometry with varying inlet hot streak magnitude.
To quantify hot streak sensitivity, two separate turbine configurations are ana-
'OTDF = max(T, 4 (r, 0) - Tk1)/(T/ - Ttj') where Al denotes mass average, station 3 is thecompressor-combustor interface, and station 4 is the combustor-turbine interface.
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(a) Meridional view of vane and rotor mesh (b) Rotor tip mesh
Figure 5-1: Vane and rotor surface mesh, TG-2%
lyzed: one with a finite tip gap and another without a tip gap. The first, with no tip
gap, is referred to as the 0% (TG-0%) clearance case. The second geometry has a tip
clearance of 2% of the rotor span (TG-2%). Both turbine geometries share a common
vane geometry and a common rotor geometry with a different casing endwall. Steady
calculations include vane and rotor and utilize a mixing plane at an interstage station
between them. The mixing plane circumferentially mixes the flow exiting the vane
and permits coupled steady CFD calculations of the two computational domains. The
unsteady calculations utilize a phase-lag boundary condition and are initialized from
the converged mixing-plane calculations.
All results related to hot streak processing utilize the Rolls-Royce proprietary CFD
code HYDRA, which solves the Reynolds-Averaged Navier-Stokes equations (RANS)
and unsteady RANS (URANS) equations. All geometries use a structured mesh and
the HYDRA solver utilizes an unstructured node based solver. An example of the
mesh used for the TG-2% case is shown in Figure 5-1. Both meshes used in this study
have an average y+ of 1 to resolve the boundary layers.
The Spalart-Allmaras (SA) one equation turbulence model is used and initialized
with a turbulent to laminar viscosity ratio of 100 at the inlet to account for high
levels of turbulence of the fluid exiting the combustor [1]. The hot streak sensitivity
is found to be weakly dependent on the turbulent viscosity ratio; the sensitivity
56
reduced by 11% when the viscosity ratio was lowered from 100 to 10, much smaller
than the variations caused by geometry alterations (250%). It is shown that the
change in tip leakage flow mixing with the main flow is the dominant mechanism
for turbine sensitivity reduction with hot streak strength. Huang also found that tip
leakage losses are insensitive to the inlet turbulent viscosity ratio [71, supporting the
preceding comments about turbulent viscosity ratio.
5.2.1 Turbine Geometry and Mesh Specification
The turbine simulations in this thesis utilized a mixing plane for the RANS solver and
a phase-lag boundary condition for the URANS solver to preserve full annulus blade
counts. All calculations described utilize thirty-six vanes and fifty-eight blades per
revolution. The combustor contains eighteen burners and the computational domain
includes two vanes to match the burner count, yielding a flow periodicity of one-
half revolution. A method is presented in Section 5.2.3 to reduce the computational
complexity of time-averaging efficiency and eliminate the need for the full period.
A meridional view of the turbine with the mixing plane included is shown in Figure
5-2. The black line denotes the TG-0% and red denotes TG-2%. The black vertical
line is the mixing plane and the gray lines are the vane and rotor. The rotor and vane
geometry was held constant between tip gap configurations and the casing endwall is
shifted as in Figure 5-2. No cooling flow is included and all surfaces are modeled as
adiabatic. The fluid is an ideal gas with constant specific heats, and -y = 1.3.
x
Figure 5-2: First stage meridional view comparison for TG-0% and TG-2%
57
The stage parameters associated with the turbine rotor and two cases used are
shown in Table 5.1.
Tip Clearance 0.00% 2.00%Work Coefficient 2.03 1.97Flow Coefficient 0.44 0.46Stagnation-to-Static Pressure Ratio 1.94 1.96Solidity 0.97Aspect Ratio 1.25
Table 5.1: Turbine stage parameters, OTDF = 0.0
5.2.2 Boundary Conditions
The inlet boundary condition is held constant for the simulations with the TG-0% and
TG-2% configurations for a given hot streak strength. A two-dimensional distribution
of stagnation pressure, stagnation temperature, turbulent to laminar viscosity ratio,
and flow angle is specified at the turbine inlet in the r, 0 plane. At the outlet, the
static pressure at the hub is specified and the radial distribution of static pressure
that satisfies radial equilibrium is established by the solver. All walls have no slip
boundary conditions.
