Journal of Applied Fluid Mechanics, Vol. 4, No. 2, Issue 1, pp. 137-149, 2011.Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.

Convective Heat Transfer in Impinging- Gas- JetArrangements

J. M. Buchlin†

von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, Rhode- Saint- Genèse, B- 1640, Belgium

†Corresponding Author Email: buchlin@vki.ac.be

(Received July 16, 2010; accepted March 13, 2011)

ABSTRACT

The paper deals with heat transfer by convection between impinging gas jets and solid surfaces. It considers bothsingle and multiple jet systems. It emphasizes the flow and geometrical parameters as well as the environmentconditions at which the jet emerges. In particular, it points out the effect of the jet tilting, thermal entrainment and jetconfinement. ASN and ARN schemes are illustrated through industrial and aeronautical applications. Designcorrelations are proposed. Experimental data obtained from infrared thermography are compared to CFD simulations.

Keywords: Convective impinging, Cooling & heating, IR Thermography, CFD simulation.

NOMENCLATURE

D Nozzle diameter (m)E Emergence distance (m)e Plate thickness (m)h Heat transfer coefficient (W/m2K)f Frequency (Hz)k Thermal conductivity (W/m.K)Nu Nusselt numberRe Jet Reynolds numberq Heat flux (W/m2)r Radial coordinate (m)T Temperature (oC or K)U Jet velocity (m/s)W Nozzle- to- nozzle spacing (m)x Abscissa or axial coordinate (m)

y Ordinate or transversal coordinate (m)Z Standoff distance (m)Greek letters

EmissivityRecovery factor

Superscripts- - - Spatial averageSubscriptsa Air or ambiantaw Adiabatich Hydraulicj Jeto Stagnation

1. INTRODUCTION

The conversion and control of energy requiresimproving and mastering heat exchange mechanisms,which finally determine the efficiency of all theenergetic systems.

Among heat transfer devices, impinging fluid jets areextensively exploited because of their ability to producehigh local transport coefficients. Indeed, the large heattransfer rate obtained with impinging streams,compared with classical boundary layer flows explainthe popularity of this technique. In addition,impingement is often attractive for the designer, whocan easily control the area and the distribution ofthermal exchange. Impinging jet systems are present inmany industrial and engineering processes where heatand/or mass transfer prevail. Typical examples are theannealing of metal and plastic belts, the tempering ofglass sheets, the drying of paper and textiles, the

cooling of turbine blades, the chemical vapourdeposition, propulsion jet- to- flaps interaction in STOLaircraft and the aircraft antiicing.

The jet can be formed by round (SRN) or slot nozzle(SSN) depending on the application. In some situations,the jet expands in a confined space either because thestandoff distance of the nozzle exit with respect to thesolid surface is small or because roofing exists aroundthe jet or because the jet is surrounded by otherneighbouring jets. If the impacted surface is concavethe jet may flaps naturally. Moreover, most of the heattransfer systems rely on arrays of nozzles oftencharacterised by small pitch ratio. All thesecircumstances may affect the jet development andmodify the impingement conditions so that the heattransfer differs from the classical unconfined single jetconditions.

In this perspective, the paper discusses the thermalconvective exchange between impinging

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incompressible gas jets and solid surfaces. The singleand multiple jet systems are successively considered.The flow and geometrical parameters and theenvironment conditions at which the jet emerges areemphasised. In particular, the effect of the jet tilting,thermal entrainment and jet confinement are pointedout. Array of slot nozzles (ASN) and array of roundnozzles (ARN) schemes are illustrated throughindustrial and aeronautical applications. Designcorrelations are proposed. Experimental data obtainedfrom infrared thermography are compared to CFDsimulations.

2. EXPERIMENTAL METHODOLOGY

Different methods have been proposed to determine thelocal and average convective heat transfer on surfaceimpacted by fluid jets. Most of them are experimental.They generally rely on the use of heated or cooled flatplate instrumented with temperature sensors and/orcalorimeters (Huang 1963; Hollworth & Berry 1978;Hrycak 1983; Goldstein & Behbahani 1982; Hollworth& Wilson 1984; Hollworth and Gero 1985; Goldstein etal. 1986, 1990). However, mass transfer analogyinvolving water evaporation (Martin 1977), naphthalenesublimation (Koopman & Sparrow 1976; Sparrow &Lovell 1980) or diffusion- controlled electrolysis(Vallis et al. 1978) is also adopted.

Nowadays, electro- optical techniques with (quasi) non-intrusive property such as liquid crystal method andinfrared thermography have emerged. They yield bothflow visualization and quantitative measurements whenassociated with digital image processing (Buchlin 1986a- b; Buchlin & Arts 1991; Balageas 1993; Carlomagno1993, 1997; and Carlomagno et al. 1998). Liquidcrystal technique has been successfully applied to heattransfer of single jet and arrays of jets (Den Ouden &Hoogendoorn 1974; Goldstein & Timmers 1982;Baughn & Shimizu 1989). The author has initiated theapplication of quantitative thermography to thermaldiagnostic of jet impingement onto a thin heated foil(Buchlin 1986a; Gartenberg 1992). Further studies haveproved that such a technique is a convincing tool fortemperature measurements of high resolution at theimpact zone of an impinging jet (De Luca et al. 1992;Page et al. 1993; and Meola et al. 1994, 1995, 1996).The potency of the quantitative infrared thermographyto determine accurately the convective heat transfercoefficients in many flow situations has beenextensively demonstrated (Buchlin 1993; Buchlin &Tasse 1996; Buchlin & Pelmann 1996; Carlomagno1997; Carlomagno et al. 1998; Buchlin & Chartier1999; Buchlin 2002; Buchlin 2010).

