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Akhilesh Rallabandi1Turbine Heat Transfer Laboratory,
Mechanical Engineering Dept.
Texas A&M University,
College Station, TX 77843-3123
Jiang Lei2Turbine Heat Transfer Laboratory,
Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843-3123
Je-Chin HanTurbine Heat Transfer Laboratory,
Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843-3123
e-mail: [email protected]
Salam AzadSiemens Energy, Inc.,
4400 Alafaya Trail,
Orlando, FL 32826
Ching-Pang LeeSiemens Energy, Inc.,
4400 Alafaya Trail,
Orlando, FL 32826
Heat Transfer Measurementsin Rotating BladeShapeSerpentine
Coolant PassageWith Ribbed Walls at HighReynolds NumbersFlow in the
internal three-pass serpentine rib turbulated passages of an
advanced highpressure rotor blade is simulated on a 1:1 scale in
the laboratory. Tests to measure theeffect of rotation on the
Nusselt number are conducted at rotation numbers up to 0.4
andReynolds numbers from 75,000 to 165,000. To achieve this
similitude, pressurized FreonR134a vapor is utilized as the working
fluid. Experimental heat transfer coefficient meas-urements are
made using the copper-plate regional average method. Regional heat
trans-fer coefficients are correlated with rotation numbers. An
increase in heat transfer ratesdue to rotation is observed in
radially outward passes; a reduction in heat transfer rate
isobserved in the radially inward pass. Strikingly, a significant
deterioration in heat trans-fer is noticed in the hub regionbetween
the radially inward second pass and the radi-ally outward third
pass. This heat transfer reduction is critical for turbine
coolingdesigns. [DOI: 10.1115/1.4026945]
Introduction
Gas turbine rotor blades and stator vanes use
rib-turbulatedinternal convective cooling for thermal management.
Newer land-based gas turbine engines (with a higher power-rating)
are physi-cally larger in size than aviation turbine blades and
require higherhydraulic diameter internal passages. This results in
a higher inter-nal Reynolds number (of up to 500,000). The goal of
this work isto acquire heat-transfer coefficient data for a
full-scale rotatingturbine blade (Fig. 1) with high internal flow
Reynolds numbers.A significant amount of open literature has been
generated for
rib-roughened internal channels over the years. Han [1]
conductedtests on channels with various aspect ratios using
orthogonal lowblockage ratio ribs (0.02< e/D< 0.08) for
spacing to height (p/e)ratios ranging from 10 to 20. It was
concluded that, for the spacingvalues studied, taller ribs placed
closer together (higher e/D andlower p/e) performed the best. Han
and Park [2] and Park et al. [3]studied heat transfer with
nonorthogonal ribs and concluded thatthe secondary flows induced by
the ribs increase the heat transfercoefficient on the ribbed
surface. They concluded that using ribsangled at 45 deg60 deg was
the most beneficial from a thermalperformance point of view.The
effect of channel aspect ratio has been studied by Han and
Park [2] and Park et al. [3]. Though the ribbed side heat
transferaugmentation is of the same order in all cases, the
friction factor
is much higher for channels with wider aspect ratios. Studies
byTaslim et al. [4] have focused on cooling passages embedded inthe
leading edge of the blade. Zhang et al. [5] performed studieson a
ribbed triangular channel. A flow visualization of the second-ary
flows is presented in Ref. [6], and a computational picture
ofsecondary flows is discussed in Ref. [7]. Su et al. [8]
performedcomputations on a rotating channel with inclined ribs and
pre-sented predictions of secondary flows in the first channel.
Highblockage channels have been investigated by Taslim and
Leng-kong [9] and more recently by Bunker and Bailey [10] and
Ralla-bandi et al. [11]. They found that friction factors increased
withreduced rib spacing; the Normalized Nusselt number ratio
(Nu/Nu0) was reduced by increasing the Reynolds number. They
alsofound a monotonic dependence of Nu on e/D.Further derivatives
of the inclined rib concept (crossed ribs,
v-shaped ribs, inverted v-shaped ribs [12], broken parallel
ribs,v-shaped broken ribs, d, and wedge shaped ribs [13], etc.)
havebeen studied. V-shaped ribs are shown to enhance heat
transferover parallel ribs at lower friction factors than
comparable parallelribs. The broken v-shaped ribs are found to
enhance heat transferfurther at a comparable pressure drop. Studies
have shown a dete-rioration in heat transfer enhancement due to the
filleting, thoughcompensated by a reduction in corresponding
friction factor[10,1416]. This deterioration in heat transfer
coefficient wasfound to be less at higher Reynolds numbers [11].
