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Experimental Thermal and Fluid Science 31 (2007) 559–565

A study of the heat transfer characteristics of turbulentround jet impinging on an inclined concave surface using

liquid crystal transient method

C.H. Lee a, K.B. Lim b,*, S.H. Lee b, Y.J. Yoon a, N.W. Sung a

a Department of Mechanical Engineering, Hanyang University, 1271 Sa1-dong, Ansan Kyungki-do 425791, Republic of Koreab Department of Mechanical Engineering, Hanbat University, Daejon, Republic of Korea

Received 22 March 2006; received in revised form 6 June 2006; accepted 7 June 2006

Abstract

The effects of concave hemi-spherical surface with an inclined angle on the local heat transfer from a turbulent round impinging jetwere investigated through experimentation. The liquid crystal transient method was used in this study. This method suddenly exposes apreheated wall to an impinging jet and then a video system records the response of the liquid crystals to measure the surface temperature.The Reynolds numbers 11,000, 23,000 and 50,000; were used nozzle-to-surface distance ratio was from 2 to 10 and the surface angleswere a = 0�, 15�, 30� and 40�. The correlations of the stagnation point Nusselt number according to Reynolds number, jet-to-surfacedistance ratio and dimensionless surface angle were also presented. In the stagnation point, in terms of Ren, where n ranges from0.43 in case of 2 6 L/d 6 6 to 0.45 in case of 6 < L/d 6 10, there roughly appears to be a laminar boundary layer result. The maximumNusselt number, in this experiment, occurred in the upstream direction. The displacement of the maximum Nusselt number from thestagnation point increases with increasing surface angle or decreasing nozzle-to-surface distance. Under this condition, with surfacecurvature at D/d = 10, the maximum displacement is about 0.7 times of the jet nozzle diameter.� 2006 Elsevier Inc. All rights reserved.

Keywords: Transient liquid crystal method; Impingement jet; Heat transfer Nusselt number; Reynolds number; Concave surface

1. Introduction

The arrangement of single jet or jets is used to calculatethe coefficient elevated by heating, cooling and drying.Impinging jet is the most favored method used to improvethe heat-transmission efficiency of heat-fluid equipment,which has been used in the heating and cooling processof industries. It is also used to refrigerate steel plates, todry papers, thin films and fabrics, to cool large scale inte-gration, and is even used as a part of gas turbines.

Impinging jet has been an object of study by many engi-neers because its properties are affected by the speed of thejet, warm current intensity, form of jet participle surface,

0894-1777/$ - see front matter � 2006 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2006.06.004

* Corresponding author. Tel.: +82 42 821 1061; fax: +82 42 821 1153.E-mail address: kblim024h@hanbat.ac.kr (K.B. Lim).

shape of the jet nozzle and 10 boundary conditions. Theheat transfer caused by impinging the jet can be classifiedinto convex surface, flat surface and concave surface andmany researches have been done on this [1–4]. But imping-ing jet is not only a two-dimensional heat transfer, butrather a three-dimensional heat transfer. Therefore, it is adifficult problem to be solved. Impinging jet problem ona curved surface is a common problem in refrigerated heatfluid, and we can find impinging jet out of plumb ratherthan perpendicular due to the limitation of the shape ofsurface or location of nozzle, but researches done on thissubject are not enough.

Goldstein [5] conducted an experiment on heat transferin inclined impinging jet on a flat surface, where he mea-sured the local heat transfer coefficient in the conditionwhere Re is between 10,000 and 35,000, L/d = 4, 6, 10

Fig. 1. Schematic diagram of impinging jet for transient liquid crystalmethod.

Nomenclature

Cp specific heat of Plexiglas [J/kg K]D Plexiglas diameter [m]d jet diameter [m]h local heat transfer coefficient [W/m2 K]k thermal conductivity of Plexiglas [W/m K]L jet-to-plate distanceR radial coordinate of convex surfacet time [s]T temperatureNu local Nusselt numberRe jet Reynolds number

Greek symbols

c quantity defined in Eq. (2)q density of Plexiglase emission capacity of test surface

Subscripts

lc liquid crystal0 initials stagnation pointw wall (Plexiglas)1 air (ambient)m maximum

