deo et al. 2007 - comparision of turbulent jets issuing from rectangular nozzles with and without...

7/31/2019 Deo et al. 2007 - Comparision of Turbulent Jets Issuing From Rectangular Nozzles With and Without Sidewalls

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Comparison of turbulent jets issuing from rectangular nozzleswith and without sidewalls

Ravinesh C. Deo *,1, Graham J. Nathan, Jianchun Mi 2

School of Mechanical Engineering, The University of Adelaide, SA 5005, Australia

Received 3 December 2006; accepted 26 June 2007

Abstract

This paper reports a systematic study of a turbulent jet issuing from a rectangular slot nozzle of high-aspect ratio, AR ( w/h, where wand h are the long and short sides of the slot, respectively) tested with and without sidewalls. The solid sidewalls were flush with each ofthe slots short sides vertically and extend axially along the streamwise direction of the jet. Hot-wire measurements were conducted at aReynolds number based on slot-width (h) and exit centerline velocity ofReh % 7000 (for AR = 30 and 60) and at 10,000 (for AR = 30) upto 160 h downstream. All jets have a potential core in which the local centerline velocity is approximately constant, followed by a tran-sition region and then a statistically two-dimensional (2-D) region where the centerline mean velocity, Uc $ x

1/2. The potential core ofthe jet without sidewalls is shorter than that with sidewalls. Near field power spectral analysis reveals that the primary vortex sheddingrate is higher for the jet without sidewalls than the jet with sidewalls. The 2-D region of the jet with sidewalls is found to extend over alonger axial distance than that of the jet without sidewalls. It is also demonstrated that both the decay and spread rates of the jet withinthe 2-D region are lower for the case with sidewalls. Beyond the 2-D region, the jet without sidewalls enters into a far field transitionalphase and then tends to behave statistically like an axisymmetric jet with Uc $ x

1. The centerline turbulence intensity of the jet withsidewalls becomes asymptotic closer to the nozzle exit than the jet without sidewalls. The skewness and flatness factors confirm furtherstatistical differences between the jet with and without sidewalls.Crown Copyright 2007 Published by Elsevier Inc. All rights reserved.

Keywords: Plane jet; Planar jet; Rectangular jet; Effect of sidewalls

1. Introduction

The standard nozzle configuration used to produce aplanar jet comprises by a rectangular slot of dimensionsw h and high aspect ratio, AR ( w/h, where w and h

are nozzles long and short sides) with two parallel platesattached as sidewalls to the slots short sides. The sidewallsextend axially in the direction of jet propagation. Thisarrangement ensures statistical two-dimensionality because

the jet is forced to entrain the ambient fluid only in thedirection normal to the nozzles long sides. For instance,the early work of Heskestad [1], Bradbury [2] and Gutmarkand Wygnanski [3] warrant the use of sidewalls to create astatistically two-dimensional (planar) jet. In contrast, a jet

issuing from a similar rectangular slot but configured with-out sidewalls are termed rectangular even though the jetis only truly rectangular at the exit plane. For example,Sforza et al. [4], Trentacoste and Sforza [5], Sfeir [6] andQuinn [7] have used the terminology rectangular jet toassess the development characteristics of a jet from a rect-angular nozzles without sidewalls. We also adopt this ter-minology for consistency, where applicable in this paper.

If the aspect ratio of a rectangular nozzle is sufficientlylarge, this jet, too, behaves like a planar jet up to a certaindownstream distance [8]. This downstream distance,

0894-1777/$ - see front matter Crown Copyright 2007 Published by Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2007.06.009

* Corresponding author. Tel.: +61 8 8303 5460; fax: +61 8 8303 4367.E-mail address: [email protected] (R.C. Deo).

1 Present address: Center for Remote Sensing and Spatial InformationSciences, School of Geographical Sciences and Planning, The Universityof Queensland, Brisbane 4072, Australia.2 Present address: Department of Energy and Resource Engineering,

College of Engineering, Peking University, Beijing 100871, China.

www.elsevier.com/locate/etfs

Available online at www.sciencedirect.com

Experimental Thermal and Fluid Science 32 (2007) 596606
mailto:[email protected]:[email protected]


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however, depends on the nozzle aspect ratio [9,10]. It is per-haps for these reasons, or others, that some previous inves-tigations have treated the two configurations as if theycould be used interchangeably. For example, Krothapalliet al. [11], Hussain and Clark [12] and Namar and Otugen[13] have used the term planar to describe a jet thatissued from rectangular nozzles of high-aspect ratio butconfigured without sidewalls. This approach is reasonablegiven that the mean velocity decay rates in the self-similarregion of both jets obey the relation Uc $ x

1/2, and thusexhibit statistically two-dimensional behaviour.

