Deo et al 2007 - The Influence of Nozzle Exit Geometric Profile on a Turbulent Plane Jet

7/31/2019 Deo et al 2007 - The Influence of Nozzle Exit Geometric Profile on a Turbulent Plane Jet

1/15

The influence of nozzle-exit geometric profile on statistical propertiesof a turbulent plane jet

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

Turbulence Energy and Combustion [TEC] Research Group, School of Mechanical Engineering, The University of Adelaide, SA 5005, Australia

Received 19 June 2006; accepted 25 June 2007

Abstract

The paper reports an investigation of the influence of geometric profile of a long slot nozzle on the statistical properties of a plane jetdischarging into a large space. The nozzle-exit profile was varied by changing orifice-plates with different exit radii (r) over the range of0 < r/h < 3.60, where h is the slot-height. The present measurements were made at a slot-height based Reynolds number (Reh) of1.80 104 and a slot aspect ratio (span/height) of 72. The results obtained show that both the initial flow and the downstream floware dependent upon the ratio r/h. A top-hat mean exit velocity profile is closely approximated when r/h approaches 3.60. The decayand spread rates of the jets mean velocity decrease asymptotically as r/h is increased, with the differences becoming small as r/happroaches 3.60. A decrease in r/h results in a higher formation rate of the primary vortices in the near-field. The far-field values ofthe centerline turbulence intensity are higher for smaller r/h, and display asymptotic-like convergence as r/h approaches 3.60. Overall,the effect of r/h on the mean and turbulence fields decreases as r/h increases.Crown Copyright 2007 Published by Elsevier Inc. All rights reserved.

Keywords: Plane jet; Turbulence structure; Nozzle-exit geometry; Turbulence statistics

1. Introduction

Plane jets have received significant attention after thework of Schlichting [1], e.g. [24]. One reason is becausetheir two-dimensional nature offers advantages in numeri-cal modeling, e.g. the validation of turbulence models [5].However they also have application in heat and mass trans-fer in air curtains [6] and ventilation and air conditioningunits [7]. In a laboratory experiment, a plane jet is pro-

duced by a rectangular slot of dimensions w h, wherew ) h and two parallel plates, known as sidewalls,attached to the slots short sides. The configuration ensures

mean jet propagation in streamwise (x) direction, spread inthe lateral (y) direction and no entrainment in the spanwise(z) direction due to the presence of sidewalls parallel to thexy plane. Such a configuration has been found to result instatistical two-dimensionality over a reasonably largedownstream distance, although this depends upon the noz-zle aspect ratio, AR w/h [8].

In most cases, smoothly contoured plane nozzles havebeen used to produce a top-hat mean velocity profile

[3,4] and a laminar flow state at the nozzle exit, while somehave adopted a sharp-edged orifice-plate [2,9], which pro-duces a saddle-backed velocity profile. A conventionalsharp-edged orifice-plate has an upstream-facing 45 bev-eled edge at the nozzle exit. However, there are very fewstudies using a plane jet issuing from a sharp-edged ori-fice-plate [10], perhaps due to its initial and near-field flowstructure being far more complex (e.g. the existence of avena contracta) than that from a smoothly contractingplane nozzle. Nevertheless, due to the simplicity of itsdesign and manufacture, investigations on most non-planar

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

doi:10.1016/j.expthermflusci.2007.06.004

* 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 Sciences,School of Geographical Sciences and Planning, The University ofQueensland, 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) 545559
mailto:[email protected]:[email protected]


2/15

and non-circular jets have employed sharp-edged orifice-plates [1113].

Experimental evidence reveals that nozzles of differentgeometry produce significantly different downstream flows[14] and the choice of each configuration depends on theapplication. In addition, although the impacts of initialconditions on downstream flow are becoming well-known[15,16], seldom, if ever, has any study investigated planenozzles of different geometry in identical flow facilities.To address this need, the present study aims to report thestatistical behavior of a plane jet by exploring the impactsof varying nozzle contraction profile, as characterized bythe parameter r/h, where r is the nozzles inner-wall con-traction radii.

Our choice of varying the nozzle-exit geometric profile ismotivated by a number of round andplane jet investigations,which provide substantiating evidence that a jets down-stream behavior is significantly governed by upstream (exit)conditions. While comparing the scalar mixing fields from

three types of (axisymmetric) nozzle geometries, Mi et al.

