of the p International
Dynamics of Rotating Machinery,
Proceedings

NUMERICALGAS

Symposiumofi Transport Phenomena
ISROMAC- g, VoL iI, Mad
too0

STUDY
TURBINE

KazuyaON ADVANCEDBLADES
WITH

Tatsumi,Hiroshiand

INTERNAL
COOLINGRIB TURBULATORS

Iwai

and

KenjiroOF

Suzuki

Departmentof Mechanical Engineering
Kyoto University
Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501,JapanFax : 81-75-771-7286,
E-mail : tatsum28@htrans.mech.kyoto-u.ac.jp

Kyoji

InaokaDepartmentof Mechanical and Systems Engineering
Doshisha University
Kyotanabe, Kyoto 610-0321,JapanFax : 81-774-65-6802

KEY

WORDS:

Rib

Turbulators,

Numerical

Analysis,

ABSTRACT
Many studies
have been carriedout over turbulent
flows in a ribbed channel.
However,flow structureand
its related
heat transfer
have not still been clarified
indetail. The present study showsa three-dimensional
numerical work on full-spanribs and interrupted
ribs to investigate
the local fluid and heat transfer
characteristics.
Eventually,
the rib having gaps in the spanwise
direction
generates
vortices
downstream
and showeda higher performancecomparingto the full-spanrib. Especially,therib with a gap in the middle is suggested
to be best in
performancefor cooling the duct sidewalls
effectively.

INTRODUCTION
Becauseof its high efficiency
comparedto those ofother power generating
systems,
advanced
gas turbines
are consideredeffective
to reduce
CO2
emission
andtherefore
to give a remedy
for global warming
and tosave naturalenergy resources.
In order to increasetheefficiencyof the gas turbine
cycle. as is well known,
itis necessary
to raise the inlet gas turbine
temperature,
the temperatureof the gas flowing
into the turbine.
Onthe other hand, a serious
fracture
problemis caused in
the high temperature
condition
for the materials
of gasturbineelements,
especiallyof the turbine
blades.
The
rib turbulators
are well known
to be effective
to enhance
the convective
heat transfer.
Therefore,
they are widelyused for internalcooling,or for the coolingpassage,ofthe gas turbine
blade.
Many studies
have been carriedout over heat transfer in ribbed channels
for various
types of ribs. Discrete

800

Heat

Transfer,

Vortices.

ribs and V-shaped
ribs have been reported
to increase
heat transfer
comparingwith the full-spanribs(Lauetal., 1991). Ribs placed in various angles under the condition of rotating
channels,
have also been studied experimentally(Zhang
et al.1994; Dutta et al., 1995). However,the fluid and heat transfer
characteristics
of turbulated
flows with such ribs have not been studied in detail andfurther
researchworks
on those topics are necessary.
To effectively
enhance the heat transfer
with the rib
turbulators,
it is important
to investigate
the structureofflow and related thermal
fields in the rib-attachedchannel. Basically,
rib turbulator
evokes separation
and reattachmentof the flow.
As is well known,
flow reattachment causes noticeable
spatial variationsof the local heattransfercoefficient.
On the other hand, interrupted
rib
turbulators,
which have gaps in the spanwise
direction,
show a significant
difference
from the full-spanribs inthe characteristicsof fluid flow and heat transfer.
This
is related to the existenceof the gaps. lry which the secondary flow. such as vortices,
are generated
downstreanl
the rib. Combinationof the flow reattachment
effect andthe secondary
flow effect makes the phenomenon
complicated but, is worth to analyze in order t,o establish
bett.erinternal
cooling of gas turbine
blades.
Furthermore,theratio of the gap width
and the duct width
is an essential
factor affecting
the performanceof the interrupted
rib inrelationwith the secondary
flow effect mentioned
above.
For this reason: it should be importantto analyze systematically the total performanceand the Huid and thermal
characteristicsof the ribs for various geometry.
In the present study, three-dimensionalulationis carriedout for the duct How

numerical
simwith a rib tur-bulator
attachedon its bottom
wall.
The structureofturbulentflow and related thermal
fields will be studied
and eventuallysome suggestion
will be developed
for theimprovementof the efficiency of the related heat transfer.

.

COMPUTATIONAL

PROCEDURES

Time-averaged
forms
momentumand energy
merical computations.

of three-dimensional
equations
are solved

continuity,in the nu-

Wd

(a)

DP
g3
E
= -p ( ax, >
DpLA
-=
Dt

.

