NASA Technical Reports Server (NTRS) 19910010130: Heat transfer in rotating serpentine passages with trips normal to the flow

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by  NASA Technical Reports Server (NTRS)

"7
NASA Technical Memorandum 10_3758_ ,ii i ? ii
Heat Transfer in Rotating Serpentine
Passages With Trips Normal
to the Flow
J.H. Wagner and B.V. Johnson
United Technologies Research Center
East Hartford, Connecticut
R.A. Graziani
Pratt & Whitney
East Hartford, Connecticut _
and
F.C Yeh
Lewis Research Center
Cleveland, Ohio
Prepared for the
36th International Gas Turbine and Aeroengine Congress and Exposition
sponsored by the American Society of Mechanical Engineers
Orlando, Florida, June 3-6, I991 ......
NI A
N91-19443
7- (NASA-TM-I07,756) HFAT TRANSFER IN RUTATING
SERPENTINE PASSAGES _[TIt TRIPS NORMAL TQ THE
,_ -.__-
FLOW (_IASA) 15 p CSCL }_B
Uric l as
G3/37 O001Ont_

HEAT TRANSFER IN ROTATING SERPENTINE
PASSAGES WITH TRIPS NORMAL TO THE FLOW
J. H. Wagner R.A. Graziani F.C. Yeh
B. V. Johnson Group Engineering NASA Lewis Research Center
United Technologies Research Center Pratt & Whitney Cleveland, OH 44135
East Hartford, CT 06108 East Hartford, CT 06108
NB Nusselt number, hD/k
ABSTRACT p Trip spacing, i.e. pitch
Experiments were conducted to determine the effects of buoyancy R Radius
and Coriolis forces on heat transfer in turbine blade internal coolant Re Reynolds number, (mD)/(p.A)
passages. The experiments were conducted with a large scale, Ro Rotation number, D.D/V
multi-pass, heat transfer model with both radially inward and outward T Temperature
flow. Trip strips on the leading and trailing surfaces of the radial V Mean coolant velocity
coolant passages were used to produce the rough walls. An analysis of x Streamwise distance from inlet
the governing flow equations showed that four parameters influence the tt Absolute viscosity
heat transfer in rotating passages: coolant-to-wall temperature ratio, v Kinematic viscosity
Rossby number, Reynolds number and radius-to-passage hydraulic
Coolant density
diameter ratio. The first three of these four parameters were varied over P
_o/p Density ratio, (Pb - pw)/Pb
ranges which are typical of advanced gas turbine engine operating t2 Rotational speed
conditions. Results were correlated and compared to previous results
from stationary and rotating similar models with trip strips. The heat
Subscripts:
transfer coefficients on surfaces, Where the heat transfer increased with
b Bulk property
rotation and buoyancy, varied by as much as afactor of four. Maximum
f Film property
values of the heat transfer coefficients with high rotation were only i Inlet to model
slightly above the highest levels obtained with the smooth wall model. w Heated surface location
The heat transfer coefficients on surfaces, where the heat transfer
o_ Fully developed, smooth tube
decreased with rotation, varied by as much as a factor of three due to
rotation and buoyancy. It was concluded that both Coriolis and
Superscripts:
buoyancy effects must be considered in turbine blade cooling designs
- Average
with trip strips and that the effects of rotation were ma_,kedly different
' Distance from beginning of second passage
depending upon the flow direction.
" Distance from beginning of third passage
NOMENCLATURE
INTRODUCTION
A Area of passage cross-section
D Hydraulic diameter Advanced gas turbine airfoils arc subjected to high heat loads that
e Trip height require escalating cooling requirements to satisfy airfoil life goals. The
Or Rotational Grashof number efficient management of cooling air dictates detailed knowledge of
h Heat transfer coefficient local heat load and cooling air flow distribution for temperature and life
k Thermal conductivity predictions. However, predictions of heat transfer and pressure loss in
m Mass flowrate airfoil coolant passages currently rely primarily or1correlations derived
from the results of stationary experiments. Adjustment factors are effects of rotation on heat transfer in passages with trips. These
Usually applied to these correlations to bring them into nominal investigators have documented strong secondary flows and have
correspondence with engine experience. This is unsatisfactory when identified aspects offlow stability which produce streamwise oriented,
blade cooling conditions for new designs lie outside the range of vortex-like stractures in the flow of rotating radial passages.
previous experience.