Namar and Otugen [13] have checked the jets spanwisevelocity distribution to further confirm statistical two-dimensionality of jets from rectangular nozzles withoutsidewalls. They found that the spanwise distribution ofmean velocity and turbulence intensity were fairly uniformin the downstream region. Furthermore, Mi et al. [8] veri-fied experimentally that the relation Uc $ x

1/2 also holdstrue in the 2-D region of rectangular jets, but only withina limited axial distance. Nevertheless, given the sensitivityof all shear flows to boundary conditions, some differencescan be expected to result from the presence or absence ofsidewalls. This issue remains to be explored at present.

A study undertaken by Hitchman et al. [14] to identifydifferences between jets with and without sidewalls is incon-clusive. It showed that the mean centerline velocity of thejet without sidewalls decays slower than for the jet withsidewalls, while its spreading rate is higher than the jet withsidewalls. This clearly contradicts the law of mass conser-vation, since a jet which decays faster must also spread fas-ter, by virtue of a higher rate entrainment of ambient fluid.No other direct comparisons of a jet with and without side-walls currently exist, thus no detailed statistical informa-tion is available. Hence the present investigation seeks toaddress this need.

An assessment of the impacts of the presence or absence

of sidewalls is also of relevance to the broader understand-

ing of the effects of boundary conditions on turbulent shearflows. It has been well established by George [15] andGeorge and Davidson [16], both analytically and experi-mentally, that differences in boundary conditions propa-gate into the greater flow field. However, the extent ofsuch influences is not so well known. The present investiga-tion aims to provide more detailed statistical comparisonof otherwise identical jets of large aspect ratio with andwithout sidewalls over a flow region of up to 160 h usinghot-wire measurements.

2. Experimental details

The present nozzle facility, shown schematically inFig. 1, consists of an open circuit wind tunnel of hexagonalcross section built to generate uniform flows. The wind tun-nel, made of wooden modules with polished inner surfaces,was driven by a 14.5 kW aerofoil-type centrifugal fanmounted firmly to the floor so that the entire rig is vibra-tion free. The tunnel employed a wide angle (25) diffuserspanning 2100 mm in length into a settling chamber.Within the diffuser are two screens of 60% porosity at inter-vals of 600 mm that aid in reduction of velocity defect inthe turbulent boundary layer and streamlines the incomingairflow. The settling chamber (of length 1400 mm) con-tained a honeycomb of length 150 mm assembled viadrinking straws aligned horizontally with the main streamflow to reduce swirl. Following the honeycomb are threescreens apart followed by a 150 mm and a further600 mm before the start of the contraction which assistsin effective flow conditioning to reduce turbulence levels.The wind tunnel contraction had an area ratio of 6:1 andemploys a smooth contraction profile based on third orderpolynomial curve to enhance flow uniformity.

The test section consisted of a rectangular nozzle with a12 mm radial contraction profile on its long sides (Fig. 1a).

This was mounted to the end of the tunnel contraction

Nomenclature

AR nozzle aspect ratio (AR = w/h)e dissipation rate of this energy, assuming isot-

ropy with e ffi 15tU2c ou=ot2

Fu centerline flatness factor, Fu = hu4

i/(hu2

i)2

h slot-width of a rectangular nozzleKu decay rate of mean centerline velocityKy jet spreading (widening) rateRe Reynolds number Reh Uo,c h/tSu centerline skewness factor, Su = hu

3i/(hu2i)3/2

u fluctuation component of mean velocity instreamwise (x) direction

u0 root-mean-square (rms) of the velocity fluctua-tion, u0 = hu2i1/2

Uc local mean velocity on the centerlineUo,c mean exit centerline velocity

w slot-span of a rectangular nozzlex01 virtual origin of the normalized mean centerline

velocity

x02 virtual origin of the normalized velocity half-widthxp length of the jets potential corey0.5 velocity half-width, calculated at the y-location

at which Ux 12 Ucxm kinematic viscosity of the air (% 1.5

105 m2 s1 at 20 C)x,y,z streamwise or axial (x), lateral (y) and spanwise

or transverse (z) coordinatez0.5 velocity half-width, calculated at the z-location