Hd

Full-span(FS)

rib

(2)

DPO
-=
D1

--

- Pa-

)

in orderto calculatetheFor turbulencemodel.
Reynolds
stressin eq.(2),the /c-c model proposedbyLaunderand Sharma(Launderand Sharma,
1974) isadopted.
Furthermore,
the correction
term introduced
by Yap(Yap,
1987) is attachedinto the dissipation
equation of this model.
In this computation,
turbulentheatflux is assumed
to be proportional
to the temperature
gradient,
i.e.

-

-u,Q

=

l!Lprtaeax,Turbulent
Prandtlnumberwas assumed
to be constantand Prt = 0.9.
Fully implicit
forms of finite difference
equivalentsofthe above mentioned
equationswere solved numericallyalong the time axis. For the finite-difference
methodofthe governing
equations,a forth-order
central-difference
scheme was employed
for the diffusion
terms while thefifth-order
upwindschemewas employed
for the convection
terms in the case of momentum
equation.
Inthe energy equation and in the two turbulencetransport
equationsof /c and E, a first-order
upwindscheme wasadopted for the convection
terms and a central-difference
scheme for the diffusion
terms.
For the solution
algorithm adopted for the pressure
equation,
SIMPLE
algorithm was employed.
In order to relax the solutionsofthe above types of elliptic differential
equations,
iterative
procedure
was applied at each time step. In this procrdure, alternating
direction
implicit(ADI)
methodwasalso combined.
The computational
domains in the present study are illustrated
in Fig. 1 together
with the coordinate
system to
be used. Three types of ribs were investigated,which are;(a) a full-spanrib (hereinafterreferredas FS rib), (b) arib having gaps at both side ends (hereinafterreferredasSG rib) and (c) a rib having a gap at middle(hereinafterreferred as MG rib). The origin of the coordinate
systemis located at the center of the rear bottom
corner of therib. The inlet to the domain was located at about ten ribheights (10H) upstreamof the front rib surface,where afully developed
turbulentflow was assumed
to flow in.
Inlet flow conditions
were establishedby a preliminary(b) SG rib(gaps
at bothsides)
Figure1 Computational(c) MGrib(gap at middle)
domain.

computation
for a 3-D duct flow. The outlet of the computational
domain was located at about thirty rib height.s(30H)
downstream
the rib, where gradientsof all var:iables (except
pressure)
in the direction
normalto theoutlet surface were set equal to zero.
The present investigation
was made for three different
levels of Reynolds
number at 10,000 to 20,000 and parameter study was made for rib width to duct width
ratio forthe interrupted
rib. The gap width
to duct width
ratios(lV~/Cl/d)
were changed in three style 0.25, 0.2 and 0.15
for SG rib and were 0.5, 0.4 and 0.3 for MG rib. The
rib height to duct height ratio (H/Hd)
was set equal toto unity, i.e. a
0.15 and the aspect ratio (AR=Hd/CVd)square shaped duct, for all computations.
For boundary
conditions
at walls, all variables
excepttemperature
were set equal to zero.
For the thermalboundary
conditions,
all walls including
the rib surfaces
were set constantin heat flux throughall the computa.tions.
RESULTSANDDISCUSSION
3-D simulations
for FS rib
Fundamental
characteristicsof the two-dimensional
flow with a rib turbulator
are well discussed
and knowledge were acquired
for flow separation
and reattachment.
However,study
has not fully been made for the effect of
the sidewall,
which inevitably
exists in the cooling of gas
turbineairfoil.
In this section, results of 3-D calculations
are reported
to investigate
the three-dimensional
effectof the sidewalls
on the flow and thermal
fields.
For all three conditionsof different
values of Re, theflow structure
showed similarity
except that the reattachment location
shifts downstream
as Re increases
in therange from s/H=9.3
to 10.6, if measured
at the centerline. Here, the case of Re=20,000 is discussed
to demonstrate
the local fluid and thermal
characteristicsof therib turbulator.
Figures 2 and 3 illustrate
the distributions
respective1.yof the skin friction
coefficient,
Cl and the Nusselt

80 ‘I

-5

10

5

0

15

-0.02

xm

Figurewall.

2 Skin Friction(Re=20,000)

coefficient,

Cf at bottom
30

0.5

go.0

-0.5

-5

0

Figure3 Nusselt

5
number,

10
Nu

xlH

15

0

at bottom

wall.

(Re=20,000)
-5

0.5

0

10

Figurewall.