The effects ofbuoyancy onheat transferwithout the complicating
Knowledge of the local heat transfer in the cooling passages is effects of Coriolis generated secondary flow have been studied in
extremely important inthe prediction of blade metal temperatures, i.e. vertical stationary ducts. Effects of buoyancy on heat transfer were
blade life. Rotation of turbine blade cooling passages gives rise to reported byEckertetall.(1953), Metals andEckert (1964) andBrundrett
Coriolis and buoyancy forces which can significantly alter the local and Burroughs (1967). Flow criteria for forced-, mixed- and
heat transfer inthe internal coolant passages due tothe development of free-convection heat transfer was developed for parallel flow and
cross stream (Coriolis), as well as, radial (buoyant) secondary flows. coumer flow configurations by Eckert et al. (1953) and Metais and
Buoyancy forces ingas turbine blades are substantial because of the Eckert 0964). Based on these experimental results, buoyancy forces
high rotational speeds and coolant temperature gradients. Earlier would be expected to cause significant changes inthe heat transfer in
investigations (e.g. Eckert et al., 1953) with single pass co- and turbine blade coolant passages and to bestrongly dependent on flow
counter-flowing stationary coolant passages indicated that there dan _ion (radially inward vs. radially outward).
also be substantial differences in the heat transfer when the buoyancy
The combined effects of Coriolis and buoyancy forces on heat
forces are aligned with or counter to the forced convection direction.
transferhas been stud/ed by• number ofinvestigators. Heat transferin
A better understanding of Coriolis and buoyancy effects and the
rotating models has been reported by Wagner et al. (1989 and 1990)
capability topredict the heat transfer response tothese effects will allow
Taslim et al. (1989), Guidez (1988), Clifford (1985), Iskakov and
the turbine blade designer to achieve cooling configurations which
Trushin (1983), Morris (1981), Morris and Ayhan (1979), Lokai and
utilize less flow and which reduce thermal messes in the airfoil.
Gunchenko (1979), Johnson (1978), and Mori etal. (1971). With the
An extensive analytical and experimental program was originated exception of Taslim and Clifford, all of the aforementioned work was
and sponsored by NASA at the Lewis Research Center, Cleveland, conducted with smooth-wall models. Large increases anddecreases in
Ohio, as part of the Hot Section Technology (HOST) program. The local heat transfer were found to occur by some investigators under
objectives of this program were (1) to gain insight on the effect of ceriain conditions of rotation while other investigators showed lesser
rotation on heat transfer in turbine blade passages, (2) to develop a effects. Analysis of these results do not show consistent trends. The
broad database forheat transfer and pressure drop in rotating coolant inconsistency of the previous results is attributed to differences inthe
passages, and (3) to improve computational techniques and develop measurement techniques, models and test conditions.
correlations that can be useful to the gas turbine industry for turbine
blade design. The attainment of these objectives become even more Objectives
critical with the advent of the Integrated High Performance Turbine
Under theNASA HOST program, • comprehensive experimental
Engine Technology (IHFTET) initiative. As part of the IHPTET goal,
project was fmmulated in 1982 to identify and separate effects of
the turbine would operate at near stoichiometric (3500-4000F) inlet
Coriolis and buoyancy forces for the range dimensionless flow
temperatures, maintain efficiencies inthe 88-94% range, and require
parameters encountered inaxialflow, aircraft gas turbines. Thespecific
total coolant flows ofonly 5%of the engine air flow rate. Toattain these
objective of this experimental project was to acquire and correlate
ambitious goals, a thorough undemanding on the rotational effects of
heat transfer and flow inturbine blade passages ismandatory. benchmark-quality heattransfer datafor amulti-pass, coolant passage
underconditions similartothose experienced inthe blades of advanced
aircraf_ gas turbines. A comprehensive test matrix was formulated,
Previous Studies
encompassing the range of Reynolds numbers, rotation numbers, and
Heat transfer experiments inmultiple-pass coolant passages with heating rates expected in amodem gas turbine engine.
normal trips have been conducted in stationary models by several
The results presented inthispaper are from the second phase of a
investigators toobtain • database forthe thermaldesign ofgas turbine
three phase program directed at studying the effects of rotation on a
airfoils, e.g. Boyle (1984), Han et al. (1986), Metzger et al. (1988).
multi-pass model with smooth and rough wall configurations. The first
These data bases are directly applicable to the cooling designs of
phase utilized the smooth wall configuration. Initial results foroutward
stationary vanes. However, the effects of Coriolis forces and buoyancy,
flow inthefirstpassage werepreviously presented byWagner, Johnson
due to the large rotational gravity forces (up to 50,000 g), are not
and H•jek (1989). The effects of flow direction and buoyancy with
accounted for.
smooth wails were presented byWagner, Johnson and Kopper (1990).