The reductionin friction factor was found to be larger at a higher
e/D ratio[10,11,14], indicating that this effect could actually be
beneficial.Dippery and Sabersky [17] detailed a method to
analyze
the pressure drop and heat transfer in a rough duct using
nondi-mensional parameters based on the turbulent boundary
layerlaw-of-the-wall. Han et al. [2,15,18] adapted these parameters
torib-roughened channels. This correlation has been applied to
vari-ous rib configurations (v-shaped, v-shaped broken, etc.) [12]
andaspect ratios [3]. At lower Reynolds numbers in the ribbed
chan-nel, both the friction factor and average fully developed
Nusseltnumber are found to be relatively low. The typical friction
factor
1Current address: Test R&D Engineer, Intel Corporation, 5000
West ChandlerBoulevard, Chandler, AZ 85226.
2Current address: Lecturer, SKL SVMS, Xian Jiaotong University,
Xian,Shaanxi 710049, China.
Contributed by the International Gas Turbine Institute (IGTI) of
ASME forpublication in the JOURNAL OF TURBOMACHINERY. Manuscript
received January 8,2014; final manuscript received February 18,
2014; published online March 17,2014. Editor: Ronald Bunker.
The content of this paper is copyrighted by Siemens Energy, Inc.
and is licensedto ASME for publication and distribution only. Any
inquiries regarding permissionto use the content of this paper, in
whole or in part, for any purpose must beaddressed to Siemens
Energy, Inc. directly.
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tends to attenuate to a constant value as the Reynolds number
isincreased [9,14]. The Nusselt number shows a
monotonicallyincreasing trend with Reynolds number.The effect of
rotation on the heat transfer in a rotating configu-
ration has been studied extensively in literature. Of special
signifi-cance are the works of Wagner and Johnson [1922]. The
fluiddynamics in rotating turbine blades with heated walls is a
complexinterplay of various forces: internal, viscous, Coriolis,
and centrif-ugal buoyancy. In radially outward flow configurations,
the Corio-lis force induces secondary circulations within the flow
field,which results in the accumulation of the warm fluid near the
lead-ing surface, and cool fluid near the trailing surface. This
results ina reduction in heat transfer along the leading surface
and anincrease on the trailing surface. Furthermore, the warm fluid
nearthe leading surface experiences a Buoyancy force radially
inward,creating a recirculation tendency in the flow field.Various
studies [1928] show an increase in heat transfer on
the trailing surface on radially outward passes and
deteriorationon the leading surface. This occurs even when
roughness elementsare provided in the channel. For instance, Wagner
and Johnson[21] report that using skewed turbulators undergoes a
smallerdeterioration in heat transfer on the leading surface (in
the firstpass) in comparison with smooth surfaces.From the brief
review of open literature, the majority heat trans-
fer studies are simulated by physically scaled up flow
channelmodels. Most of studies are based on Reynolds numbers
from10,000 to 30,000 with rotation numbers around 0.20.4.
Theresults can be applied to simulate internal coolant passage
designsfor aircraft engines. However, for land-based gas turbine
blades,Reynolds numbers can be as high as 100,000 to 200,000,
withrotation numbers around 0.20.4. Since it is not easy to reach
highrotation numbers at very high Reynolds numbers in
laboratoryconditions, open literature does not provide heat
transfer informa-
tion in real 1:1 scale blade-shaped coolant passage at
simulatedengine cooling flow rotation conditions. The objective of
the cur-rent study is to provide heat transfer enhancement under
stationaryand rotating condition for real serpentine blade-shaped
ribbedchannels in a real size land-based gas turbine blade. This
studyfocuses on the rotation effect on heat transfer enhancement
onchannel midspan as well as before and after the tip and hub
turnregions at high Reynolds number and high rotation
numberconditions.