Finally, it is worth noting that Martin (1977) andJumbunathan et al. (1992) have presented extendedreviews of heat transfer data of impinging, wheredesign correlations for several nozzle types and nozzlearrangements can be appraised.

Figure 1 outlines a typical arrangement of theexperimental IR Thermography set- up commonlyoperating at the VKI for SRN, SSN, ARN and ASNinvestigations. For SRN, simple pipe or aerodynamicconvergent nozzle may produce the round air; the exit

diameter D is ranged from 0.005 m to 0.05 m. For SSN,the slot size may vary from 0.001m to 0.08m.

A heat exchanger controls the air temperature of theresulting jet(s). The impacted target consists of ahorizontal flat or concave plate made of a thin copperfoil, 40 m thick, fixed on an epoxy sheet withthickness less than 1mm. The foil is chemically treatedor machined to produce tight groves of about 1 or 2 mmforming a continuous electrical resistance of high value.The resulting circuit is connected to an electricalgenerator monitored by ammeter and voltmeter. Thefoil is uniformly heated by Joule effect.

nozzle

mirror

IR scanner

IR ProcessorHost PC Air supply

Flowmeter

HeatExchanger

Heated foil

nozzle

mirror

IR scanner

IR ProcessorHost PC Air supply

Flowmeter

HeatExchanger

Heated foil

Fig. 1. Principle of IRTh test setups

The rear face of target is scanned by the IR camera; it iscoated with a black paint of emissivity w = 0.96 toimprove the IR thermography measurements and allowcorrection for radiation. It is worth noting that thethermo foil Biot number, Bi=h.e/k, is generally smallenough (< 0.1) to neglect temperature variation throughthe plate. Nevertheless, the plate encompasses flushmounted thermocouples that allow the fine calibrationof the IR measurements.

The local convective heat transfer coefficient is inferredfrom the steady- state temperature of the local wall Twby application of the Newton law:

cv

w ref

qhT T

(1)

Tref is a reference jet temperature; it could be therecovery temperature Taw or the plenum temperature Tj.The choice of Tref depends on the exit jet conditionssuch as the jet Mach number (compressibility effect),the mismatch temperature between the jet and thesurounding environment, (§ 3.1.4)

The convective flux qcv is determined by subtracting theheat losses, ql , to the Joule heating, qJ . The heat lossesinclude the contribution of the radiation, qrad , of theconduction, qcd, and of a possible natural convection onthe face not exposed to the jet flow. The two-dimensional fin theory allows the derivation of thefollowing expression:

w tot w aq e k T h T T (2)

The global heat transfer coefficient, htot, models bothnatural convection and thermal radiation effects. Eqs.(1) and (2) show that the convective heat transfercoefficient is determined readily once the foil propertiesand the temperature field Tw are known.

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The evaluation of the conduction term is trickier: itrequires an estimation of the second derivative of thewall- temperature distribution. Such a computation,which may introduces significant noise, demands tosmooth properly the IR raw data before finalprocessing. In steady state experiments as it it is thecase here, the noise reduction can be achieved byaveraging a sufficient number of thermogrammes(thermal images) acquired in a time sequence. Anotherprocedure consist applying a filtering algorithm. Forinstance, a fast Fourier transform of the signal andappropriate restoration of the thermogramme allow theelimination of spurious high frequency oscillations inthe temperature field.

The aforeproposed thin- foil design, where the groovesare perpendicular to the heat flow direction both for theround and slot jets leads to minimise the conductionloss, which typically does not exceed 2% of theconvective flux. The heat loss by radiation remainsgenerally smaller than 5% of the total flux. Detailederror analysis indicates that the local uncertainty of theconvective h- value is around 10%.

3. RESULTS

3.1 SRN Jet

3.1.1 Isothermal Round JetExperiments have been conducted with isothermal(temperature equal to ambiant temperature) round jetimpinging perpendicularly to a flat plate. Figure 2shows a typical IR thermogramme (false colors). Itdemonstrates the good axisymmetry of the thermal field.The non- uniform temperature field exhibits concentriccold and hot rings revealing the presence of high andlow heat transfer regions.

Tw - Profile

Hot ring

2nd Cold ring

T [ºC]

Stagnationarea

1st Cold ring

Fig. 2.Temperature mapping at the impingement of aperpendicular SRN jet.

Such a thermal distribution agrees perfectly withvelocity field obtained by PIV measurements aspresented in Fig. 3 (Buchlin & Laperches 1998).

