A Transient Method Using Liquid Crystal for Film Cooling Over a Convex surface

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A

Transient

Method

Using

Liquid

Crystal

for

Film

Cooling

Over

a

Convex

Surface

PING-HEI CHEN*, MIN-SHENG HUNGandPEI-PEIDING

Department_ofMechanical Engineering, National Taiwan University, Taipei 10617, Taiwan

(Received23May2000;Infinalform27May 2000)

Inordertoexplorethe effect of blowingratio on filmcoolingover a convexsurface,the present study adopts the transient liquid crystal thermography for the film cooling

measurement on astraight circular hole configuration. Thetestpiece hasastrengthof curvature (2r/D) of92.5, pitch to diameter ratio (P/D) of 3 and streamwise injection

angle (7) of 35 All measurements were conducted under themainstream Reynolds

number (Red) of 1700 with turbulence intensity (Tu) of3.8%, and the density ratio between coolant andmainstream(P/Pm)is0.98. Incurrentstudy,theeffect of blowing ratio(M)onfilm coolingperformanceisinvestigatedbyvarying therangeof blowing

ratiofrom 0.5 to 2.0. Twotransient tests of differentinjection flow temperaturewere

conductedtoobtainbothdetailedheat transfer coefficientand film cooling effectiveness distributions of measured region. The present measured results show that both the spanwiseaveragedheat transfer coefficient and film cooling effectivenessincreasewith decreased blowingratio.

Keywords: Convexsurface;Filmcooling; Liquidcrystal thermography

INTRODUCTION

Film coolingis a technique of cooling gasturbine

blades to protect them from high temperature

gases. The technique could be used by injection of

afilmof coolingair ontotheblade surfacethrough

discrete holes. These holes are typically inclined

at approximately 30 to 40 with respect to the

surface. Past film cooling studies have

concen-trated on film cooling effectiveness and heat

transfer coefficient of flat surfaces.

However,

the

flow through turbine passages will experience

strong curvature effect, which is not observable

inflow overflat surfaces.

Itoetal.

(1978)

conducted coolingfilm

measure-ments on curved surfaces for a wide range of

blowingratesbymasstransferanalogy. Theyused

a foreign gas injection technique to measure

impermeable wall concentrations downstream of

a row of injection holes and to obtain the

impermeable-wall effectiveness. Their research

showed thatfilm coolingeffectivenessofa convex

*Corresponding author.Tel.: 886-2-23621522 ext11(0), Fax:886-2-23644871,e-mail:[email protected]

surface is higher than both flat and concave surfaces when the tangential component of

injec-tion flow momentum flux ratio

(I

cos2"y)

is less

than unity at injection angle between 0 to 90

.

Ko et al.

(1986)

measured the static pressure and

the film cooling effectiveness of both convex and

concave surfacesat different blowingratios. Their

experimental results suggested that the distance

between cooling holes on the convex surface

should be smaller than those on concave surface.

A

smaller blowing ratio should also be used on

convex surface, because the recirculationis

stron-gerontheconvex surface thanonconcavesurface

even atlow blowing ratio of0.5.

Schwarzetal.

(1991)

usedaforeign gas injection

techniquetostudytheeffects ofstrengthofconvex

surfacecurvature onthefilmcoolingperformance.

They considered three different strengths of

curvature (ratio of radius of curvature to radius

of injection hole), density ratios of 0.95 and 2.0,

and blowing ratios of 0.3 to 2.7. Their

experi-mental results showed that cross-stream pressure

gradient tends to shift film cooling jets onto the

convex surface and away from the concave

surface.

At

low blowing ratio, where both

tangen-tial and normal momenta are weak, the film

cooling on a convexsurface is moreeffective than

a flat surface that has better performance than a

concave surface. Goldstein et al.

(1997)

measured

film cooling effectiveness on both convex and

concave surfaces at different injection angles and

blowingratiosby usingmasstransferanalogy.The

flow field was visualized by an ammonia vapor

injection system. They found that at very low

blowing ratios, the injection flows were ejected

gentlyintothe boundary layer of mainstream, and

the film cooling effectiveness would increase with

blowingratio independently of injectionangle.