[13] found the highest mean scalar decay and highest fre-quency of the primary vortex formation from a sharp-edgedorifice-plate, followed by a smoothly contoured nozzle andthe lowest for a pipe-jet. Likewise, in another comparisonof the same three flow types, Mi and Nathan [17] concludedthat the highest velocity decay rate occurs in the flow from asharp-edged orifice-plate, following by a smoothly con-toured nozzle and the lowest for a pipe-jet. Other investiga-tors, e.g. Antonia and Zhao [16], Hussain and Zedan [18]studied smoothly contracting axisymmetric nozzles andpipe-jets, and arrived at similar conclusions. Further infor-mation is available from Mi et al. [19] who measured jet flowsfrom nine nozzle configurations, comprising of a smoothlycontoured circular, an elliptical, a triangular, a square, arectangular, a cross-shaped and a star-shaped exit. Theirresults revealed that, relative to the circular jet, the centerlinemean velocity of non-circular jetsdecay morerapidly, imply-ing an increased entrainment rate of theambient fluid. Hencetheir investigation found a significant influence of nozzle

geometric profile on jets from differently configured nozzles.

Nomenclature

AR nozzle-exit aspect ratio, AR = w/hdd boundary layer displacement thickness, dd

Rh=2

0 1 U=U0;cdyf

*

normalized vortex shedding frequency (f*

=fh/U0,b)Fu centerline flatness factor, Fu = hu4i/(hu2i)2Fmaxu maximum value of centerline flatness factorh slot-height of a plane nozzleH shape factor of the initial velocity profile, H=

dd/hmKu decay rate of centerline mean velocityKy jet-spreading (widening) rateL vertical dimension of wind tunnelMx axial component of jet momentumM0y lateral component of jet momentumhm boundary layer momentum thickness, hm

Rh=20 1 U=U0;cU=U0;cdyr radius of contraction (plate thickness) of con-

toured nozzlesReh Reynolds number based on slot-height (h),

Reh U0,bh/tRehm Reynolds number based on momentum thick-

ness, Rehm U0;bhm=mSuww centerline skewness factor, Su = hu3i/(hu2i)3/2Sminu minimum value of centerline skewness factorU exit mean velocityu fluctuation component of jet velocityu0 root-mean-square (rms) of the velocity fluctua-

tion, u 0 = hu2

i1/2

u0c;1 asymptotic value of centerline turbulence inten-sity

u0p peak fluctuation component of the jet velocitywithin jets shear-layers

u0n;c normalized centerline turbulence intensity,

u0n;c u0c=Uc, where the subscript c standsfor centerline valueu0outUout

ratio of non-uniformities in streamwise compo-nents of velocities

Uc centerline local mean velocityU0,b exit area-averaged bulk mean velocityUm-a momentum-averaged exit mean velocity (or the

characteristic normalization scale suitable fornozzles of different exit velocity profiles)

U0,c mean exit centerline velocityUm,c maximum centerline velocityUn,c normalized centerline mean velocity, Un,c =

Uc/U0,bv0outUout ratio of non-uniformities in lateral components

of velocitiesw slot-span of the plane nozzlex01 virtual origin of the normalized mean centerline

velocityx02 virtual origin of the normalized velocity half-

widthxp length of the jets potential corex,y, z streamwise (x), lateral (y) and spanwise (z) coor-

dinate systemy0.5 velocity half-width, calculated at the y-location

at which Ux 12Ucxm kinematic viscosity of the air (%1.5 105 m2 s1 at 20 C ambient temperature)

546 R.C. Deo et al. / Experimental Thermal and Fluid Science 32 (2007) 545559


3/15

From measurements in a plane jet, Hussain and Clark[20] found that an initially laminar boundary layer resultsin a higher rate of change of the mass flux (spreading rate)and the attainment of asymptotic state closer to the exitplane. In a similar investigation using Schlieren photogra-phy and spectral analysis, Chambers et al. [21] found more

organized and symmetric large-scale shear-layer structuresto be dominant in the initially laminar jet than in the ini-tially turbulent one. While a higher centerline decay ratewas noted for the laminar case, the initially turbulent caseproduced more three-dimensional and asymmetric struc-tures, indicating that the nature of the initial boundary layercontrols the development of large-scale structures. Goldsch-midt and Bradshaw [22] studied the effect of exit centerlineturbulence intensity on the flow field of a plane jet. Impor-tantly, they found a larger jet-spreading angle for jets ofhigher exit turbulence intensity. This stands in contrast tothe spreading rate of a pipe-jet, which has higher exit turbu-lence intensity than a smooth contraction nozzle, but a

