Experimental Thermal and Fluid Science 34 (2010) 633–637

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Experimental Thermal and Fluid Science

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A note on unsteady impinging jet heat transfer

S. Bhattacharya *, A. AhmedAerospace Engineering Department, Auburn University, Auburn, AL 36849, USA

a r t i c l e i n f o

Article history:Received 14 July 2009Received in revised form 9 November 2009Accepted 14 December 2009

Keywords:Impinging jetIn line jetImpinging jet heat transfer

0894-1777/$ - see front matter � 2009 Elsevier Inc. Adoi:10.1016/j.expthermflusci.2009.12.004

* Corresponding author. Tel.: +1 334 444 1674; faxE-mail addresses: bhattacharya.30@buckeyemai

aahmed@eng.auburn.edu (A. Ahmed).

a b s t r a c t

Reported are the results of experiments on a regular in-line-jet that was modified prior to its impinge-ment to improve heat transfer on the plate. Modifications consisted of insertion of two bluff bodiesand a streamlined body in the jet. The improvement in transport coefficients was attributed to the peri-odicity in the flow which caused the attachment point to sweep the reattachment region and the turbu-lence created was distributed over a large area compared to simple attachment.

� 2009 Elsevier Inc. All rights reserved.

1. Introduction

Impinging jets have been studied over the years for their impor-tance in industrial applications, mainly in cooling, heating or dry-ing. The high levels of convective heat and mass transfer that canbe achieved are the prime motivation for their continued use[15,10,9,3]. Impingement of jets from a number of different nozzlegeometries and configurations such as planar, single and multipleround and elliptical nozzles have been investigated to date[4,1,6]. However single round jets are preferred due to symmetricboundary conditions and simplicity. Martin [16], Down and James[5] and more recently Jambunathan et al. [12] provide an excellentreview of the heat transfer characteristics of circular impingingjets.

From the previous work it is evident that the important factorsthat play a significant role in the enhancement of the transportproperties of impinging jet are the Reynolds number, nozzle diam-eter, impingement distance i.e. spacing between the nozzle and thewall, and turbulence levels in the jet. Lee et al. [13] showed that lo-cal Nusselt number increased in the stagnation point region withan increase in the nozzle diameter and attributed it to the increasein the jet momentum and turbulent intensity levels attained withlarge nozzle diameter. In the case of annular jets it has been shownthat with decreasing distance between the nozzle and the plate,the velocity approaching the impingement surface increasedresulting in higher heat transfer along the flow direction and in

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: +1 334 844 6803.l.osu.edu (S. Bhattacharya),

the vicinity of the attachment point [11]. Popiel et al. [17] recom-mended placement of the flat plate at the end of the potential coreregion of the jet in order to attain maximum heat fluxes at the stag-nation point. Guo and Wood [8] made measurements along thestagnation streamline of a plane jet impinging on a flat plate andmaintained the spacing in such a way so that the stagnationstreamline remained in the potential core of the jet. They foundthat in the region close to the plate the attenuation of streamwisevelocity caused a large velocity gradient which contributed to in-creased level of normal stress. The spectral decomposition of thevelocity and pressure fluctuation showed that the increase in thelevel of energy production was mainly due to the low frequencymotion.

A typical streamline pattern of an impinging jet without excita-tion or flow modification is shown in Fig. 1. Since the heat transferis high in the vicinity of the stagnation point, two techniques havebeen attempted in experiments to improve the performance ofin-line jets. First by increasing the turbulence levels by pulsation[2], excitation [14], or by introducing intermittency in the flow[18], and secondly by physically displacing the stagnation stream-line over a wider region [7].

This paper describes experimental investigation of an inexpen-sive and simple method to improve convective heat transfer of animpinging jet. Unsteadiness in the jet was introduced by placing aneccentrically mounted round cylinder and an airfoil near the nozzleexit. As a result of the fluid–structure interactions both oscillatedfreely about the longitudinal axis and imparted multiple scales tothe jet in addition to oscillatory dislocation of the stagnationstreamline from its mean trajectory. In addition a stationary roundcylinder was also tested. The heat transfer coefficients and the sur-face pressure distributions of all three were compared with theunperturbed in-line jet.

Fig. 1. Streamlines of an impinging jet.

