impingement slot

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Experimental study of convective heat transfer under arraysof impinging air jets from slots and circular holes

M. Can, A. B. Etemoglu, A. Avci

Abstract Impinging air jets are widely used in industry,for heating, cooling, drying, etc, because of the high heattransfer rates which is developed in the impingement re-gion. To provide data for designers of industrial equip-ment, a large multi-nozzle rig was used to measure averageheat transfer coefcients under arrays of both slot nozzlesand circular holes. The aim of the present paper is todevelop the relationship between heat transfer coefcient,air mass ow and fan power which is required for theoptimum design of nozzle systems. The optimum free areawas obtained directly from experimental results. The the-ory of optimum free area was analysed and good agree-ment was found between theoretical and experimentalresults. It was also possible to optimise the variables, toachieve minimum capital and running costs.

List of symbols Af free area, %B slot width, mmC 0 correlation constantC D coefcient of discharge, constant

D nozzle diameter, mmDn nozzle to nozzle spacing, mmG mass ow rate of air/unit area of heat transfer

surface, kg/m 2 sh average heat transfer coefcient, W/m 2 KK constantl slot length, mm_mw water mass ow rate, kg/s

Nu Nusselt numbern number of nozzlesPr Prandtl numberP blower power/unit area of heat transfer surface,

W/m 2Re Reynolds numberT s surface temperature, CT A air temperature, CV E air jet velocity, m/s X n nozzle to nozzle spacing, mm

Greek symbolq air density constant, kg/m 3

SubscriptsA airE nozzle exits surface

Superscript

average value

1IntroductionSingle and multiple impinging air jets are widely used inmany industrial applications because of the high heat andmass transfer coefcients which are developed in the im-pingement region. They are most commonly applied inprocesses such as print drying, drying of paper and tex-tiles, tempering of plate glass, annealing of metal, printingon plastic, the system of cooling assemblies of gas turbineblades, VTOL aircraft design, cooling of electronic com-ponents and thermal development of photographic lms.

In general, two types of jets have been used either singly or in arrays:

1. circular or axisymmetric jets,2. slot or two-dimensional jets.

In industrial applications such as paper mill roller coolingor cooling of high energy density electronic components,where highly localised cooling is desired a single or a row of widely spaced jets is usually used. When heat transferfor large surfaces is involved, as in the case of an im-pingement dryer for packaging or converting industry,multiple rows or arrays of impinging jets are used.

Due to the complex nature of the ow eld associatedwith an impinging jet, most investigations have been ex-perimental with the resulting correlations being used forpredicting average heat transfer coefcients. Most experi-mental work has been carried out on a single jet ratherthan on arrays of multiple jets. Friedman and Mueller [1]were the rst to measure the average heat transfer coef-cients produced by air jets emerging from circular holes.The technique of using high velocity impinging air jets tospeed up the drying of paper and other continuous web of materials appears to have been originally developed by Gardner [2] ``Gardner'' drier consisted of a large numberof closely pitched, very narrow slot jets. Hardisty [3]studied the accelerating evaporative ink drying on rotary printing presses for the packaging and converting indus-

try. A non-contact infra-red technique has been developedfor the continuous measurement of dryness (solvent)

Heat and Mass Transfer 38 (2002) 251259 Springer-Verlag 2002DOI 10.1007/s002310100249

Originals

Received on 21 November 2000 / Published online: 29 November 2001

M. Can (& ), A. B. Etemoglu, A. AvciUniversity of Uluda g Faculty of Engineering and

Architecture Department of Mechanical Engineering,Goru kle Campus TR-16059, Bursa, Turkey

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throughout the drying process. On the mass transfer sidethe published information appears to be rather limited.The reason for the scarcity of data on mass transfer wouldappear to be the experimental difculties involved in ob-taining information. Korger and Krizek [4] using an ex-perimental technique based on the sublimation of naphthalene, determined mass transfer coefcients. Ex-perimental investigations were carried out by Gardon andCobonpue [5] into circular jets and by Gardon and Akrat[6] into two-dimensional jets. In these investigations,Gardon used a novel miniature heat ux meter, of his owninvestigation, to measure point values of the heat transfercoefcient in the impinging region.

