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Proceedings of ASME TURBO EXPO 2004:
International Gas Turbine & Aeroengine Congress & Exhibition
June 14-17, 2004, Vienna, Austria
GT2004-53370
Influence of Hot Streak Circumferential Length-Scale in Transonic Turbine Stage
L. He,
V. Menshikova
School of Engineering, University of Durham
ABSTRACT
A computational study is carried out on the influence of turbine
inlet temperature distortion (hot streak). The hot streak effects
are examined from both aeromechanical (forced blade
vibration) and aero-thermal (heat transfer) points of view.
Computations are firstly carried out for a transonic HP turbine
stage, and the steady and unsteady surface pressure results are
compared with the corresponding experimental data.
Subsequent analysis is carried out for hot-streaks with variable
circumferential wavelength, corresponding to different numbers
of combustion burners. The results show that the
circumferential wavelength of the temperature distortion can
significantly change unsteady forcing as well as the heattransfer to rotor blades. In particular, when the hot-streak
wavelength is the same as the nozzle guide vane (NGV) blade
pitch, there is a strong dependence of the preferential heating
characteristics on the relative clocking position between hotstreak and NGV blade. However, this clocking dependence is
shown to be qualitatively weakened for the cases with fewer
hot streaks with longer circumferential wavelengths.
NOMENCLATURE
C – blade axial chord
h – spanwise distance
P – pressure
T – temperature
H.S. – hot streak
Subscript:
1 – inlet
o – stagnation parameters
av – time averaged value
isen – isentropic
INTRODUCTION
Gas turbine performance is crucially influenced by the turbine
inlet temperature, which is limited by the required blade
mechanical integrity and life span. The heating of high-pressure
B. R. Haller
Demag Delaval Industrial Turbomachinery
(HP) turbine blades can lead to thermal fatigue and degrade
turbine performance. An important issue to be considered
during design is the non uniform gas temperature profile
supplied to the HP turbine inlet due to circumferential discrete
combustion burners. Non-uniform inlet temperatures (‘hotstreak’) can have effects on HP turbine aero-thermal
performance (load and efficiency), blade heat transfer and blade
aeromechanics (forced vibration/response). As such, predictive
capability and understanding of the effects of non-uniform
temperature profiles are required to maximize turbine
performance and reliability.
Basic understanding of the kinematic behavior of hot streaks
and impacts follows the work on general turbomachinery
unsteady wake transportation by Kerrebrock and Mikolajczak
[1]. It is known that the hot streak causes significant heat load
on HP turbine rotor blades, in particular rotor pressure surfaces
tend to be heated further. This so called ‘preferential heating’ is
due to an enhanced cross-passage fluid movement from the
suction surface to the pressure surface in a hot portion of gas
due to an increased incidence. This is confirmed experimentally
by Butler et al [2], and computationally by Dorney et al [3],
Krouthen and Giles [4]. A further modification of the heating
effect can result from the NGV-rotor potential interaction, and
as such the heating on rotor blades can be reduced by choice of
the NGV/rotor blade count ratio, as reported by Shang and
Epstein. [5]. Sondak et al [6] also show a considerable
dependence of the heating behaviour on the NGV/rotor blade
count.
In a turbine stage environment, the lossy fluid within a wake
shed from the upstream relatively rotating row will be
convected from the pressure surface to the suction surface
because of the velocity deficit, so called ‘negative jet’.
Similarly the cross-passage movement within a hot streak can
be regarded as a ‘positive jet’. When these two opposing
movements happen at the same time and in the same location
within blade passage, they suppress each other. As such the
lossy fluid in a wake will be less likely to be accumulated on
the suction side, and the high temperature fluid in a hot streak is
less likely to be accumulated on the pressure side. This phasing
between the two leads to the clocking dependence of the
1
Copyright © 2004 by ASME
preferential heating effects as studied by Dorney and GundyBurlet [7], Takahashi et al [8].
Apart from blade heat transfer, the effects on blade
aeromechanics (forced response) will also need to be
considered during design. The work by Manwaring et al [9]
shows clearly that a temperature distortion at the turbine inlet
can go through a multi-stage turbine and generate large
unsteady forcing and thus blade vibratory response even in the
last stage of the low-pressure turbine in a realistic aeroengine
configuration.