560 C.H. Lee et al. / Experimental Thermal and Fluid Science 31 (2007) 559–565

and the inclined angle is between 30� and 90�. He also pre-sented the local heat transfer coefficient related formula.Lamomt [6] and Rubel [7] examined the fact that the heattransfer or stagnation in case of inclined impinging jetoccurs at the point which is moved from the point of inter-section. Gau and Chung [8] conducted an experiment onthe effect of heat transfer on a cylinder-shaped convex sur-face and concave surface, representing the related formulabetween local heat transfer coefficient and average heattransfer coefficient on a curved surface. Moreover, in thestudy of the heat transfer on a cylinder-shaped convex sur-face and concave surface [10,15,17], which is sprayed bytwo-dimensional slot jet, they examined closely the heattransfer at the point of stagnation where the convex sur-face is promoted by a three-dimensional whirlpool thatincreases the transmission of momentum, and a flow onthe surface is relieved by the centripetal force that the heattransfer rate is decreasing. Yan [9,12] measured the heattransfer coefficient of completely developed circle jet collid-ing on the surface by using liquid crystal.

In this study, we are going to examine the property ofheat transfer of the inclined impinging jet which is sprayedon the concave surface by using the liquid crystal transientmethod. We sprayed turbulent circle jet on a semi-sphericalconcave surface and found the property of heat transferwhen Re = 11,000–50,000. To measure the local heat trans-fer coefficient, an investigation on the relations by distancesbetween collision angle and exposure gateway and collisionsurface, and a research on the heat transfer properties ofturbulent impinge jet have been done in this study.

2. Experimental apparatus and procedures

2.1. Experimental setup

Fig. 1 shows the outline of the experimental devices usedto examine the property of heat transfer of the inclinedimpinging jet sprayed on the concave surface by usingliquid crystal transient method. We sprayed warm current

circle jet on a semi-spherical concave. The device is com-posed of three main parts.

It is composed of blower part, long pipe part, which isdesigned for completely developed flows, and a collisionsurface. To maintain a certain flow, we put a manometerin front of the blower to measure the velocity of the wind.We also put a heat exchanger to maintain a certain jet tem-perature. The hemi-spherical diameter and Plexiglas’s thick-ness of the experimental device are 300 mm and 4.7 mm.These devices are composed of a Plexiglas dome, glass wooland Styrofoam insulator to prevent the loss of heat. And wealso put an angle adjusting device to adjust the inclineddegree. On the collision surface, to record the change of colorby temperature, we put a thin (0.03–0.05 mm) liquid crystal(R35C1W) membrane. All of the measured data and results(like change of color) are recorded using a CCD camera(PULNIX TMC-7) and screen recording device.

The jet exit velocity and turbulent intensity distributionacross the impinging jet have been measured with a hotwire anemometer. The center line velocity is checked bythe results of a Pitot tube measurement with a micro-manometer. These characteristic results of the impinging

Table 1Uncertainty analysis

Parameter Xi Typical value dXidX iNu

oNuoX i

� �� 100%

R/d = 0 4

d 0.030 (m) 0.0002 0.7 0.7t 9.58; 44.52 (s) 0.06 0.4 0.9Tw0 48.5 (�C) 0.2 3.7 3.9T1 26.2 (�C) 0.5 2.9 3.1Tlc 34.9 (�C) 0.25 4.8 5.2ffiffiffiffiffiffiffiffiffiffiffi

qCpkp

569 29 5.4 5.8e 0.5 0.1 1.3 2.9

dNu/Nu = 8.8 9.8 (%)

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of jet would provide very basic information for theimpingement of jet heat transfer experiments. The typicalflow measurements used for density calculation with tem-perature were made for all the Reynolds numbers tested.