As

the blowing ratio is increased beyond the lift-off

blowing ratio

(the

blowing ratio at which the

cooling jets lift away from the surface and

effectiveness begins to drop), the shallower

injec-tion angles perform better. The trajectory of

shallower injection flows being somewhat closer

to thesurfaces than that of steeper injection flows.

Recently, some researchers have predicted the

film cooling effectiveness by numerical method.

Berheetal.

(1999a)

used algebraicrelations forthe

turbulent viscosity and the turbulent Prandtl

number in a modified k-e turbulence model to

study the effects of surface curvature on film

cooling performance. Computations were

per-formed at blowing ratios of 0.5, 1.0 and 1.5 with

a density ratio of 2.0 along convex, concave and

flat surfaces. Berhe etal.

(1999b)

also investigated

the effect of several film cooling parameters

including blowing ratio, injection angle, hole

length, hole spacing and hole staggering. Lin

et al.

(1998)

used a low-Reynolds number

turbu-lence model to investigate film cooling of flat and

convex surfaces. They showed that the injection

flow lift-offphenomenon depends notjust on the

momentum flux ratio but also on the profile of

boundary layer and the ratio of boundary layer

thickness tohole diameter.

According to published studies, the

environ-mental conditions must be well-controlled during

measurements using the liquid crystal

thermogra-phy. Camci etal.

(1992)

investigated the effects of

the strength of the light source illuminating the

heat transfer surface, the orientation of the light

source with respect to the surface, the uniformity

ofcoated liquidcrystal layer,and the repeatability

of the measured results. They suggested that the

image capturing process should beperformedwith

the same illumination angle and the illumination

source should be fixed at a specific location for

both the calibration process and measurement.

Behleet al.

(1996)

showed that the calibration of

camera and light source as the calibration step is

very important to avoid an unreliable hue versus

temperature relation. Besides the hue versus

temperature relations that depend strongly on

the coating thickness, the signal noise versus

temperature relation was compared. They used

both the TLC spray (34gin) and sheets to

investigate the dependence of the hue values on

variation of illumination and viewing angle foran

off-axis and an on-axis camera and light source

Since the film cooling phenomena on curved

surfaces are more complex than on flat surfaces,

the detailed studies on local film cooling

perfor-mance over the whole area of the curved surface

areneeded for theturbineblade design purpose.In

this study, detailed heat transfer coefficient and

film coolingeffectiveness distributions are

demon-strated over a convex surface by employing

transient liquid crystal thermography

(Vedula

and

Metzger,

1991; Ekked et al., 1997a, b and Chen et al.,

1998).

For the present experimental

measurement, thestreamwise injectionangle

(3’)

is

35 and the spanwise injection angle is 0

.

The

blowing ratio

(M)

wasvariedfrom 0.5 to 2.0 at a

mainstream Reynolds number

(Red)

of 1700 with

turbulence intensity of 3.8%, and the curvature

strength

(2r/D)

ofconvex testpiece is 92.5.

THEORY

The present experiment used the thermochromic

liquidcrystalforthesurface temperature

measure-ment. Liquid crystal is very suitable to show the

transientsurface temperature, since theirresponse

is repeatable and their colors can be easily

recorded with a video system. The local heat

transfer coefficient over the liquid crystal coated

surface without cooling film can be obtained by

one-dimensional semi-infinite. The

one-dimen-sional transient heat conduction equation, the

convection boundary conditions, and the initial

condition on the liquid crystal coated surface are:

02T

OT k

-O-z

2 p Cps _O

(1)

OT

h(Vw-T Ti

(2)

at

t=O,

T=Ti

(3)

where k, Cp and p are respectively the thermal

conductivity, the specific heat and the density of

testpiece. The analytic solution of

Eq. (1)

on the

surface

(z

0)

becomes:

Tw-Ti_l_exp(h2ct)

(hV/-)

Tm-

Ti-

erfc k

(4)

The film cooling over a surface involves three

temperatures, including the mainstream

tempera-ture, coolant flow temperature and wall surface

temperature. The mainstreamtemperature

(Tm)

in

Eq.