at which Ux 12 Ucx

R.C. Deo et al. / Experimental Thermal and Fluid Science 32 (2007) 596606 597


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using tight rubber seals at the edges of contact to avoidleakage. Where present, the sidewalls were mountedflushed to the slots short sides and aligned in the xy plane(Fig. 1b). The sidewalls extended 2000 mm downstreamand 1800 mm vertically, and were secured tightly by boltsto the laboratory ceiling to avoid vibrations during the tun-nel operation. The slot-width (h), aligned with the lateraldirection (y-coordinate) of the nozzle, was fixed at5.60 mm. The slot-span (w), aligned along the z-direction,

was 340 mm for the large aspect ratio, AR w/h = 60,

which was tested with and without sidewalls. The smallernozzle had a 36-mm radial contraction profile and 5 mmslot-height but half the span, so that w = 170 mm and thesidewalls were moved inwards so that AR = 30. This wasonly tested without sidewalls so that the effect of slot aspectratio on statistical two-dimensionality of the jet could beassessed. The normalized radius of curvature of r/h % 2.14, and 7.20 conforms to our previous finding thata nozzles mean exit flow closely approximates top-hat

profile for r/h > 2.0 [8,17].

Fig. 1. Schematic view of the experimental setup: (a) the wind tunnel details and nozzle attachment; (b) the side view showing nozzle parameters and thecase with sidewalls; (c) jet development characteristics; and (d) the experimental apparatus. Note that diagrams drawn are not to scale.

598 R.C. Deo et al. / Experimental Thermal and Fluid Science 32 (2007) 596606


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The entire jet facility was located in a laboratory ofdimensions 18 m (long) 7 m (wide) 2.5 m (high), andwas acoustically isolated from externally driven noise.The distance from the jet exit to the front wall of the roomwas approximately 1400h and that between the jet and theceiling/floor was approximately 125h, allowing these iso-

thermal jets to entrain stagnant air freely. Based on a sim-ilar the approach to that of Hussein et al. [18], the presentmomentum loss is

)1/2

/U

o,c

Fig. 2. Lateral profiles of the mean velocity, U/Uo,c (denoted by symbolO,h), and turbulence intensity, u 0/Uo,c (denoted by symbol j, d

) measured at x/h = 0.25 for AR = 60, Reh = 7000.



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uncertainty in the momentum integral, the differences aresignificant enough to demonstrate that the sidewalls, andprobably also the shape of the contraction, do influencethe initial shear layer intensities.

We characterize the jet exit conditions by estimating theboundary-layer displacement (dd) and momentum thick-

ness (hm) via the integral equations,

dd

Rh=20 1U=Uo;cdy and hm

Rh=20

1 U=Uo;cUc=Uo;cdy using themean exit velocity profiles. These estimates are somewhatcrude due to the coarse measurement grid. In addition,the momentum integral does not take into account theslight overshoot of the mean velocity for the case withoutsidewalls. These contribute to an estimated uncertainty inintegral quantities of up to 8%. For both cases, the presentvalues ofdd and hm are about 0.15h and 0.059h. Likewise,the corresponding shape factors, H= (dd)/(hm), which rep-resents the flatness (uniformity) of the mean velocity pro-files [21], are %2.55 compared with a value of %2.60 for aBlasius exit velocity profile. Given the closeness of the

shape factors to that of an ideally uniform mean exit veloc-ity profile, both jets are characterized as having laminarboundary layers at their nozzle exit [22].

Fig. 3 presents, with a logarithmic abscissa, the normal-ized mean centerline velocity, Uo,c/Uc for jets without side-walls measured at (Reh,AR) = (7000,60) and (Reh,AR) = (10,000,30) and the jet with sidewalls measured at(Reh,AR) = (7000,60) (see Table 1). The jets are qualita-tively similar, but quantitatively different in the first 40

slot-heights downstream and then diverge significantlyfrom each other into the far field. Both jets exhibit thewell-known non-decaying potential core region, i.e.Uc % Uo,c, followed by a 1/2-power law inverse decayingregion, where Uc $ x

1/2. Further downstream, the jetwithout sidewalls exhibits a transition region, where Uc

does not appear to obey any systematic dependence on x,to an inversely-linear decaying region, where Uc $ x1. In

contrast, the inverse square decaying region extendsthroughout the measured range for the jet with sidewalls.(However, it should be noted that, further downstream(i.e. x/h ) 160), the jet with sidewalls, too, will enter atransition phase; see Deo et al. [10]).