2.2. Method

We used the liquid crystal transient method used by Yanand Vaughn as measuring method. Liquid crystal thermog-raphy has been widely used for the visualization and deter-mination of surface temperature distributions leading toconvective heat transfer coefficients. Liquid crystal is excel-lent for its color repetition properties and can be recordedby video system easily, making it clearer to understand thechanges. Moreover, it can visualize the whole field oftemperature at once compared to other temperature mea-suring devices. So it can be used to examine complicatedheat transfer like those in a curved duct or gas turbine.To facilitate the previous study, a liquid crystal calibrationsystem developed by Can et al. [18] using true color imagingprocessing system has been displaced up to 72� from thenormal in the liquid crystal calibration set-up. If we ignorethe heat transfer loss on the concave surface from the exper-imental devices (like Vedula [13] and Yan [11] did), we canrepresent the distribution of temperature of semi-infinitesolid solution excess heat transfer equation at the conditionof convection current coefficient boundary as below

T � ¼ ðT w � T1ÞðT w0 � T1Þ

¼ ec2

erfcðcÞ ð1Þ

c ¼ hffiffitpffiffiffiffiffiffiffiffiffiffiffiqCpk

p ð2Þ

where Tw states the measured temperature of the surface,Tw0 is initial temperature, T1 is temperature of the jet.

After heating the experimental device in an incubator,the surface is maintained at a constant temperature takingout the insulated lid on it and spraying the collision mate-rial that refrigerates the surface. Then, an isotherm wouldappear on the surface and we can calculate the local heattransfer coefficient by using Eqs. (1) and (2). To calibratethe temperature where the R-G succession layer appears,we put liquid crystal on an aluminum stick and set the tem-perature grade. The calibrator is made of an aluminum barwith a cross-section 20 mm · 30 mm · 160 mm. Two resis-tance type heaters (30 W) are located on the top of thealuminum bar where electric power (DC) is supplied tothe bar through the heaters. In the middle section of thebar the surface for liquid crystal is sprayed on. We mea-sured the temperature indicated by the R-G successionlayer several times, and calibrated it. Consequently, theliquid crystal band temperature is 34.9 �C ± 0.25 �C. Weused K type thermocouple whose diameter is approxi-mately 0.08 mm, and we used an incubator and a PRTmade by Rosemount. We also set temperature calibrationequation until it obtains an accuracy rate of ±0.1 �C. Weallow the system to establish steady state with a linear tem-

perature gradient on the calibration section before remov-ing the insulation cover. Color band (color transition) isrecorded by a video camera and the temperatures arerecorded by data acquisition system. The translated uncer-tainty in temperature is dependent on the temperature gra-dient from run to run. The standard deviation for thefourteen runs was 0.25 �C. Moreover, to eliminate theuncertainty of experiment, we used a method representedby Kline and Mcklintock [14] to interpret the conditionof Re = 23,000, L/d = 6 and a = 30�. The total uncertaintyfrom Nusselt number was 9.8% (shown in Table 1), theuncertainty of Plexiglas’s was the biggest. R-G successionlayer was the second biggest factor.

3. Results and investigations

3.1. Heat transfer property at stagnation point

by Re number

Heat transfer property at stagnation point uses a rela-tively bigger coefficient; measuring local heat transfer coef-ficient is important in heating and cooling. In this study, wemeasured the local heat transfer coefficient (whose curverate is D/d = 10) of a circle jet at the stagnation point Re,inclines (0, 15, 30, 40) and the distances between nozzleand collision surface by using liquid crystal transientmethod. The Nusslet number according to the stagnationpoint is defined as follows. The Nusslet number at maxi-mum heat transfer coefficient is defined as Num. That ofthe 2nd stagnation point or 2nd peak point is defined as Nus.

We represented the heat transfer property at stagnationpoint when Re is between 11,000 and 50,000; heat transferproperty at stagnation point resulted by change in inclines,the distances between nozzle and collision surface as shownin Fig. 2. As shown in Fig. 2, as the distance between theimpinging jet and collision surface increases, heat transfercoefficient at stagnation grew bigger until the point. Thereason is that the heat transfer rate appeared highestat L/d = 6. 4L/d = 6 is due to increasing momentum ofinflowing jet. Likewise when we changed the incline, wefound the same result: the biggest heat transfer coefficientat L/d = 6 point. However, when we see impinging jetand the effect caused by collision angle, there is a ten-dency that the increasing incline lowers the heat transfer

Fig. 2. Effect of L/d ratio on the stagnation point Nusslet number forinclined angle and Re = 11,000, 23,000 and 50,000.

Fig. 3. Correlation of the stagnation point Nusselt numbers (Nus) on theconvex surface for 2 6 L/d 6 6, 11,000 6 Re 6 50,000 and 0� 6 a 6 40�.