lower spreading rate. Likewise, Hussain [23] noted somedependence of primary vortex formation on nozzle geome-try from flow visualization of an initially laminar plane jet.Similarly, Russ and Strykowski [24] found that as theboundary layer thickness at the exit plane increases, vortexshedding and pairing occurs further downstream, leading toa reduction in both the potential core lengths and the trans-port of jet momentum. Likewise Eaton and Johston [25]provided an evidence of the influence of initial boundarylayer thickness on downstream development of free shearflows. A more recent study conducted by Ali and Foss[26] found that the geometric design of plane nozzles pro-

duces an influence on the discharge properties of submergedplane jets. Their study revealed that for plane jets having aReynolds numbers greater than 1500, the shape of thedownstream portion of the nozzle produces an influenceon the entrainment rate of the plane jet by altering its pres-sure field at the exit plane, although they did not attempt toquantify the extent of this influence by using different noz-zle-exit geometric profiles.

From the above discussion, it is evident that the nozzleshape influences the initial boundary layer characteristicsto an appreciable extent, so causing significant differencesin the evolving flow properties of both plane and roundjets. However, no systematic study appears to have beenundertaken of the influence of nozzle contraction profileon a plane jet, such as by changing the parameter r/h. Thisinformation is of fundamental and practical relevance forthe development and validation of turbulence models andfor the optimization of nozzle designs. In addition, it is use-ful to determine what, if any, radius of contraction is nec-essary to closely approximate a top-hat exit velocityprofile, since radially contoured nozzles are easier todesign, construct and configure than are conventionalsmoothly contoured ones. With this view, we assess theinfluence of r/h on the mean flow and turbulent statisticsof a plane jet up to a downstream distance of 85h using five

nozzles of different r but identical h.

2. Experiment details

The plane nozzle facility, shown schematically in Fig. 1,consists of an open circuit wind tunnel, flow straighteningelements including a honeycomb and screens, and asmooth contraction exit of dimensions 720 mm 340 mm.

The honeycomb is composed of drinking straws, with itscells aligned with, and stacked perpendicular to the mainstream. This assists in reducing velocity fluctuations inthe transverse direction, while producing minimum effecton streamwise velocity because of the small pressure drop.Likewise, the screens help reduce the velocity defect in theturbulent boundary layer. The present screens have anopen area ratio of approximately 60% and the smooth con-traction is based on a third order polynomial curve.

Two flat plates were mounted to the end of the windtunnel contraction (Fig. 1b), with radially contractinglong-sides of four different exit radii (r) and two parallelplates, as sidewalls, attached to the slots short sides to cre-

ate a plane nozzle. The inner-wall of all flat plates was radi-ally contoured, where the radius of contraction (r) equalsthe plate thickness (see Fig. 1a). The slot-height of the noz-zle was fixed at h = 10 mm and the span (separationbetween the sidewalls) was kept at w = 720 mm, producinga large aspect ratio plane nozzle of w/h = 72.

The inner-wall radius of the nozzle plate (r) was variedfrom r = 4.5 to 36 mm by a factor of 2 for each case, asshown in Fig. 1b. This resulted in the four radially con-toured nozzles of r/h = 0.45, 0.90, 1.80 and 3.60. Duringmeasurements, the nozzle contraction faced upstream forthese four cases. In addition to these four nozzles, a fifth

configuration of r/h % 0 was achieved by reversing the ori-entation of the orifice-plates ofr/h = 0.45, so that it opensout downstream. The symbol % is used in recognitionthat this configuration is somewhat different from the con-ventional sharp-edged (45 beveled) configurations morecommonly employed [2,9,11]. Since it is not possible toachieve any configuration with an identically zero radius,and, given the sensitivity of a flow to inlet conditions, itis probable that subtle differences may exist for all typesof sharp-edged orifice-plates. Further, the presently cho-sen configuration does have a sharp right-angle oppositethe contraction side of the plate, and does give consistent(though probably not unique) trends in the data. For thesereasons, we have also chosen to use dashed lines (---) toconnect data points (shown later in results) between theconfigurations r/h = 0.45 and r/h % 0.