Experimental Details. A three-pass serpentine geometry(Figs. 2
and 3) has been used for the current study. The test sec-tion is
composed of 15 sequential regions, each region composedof either 3
(regions 5, 6, 10, 11, and 15) or 4 (all other regions)copper
plates. Each region has a trapezoidal shape (which changesin
hydraulic diameter from the first to the third passes). Withineach
region, the plates correspond to leading (suction),
trailing(pressure), and divider walls.Copper plates in each region
are thermally insulated from each
other; each region is also thermally insulated from other
regions.This thermal insulation is facilitated by the use of a
garolite insertwhich is designed to hold the plates onto the test
section surfacewithout requiring nuts and bolts. Regions 15
comprise the firstpass, 610 the second, and 1115 comprise the third
pass.Four silicone heaters are used for each passlabeled
suction
or leading; pressure or trailing; divider and leadingedge or
trailing edge. Each silicon heater contacts either 4 or 5copper
plates. The use of the garolite insert to hold the plates inplace
(described earlier) ensures that nuts and bolts are notrequired to
hold the copper-plate-heater in place. This allows theuse of
heaters without perforations for this purpose.The test section is
made of green garolite due to its structural
strength and its resistance to test temperatures (80 C). The
testsection is housed inside an aluminum pressure vessel. It is
held inplace by a compression plate secured by large 1 in.
diameter(2.54 cm) stainless steel bolts. The pressure vessel is
attached toan aluminum rotating arm (100 cm in radius). A similar
pressurevessel is located on another rotating arm housed 180 deg
from theabove arm. The second pressure vessel is a dummy pressure
ves-sel installed for rotor-dynamic stability (Fig. 4).The
three-pass serpentine resembles the internal cooling chan-
nel of an actual gas turbine blade. As shown in Fig. 1, the
centralplains of the first and second pass (as well as the second
and thirdpasses) are at an angle. The U-turn also incorporates a
change inhydraulic diameterthe first pass has a hydraulic diameter
of0.75 in. (9.05mm), the second pass 0.67 in. (17.02mm), and
thethird pass has a hydraulic diameter of 0.46 in. (11.68mm). A
Fig. 2 Internal view of test section showing various regions
ofmeasurement
Fig. 1 (a) Rotor blade cross-sectional (b) test
sectionpassages
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plenum (4 times in cross section area to the first pass) is
providedupstream of the first pass to simulate developing thermal
and mo-mentum boundary layers in the first pass. A ribbed geometry
with ane/D of 0.081 for the first pass, 0.091 for the second pass,
and 0.133for the third pass is studied. Parallel 45 deg angled ribs
are placed onboth pressure and suction walls with a staggered
pattern. The p/e(pitch to height ratio) is 10, which is a typical
value used by gas tur-bine designers. All reported results
correspond to this geometry.T-type (copper-constantan)
thermocouples are embedded in
each copper plate. For the heat transfer coefficients
encounteredin these tests, the Biot number for each copper plate
works out toless than 0.1, ensuring that the plates are isothermal
for experi-mental considerations. These thermocouples are soldered
to feedthrough wires which are routed to the stationary frame
through a200 channel slip-ring assembly which is located along the
axis ofrotation. The same slip ring/feed through wire assembly is
usedfor routing the electric power necessary for energizing the
differ-ent heaters present in the test section. The voltage to each
heateris controlled through unique external variable transformers.
A NISCXI chassis/terminal block assembly and Labview based pro-gram
is used to acquire and record the various temperaturesrecorded by
the thermocouples.The working fluid for these tests is Freon R134a
vapor. R134a
vapor(flow loop details in Fig. 5) is chosen due to its
relativelyhigher densityat 4.5 atmospheres (test conditions), its
density is18 kg/m3, similar to that of air at gas turbine operating
conditions.The molecular weight of Freon R-134 a is almost four
times largerthan air, and it can serve purpose better when
compressed to samepressure. Its Prandtl number is 0.8 at test
conditions, which is sim-ilar to that of air. Mach numbers expected
(corresponding with themaximum measured Reynolds numbers of
165,000) are< 0.1, sothe flow regime is incompressible. R134a
does not have issueswith safety as it is inert and noncombustible
at room temperature.OSHA regulations were followed while handling
the refrigerant.R134a vapor flow is established using two flow
loops (Fig. 5), a
primary boiler loop which supplies the R134a vapor for the
tests.This vapor then passes through the condenser where heat
isextracted from the vapor through a noncontact heat exchanger.The
secondary working fluid (which absorbs heat from the pri-mary
R134a, which condenses in the condenser) is also R134a.