Fig. 4. Correlation of the stagnation point Nusselt numbers (Nus) on theconvex surface for 6 6 L/d 6 10, 11,000 6 Re 6 50,000 and 0� 6 a 6 40�.

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coefficient. Unlike a flat surface, semi-spherical concaveinterrupts the exchange of momentum that occurs aroundthe potential core, it tends to decrease. Accordingly, tomaximize the heat transfer property to single collision jet,if we consider the point L/d = 6 which includes the distancebetween impinging jet and collision surface, we can findmaximized heat transfer coefficient. It can be seen fromFig. 2 that for L/d < 4, there is a gradual increases in thevariation of Nus with L/d; Nus gradually increase withL/d and reaches a maximum at L/d = 6 for Re = 11,000,23,000 and 50,000, and at L/d = 6, respectively. A maxi-mum Nus position from L/d = 6 is attributed to an increasein the potential core length with increasing Reynolds num-ber. This agrees well with the results of Lee et al., Yan, andKataoka et al., which show that the physical mechanismfor the maximum Nus occur at L/d = 6–8 and that a changein the jet centerline velocity from the initial centerlinevelocity is not only small, but also the turbulent intensityreaches roughly a maximum value in that region.

3.2. Heat transfer coefficient correlation formula

Figs. 3 and 4 show the Reynolds number for the heattransfer coefficient at the stagnation point. We formalizedexperimentally the correlation between L/d and a.

In case of 2 6 L/d 6 6, 11,000 6 Re 6 50,000, 0� 6a 6 40�, we calculated the diffusion rate at 5.6% as below

Nus ¼ 1:70ðReÞ0:43ðL=dÞ0:20ðsinð45� � aÞÞ0:08 ð3Þ

In the case of 6 6 L/d 6 10, 11,000 6 Re 6 50,000,0� 6 a 6 40�, we figured out the diffusion rate at 6.7% asbelow

Nus ¼ 8:28ðReÞ0:45ðL=dÞ�0:75ðsinð45� � aÞÞ0:08 ð4Þ

As we can find in the correlation formulas (3) and (4), inthe case of 2 6 L/d 6 6, Nu follows the Nus / (Re)0.43 for-mula. When it comes to 6 6 L/d 6 10, Nu follows theNus / (Re)0.45 formula. In general, in the case of Nus /(Re)0.5 this condition is laminar flow. That result in thiscase belongs to Nus / (Re)0.5’s laminar flow boundarylayer. Accordingly, impinging jet to the curved concavesurface in this condition still forms laminar flow boundarylayer. This is a clear evidence that the effect caused bythe incline is smaller than that caused by the surfacecurvature.

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3.3. L/d and heat transfer property by Re

The change of Re and the distance between impingingjet and collision surface, and the result of heat transferwhen the tilt angle is 15� are shown in Fig. 5.

From the result shown in Fig. 6(a), as the Re increases,Fig. 6(a) shows that when Re increases, Nu number alongthe whole plate increases and 2nd stagnation pointbecomes obvious. As the Re increases, the location ofsecond stagnation point moves backward from the center.Generally when L/d = 2, impinging jet on flat surface, itforms a 2nd stagnation point at 2nd point of diameterregardless of Re. But in case of concave hemisphere, wecan find that there is a tendency for Re to increase andthe 2nd point of stagnation to move backward. Moreover,as L/d increases, the 2nd stagnation point disappears andshows a flat decrease. For each Reynolds number,Re = 11,000, Re = 23,000, Re = 50,000, it increases at arate of 1.8%, 5.5%, 10.5%. Therefore, as Re increases, theincreased rate increases further.

Fig. 5. Comparison of Nusselt number distribution along the X directionaccording to the variation of L/d and Re number at inclined angle a = 15�.

Fig. 6. Effect of the Nusselt number as inclined angle changes with L/d atRe = 23,000.