The measure used for hot streak strength in this thesis is the overall tempera-
ture distribution function (OTDF). The OTDF represents the difference between the
maximum temperature and the mass average temperature, non-dimensionalized by
the temperature rise across the combustor. The radial temperature distribution func-
tion (RTDF) is a non-dimensional circumferentially averaged temperature. OTDF
and RTDF are defined in Equations 5.1 and 5.2 respectively. The superscript M
denotes a mass average quantity, station 4 is the combustor-turbine interface and
station 3 is the compressor-combustor interface.
Tt,4 (r, 0) - TA'OTDF = max ' - (5.1)
r,o 0 Lt,4 -L t,3
58
27r1 f Tt,4 (r, 0)- T^'d(RTDF - d (5.2)
270 T4 -T,3
The cases analyzed with CFD are shown in Table 5.2 denoted by x's. The
OTDF denotes the inlet boundary condition as defined in Equation 5.1. The case of
OTDF = 0.0 can be regarded as a baseline case with uniform inlet stagnation tem-
perature and is sometimes referred to as the reference state denoted by the subscript
0.
OTDFRANSURANS
Table 5.2: CFD inlet
0.0 0.2 0.4 0.6x X x xx X X
boundary conditions and solver
For this study, a single temperature profile was used, scaled about T by varying
OTDF. For all cases it was assumed that the OTDF is twice the maximum RTDF
value, a representative approximation at the combustor-turbine interface. Figure 5-3
shows the radial temperature profile with RTDF and min/max temperature distri-
butions overlaid for the OTDF = 0.6 case. The peak value of temperature occurs
at approximately mid-span and corresponds to OTDF = 0.6. The peak RTDF also
occurs at mid-span and corresponds to RTDF - 0.3.
Figure 5-4 shows the non-dimensional stagnation temperature profile at the combustor-
turbine interface over the domain of two vanes (10 degrees). This temperature profile,
scaled about Td by OTDF, is utilized for all cases in the following study.
Figure 5-5 displays the circumferential clocking2 of the hot streak at mid-span.
The hot streak impinges the leading edge and the majority of the hot streak travels
on the pressure surface to permit effective cooling. The figure also identifies the vane
to hot streak ratio as 2:1. The clocking configuration shown is used for all the cases
explored here.
The inlet stagnation pressure is taken as uniform. Heat addition may be approx-
imated as a steady frictionless flow with the changes in stagnation pressure given
2Circumferential position of hot streak relative to vane leading edge
59
I
0.8
-eQN
0z
0.6 -
0.4 -
0.21-
-0.9 -0.6 -0.3 0 0.3(T - T, 3)/(T,4 - T,3 )
0.61
-1.2 0.9
Figure 5-3: Circumferentially averaged inlet temperature distribution, OTDF = 0.6
-2.5 0 2.5Circumferential Position [deg]
Figure 5-4: Inlet temperature profile, OTDF = 0.6
by
dpt _y M2 dT
Pt 2 T)
If M 2 < 1, the stagnation pressure changes are small and pt can be approximated
as uniform. Steady CFD calculations were conducted where the hub and casing
boundary layers each extended into 40% of the flow and it was found that the hot
streak sensitivity only increased by 7%. The weak dependence combined with the
low Mach numbers in the combustor support the use of a uniform inlet stagnation
60
-/ /
RTDF-- Min and Max /
110
1
0.75
0.5
0.25
01
-eQt
P4
0
0-0.50-0.25
0.000.50
- 0 .0 00 .2 5- 0 .2 5
5
(5.3)
'
5
-0.3
Figure 5-5: OTDF contour, circumferential clocking of the hot streak
pressure.
5.2.3 Unsteady Phase Averaging
The unsteady calculations utilize phase-lag boundary conditions at the circumferential
bounds of the computational domain and retain the first seven temporal harmonics of
the solution. The flow is periodic over one-half a revolution and, due to computational
restrictions, a method to reduce the time period used in the time-averaging process
is necessary.