Fig. 3 Internal passage view45 deg rib arrangement
Fig. 4 Rotating rig assemblyCAD and photographic views
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This secondary R134a is a working fluid for a conventional
vaporcompression refrigeration system.Flow rate though the test
section is metered by a Coriolis flow
meter. Flow rates reported by the Coriolis flow meter have
alsobeen cross-checked by a rotameter. Flow is routed to the
rotatingframe of reference from the stationary frame of upstream
anddownstream of the test section (along the axis of rotation).
Vaporpressure of the refrigerant is controlled to 4.5 bar (abs)
immedi-ately upstream of the upstream rotary union using a PID
control-ler. Vapor temperature is controlled to 15 C to minimize
ambientexternal water-vapor condensation on fluid pipe-related
issues,using a PID controlled super-heater downstream of the
boiler.Flow rate is controlled though a PID activated needle valve
torange from 1.65 kg/min to 2.4 kg/min, resulting in a range
ofReynolds numbers from 75,000 to 165,000.Rotating speeds of up to
600 rpm are achieved, yielding rotation
numbers of up to 0.4. The axis of rotation is horizontal.
Specialefforts on balancing the assembly were necessary to ensure
thesafety of the test section, the signal (TC) and power
transmittingcables, the housing, and operating personnel.
Data Reduction. Silicone rubber heaters are used to generate
heatwhich is dissipated within the test section. The resistance of
eachheater, Res is measured before each run. The voltage, Vo volts
sup-plied across each heater is measured by a multimeter. The
thermalpower generated by the resistance heater is given by Vo2/Res
watts.Each heater provides constant heat flux along its length.
Chang-
ing the voltage across the heater changes the steady state
tempera-ture measured on each copper plate. Since heat transfer
coefficientsvary from region to region, it is not possible to
control the tempera-ture recorded for each plate to a constant
value. The voltages acrossthe heaters are actively controlled to
ensure that the temperatures ata central region for each pass
correspond to 65 C.An energy budget for each plate is performed to
obtain the heat
transfer coefficient.
h Q=A q00loss
Tw Tb (1)
Here, q00loss is the heat loss, which is determined
experimentally,based on special test. A low conductivity material
is placed inside
the test section inhibiting heat transfer within the test
section. Theheaters are energized with zero bulk flow. The voltage
across theheaters is adjusted to control the steady state
temperature at region4. Two steady state temperatures are
studiedone lower than therange encountered in the test, and one
higher. Based on these twotemperatures, a heat loss characteristic
is obtained for each of thecopper plates. Heat loss tests are run
at all RPM values.The local bulk mean temperature Tb is linearly
interpolated
from the value measured at the exit of the third pass. A is the
pro-jected (smooth) surface area which corresponds to the area of
thecopper plate. The Nusselt number for the current study is
definedas Nu hD/k, where k is the thermal conductivity of Freon
R134avapor. A nondimensional analysis similar to that provided
byWagner et al. [19] identifies the following parameters that
governthe heat transfer phenomena under rotating conditions:
The rotation number
Ro XDV
(2)
Density ratio
DR Dqq
x
Tw TBTw TB =2
x
(3)
These two parameters can be combined together with the
modelradius to diameter ratio to yield the Buoyancy number, Bo
Bo Ro2 DR R=D (4)The mean radius (R) corresponds to the distance
between the axisof rotation and the center of the test section
(Regions 3, 8, and13); the mean density ratio corresponds to the
bulk mean tempera-ture at the center of the test section. The mean
Reynolds numberis based on the mass flow rate at region 4.In order
to isolate the effect of rotation and to eliminate the
Reynolds number effect, data for rotating conditions is
presentedas a ratio, Nu/NuS, where NuS is the measured stationary
Nusseltnumber data acquired for different runs (of Re and RPM) is
corre-lated against Ro, at the corresponding buoyancy parameter
asshown in Table 2. Since Bo is directly proportional to the
square
Fig. 5 Refrigerant R134a vapor working loop schematic
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of Ro (Eq. 4), dependency of Nu/NuS is not shown in this
work.Thus, the obtained results are scalable to engine
conditions.