(4)

will bereplaced by afilm temperature

(T

_f)

during the data analysis. To find the unknown

_TU

(in terms of known quantities

_Tm

and

Tc),

a

nondimensionaltemperature is defined asthe film

cooling effectiveness:

rm

₍₅₎

r-_

Tm

Substituting

Eq. (5)

into

Eq. (4)

gives

exp

(

h2ct

-5--)

erfc

(

hx/

[ rc

+

)rm

(6)

The two unknown parameters are h and r/. In

the present study, two film cooling tests with

different

_Tc

have been completed. During

mea-surements, the temperature rises of both

main-stream and injection flow are functions of time,

insteadof step temperature change.Therefore, the

Duhamel’s Super-position should be used to

modify thetimevarying temperaturerises at inlets

of both mainstreamand injection flows.

Besides the heat transfer coefficient and film

cooling effectiveness, heat flux ratio is another

important parameter used to quantify the film

coolingperformance.The present study adopts the

expression of heat flux ratio as defined by Ekkad

etal.

(1997b)

given by

q_h(Tw-Taw)

h

(1

qo

ho(Tw

Tm)

ho

(7)

where q5 is the overall cooling effectiveness. In

EXPERIMENTAL APPARATUS

AND PROCEDURES

Thetest sectionused for the experimental analysis

ofthe film cooling effectiveness and heat transfer

characteristics is shown in Figure 1. The

experi-mental investigation was conducted in a wind

tunnel with rectangular cross-section of 10cm x

5cm and a bend of 135 The wind tunnel

consisted ofamixsection,auniformdevelopment

section, and a curved test section as shown in

Figure 1. The radii of curvature of the curved

surfaces in the test section was 16.6cm. The

mainstream velocity

(Um)

was kept at a constant

value of9.1

_m/s.

The velocity of mainstream was

measured by a hot-film anemometer

(Dantec,

Flow Master

54N60).

The free stream turbulence

intensitywascontrolled by turbulence grid formed

by cylindrical bars located upstream of the test

section. The free stream turbulence wasmeasured

using a hot-wire anemometer, which was

cali-brated byTSI intelligent flow Analyzer

(IFA-100)

withconstant temperature anemometer operation

method.

Theboundarylayerwastrippedat adistance of

10cm upstream of the leading edge of injection

Heater&Fan TemperatureControl Compressor bypass PC+FrameGrabber+LCIA Flow Flow

_Development!

section HotFilm Thermocouple TurbulanceGrid

Valve Flang-tyleOrifice Step

SonyHi-8

RecoverySection

Flow

Straightener

holesbya 1.5-mm-diatripwire.The injection flow

wasinjectedthroughasinglerowof injection holes

with hole spacing of 3D along the spanwise

direction. The hole diameter

(D)

was 3.6mm and

theratioof hole lengthtoholediameter

(L/D)

was

3.5. The strength of curvature

(2r/D)

and the

streamwise injection angle

(/)

were 92.5 and 35

respectively, as shown in Figure 2. The plexiglas

testsurfacewascoatedwithblack paint andathin

layer of thermochromic liquid crystal. The

emis-sivityofthe black paintis0.94. The injectionflow

was supplied by a reciprocating-type compressor

that hasacapacityofproducinganairflowrateof

0.0018m3/s

at pressure of 7atm.

A

calibrated

flange-type orifice was used to measure the mass

flow rate of injection flow. The injection flow

was heated by heating wires fixed at the inlet of

the injection holes. The distance between heating

wiresand the injection holes is205 mm. The

heat-ing wire diameter is 1.2mm and the ratio of the

distancebetween the wires and the injection holes

to the wire diameter is 170.8. The mainstream

temperature and the initial temperature on test

surface were measured by

T-type

thermocouples,

and a temperature recorder (Rustrak-Ranger

II)

records the time-varying temperatures during

measurements.

The injection flow andmainstream were heated

before the onset of measurement. When the

temperature of injection flow and mainstream

attained the desired experimental temperature,

both injection flow and mainstream were diverted

instantaneously into injection holes and test

section. Meanwhile, the temperature recorder

and Hi-8 video recorded thetemperature histories

of both injection flow and mainstream, and the

color-changing image of liquid crystal.

Color-changing images recordedonvideotapeswerethen

transmitted to a personal computer by a frame

grabber and analyzed using image processing

software. The transient time was taken through

LCIA V3.0 (Liquid Crystal

Image

Analyzer

Version

3.0).

The operating conditions are listed in Table I.

