Transient Liquid Crystal for Film Cooling Over Convexdownloads.hindawi.com/journals/ijrm/2001/590527.pdf · 2019-08-01 · important parameter used to quantify the film coolingperformance.Thepresentstudyadoptsthe

International Journal of Rotating Machinery2001, Vol. 7, No. 3, pp. 153-164Reprints available directly from the publisherPhotocopying permitted by license only

(C) 2001 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach Science

Publishers imprint.

A Transient Method Using Liquid Crystalfor Film Cooling Over a Convex Surface

PING-HEI CHEN*, MIN-SHENG HUNG and PEI-PEI DING

Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan

(Received 23 May 2000; In finalform 27 May 2000)

In order to explore the effect of blowing ratio on film cooling over a convex surface, thepresent study adopts the transient liquid crystal thermography for the film coolingmeasurement on a straight circular hole configuration. The test piece has a strength ofcurvature (2r/D) of 92.5, pitch to diameter ratio (P/D) of 3 and streamwise injectionangle (7) of 35 All measurements were conducted under the mainstream Reynoldsnumber (Red) of 1700 with turbulence intensity (Tu) of 3.8%, and the density ratiobetween coolant and mainstream (P/Pm) is 0.98. In current study, the effect of blowingratio (M) on film cooling performance is investigated by varying the range of blowingratio from 0.5 to 2.0. Two transient tests of different injection flow temperature wereconducted to obtain both detailed heat transfer coefficient and film cooling effectivenessdistributions of measured region. The present measured results show that both thespanwise averaged heat transfer coefficient and film cooling effectiveness increase withdecreased blowing ratio.

Keywords: Convex surface; Film cooling; Liquid crystal thermography

INTRODUCTION

Film cooling is a technique of cooling gas turbineblades to protect them from high temperaturegases. The technique could be used by injection ofa film of cooling air onto the blade surface throughdiscrete holes. These holes are typically inclinedat approximately 30 to 40 with respect to thesurface. Past film cooling studies have concen-trated on film cooling effectiveness and heattransfer coefficient of flat surfaces. However, the

flow through turbine passages will experiencestrong curvature effect, which is not observablein flow over flat surfaces.

Ito et al. (1978) conducted cooling film measure-ments on curved surfaces for a wide range ofblowing rates by mass transfer analogy. They useda foreign gas injection technique to measure

impermeable wall concentrations downstream ofa row of injection holes and to obtain theimpermeable-wall effectiveness. Their researchshowed that film cooling effectiveness of a convex

*Corresponding author. Tel.: 886-2-23621522 ext 11(0), Fax: 886-2-23644871, e-mail: [email protected]

153

154 P.-H. CHEN et al.

surface is higher than both flat and concavesurfaces when the tangential component of injec-tion flow momentum flux ratio (I cos2"y) is lessthan unity at injection angle between 0 to 90.Ko et al. (1986) measured the static pressure andthe film cooling effectiveness of both convex andconcave surfaces at different blowing ratios. Theirexperimental results suggested that the distancebetween cooling holes on the convex surfaceshould be smaller than those on concave surface.A smaller blowing ratio should also be used onconvex surface, because the recirculation is stron-ger on the convex surface than on concave surfaceeven at low blowing ratio of 0.5.

Schwarz et al. (1991) used a foreign gas injectiontechnique to study the effects of strength of convexsurface curvature on the film cooling performance.They considered three different strengths ofcurvature (ratio of radius of curvature to radiusof 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 pressuregradient tends to shift film cooling jets onto theconvex surface and away from the concavesurface. At low blowing ratio, where both tangen-tial and normal momenta are weak, the filmcooling on a convex surface is more effective thana flat surface that has better performance than aconcave surface. Goldstein et al. (1997) measuredfilm cooling effectiveness on both convex andconcave surfaces at different injection angles andblowing ratios by using mass transfer analogy. Theflow field was visualized by an ammonia vaporinjection system. They found that at very lowblowing ratios, the injection flows were ejectedgently into the boundary layer of mainstream, andthe film cooling effectiveness would increase withblowing ratio independently of injection angle. Asthe blowing ratio is increased beyond the lift-offblowing ratio (the blowing ratio at which thecooling jets lift away from the surface andeffectiveness begins to drop), the shallower injec-tion angles perform better. The trajectory ofshallower injection flows being somewhat closerto the surfaces than that of steeper injection flows.