Hardisty and Can [7] investigated the effect of changesin nozzle shape and size on heat transfer under impingingair jets. It was found that the heat transfer results wererelated not to the nominal width of nozzle, but rather tothe minimum width of the jet. Carper et al. [8] haveconducted an experimental study to determine the average

convective heat transfer coefcients for the side of a ro-tating disk, with an uniform surface temperature, cooledby a single liquid jet of oil impinging normal to the sur-face. Saad et al. [9] studied the conned multiple im-pinging slot jets without crossow effects. They showedthat interaction between adjacent jets increases the heattransfer under the exhaust ports. Experiments were con-ducted by Tawfek [10] to determine the heat transfer andsurface pressure characteristics of a round jet impingingnormal on isothermal plate. Ashfort-Fronst and Jambu-nathan [11] also studied the effects of nozzle geometry andconnement on the potential core. Preliminary resultspresented indicate that the length of the potential core isgreater for the fully developed jet exit prole. Isothermalconvective mass transfer behaviour of a horizontal rotat-ing circular cylinder exposed to a two-dimensional slot jetof air was determined by Pekdemir and Davies [12] as afunction of the ow and geometrical parameters using aphoto-evaporative mass transfer measurement technique.Fujimoto et al. [13] studied the convective heat transferbetween a circular free surface impinging jet and a solidsurface. First, the ow structure on a non-heated surfacehas been investigated and next, the steady-state ow

structure in the liquid lm as well as the heat transfer hasbeen examined. Avci and Can [14] implemented a pro-gram of research to study the analogy between the heatand mass transfer processes which constitute the inkdrying process. Recently, the impinging jet dryers includedin the listing some innovative drying technologies as well[15]. One way to improve the drying rates is to attach acollar that causes oscillations and vortex shedding in the jet exit ow to a tubular nozzle.

In this investigation, a large multi-nozzle rig has beenused to measure average heat transfer coefcients underarrays of both slot nozzles and circular holes. Because of itssize the results from this rig should prove useful for prac-tical design studies. For these arrays, the relationship be-tween heat transfer coefcient, air mass ow rate and fanpower has been determined. These studies showed that the``free area'', ratio of the total nozzle outlet area to the heattransfer surface area, was a fundamental parameter. By ex-pressing the results in terms of free area it was found pos-

sible to optimise the ratio of heat transfer to blower power.2Experimental apparatus and procedure

2.1Brief description of multi-nozzle test rigA multi-nozzle test rig has been constructed to provideheat transfer data on arrays of nozzles, Fig. 1. The hori-zontal impingement surface (calorimeter) consists of analuminium plate which is heated from below by hot waterowing in a number of narrow rectangular channels. Thechannels constrain the ow to the longitudinal directionand prevent lateral heat and mass ow. Water entering andleaving the calorimeter ows through the inlet and outletreservoirs and this ensures a uniform mass ow rate acrossthe calorimeter surface. Also the reservoirs minimise mi-nor temperature uctuations. The mass ow rate is regu-lated by means of an outlet valve and breather pipes atinlet and outlet reservoirs ensure there are no air-locks inthe calorimeter.

Water is supplied from two tanks to the calorimeter.The smaller tank acts as a constant head device which

Fig. 1. a Multi-nozzle test rig. b Assembly of hole or slot nozzle arrays to plenumchamber

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maintains steady-ow conditions; to do this it has a weirwhich limits its maximum capacity. Each tank containsthermostatically controlled immersion heaters and stir-ring paddle to give a uniform temperature distribution.Levels in the tanks can be checked with glass tubes ttedto the exterior. It is important to ensure that the supply from the main tank to the smaller tank is sufcient tomaintain the level at to the weir. To prevent any damage,a oat switch isolates the heaters if the water level falls toolow. Water ows into the calorimeter from the constanthead tank through a pipe that has an incline lter. Thewater leaving the outlet reservoir can be directed into twosump tanks. In normal running, water ows into a sumpwhich is tted with oat operated microswitches, con-nected to the circulating pump. The pump maintains thewater level between predetermined limits. The water massow rate was calculated from the time taken for water toow into a measuring tank. The water was directed intothis tank by means of a pendulum valve. The water level

was read from a transparent tube that was xed outside of the measuring tank, similar to those tted to the supply tanks.

Air is directed onto the calorimeter surface through thenozzle/hole arrangement by a centrifugal fan. Air massow rate is regulated by a blanking plate at fan dischargeand ducted to the plenum chamber. The bottom surface of the plenum chamber has a detachable frame which ac-commodates various nozzle or hole plates.