3.4. Heat transmission property toward R/d as L/d

Fig. 6 shows the effect on Nusselt number as L/d = 2, 6and 8 when Re = 50,000. As it can seen from Fig. 6(a),when L/d = 2, and in the case of vertical impinging jet,the distribution of local heat transfer coefficient at theupper stream (R/d < 0) is maximized at stagnation pointand decreases until the 2nd peak which occurred by lami-nar flow boundary layer’s succession process to the turbu-lent flow, and this 2nd peak has the maximized Nusseltnumber at R/d = 2.0 point. And this is in accordance withYan’s report which insisted Nusselt number at 2nd peak

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approaching a to value of stagnation point. In this study,as the tilt angle increases, the 2nd maximum Nusselt valuedid not occur and the Nusselt value by surface decreased.At the downstream (R/d > 0), as tilt angle increases, the2nd peak moves away from the 2nd stagnation point.Moreover, as we can see from the result of Fig. 6(b) and(c), there occurs a 2nd peak at R/d = 2.67 when L/d = 4and a=15�, 30� and 40� downstream, but we can infer thatas the distance between the nozzle and the surfaceincreases, the 2nd peak occurs nearer to the stagnationpoint from the fact that R/d value occurs at 2.0 whenL/d = 6.

3.5. Heat transfer property by the tilt angle (a)

To represent the distribution of local heat transfer coef-ficient through a concave surface, we displayed the changeof Nu when L/d = 2, 6 and the tilt angle is a = 0�, 15�, 30�and 40� as shown in Fig. 7.

As we can see from Fig. 7, when the tilt angle is a = 0�,the distribution of local heat transfer coefficient atRe = 50,000 is maximized at stagnation point and afterthat it decreases. And as the tilt angle increases, maximum

Fig. 7. Comparison of Nusselt number distribution according to thevariation of L/d and inclined angle at Re = 50,000.

heat transfer coefficient (Num) appears at the point movedfrom the stagnation point toward the upper stream(R/d < 0). The reason that the 2nd heat transfer coefficient(Num) is moved to R/d < 0 (upper stream) is because theflow of the jet collides with the wall and it is divided intotwo parts going upstream and downstream, and at thispoint in the upstream area, the direction of flow changeddrastically and an active flow mixing occurs that leads tohigh flow intensity.

When Re is 50,000, maximized Num appears at stagna-tion point when the tilt angle is a = 0�, but as we can inferfrom the fact that when the tilt angle is a = 15�,R/d = �0.23, and a = 30�, R/d = �0.67, we can concludethat as the tilt angle increases, Nu moves far from the stag-nation point. In our study, we could find this tendencywhen we set L/d = 2, 6, and 10, and the maximum distancemoved was approximately 0.7 times the diameter of thenozzle. Compared to the result of Yoon’s [16] conclusion,which insisted the movement of maximum wall pressurecoefficient moves 0.7d toward upstream under the condi-tion of a = 20�, we can conclude that the distance movedon a concave surface increases directly with the tilt angle.

4. Conclusion

In this study, we measured local heat transfer coefficientsprayed on the curved concave surface by using the liquidcrystal transient method under the condition whereRe = 11,000, 23,000, 50,000, and under five various dis-tances between impinging jet and the surface (L/d) and fourtilt angles a. And finally, we reached the followingconclusions:

(1) Nu value at stagnation point decreases as the tiltangle is increased when Re is fixed. Among all the tiltangles, the result was maximized when L/d = 6.

(2) In this study, we draw correlations between Re andL/d, a and Nus, and we found the fact that whenL/d value is 2 6 L/d 6 6, Nus value followsNus / Re0.43, and when L/d is between 6 and 10(6 < L/d 6 10), Nus value follows Nus / Re0.45, butthe jet flow relies on the tilt angle rather than Re thatkeeps Nus / Re0.5 which resulted with the flow oflaminar boundary layer.

(3) The 2nd peak point occurred with the inclinedimpinging jet on concave surface appearing far fromthe stagnation point, as Re value decreases or the tiltangle increases, and as L/d increases, it appeared nearthe stagnation point.

(4) Maximum heat transfer coefficient occurs far fromthe stagnation point as the tilt angle increases orthe distance between the nozzle and collision surfacedecreases, and when L/d = 2, a = 40�and in thisstudy, maximum distance moved was approximately0.7 times the diameter of the nozzle.

(5) Compared to Nu value at the stagnation point, theincreasing rate of maximum Nu value rises as the tilt

C.H. Lee et al. / Experimental Thermal and Fluid Science 31 (2007) 559–565 565

angle rises, and the maximum increasing rate wasapproximately 31.8% under the condition L/d = 2and a = 40�.

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