Recently, some researchers have predicted thefilm cooling effectiveness by numerical method.Berhe et al. (1999a) used algebraic relations for theturbulent viscosity and the turbulent Prandtlnumber in a modified k-e turbulence model tostudy the effects of surface curvature on filmcooling performance. Computations were per-formed at blowing ratios of 0.5, 1.0 and 1.5 witha density ratio of 2.0 along convex, concave andflat surfaces. Berhe et al. (1999b) also investigatedthe effect of several film cooling parametersincluding blowing ratio, injection angle, holelength, hole spacing and hole staggering. Linet al. (1998) used a low-Reynolds number turbu-lence model to investigate film cooling of flat andconvex surfaces. They showed that the injectionflow lift-off phenomenon depends not just on themomentum flux ratio but also on the profile ofboundary layer and the ratio of boundary layerthickness to hole diameter.According to published studies, the environ-

mental conditions must be well-controlled duringmeasurements using the liquid crystal thermogra-phy. Camci et al. (1992) investigated the effects ofthe strength of the light source illuminating theheat transfer surface, the orientation of the lightsource with respect to the surface, the uniformityof coated liquid crystal layer, and the repeatabilityof the measured results. They suggested that theimage capturing process should be performed withthe same illumination angle and the illuminationsource should be fixed at a specific location forboth the calibration process and measurement.Behle et al. (1996) showed that the calibration ofcamera and light source as the calibration step isvery 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 usedboth the TLC spray (34gin) and sheets to

investigate the dependence of the hue values on

variation of illumination and viewing angle for anoff-axis and an on-axis camera and light source

arrangement.

A TRANSIENT METHOD 155

Since the film cooling phenomena on curvedsurfaces are more complex than on flat surfaces,the detailed studies on local film cooling perfor-mance over the whole area of the curved surfaceare needed for the turbine blade design purpose. Inthis study, detailed heat transfer coefficient andfilm cooling effectiveness distributions are demon-strated over a convex surface by employingtransient liquid crystal thermography (Vedulaand Metzger, 1991; Ekked et al., 1997a, b andChen et al., 1998). For the present experimentalmeasurement, the streamwise injection angle (3’) is35 and the spanwise injection angle is 0. Theblowing ratio (M) was varied from 0.5 to 2.0 at amainstream Reynolds number (Red) of 1700 withturbulence intensity of 3.8%, and the curvaturestrength (2r/D) of convex test piece is 92.5.

THEORY

The present experiment used the thermochromicliquid crystal for the surface temperature measure-ment. Liquid crystal is very suitable to show thetransient surface temperature, since their responseis repeatable and their colors can be easilyrecorded with a video system. The local heattransfer coefficient over the liquid crystal coatedsurface without cooling film can be obtained byone-dimensional semi-infinite. The one-dimen-sional transient heat conduction equation, theconvection boundary conditions, and the initialcondition on the liquid crystal coated surface are:

02T OTk -O-z2 p Cps O (1)

OTh(Vw-

T Ti(2)

at t=O, T=Ti (3)

where k, Cp and p are respectively the thermalconductivity, the specific heat and the density of

test piece. The analytic solution of Eq. (1) on thesurface (z 0) becomes:

Tw-Ti_l_exp(h2ct) (hV/-)Tm- Ti-erfc

k(4)

The film cooling over a surface involves threetemperatures, including the mainstream tempera-ture, coolant flow temperature and wall surfacetemperature. The mainstream temperature (Tm) inEq. (4) will be replaced by a film temperature (Tf)during the data analysis. To find the unknown TU(in terms of known quantities Tm and Tc), anondimensional temperature is defined as the filmcooling 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/. Inthe present study, two film cooling tests withdifferent Tc have been completed. During mea-

surements, the temperature rises of both main-stream and injection flow are functions of time,instead of step temperature change. Therefore, theDuhamel’s Super-position should be used tomodify the time varying temperature rises at inletsof both mainstream and injection flows.