The plane jet facility, located in a low noise, fluidmechanics laboratory of dimensions 18 m (long) 7 m(wide) 2.5 m (high), was mounted horizontally, with theplane nozzle located at the mid point between the floorand ceiling. Throughout the present investigation, greatcare was taken to ensure that the experimental facilityremained isolated from any external disturbances. The dis-tance from the jet exit to the front wall of the laboratorywas approximately 1400h and between the jet and ceiling/

floor was approximately 125h, allowing the unheated jet

R.C. Deo et al. / Experimental Thermal and Fluid Science 32 (2007) 545559 547


4/15

to discharge freely into still air. Based on the approach ofHussain et al. [27], the effects of room confinement is esti-mated to produce less than 0.5% momentum loss for allplane jets at a downstream distance of 85h. Hence the pres-ent jets closely approximate plane jets in an infinite envi-ronment. For all cases of the present investigation, the(area-averaged) jet discharge bulk mean velocity was kept

fixed at U0,b % 27 ms

1, resulting in a Reynolds number

based on slot-height (h) and kinematic viscosity (m) ofReh % 1.80 104.

The velocity measurements were performed over theflow region 0 6 x/h 6 85 using a single hot-wire anemome-ter, under isothermal conditions of ambient temperature20.0 0.1 C. To avoid aerodynamic interference of theprongs on the hot wire, the present probe was carefully

aligned horizontally and with the prongs parallel to the

Fig. 1. Schematic view of experimental setup showing (a) the wind tunnel and nozzle attachment; (b) nozzles of contraction profiles denoted by (i) r/h % 0,(ii) r/h = 0.45, (iii) r/h = 0.90, (iv) r/h = 1.80, (v) r/h = 3.60 and (c) other experimental apparatus. Note that sidewalls have been omitted for clarity, anddiagrams drawn are not to scale.



5/15

plane jet. Hence its output corresponds closely to thestreamwise component of the flow velocity. The singlehot-wire anemometer, if used with caution, encountersreduced errors when compared with dual or triple wires,in which the adjacent probe can probably influence themeasured velocity [28]. However, a single wire is not able

to distinguish between streamwise and normal contribu-tions to the cooling velocity thus the issue of directionalambiguity remains to a certain degree. The hot-wire (tung-sten) sensor was 5 lm in diameter and 0.8 mm in length,aligned to be parallel to the long nozzle sides. The overheatratio of the wire was 1.5 and square wave test revealed amaximum frequency response of 15 kHz. Hot-wire calibra-tions were conducted using a standard Pitot-static tube,placed side by side with the hot-wire probe, at the jets exit(x/h % 0), where the turbulence intensity was approxi-mately 0.5%, before and after measurements of each caseof r/h. The low initial turbulence intensity, as documentedby Stainback and Nagabushana [29], is a necessity for an

accurate calibration procedure. Both calibration functionswere tested for discrepancies, and if velocity drift exceeded0.5%, the experiment was repeated. No further correctionsto the velocity measurements were applied. Thus it isexpected that measurements away from the centerline(towards the outer region of the jet) are significantly inerror, because of high velocity fluctuations relative to themean value. Nevertheless, the central aim here is to com-pare the measurement of one case of r/h with another, withmost data taken on the jet centerline. While convertingdata points from voltages to velocities using a fourth orderpolynomial curve similar to the one proposed by George

et al. [30], the average accuracy of each calibration functionwas found to be 0.2%.

The signals obtained were low-pass filtered with an iden-tical cut-off frequency of fc = 9.20 kHz to eliminate highfrequency noise at all the measured locations. The voltagesignals were offset to within 03 V (as a precautionary mea-sure to avoid signal clipping [31]) and amplified appropri-ately through the circuits, and then digitized on apersonal computer at fs = 18.4 kHz via a 16 channel,12-bit PC-30F A/D converter (Fig. 1c) of signal inputrange 05 V. The sampling duration was approximately22 s, during which 400,000 instantaneous data points weregathered. Using the inaccuracies in calibration andobserved scatter in present measurements, the uncertaintiesare estimated to have a mean error of 4% at the outeredge of the jet and 0.8% on the centerline. The errors inthe centerline mean velocity, root-mean-square (rms) veloc-ity, skewness Su hu3i/(hu2i)3/2 and flatness Fu hu4i/(hu2i)2 were found to be approximately 0.8, 1.8%,2% and 1.5%, respectively. The errors in the momentumintegral quantities and jet virtual origins are estimated tobe 3%.