5 Skin friction(W~/Wd=0.25,

15xm(c)WG&=0.15

coefficient,
0.2 and 0.15,

Cf at bottom

Re=ZO,OOO)

-00
*-

-0.5
-01234&012345
Figure4 Velocity
vectors
and turbulence
neticenergycontours
nearbottomwall.
plane,
Re=20,000)

xlH

m/s;2

number,Nu on the bottom
wall of the duct.
For Cf,the shaded parts
correspondto the area of its positivevalue
while the whiteparts to its negativevalue. Threedimensional
effect of the sidewall
is observed
both in thereattachment
region and flow recirculating
region bothat, the front and backsideof the rib.
Especiallyfor theregion just downstream
the rib, wall effect. is obvious
and the local heat transfer
shows
a distinctive
deterioration near the sidewalls.
This lower heat transfer
performanceis caused by the tornado
likeverticalvortices
generated
at, such positions.
Figure4 shows
the velority vectors
and turbulenct~kinet,ic energy contours
in aplane of y/N=O.03
near the bottom
wall.
These vortices are producedI)y the combined
effects of the reverse
flow in the central region toward
upstreamfrom the reattachment
point and the downward
inclinationof the flow
passing the rib near its side ends. Kinetic
energy of the
turbulenceis small at the center of these vortices,which
causes the low heat transfer
efficiency.
3-D0ki(z-zsimulationsfor SG rib
Variousreports
indicatedthat the interrupted
rib turbulators,
ribs having gaps at both ends, increase the heattransfer
efficiency
and total performance(Lau et al.,-50(a)Wo ii d ~0.25

10

xlH

15

10

x/H

15

(c)w&d=o.15

Figure6 Nusselt
number,Nu at bottom(LZ’c/ll/h=0.25,
0.2 and 0.15, Re=20,000)

wall.

1991; Balatka
et al., 1997).
In this section,
resultsof
3-D calculations
are reported
for the ribs having gaps at
both ends under three different conditionsof changing the
gap width
to rib width
ratio, i.e. W’~/Wd=0.25,
0.2 and0.15. Reynolds
number was also changed in three stepsof Re=lO,OOO,
15,000 and 20,000.
Actually,
Reynolds
number
did not show a large influence
to the basic flow
structureitself except that the positionof theFigurecontours.

tlwd
z/wd
7 Velocity
vectorsandtemperature(y-z plane,
W~/W’d=0.25,
Re=20,000)

Lreattachment
point moved
downstream
as Re was increased.
This was also the case of FS rib. In the caseof Re=lO,
000, unsteadinessappearedin the calculationfor each gap width
to rib width
ratio so that time averagevalue was taken for its results.
Figure5 and 6 illustratespatialdistributionof C,
and NILon the bottom
wall of the duct for the casesof CZ’~/Ct’d=0.25,
0.20 and 0.15 and at Re=20.000.
Asseen from the comparison
with the results for the FS rib,
flow and thermal
fields differ largely due to the gap existence. The reattachment
point is located upstream
thanthat of the FS rib and the size of the recirculation
regionis reduced.
Distribution
of NIL is symmetricwith respect
to the duct centerline.
High Nu region elongated streamwisely
appears
at positions
offset from the duct centerline. High heat transfer
in this region is producedby thedownwashflow appearing
in relation
withtwo pairs oflongitudinalvortices.
These vortices
are observedin Fig. 7 which shows thevelocity
vectors with temperature
contours
for the caSe of
CVG/IZ’D=O.~~,
Re=20,000
in cross-sections
at the locations of x/ H=5 and xfH=lO.
The downwash
flows produced by the clockwise
vorticesconveysthe cooler flowfrom above toward
the bottom
wall and brings about
large value of NIL. Furthermore,anti-clockwise
vorticesare generated
in the cornersof the duct.
Upwashflows
producedby these vortices
pump up hot fluid producedby the heated wall. Heat transfer
coefficients
is found tobe smaller
there as shownin Fig. 6.
Reverseflows also exist on the duct sidewalls
downstream
the gaps, where
CI takes negativevalue. whichis indicatedby the whit.e parts in Fig. 5. This reverse
flow did not appear in the case of FS rib and is related
to the flow passing the gaps and to the longit.udinalvortices.
The height of this reverse
flow region was about
the salue as the rib height.
By this reverse flow, the local
heat transfer
shows deteriorationnear it.s area especiallyon the duct sidewalls.
This matter
will be discussed
inthe next section
togetherwith the resultsof FS rib andhIG rib.
3-D

Simulationsfor MG
Rib
Study
is now made for the characteristisof the fluid
and thermal
fields of the case with a rib turbulator
havinga gap in the middle.
Gap widthto duct width
ratio hasbeen changed in steps. i.e. W~/Wd=0.5,
0.4 and 0.3 andthe Reynolds
numberalso in three steps of Re=lO, 000,

“..,

-5
Figure
wall.