Besides the heat transfer coefficient and filmcooling effectiveness, heat flux ratio is anotherimportant parameter used to quantify the filmcooling performance. The present study adopts theexpression of heat flux ratio as defined by Ekkadet al. (1997b) given by

q_h(Tw-Taw) h (1qo ho(Tw Tm) ho(7)

where q5 is the overall cooling effectiveness. Incurrent study, q5 0.6 is used.


EXPERIMENTAL APPARATUSAND PROCEDURES

The test section used for the experimental analysisof the film cooling effectiveness and heat transfercharacteristics is shown in Figure 1. The experi-mental investigation was conducted in a windtunnel with rectangular cross-section of 10cm x5cm and a bend of 135 The wind tunnelconsisted of a mix section, a uniform developmentsection, and a curved test section as shown inFigure 1. The radii of curvature of the curvedsurfaces in the test section was 16.6cm. The

mainstream velocity (Um) was kept at a constantvalue of 9.1 m/s. The velocity of mainstream was

measured by a hot-film anemometer (Dantec,Flow Master 54N60). The free stream turbulenceintensity was controlled by turbulence grid formedby cylindrical bars located upstream of the testsection. The free stream turbulence was measuredusing a hot-wire anemometer, which was cali-brated by TSI intelligent flow Analyzer (IFA-100)with constant temperature anemometer operationmethod.The boundary layer was tripped at a distance of

10cm upstream of the leading edge of injection

Heater&FanTemperature Control

Compressor

by pass

PC+Frame Grabber+LCIA

Flow

Flow Development!section

Hot Film

Thermocouple

Turbulance Grid

Valve Flang-tyle Orifice Step

Sony Hi-8

Recovery SectionFlow

Straightener

FIGURE Schematic view of test facility.


holes by a 1.5-mm-dia trip wire. The injection flowwas injected through a single row of injection holeswith hole spacing of 3D along the spanwisedirection. The hole diameter (D) was 3.6 mm andthe ratio of hole length to hole diameter (L/D) was3.5. The strength of curvature (2r/D) and thestreamwise injection angle (/) were 92.5 and 35respectively, as shown in Figure 2. The plexiglastest surface was coated with black paint and a thinlayer of thermochromic liquid crystal. The emis-sivity of the black paint is 0.94. The injection flowwas supplied by a reciprocating-type compressorthat has a capacity of producing an air flow rate of0.0018m3/s at pressure of 7atm. A calibratedflange-type orifice was used to measure the massflow rate of injection flow. The injection flowwas heated by heating wires fixed at the inlet ofthe injection holes. The distance between heatingwires and the injection holes is 205 mm. The heat-ing wire diameter is 1.2mm and the ratio of thedistance between the wires and the injection holesto the wire diameter is 170.8. The mainstreamtemperature and the initial temperature on testsurface were measured by T-type thermocouples,

and a temperature recorder (Rustrak-Ranger II)records the time-varying temperatures duringmeasurements.The injection flow and mainstream were heated

before the onset of measurement. When thetemperature of injection flow and mainstreamattained the desired experimental temperature,both injection flow and mainstream were divertedinstantaneously into injection holes and testsection. Meanwhile, the temperature recorderand Hi-8 video recorded the temperature historiesof both injection flow and mainstream, and thecolor-changing image of liquid crystal. Color-changing images recorded on videotapes were thentransmitted to a personal computer by a framegrabber and analyzed using image processingsoftware. The transient time was taken throughLCIA V3.0 (Liquid Crystal Image AnalyzerVersion 3.0).The operating conditions are listed in Table I.