Although a smoothly contoured wind tunnel is used togenerate reasonably uniform flows, and to avoid significantflow separation upstream from the exit plane, any abrupt

change in the nozzle shape within the vicinity of the nozzle

plates, as in the present case, produces some inevitable flowseparations. This is due to unsteadiness in separations onthe curved walls, leading to fluctuations in the y-compo-nent momentum at the exit, thus altering the flapping ofthe jet in the xy plane. This effect, if substantial, can resultin an increase in spreading rate. One would expect this phe-

nomenon to depend to some extent on nozzle shape and inparticular on the magnitude of r. For the present measure-ments, it is expected that the turbulence in the main con-traction is very low; hence these separations are expectedto be not much unsteady, and thus insignificant. That thisis indeed the case is demonstrated in Appendix 1.

3. Characterization of jet exit flow

The exit flows of each plane nozzle were characterized bymeasuring the velocity profiles at x/h % 0.2 for r/h = 0.453.60 and at x/h = 1 for r/h % 0 along the lateral (y) directionover the range

0.60 6 n 6 0.60, where n = y/h. These are

presented in Fig. 2ae. Herein, U0,c is the exit centerlinemean velocity. Clearly, the exit velocity profiles depend onr/h and specifically undergo a substantial transition frombeing saddle-backed for r/h % 0 (Fig. 2a) to closely approx-imate a top-hat profile for r/h = 1.80 and 3.60 (Fig. 2dand e). Although the present case for r/h % 0 cannot be clas-sified as a conventional sharp-edged orifice-plate, the sad-dle-backed velocity profiles indicate that the reversing ofthe nozzle plates of smallest contraction radius (Fig. 1b(i), r/h % 0) produce an exit flow close to that of a sharp-edged orifice-plate. It is also interesting to note that the exitvelocity profiles for the cases of r/h 6 0.90 have the highest

velocity located towards the edge of the jet, resulting in theobserved saddle-back. The cases r/h 6 0.90 are found togenerate vena contracta immediately downstream fromthe exit plane. Interestingly, the smaller the value of r/h,the greater is the velocity deficit on the centerline relativeto the maximum value close to edge of the jet. This trendsuggests that the nozzle configuration will approach asharp-edged orifice-plate with a sufficiently small radius ofcontraction. The presence of vena contractas for nozzlesof r/h 6 0.90 is also broadly consistent with a number ofprevious investigations such as Quinn [11], Mi and Nathan[12],Mietal. [13] and Tsuchiya [32], all of which found venacontractas in jets issuing from sharp-edged orifice-plates.The exit flow appears to be uniform within the regionjnj 6 0.45 for the cases of r/h = 1.80 and 3.60.

There is also a consistent trend in the initial turbulenceintensity profiles, u0n hu2i1=2=U0;c, with changes in r/h(Fig. 2, Table 1). As r/h is increased from 0.45 to 3.60,the turbulence intensity in the shear-layer decreases fromabout 17% to 4%, as does that in the middle of the jet, fromu0n % 2:0% for r/h = 0.45 to u0n % 1:5% for r/h = 3.60. Thisobservation stands in contrast to round orifice-plates [33],which typically produce weaker velocity fluctuations andthus lower rms values. Such a difference underlines the fun-damental influence of nozzle-exit geometry (i.e. planar ver-

sus round) on the exit velocity field of these two jets.

http://-/?-http://-/?-


6/15

An estimate of the initial boundary layer characteristics

is undertaken, since jet development has previously been

found to be dependent on exit conditions [18,20]. Using

Fig. 2, the exit conditions are characterized by estimating

0

0.25

0.50

0.75

1.00

1.25

-0.6 -0.3 0 0.3 0.60

0.05

0.10

0.15

0.20

0.25

0

0.25

0.50

0.75

1.00

1.25

-0.6 -0.3 0 0.3 0.60

0.05

0.10

0.15

0.20

0.25

u'/Uo,c

u'/Uo,c

u'/Uo,c

u'/Uo,c

u'/Uo,c

-0.6 -0.3 0 0. 3 0. 60

0.05

0.10

0.15

0.20

0.25

-0.6 -0.3 0 0.3 0.60

0.05

0.10

0.15

0.20

0.25

U/Uo,c

0

0.25

0.50

0.75

1.00

1.25

U/Uo,c

0

0.25

0.50

0.75

1.00

1.25

U/Uo,c

0

0.25

0.50

0.75

1.00

1.25

U/Uo,c

U/Uo,c

= y/h = y/h

= y/h = y/h

-0.6 -0.3 0 0.3 0.6

0

0.05

0.10

0.15

0.20

=y/h

Fig. 2. Lateral profiles of the mean velocity, U/U0,c (denoted by the symbol - -h--) and turbulence intensity, u0/U0,c (denoted by the symbol s) for

(i) r/h % 0 at the x/h = 1, (ii) r/h = 0.45, (iii) r/h = 0.90, (iv) r/h = 1.80 and (v) r/h = 3.60 at the x/h = 0.2.