The isentropic efficiency for a turbine is defined as
ht, 1 - ht,2(54r/ = ,(5.4)
ht, 1 - ht,2sl
where ht,2, is the ideal exit enthalpy for an isentropic process occurring between the
inlet stagnation pressure and temperature and exit stagnation pressure of the turbine.
Station 1 is the inlet and station 2 is the exit. Figure 5-6 shows an evaluation of
Equation 5.4 in the time domain for a turbine where OTDF = 0.4. Figure 5-6 shows
61
a full revolution of the turbine with red and blue lines representing separate half
revolutions to convey the temporal convergence. The unsteady efficiency is compared
to the mixing plane efficiency (77steady) for the same turbine.
3-
2-
0-
-2-
-30 0.1 0.2 0.3 0.4 0.5
Revolutions
Figure 5-6: Instantaneous efficiency over two cycles, OTDF = 0.4
The unsteady efficiency in Figure 5-6 has a dominant mode with frequency, 18/rev,
that scales with OTDF. This oscillation is caused by unsteady chopping of the hot
streak by the blade and a subsequent oscillation in T, 2 as the hot streak exits the
computational domain. The black line in Figure 5-6 is a moving average with an
averaging period of 27r/18Q where 27r/Q is the period of revolution and Q is the
rotational frequency. The moving average removes the hot streak induced amplitude
but retains the time averaged mean. The moving average (black line in Figure 5-6)
has a low frequency oscillation (27r/4 Q) and an amplitude of 0.15%.
A power spectrum of an instantaneous evaluation of Equation 5.4 is given in Figure
5-7. The peaks describe the amplitude of the unsteady modes in Figure 5-6. Figure
5-7 shows that the dominant frequencies in the efficiency are multiples of the vane
count, the hot streak count, and at a lower magnitude, a low frequency harmonic
with four cycles per revolution.
The time averaging methodology is now described. Time averaging of quantity
62
1.5RTDF = 0.2
_RTDF = 0.1RTDF = 0.0
0.5
00 0.5 1 1.5 2 2.5 3 3.5 4
Vane Frequency 2irf /Q N,
Figure 5-7: Power spectrum of instantaneous efficiency
A (t) where A(t) is periodic over time interval T is defined as
A= lin A' (t ) dt' = A (t ) dt. (5.5 )0 0
The proposed averaging method reduces T from one half of a revolution to one sixth
of a revolution. As shown in Figure 5-6 the quantity is filtered with a moving average
over period 27r/18 Q , the hot streak period. The resulting moving averaged efficiency
has an amplitude of 0.15% over a periodicity of 2 7r/4 Q. Finally, a sinusoidal regres-
sion of the moving averaged efficiency yields the time-averaged value of the original
quantity.
5.3 Generalized Efficiency Definition for Unsteady
Non-Uniform Flows
At a snapshot in an unsteady flow, enthalpy is not conserved between the inlet and
exit; there are changes in energy (unsteady energy equation has dE/dt) within the
control volume. Over time period, T, the unsteady term time averages to zero and
63
the power and ideal power can be expressed as a function of the inlet and exit fluxes.
The time averaged power extracted by the turbine over the period is defined by
Equation 5.6.
Power = (Th T M - T2 rM) dt (5.6)
If the exit pressure is approximately constant, the ideal power can be defined by
an isentropic expansion from the inlet stagnation temperature and pressure to the exit
stagnation pressure. This is shown in Equation 5.7 where wa denotes work averaging
and X denotes mixed out averaging.
Cp T M T ( X
Ideal Power T T, 1 t,2 dt (5.7)
Work average stagnation pressure, pfa, has been presented by Cumptsy and Hor-
lock [2] who defined it as
p a [ f A (T _ d. (5.8)
The work averaged stagnation pressure conserves work output across the stage
between the non-uniform flow and the average. The mixed out average represents
the state of the flow after fully mixing out to a uniform state in a constant area,
adiabatic, and frictionless duct.