The mainstream velocity measured by hot-filmanemometer was 9.1m/s at 25cm upstream ofinjection holes. The mainstream Reynolds numberwas 1700 based on the inlet diameter of injection

lO.8nnnr’----I

r" 7

0-O- T J’

X

L J

FIGURE 2 Convex test piece with simple hole configuration.


TABLE Test conditions for the measured results shown in Figure 3

Authors P/D LID Pc/Pro 2riD 7 I/D M

Goldstein et al. (1997) 2.96 10 0.95 92.5 45 0.5 1.0

Schwarz et al. (1991) 3 10 0.95 94 35 0.9 1.01The present study 3 3.5 0.98 92.5 35 0.12 1.0

hole. The measured turbulence intensity was 3.8%.Measurements were conducted at five differentblowing ratios of 0.5, 0.75, 1.0, 1.5 and 2.0.The estimated uncertainty in the effective data

was + 5 percent estimated by the root mean squaremethod by Moffat (1988). There are a few factorsthat affect the uncertainties of h and r/, includingmainstream temperature, injection temperature,initial temperature, wall temperature., and the timeof liquid crystal color change. For the experimentsdone in this study, the total uncertainties of hand r] were respectively around 7.2% and 10.4%of their nominal values (h=29.038W/m2K and

r/= 0.3232). Furthermore, the estimated uncertain-ties for the Reynolds number, blowing ratio,mainstream turbulence intensity, and boundarylayer displacement thickness were respectively3.4%, 2.8%, 4.3% and 5.6%.

0.4

0.35

0.3

0.25

0.2

0.15

0.1y

0.05

CoflvexM=I.0 Prsent Study

Q M=I.0 Goldstein & Stone(1997)---E]--- M=I.01 Schwarz& Goldstein(1991)

o0 5 10 15 20 25

FIGURE 3 Comparison with prior measured results of span-wise averaged film cooling effectiveness over convex surfacewith simple hole configuration.

RESULTS AND DISCUSSION

In Figure 3, the spanwise averaged film coolingeffectiveness result is compared with the experi-mental results of Goldstein et al. (1997) andSchwarz et al. (1991). The present result is

close to the result of Schwarz et al. The lowervalues in the result of Goldstein et al. might bedue to the larger injection angle of 45. Goldsteinet al. stated that shallower injection angles havethe better effectiveness near injection holes on aconvex surface, as show in the comparison resultof Figure 3.

Detailed distributions of local heat transfercoefficient ratio (h/ho) at four different blowingratio of 0.5, 1.0, 1.5 and 2.0 are shown in Figure 4to demonstrate the influence of cooling film on aconvex surface. At blowing ratio (M) of 0.5, it isobvious that h/ho increases just downstream of

Convex Simple Hole M=0.54 7;,,, .,2

Y/Yo!(a) xm

4

Y/Yo o

-2

(b)

Convex Simple Hole M=I.0

0 10 15 20 25X/D

h/h

;1.68571i’i;"::il i.62857

i.514291.45714i.4

1.285711.228571.17143

14291,05714

h/h1.81.742861.685711.628571.571431,514291.457141.41,342861.28571.228571.171431.114291,05714

FIGURE 4 Local heat transfer coefficient ratio distributionsat (a) M=0.5; (b) M= 1.0; (c) M= 1.5; (d) M= 2.0.