The arrows in Fig. 3 draw attention on the mainobservations, which agree in every respect with thesparse literature on the subject (Landreth et al. 1990;Meola et al. 1996). A radial acceleration zone isdetected just after the stagnation point in a regionlocated between 0.6 and 1 r/D. Then a wall jet buildsup counter rotating primary and secondary vortex rings(the latter not very well captured due to light reflectionproblem): that provokes local flow detachment causingheat transfer decrease, and then flow reattachmentlocated at about r/D=2.4 (with a good repeatability)where transition to turbulence of the wall jet is

anticipated and subsequent heat transfer rise is detected.

Reattachment Acceleration

r/D

primary vortex ringssecondary vortex rings

Z/D

0.6JetRe=60000 ; Z/D=1

Reattachment Acceleration

r/D

primary vortex ringssecondary vortex rings

Z/D

0.6JetRe=60000 ; Z/D=1

Fig. 3. Velocity vector mapping from PIV at theimpingement of perpendicular SRN jet

The radial distribution (along line drawn in Fig. 2) ofthe local Nusselt number, Nu= hD/ka, is plotted inFig. 4. The effect of the jet Reynolds number Re andthe normalised standoff distance Z/D on the radialNusselt number distribution is emphasized.

At very small standoff distance the Nu- profile displaystwo distinct peaks. The inner (primary) maximumhappens around r/D=0.7 while the outer (secondary)peak is situated close to r/D=2.4. These two heattransfer peaks correlate very well with the accelerationand the reattachment and/or turbulent zones of the walljet as depicted in Fig. 3. At small discharge distance, thesecondary peak dominates as Re increases. As higherstandoff distance and/or as the Reynolds numberdecreases the inner and outer peaks vanish and themaximum heat transfer moves to the stagnation point;there, the distribution takes a conventional bell shapeprofile. All these heat transfer distributions corroboratevery well with other findings published in the literature(Gardon & Akfirat 1965; Den Ouden & Hoogendoorn1974; Baughn & Shimizu 1989; and Meola et al. 1994).

0 1 2 3 40

50

100

150

200

250

Z/D=1.5r/D

Nu

Re24000 42000 51000 60000

0 1 2 3 40

50

100

150

200

250

Z/D=5.6r/D

Nu

0 1 2 3 40

50

100

150

200

250

Z/D=1.5r/D

Nu

Re24000 42000 51000 60000

0 1 2 3 40

50

100

150

200

250

Z/D=5.6r/D

Nu

Fig. 4. Radial Nu- profile for perpendicular SRN jet.Effect of Reynolds number and standoff distance

The magnitude and position of the two heat transferpeaks are plotted in function of the standoff distance inFig. 5. The primary peak remains located at r/D=0.7where flow acceleration develops. The position of thesecondary peak, which is linked to the flowreattachment and/or turbulence occurrence, evolves: itmoves outwards as Z/D increases and stops at aboutr/D = 2.4 when Z/D becomes larger than 2. Such

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behaviour agrees well with the Lytle & Web data (1991).Below Z/D = 2 the outer peak is the stronger, especiallywhen Re is large; above Z/D=3, the heat transfer profiletends to the conventional bell shape.

0 1 2 3 4 5 60

50

100

150

200

250

PeakSecondaryPrimaryStagnation

Nu

Z/D

Re=60000

Re=24000

0 2 4 60

1

2

3

Re peak60000 secondary60000 primaryLytle & Webb24000 secondary24000 primary

r/D

Z/D

Fig. 5. Behaviour of heat transfer peaks forperpendicular SRN jet.

The VKI IR results shown in Fig. 6 reproduce theexperiments that conducted Hollworth & Gero (1985)with the microfoil – heat – flux - sensor technique.Although the IR results are somewhat above the dataobtained Hollworth & Gero, good agreement is foundfor the stagnation heat transfer that yields the followingcorrelation:

0.650 oNu = C Re (3)

Eq. (3) indicates that the flow in the stagnation zone israther close to laminar regime, which is usuallymodelled by Re0.5.

-6 -4 -2 0 2 4 60

40

80

120

160Re = 20000Re = 10000Re = 5000

000

r/D

Z/D= 6

VKIHollworth

& GeroNu

Fig. 6. Comparison between IR data and literature

An averaged stagnation Nusselt number Nuo defined asthe mean coefficient between the stagnation value andthe inner peak value when existing, is plotted versus thenormalised standoff distance Z/D in Fig. 7. The IR-thermography results compared well with data obtainedwith several other measurements techniques (Gardon &Akfirat 1966; Hrycak 1983; Hollworth & Gero 1985;Goldstein et al. 1986; Baughn & Shimizu 1989; Gau &Chung 1991). Most of the data confirm that themaximum of the stagnation heat- transfer rate isobtained when the normalised standoff distance has avalue ranged between 6 and 8. This maximum, whichdepends also of the initial jet turbulence intensity(nozzle design) (Nakatogawa & Nishiwaki 1970)occurs when the axial increase of turbulence in the jetdue to air entrainment (mixing- induced turbulence),does not compensate for the fall in the jet velocity. Inother words, that corresponds more or less to the end ofthe potential core and the arrival of turbulence from theshear layer at the stagnation zone.