The time averaged efficiency definition based on Equations 5.6 and 5.7 is then the
power divided by the ideal power.
f T rh TAI TMr,) dt(59
-1 2 T dt1h T wa dt
The two conclusions from Equation 5.9 are the use of the work average and the
mixed out average in the stagnation pressure ratio. The definition in this equation is
64
referred to as the mixed-work efficiency. The definition is essentially a work-averaged
efficiency with the exit state defined as a mixed out condition so that exit length of the
domain is removed from the sensitivity, i.e. the turbine is penalized for downstream
mixing.
5.4 Effect of Tip Gap and Hot Streak on Efficiency
The drop in efficiency of a turbine when subjected to a hot streak is quantified by
rq(OTDF) - 7, where q, is the efficiency with uniform inlet stagnation temperature
(OTDF = 0.0). Figure 5-8, which utilizes the efficiency definition in Equation 5.9,
shows a comparison of the efficiency for all the cases listed in Table 5.2. The y-axis
represents the change in efficiency from the value at OTDF = 0.0. In the range of
OTDF = 0.2 to OTDF = 0.6, the turbine with no tip gap is 2.5 times more sensitive
to inlet hot streak strength and decreases by approximately 3% per OTDF.
We now examine the different loss generation terms and their scaling with OTDF
and tip gap. Tip gap loss (also referred to as Gap in Figure 6-7) in this context is
defined as the entropy generation that occurs within the tip gap. The tip leakage flow
mixing loss is defined as the loss incurred by mixing of the tip leakage flow with the
mainstream flow.
Figure 6-7 from Huang I7] presents a decomposition of the entropy generation
terms for a similar turbine design with tip gaps of 0% and 2%. In Figure 6-7 the
y-axis, , is defined as
Tt,2 As( = ' ,(6.15)Aht
a non-dimensional loss metric. The rotor geometry in this thesis and Huang's is the
same from 0% to 50%. Figure 6-7 indicates the order of magnitude of the different
loss components for a similar turbine. The primary differences between the two
77
I
0.7
0.75
0.5
OTDF =0.0- - OTDF= 0.6
0.250 0.2 0.4 0.6 0.8 1
X/cX
Figure 6-5: Pressure contour at 95% span, TG-2%
geometries in Figure 6-7 is the existence of a tip gap loss and a more importantly,
a loss associated with the tip leakage flow mixing with the mainstream in the upper
half of the span. The latter effect accounts for the majority of the difference seen in
the total viscous loss.
Figure 6-8 shows the scaling of losses within the tip gap with respect to OTDF
for the TG-2% geometry defined in this thesis. Figure 6-8 shows that losses in the
tip gap reduce by 11.5% at an OTDF of 0.6, a result of the 10.5% reduction in tip
mass flow in Figure 6-6. More importantly, Figure 6-7, shows that the contribution
of tip gap losses is small compared to mixing losses in the upper half span. In the
TG-2% configuration, tip gap losses contribute just 12% of the overall loss. Our focus
is thus on the tip flow leakage mixing loss which represents a larger influence on stage
efficiency and hot streak sensitivity.
Denton describes a control volume model for mixing out of tip leakage flow in a
mainstream flow [3] which is applicable when pressure gradients in the mainstream are
small. A scaling conclusion from the control volume analysis is that the mixing losses
scale with the non-dimensionalized mass flow rate of the tip leakage flow, ritip/rmain.
As shown in Figure 6-7, the difference in entropy generation between TG-0% and
78
5.4
5.2-
5 --
4.8
4.60 0.2 0.4 0.6
OTDF
Figure 6-6: Tip leakage mass flow rate reduction with OTDF
TG-2% is attributed to losses imposed by the finite tip gap. We can scale the tip
leakage flow mixing losses by mhtip/mmrnain as an estimate of change in tip leakage
mixing losses. Figure 6-9 shows the variation in efficiency with OTDF using the
scaling for tip leakage flow mixing losses and the calculated tip gap losses. Figure 6-9
shows modifications to the TG-2% efficiency curve to approximate the TG-0% curve.