Convex Simple Hole M=l.5

Y/Yo o

-2

-410 15 20 25

(c) x/D

Convex Simple Hole M=2.0

Y/Yo-2

-45 10 15 20 25

(d) X/D

FIGURE 4 (Continued).

lffh

1.742861.685711,628s7

1.514291.457141.4!,342861,285711.228571.171431.114291,05714

h/h

1.742861.685711,62857

iiiii 571431.514291,457141.41,34286

1.285711.228571.1714311429

1.05714

injection holes. Moreover, high heat transferregions around both sides of injection holes, whichmay be caused by counter-rotating vortex pairs atthe exit of holes is clear too. Therefore, the h/ho onthe centerline regions downstream (3 < X/D < 8)of injection holes becomes lower than the regionsadjacent to it because the counter-rotating vortexpairs has brought the hot gas away from thesurface.The centerline region with h/ho> 1.8 down-

stream of injection hole for M= 1.0 is smallerthan at M--0.5, as shown in Figure 4(b). Becauseof higher h/ho at a low blowing ratio of 0.5, it isexpected that the spanwise averaged value of h/hoat M 1.0 will be lower than the value at M 0.5.In Figure 4(c), when blowing ratio increases to 1.5,the increased mass of injection flow will increasethe mainstream boundary layer thickness anddecrease h/ho at downstream regions of X/D > 7.When the blowing ratio is increased to 2.0 asshown in Figure 4(d), the h/ho at regions betweentwo injection flows become higher than thecenterline downstream regions of injection holesdue to the strong interaction of formed horseshoevortices between neighboring holes. This phenom-enon indicates the instantaneous disturbance of

mainstream caused by the injection flows ejectedthrough film cooling holes.At low blowing ratio, the injection flows stay

close to the convex surface because of the lowermomentum ratio. Therefore, the injection flowsincrease the surface heat transfer effect on convexsurface. As the blowing ratio increases, the ejectedjets will lift-off the surface immediately afterleaving the injection holes, and form the lowerheat transfer value than M= 0.5 even at low X/Dregion. At high blowing ratio, the counter-rotatingvortex pairs formed within the ejected jet arestrong. The interactions among the vortices ofneighboring injection flows provide high h/ho onthe regions between injection flows. Fric et al.(1994) observed that the injection flows will liftaway from the wall immediately after the injectionflows exit the injection holes because both injectionflow mass flux and momentum ratio are increasedwhen blowing ratio increases. The horseshoevortex will be formed when the mainstreamencounters the ejected jets, and wake vortices willappear at downstream regions along centerline ofinjection holes. A reproduction of Figure in thework of Fric et al. is given as Figure 5. Boththe horseshoe vortex and wake vortices increasethe surface heat transfer. It is shown that h/ho atmost regions of M--2.0 is higher than M--1.5in Figure 4 of the present study.

Figure 6 illustrates the effect of blowing ratio onthe spanwise averaged heat transfer ratio (h/ho)for 2.9 < X/D < 25. The spanwise averaged resultsfor regions of X/D < 2.9 are not provided in thiswork since the one-dimensional heat conductionmodel 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, it is obvious that the value of h/ho

rises at blowing ratios of 0.5 and 0.75, becauseinjection flows of lower mass and momentum ratiowill be constrained against the wall by main-stream. Therefore, h/ho is higher at lower blowingratio at most measured regions as shown inFigure 6. The injection flows ejected into theboundary layer of mainstream would increase the


Counter-rotatingvortex pair

Jet shear-layervortices

Horseshoe vortices

Wake vortices

Wall

FIGURE 5 Cartoon depicting four types of vortical structure associated with the transverse-jet near field. (reproduction of Fig.in Fric et al., 1994.)

l’l/h

1.8

1.6

1.4

1.2

Convex Simple Hole

M=0.5M 0.75M 1.0M=l.5M=2.0

0 5 10 15 20 25

FIGURE 6 Effect of blowing ratio on the spanwise averagedheat transfer coefficient.