Uncertainties. The main source of error in determining
theReynolds number is the resolution of the Coriolis flow meter
tomeasure the mass-flow rate (0.01 lb/min 0.00 45 kg/min)
andtemperature measurements to estimate the properties of
R134aaccurately. Reynolds numbers are thus estimated with an error
ofless than 1%.The primary contribution to the error in Nusselt
number mea-
surement is the thermocouple accuracy. Assuming a 0.1V
voltageerror and a 1 C temperature measurement uncertainty (per
infor-mation supplied by DAQ supplier), for a typical bulk
temperaturedifference (30 C), the error in Nusselt number
measurement(based on the KlineMcClintock [29] error propagation
scheme)is less than 4%. The error estimate for the Nusselt
numberenhancement due to rotation (NuNuS) is 8%. This value
ishigher because of errors in the rotating Nusselt number as well
asthe stationary Nusselt numbers.
The measured resistance of the heaters is found to change
lessthan 0.5% for the operating range of temperatures.
Additionalresistance contribution of the slip rings is measured to
be negligible.
Results and Discussions
Stationary Channel Results. The Reynolds numbers studiedare
depicted in Figs. 68. Table 1 shows that Reynolds numbergradually
increases from the first passage to the third passage.Due to a
reduction in hydraulic diameter going from the first passto the
third (the channels have the largest cross section in theupstream
portion of the serpentine channel, closer to the leadingedge
portion of the blade), the Reynolds number graduallyincreases from
the first pass to the third. A large volume of litera-ture exists
on the subject of roughened channel heat transfer.Acquired results
for stationary channels (reported for the leadingand trailing
surfaces of the first passage, in open literature the45 deg
inclined rib turbulators increase the heat transfer to around23
times of the DittusBoelter correlation (Eq. 5)) depending
onReynolds numbers. For comparison with simple shaped
channels,stationary NuS/Nu0 data with p/e 10, e/D 0.1, 45 deg rib
anglefor Re 60,000200,000 from Rallabandi et al. [30] wereincluded
in Fig. 6 at region 8. The current data show slightlyhigher than
those of Ref. [30] due to complicated 180 deg tip turn-ing effect.
The comparison of data trend is considered asacceptable.
Nu0 0:023Re0:8Pr0:4 (5)
Fig. 6 Variation of internal NuS/Nu0 for representative
regionsin the first pass (Region 3), second pass (Region 8), and
thirdpass (Region 13). Results from region 8 are compared withRef.
[31].
Fig. 7 Variation of internal NuS/Nu0 in regions around the
firstturn of the serpentine passage
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It is noticed that heat transfer in the first passage is higher
thanthe second and third passagesbefore the turn is higher than
afterthe turn. This is due to the combinational effects of 45 deg
ribangle and 180 deg sharp turn, as well as channel cross section
andorientation between passages.Since the channel in consideration
is a ribbed channel (and the
Reynolds numbers are very high), the flow in the channel is
turbu-lent. This results in a relatively short development length
and arelatively constant heat transfer coefficient throughout the
chan-nel. Local increases in the heat transfer coefficient occur
inregions 5, 6 and 10, 11, since these regions correspond with
U-turns. This is consistent with results in the open literature
with sta-tionary channels with U-turns.Asymmetry in the Nu/Nu0
results between the pressure and suc-
tion sides can be attributed to three factors: (a)
geometrythetrapezoidal cross section of the channel results in a
deviation insymmetry from the square/rectangular channel case, (b)
staggeredrib turbulators, (c) vorticity triggered by relative
angularity andchange in cross section between the first, second,
and third passes.
Rotating Channel Results. Similar data has been obtained atthe
three rpm values (0, 300, and 500) for Reynolds numbers
Fig. 8 Variation of internal NuS/Nu0 is regions around thesecond
turn of the serpentine passage
Table 1 Nominal and actual Reynolds numbers in study
Nominal case 75 k 100 k 125 k 150 k
1st passage 72,696 94,820 118,526 142,8632nd passage 79,932
104,259 130,323 157,0833rd passage 84,142 109,751 137,188
165,358
Fig. 9 Nondimensional parameter range studied
Fig. 10 Effect of rotation: variation of internal Nu/NuS
versusrotation number (Ro) for regions 3 (first pass), 8 (second
pass),and 13 (third pass). Results from region 8 are compared
withresults from Lei et al. [33].
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ranging from 75,000 to 165,000. Rotation numbers of up to 0.4are
obtained in the first pass. A detailed test parameter range
ispresented in Fig. 9. The effect of rotation is best visualized
byusing Nu/NuS as the ordinate and Ro as the abscissa. At Ro 0,the
case in consideration is stationary and the corresponding Nu/NuS 1.