The complex coupling of the Coriolis and buoyancy forces has The present paper covers the phase with surface roughness elements
prompted many investigators to study the flow field generated in oriented at 90 degrees tothe flow direction. Comparisons will bemade
unheated, rotating circular andrectangular passages without the added with the results forsmooth walls inthe same model and with previous
complexity of buoyancy, i.e., Hart (I971),Wagner and Velkoff (1972), rotating and stationary experiments employing trips90 degrees to the
Moore (1967) andJohnston etal. (1972). The effects ofrotation on the flow direction. Results from the remaining phase of the program with
location of flow reattachment after• backward facing step presented by trips oriented 45 degrees to the flow direction will be discussed in •
Rothe and Johnston (1979) is especially helpful in understanding the subseqeem paper.
The facility, data acquisition and data reduction techniques theheat U'ansfertest sections with trips, i.e., average model radius, was
employed inthis experiment were discussed inthe Wagner etal. (1989) 26.1 in. (663 mm). The power to each element was adjusted to obtain
paf_ and will notberepeated. However, the description ofthe model an isothermal watl boundary condition. In practice, temperature
wd! berepeated for the convenience of the reader. differences less than 2F (1C) were achieved. The heat flux between
elements with a2F(1C) temperature difference was estimated tobeless
DESCRIPTION OF EXPERIMENTAL EQUIPMENT than 2percent of atypical stationary heat flux.
Tripstrips were machined inastaggered pattern ontheleading and
Heal Transfer Model
trailing surfaces of the 6 inch (152.4 mm) straight length of each
The heat transfer model was designed to simulate the internal passage. No trips were on the guard elements (x/D < 3) in the first
passage. The height, (e/D = 0.1), shape (circular) and spacing (P/e =
muhi-passage geometry of acooled turbine blade (Figure 1). The
model consists of three straight sections and three tam sections which 10) of the trips are shown in Figure 3. These geometrical parameters
were instrumented followed byone uninstmmented straight section, as are typical of the trips cast on the coolant passage walls of turbine
blades.
shown in Figure 2. Data presented herein were obtainedin the fwst,
second andthird passages with radially outward, inward and outward Testing was conducted with air at dimensionless flow conditions
flow, respectively. The model passages are approximately square with typical of advanced gas turbine designs. The required dimensionless
acharacteristic dimension of 0.5 in. 412.7 mm). Four elements form rotation numbers were obtained withrotation rates of i100RPM orless
thewails ofthesquarecoolant passage ateach s_reamwise location. The byoperating the model at apressure of approximately 10atmospheres.
heated length of the first passage is 14 hydraulic diameters and is The model inletair temperature was typically 80F (27C) andthecopper
comprised of sixteen heated copper dements at four streamwise elements were held at 120F, 1601=,200F and 240F (49C, 71C, 93C and
locations. The heated copper elements atthe f'nmstreamwise location 116C) for coolant-to-wall temperature differences of 40F, 80F, 120F
were all smooth wails and were used as guard heaters. The two and 160F (22C, 44C, 67C and 89C). Temperatures of the copper
cross-section views shown in the figure show the orientation of the elements were measured with two chromel-alumel thermocouples
leading, trailing and sidewall surfaces. Each copper element is heated inserted indrilled holes ofeach element. Heat transfercoefficients were
onthe side opposite the test surface with athin film, 0.003 in.40.1ram), determined by performing an energy balance on each copper element
resistance heater. Each dement is 0.150 in. (3.8 mm) thick and is toobtain theconvected heat fluxand the local coolant bulk temperature.
thermally isolated from surrounding elements by 0.060 in. (1.5 ram) The heat transfer coefficients were based on the projected arearather
thick fiberglass insulators. The insulating material separating the
copper elements at each streamwise location resulted ina0.04 in. 41.0
ram) chamfer inthe comers, which yielded ahydraulic diameter, D, in
Leading
thestraight sections of 0.518 in. (13.2 nun). The radius atthe center of
side side B
0 0
Turbulence S1d"• A 2" |Direction
Trailing Jof Rotation
Promoters ] Shaped Internal Side
r- Passages
Cover--.
I I !
Vessel I ¢_1 _ ¢_ Nl|]ll.Unheated
Turbulence
., ?omotere
SulkInletI i IIlllI!I
The_°c°upl:i IHi _I IHI IIIIIiBulk Outlet
--Pin Fins _ T LAocouple
lI"F¢_I _ Plenum
Cooling Air
) Axis of Rotation
Fig. Typical Turbine Blade Internal
Convection Cooling Configuration Fig. 2 Cross Sectional Views of Coolant
(from Han et. al. [19S6]). Passage Heat Transfer Model Assembly.