The axial extent of the statistically two-dimensionalregion depends on nozzle aspect ratio. Fig. 3 also plotsthe decay of the AR = 30-jet without sidewalls, whichexhibits statistically two-dimensional behaviour only upto x/h % 30. This dependence of the axial extent of statisti-cal two-dimensionality on nozzle aspect ratio for both rect-

angular (without sidewalls) and planar (with sidewall) jetshas already been demonstrated [8,10]. However, the pres-ent work shows that, without sidewalls, a jet has a longerregion of statistically two-dimensional flow only if the noz-zle aspect ratio is sufficiently large. Importantly, the meanfield implies that without sidewalls, the jet appears to trans-form into an axisymmetric form, characterized byUc $ x

1, in the far field. Our findings are consistent withthose of Trentacoste and Sforza [5] and Sfier [6] whosemean velocity and scalar decay of rectangular jets (withoutsidewalls) behaved statistically like axisymmetric jets in thefar field. Likewise, the rectangular jet data of Quinn [7],

reproduced in Fig. 3, shows these four regions in the decayof Uc. It is important to note that the logarithmic scale inthe abscissa is essential to identify the points of transitionfrom statistically two-dimensional to three-dimensionalmean flow. Previous investigators, e.g. Quinn [7], Tsuchiyaet al. [23] did not use this approach and therefore, did notspecifically identify this transition region.

The length of the jets potential core, xp (the maximumaxial (x) distance up to which Uc % Uo,c) is different for thejets with and without sidewalls. For the case without side-walls, xp % 4h, while for that with sidewalls, xp % 6h. Thisdifference, which cannot be attributable to an experimentalerror, implies a significantly higher rate of near fieldentrainment by the jet without sidewalls. The influence ofthe sidewalls on the spread in the spanwise direction cannotexplain such a dramatic difference in xp on the nozzle axisfor this high-aspect ratio jet. Rather it is important to notethat the initial shear layer of the jet without sidewalls has

1

2

5

10

1 10 100

with sidewalls;AR = 60without sidewalls;AR = 60without sidewalls;AR = 30

Uc U

o,c

300

Quinn (1992); without sidewalls

Uc~x

-1/2

Uc~x

-1

x/h

Uo,c

/U

c

Quinn [7];AR = 20rectangular; without sidewalls

Fig. 3. The normalized centerline mean velocity Uo,c/Uc for AR = 30,Reh = 10,000 and AR = 60, Reh = 7000. Also shown are the rectangularjet data of Quinn [7] for Reh = 36,000 and AR = 20.

Table 1The measured jet configurations and initial conditions for the cases with and without sidewalls.

Configuration Reh AR dd hm H= dd/hm u0c=Uc u

0p=Uc

With sidewalls 7000 60 0.15h 0.059h 2.55 0.5 2.6Without sidewalls 7000 60 0.15h 0.059h 2.55 0.5 3.6

Without sidewalls 10,000 30 0.5 3.6



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higher turbulence intensity than that with sidewalls(Fig. 2b). Since the length of the potential core is domi-nated by the growth of the shear layer in the xy plane[24], the higher initial turbulence intensity of the jet withoutsidewalls is consistent with its shorter potential core.

Next, we assess whether the higher shear exit layer tur-

bulence intensity (Fig. 2) and a consistently shorter poten-tial core (Fig. 3) might be caused by the jet withoutsidewalls undergoing larger amplitude near field flappingthan the jet with sidewalls. Were such a flapping to be pres-ent, it would be evident in a low-frequency oscillation inthe power spectrum. To determine whether this was pres-ent, we have calculated the power spectra of centerlinevelocity fluctuations at the beginning and the end of thepotential core (i.e. x/h = 3, 4 and 5) of the jet with andwithout sidewalls by filtered instantaneous velocity fluctua-tion data at fc = 250 Hz. The spectra (Appendix 1) showthat there exist no genuine significant difference in thelow-frequency spectra, and no significant peaks for either

case (A small peak at 50 Hz was found in each case, whichis attributed to electronic noise). Hence it is deduced thatthe higher shear layer intensity is not attributable to suchflapping motions, but rather to increased three-dimension-ality of the jet without sidewalls, due to differences in theirunderlying vortex motions (as discussed in detail below).Although the measurements of other turbulence parame-ters (e.g. shear stresses) could confirm this, it was beyondthe scope of present investigation since data here are lim-ited to single component velocity measurements.