0

10
15
(C)Wc+nz~ =0.3
8 Skin friction
coefficient,
Cf at bottom(wc/wd=O.5,
0.4 and 0.3, Re=20,000)

0.5

$0.0

-0.5
-5

0

xM

15

Figure9 Nusselt
number,Nu at bottom(\\“G/\ih=0.3,
0.4 and 0.3, Re=20,000)

wall.

(c)WQ/&=0.3

1001.5000 and 20.000.
Flow unsteadiness
was observed
inthe low Reynolds
number case of Re=lO, 000. However,
if comparing
the time average characteristicsof flow andthermalfields, difference
was found to be small among
the three cases of different
values of Re.
Figures
8 and 9 show the distributionsof Cf and Nu
on the bottom
wall of the duct for all three cases ofwG/Lvd=O.5.
0.4 and 0.3 at Re=20,000.
Cl takes negative value in the reverse flow region observed
both in front

80:3

and behind the ribs. Flow circulationand tornado
type
vortices
appear there.
At the position
where these vortices sit, low heat transfer
occurs due to slow time mean
flow and the low kinetic turbulenceenergy.
Reverse flow
also appears
aroundthe centerline
near the duct bottom wall, where C, takes negative value and Nu smaller
value. At the conditionof ll’~/ll>=O.3,
this reverse flow
is observedin one single area aroundthe center.
However, as the ribs width
are reduced and the gap at thecenter increases,
the reverse flow regions appear in a pairon both sides of the centerline.
On the other hand, high heat transfer
efficiency
isobtaineddownstream
the ribs near the duct sidewalls
where downwash
flows generated
by the vortices
exist.
Cross-sectional
flow structure
relatedto these vortices
is shown in Fig. 10 as a velocity
vector map superposedwith temperature
contours
at two locationsof x/H=5
and x/H=lO.
It is seen that cooler fluid is directed downwards to the duct bottom
surface near the corner regionof the duct.
Distributionof Nu on sidewall
is shown
in Fig. 11 forFS rib, SG rib(W’~/W’~=O.l5)
and MG rib(&‘c/Wd=0.3)
for Re=20,000.
For FS rib, large value of Nu is observed
at several parts downstream
the rib along the streamlineof the flow passing over the rib edge. On the other hand,
low heat transfer
efficiency
is obtainedin a higher regionof y/Hd 1 0.3. For SG rib, Nu distribution
shows smallvalue near the bottom wall downstream
the rib. This lowheat transfer
performanceis related to twofold.
First isthe warmer
upwashflow sweeping
the sidewall,
which
is producedby the counterclockwise
vortices
located at
the bottom
cornerof the duct.
Second is the reverse
flow at the duct sidewalls
downstream
the rib mentioned
in the previous
section.
In the case of MG rib, large
NU distribution
is observedin a wide area aroundandfurtherdownstream
the rib. This high heat transfer
performancedownstream
the rib results from the downwash
flow sweeping
the sidewalls
producedby the clockwise
vortices
appearingnear the bottom
corner of the duct.
Comparisonsof heattransfer

efficiency

In the previous
three sections,
fluid and heat transfer
characteristics
were investigated
for three different
kinds
of ribs. It is important
to make a further
study on the
total heat transfer
efficiencyof each rib case to thermally
optimizethe designingof gas turbine
blades.
Figure12 shows
the spatiallyaveragedof Stanton
number,St for whole surfaceof the duct and the rib
walls in the Reynolds
numberranged from Re=lO,OOO
to Re=20,000.
Comparing
the three different
kinds ofribs, it is indicatedhere that for all Re numbers,
MG ribshows the highest heat transfer
among the three.
Table 1 shows the spatiallyaveragedvalue of Nu forall surfacesof the duct and rib walls and the pressure
drop coefhcientlC, calculated
over the distance
betweenx/H=-5and x/H=15.
Also the efficiency,
n calculatedby Nu/C,is indicatedin the table and also in Fig. 13. As
mentioned
above, MG rib shows slightly
but distinctively
larger Nu value comparing
with the other two ribs. This

804

-0.5
Figurecontours.

10

fld
0.0

0.5-0.5

Velocity(y-z plane,

vectors

0.0
and

0.5

IO
Co

temperaturme

Wc/Wd=O.5,

Re=20,000)

1.0

0.0
-5

0

(a)FS ,5b

10

x/H

15

1.0

$0.5

0

t?b
(b)SG

15

=dp,)
(w&,,,

flgo.5

0Figure11 Nusselt
SGfor
FS rib,rib(Wc/Wd=0.5).