The present work is aimed at further examining hot streak
behaviour and effects both in terms of heat load and unsteady
forcing. The analysis is focused on a transonic turbine stage
configuration, noting that many of previous investigations on
hot streaks are for low speed configurations. A particular aspect
of interest is the circumferential wave-length of the hot streak
(‘hot-streak count’). This is particularly relevant as most of the
previous studies on the clocking (‘indexing’) effect adopt a hotstreak/NGV count ratio of 1:1. In realistic engine combustion
configurations, the number of combustors/burners tends to be
much smaller that that of the NGV blades. The aerodynamic
loss characteristics of a multi-stage turbine subject to highly
distorted inlet flow due to a partial admission are shown to be
strongly dependent on the distortion circumferential wavelength, (He [10]). Therefore, it would be of interest to clarify
the issue for situations with temperature distortions. The results
should offer some guidance on the applicability of the findings
based on an equal hot-streak/NGV count, they should also be
relevant to the design choice of number of combustors/burners
and cooling arrangement.
COMPUTATIONAL METHOD
The method used in the present study is a three-dimensional
unsteady Navier-Stokes solver for general turbomachinery flow
simulations [11]. The flow equations are solved numerically in
a cylindrical coordinate system. For the turbulence closure, the
option of the mixing length model by Baldwin and Lomax is
adopted in the present studies. Some initial test calculations are
carried out using the Spalart-Allmaras one equation model,
giving very small difference in terms of the blade surface
pressure and temperature distributions compared to those by
using the mixing-length model.
The governing equations are discretized in space using a cellcentered finite volume scheme, together with the Jameson type
blend 2nd and 4th order artificial dissipation to damp numerical
oscillations. The baseline temporal integration of the discretized
equations is carried out using the explicit four-step Runge-Kutta
scheme. The explicit time-marching scheme is subject to a
limitation on the length of time-step due to the numerical
stability requirement, and this is very restrictive on unsteady
viscous flow calculations. This difficulty can be overcome by
using the solver options of the Dual-time stepping [12] and the
time consistent multi-grid [11].
The computations are carried out in a multi-passage and multirow domain, as shown in Fig.1 for a mid-span section of a
turbine stage. The relatively moving rotor and stator meshes are
patched together at the interface. There are two options for the
interface treatment. The steady flow multiple-row solution is
obtained by using the mixing-plane technique. At each spanwise
section, the ‘mixed-out’ variables at both the rotor and stator
sides are flux-averaged. The difference in the mixed-out
variables across the interface represents a jump in
characteristics. The procedure is to drive characteristics jumps
to zero in a non-reflective manner. The second method is for
unsteady flow calculations. A 2nd order interpolation and
correction method enables local instantaneous information to be
transferred directly across the interface.
On blade/endwall surfaces, the log-law is applied to determine
the surface shear-stress and the tangential velocity is left to slip.
This slip wall condition is preferred for unsteady 3D multipassage calculations because of the relatively coarse meshes to
be used. For the present H.P. turbine case, the over-tip leakage
effect is not included. For the energy equation, the adiabatic
wall condition is applied. This means that the heat transfer
between the fluid and the surface is not included. It is
recognized that this will introduce errors in calculated surface
temperature distributions. But as the cross-passage migration
and redistribution of the temperature field associated with the
influence of hot streaks are largely determined by the
corresponding fluid kinematics, the use of the adiabatic wall
condition should not have significant bearing in the qualitative
characteristics of rotor blade heat loads caused by different hot
streak configurations considered here.
At the circumferential periodic boundaries, the direct periodic
(repeating) condition is used in the present study. This means
that the numbers of rotor and stator passages included in the
domain need to be such as to have the same total
circumferential length.
At the inlet, stagnation parameters and flow angles are
specified. The detailed inlet stagnation temperature profiles will
be described later. At the exit, the pitchwise mean static
pressure at each spanwise section is specified, and the local
upstream-running characteristic is formulated to drive the
pitchwise average pressure to the specified value, while the
local pitchwise non-uniformity is determined by the
downstream-running characteristic.