To investigate the near field flow structure of the twoAR = 60 jets more closely, we have plotted the power spec-

tra of the centerline velocity fluctuations within the poten-tial core region (i.e. at x/h = 3) shown in Fig. 4. Here, thedominant peak is normalized so that the vortex shedding

frequency, f* fh/Uo,c, andRUufdf 1. The appear-

ance of broad peaks in power spectra confirms that bothnozzles generate regularly-occurring primary vortices, afeature which is well known to occur in other smoothlycontoured nozzles as well. The smoke visualization experi-ment of Tsuchiya et al. [23] on rectangular jets revealed

streamwise vortex structures between 04 nozzle-widthsdownstream, as did the planar jet flow visualization ofShlien and Hussain [27]. However, it is particularly inter-esting to note that the present jet without sidewalls shedsvortices at f* = 0.36 whereas, for the jet with sidewalls, vor-tex shedding occurs at f* = 0.22. This significant differencein f* confirms distinct differences in their underlying nearfield flow structure.

It is hypothesized that the differences in spectral peakscan be attributed to structural differences in vortices (e.g.a higher degree of three-dimensionality) in the near fieldflow of the jet without sidewalls [26]. It is known that arectangular jet, configured without sidewalls, is known to

produce ring-like three-dimensional primary vortices(Grinstein [28], Grinstein et al. [29]) while the 2-D roller-like vortices are found in a planar jet, configured with side-walls (Browne et al. [30]). The differences in the vortexdynamics of both jets are described below.

The primary ring-like vortices produced by a jet withoutsidewalls (e.g. a rectangular jet) are probably initially inter-connected in a loop that stretches around the circumfer-ence of the jet [25]. These vortex loops undergo substantialtwisting and turning at the corners, and cause more rapidspread along the shorter side than the longer side as thejet spreads in the spanwise (z) direction. The non-uniform

growth rates of the long and short sides causes increaseddistortion of the ring, leading to axis switching and therings eventual destruction. Evidence of this behaviour canbe found from the flow visualization experiments of Tren-tacoste and Sforza [5]. They studied decay rates of primaryvortex rings in rectangular jets, noting that the vortex ringsfirstly issue as an ellipse, whose major is axis aligned withthe major axis of the nozzle. This then proceeds down-stream and become circular and then, still further down-stream become elliptical again, but with its major axisrotated 90 to that of the nozzle slot. Typically, multipleaxis switching is observed in rectangular jets which arenot constrained by sidewalls in the xy plane (Piffaut[31]). Another useful description of the ring-like vorticesin rectangular jets can be found in the flow visualizationobtained by DNS of Grinstein et al. [28]. They found, inaddition to the primary ring-like vortices, secondary (hair-pin or braid) vortices extending longitudinally. Impor-tantly, their flow topology revealed these large-scalespanwise vortex ring and streamwise braid vortices to havestrong inter-scale interactions, which increases three-dimensionality and the degree of disorganization.

In contrast, the jet with sidewalls produces counter-rotating streamwise vortices within the near nozzle regionthat are more two-dimensional than the vortices produced

by a jet without sidewalls. The early flow visualization of

10-5

10-4

10-3

10-2

0 0.5 1.0 1.5

with sidewalls

without sidewalls

f* 0.36

f* 0.22

f* =f h /Uo,c

u

(f*)

Fig. 4. Power spectra, Uu(f*), of the centerline velocity fluctuations

measured at x/h = 3 for the jets of AR = 60, Reh = 7000.

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Brown [32] and of Beavers and Wilson [33] revealed sym-metrical (cylindrical) vortices on alternate sides of thepotential core. These initial vortices grew into larger vorti-ces by coalescence with their adjacent counterparts as thejet propagates downstream. The process of coalescencetypically depends on the exit conditions. For instance, Sato

[34] showed that acoustic excitation at a frequency close tothe natural vortex shedding frequency, causes these vorti-ces to coalesce closer to the nozzle exit. Importantly, unlikejets without sidewalls, the counter-rotating vortices in jetswith sidewalls are mostly two-dimensional (double roller)in nature. Thus increased three-dimensionality of the rect-angular jet over the planar jet is likely to be significant in itshigher near field entrainment implied by the shorter poten-tial core (Fig. 3). The structural differences in the vorticesof jets with and without sidewalls are also evident in thepower spectrum (Fig. 4). Not only do their dominant vor-tex shedding frequencies differ but it is also apparent thatthe spectrum of the jet without sidewalls exhibits a multi-

modal behaviour with four distinct sub-peaks (harmonics)in f*. These are evidence of multiple length scales in theflow and hence three-dimensional motions.