The mainstream velocity measured by hot-film

anemometer was

_9.1m/s

at 25cm upstream of

injection holes. The mainstreamReynoldsnumber

was 1700 based on the inlet diameter of injection

lO.8nnn r’----I r" 7

0-O-

_T

J’ X L J

TABLE Testconditions forthe measured resultsshown inFigure3

Authors P/D

LID

Pc/Pro 2riD 7 I/D M

Goldsteinetal. (1997) 2.96 10 0.95 92.5 45 0.5 1.0

Schwarzetal. (1991) 3 10 0.95 94 35 0.9 1.01

Thepresentstudy 3 _3.5 0.98 92.5 35 0.12 1.0

hole.Themeasured turbulence intensitywas3.8%.

Measurements were conducted at five different

blowing ratios of 0.5, 0.75, 1.0, 1.5 and 2.0.

The estimated uncertainty in the effective data

was

+

5 percentestimatedby theroot meansquare

method by Moffat

(1988).

There are afew factors

that affect the uncertainties ofh and r/, including

mainstream temperature, injection temperature,

initialtemperature, wall temperature., and thetime

of liquid crystalcolorchange. Forthe experiments

done in this study, the total uncertainties of h

and r] were respectively around 7.2% and 10.4%

of their nominal values

(h=29.038W/m2K

and

r/=

0.3232).

Furthermore,theestimated

uncertain-ties for the Reynolds number, blowing ratio,

mainstream turbulence intensity, and boundary

layer displacement thickness were respectively

3.4%, 2.8%, 4.3% and 5.6%. 0.4 0.35 0.3 0.25 0.2 0.15 0.1y 0.05 Coflvex

M=I.0 PrsentStudy Q M=I.0 Goldstein& Stone(1997)

---E]---M=I.01 Schwarz&Goldstein(1991)

o0

5 10 15 20 25

FIGURE3 Comparisonwithprior measured resultsof span-wise averaged film cooling effectiveness over convex surface withsimpleholeconfiguration.

RESULTS AND DISCUSSION

In Figure 3, the spanwise averaged film cooling

effectiveness result is compared with the

experi-mental results of Goldstein et al.

(1997)

and

Schwarz et al.

_(1991).

The present result is

close to the result of Schwarz et al. The lower

values in the result of Goldstein et al. might be

due to the larger injection angle of45

.

Goldstein

et al. stated that shallower injection angles have

the better effectiveness near injection holes on a

convex surface, as show in the comparison result

ofFigure 3.

Detailed distributions of local heat transfer

coefficient ratio

(h/ho)

at four different blowing

ratioof 0.5, 1.0, 1.5 and 2.0are shown in Figure 4

to demonstrate the influence of cooling film on a

convex surface. At blowing ratio

(M)

of 0.5, it is

obvious that

h/ho

increases just downstream of

ConvexSimple Hole M=0.5

4_7;,,,

.,

2

Y/Yo!

(a) xm 4

Y/Yo

o -2 (b)

Convex Simple Hole M=I.0

0 10 15 20 25 X/D h/h ;1.68571 i’i;"::il i.62857 i.51429 1.45714 i.4 1.28571 1.22857 1.17143 1429 1,05714 h/h 1.8 1.74286 1.68571 1.62857 1.57143 1,51429 1.45714 1.4 1,34286 1.2857 1.22857 1.17143 1.11429 1,05714

FIGURE4 Localheat transfer coefficient ratio distributions at(a)M=0.5;(b)M= 1.0;(c)M= 1.5;(d)M=2.0.

ConvexSimple Hole M=l.5

Y/Yo

o -2 -4 10 15 20 25 (c) x/D

Convex SimpleHole M=2.0

Y/Yo

-2 -4 5 10 15 20 25 (d) X/D FIGURE4 (Continued). lffh 1.74286 1.68571 1,628s7 1.51429 1.45714 1.4 !,34286 1,28571 1.22857 1.17143 1.11429 1,05714 h/h 1.74286 1.68571 1,62857

iiiii

57143 1.51429 1,45714 1.4 1,34286 1.28571 1.22857 1.17143 11429 1.05714

injection holes.

Moreover,

high heat transfer

regions around bothsidesof injectionholes,which

may be caused bycounter-rotating vortexpairsat

theexit ofholesisclear too.Therefore,the

h/ho

on

the centerline regions downstream

(3

<

X/D < 8)

ofinjection holes becomes lower than the regions

adjacent toit because the counter-rotating vortex

pairs has brought the hot gas away from the

surface.