2.2Calculation of heat transfer coefficientA set of experiments has been carried out for the followingrange of the various parameters:

(a) nozzle to plate distance 4 < Z =B < 20 ()(b) percentage of free area 0 :5 < Af < 12:5 (%)(c) air jet velocity 20 < V E < 60 (m/s)(d) two types of slots B 2 and 2.5 (mm)(e) two sizes of holes D 5 and 10 (mm)(f) surface temperature 85 < T s < 90 ( C)(g) air temperature 20 < T A < 30 ( C)(h) water mass ow rate _mw 0:375 (kg/s)

Before each test the horizontal level of the calorimeter waschecked by raising it until it was just touching the nozzlesand adjusting it until the nozzle to plate spacing wasuniform. For each test condition the rig was lowered to thedesired Z =B value by rotating the four handwheels, seeFig. 1, the same number of turns. Temperatures are mea-sured using ChromelAlumel thermocouples xed in thefollowing positions:

(a) fan inlet,(b) water inlet to calorimeter,(c) water outlet from calorimeter,(d) plenum chamber,

All thermocouples were conducted through a junction boxto a D.V.M. whose full scale reading was 110 mV. Air jetvelocity was calculated from the measured value of staticpressure in the plenum chamber, read from a water lled

differential manometer. The air jet velocity itself was ad- justed by restrictor plate at fan outlet.

As the hot water passes through the calorimeter, thecooling effect of the array of air jets, causes the watertemperature to decrease. Losses found to be approximately 1%. As this is less than accuracy of the experimental data,it was neglected. Check-measurements showed that thetemperature difference across the aluminium plate wasnegligible.3Heat transfer correlationsAs noted earlier there is inadequate information aboutheat transfer under multiple jets. The available predictiveequations generally do not take into account such vari-ables as type of recirculation system, jet turbulence and jetinterference. In other words, single nozzle data can bedirectly be used to predict the performance of multiplenozzles, because of the effect of jet interaction. This hasmainly two aspects:

1. at the secondary stagnation point

2. the effect of nozzle exhaust and secondary cross ow.As an approximate guide, when comparing average heattransfer data for single and multiple nozzles, the interac-tive effects mentioned above, increases the heat transferrates from multiple nozzles some 515% over the com-parable single nozzle data. This can be expressed by theequation:

hm K hs 1

where hm is the multi nozzle average heat transfer coef-cient, W/m 2 K; hs the single nozzle average heat transfercoefcient, W/m2 K and K the function of the free (open)area and the Reynolds number.

Comparison of a single two-dimensional jet with mul-tiple jets is shown in Fig. 2.

4Theory of optimum free areaThe free (open) area, Af , is dened as the ratio of total jetarea to heat transfer area. The two cases considered are asfollows:

1. Arrays of slot nozzles:

Af Area covered by slot nozzles

Total surface area

nBl As nBl nX n l B X n 2

2. Arrays of circular holes:

Af Area covered by circular holes

Total surface areanp D2=4

Asnp D2

4n 3p 2 D2np D2

2 3p D2n3

The free (open) area, Af , plays an important role in thedesign of multiple nozzle arrays. At small values of Af ,increasing Af by increasing the number of nozzle serves toincrease the average heat transfer coefcient h. However,

at large values of Af , further increases in the number of nozzles may serve largely to increase the jet interaction.

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where

C 2 C 12m=3 Af C D 2m=3 C 12n=2 Af C D n n 2m=3To get an analytic solution, it is assumed that C 1 has theform

C 1 C 0 SAf The particular form chosen for this equation will be jus-tied later by the experimental results. For constantblower power P

h C 2 P q 2m=3 C 12n=2 Af C D

n P q 2 m=3

h C C 0 SAf Anf hence,

h C C 0 Anf SA1 nf 9The functions in Eq. (9) possess an maximum, the posi-tion of which may be determined by differentiation andthen equating the result to zero.

i.e.dhd Af

0

dhd Af

C C 0nAf n1 S 1 n Anf 0C 0nAn1f S 1 n Anf An1f Anf

S 1 nC 0n

Af C 0nS 1 n 10

Optimum free area Af is directly proportional to C 0 and n,and inversely so to S. Af also tends to zero at small valuesof n. (n varies in the range 0 < n < 1).

5Experimental results

5.1Slot jetsIt is noteworthy to state that it was difcult to get exper-imental heat transfer data for slot jets with variables freearea Af due to the practical difculties of manufacturingand measuring such slot jets. This is probably the reasonwhy published data on multiple slot jets is scarce.

The average heat transfer coefcients for two differently shape nozzles and widths corresponding to free area of 0.88, 2.25, 3, 4, 7 and 12.3% were measured. In each casethe height of the calorimeter was varied to give a range of values for Z =B between 4 and 20.