Fig. 5 investigates the decaying behaviour of the meanvelocity field by presenting Uo;c=Uc

2 versus x/h withinthe statistically two-dimensional region of the jets withand without sidewalls. The self-similar relationship of theform (Uo,c/Uc)

2 = Ku(x/h + x01/h) holds true over the axialrange 10 6 x/h 6 40. Here, Ku and x01 are the jet decay rateand virtual origin, respectively. Both jets have distinct dif-ferences in velocity decay rates, presented for clarity in theinsert of Fig. 5. In particular, the jet without sidewalls

(Ku % 0.20) decays at a rate of some 15% higher than doesthe jet with sidewalls (Ku = 0.17). This implies that the farfield entrainment rate of the jet with sidewalls is lower thanthe jet without sidewalls.

To assess the spreading behaviour of both jets, Fig. 6presents the axial evolution of velocity half-widths, y0.5 in

the lateral (y) direction. The half-width is the location atUx;y0:5

12Ucx obtained from the mean velocity pro-

files (Fig. 1c). Also presented the velocity half-widths ofQuinn [7] measured along both lateral (y) and spanwise(z) directions. The values of y0.5 vary linearly with x, andfollow the relationship y0.5/h = Ky(x/h + x02/h), where Kyis a measure of the spreading rate and x02 is the virtual ori-gin of that jet spread. In the self-similar region, y0.5 $ x,further confirming statistical two-dimensionality. The jetwithout sidewalls spreads at a rate of about 24% higher(Ky % 0.14) than does the jet with sidewalls (Ky % 0.11).

Importantly, Figs. 5 and 6 are internally consistent, sinceboth find the decay and spreading rates of the jet withoutsidewalls to be higher than that with sidewalls. They arealso consistent with a shorter potential core of the jet with-out sidewalls, which again suggests it has a higher entrain-ment rate.

A jet which is not constrained by sidewalls in the xyplane spreads along the spanwise (z) direction of the nozzleas well. From Quinns [7] data, we can see that, generally,for jet without sidewalls, y0.5 grows initially at a substan-tially greater rate than does z0.5. This is probably due tostretching of the vortex rings as discussed earlier. Thegrowth of y0.5 is approximately linear until it crosses overz0.5 where the so called axis switch occurs. It is apparentthat z0.5 decreases slightly, and then continues to increaseat a similar rate to that of y0.5. Further downstream, y0.5enters a transition phase, where it decreases in magnitude,while z0.5 continues to increase linearly. In the regionx/h > 130, both spreading rates (i.e. z0.5 and y0.5) convergeinto each other. This provides further evidence of axis-switching phenomenon of the unconfined jet.

Fig. 7 presents the local centerline turbulence intensity,u0c=Uc of both jets. The term u

0c hu

2c i

1=2 where ucis the cen-terline velocity fluctuation, and Uc is the mean centerlinevelocity. Also included in the figure are the u0c=Uc values

of Quinn [7] measured at (Reh, AR) = (36,700, 20) for a

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180

with sidewalls;AR = 60without sidewalls;AR = 60

x/h

(U

o,c

/U

c)

2

(U

o,c

/Uc

)2

4

8

00 10 20 30 40 50

x/h

Fig. 5. The profiles of (Uo,c/Uc)2 versus x/h for jets of AR = 60,

Reh = 7000.

0

4

8

12

16

20

0 20 40 60 80 100 120 140 160 180 200

with sidewalls;AR = 60without sidewalls;AR = 60

closed symbol (circle):z0.5

open symbol (circle):y0.5

Quinn (1992); AR = 20rectangular, without sidewalls

x/h

yo.5

/h;z0.5/h

Quinn [7];AR = 20

rectangular; without sidewalls

Fig. 6. The mean velocity half-width for the jets of AR = 60, Reh = 7000.



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rectangular jet (without sidewalls), Antonia et al. [35] for aplanar jet (with sidewalls) measured at (Reh,AR) =(7000,44) and Mi et al. [36] for a free circular jet. The over-all shape of graph of the data of Quinn [7] is similar to thatof our jet without sidewalls. The qualitative features in thedata of Quinn [7] are similar to that of our jet without side-walls. This is despite the fact that the magnitudes and axiallocations of major features (e.g. humps) are different.The differences reflect the different initial conditions

between our jet without sidewalls and that of Quinn [7](i.e. nozzle aspect ratio, AR = 60 versus 20, Reynolds num-ber, Reh = 7000 versus 36,000, nozzle contraction profile,radially contoured versus sharp-edged orifice plate).