Correction 1 denotes the removal of the tip leakage mixing loss calculated using the
Denton scaling argument. Correction 2 denotes the removal of both the tip leakage
mixing loss and the calculated tip gap losses. Figure 6-9 confirms the hypothesis that
losses in the tip gap have a small contribution. The tip gap losses and tip leakage
mixing losses captures 82% of the hot streak sensitivity difference seen between the
two geometries, a 205% increase in hot streak sensitivity from TG-2% to TG-0%.
6.3.5 Efficiency Sensitivity to Inlet Hot Streak
The hot streak sensitivity is different for the two turbine geometries due to different
amounts of viscous entropy production in the two geometries, but the efficiency is
also non-linearly related to entropy generation and thus the hot streak sensitivity
79
0.12
0.1
0.08
4 0.06 00% clearance
M2% clearance0.04 --
0.02
0Total Viscous Gap Blade + Hub Lower Half Upper Half
Loss Freestream Freestream
Figure 6-7: Turbine stage loss components
varies with the reference efficiency, r, of the turbine. The efficiency is defined as a
function of non-dimensional entropy generation, T, 2 S/rhAht, in Equation 6.16. We
wish to quantify the sensitivity of rT to entropy production at different values of S
and describe how the efficiency will change with an additional loss source, A5..
1r7' 1 (6.16)
1+ Tt,2 svh Aht
If we assume that the viscous loss scaling is independent of tip clearance, we
can determine a relationship between the efficiency and the entropy generation when
OTDF = 0.0. In other words, we can view the inlet hot streak as a perturbation
from the baseline flow field and quantify the stage sensitivity for perturbations with
both TG-0% and TG-2%. Equation 6.17 decomposes the entropy generation into an
So term that represents the entropy generation for a given geometry at OTDF = 0.0
and a perturbation in viscous mixing losses due to by the inlet hot streak, Alc.
= (6.17)1 + S0 +ASv
Tv Aht
Taking the first derivative with respect to Al5, evaluated at OTDF = 0.0, we find
80
U
-5
-10
-150 0.2 0.4 0.6
OTDF
Figure 6-8: Entropy generation in the tip gap, TG-2%
1c- 2.(6.18)
d (A,) OTDF=O ( O 1)m
T4Aht
Equation 6.18 states that the sensitivity of turbine efficiency to a loss perturbation
scales with 1/502, so a turbine stage with a higher efficiency is more sensitive to
increases in viscous dissipation than a stage with a lower efficiency.
Figure 6-10 shows a curve of efficiency, ij, versus non-dimensional entropy gen-
eration, T, 2 S/rhAht, based on Equation 6.16. The two curves include the linear
assumption for high efficiency turbines and the efficiency definition in Equation 6.16.
The slope of the curve in Figure 6-10 shows the change in efficiency for a given change
in entropy generation. Figure 6-10 shows that a more efficient stage will change effi-
ciency more than an inefficient stage.
For the two turbines in this study, the difference in ro and thus efficiency sensitivity
to perturbations in viscous dissipation accounts for 15% of the difference in hot streak
sensitivity between TG-0% and TG-2%. This effect is relatively small and thus the
reduction in tip leakage mixing losses associated with blade loading is identified as
the dominant mechanism.
81
N ~.
-- TG-O%TG-2%
- - - TG-2% Correction 1- - - TG-2% Correction 2
0.2
N'NN N''NNN.N
N NNN N
NN
0.4 0.6OTDF
Figure 6-9: Efficiency with control volume model correction
100
90
80
70
60
500 0.25 0.5
-T, 2 S/IT Ah0.75 1
Figure 6-10: Efficiency sensitivity to entropy production
82
0
-0.5
-1
1.5
-20
1/(1 + T, 2 $/Aht)- - 1-T, 2 S/Ah .
-4
Chapter 7
Summary, Conclusions, and
Recommendations for Future Work
7.1 Summary and Conclusions
Turbine stage performance dependence on inlet non-uniformities has been assessed
through two model problems, upstream wake attenuation and hot streak effects on
turbine efficiency. A combination of two-dimensional and three-dimensional, RANS
and URANS, calculations have been used.