0 5 10 15 200

0.5

1

1.5

VKIBaughnGoldsteinGardon

GauHrycakHollworth

Nuo/Numax,o

Z/D

Fig. 7. Effect of the normalized standoff distance on thestagnation Nusselt number

3.1.2 Isothermal Lobed JetThe design of the nozzle exit influences the jetbehaviour and consequently may enhance or deterioratethe resulting convective heat transfer. In this purposelobed nozzles have received also peculiar attention atthe VKI (Herrero Martin and Buchlin 2010). Nozzleswith the same hydraulic diameter but shaped with three(L3) and four (L4) lobes have been tested. Typicalthermogrammes obtained with these nozzles aredisplayed in Fig. 8.

L3 L4

Fig. 8. Typical thermograms: Re=9000 and Z/Dh =1

As illustrated in Fig. 9, it turns out that for Reynoldsnumber higher than 10000 the effect of the exitsilhouette affects noticeably the heat transferdistribution. In terms of enhancement, the nozzle L3prevails over the L4 nozzle, which yields similarperformance than the round nozzle.

-6 -3 0 3 60

100

200Nozzle

3 Lobes4 LobesRound

Nu

r/Dh

Re=18000

-6 -3 0 3 60

100

200

300

400Nozzle

3 Lobes4 LobesRound

Nu

r/Dh

Re=50000

Fig. 9. Nusselt number distribution for lobed ad roundnozzles: Z/Dh=1.3.

3.1.3 Isothermal Tilted JetIn many applications, the shape of the target or theconstraints on the nozzle positioning may lead to theformation of an oblique jet (Kamoi & Tanaka 1972;

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Sparrow & Lowell 1980). The jet impacts the targetwith a tilting angle. This situation has been studied inrelation with jet/flap interaction (Foss & Kleis 1972,1973) and for confined liquid jet (Smirnov et al. 1961).Such a situation is also encountered when theimpinging jet emerges in a cross flow which may becaused by the spent air in the case of arrays of nozzles.(Metzger & Korstad 1970; Bouchez & Goldstein 1975;Metzger et al. 1979; Goldstein & Behbahani 1982;Florschluetz et al. 1984; Obot & Trabold 1987).

As the jet impinges the solid surface with an angle ofattack smaller than 90 (with respect to the horizontaldirection) the thermal field at the impact is distortedand an unbalanced local heat transfer is observed on theuphill and downhill sides. The thermogrammesdisplayed in Fig. 10 illustrate this effect.

=60 Re=20000,Z/D=2

= 15 , Re= 65000,Z/D=7

Fig. 10. Thermogrammes of impinging round jet

The tilting of the jet results in an enlargement the heattransfer area in the flow direction and a subsequentdiminution of the heat transfer coefficient as shown inFig. 11 where the reduced Nusselt number Nu*, definedas the ratio of Nu( ) to Nu(90 ) determined at thestagnation point for the same flow conditions, is plottedversus the angle of attack.

10305070900

0.2

0.4

0.6

0.8

1

Re100004000065000 [ ]

Nu* Z/D = 2

10305070900

0.2

0.4

0.6

0.8

1

Re100004000065000MT- 5000

[ ]

Nu* Z/D = 7

10305070900

0.2

0.4

0.6

0.8

1

Re100004000065000MT - 5000 [ ]

Nu* Z/D = 15

Fig. 11. Effect of the jet tilting angle on the stagnationNusselt number

Notice that in agreement with published literature, thestagnation heat transfer point is displaced downstreamand does not correspond to the geometrical impact ofthe jet (Bouchez & Goldstein 1975; Sparrow & Lowell1980; Goldstein & Behbahani 1982). This displacementincreases as decreases. The modest scatter of thedata leads to the conclusion that Nu* is a weak functionof Re in the range investigated (10000 Re 60000).Typically, as the angle of attack decreases of 50%, thestagnation Nusselt number drops by 40% almostindependently of the reduced standoff distance in thelarge range tested (2 Z/D 15). This behaviour ismuch marked than the influence shown by the results ofSparrow & Lowell (1980) when applying a masstransfer technique (MT=triangles in Fig. 11). Thediscrepancy may be explained by the lower value of theReynolds number used in the mass transferexperiments.

3.1.4 Non-Isothermal JetIn some impingement schemes, the jet is discharged inan environment at different temperature Ta. Due tomomentum exchange, the jet entrains within it anamount of the surrounding air so that the effective fluid-to- wall temperature difference is modifiedcomparatively to the case of isothermal jet. Such anaerothermal process affects the performance of non-isothermal impinging jets. Literature reports severalanalytical and experimental studies devoted to thiseffect (Schauer & Eustis 1963; Vlachapoulos & Tomich1971; Striegl & Diller 1984; Flor- schuetz et al. 1984;Hollworth & Wilson 1984a,b; Hollworth and Gero1985).

To address such a rather complex problem, the simplestmodel of single, cooled or heated air jet, submerged in aquiescent air at room temperature and impingingnormal to a constant- heat- flux flat plate is selected.The resulting data allow the identification of themismatch temperature effect, T= Tj- Ta , on theconvective heat transfer coefficient.