mainstream boundary layer thickness. This effectof increasing boundary layer thickness will becomemore obvious as the blowing ratio increases, andthereby decreases the h/ho at X/D > 8. As blowingratio is increased to 2.0, the injection flows ofrelatively high momentum tend to lift-off theconvex surface after injection. Each injection flowbecomes an inclined cylinder for the mainstream.Hence, a horseshoe vortex will be formed aroundthe injection flow and also wake vortices will beinduced (Fric et al., 1994). The interactions of thehorseshoe vortices among the injection flows are

strong and will increase the surface heat transfer atregions between holes. Moreover, the wake vor-

tices will increase the surface heat transfer at

regions downstream of holes. Therefore, the h/hoat most measured regions increase as blowing ratiois increased to 2.0.At low blowing ratio, Goldstein and Stone

(1997) observed similar phenomena from the flow


visualization results. In curved flows, a cross-stream pressure gradient that holds low momen-tum fluid particles against the convex surfaceexists. The effect on the mainstream boundarylayer is to suppress mixing and entrainment inthe convex surface boundary layer. Therefore,on the convex surface, injection flow ejected atlow blowing ratio stays close to the surface andremains in-line with the injection hole.

Figure 7 shows the detailed distributions of localfilm cooling effectiveness (r/) at M 0.5 to M-- 2.0.At blowing ratio of 0.5, the injection flows stayclose to the convex surface and block the main-stream from the surface, thereby increasing thefilm cooling effectiveness gradually as shown inFigure 7(a). The protection of the injection flowson the convex surface against the hot gas isdecreasing with increased blowing ratio. Whenblowing ratio increases to 1.0, the film coolingeffectiveness of regions between holes becomes lessthan 0.05 for 3 <X/D< 10. The regions with

r/< 0.05 extends to X/D’ 14 at blowing ratio of2.0, as demonstrated in Figure 7(d). The momen-tum flux ratio demonstrates the cause of theinjection flows leaving the convex surface at higherblowing ratio. The large normal component of


Y/Yoo

(a) x

Convex Simple Hole M=I.0

Y/Y

i(b) X/D

0,6

0.5571430.5142860.4714290.4285710.3857140.3428570.30.2571430,214286

0.1285710.08571430.0428571

0,5571430.514280,4714290,4285710,3857140,342857

0.30.2571430,214286O, 171429O, 128570,08571430,0428571

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


10 15 20 25


10 15 20 25

0.471429

0.3857140.342857

0.2571430.214286

1285710o08571430.0428571

0.557143

0.4714290.4285710.385714

i 0.342857

0.2571430.2142860.171429O. 1285710.08571430.0428571

FIGURE 7 (Continued).

momentum of injection flows (I sin27) pulls theinjection flows away from the convex surface anddegrades the film cooling effectiveness on thesurface. Although the increase in mass per unitarea at higher blowing ratio tends to increase r/,

the effect of decreasing r/caused by strong vorticeswill be more severe.The results of spanwise averaged film cooling

effectiveness (/) at various blowing ratios areshown in Figure 8. It is shown that decreases asblowing ratio increases. At blowing ratio of 0.5,the spanwise averaged effectiveness is the bestamong all tested blowing ratios. At downstreamregions, mixing with the mainstream dilutes theinjection flows, thereby lower /obtained. Also, thelower injection flow mass flux of injection flow forM=0.5 causes the steep descent in /at X/D > 8.In general, higher blowing ratios produce in-creased mass per unit area, larger momentum butgreater jet penetration. Increase of mass canincrease the spanwise averaged film cooling effec-tiveness at downstream regions and provide aneven film coverage along X/D. As shown inFigure 7(d), at blowing ratio of 2.0, the increaseof r/ for X/D > 15 at regions between injectionflows shows that the reattachments of injectionflows have occurred, so increasing the / fardownstream in Figure 8.


0.5

0.4

0.3

0.2

0.1

00

Convex Simple Hole

M=0.5M 0.75M-- 1.0M=l.5

I,10 15 20 25

FIGURE 8 Effect of blowing ratio on the spanwise averagedfilm cooling effectiveness.

q/qo

1.8

1.6

1.4

1.2

0.4

0.2

Convex Simple Hole

M=0.5M= 0.75M 1.0M=l.5

O0 5 10 15 20 25

FIGURE 9 Effect of blowing ratio on the overall heat fluxratio.