7.1.1 Reversible Wake Attenuation
" An upstream wake was represented as vorticity convected by a steady back-
ground flow. The geometric distortion of the wake, Kelvin's theorem, and a ID
distribution of infinitesimal control volumes along the wake was used to esti-
mate the evolution of wake velocity defect in the turbine passage. Reversible
wake attenuation of the 46% was seen.
" The process of wake attenuation in a turbine is different than for a compressor
because, velocity gradients normal to the wake orientation deform the wake,
i.e. wake segments do not remain straight. An inviscid attenuation of 74% was
demonstrated for a representative geometry with unsteady CFD. It was also
83
shown that the wake can increase in stagnation pressure above the freestream
near the pressure surface if the wake is turned such that the velocity defect
vector points downstream.
e Two-dimensional unsteady calculations identify two wake attenuation mecha-
nisms. Bowing and turning of the segments can reorient the velocity defect
from pointing upstream to downstream, decreasing or increasing the wake flow-
through time compared to freestream. Wake segments in a turbine are not
purely stretched or compressed as can be approximated for a compressor. The
unsteady pressure field in the relative coordinate system can also provide work
extraction from the wake relative to the freestream in the passage.
7.1.2 Effects of Hot Streaks on Turbine Stage Efficiency
* Steady three-dimensional RANS calculations have shown that blade loading
near the tip and thus tip leakage flow rate, are the primary cause for different
hot streak sensitivity between a turbine geometry with a finite tip gap and one
with no tip gap.
" A numerical example is used to convey the importance of efficiency definition
for both steady and unsteady CFD with non-uniform inlets.
" The calculated efficiency sensitivity to inlet hot streak for a rotor with a tip
clearance is similar for steady CFD with a mixing plane and unsteady CFD
case with phase-lag boundary conditions.
* For the turbine geometry examined, a turbine rotor with a 2% clearance is
roughly twice as sensitive to hot streaks than the same rotor with no tip gap.
The difference in hot streak sensitivity is attributed to a reduction in tip leakage
mass flow and thus tip leakage mixing losses, compared to the rotor operating
without a hot streak.
" A turbine performance efficiency definition has been proposed for evaluating
turbine sensitivity to hot streaks. The efficiency definition utilizes a work-
84
averaged inlet conditions and mixed out exit conditions to conserve enthalpy
flux and work output between the original three-dimensional unsteady flow field
and the averages.
7.2 Recommendations for Future Work
(i) A next step in the second research problem could be to augment the blade
count to permit sliding plane unsteady calculations of a similar geometry, i.e.
to change the rotor and vane count from 58 and 36 respectively to 54 and 36.
The geometry change reduces flow periodicity from one-half a revolution to one-
eighteenth. The reduced solution time permits time averaging of flow parameters
(e.g entropy generation and inlet flow angles) and further investigation of how
well mixing-plane calculations capture the unsteady three dimensional flow field.
(ii) The effect of an asymmetric vane row may also be evaluated. A proposed
design could include two vanes, one designed for hot streak impingement and
one designed for the neighbor vane without a hot streak. The spanwise turning
angle distribution could be designed such that the turning of the hot streak
aligns the relative flow angles exiting the vane row for vane with hot streak and
its neighboring vane without a hot streak. This reduces the unsteadiness of
the flow entering the rotor and permits a single point optimization of the rotor
rather than a robust design for the periodic alternating flow angle currently seen
at the rotor inlet.
(iii) The effect of swirl and corresponding radial migration should be analyzed.
Swirling flow at the inlet may be used to cause radial migrations towards the
hub in the vain and a reduction in hot streak ingestion at the rotor tip.
(iv) Finally, the convected wake analysis in a steady flow can be augmented with
a one-dimensional momentum equation to predict unsteady pressure variations
within the wake. Currently the model assumes that the pressure in the wake
is the same as the pressure in the freestream. A one-dimensional momentum
85
equation may be included in the model which uses the velocity defect vector
variation and the freestream pressure to determine &p/&t in the wake. If the
model agrees with the unsteady calculations, the parameterization of reversible
wake attenuation can be used for design.
86
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