TURBINE STAGE AND UNIFORM INLET RESULTS
The test configuration used in the present study is a transonic
HP stage, MT1, which has been extensively tested for heat
transfer and aerodynamic performance at QinetiQ, as described
by Chana et al [13]. The rotation speed is 9500 RPM and the
calculated stage pressure ratio is about 2.8. The turbine stage
has 32 NGV blades and 60 rotor blades. Initial calculations are
conducted using the mixing-plane option which needs only one
NGV passage and one rotor passage. The unsteady stage
computations are carried out in a multi-passage domain. For
this case, the domain needs to contain 8 NGV blade passages
and 15 rotor blades passages to enable the direct
periodic/repeating condition to be applied at the circumferential
boundaries. A mesh density of 40x77x40 per NGV passage and
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Copyright © 2004 by ASME
40x89x40 per rotor passage is used, giving 3.12 millions grid
points for the total of 23 passages. Fig. 1 shows the stage mesh
views on a blade-to-blade section and on a meridional plane.
mixing-plane solution hits the suction surface farther upstream.
The trailing-edge overshoot of the pressure on the pressure
surface is much reduced in the unsteady result. Following a
typical flow pattern around a turbine blade trailing edge, both
these two features seem to imply that the NGV exit flow angle
predicted by the steady mixing–plane treatment would be
smaller (hence less turning) than the time-averaged one from
the unsteady solution. Overall, the comparison between the
unsteady solution and the experimental data for the NGV is
very good.
1.4
time-averaged
1.2
mixing-plane
Misen
1
experiment
0.8
0.6
0.4
a)
Blade-blade view (mid-span section)
0.2
0.32
R
0
NGV
0.3
0
Rotor
0.2
0.4
0.6
0.8
1
X/C
Fig. 2 NGV mid-span isentropic Mach number distribution
0.26
0.24
0
0.05
X
0.1
0.15
b) Meridional Section view.
Fig. 1 Computational mesh for a turbine stage
The first set of calculations is carried out at a uniform inlet
stagnation temperature of 444 K, a uniform inlet stagnation
pressure 460 kPa, and an exit static pressure 142.8 kPa. A
well-established periodic solution can be obtained in 3 beating
periods (1500 time steps for each beating period, which covers
15 rotor blade-passing periods and 8 NGV blade-passing
periods) when a multi-passage unsteady computation is started
from a single-passage steady mixing-plane solution.
Fig. 2 shows the NGV blade surface isentropic Mach number
distributions at the mid-span in comparison with the timeaveraged experimental data. The calculated results are from a
pure steady flow solver (the mixing-plane treatment), and the
time-averaged results of the unsteady simulation. The unsteady
potential interaction between the NGV and rotor should mainly
affect the region near the NGV trailing edge, and this is the area
where we can see some clear difference between the steady and
unsteady solutions. The unsteady result is closer to the
experimental data than the steady one. In particular, around
80% chord on the suction surface, the unsteady solution
produces a larger supersonic region similar to that in the
experiment, whilst the oblique trailing-edge shock from the
For the rotor, the result at the rotor mid-span section is not as
good as that for the NGV, as shown in Fig. 3. The pressures
are all normalized by the maximum surface pressure,
corresponding to the rotor stagnation pressure. The calculated
surface pressures for the most of the suction surface are higher
than the experimental data. Nevertheless, the time-averaged
unsteady calculation is closer to the experimental data than the
steady mixing-plane solution. Compared to the mixing-plane
results, the time-averaged unsteady flow field around the rotor
seems to be subject to a higher incidence, as indicated by the
pressure distribution over the frontal part of the suction surface.
This is in line with the higher turning provided by the NGV in
the unsteady calculations discussed earlier.
time-averaged
1.2
mixing-plane
1
experiment
0.8
P/Pmax
0.28
0.6
0.4
0.2
0
0
0.2
0.4
X/C
0.6
0.8
1
Fig. 3 Rotor mid-span surface static pressure distribution
The calculated unsteady pressure variations are compared with
the experimental data, as shown in Fig. 4 and Fig. 5. The
results are for the unsteady pressures at different chordwise
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Copyright © 2004 by ASME
1.2
P/Pavg
locations of the rotor blade mid-span section, normalised by the
corresponding local time-averaged values. The reference phaseangle is chosen to match the calculated phase with the
experimental value for the leading edge on the suction surface.
X/C=0.07
1
0.8
X/C=0.004
1.2
1
P/Pavg
P/Pav
1.3
0.7
X/C=0.22
1
0.8
X/C=0.16
1
0.7
P/Pavg
P/Pav
1
0.7
0.8
X/C=0.71
1.2
1
0.8
X/C=0.71
1.3
1.2
1
P/Pavg
P/Pav
1
X/C=0.51
1.3
0.7
X/C=0.89
1
0.8
0
X/C=0.88
1.3
P/Pav
X/C=0.48
1.2
P/Pavg
P/Pav
1.3
0.2
0.4
0.6
0.8
1
Time/Blade passing period
1
Fig. 5 Unsteady pressures at different chordwise positions
(PRESSURE SURFACE), __ Calculation; g Experiment.