634 S. Bhattacharya, A. Ahmed / Experimental Thermal and Fluid Science 34 (2010) 633–637

2. Experimental setup

The test setup is presented in Fig. 2. The nozzle consisted of astraight tube of 50 mm inside diameter and 15 cm in length con-nected to a reservoir with flow conditioning screens and honey-comb. A separate attachment was clamped near the exit of thenozzle to hold the cylinder and airfoil without disturbing the jet.Cylinder models were made from solid aluminum stock of nominaldiameter of 1 cm. One cylinder had a mounting pin at the centerand the second cylinder had the pin located at 2.5 mm from thecenter allowing the cylinder to oscillate when positioned in thejet. The streamlined airfoil consisted of a NACA 23012 airfoil sec-tion and had a chord length of 12 mm. It was equipped with themounting pin that was located at 3 mm from the leading edge. Be-cause of the camber of the airfoil the flow was not symmetric andas a result the airfoil oscillated when placed in jet.

Tests consisted of measurement of mean surface pressures andheat transfer on a flat plate during jet impingement for four casesconsisting of (1) in-line jet, (2) in-line jet with stationary cylinder,(3) in-line jet with eccentrically mounted oscillating cylinder, and(4) in-line jet with oscillating cambered airfoil. A calibrated in-lineflow meter was used to determine the flow rate through the noz-zle. The mass flow rate was held constant at 0.061 kg/s that re-sulted in a jet exit velocity of 25 m/s and a correspondingReynolds number of 83,000 based on nozzle diameter. Exit velocitywas also calculated from the difference between the stagnationpressure and the atmospheric pressure and was found to be ingood agreement with the velocity calculated from the flow meter.

Fig. 2. Setup.

2.1. Pressure measurement

An acrylic flat plate with a single pressure tap in the middlewas used for pressure measurement. The plate was mounted ona computer controlled single degree of freedom traversing systemthat traversed the plate±10 cm from the centerline of the jet. Thevertical spacing between the nozzle and the plate was 10 cm andwas held constant for all tests. The pressure tap was connected toa calibrated differential pressure transducer. Analog signals fromthe pressure transducer and traversing system were digitizedusing an A/D board and sampled at 1500 Hz. At each position5 s of data was recorded with a 10seconds of settling time. Pres-sure transducer calibration was checked before and after eachtest condition. From the datasheet provided by the manufacturer,the accuracy of the pressure transducer was found to be 0.5% offull scale output. The total relative standard uncertainty due totransducer calibration and A/D board resolution error was below3%.

2.2. Temperature measurement

Test setup for the heat transfer measurement is presented inFig. 3. An Inconel 600 nickel alloy foil of 1 mil (25.4 lm) thicknesswas held securely on a porous acrylic plate mounted on a plenumconnected to a vacuum pump. With adequate seals provided at theedges a slight vacuum ensured flatness of the foil. Two linear rollertype electrodes were connected to a power supply for heating thefoil at a constant voltage and for energy input calculations. A ther-mal image of the unheated foil (with the airflow coming out of thenozzle and impinging the foil) was taken to establish a base tem-perature distribution. A power of 50 W was supplied from a powersource (HP model 6023A) with an average of 2 V and 25 amperecurrent. After the voltage was applied across the foil, it was al-lowed to reach steady state in approximately 20 min. Then a sec-ond thermal image of the heated foil with impinging jet wasrecorded. Both the images were stored in the computer digitallyand then the image of the unheated foil was subtracted from theimage of the heated foil. Considering the foil material to be homog-enous (without any imperfection which promote formation of hotspots), the heat input per unit area can be taken as constant. Sincethe temperature change and energy per heated area is known, localheat transfer coefficient can be calculated using the followingrelationship:

q ¼ hðTh � TcÞ

Here h is the convection heat transfer coefficient and Th and Tc

refers to hot and cold temperatures of the foil.

Fig. 3. Setup for temperature measurement.

S. Bhattacharya, A. Ahmed / Experimental Thermal and Fluid Science 34 (2010) 633–637 635

This process was repeated for each test configuration. Theuncertainty in the thermal imaging experiment was well within5% for 15 image average.