Effect of Z =BFigure 3 shows the heat transfer coefcient obtained with2.0 mm slot nozzles of varying free areas for range of Z =B

between 4 and 20 at a xed Reynolds number. For smallvalues of free area, Af , the average heat transfer coefcientincreases and linearly with Af . Thus, it appears that forvalues of Af less than about 5% and with values of Z =B lessthan about 6, the heat transfer under each jet is indepen-dent of, and is not inuenced by, the presence of theneighbouring jet. Under these circumstances, increasingthe free (nozzle) area, Af , simply has the effect of acti-vating a proportionally larger fraction of total heat transfersurface. As Af becomes larger, the average heat transfercoefcient increases less rapidly. This may be expected by virtue of the fact that as the jets come relatively closertogether the areas of high heat transfer under the separate jets begin to overlap, and part of the potential effectivenessof each jet is lost.

For a free area of 1.6% the average heat transfer coef-cient remains essentially constant with Z =B, decreasingsomewhat at large values of Z =B. As the free area increases,the effect of Z =B on heat transfer coefcient increases. At

Fig. 3. Average heat transfer coefcientfor multiple slot jets

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the nozzle outlet the turbulence level in the jet is relatively low. Due to intense mixing with the surrounding air theturbulence level rises and reaches a maximum at approx-imately 8 effective slot widths from the nozzle outlet. Thisrequires a knowledge of the discharge coefcient. For thisreason, experiments show that the stagnation point heattransfer coefcient h0 exhibits a maximum when the im-pingement surface is positioned at Z =BH 8. Similarly, theaverage heat transfer coefcient h which is required forpractical purposes is a maximum providing Z =BH 8 forany shape of nozzle congurations. Hardisty and Can [7]proved that the heat transfer coefcients exhibited amaximum at a dimensionless nozzle-plate spacing Z =BH 8, independent of shape. They also found that forthe nozzles used in this research the effective width BHDH)was related the actual size B D by the formulaBHDH B D C D, where C D is coefcient of discharge. At Z =B 6 i.e. Z =BH 8, a maximum value of heat transfercoefcient can be seen. This maximum value, although

clearly apparent, is not much higher than adjacent values.In fact, the maximum value at Z =B 6 is only some 10%larger than the values of average heat transfer coefcient,determined for the range Z =B 4 to 15.

Effect of free areaA number of tests were carried out, at different air ve-locities, to determine the effect of free area on heat transfercoefcient. Figure 4, shows one set of data, for a velocity of 40 m/s. An attempt was made to correlate data from all thetests in the dimensionless form:

Nu C Re0:52 Pr0:33 11

From Fig. 4 it can be seen that the data can in fact becorrelated in this manner. As the free area, Af , increasesbeyond 5% the average heat transfer coefcient reaches amaximum level and then decreases. This reduction in heattransfer coefcient which may be caused by cross-ow interference between jets is more pronounced and occurs

for smaller values of the free area Af . The average heattransfer coefcient increases with 0.52 power of Reynoldsnumber.

It was found that all of the slot nozzle data, for a givenplate and spacing, could be expressed by means of thefollowing equation:

h C 1G0:47 12where C 1 was a constant dependent upon both free areaand slot width (i.e. for given values of G and Af , averageheat transfer coefcient is the highest with small nozzlewidth).

From a knowledge of discharge coefcient, the free areaof the plate, and equation h C 1G0:47, the relationshipbetween h and fan power P can be written by the equation:

h C 2P 0:16 13

High values for C 2 represent high values of the averageheat transfer coefcient for a given power. Power con-

sumption is one of the important practical aspects of anair-impinging system.

5.2Circular holesThe nozzles were removed and replaced by arrays of holespunched in at plates. The arrays used corresponded tofree areas varying between 0.72% and 6%. Heat transfercoefcients were calculated over the range of Z =D between3 to 12.

Effect of Z =DFigure 5 shows the variation in heat transfer coefcientswith Z =D for holes diameter 5 mm with varying free areas.As with slot nozzles, increases in free area up to 3%,produce a corresponding increase in heat transfer.

As the free area increases the heat transfer coefcient atlarge values of Z =D falls away more sharply. At Z =D 5(i.e. Z =DH 8 , a peak value of heat transfer coefcient has

Fig. 4. Effect of nozzle widthand free area on average heattransfer coefcient

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developed. This peak or maximum value, is more pro-nounced than on similar graphs for slot nozzles. Indeed,the maximum value at Z =D 5 is approximately 19%larger than other values for heat transfer coefcient hasfound across the range for Z =D 3 to 12.