(c)MG:bw

w

number,rib(WG/Wd=0.15)

=C%)

Nu

x/H

at

15

sidewallandMG

can be explainedby comparing
the heat transfer
coefficient for each divided
parts of the duct wall surfaces
among the three types of the ribs.
On the bottom
wall, especiallydownstream
the rilbs,
the spatiallyaveragedvalue of Nu showeda larger value
for h’l(: rib than for the other two ribs, FS and SG rilbs.
The reason of this is twofold.
First the vortices
generatedby the RIG rib cover and cool the bottom
wall widely.
Second by downwash
flows produced
accompaniedwilth
the longitudinalvortices
reducesthe space of the flow recirculation.
where low heat transfer
is obtained.
.4t theduct sidewalls,
the average Nu there shows a larger value
for the MG rib than for the other two ribs. For example,
Nu,=9.2,
9.4 and 11.2 for FS rib, SG rib(l2’G/Wd=0.15)
and MG(W~/W’~=0.5)
rib at Re=20,000,
respectively.
This is related to the downwash
flow sweeping
the sidewalls accompaniedwith the vortices.
Moreover,considering
the C, and 7, interrupted
ribswith gaps shows a fairly higher efficiency
comparingwith15000
Re

10000

Figure12 Stanton

20000
number,St.

sidewall.
Especiallyfor the ribs with gaps,of the duct
the flow showed
a complicate
three-dimensional
flow andthermalstruct,urecaused l,y tile gaps.
For these interrupted
riles. vortices
are generated
from
the gap side edges and the do\vvllwash
flow appearing
accompaniedwithvorticesincreased
the heat transfer
atthe bottom
wall and at the sidewallst,oo for MC rib.
The area of flow recirculation
region is also reducedbythis downwash
flow.
In this relation,
MG rib showed
the highest heat transfer
efficiency
among the three ribs.
Considering
the pumping
power, the interrupted
ribs exhibit a fairly efficiency
comparingwith FS rib
Nomenclature

Table

1 :

(Re=20,000)
Hd, H = duct
W’G

AR

= 2,

aspectD = ducthydraulic

Re = F,I[ 10.4
1 10.6

MG rib iW’ijlVi=0.4j
MG rib (IQ’c/Clh=0.3)

1.19
1.41

10.2
7.5

14
12
10
6

1

(a) SG (bk%h+.25)@) SC (M /wd =0.20)(c) SG (W~&%!j=o.l5)(4 MG (%Iwd=o.5)(e) h% (wG/wd =0.4)(t) MG (wG/wd
=0.3)

F6
4
2

n
20

f4 (W (“1’!d) (e) (?
SG

FigureribMG

13 Efficiency,

rib~=NuIC,.

the FS rib. This is strongly
related to the gap existence
where the main flow is possible to pass through.
From the discussions
made above, the interrupted
ribs
show higher efficiency
under a constant
power or pressure loss comparing
with the FS rib. EspeciallyhlG rib
indicates
the largest total heat transfer
efficiency.
Mrhat
is more, is that the hlG rib is also effective
to cool theduct sidewalls
and is practical]!:available for cooling air
passages in the internal cooling of the gas turbine
blades.
CONCLUSION
Three-dimensional
numerical
computations
for a flow
over rib turbulators
were carried out for the cases of threedifferent
kinds of rib geometry.
The Reynolds
numberwas changedin thr range from Re=lO, 000 to 20,000
and the gap width
to duct width
was changed
for theribs having gaps in the spanwise
direction.
The results
obtainedfrom the computations
revealed a strong threedimensionalityof flow and thermal fields due to the effect

=

and

Wd,

duct

rib height, mand gap width,m
ratio
dimater:

Reynoldsmnumbermean Nusselt
numberp t,>H[X(T*.,-T,,)]’
‘211,
mean
Stantonnumber
St = [pC,,L’,el(T,,I-T,))l’mean skin friction
coefficientc, =bU,:;W
Tut = wall shear stress, N/m2
9 - wall heat flux, L+‘/m2
Tz,>o= wall and inlet Temperature,K
p = densityof air, Kg/m2
cp = heat capacity
at constantpressure,
J/KgK
X = fluid thermal
conductivity,
L+‘/rnKmean velocity,m/sU,,f= inlet freestream
Prl = turbulent
PrandtlnumberNu=

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1987, PhD Thesis,
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R.D. and Han, J.C. 1991, Turbulent
Heat Transfer
and Friction
in a Square Channel with Discrete Rib Turbulators,
ASME
Journalof Turbomachzncry, Vol.
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805