2.3. Flow visualization

Flow visualization experiments were conducted in a water tun-nel to understand the kinematics of the flow. An Argon Ion laserwith a combination of cylindrical and spherical lenses was usedto produce light sheet that illuminated the jet impinging on thetunnel floor. A Panasonic CCD camera and a VCR were used to ob-tain and record the data. Video records were played back frame byframe for qualitative analysis. The entire nozzle assembly was in-stalled in the water tunnel on a three axis traversing system. Waterwas supplied to the nozzles by a flexible hose and metered withthe help of a King Instruments rotameter. Average flow rate wasmaintained at 120 L/min that provided jet exit velocity of 1 m/sand a Re of 50,000. Because of the high flow rate, hydrogen bubblesand injection of fluorescent dye were not successful. However itwas noted that an adequate amount of air was present in the oscil-lating jet system for flow visualization.

3. Results and discussion

Surface pressures measured along the plane of symmetry of thejet for four cases are presented in coefficient form in Fig. 4. Pres-sure coefficients were calculated using:

Cp ¼p� patm12 qjetU

2jet

Here p � patm is the differential pressure referenced to atmo-spheric pressure and qjet and Ujet are density and exit velocity ofthe jet respectively.

As can be seen in Fig. 4 the spread of jet after impingement isconfined to ±2 jet diameters from the centerline and becomes awall jet that loses momentum rapidly as it moves outwards. In-linejet produces a single high pressure peak directly underneath the jetand is symmetric. With the cylinder in place the pressure coeffi-cient plots shows two distinct peaks that are due to the impinge-ment of shear layers from either sides of the cylinder with oneside dominating and is typical of bluff body wakes. Interestingly

Fig. 4. Mean surface pressure distribution.

enough the stationary and oscillating cylinders show similar trendsbut that was expected as the amplitude of oscillations was ob-served to be well within the range of shear layer excursions. How-ever the pressures registered for the oscillating cylinder are higherand is attributed to the narrowing of the wake. In comparison thecambered airfoil produced less velocity deficit because of thestreamlining and hence the jet traversing the airfoil imparted high-er momentum to the wall. Asymmetry in the pressure distributionis due to the camber of the airfoil. The lowest centerline pressurewas exhibited by the stationary cylinder. The oscillating cylinder,being free to rotate, allowed more fluid to be driven down towardthe plate directly below it than the stationary cylinder.

The image presented in Fig. 5 shows the temperature differen-tial after the thermal image of the unheated foil with impingingjet was subtracted from the thermal image of the heated plate withimpinging jet, taken in quiescent environment. Thus a lower tem-perature indicates higher heat transfer rate. Although the experi-mental setup prevented viewing of the region directly, it did notsignificantly affect the extraction of important thermal parameters.It is evident that the region of highest heat transfer exists directlybelow the jet surrounded by a ring of lower heat transfer as theflow moves outwards. Because of the high velocity, jet cannot turnsmoothly after impingement and consequently it separates andreattaches resulting in the formation of secondary ring around 1nozzle diameter from the centerline. This ring also signifies thepresence of a separation bubble or recirculation region consistingof trapped eddies. Trapped eddies are a common feature howevertheir residence time in a ‘‘trapped position” varies for differentflows. Eventually they are ejected and replaced by other eddies.In an instantaneous snap shot, these eddies do appear as trapped.A separation bubble is a characteristic of impinging jets. They areformed as a consequence of impingement, separation and reattach-ment of shear layer vortices on the plate .This feature was observedfor all cases and confirmed during flow visualization tests.

In calculating the Nusselt number Nu ¼ hdk , the local convective

heat transfer coefficient was determined for a given element ofarea A from:

hloc ¼Q conv

AðTplate � T jetÞ:

For the average Nusselt number, the average heat transfer coef-ficient then written as

havg ¼2pR Rf

R00 hloc

rR0

� �d r

R0

� �

pR2

f

R0

� �

In which r/R0 is a dimensionless radius measured from the jetcenterline and Rf/R0 is the dimensionless radius over which theintegration is performed. The value of havg at a given radial locationRf is the effective heat transfer coefficient for the entire disk fromr = 0 to r = Rf.

Fig. 5. DT distribution for oscillating jet.

Fig. 6. Distribution of local Nusselt number.