Flow number (aflow parameter), the streamwise distance from the inlet, x/D
Trip (ageometric parameter), andthe geometry of the augmentation device.
However, when rotation is applied, the heat transfer is also strongly
influenced by the coupled effects of Coriolis and buoyancy and
becomes asymmetric around thepassage. An unpublished analysis of
the equations ofmotion by Suo (1980), similar toOat of Guidez (1988),
p -
showed that the basic dimensionless fluid dynamic parameters
governing the flow in a radial coolant passage were the Reynolds
number, the rotation number, Ro, the fluid density ratio, riO/P, and the
Fig. 3 Cross Sectlonal Vlew of Normal geometric parameter, R/D. The same analysis of the equations of
Trip Layout.
motion produces the rotational Reynolds number, J= t'lD2/v as an
altemate governing parameter. Note also that Roequals J/Re. Note that
than the total heat transfer surface area dueto trip geometry. (The total the rotation parameter is the reciprocal of the Rosaby number, VA'ID,
heat transfer surface ares was 1.11 times the projected area.) See and governs the formation of cross-stream secondary flow. The
Wagner et al.(1989) foradditional information about the datareduction rotation number, Ro, the fluid density ratio, Ap/p, and the geometric
procedure. parameter, P/D, appear in the governing equation as a buoyancy
Nusselt numbers and Reynolds numbers were calculated foreach parameter. This buoyancy parameter, (A0/p) (IL/D)(_D/V) 2,issimilar
element. The fluid properties in the Nusselt and Reynolds numbers to Gr/Re2 for stationary heat transfer. The difference between our
were evaluated atthe trdmtemperature, i.e., Tf-- (Tw+Tb)/2. All ofthe rotational buoyancy parameter and the stationary Gr/Re2is that/_o/p
heat transfer results presented herein have been normalized with a =(Tw- Tb)/Twratherthan BAT=(T,- Tb)/Tb. Thedifference between
correlation for fully developed, turbulent flow in asmooth tube. The the parameters decreases asTwapproaches Tb. Thus, with rotation, the
constant heat flux Colbum equation, adjusted for constant wall heat transfer is a function of three geometric parameters (surface
temperature was used toobtain the Nusseh number forfullydeveloped, roughness geometry, x/D and surface orientation relative to the
turbulent flow in a smooth tube (Kays and Perkins (1973)). The direction of rotation) and three flow parameters (Reynolds number,
resulting equation for the constant wall temperature condition with a rotation number and the buoyancy parameter).
Prandtl number equal to 0.72 is as follows. Due to the vector nature of the equations ofmotion, itcanalso be
expected that flow direction can also have asignificant effect on the
Nu,,. =0.0176 Re°'!
coolant flow. In the parallel flow case, the flow is radially inward,
coincident with buoyancy driven flow for beated walls. For the
An uncertainty analysis of the datareduction equations using the
counter-flow case the flow isradially outward, opposite tothe direction
methods of Kline and McClintock (1953) showed that approximately
of the buoyancy driven flow. Flow direction (i.e. radially inward or
3/4 ofthe estimated uncertainty in calculating heat transfer coefficient
outward) and afixed radially outward directed force field, created by
was due to the measurement oftemperatures in the model. The
the rotating reference frame, establish the potential for parallel and
uncertainty of the heat transfer coefficient is influenced mainly bythe
counter flow situations as observed by Eckert et al. (1953) in their
wall-to-coolant temperature difference and the net heat flux from each
vertical tube experiments.
element. Uncertainty in the heat transfer coefficient increases when
either the temperature difference or the net heat flux decreases. For The references used inthe text forlow and high pressure surfaces
increasing x/D, the uncertainty increases because the wall-to-coolant are consistent with the leading to trailing side, Coriolis-generated,
temperature difference decreases. For low heat fluxes (i.e. low pressure gradients. In general, high pressure surfaces are expected to
Reynolds numbers and on leading surfaces with rotation) the have normal components of flow towards the surface while low
uncertainty in the heat transfer increased. Estimates of the error in pressure surfaces are expected to have normal components of flow
calculating heat transfer coefficient typically varied from away from the surface. Therefore, trailing surfaces inthe first passage
approximately i-6 percent atthe inlet to +30 percent atthe exit of the with outward flow are on the high pressure side of the passage.