The entrainment process leads to a non uniform fluidtemperature distribution at the plate surface. It can bereadily determined by measuring the recovery oradiabatic temperature Taw measured on the plate fornon- heating condition. The results are plotted inFig. 12 in terms of the recovery factor defined as:

aw a j aT T T T (4)

-8 -4 0 4 80

0.2

0.4

0.6

0.8

1Z/D

369Model

r/D

Re=20000

Fig. 12. Typical radial distribution of the recoveryfactor

For isothermal conditions, = 1. For non- isothermaljet, exhibits a radial variation. A maximum is locatedat the stagnation point where impinging flow preservesa temperature close to the plenum jet temperature Tj.The recovery factor decreases radially as the wall jetdevelops. That denotes the predominant presence of theentrained fresh air on the edges of the jet. Goldstein andBehbahani (1986) show that the recovery factor doesnot depend on the jet Reynolds number Re. On otherhand, Hollworth and Wilson (1984) point out that above3, the normalised standoff distance has a weakinfluence on : subsequently, they suggest modellingthe radial - variation by:

ba r / D for 1 (5)Eq. (5) is plotted in Fig. 12 for a=1 and b=- 0.5

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(exponent b different from the value of 0.95 proposedby the previous authors). Agreement is obtained in thewall jet region (typically for r/D >2).

To include the thermal entrainment effect in the heattransfer correlation, the recovery temperature Taw istaken as reference instead of Tj in the definition of theconvective coefficient (Eq. (1)). The Nu-definitionbecomes:

cvw aw a

q DNu'T T k

(6)

Figure 13a proves the consistency of Eq. (4) since thestagnation Nusselt number Nuo’ remains fairlyindependent on the stagnation recovery factor o. Thedata scatter observed in Fig. 13a reflects the impliciteffect of the standoff distance, which is clearly pointedout in Fig. 13b.

Whatever the sign of the mismatch temperature, theadiabatic temperature allows the account of the non-isothermicity of the jet. Moreover, Fig. 13b reveals alsothat significant discrepancy may appear between theNusselt number values according to the temperaturereference chosen.

0.4 0.6 0.8 10

50

100

150

Re1000020000

Nuo' 3 Z/D 9

0 5 10 15 200

100

200

300

Nu' DT<0Nu' DT>0Nu DT<0Nu DT>0 Z/D

Nuo Re = 20000

=0

(a) (b)Fig. 13. Stagnation Nusselt number based on the

adiabatic temperature

3.1.4 Slot Jet on Concave SurfaceJet impingement on a concave surface may lead tooscillating flow. The resulting convective heat transferdue to such a jet fluctuation may differ from the case ofsteady jet onto flat plate. Buchlin et al. (2008) havestudied this flow situation; they investigated thebehaviour of a planar jet impacting the internal apex ofa V- shaped corner. Cheng- Kuang Lin et al. (1993) andGwo- Bin Lee (2002) have proved that such geometryinduces readily a periodic flapping motion of impingingslot jet.

Hot wire tests have been dedicated to the determinationof the flapping frequency, f, of the jet. FFT dataprocessing of the output signal shows that the Strouhalnumber Sr= f.Z/U is constant in the range of theReynolds number tested, as depicted in Fig. 14.

The flapping behaviour of the jet produces a change intime of the convective heat transfer as observed inFig. 15. Such results are proving that IR thermographytechnique is efficiently able to capture the trace of thesweeping jet and indicate that the local heat flux canvary by more than 20%.

10 11 12 13 14 150

0.25

0.5Sr

Z/Dh

2000 Re 6500Jet N

ozzl

eV-shap

e plat

e

Jet Noz

zleV-sh

ape p

late

Fig. 14. Flapping Stroual number

1 2 320

40

60

80f [Hz]

6 3.5

t [s]

h [W/m2K]

Fig. 15. Time variation of local heat transfer.

Figure 16 compares heat transfer data for V-shaped andflat plates obtained for same Reynolds number and apexstandoff distance. The time average Nusselt number isplotted versus the transversal normalized distance. Oneobserves that the jet flapping yields higher heatexchange performance mainly due to the periodic flowbehaviour and reduction of the effective standoffdistance when the jet is sweeping periodically.

0 5 10 15 200

10

20

30V-shapeFlat

Nu

y/Dh

Z/Dh = 15.8Re = 5270

Fig. 16. V- shape - flat plate comparison

3.2 Multiple Jet SystemsCooling devices based on impinging jets involvemainly arrangements of circular or plane jets.

ASN schemes are often used in paper drying, glassmanufacturing and fast cooling of metal strip (Buchlin& Dubois 1992; Buchlin at al. 2002b).

ARN schemes are frequently encountered in theinternal cooling of high- performance gas turbineengines, in particular for gas combustor and both statorvanes and blades (Hollworth & Berry 1978;Behbahani & Goldstein 1983; Florschuetz et al. 1984;Florschuetz & Su 1987; Al Dabagh et al. 1990;and Seol & Goldstein 1991). They are also extensivelyapplied to strip cooling (Buchlin et al. 2004) andthermal deicing systems of airplanes (Buchlin et al.1994; Planquart et al. 2005).