For the film cooling effectiveness, Schwarz et al.(1991) noted that the effect of cross-streampressure gradient greatly overshadow the effectsof the normal and tangential momentum of the jetat low blowing ratio, thereby pushing the injectionflows onto the convex surface. Farther down-stream, at low blowing ratios, mixing with themainstream dilutes the coolant gas and then /degrades. Berhe and Patankar (1999b) mentionedthat the pairs of counter-rotating vortex would bestronger at high blowing ratios. This phenomenoncauses the decrease in / because the pairs ofcounter-rotating vortex lift the injection flow awayfrom the surface and entrain the hot gases fromthe surroundings to the surface. For the presentstudy, a pair of counter rotating vortices obviouslydecreases when M > 1.0.The film cooling performance of test surface is

best indicated by the result of spanwise averagedheat flux ratio shown in Figure 9. The q/qo ofvalues lower than 1.0 at low blowing ratioindicates better film cooling performance. AtM-0.5 and 0.75, the injection flows reduce theheat flux ratio effectively over most measuredregions because the low normal momentum ofejected injection flows tend to lead the flows to stay

close to the surface. But the low mass flux ofinjection flows is unable to provide film protectionat further downstream, and therefore increases themagnitude of q/qo at X/D > 9. When M is furtherincreased to 1.0, 1.5 and 2.0, both the increasednormal momentum and counter-rotating vortex

pairs will promote lift-off and therefore performpoor protection just after injection. Furthermore,at downstream of X/D-12, the value of q/qo atM= 1.0 is larger than the value at M--1.5. This

phenomenon reveals the effect of higher massflux on surface protection at downstream regions.As a summary, at high blowing ratio, the highnormal momentum of ejected injection flowpromotes lift-off phenomenon and degrades theprotection on the convex surface. For the testedconvex surface in the present study, the lowblowing ratio of 0.5 shows the best film coolingperformance.

CONCLUSIONS

The present study demonstrates the influence ofblowing ratio on convex surface film coolingperformance. By using transient liquid crystal


thermography, the film cooling performance of aconvex surface (2riD 92.5) with a row of straightcircular holes (7= 35 was investigated. Experi-mental results show that high blowing ratio hasadverse effect on film cooling performance. Athigh blowing ratio, the injection flows will liftaway from the surface and will also reduce the filmcooling effectiveness on the convex surface. How-ever, the larger mass of injection flow ejected intothe mainstream at higher blowing ratio causesadjacent injection flows to merge far downstreamof injection holes and increases the film coolingeffectiveness. In the present study, injection flowsare not able to offer better protection on theconvex surface when M> 1.0. For the testedconvex surface in the present study, the optimumblowing ratio is found to be 0.5 among the presenttested 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 beachieved without their support.

NOMENCLATURE

ILMPqqo

D injection hole diameter on the inlet plane [m]h heat transfer coefficient with film injection

[W/mZK]ho baseline heat transfer coefficient without film

injection [W/mZK]momentum flux ratio . 2OcUc /OmUmlength of injection hole [m]blowing ratio DcUc/pmUmpitch of injection holes Ira]heat flux per unit area [W/m]baseline heat flux per unit area without filminjection [W/m2]

r radius of curvature of convex surface [m]Red mainstream Reynolds number based on the

inlet dia-meter of injection hole pmumD/ll,

Y

time [s]temperature [K]mainstream turbulence intensity [%]velocity [m/s]axial distance from the center of injectionhole [m]spanwise coordinate from the center ofinjection hole Ira]coordinate axis perpendicular to the testsurface [m]

Greek Symbols

thermal diffusivity of test surface [m2/s]displacement thickness [m]overall film cooling effectiveness (Tw- Tm)/

injection hole angle with respect to the testsurface as projected into the streamwise/normal plane (inclination angle) [deg.]film cooling effectivenessspanwise averaged film cooling effectivenessdynamic viscosity of mainstream [kg/ms]density [kg/m3]

Subscripts

c coolant flow ejected from the injection holern mainstreams test piecew surface of test piece

initial condition

References

Behle, M., Schulz, K., Leiner, W. and Fiebig, M. (1996) Color-based Image Processing to Measure Local TemperatureDistributions by Wide-Band Liquid Crystal Thermography,Applied Scientific Research, 56, 113-143.