Increasing Ro (simulated by increasing the rpm) effectsthe Nusselt
number enhancement. This effect on the enhancementis dependent on
the location under consideration.Figures 10, 11, and 12 show the
effect of increasing the rotation
number on the measured heat transfer coefficient. For the
parameterrange studied (for Re 100,000200,000; Ro 0.20.4), the
effectof the Coriolis flow on the flow field seems reduced;
rotationinduced asymmetry in heat transfer coefficient between the
leadingand trailing surfaces is not very obvious, as compared with
those inopen literature (for Re 10,00030,000, Ro 0.20.4).Table 2
shows the relations between Reynolds number, rotation
number, and local buoyancy parameter in the first, second,
andthird passage, respectively. The effect of rotation in the first
passis to increase the average heat transfer coefficient (as seen
inFig. 10, Pass 1: Region 3). The flow in the third pass (region
13)is also radially outward, but rotation is observed to have a
moremuted effect.This can be attributed to the lower rotation
numbers in the third
pass and due to increased local Reynolds number. In the
secondpass (Region 8), however, the effect of rotation is to
suppress theheat transfer coefficient up to 15%. This can be
attributed to rota-tional (centrifugal) buoyancy. Since the
centrifugal force actsradially outward (i.e., heavier fluid
particles are pushed outwards)in a rotating frame of reference, the
buoyant force has an oppositedirection. Warmer (i.e., lighter)
fluid pockets are subject to a netforce which acts radially inward
in all the three passes. In the firstand third passes, the buoyant
force (directed radially inward) is
opposing the bulk fluid flow. In the second pass, the buoyant
forcealigns itself with the bulk fluid flow.A survey of literature
[31,32] indicates that a reduction in heat
transfer coefficient is indeed expected in turbulent internal
flowfields when buoyancy is aligned with bulk flow. This explains
thereduction in heat transfer in the second (radially inward)
pass.This phenomenon is attributed to the suppression of
turbulencegeneration due to increase in momentum aligned to the
bulk flow
Fig. 11 Effect of rotation: variation of internal Nu/NuS
versusrotation number (Ro) along turn between the radially
outwardfirst pass and the radially inward second pass
Fig. 12 Effect of rotation: variation of internal Nu/NuS
versusrotation number (Ro) along the turn between the radially
inwardsecond pass and the radially outward third pass
Table 2 Rotation numbers and local buoyancy parameters
Rotate speed 300 rpm 500 rpm
Region Re 75 k 100 k 125 k 150 k 75 k 100 k 125 k
R3 Ro 0.2388 0.1831 0.1464 0.1215 0.3995 0.3063 0.2450Bo 0.3401
0.2062 0.1986 0.1427 0.9358 0.5828 0.3875
R5 Ro 0.2388 0.1831 0.1646 0.1215 0.3995 0.3063 0.2450Bo 0.2576
0.1585 0.1083 0.0794 0.6719 0.3922 0.2823
R6 Ro 0.1745 0.1338 0.1070 0.0888 0.2919 0.2238 0.1791Bo 0.1131
0.0748 0.0519 0.0379 0.3003 0.1758 0.1258
R8 Ro 0.1745 0.1338 0.1070 0.0888 0.2919 0.2238 0.1791Bo 0.1733
0.1061 0.0731 0.0528 0.4831 0.2789 0.1946
R10 Ro 0.1745 0.1338 0.1070 0.0888 0.2919 0.2238 0.1791Bo 0.2968
0.1785 0.1154 0.0813 0.8463 0.4969 0.3249
R11 Ro 0.0770 0.0591 0.0472 0.0392 0.1289 0.0988 0.0791Bo 0.0285
0.0177 0.0117 0.0087 0.0837 0.0505 0.0346
R13 Ro 0.0770 0.0591 0.0472 0.0392 0.1289 0.0988 0.0791Bo 0.0387
0.0239 0.0162 0.0119 0.1001 0.0613 0.0426
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direction in warm fluid pocket. The effect is opposite in
radiallyoutward passesresulting buoyant force in warm fluid
pockets(close to the wall) opposes the bulk flow and therefore
increasesshear and generates turbulence increasing heat transfer
coefficients.Similar measurements have been made by Wagner and
Johnson [19].For comparison with simple shaped channels, rotating
Nu/NuS
data with p/e 8, e/D 0.1, 45 deg rib angle for Re 10,00040,000
from Lei et al. [33] were included in Fig. 10 atregion 8. The
current data show much lower Nu/NuS values thanthose of Ref. [33].