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3.2.1 ASN SchemesThe study of ASN scheme involves a new designparameter, which is the nozzle- to- nozzle spacing, W,normalised by the hydraulic diameter Dh. The ASNdesign is first investigated by testing a 3- jet array. Sucha simple configuration features the main phenomenathat occur in multiple slot systems.

Experimental findings for Re=11000 and W/Dh=10 arepresented in Fig. 17, where the Nusselt numberdistribution along the mid plane of the target, is plotted.The non- symmetry of the Nu- distribution with respectto the axis of the central jet, highlights the jet- to- jetinterference as reported by Gardon & Akfirat (1966),Hollworth & Berry (1978), and Goldstein & Timmers(1982).

At small normalised discharge distance equal to 8, jet-to- jet interaction occurs before impingement and heattransfer peaks are no longer equal. Such a jet layout isnot stable, indeed: small difference in air supply mayprovoke unbalanced entrainment and subsequentdestabilization. This is reflected by the deflection of theouter left jet, which triggers a drop of the heat transfercoefficient similarly to oblique impingement.

At higher standoff distance, Z/Dh=20, and sameReynolds number, smoke flow visualization performedwith laser- sheet technique, discloses the existence oflarge oscillations of the central jet. This jet flapping ischaracterized by a Strouhal number based on standoffdistance, equal to 0.013; this value is very close to thatobtained previously with the V- shape plate (§3.1.4). Inthe present case the jet sweeping smoothes out thepresence of the central stagnation heat transfer peak asshown in Fig. 17.

-2 -1 0 1 20

10

20

30

40

50

Z/Dh820 : flappingGardon x/W

Nu 3 slot nozzles

Re = 11000W/Dh = 10

Fig. 17. Nu- profile for ASN: effect of Z/Dh

Figure 18 reports an attempt to reproduce theseexperiments by CFD simulation, which is performedwith Fluent code using a k- turbulent model based onthe Renormalization- group theory (Smith 1991). Goodagreement is reached for the smaller standoff distance.As expected, the numerical computation does notcapture the case of flapping condition although thepredicted heat transfer peak values of the external jetsdo not differ drastically from the experimental data.From this experimental- CFD comparison, one canconclude that the central oscillating jet has not a sostrong influence on the heat transfer in the stagnationzone of the two other neighbouring jets.

0 0.25 0.5 0.75 10

10

20

30

40

50IR-dataCFD

Re=11000Z/Dh=8W/Dh=10 x/W

Nu

-1 -0.5 0 0.5 10

10

20

30

40IR-dataCFD

x/W

Nu

Re=11000Z/Dh=20W/Dh=10

Fig 18. Experiment- CFD comparison: 3 slot nozzles

To get rid of end effect, the experiments are repeatedwith an array of 8 slot nozzles. Good repeatability ofthe heat transfer distribution is noticed in the centralzone of the array. For design purpose, it is moreconvenient to express the heat transfer correlation interms of an average dimensionless convective heattransfer coefficient defined as follows:

2

2

W/h

a W/

DNu h x dxk W

(7)

The results are plotted in Fig. 19, where the IR- data arecompared to predictions obtained with the correlationderived by Martin (1977) from mass transfer data, andCFD simulations achieved with Fluent code. Rathergood agreement is noticed.

0 20 40 60 80 1000

20

40

60

80

100

CFDIR data

NuIR

NuMT

3500 Re 200005 Z/Dh 409 W/Dh 100

_

_

Fig. 19. Experiment- CFD comparison: ASN scheme

To assess the suitability of the ASN- correlationproposed in Fig. 18 to industrial situation, temperaturemeasurements have been performed on an industrialgalvanization line. Mean temperature of movingmetallic strip has been measured with contactthermocouples at the inlet and outlet of a coolingsystem based on multiple slot jets. Simple lumpcapacity model is used to retrieve the values of the heattransfer coefficient from temperature measurements.

The good agreement depicted in Fig. 20 between theASN- correlation and industrial data, confirm itsapplicability even for the high jet Reynolds numberpractised in the present galvanisation line. ASNexperiments have also been conducted on a modelreproducing at scale 1/3 a industrial fast cooling plenumdesigned for continuous annealing or galvanizing lines.The schematic proposed in Fig. 20 shows that theplenum is composed of perpendicular (90º) and tilted(60º) slot nozzles with given emergence length, E.The normalised nozzle spacing may vary in the range

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6 W/Dh 18; the normalised nozzle emergencelength, E/Dh, from 5 to 17 and the normalised standoffdistance Z/Dh from 3 to 10. The maximum Reynoldsnumber can reach 100000.

0 25 50 75 10025

50

75

100

Line dataASN Cor.

<Nu>

10-3Re

Z/Dh=6W/Dh=24

Fig. 20. Applicability of the ASN - correlation togalvanisation line

Figure 21 provides also a restored IR thermogrammecorresponding to a typical slots arrangement. It is afaithful representation of the impinging flow. Thelowest temperatures are found at the impingement of90 jet. The cooling rate decreases as the jet angledecreases. The very low spanwise distortion of theisotherm contours denotes the quasi two- dimensionalcharacter of the impinging flow for this specificconfiguration.