Berhe, M. K. and Patankar, S. V. (1999a) Curvature Effectson Discrete-Hole Film Cooling, ASME Journal of Turbo-machinery, 121, 781 791.

Berhe, M. K. and Patankar, S. V. (1999b) Investigationof Discrete-Hole Film Cooling Parameters using Curved-Plate Models, ASME Journal of Turbomachinery, 121,792-803.

Camci, C., Kim, K. and Hippensteele, S. A. (1992) A New HueCapturing Technique for the Quantitative Interpretation of


Liquid Crystal Images used in Convective Heat TransferStudies, ASME J. of Turbomachinery, 114, 765-775.

Chen, P. H., Ai, D. and Lee, S. H. (1998) Effects of CompoundAngle Injection on Flat-Plate Film Cooling Through a Rowof Conical Holes, ASME Paper No. 98-GT-459.

Ekkad, S. V., Zapata, D. and Han, J. C. (1997a) Heat TransferCoefficients over a Flat Surface with Air and CO2 Injectionthrough Compound Angle Holes using a Transient LiquidCrystal Image Method, ASME J. Turbomachinery, 119,580-586.

Ekkad, S. V., Zapata, D. and Han, J. C. (1997b) FilmEffectiveness over a Flat Surface with Air and CO2 Injectionthrough Compound Angle Holes using a Transient LiquidCrystal Image Method, ASME J. Turbomachinery, 119,587-593.

Fric, T. F. and Roshko, A. (1994) Vortical Structure in thewake of a Transverse Jet, J. of Fluid Mech., 279, 1-47.

Goldstein, R. J. and Stone, L. D. (1997) Row-of-Holes FilmCooling of Curved Walls at Low Injection Angles, ASMEJ. of Turbomachinery, 119, 574-579.

Ito, S., Goldstein, R. J. and Eckert, E. R. G. (1978) FilmCooling of a Gas Turbine Blade, ASME J. ofEngineeringforPower, 100, 476-481.

Ko, S.-Y., Yao, Y.-Q., Xis, B. and Tsou, F.-K. (1986)Discrete-Hole Film Cooling Characteristics over Concaveand Convex Surfaces, Heat Transfer 1986, Proceeding of8th International Heat Transfer Conference, San Francisco,3, Hemisphere Publishing Corp., New York, 1297-301.

Lin, Y.-L. and Shih, T. I.-P. (1998) Computations of Discrete-Hole Film Cooling over Flat and Convex Surfaces, ASMEPaper, No. 98-GT-436.

Moffat, R. J. (1988) Describing the Uncertainties in Experimen-tal Results, Experimental Thermal and Fluid Science, 1, 3 17.

Schwarz, S. G., Goldstein, R. J. and Eckert, E. R. G. (1991)The Influence of Curvature on Film Cooling Performance,ASME J. of Turbomachinery, 113, 472-478.

Vedula, R. J. and Metzger, D. E. (1991) A Method for theSimultaneous Determination of Local Effectiveness and HeatTransfer Distributions in Three-Temperature ConvectionSituations, ASME Paper, No. 91-GT-345.

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Transient Liquid Crystal for Film Cooling Over Convexdownloads.hindawi.com/journals/ijrm/2001/590527.pdf · 2019-08-01 · important parameter used to quantify the film coolingperformance.Thepresentstudyadoptsthe