heat transfer model for the baseline stationary test conditions. The Similarly, leading surfaces inthe second passage with inward flow are
uncertainty in the lowest heattransfer coefficient ontheleading side of on the high pressure side. In terms of turbine airfoils, the leading
the third passage with rotation isestimated to be40percent, primarily surfaces of the coolant passage are adjacent to the suction side of the
due tothe uncertainty inthe calculated bulktemperature. Although the airfoil and the trailing surfaces of the coolant passage ate adjacent to
uncertainty analysis was useful in quant_ing the max_um possible thepressure side of the airfoil.
uncertainty in calculating heat transfer coefficient, multiple The format of this paper is to show the effects of each of the
experiments at the same test condition were repeatable within ranges primary variables (x/D, rotation number, density ratio) on the heat
_maller than those suggested by the analysis. transfer about abaseline flow condition todevelop an understanding of
the cause/effect relationships. The entire body of experimental results
RESULTS are then examined to determine the effects of the buoyancy parameter
on the beat transfer inselected locations of the coolant passage.
Forward
Heat transfer in stationary experiments with augmentation
devices on the passage walls is primarily afunction of the Reynolds
Bg_ine Experiments The heat transfer from the walls with trips (denoted leading and
trailing) in the first outward straight (3 < x/D < 14) passage has beat
Two baseline experiments, one stationary and one rotating, were
transfer coefficients more than twice that from the fully-developed,
conducled to obtain data for comparison with all other data generated
smooth-wall correlation. Note that the heat transfer coefficients for the
m this program. The stationary and rotating baseline experiments had
dimensionless flow conditions which consisted of aReynolds number normal trips do not decrease significantly with x/D in each passage as
of 25,000 and an inlet density ratio, (Ap/p)i = (Tw-Tb)frw, of 0.13. The they did for the smooth wail in the same model. Some differences in
heat transfer are observed between the leading and trailing surfaces for
rotating baseline experiment had arotation number, lID/V, of 0.2A and
this stationary baseline condition. The exact cause of the difference is
aradius ratio atthe average model radius, R/D, of 49. These values were
selected because they are in the central region of the operating range of not known but may be due to the staggering of the trips on the two
surfaces. The heat transfer coefficients measured in the remaining two
current large aircraft gas turbine engines.
passages (i.e., 20 < x/D < 31 and 36 < x/D < 48) show similar
Stationary. Streamwise variations of Nusselt number for the
characteristics. However, the greatest increase in heat transfer from the
s_ationary baseline test are shown in Figure 4. The Nusselt number for
trips was less (i.e. 10 and 20 percent, respectively) than that obtained
fully developed, turbulent flow in a smooth tube with constant wall
in the first outward straight section. This general reduction in heat
temperature and the results from the previous (Wagner et al. 1990)
transfer was attributed to the increased uncertainty in the bulk
smooth wall experin_ents are shown for comparison.
tem_rature for the model with the nomml trips. The increased heat
(_/p), = o. z2 transfer compared to the smooth wall model causes the difference
between bulk temperature and the waft temperature to decrease and
Re = 25.000 (Baseline)
AT = 806 F (Baseline) hence the uncertainty of the heat transfer coefficient determined to
io I Lo io ] increase,
[Locati_r Side A Side B Leading TraiLin_ The heat transfer in the turn regions was generally less for the
Outward Inward Outward present experiment than for the previous smooth wall experiments.
Straight Straight Straight changes on the leading and trailing surfaces of the turn sections
200 - are attributed in part to the differences in the velocity profdes expected
atthe emzance to the rum regions. For the smooth wall flow condition,
¢
z 160- the velocities are expected to be high in the comers of the duct (e.g.
,2 0 Schlictling, 1968). For flow over normal trips, the velocity can be
expected to be peaked in the center of the channel due to the large
E 12o-
momentum losses ateach trip. The changes in heat transfer on the sides
Z A & B (outside walls of turn sections) attest to the complexity of the
_ 80- X__..J _ flow structure in the turns and is not yet explained.
ul
The results from the fast outward straight coolant passage are
z 40-
compared with _ults from Boyle (1984) and Han et at. (1986) in
Figure 5. The present results in the region with trips, 3< X/D < 14, are
O- ' ' I I I t almost identical with those from Boyle. The Boyle results were
0 12 24 36 48 obtained for aconstant heat flux boundary condition and sharp cornered
X/D
200
_0 -
Z AHan et. al. ]1986]
z 160 I-IBoyle [1984J
_2 D N Z _, •0 LTeraaidliinngg SSuurrffaaccee
_k _3
E 120 A °i
O_O _
Z
L
*" 80 _ ,
ul
m 9
z 40 E-'
0 J ' i ' I i ' I i , I
0 12 24 36 48 1 -
x/D 0 4 8 12
x/D
Fig. 4 Heat Transfer Results for Stationary
Flow Condition; --- correlation for Fig. 5 Comparison of Stationary Heat
smooth-wall fully developed flow, Transfer Results From Leading and
--smooth-wall experiments (Wagner, Trailing Surfaces With Hen st. el.