0.7
0
0.2
0.4
0.6
0.8
1
Time/Blade passing period
Fig. 4 Unsteady pressures at different chord-wise positions
(SUCTION SURFACE), __ Calculation; g Experiment.
Note the plot for the suction surface (Fig. 4) is not in the same
scale as that for the pressure surface (Fig. 5). It is clear that
highest unsteady pressures are around the frontal part of the
suction surface. The large phase change (higher than 180°)
between the leading edge and 51% chord indicates the suction
surface pressure variation is dominated by the sweep of the
NGV trailing edge shock wave, typical of transonic turbine
stages (e.g. Miller et al[14], Denos et al [15]). The pressure side
is, on the other hand, not so directly affected by the NGV shock
wave. The unsteady pressure amplitudes change much less
along the chord, and the slight phase lead in the rear part of the
pressure surface indicates that the local flow is subject to the
upstream propagation of reflected waves. Overall, the
calculated magnitudes and relative phase angles of unsteady
pressures compare well with the experimental data.
ANALYSIS OF INLET TEMPERATURE DISTORTIONS
For the hot streak calculations, stagnation temperature profiles
are specified at inlet to the computational domain. The main
interest here is to analyse the influence of the circumferential
wave length of the hot streaks. The results for two different hot
streak configurations, 32 or 8 hot streaks are presented here.
The computational domain containing ¼ of the annulus,
therefore have 8 or 2 hot streaks as shown in Fig. 6. The
stagnation temperature profile is chosen with the same
sinusoidal radial distribution of the pitchwise-mean value as
shown in Fig. 7. At each spanwise section, the stagnation
temperature also varies in a sinusoidal fashion in the
circumferential direction, according to a given wavelength
(number of hot streaks). For all the cases calculated, the
minimum value of the stagnation temperature is taken to be
400K and the maximum is 600K. Hence the peak temperature
ratio at inlet is:
To max
To min
4
= 1.5
Copyright © 2004 by ASME
0.3
0.2
0.2
600
500
Y
Y
0.3
400
0.1
0.1
00
0.1
X
0.2
00
0.3
a) 8 hot streaks
Fig. 6.
0.1
X
0.2
0.3
b) 32 hot streaks
Inlet stagnation temperature profile
1
Pitch-average To
0.8
h/span
0.6
RTDF values, regardless of the number of hot-streaks and the
corresponding wave-length.
Rotor Surface Temperatures (32 Hot-Streaks)
The calculations firstly are conduced for 32 hot streaks,
corresponding to Fig. 6b). Note that the number of NGV blades
is also 32. The hot streak configuration with the same hot
streak-NGV blade count is widely used in previous studies in
particular with respect to the hot streak-NGV clocking effects.
It is useful to adopt this configuration first to compare the
present results with those from the previous work, before
looking at the effects of different hot streak wave lengths. For
high-speed turbines, the temperature migration due to the hot
streak can be clearly traced in terms of contours of entropy due
to its convective nature. The mid-span instantaneous entropy
contours for the case with the inlet hot streaks located at the
mid-passage of NGV blades are shown in Fig.8a. Those with
the hot streaks impinging on the NGV blade leading edge are
shown in Fig. 8b.
Uniform Inlet
0.4
H ot-S treak
0.2
0
300
400
To
500
600
E xp(-S /R )
1 .4
1 .3 3 5 7 2
1 .2 7 1 4 3
1 .2 0 7 1 5
1 .1 4 2 8 6
1 .0 7 8 5 7
1 .0 1 4 2 9
0 .9 5 0 0 0 4
0 .8 8 5 7 1 8
0 .8 2 1 4 3 2
0 .7 5 7 1 4 6
0 .6 9 2 8 6 1
0 .6 2 8 5 7 5
0 .5 6 4 2 8 9
0 .5 0 0 0 0 4
Fig. 7 Spanwise variation of pitchwise-averaged stagnation
temperature at inlet
This temperature ratio is typical of those used in previous
studies on the hot streak effects. The overall averaged value at
the inlet matches closely that for the uniform inlet case
presented earlier.