E

W

Fig. 21. Schematic and IR thermogramme of ASNplenum

However, 3D numerical simulations of such a situationhas been performed with the code FLUENT. Themesh grid is composed of hexahedral elements leadingto 300000 cells. Figure 22 displays the completesurface mesh of the computational domain. Standardk- turbulence model with wall functions is used forthe computation. Second order upwind discretisationscheme is used for all the equations solved in steadystate. The standard Simple algorithm is adopted forthe pressure- velocity coupling. The boundaryconditions are imposed based on the experimentalconditions (temperature and velocity of the impingingjets, temperature of the ambient air, heat flux imposedon the heated plate).

Fig. 22. Surface grid of the of ASN plenum simulation

Figure 23 exemplifies the comparison between IRmeasurements and CFD simulation. The Nusseltnumber distribution along the centre line of the plate isplotted versus the normalized axial distance. On thewhole, one can spot good agreement considering such acomplex flow topology. Maximum predicted Nu-values are within 10 % of the experimental data. Yetminimum CFD Nu- values occurring between the jetsare smaller than the experimental data. Thisdiscrepancy results from the weak capability of thepresent steady state CFD modelling to capture theposition of the separation point and the associated dropof heat transfer rate.

-30 -20 -10 0 100

100

200

300

400

IR dataFLUENT

Re = 60000 Z/Dh = 4.55W/Dh = 14.5 E/Dh = 11.3

Nu

X/Dh

Fig. 23. Experimental - numerical comparison for ASNplenum

3.2.2 ARN SchemesTypical distribution of the dimensionless heat transfercoefficient in the case of three collinear round jetsproduced by nozzles separated by 4 orifice diameters isdisplayed in Fig. 24. A turbulent jet Reynolds numberequal to 22000 characterizes the flow conditions. TheNu- profile plotted along the central impingement lineis limited to the region including the inner and oneouter jet. Figure 24 affords additional interestinginformation compared to Fig. 17.

At low nozzle- to- plate distance (Z/D=2), the mainstagnation region of the jets exhibits a heat transferminimum, however less pronounced than in the case ofsingle jet, indicating that the jet- to- jet interactionenhances the mixing- induced turbulence that penetratesfurther in the core of the jet. Midway between theimpingement points, a secondary heat transfer peakarises. In their study, Gardon & Akfirat (1966) andGoldstein & Timmers (1982) make the sameobservation. Additional static pressure measurementson the plate testify that the secondary Nu maximum iscorrelated to a secondary pressure peak and providephysical explanation. As the wall jets approach one

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another, the pressure gradient increases provoking athickening the boundary layer: hence, a flow separationshould follow leading to the formation of a complexthree- dimensional vortical flow topology. FollowingDidden & Ho (1985), one anticipates that such aboundary layer separation evolves into the formation ofa large primary vortex associated with an intensesecondary vortex of opposite rotation that downwashesthe wall creating a high heat transfer rate.

-6 -4 -2 0 2 4 60.3

0.6

0.9

1.2 Z/D

27

Nu/Numax

x/DRe =22000

outer jetcenter jet

secondarypeak

Fig. 24. Nu distribution for collinear round jets.

Figure 25 displays typical mappings of the convectiveheat transfer coefficient in the case of staggered andnon- staggered round jet configuration.

Re =40000 Re=85000

(a) Staggered (b) Non staggeredFig. 25. IR thermogrammes in ARN.

An average Nusselt number is calculated on the cellarea defined by dashed contour specified in Fig. 25. Arelevant way to compare the present IR findings topublished data is to reformulate the results in terms ofdimensionless groups introduced by Martin (1977). Theaveraged Nusselt number is normalised by the fluidPrandt number, Pr, and geometrical functions, whichaccount for the effect of Z/D and W/D as follows:

23

0 42.NuNu* Re

Pr G * K (8)

where

0 3

2

1 1

0 61

4

.if F Z DG with F=

. fF if F

Dand f

Averaging Area

and

1 2 221 0 2 6

. fK f. Z D f

)

The correlation (Eq. 8) is announced to be valid for2 Z/D 12, 2000 Re 100000 and 0.004 f 0.04.The IR data for square and triangular patterns, whichsatisfy as close as possible the conditions of application

of the correlation (8) are plotted in Fig. 26. They arecompared to different published experimental data.Figure 26 points out that the IR data could be 15% to30% lower that the prediction obtained by thecorrelation (8) plotted as continuous line. Although thetrend Re2/3 is well reproduced, the spreading of the dataat constant Re indicates that Eq. (8) does not take intoaccount satisfactorily the effect of the geometricalparameters such as Z/D and W/D. Additionally the dataindicate that arranging the round nozzles in a square ortriangular pattern does not yield any difference in thefinal mean heat transfer coefficient.

1 2 3 4 5 6 7 8 9101

3

5

10

20

Freidman & MuellerGlaserHilgerothKrotzschOtt

15/1000.5Re^2/3-15/100-30/100VKI data 10-4Re

10-2NU*__

Fig. 26. Heat transfer correlation for ARN systems.