All jets exhibit a rapid increase ofu0c=Uc in the near field,reflecting the streamwise growth of the shear-layer instabil-ities associated with the large-scale structures [35,37]. Suchlarge-scale structures produce large-scale engulfment ofambient fluid, resulting in higher velocity fluctuations andgreater decay of jets mean velocity. For the present data,there is negligible difference in the turbulence intensity ofboth jets between the exit plane and x/h = 10. Although,

both jets produce a hump in u0

c=Uc between 106

x/h 6 12, the hump for the jet without sidewalls is discern-ibly higher than the jet with sidewalls. It also appears thatfor both jets, this hump is about 10% higher than theirrespective asymptotic values. The occurrences of humpsin turbulence intensity have been attributed to the laminarstates of the boundary layer at the nozzle exit (e.g. [38] andFig. 2a). The appearance of the humps in both jets is attrib-utable to the collision of double roller structures, emanat-ing from alternate sides of the shear layers beyond thepotential core region, e.g. Mumford [39], Browne et al.[30]. The difference in the magnitude of the humps suggeststhat the presence of sidewalls increases the coherence of the

shear layer vortex structures in the jet with sidewalls. Thisanalogy is drawn from published information. For exam-ple, a smoothly contoured round nozzle produces analo-gous coherent vortex structures and also exhibits a nearfield hump, while a pipe jet with much less coherent vorti-ces does not (Mi et al. [40]). As such, the magnitude of the

humps is expected to reflect the strength of the overallinteraction between coherent vortical structures and theinduced ambient fluid (Mi et al. [41]).

The turbulence intensity of the jet with sidewalls reachesan asymptotic value of about 0.21, which is very close tothat of a round smooth contraction jet. In contrast, forthe jet without sidewalls, u0c=Uc decreases significantly tovalues of about 75% of those with sidewalls over the range30 6 x/h 6 100. Note that the small variations of u0c=Ucfor the case with sidewalls are within the experimental

0

0.05

0.10

0.15

0.20

0.25

0 20 40 60 80 100 120 140 160 180

without sidewalls;AR = 60with sidewalls;AR = 60

Mi et al. (2000)round jet

Antonia et al. (1982);AR = 44

with sidewalls

Quinn (1992);AR = 20without sidewalls

x/h

u'c/U

c

Quinn [7];AR = 20rectangular; without sidewalls

Antonia et al. [34];AR = 44

planar; with sidewalls

Mi et al. [35]

round jet

Fig. 7. The normalized centerline turbulence intensity u0c=Uc of AR = 60,

Reh = 7000.

-1

0

1

2

3

4

5

0 2 4 6 8 10 12 14 16

Su

= /()

3/2

Fu= /()

2

-1

0

1

2

3

4

5

0 20 40 60 80 100 120 140 160 180

without sidewallswith sidewalls

Su= /()

3/2

Fu= /()

2

x/h

x/h

Fig. 8. Streamwise evolutions of the skewness, Su, and flatness, Fu, for thejets of AR = 60, Reh = 7000, measured in: (a) the near field and (b) theentire field.



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uncertainty. The convergence of the turbulence intensity ofpresent jet with sidewalls to an asymptotic value is consis-tent with the planar jet of Antonia et al. [35] of(Reh,AR) = (7000,44) issuing from a smoothly contourednozzle although their asymptotic value is somewhat 10%lower. In contrast, the far field values ofu0c=Uc of the pres-

ent jet without sidewalls are only about three-quarters ofthe magnitude of the jet with sidewalls.To further show the difference between the jets with and

without sidewalls, Fig. 8 displays the centerline evolutionsof the skewness, Su = hu

3i/(hu2i)3/2 and flatness, Fu = hu4i/

(hu2i)2 factors of AR = 60-jets. Here, Su and Fu were deter-mined from a reasonably large sample, having approxi-mately 400,000 data points of the instantaneous velocity.This ensures that the convergence of the calculations isgood. In the near field (0 6 x/h 6 20), the location of thepeaks in Fu and Su are further downstream for the jet with-out sidewalls, consistent with it having a shorter potentialcore. For each jet, Su displays a local maximum at

x/h % 4 (without sidewalls) and x/h % 4 (with sidewalls)and a local minimum at x/h = 5 (without sidewalls) andx/h = 7 (with sidewalls). The minimum value of Su occursat almost the same location as the maximum in Fu for eachjet. Such evolutions ofSu and Fu are typical of two-dimen-sional jets, and have been reported previously (e.g. Deoet al. [10], Deo [17]).

Within the region where the two jets both exhibit statis-tically two-dimensional behaviour in the mean field(10 6 x/h 6 40), both Fu and Su are significantly different

for the jets with and without sidewalls. For example, atx/h = 30, their respective values are 2.7 and 2.9 for Fuand 0.02 and 0.34 for Su for the jets with and withoutsidewalls, respectively. Hence, even in this region, the twojets behave significantly differently.