a). Hot Streak located at NGV mid-passage
It should be mentioned that combustion exit temperature
distortions are typically measured in terms of the Radial
Temperature Distribution Factor (RTDF),
H o t- S tre a k
T o pitch − T o overall
T o overall − To combustor entry
E x p ( - S /R )
1 .4
1 .3 3 5 7 2
1 .2 7 1 4 3
1 .2 0 7 1 5
1 .1 4 2 8 6
1 .0 7 8 5 7
1 .0 1 4 2 9
0 .9 5 0 0 0 4
0 .8 8 5 7 1 8
0 .8 2 1 4 3 2
0 .7 5 7 1 4 6
0 .6 9 2 8 6 1
0 .6 2 8 5 7 5
0 .5 6 4 2 8 9
0 .5 0 0 0 0 4
and the Overall Temperature Distribution Factor (OTDF),
To max − T o overall
T o overall − To combustor entry
In the present cases with different numbers of hot streaks, the
pitchwise averaged value T o pitch , the maximum value
To max , and the overall averaged value T o overall are kept the
same. Hence the two cases should have the same OTDF and
b). Hot Streak impinging at NGV leading-edge
Fig. 8 Instantaneous entropy contours at mid-span section
For a typical stator-rotor stage without inlet hot streak, high
entropy fluid of wake shed from NGV will be accumulated on
the rotor suction surface due to a pressure surface to suction
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Copyright © 2004 by ASME
surface cross-passage movement, ‘negative jet’. However, for a
case subject to a non-uniform temperature field, the opposite
happens within a hot streak due to an extra relative velocity
caused by heating. Consequently, the hot fluid with high
entropy would tend to be convected towards the pressure
surface. This so called preferential heating is clearly
identifiable by the high entropy fluid (in blue) accumulated on
the rotor pressure (Fig. 8a). The NGV mid-passage hot streak
gives the strongest preferential heating effect because the two
opposing cross-passage movements are now completely
staggered. The negative-jet convects the lossy fluid in a NGV
wake to the suction side without strongly interacting the
positive-jet which convects hot fluid towards the pressure side.
higher than that of the mid-passage hot-streak case around the
rotor leading edge at 10% span (Fig. 9a). The radially inward
migration in the NGV row by the secondary flow mechanism
should also lead to a relatively lower rotor inlet temperature at
the mid-span for the impinging hot-streak case, as shown in
Fig. 9b.
 Uniform inlet, • • Mid-passage H.S., - - Impinging H.S.
1.1
T/To
It follows then that the preferential heating should be
considerably hindered when the hot streaks are impinged on the
NGV blades. Now the hot-streaks are in phase with the NGV
wakes. The net cross-passage movement will depend on
relative strengths of the two opposing mechanisms. For the
present case, the temperature difference is quite high so that the
cross-passage movement is still determined by the positive jet.
But the preferential heating is seemingly weakened (Fig. 8b).
Unlike Fig. 8a, the hot fluid accumulation on the pressure now
is not easily identifiable. It is conceivable that the preferential
heating on the pressure side may disappear or be reversed if the
temperature difference (temperature ratio) of hot streaks
impinging on NGV blades is sufficiently small.
P. S. (10% span)
1
0.9
0.8
0.7
0.6
0
0.2
0.4
0.6
0.8 X/C 1
a). 10% span
1.1
T/To1
So far the discussions are based on a 2-D consideration. The
temperature migration behaviour is also affected by 3-D effects.
The pressure surface temperature distributions on rotor blades
at 10%, 50% and 90% span sections are shown in Fig. 9. Firstly
some comments need to be made regarding the NGV exit /
rotor inlet flow. Note the time-averaged temperature
differences around the leading-edge of the rotor blades as
shown in Fig. 9. The rotor leading-edge region should not be
affected as the rotor cross-passage movement and the
preferential heating mechanism. In terms of the pitch-averaged
value, the two inlet hot streak cases should give a higher
temperature at the mid-span than those at the tip and hub
sections, compared to the uniform inlet case (see Fig. 7). The
lead-edge temperatures for the hot-streaks located in the NGV
mid-passage follow the expected trend. For the impinging hot
streaks case, however, the temperature follows the expected
variation only at 90%span (Fig.9c). At the mid-span (Fig.9b),
the rotor leading-edge temperatures for the two hot streak cases
are noticeably different. At 10% span (Fig. 9a), the temperature
of the impinging hot streak case is even higher than that of the
uniform inlet. Thus the spanwise location of hot streaks as they
leave the NGV would depend on the NGV-hot streak clocking.