st. el. 1990). (1986).
trips transfer on the leading surface for flow inward does not increase
which are modest variations from the present experiment. Heat
transfer ratios from the surfaces with trips are generally consistent with noticeably. These results are qualitatively similar to those obtained for
the data band for Han's measurements. Note that the heat transfer the smooth wall model. Further comparison with the smooth wall
model results will be made in alater section.
results from the present program for x/D < 3 are from the smooth wall
surfaces near the inlet of the first passage. However, in general, the The baseline results with rotation showed significant changes in
levels of heat transfer augmentation due to the presence of the trips are the heat transfer in the first passage on the leading, trailing, and turn
consistent with those of Boyle and Han et al. surfaces but relatively smaller changes on the sidewall surfaces.
Rotating. The streamwise distributions of heat transfer ratio for Therefore, the following discussion will focus on the heat transfer
results from only the leading and trailing surfaces in the straight
the rotating baseline condition for the first two coolant passages are
shown in Figure 6. These results and those discussed in the following sections of the coolant passage with both inward and outward flow and
will focus on the differences between inward vs. outward flow.
sections are shown as heat transfer ratio, Nu/Nu_. Nu, is thatexpected
Discussion of effects of rotation on the heat transfer in the turn regions
from the Kays and Pezkins (1973) conelatiou for fully developed,
turbulent flow. The results will be shown in this manner to minimize of the coolant passage are deferred to asubsequent paper.
effects of Reynolds number variations from test to test.
Varying Rotation Number
The most important feature of these results is the decrease in heat
transfer on the "low pressure" sides shown for the leading surfaces for The rotation number, DD/V, was varied from 0 to 0.35 for this
flow outward (x/D < 14) and the trailing surfaces for flow inward (x/D series of flow conditions. The Reynolds number, inlet density ratio and
< 31). The lowest values of Nu/Nu_ are less than one--half the radius ratio were held constant atthe nominal values of 25,000, 0.13 and
nonrotating values. The heat transfer on the high pressure side of the 49, respectively.
coolant passage with flow outward (i.e., the trailing surfaces) increases
High Pressure Surfaces. Increasing the rotation rate causes
about 50 percent compared to the stationary case. However, the heat
significant increases in heat transfer on the trailinsgurfaces (Figure 7a)
of the first passage but relatively small increases occurred on the
leading surfaces in the second passage (Figure 7b). Heat transfer in the
0000
Symbol 0 2R3o8 first passage increased by more than 60 percent for the largest value of
rotation parameter (0.35) compared to stationary heat transfer values.
The substantial increases in heat transfer in the first passage are
=8 Leading Surface Trailing Surface consistent with the results of Rothe and Johnston (1979). They found
}. , that as rotation rate was increased, the reattachment length after astep
.. [ _
i:..., i decreased. For the trip spacing of the present program (P/e = 10), this
would translate into an increase in the effective heat transfer area
II - between the trips with attached, turbulent flow, thereby, causing an
_: _l - I increase inthe beat transfer. Compared to the stationary results, the beat
s a
_1- l transfer on the leading, high pressure side of the second passage
increased approximately 10 percent. The effects on heat transfer due
•_ Low
to Coriolis generated secondary flows and flow reattachrnent might be
[._ t" Pressure u
expected tobe approximately the same for the first and second passages.
The differences in heat transfer between the outward and inward
0 12 24 _6 0 12 24 a6
x/D x/D flowing passages are therefore attributed to the different effects of
8 buoyancy in the counter-flowing first passage (radially outward flow)
Side A Side B and the co-flowing second passage (radially inward flow). Ingeneral,
1-q
the trends noted above are compatible with those obtained for the
smooth wall test surfaces in the same model (Wagner et al. 1990),
The small increase in the heat transfer ratio on the high pressure
'l[:l side of the second passage relative to the fwst passage is attributed to a
lille'-el Ioe
reduction inthe generation of near-wall turbulence. Inthe first passage,
the near-wall buoyancy driven flow was inward toward the axis of
rotation and the coolant flow was outward. This counter flow is
expected to generate additional near-wail turbulence due to the strong
-_ 4- I 1 shear gradient. The large increases in heat transfer in the firstpassage
0 12 24 36 0 12 24 36
:= x/D x/D are attributed to the destabilizing effects of the shear flow combined
with the cross stream secondary flows generated by Coriolis forces.