Further downstream, the Su and Fu factors of the jet

with sidewalls remains approximately constant, at valuesclose to the Gaussian, as has been reported previously. Incontrast, those for the jet without sidewalls are never trulyGaussian anywhere in the measured range, although theyare closest to it in the range 30 6 x/h 6 110. Forx/h > 120, Su and Fu depart significantly from the Gaussianvalues, consistent with jet having not yet completed to itstransition to the asymmetric flow (Fig. 3).

The characterization of the flow dynamics of jet withdifferent boundary conditions falls short without attribut-ing the role and dependence of large-scale coherent struc-tures on jet boundary conditions. Since this study hasused a single wire probe and thus does not enable us to

quantify the dominance/relevance of inter-scale interac-tions of coherent structures in the two jet flows directly,present statistics do indicate the inherent role played bythese structures in producing widely different near and farfield states. The statistical differences in present results sup-port the deduction that sidewalls impose a modification ofthe jet turbulence structure, and therefore, warrant furtherin-depth investigation (e.g. a flow visualization or two-point cross correlation analysis) on the role of large-scaleeddies on different exit boundaries. Although this could

Fig. 9. Side and top views of the typical flow field of: (a) the jet without sidewalls; and (b) the jet with sidewalls.



10/11

be taken as a very useful exercise, it was beyond the scopeof the present study, and awaits another independentinvestigation.

4. Conclusions

In summary, the flow fields of jets with and without side-walls from rectangular nozzles are consistently statisticallydifferent. Indeed, perhaps surprisingly, even the exit velocityprofiles very close to the exit (x = 0.25h) are also changedslightly by the presence or absence of sidewalls. The nearfield flow also reveals clear distinctions in the length ofthe potential core being greater for the case with sidewallswhich implies a lower rate of near field entrainment. Thenear field vortex shedding rate of the jet with sidewallshas both a lower dominant shedding frequency and higherfrequency peaks. This, together with low-frequency spectra,implies that a jet with sidewalls has a less three-dimensional

near field structure. These differences in the near field flowstructure are possibly to be caused by different vortex types(ring-like in jet without sidewalls and roller-like in jet withsidewalls). In common, both jets have characteristic regionsof two-dimensional (2-D) mean velocity decay, which fol-low the scaling Uc $ x

1/2 in their respective self-similarfields. However, the decaying and spreading rates are lowerfor the case with sidewalls than the jet without sidewalls.This is also consistent with a more three-dimensional under-lying structure for the case without sidewalls.

Further downstream following the 2-D region, the meanvelocity decay of the jet without sidewalls follows the scale

Uc $ x

1

after an apparent transition zone. This providesfurther evidence that a jet unbounded by sidewalls follow-

ing axis switching, undergoes a transition to axisymmetricflow. Other jet properties, e.g. turbulence intensity, skew-ness and flatness factors of the velocity fluctuations are alsodifferent, confirming that flows from the two nozzle config-urations are statistically different.

It must, therefore, be recognized that, although rectan-

gular nozzles without sidewalls of sufficiently large aspectratio generate statistically two-dimensional mean velocityfields, their other flow development characteristics do notresemble those of planar nozzles which are configured withsidewalls. This is primarily because the presence of side-walls has a profound effect on both the near and far fieldflow. This, together with low-frequency spectra, impliesthat a jet with sidewalls has a less three-dimensional nearfield structure. The far field of flows from rectangular noz-zles without sidewalls exhibit more three-dimensionalunderlying large-scale coherent motions than those fromrectangular nozzles with sidewalls, which produce moretwo-dimensional coherent structures (see Fig. 9).

Acknowledgement

This paper reports results from the first authors PhD re-search completed through the support of Endeavor Inter-national Postgraduate Scholarship, Adelaide AchieversScholarship and an ARC Discovery Grant in collaborationwith FCT. We also thank the two anonymous reviewers

10-7

10-5

10-3

10-1

1 10 100 1000 10000

x/h=5x/h=4x/h=3

f (Hz)

u

(f)

with sidewalls

10-7

10-5

10-3

10-1

1 10 100 1000 10000

without sidewalls

Fig. A1. Power spectra of velocity fluctuations at x/h = 3, 4 and 5 for jets with and without sidewalls.

Appendix 1

See Fig. A1.



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whose comments have improved the overall clarity of ourpaper.

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