NGV blade surface temperature contours (not shown here)
indicate that when hot streaks impinge on the NGV blades, the
fluid within a hot streak is radially shifted from the mid-span
towards the hub section over the rear part of the NGV blades.
A possible explanation is that the radial pressure gradient as
required to maintain the swirl at the NGV exit would drive the
low momentum fluid in the blade boundary layer and wakes to
move inwards. Hence the hot fluid will also be convected
radially inward by the NGV secondary flow of this kind if the
hot streak impinges on the NGV blade. This should explain
why the temperature for the impinging hot streak case is much
P.S. (50% span)
1
0.9
0.8
0.7
0.6
0
0.2
0.4
0.6
0.8 X/C 1
b). 50% span
1.1
T/To1
1
P.S. ( 90% span)
0.9
0.8
0.7
0.6
0
0.2
0.4
0.6
0.8
X/C 1
c). 90% span
Fig. 9 Time-averaged temperatures at 3 spanwise
sections of rotor pressure surface (32 Hot Streaks)
6
Copyright © 2004 by ASME
To
420
410
400
390
380
370
360
350
340
330
320
310
300
290
280
Ω
S.S.
P.S.
Fig. 10 Instantaneous stagnation temperature contours
(90% chord of rotor, 32 hot streaks impinging on NGV blades ).
Regarding the flow kinematics inside the rotor passage, there is
also a strong secondary flow due to the rotor passage-vortex.
Fig. 10 shows instantaneous stagnation temperature contours at
an axial mesh plane 90% rotor chord for the impinging hot
streak clocking position. The rotor blading sections are leaned
along span, positively (pressure surface facing inward) near the
hub and negatively near the tip. This kind of compound lean
stacking is typically used to reduce the secondary flow in tip
and hub regions. For this case, there seems to be a stronger
secondary flow due to a passage-vortex in the hub region than
that near the tip. In the mid-span region, the contours show the
signature of the migration of hot fluid from the suction surface
to the pressure surface, as expected from the preferential
heating view point. They also indicate clearly the spanwise hot
streak migration towards the hub. This might to some extent be
attributed to the buoyancy effect as discussed by Shang and
Epstein [5]. However, this spanwise inward migration can
hardly be traced in the corresponding contours (not shown here)
for the case with hot streaks located at the NGV mid-passages.
Therefore the buoyancy mechanism, which should be largely
independent of the NGV clocking, is not judged to be the main
contributor to the noticeable hot streak movement towards the
hub. The rotor passage secondary flow seems to be the key.
Also shown in Fig. 10 is a close-up of one passage
superimposed with the instantaneous secondary flow velocity
vectors. A strong passage-vortex near the hub is clearly visible.
The corresponding secondary flow velocity component will
convect the mid-span hot fluid on the pressure surface towards
the hub. Furthermore, the passage vortex would actually
convect the hot fluid from the hub-pressure surface corner
towards the suction surface, as the shape of the high
temperature contours around the corner indicates.
It is also useful to note that when hot streaks impinge on the
NGV blades, they are in phase with the NGV wakes. Hence the
hot areas seen on the contour plot (Fig. 10) are also the
instantaneous signature of the NGV wakes. The cross-passage
movement due to the NGV wakes is in the same sense as that in
the hub region caused by the passage vortex. This phasing
between the NGV wake and rotor passage vortex would
enhance the cross-passage movement from the pressure surface
to the suction surface near the hub.
Overall the cases with 32 hot streaks show a strong dependence
on the clocking between the hot-streaks and the NGV blades.
The key seems to be the phasing among several fluid kinematic
features with both temporal and spatial length-scales being the
NGV blade passage. The results for unsteady surface pressures
and blade forces as presented later will also show that for this
case, the hot streaks have a relatively small influence on the
rotor passage flow in a dynamic sense.
7
Copyright © 2004 by ASME
Rotor Surface Temperatures (8 Hot-Streaks)
When the number of hot streaks is reduced to 8, the
circumferential wavelength is increased by a factor of 4. Again
two hot streak-NGV clocking positions are considered. The
case with hot streaks impinging on the NGV blades is as shown
in Fig. 6a. Similar to the 32 hot streaks case, a ‘mid-passage
hot streak’ situation is achieved by circumferentially shifting
the temperature profile by half a NGV blade pitch.