Recent designs of deicing or antiicing devices of wingand tail surfaces of airplanes are based on theaerothermal effect of ARN arrangements. A perforatedduct called ’’piccolo ’’ supply hot round as sketched inFig. 27. Such a configuration, which emphasises theimpingement of multiple jets on concave target, is alsoencountered in the cooling of turbine blades (Metzger etal. 1969). The hot air issuing from the holes andflowing on the inner surfaces of the skin prevents theice formation on the leading edge of the wing whenadverse flight conditions are experienced.

The operating window of thermal antiicing devices maybe rendered rather narrow due to the limited amount ofhot air delivered by the engines. Therefore, efficientdesign requires identifying the key parameters thatcontrol the convective heat transfer coefficient. Itsdistribution on the concave surface that constitutes theleading edge of an airfoil can be obtained by use of thequantitative IR thermography.

Fig. 27. Principle of thermal deicing

A typical mapping of the convective heat transfercoefficient for an arrangement of four rows of jets isshown in Fig. 28. It results from IR camera scanningfrom the intrados to the extrados of the leading edge.The abscissa x, and ordinate y, are normalised by the

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model length l and the chordwise length L, respectively.The confinement effect of the two central rows isdepicted by the highest h- values obtained in this zone.A sharp decrease of thermal exchange is also observedon the far intrados and extrados where the multiple jeteffect becomes weak.

Fig. 28. Heat transfer map in antiicing system

As usual, engineering consideration demands tocalculate a mean heat transfer coefficient. Here, theaverage area is the cell of the jet array. Dimensionalanalysis recommends plotting the dimensionless group<Nu>/RemPrn versus a geometrical factor Go defined asfollowing:

ba cpa c

jSS ZGo n

D D D (9)

where nj is the number of jets in the cell. Figure 29demonstrates the pertinence of the present Piccolocorrelation. Since the Prandtl number does not varysubstantially in the IR experiments, the exponent n isset equal to 0.4 to be consistent with literature. TheReynolds exponent m is found equal to 0.8 in goodagreement with data of Hollworth & Berry (1978),Behbahani & Goldstein (1983) and Florschuetz et al.(1984). However, it differs from the value of 0.7obtained by Jusionis (1970) and from the data of Meolaet al. (1994) who reach a surprising high value of 1.39.The curve- fit shown in Fig. 29 yield a=0.4, b=0.9 andc=0.1.

0 0.02 0.040

0.005

0.01

0.015

IR-dataFLUENT

Go

4.08.0 PrReNu

Fig. 29. Piccolo Heat transfer correlation

In the range of the geometrical parameters investigated,the normalised piccolo- to- skin distance has a smallinfluence on the convective thermal exchange. Such aresult fits the conclusion drawn by Kercher & Tabakoff(1970), Hollworth & Berry (1978) and Meola et al.(1994) while the Jusionsis’s correlation predicts a morepronounced effect since c=0.4.

The dominant parameter is the reduced spanwise jetspacing: as Sp/d decreases the dead zone between the jetimpingement shrinks and the average heat transfer rises.

The results of 3D numerical simulation performed withFluent code are also plotted in Fig. 29. They show thatCFD simulation approaches well the Piccolocorrelation.

4. CONCLUSIONS

Convective heat transfer at the impact of impinging gasjets on a solid surface is presented. Single and multiplejet systems based on round or slot nozzles areconsidered. The heat transfer data are obtained from theapplication of infrared thermography. Some PIV, hotwire and pressure measurements support the physicalflow interpretation. Additionally numerical simulationis conducted with the FLUENT code. The flow andgeometrical parameters as well as the environmentalconditions at which the jet emerges are emphasised.

The impingement zone is generally characterised by acomplex vortical flow topology. At low normalisednozzle- to- wall distance, the heat transfer distributionof single isothermal vertical jet may exhibit twomaxima controlled by flow acceleration and transitionto turbulence. As the discharge distance increases, themixing- induced turbulence leads to a moreconventional bell- shape profile. Stagnation heattransfer coefficient reaches a maximum for standoffdistance ranging between 6 to 8 orifice diameters. Heattransfer coefficient increases with the jet Reynoldsnumber with an exponent- value ranging from 0.5 to0.8.

The design of the nozzle exit may influence the jetdevelopment and consequently may affect theconvective heat transfer. The tilting of the jet provokesa distortion of the heat transfer distribution and adecrease of the stagnation value. Jet impingement on aconcave surface may lead to oscillating flowcharacterised by a constant flapping Strouhal number;the resulting jet sweeping enhances heat exchange.

Heat transfer performance of a non- isothermal jet isaffected by the thermal entrainment process and reliableheat transfer correlation has to be based on the adiabaticwall temperature. Such an entrainment phenomenonmay become a key parameter in single jet confinementor multiple jet arrangements.

In nozzle array systems the standoff distance and thenozzle- to- nozzle spacing control the jet- to- jetinteraction. Jet flapping has also been observed in ASNschemes; in this case the jet fluttering brings about asmoothing of the heat transfer distribution. In ARNschemes and at low standoff distance, a secondary heattransfer peak may arise midway two jets due to theirstrong interaction. The ASN and ARN layouts areillustrated through industrial and aeronauticalapplications such as the fast cooling of moving metallicstrips and the thermal anticing of airplanes. IR-thermography provides reliable design correlationswhich compare well to literature and CFDcomputations.

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