Effect of free areaThe effect of nozzle diameter and free area on average heattransfer coefcient is seen in Fig. 6. At constant velocity and Z =D; the average heat transfer coefcient increaseswith decreasing nozzle diameter. The average heat transferdistribution shows a difference of some 7%, when the

nozzle diameter D increases by a factor of 2. It can be seenfrom Fig. 6 that the data can be correlated in the dimen-sionless form:

Nu C Re0:50 Pr0:33 14

As the free area, Af , increases beyond 3% the average heattransfer coefcient reaches a maximum level and thendeclines. Once again, this may be explained from the factthat the ow interference between jets is more pronouncedand occurs for larger values of the free area Af .

The results for circular holes are in good agreementwith the various data of Friedman and Mueller [1]. How-ever, there is some differences with the data of Martin [16].

Data for circular holes, for a given plate and spacing,can also be correlated in the form of Eq. (7), suggestedearlier:

h C 1G0:47 15where C 1 is a function of free area and nozzle diameter.

Provided that the experimental data is plotted in theform h C 1G0:47, then this can be used to deduce the re-lationship between fan power P and average heat transfercoefcient h. Then the experimental data can be correlatedby the equation:

h C 2P 0:16 16In all the correlations the maximum relative correlationerror has been found to be within 5%. High values for C 2represent high values of heat transfer coefcient for a givenpower. Optimum free area for circular holes is about 3%.

However, it is of interest to note that the optimum valueof the free area Af found from experiment agrees reason-

ably well with the value also determined experimentally by Friedman and Mueller [1].

6Optimum free area comparison of experimentwith theoryComparisons were made between the optimum values of free area which had been determined by experiment andpredicted from theory. These comparisons, and the per-centage discrepancy between them are shown in the tablesbelow.

Fig. 5. Average heat transfer coefcient for circular holes

Fig. 6. Effect of nozzle diameter and free area on average heattransfer coefcient

Table 1. Comparison for slot jets

Width of nozzleslot, B (mm)

Optimum value of freearea, Af , (%)

Agreement (%)

Experimental Theoretical

2.0 4.5 4.69 4.02.5 4.5 4.67 3.7

Table 2. Comparison for circular holes

Diameter of circularnozzle, B (mm)

Optimum value of freearea, Af , (%)

Agreement (%)

Experimental Theoretical

5.0 3.0 3.21 6.510.0 3.0 3.28 8.5

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7Comparison between circular holes and slot jetsThe average heat transfer coefcients that can be attainedusing the optimal arrays as determined above, are almostidentical for both slots and holes, provided that the air jetvelocities and Z =B (or Z =D) are the same. This is shown inFig. 7. The heat transfer coefcients increase with de-creasing nozzle diameter or width.

Figure 8 shows that the average heat transfer coef-cients h that can be achieved by the optimal arrays of circular holes D 5 are about 4% higher than those foroptimal array of slot nozzles of B 2 mm provided theblower ratings are equal in both cases. From Fig. 8, it may also be seen that, if the nozzle diameter is halved whilemaintaining the same free area Af and fan power P , theheat transfer coefcient increases by as much as 10%.Similarly, when comparing nozzles of width B 2 and2.5 mm, maintaining the same fan power P and freearea Af , the heat transfer coefcient increase approxi-

mately 4%.

8ConclusionsParticular attention has been given to the heat transferproblem under arrays of impinging air jets from slots andcircular holes. The optimum free area has been obtaineddirectly from experimental results. Also the theory of op-timum free area was analysed and good agreement hasbeen found between theoretical and experimental results.

However, in industrial applications, selection of jetconguration is governed not only by the relative magni-tude of average heat transfer coefcient but also by thedesired heating pattern and the economics of the blowersystem used. The relationship between heat transfer coef-cient, air mass ow and fan power which is required forthe optimum design of nozzle systems has been developed.

Some of the studies involving arrays of jets were con-ducted with sharp-edged orices which are preferred inparticular industrial installations owing to the ease of fabrication. Although, simple sharp-edged orices are easy

to fabricate from at strips, the thin material can not stand

Fig. 7. Comparison betweenslots and circular holes invariation of average heattransfer coefcient with freearea

Fig. 8. Comparison betweenslots and circular holes in

variation of fan power with freearea

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high plenum pressures and in practical such simple slotnozzles will bend. Making a simple circular holes are anadvantage but because of bending at high plenum pres-sures, a trade off has to be made between strength and costof material required and corresponding gains from high airvelocities. Finally, it is recommended that future researchshould be carried out in close co-operation with industry.

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14. Avci A; Can M (1999) The analysis of the drying processes onunsteady forced convection in thin lms of ink. Appl ThermalEng 19: 641657

15. Devahastin S (2000) Mujumdar's Practical Guide to IndustrialDrying; Principles, Equipment and New Developments.Exergex Corp., Quebec

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