636 S. Bhattacharya, A. Ahmed / Experimental Thermal and Fluid Science 34 (2010) 633–637

Fig. 6 show the variation of local Nusselt number in the radialdirection starting from the region near the geometric centerlineof the impinging jet. Note that a slight displacement of curves fromr/d = 0 is primarily due to the experimental setup that blocked thethermal imager view of the plate directly under the jet. The in-linejets shows a rapid drop of Nusselt number away from the stagna-tion point followed by another increase around r/d = 2 and taperingoff beyond that point. Similar characteristics of outer flow are alsovisible for other cases as well and are attributed to the interactionbetween the shear layer and the boundary layer on the plate as theflow moves outwards as a decaying wall jet. In contrast, all otherimpinging jets produced a gradual drop in Nusselt number andhigher heat transfer compared to the in-line jet. These trends alsoapply to the average Nusselt number plot presented in Fig. 7. Theoscillating jets show improvements over the in-line jet by as muchas 20% for the configuration tested, with the oscillating airfoilshowing the highest heat transfer coefficients. Also, a drop in Nus-

Fig. 7. Distribution of average Nusselt number.

selt number corresponding to the low heat transfer is discussedearlier in conjunction with the Fig. 5.

Results of oscillating cylinder can be explained in terms of thewake vorticity dynamics. Both configurations produced Karmanvortices however in the case of oscillating cylinder; the stagnationstreamlines moved a finite distance away from the centerline. Theoverall heat transfer therefore is a result of higher turbulent mixingdue to a combination of shed vortices and excursions of attach-ment flow in the stagnation region. Airfoil wakes have concen-trated vorticity near the trailing edge and for low angle ofincidences there are no large vortices. Results however show thatthe oscillating airfoil had the highest heat transfer. This is attrib-uted to the curvature of streamlines in the wake due to the airfoilcamber. Consequently, the attachment streamlines were displacedover a larger area and hence the higher heat transfer.

Limited flow visualization experiments were pursued to quali-tatively determine the flow properties that governed the heattransfer characteristics. The oscillating cylinder and the stationarycylinder showed similar flow pattern however the Karman vorticeswere more stable in the stationary cylinder wake. Because of thepresence of wall, shear layers on either sides of the cylinder werecompressed in way that reduced the spacing between the Karmanvortices and shortened the vortex formation region. A topologicalcartoon of the flow presented in Fig. 8 shows the presence of saddlepoints between the vortices and the stagnation point in itself is ahalf saddle of attachment. A considerable amount of recirculationwas also observed. As the flow turned outwards, vorticity in theshear layer and the boundary layer being of opposite sign helped

Fig. 8. Flow pattern with stationary/oscillating cylinder.

Fig. 9. Flow pattern with oscillating airfoil.

S. Bhattacharya, A. Ahmed / Experimental Thermal and Fluid Science 34 (2010) 633–637 637

diffuse the flow more rapidly as evident from the relaxation of sur-face pressures in Fig. 4.

In the case of the oscillating airfoil, a single stable vertical struc-ture was observed (Fig. 9). This vortex was spatially not very stableand was driven outward by the flow soon after its formation. Thestagnation point (again a half saddle point) was not stationary,and no trapped recirculating eddy was observed. The last twoobservations explain the high heat transfer coefficient of theimpinging jet with airfoil induced oscillations. The fact that the air-foil had only a small effect on the pressure distribution but higherheat transfer characteristics after impingement indicate that thiswas primarily due to the oscillatory dislocation of the stagnationstreamline.

4. Conclusion

A simple method of improving the transport properties of in-line jets by inducing oscillations in the flow was tested. Three con-figurations were used for this purpose, a stationary cylinder, aneccentrically mounted cylinder and an airfoil subjected to self in-duced oscillations. The ensuing oscillating jet configurationsshowed higher heat transfer rates than in-line jet tested underthe similar conditions. The improved heat transfer characteristicsof the impinging jet were attributed to two mechanisms consistingof enhanced mixing/turbulence due to bluff body wakes vortexdynamics and oscillatory dislocation of the stagnation streamline.The oscillating airfoil showed the greatest heat transfer rates ofthe four configurations tested. The airfoil produced the greatestdislocation of the stagnation point on the plate, and it had a min-imal amount of recirculation directly under the airfoil. This simpletechnique has promise in mixing and drying applications withminimum external energy input.

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