This might be due to high Reynolds numbersand complicate 180 deg
tip turning effect. This implies rotatingdata from the simple
multipass channels with same channel angleto rotation direction,
such as rectangular-to-rectangular multipasschannels at Reynolds
numbers from 10,000 to 40,000 and rotationnumbers up to 0.3 [33]
might be different from the complicatereal multipass channels with
different channel angle to rotationdirection, such as
trapezoidal-to-trapezoidal channels at Reynoldsnumbers from 75,000
to 165,000 and rotation numbers up to 0.3.Comparing Figs. 11 and
12, a qualitative reduction in heat
transfer rates due to rotation is observed in the turn
correspondingwith the hub region (regions 10 and 11). The trend in
Fig. 11(the turn corresponding with the tip region) is reverse;
rotationincreases the heat transfer in the internal passage near
the tipregion. This difference can be attributed to the arrangement
of thebuoyancy driven secondary flows, which, as discussed in the
pre-vious paragraph, are always directed towards the hub. The
warmerfluid in the buoyancy driven boundary layer impinges on
thehub region, suppressing the internal cooling ability at the
hub.
Conclusions
A significant amount of internal channel heat transfer
coeffi-cient data is collected on a 1:1 scaled turbine blade
replica in thelab at simulated engine conditions for high Reynolds
numbersfrom 75,000 to 165,000 and high rotation numbers up to 0.4.
Theeffects of rotation (i.e., the composite of the Coriolis and
theBuoyancy effect) are studied. Results obtained reflect the
compli-cated nature of flow field (the effect of rib turbulators,
channelshape, sharp turns, rotation etc.).
(1) Using R134a as a working fluid, prominent trends in
openliterature (obtained using air as a working fluid) can
bereproduced. Nondimensional numbers corresponding toactual engine
conditions (high Reynolds numbers and highrotation numbers) can be
more easily simulated with R134adue to its higher density.
(2) Rib turbulators are found to increase the heat
transfercoefficient to around 23 times the value predicted by
theDittusBoelter correlation. The NuS/Nu0 values decreasewith
Reynolds numbers, a trend widely documented inopen literature.
(3) For the high Reynolds numbers studied, the effect of
theCoriolis force in generating asymmetry between the leadingand
trailing surfaces is reduced.
(4) Heat transfer is found to be relatively suppressed in the
sec-ond pass up to 15%, which has radially inward flow. Thiseffect
is attributed to the suppression of turbulence genera-tion due to
the alignment of the buoyancy force acting onthe warmer fluid
pockets and the bulk flow.
(5) Heat transfer is found to be suppressed in the hub
regionpressure side (the region between the second and the
thirdpasses) up to 25%. This is also attributed to buoyancyeffects.
This heat transfer reduction is critical for turbinecooling
designs.
Acknowledgment
This project was sponsored by Siemens Energy Company (theproject
initiated by Sanjay Chopra in 2004). The authors from
Texas A&M University would like to acknowledge and
extendtheir gratitude to Randy Tucker, Lesley Wright, Mike Huh,
andYao-Hsien Liu who have made contributions to the project
duringtheir study in TAMU-Mechanical Engineering. The project
wasalso partially supported by TAMU-Marcus Easterling
endowmentfund.
Nomenclature
D hydraulic diameter of channelh heat transfer coefficient, W/m2
Kk thermal conductivity of Freon R134a vapor
Nu Nusselt numberNuS measured Nusselt number for stationary case
at same
Reynolds numberNu0 number for smooth duct, based on the
DittusBoelter
correlation (Eq. 5)Pr Prandtl numberPS trailing side of internal
passages, corresponding to blade
external pressure sideQ heat dissipated by heater, W
q00loss local heat loss, W/m2R mean radiusRe Reynolds number in
channel (for pass consideration)Res electrical resistance of
heater, ohmsRo rotation numberSS leading side of internal passages,
corresponding to blade
external suction sideTb local bulk mean temperatureTi test
section inlet temperature, 22 CTw local wall temperatureV fluid
velocity, m/s
Vo voltage, voltsl dynamic viscosityq densityX angular velocity,
rad/s
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