The centerline region with

h/ho>

1.8

down-stream of injection hole for M=1.0 is smaller

than at M--0.5,as shownin Figure

4(b).

Because

ofhigher

h/ho

at a low blowing ratio of 0.5, it is

expected that the spanwise averaged value of

h/ho

atM 1.0willbe lower than the valueatM 0.5.

In Figure

4(c),

when blowing ratioincreases to 1.5,

the increased mass of injection flow will increase

the mainstream boundary layer thickness and

decrease

h/ho

at downstream regions of

X/D >

7.

When the blowing ratio is increased to 2.0 as

shownin Figure

4(d),

the

h/ho

atregions between

two injection flows become higher than the

centerline downstream regions of injection holes

due tothe strong interaction of formed horseshoe

vortices between neighboring holes. This

phenom-enon indicates the instantaneous disturbance of

mainstream caused by the injection flows ejected

through film cooling holes.

At

low blowing ratio, the injection flows stay

close to the convex surface because of the lower

momentum ratio. Therefore, the injection flows

increase the surface heat transfer effect onconvex

surface.

As

the blowingratioincreases, the ejected

jets will lift-off the surface immediately after

leaving the injection holes, and form the lower

heat transfer value than M=0.5 even at low

X/D

region.

At

high blowing ratio, the counter-rotating

vortex pairs formed within the ejected jet are

strong. The interactions among the vortices of

neighboring injection flows provide high

h/ho

on

the regions between injection flows. Fric et al.

(1994)

observed that the injection flows will lift away from the wall immediately after the injection

flowsexitthe injection holes because both injection

flowmassflux andmomentumratio are increased

when blowing ratio increases. The horseshoe

vortex will be formed when the mainstream

encounters the ejected jets, and wake vortices will

appear at downstream regions along centerline of

injection holes.

A

reproduction of Figure in the

work of Fric et al. is given as Figure 5. Both

the horseshoe vortex and wake vortices increase

the surface heat transfer. It is shown that

h/ho

at

most regions of M--2.0 is higher than M--1.5

in Figure4 of the present study.

Figure 6 illustrates the effect of blowing ratioon

the spanwise averaged heat transfer ratio

_(h/ho)

for 2.9

<

X/D

<

25. The spanwise averaged results

for regions of

X/D

<

2.9 are not providedin this

work since the one-dimensional heat conduction

model used in data analysis might not be

applic-able to the three-dimensional thermal-fluid

be-havior around these injection holes.

For

X/D >

8,itisobvious that the value of

h/ho

rises at blowing ratios of 0.5 and 0.75, because

injection flows of lowermassandmomentum ratio

will be constrained against the wall by

main-stream. Therefore,

h/ho

is higheratlower blowing

ratio at most measured regions as shown in

Figure 6. The injection flows ejected into the

Counter-rotating

vortex

pair

Jet shear-layer

vortices Horseshoe vortices Wake vortices

Wall

FIGURE5 Cartoon depictingfour typesofvortical structure associated with thetransverse-jetnearfield.(reproductionof Fig. in Fricetal.,1994.) l’l/h 1.8 1.6 1.4 1.2

Convex Simple Hole

M=0.5 M 0.75 M 1.0 M=l.5 M=2.0 0 5 10 15 20 25

FIGURE6 Effect ofblowingratioonthespanwise averaged

heat transfer coefficient.

mainstream boundary layer thickness. This effect

of increasingboundary layerthickness willbecome

more obvious as the blowing ratio increases, and

therebydecreases the

_h/ho

at

X/D >

8.

As

blowing

ratio is increased to 2.0, the injection flows of

relatively high momentum tend to lift-off the

convex surface after injection. Each injection flow

becomes an inclined cylinder for the mainstream.

Hence,

a horseshoevortex will be formed around

the injection flow and also wake vortices will be

induced (Fricetal.,

1994).

The interactions of the

horseshoe vortices among the injection flows are

strong and willincreasethe surfaceheattransferat

regions between holes.

Moreover,

the wake

vor-tices will increase the surface heat transfer at

regions downstream of holes. Therefore, the

_h/ho

at mostmeasured regionsincrease asblowingratio

is increased to2.0.