The
calculated time-averaged temperatures on the rotor blade
pressure surface at 10%, 50% and 90% span sections are shown
in Fig. 11.
The results for this long wave length case are qualitatively
different from those for 32 hot streaks. The time-averaged
surface temperatures are almost identical, showing no
dependence on the hot streak-NGV clocking position. Looking
at the unsteady temperatures in terms of the maximum and
minimum values, we also see only very small differences
between the two hot streak clocking positions (Fig. 12).
• • Mid-passage H.S.,
difference in length scales between the hot streaks and the
NGV blade passage. Basically the rotor is now subject to two
temporal disturbances, a). the aerodynamic disturbance from
the NGV, and b) the NGV modulated hot streaks. For the 32
hot streak cases, both disturbances have the same temporal and
spatial frequencies. As such the phasing between the two in
terms of the corresponding kinematics can either enhance or
reduce the cross-passage movement and migration. But for the
8 hot streak case, a phasing between two disturbances at
different frequencies no longer matters.
A further comparison is made between the 8 hot streak case and
that with 32 hot streaks for the clocking position when the hot
streak is placed at the NGV mid-passage. The time-averaged
temperatures are given in Fig 13. The maximum and minimum
unsteady temperatures are shown in Fig. 14. Because the
temperature field of a hot streak can no longer be phased with
the NGV velocity field, the 8 hot streak case shows a
noticeably reduced preferential heating effect. The timeaveraged temperature is about 5% lower than that of 32 hot
streaks for most of the pressure surface (Fig. 13).
- - Impinging H.S.
32 Hot Streaks
1
T/To1
1.1
50%span
1
10%span
0.9
8 Hot Streaks
0.9
T/To1
0.8
90%span
0.8
0.7
0.7
0
0.2
0.4
0.6
0.8
1
0.6
X/C
0
0.2
0.4
0.6
0.8
1
X/C
Fig. 11 Time-averaged temperatures at three spanwise sections
of rotor pressure surface (8 Hot-Streaks)
• • Mid-passage H.S.,
T/To1
1.2
- - Impinging H.S.
Fig. 13 Time-averaged temperatures at mid-span
section of rotor pressure surface (NGV mid-passage
hot-streaks).
Tmax
1.1
1
T/To1
Tmax (32 H.S.)
0.9
1.2
Tmin (32 H.S.)
0.8
1.1
Tmax (8 H.S.)
1
Tmin (8 H.S.)
Tmin
0.7
0.9
0.6
0
0.2
0.4
0.6
0.8
X/C
1
0.8
0.7
0.6
Fig. 12 Maximum and Minimum unsteady temperatures at
mid-span of rotor pressure surface (8 Hot-Streaks)
X/C
0
0.2
0.4
0.6
0.8
1
Fig. 14 Maximum and Minimum unsteady temperatures
at mid-span section of rotor pressure surface
(hot streaks located at NGV mid-passage)
The insensitivity of rotor surface temperatures to the hot streak
clocking for the 8 hot streak case is directly attributed to the
8
Copyright © 2004 by ASME
On the other hand, the unsteady temperature variation for the 8
hot-streak case is roughly by a factor of 3 larger than the 32 hot
streak case (Fig. 14), although both cases have the same inlet
temperature distortion magnitude (OTDF and RTDF). The
longer residence time for the long wavelength case with 8 hot
streaks generates much larger unsteady response. This
behaviour is similar to that of a rotor pressure field under an
influence of an inlet stagnation pressure distortion. It is also
noted that the maximum unsteady temperature for the 8 hot
streak case is about 8-10% higher than that with 32 hot streaks
(Fig. 14). The maximum temperature should be relevant to
blade thermal fatigue life. This marked influence of the
circumferential wavelength /number of hot streaks on the rotor
blade heat load is certainly relevant as realistic industrial gas
turbines typically have 6 or 8 combustion burners. Hence the
clocking characteristics gathered from a configuration, where
the number of hot streak is taken to be the same as that of NGV
blades, may not be applicable to situations with fewer hot
streaks.
Rotor Blade Forcing
Given that the rotor incidence changes with hot streak, the
associated unsteady loading needs to be examined for
aeromechanical design considerations.
a). Uniform Inlet
Amplitude
0.2
0.15
0.1
0.05
0
0
16
32
48
64
80
96
112 128 144
Events per Rev.