Fig. 6 Variation of Heat Transfer Ratio with However, when the flow and the buoyancy driven near-wsil flows are
Streamwlse Location for "Rotating" coincident, as in the second passage, the generation of near-wall
Baseline Flow Condition; Re-25000,
turbulence may be dimims"bed because of the relatively weaker
24 I (Ap/p) ira0.13.
R_10.
near-wall shear layer. The expected lower near-wall turbulence and Low Pressure Surfaces. In contrast to the continual increase in
weaker shear flows may also contribute to increases in reartachment heat transfer with increasing rotation number on the trailing side, the
k,n_hs following the trips. Therefore, the reduced effects of the heat transfer ratio decreases with increasing rotation number on the
buoyant and the cross stream secondary flows coupled with possible leading side of the passage near the inlet, i.e. x/D < 6. For Ill of the
increases in reattachment lengths in the second passage may have remaining locations on the leading side of the passage, the heat transfer
resulted in lesser changes in heat transfer. The magnitude of the ratio decreases and then increasesagain with increasingrotation
beoyancy effect on the heat transfer is unclear in that the buoyancy number. Heat transferfrom thetrailingl,ow pressuresurfacesofthe
effect on the heat transfer in the second passage may be zero (which secondpassagealsohad largedec_ inheattransfer.Heat transfer
tmplies amodest Coriolis dominated heat transfer increase) or negative inthefirstand secondpassagesdecreasedtoalmost50percentofthe
{which implies alarger Coriolis dominated beat transfer increase which stationaryheat transferlevels.In both passages,the heat transfer
is offset by a reduction due to buoyancy). Future results from decreased and then subsequently increased again as the rotation rate
conc_rrem numerical simulations of the_ flow conditions are expected was increased.
to assist in the undemanding of this complex flow field.
The decreases in the heat transfer ratio are am'ibuted to the
cross-stream flow patterns as well as the stabilization of the near-wall
flow on the leading side of thepassage, e.g, Johnston et al. (1972). The
Symbol OD/V cross-stream flows cause heated, near-wall fluid from the trailing and
@ 0.00 sidewall surfaces to accumulate near the leading side of the coolant
Z_ 10.12
• 0.23 passage resulting in reduced heat transfer. In addition, as described by
0 o.35
Rothe and Johnston (1979), it can be expected that flow reattachment
a) Trailing Surface after trips on low pressure mu'faces occurs at larger distances from the
trips with increasingrotationnumber. Longer reattachrnent lengths,
due to the stabilizing effects, will decrease the effective heat transfer
64 area between trips, thereby, further reducing the turbulent transport of
heat. The increase in the heat transfer ratio in the latter half of the
t ....
coolant pma_e for the larger rotation numbers is attributed to
2 buoyancy effects, possibly caused by buoyancy enhanced flow in the
recirculation cells downstream of the trips. Similar effects of rotation
are noted for the low pressure surfaces in both the first and second
passages, with flow radially outward and radially inward, respectively.
!
These results suggest that the decrease in heat transfer on low pressure
s High Low
surfaces with trips is dominated by Coriolis generated cross-stream
Pressure Pressure
e_ s flows which cause astabilization of the near-wall flows and that the
q_
heat transfer on the high pressure surfaces is affected by acombination
4.
of Coriolis and buoyant effects. Therefore, it can be expected that the
12 24 36
correlations of local heat transfer data may be substantially different,
x/D
depending onlocal flow conditions (i.e. due to differing near-wall shear
gradients).
b) Leading Surface
8
Z Varying Density Ratio
4 The inlet density ratio, (,_o/p)i, was varied from 0.07 to 0.22 for
this series of flow conditions. The Reynolds number, rotation number
0- "0--0-- and radius ratio were held constant atthe baseline values of 25,000, 0.24
t and 49, respectively. Heat transfer was obtained at a fLxed rotation
number and, therefore, conclusions can be obtained regarding the
effects of buoyancy for flow conditions near the rotating baseline flow
conditions.