At

low blowing ratio, Goldstein and Stone

visualization results. In curved flows, a

cross-stream pressure gradient that holds low

momen-tum fluid particles against the convex surface

exists. The effect on the mainstream boundary

layer is to suppress mixing and entrainment in

the convex surface boundary layer. Therefore,

on the convex surface, injection flow ejected at

low blowing ratio stays close to the surface and

remains in-line with the injection hole.

Figure 7 shows the detailed distributions of local

filmcoolingeffectiveness

(r/)

atM 0.5 toM--2.0.

At blowing ratio of 0.5, the injection flows stay

close to the convex surface and block the

main-stream from the surface, thereby increasing the

film cooling effectiveness gradually as shown in

Figure

7(a).

The protection of the injection flows

on the convex surface against the hot gas is

decreasing with increased blowing ratio. When

blowing ratio increases to 1.0, the film cooling

effectivenessof regions between holes becomes less

than 0.05 for 3

_<X/D<

10. The regions with

r/<0.05 extends to

X/D’

14 at blowing ratio of

2.0, as demonstrated in Figure

7(d).

The

momen-tum flux ratio demonstrates the cause of the

injection flows leaving theconvexsurfaceathigher

blowing ratio. The large normal component of

Convex

Simple Hole M=0.5

Y/Yoo

(a) x

Convex

Simple Hole M=I.0

Y/Y

i

(b) X/D 0,6 0.557143 0.514286 0.471429 0.428571 0.385714 0.342857 0.3 0.257143 0,214286 0.128571 0.0857143 0.0428571 0,557143 0.51428 0,471429 0,428571 0,385714 0,342857 0.3 0.257143 0,214286 O, 171429 O, 12857 0,0857143 0,0428571

FIGURE 7 Local film cooling effectiveness distributions at

(a)M=0.5;(b)M--1.0;(c)M= 1.5;(d)M=2.0. 4 2

Y/Yoo

-2 (c) 4 2

Y/Yoo

-2 0

ConvexSimple Hole M=1.5

10 15 20 25

ConvexSimpleHole M=2.0

10 15 20 25 0.471429 0.385714 0.342857 0.257143 0.214286 128571 0o0857143 0.0428571 0.557143 0.471429 0.428571 0.385714

i

0.342857 0.257143 0.214286 0.171429 O. 128571 0.0857143 0.0428571 FIGURE 7 (Continued).

momentum of injection flows

(I

sin27)

pulls the

injection flows away from theconvex surfaceand

degrades the film cooling effectiveness on the

surface. Although the increase in mass per unit

area at higher blowing ratio tends to increase r/,

theeffectof decreasing

r/caused

by strongvortices

willbe more severe.

The results of spanwise averaged film cooling

effectiveness

(/)

at various blowing ratios are

shownin Figure 8. Itis shown that decreasesas

blowing ratio increases.

At

blowing ratio of 0.5,

the spanwise averaged effectiveness is the best

among all tested blowing ratios.

At

downstream

regions, mixing with the mainstream dilutes the

injectionflows,thereby lower

/obtained.

Also, the

lower injection flowmassflux of injectionflow for

M=0.5 causes the steep descent in /at

X/D >

8.

In general, higher blowing ratios produce

in-creased massper unit area, largermomentum but

greater jet penetration. Increase of mass can

increase the spanwiseaveraged film cooling

effec-tiveness at downstream regions and provide an

even film coverage along

X/D. As

shown in

Figure

7(d),

at blowing ratio of2.0, the increase

of r/ for

X/D >

15 at regions between injection

flows shows that the reattachments of injection

flows have occurred, so increasing the / far

0.5 0.4 0.3 0.2 0.1

00

Convex Simple Hole

M=0.5 M 0.75 M--1.0 M=l.5 I, 10 15 20 25

FIGURE8 Effect ofblowingratioonthespanwise averaged

filmcoolingeffectiveness.

q/qo 1.8 1.6 1.4 1.2 0.4 0.2

Convex Simple Hole

M=0.5

M=0.75

M 1.0 M=l.5

O0

5 10 15 20 25

FIGURE9 Effect ofblowing ratio on the overall heat flux ratio.

Forthe filmcooling effectiveness, Schwarzetal.