Amplitude
However, we have a very different picture for the case with 8
hot streaks. The unsteady forcing is indicated by the peak at a
frequency of 8 per revolution (Fig.15c). Now the amplitude is
about 8% (~16 % peak-to-peak) of the time-averaged
tangential force. It is also of interest to note that apart from the
two primary disturbances (the hot streak at 8 per rev and the
NGV at 32 per rev) and their higher harmonics, the subharmonics due to the cross-coupling/nonlinear interaction
between the two primary disturbances (i.e. components at
frequencies of m ωNGV ± n ωhot streak for any integers m and
n) also show up on the spectrum (e.g. the component at 24 per
rev). Nevertheless, the relatively small magnitudes of the subharmonics suggest that the unsteady flow responses are still
largely linear.
Finally, it should be commented that the calculated rotor blade
forcing shows little dependency on the hot streak/NGV
clocking for 8 hot streak cases. This is similar to the
temperatures (Fig. 11 & 12). For the case with 32 hot streaks
on the other hand, the clocking effect on the unsteady forcing is
also shown to be insignificant, simply because the magnitude of
the forcing component attributed to the hot streak with a short
wavelength is very small.
b). 32 Hot Streaks
0.2
The spectra of unsteady tangential forces on rotor blades are
shown in Fig. 15 for the cases calculated. For the case with 32
hot streaks, the frequency of the hot streaks is the same as the
NGV blade passing frequency (i.e. 32 events per revolution).
The influence of the hot streaks on unsteady forcing can thus
be qualitatively measured by comparing the force amplitudes
(Fig.15b) with that of a uniform inlet (Fig.15a). The results
show that the extra unsteady forcing contributed by the hot
streaks is very small, in a region of around 1% of the timeaveraged force. The differences in higher harmonics of the
fundamental hot streak/blade passing frequency are also
proportionally small. This is in line with the most of the
previous researches showing relatively small hot streak
influence on the rotor pressure field. The secondary flow
velocity field such as that shown in Fig. 10 indicates no
detectable difference with or without the inlet temperature
distortions. The corresponding temperature field is largely
driven passively by the passage velocity field in both NGV and
rotor rows.
0.15
0.1
0.05
0
0
16
48 64 80 96
Events per Rev.
112 128 144
0.15
0.1
0.05
0
0
16
32
48 64 80 96
Events per Rev.
CONCLUDING REMARKS
In the present work, steady and unsteady calculations for a
transonic turbine stage at an uniform inlet condition are firstly
carried out. The results are in reasonable agreement with the
experimental data for validation purposes. Further analysis with
different hot-streak circumferential length-scales reveals
significant influence on both rotor blade forcing and heat load.
c). 8 Hot Streaks
0.2
Amplitude
32
112 128 144
Fig. 15 Spectrum of tangential force amplitude on rotor blades
(normalized by time-averaged value)
When the number of hot streaks is the same as that of NGV
blades, the rotor blade heat load is strongly dependent on the
hot streak-NGV clocking, giving a maximum difference of 8%
in time-averaged temperature on the rotor pressure surface.
The unsteady pressure and force on rotor blades, however, are
largely unaffected by the hot streaks. The temperature
migration inside the rotor row is dictated by the phasing among
9
Copyright © 2004 by ASME
several cross-passage motions associated with NGV wakes
(negative jet), hot streak heating (positive jet), NGV and rotor
passage secondary flows.
For the case with 8 hot streaks, the hot-streak/NGV clocking is
shown to have very little effect on rotor surface temperature
distributions. The time-averaged temperature on the pressure
surface is around 5% lower than that for 32 hot streaks located
at the NGV mid-passage. However, the unsteady temperature
fluctuation is much larger, with the maximum temperature
being 8-10% higher than that for 32 hot streaks. Regarding
blade aeromechanics, the unsteady forcing on the rotor blades
due to the hot-streaks is at least 5 times higher than that with 32
hot streaks. The marked differences in both unsteady forcing
and surface temperature between the two cases imply that the
number of combustor/burners might be used as a design
variable for HP turbine blade aeromechanics as well as heat
transfer.
ACKNOWLEDGMENTS
The work is sponsored by Demag Delaval Industrial
Turbomachinery Ltd (a wholly owned subsidiary of Siemens).
The authors would like to thank Dr Gurnam Singh (ALSTOM)
for providing the computational mesh and Dr Kam Chana
(QinetiQ) for providing the experimental data for the MT1
stage.
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