E- s
Low High Increasing the inlet density ratio (i.e., the waIl--to-coolam
Pressure Pressure
a) temperature difference) from 0.07 to 0.22 causes the heat transfer ratio
in the fLrst passage to increase on all trailing surfaces by as much as 25
4- t I I I I i percent (Figure 8a) and on the leading surfaces by asmuch as 20percent
0 12 24 36
(Figure 8b). The exception to the general increase in he_ transfer whh
x/D
increasingdensity ratio occurredneartheinlet ofthefirst passage on
Fig. 7 Effect of Rotation Number on Heat the leading side, where the heat transfer ratio is observed tobe relatively
Transfer Ratio; Re-25000, (Ap/p) i--0.13, unaffected by varying density ratio. Heat transfer in the second,inward
R/D-49. flowing passage on the low pressure side increased as much as 70
percent with increases in the temperature difference (Figure 8a). the rotation number to obtain the value of the heat transfer ratio at a
(Larger effects of density ratio were obtained forarotation number of density ratioof 0.0 (i.e., limit asAT approaches 0.0). The heat transfer
0.35.) results obtained from the experiments plus the extrapolated values for
adensity ratio of 0.0 (dashed lines) are presented in Figure 9 as the
_,=rying Rotation Number and Density Ratio variation ofheat transfer ratiowith the rotationnumber with the density
ratio as the secondary variable for three sucamwise locations for the
Additional data from parametric variations of density ratio and
firstand the second passage. The following discussion wi!1concentrate
rotation parameter were necessary to determine the effects of rotation
onthe differences inthe heat transfer fromthe first and second passages.
and buoyancy over the range of interest. The inlet density ratio was
varied from 0.07 to 0.23 forselected rotation numbers. Heat transfer High Pressure Surfaces. Heat transfer results from the high
results from these experiments were plotted vs. inlet density ratio with pressure side of the fwst and second passages isshown inFigure 9a and
rotation number as asecondary variable. The variation of heat transfer bforranges of rotation number and density ratio. Note d.mt no effect
ratio with density ratio (not shown) was extrapolated foreach value of of density ratio on the heat transfer ratiowas expected (e.g. Wagner et
=1.1990) for arotation number of 0when f_m properties are used for
the dimensionless heat transfer and flow parameters, Increasing the
rouaion number causes local increases in the heat transfer in the fwst
Symbol (&%/P)( passages byas much as75percent compared to the heat transfer fora
o 0.07 rotation number of 0. Whereas the heat transfer ratios for the high
• 0.12 pressure surfaces inthe fu_ passage increase sharply with increases in
_. 0.23
either the density ratioorthe rotation number, the heat transfer ratios
in the second passage are less affected (increases of 30to 35percent)
a) TrailingSurface
by variations of either parameter.
s
Low Pressure Surfaces. The heattransfer from the low pressure
surfaces from the firstand second passages (Figure 9a and b) ismore
complex than that from the high pressure surfaces. The heat transfer
d
ratio inthe firstpassage decreases with increasing rotation number for
low values of rotation number (i.e., CID/V < 0.25 at the downstream
location) andthen increases with increases inrotation forlargervalues
of rotation numberdepending ondensity ratio. The heat transfer ratio
increases with increases in the density ratio, similar to the results
obtained for thetrailing surface of the first passage.
High Low
Pressure Pressure
°i The effects of density ratio onthe heat transfer ratioare larger in
the second passage with radially inward flow than in first passage, (a
factorofthree forthe second passage compared toafactor less than two
0 12 24 36 forthefirstpassage) forinletdensity variations from 0.07 to0.23. Note
x/D that thelocal density ratios in the second passage will be about half of
the inlet values.
b) Leading Surface The more complicated heat transfer distni_utions on the low
8
Z pressure surfaces of the coolant passages are attributed to 1) the
combination of buoyancy forces andthe stabilization of the near-wall
4
Z flow for low values of the rotation number and 2) the developing,
Coriolis driven secondary flow cells and 3) the increases in flow
reattachment lengths after trips for the larger values of the rotation
cO
= number. Itispostulated thatthe relatively small effects h'om variations
indensity rationeartheinlet ofthe second passage and the large effects
near the end of the second passage aredue to the development of the
near-wall thermal layers (i.e. thickening for the normal trip model
Low High compared to thinning forthe smooth wall model). Near the inletof the
Pressure Pressure
second passage, the thermal layers are postulated tobe thin because of
_ e
the strong secondary flows inthe fast turnregion. Withincreasing x/D,
4 J = I = I = the turn dominated secondary flows diminish and the counteracting
0 12 24 36 effect ofbuoyancy and theCoriolis generated secondary flow increases.
x/D
Fig. g Effect of Wall-to-Coolant Density CORRELATING PARAMETERS
Difference on Heat Transfer Ratio;
Re-25000, Ro.0.24 ,R/D=49. The analysis of the equations of motion forflow inrotating radial