(1991)

noted that the effect of cross-stream

pressure gradient greatly overshadow the effects

of the normal and tangentialmomentumof the jet

atlow blowing ratio, therebypushing the injection

flows onto the convex surface. Farther

down-stream, at low blowing ratios, mixing with the

mainstream dilutes the coolant gas and then /

degrades. Berhe and Patankar

(1999b)

mentioned

that thepairs ofcounter-rotatingvortexwould be

stronger athigh blowingratios. Thisphenomenon

causes the decrease in / because the pairs of

counter-rotatingvortexliftthe injection flow away

from the surface and entrain the hot gases from

the surroundings to the surface. For the present

study,apair ofcounterrotatingvorticesobviously

decreases when M

>

1.0.

The film coolingperformance oftest surface is

best indicated by the result of spanwise averaged

heat flux ratio shown in Figure 9. The

q/qo

of

values lower than 1.0 at low blowing ratio

indicates better film cooling performance.

At

M-0.5 and 0.75, the injection flows reduce the

heat flux ratio effectively over most measured

regions because the low normal momentum of

ejected injection flows tendtoleadthe flows tostay

close to the surface. But the low mass flux of

injection flowsisunable toprovidefilmprotection

atfurtherdownstream, and thereforeincreasesthe

magnitude of

q/qo

at

X/D >

9. WhenMis further

increased to 1.0, 1.5 and 2.0, both the increased

normal momentum and counter-rotating vortex

pairs will promote lift-off and therefore perform

poor protection just after injection. Furthermore,

at downstream of

X/D-12,

the value of

q/qo

at

M=1.0 is larger than the value at M--1.5. This

phenomenon reveals the effect of higher mass

flux on surface protectionat downstream regions.

As

a summary, at high blowing ratio, the high

normal momentum of ejected injection flow

promotes lift-off phenomenon and degrades the

protection on the convex surface. For the tested

convex surface in the present study, the low

blowing ratio of 0.5 shows the best film cooling

performance.

CONCLUSIONS

The present study demonstrates the influence of

blowing ratio on convex surface film cooling

thermography, the film cooling performance ofa

convex surface(2riD

92.5)

with a rowof straight

circular holes

(7=

35 was investigated.

Experi-mental results show that high blowing ratio has

adverse effect on film cooling performance.

At

high blowing ratio, the injection flows will lift

away from the surfaceand willalso reducethe film

cooling effectiveness on the convex surface.

How-ever, the largermass of injection flow ejected into

the mainstream at higher blowing ratio causes

adjacent injection flows to merge far downstream

of injection holes and increases the film cooling

effectiveness. In the present study, injection flows

are not able to offer better protection on the

convex surface when M> 1.0. For the tested

convex surface in the present study, the optimum

blowingratio isfoundto be 0.5 among the present

tested blowing ratios.

Acknowledgment

The authors deeply appreciate the financial

sup-port by NSC under the grant number

86-2212-E-002-080. The work in this study could not be

achieved without their support.

NOMENCLATURE I L M P q qo

D injection holediameter ontheinletplane

[m]

h heat transfer coefficient with film injection

[W/mZK]

ho

baselineheat transfercoefficient without film

injection

[W/mZK]

momentumflux ratio

.

2

OcUc

/

OmUm

length of injection hole

[m]

blowing ratio DcUc/pmUm

pitch ofinjection holes Ira]

heat flux per unit area

[W/m

]

baseline heat flux perunit area without film

injection

[W/m

2]

r radius ofcurvature ofconvex surface

[m]

Red

mainstream Reynolds number based on the

inlet dia-meter ofinjection hole pmumD/ll,

Y

time

[s]

temperature

[K]

mainstreamturbulence intensity

[%]

velocity

[m/s]

axial distance from the center of injection

hole

[m]

spanwise coordinate from the center of

injection hole

Ira]

coordinate axis perpendicular to the test

surface

[m]

Greek Symbols

thermal diffusivity of testsurface

[m2/s]

displacement thickness

[m]

overallfilmcoolingeffectiveness

(Tw- Tm)/

injection hole angle with respect to the test

surface as projected into the

streamwise/

normal plane (inclinationangle) [deg.]

filmcooling effectiveness

spanwise averaged film cooling effectiveness

dynamic viscosity of mainstream [kg/ms]

density [kg/m

3]

Subscripts

c coolant flow ejected from the injection hole

rn mainstream

s testpiece

w surface oftestpiece

initial condition

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