7/15

the boundary layer displacement (dd) and momentum(hm) thickness using momentum integral equations: dd Ryh=2y0 1 U=U0;cdy and hm

Ryh=2y0 1 U=U0;cU=

U0;cdy (Table 1). To compensate for the comparativelylow measurement resolution and paucity of data pointsthrough the boundary layer, a best-fit spline curve was usedto perform the numerical integration of two momentumequations, on both sides of each velocity profile (i.e. fromy = 0 to h/2 and y =

h/2 to 0), yielding two independent

values of dd and hm. Both were then averaged to furtherreduce errors. Note also that the case r/h % 0 has anentirely different geometry, which required that the mea-surements be conducted further downstream (x/h = 1).This prevented a reliable estimate of its boundary layerthickness.

Table 1 reveals that, as r/h is increased from 0.45 to 3.60,the boundary layer thickness, dd increases from 0.054h to0.151h, while hm increases from 0.030h to 0.061h and sodoes the Reynolds number based on hm. The decrease in tur-bulence intensity at x/h = 0.2 as r is increased (Fig. 2be), ispartly attributable to the flapping of initial mixing layer,

which produces rms-fluctuations as the mean velocity pro-file oscillates in the y-direction further downstream fromthe measurement point, although this effect is quite small.It is expected that these variations in the exit flow, whichcontrol the shear-layer development, have a significantinfluence on downstream behavior of present plane jets.This is borne out in the data presented in the next section.

The maximum cumulative error in momentum integralquantities is 6%. This, combined with the consistent trendsevident in Table 1, gives confidence in the results. However,it must be noted that the measurements were performed atx/h = 0.2, so that the values will differ somewhat from theactual exit values. The corresponding shape factors(H= dd/hm), which are often used to determine the flatness(uniformity) of the mean velocity profiles [34], possess val-ues between 1.80 and 2.48, compared with a value of 2.60for a true Blasius exit velocity profile. Thus the presentplane nozzles of r/h = 1.80 and 3.60 may be characterizedas having an initially laminar boundary layer, since theshape factors closely resemble those of a Blasius velocityprofile [35].

4. Statistical properties of the downstream flow

Fig. 3 shows the near-field evolution of mean centerline

velocity, Uc, normalized by bulk mean exit velocity, U0,b.

As expected, there is a consistent dependence of Uc/U0,bon r/h, in particular, the case of r/h % 0 being discerniblydifferent from that for other cases. A hump in Uc/U0,b (atx/h % 2 for the cases 0 6 r/h 6 0.90) becomes obvious,although its magnitude tends to decrease as r/h isincreased. This hump is yet another feature which unam-biguously supports the existence of vena contractas fornozzles of r/h 6 0.90 and is consistent with Fig. 2ac.Fig. 3 also shows that, for x/h > 6, the decay rate of themean centerline velocity depends on r/h, with the jet issuingfrom r/h % 0 decaying at the highest rate. This trend is con-sistent with previous findings of round orifice-jets [13].

An assessment of the dependence of the near-field humpofUc/U0,b on r/h (at x/h % 2) is shown in Fig. 4. That is, asr/h is increased from 0 to 3.60, the ratios of the maximumcenterline velocity Um,c to the exit bulk mean velocity U0,bare found to decrease asymptotically from approximately1.30 to 1.00. Interestingly, the nozzle profile with r/h % 0produces Um,c/U0,b % 1.30. This value is lower thanUm,c/U0,b % 1.55 found by Quinn [11] from a sharp-edgedorifice-plate, although the trends are similar (Fig. 3). Takentogether, Figs. 24 provide sufficient evidence to show thatthe present case of r/h % 0 produces an exit and near-fieldflow structure that is qualitatively similar to other sharp-edged orifice-plate flows, with the subtle differences attrib-utable to the differences in the nozzle designs.

To investigate the influence of r/h on the primary vortex

shedding in the near-field, we have analyzed the centerline

Table 1Initial boundary layer characteristics obtained at x = 0.2h

r/h dd hm H= dd/hm Rehm U0;bhm=m u0c=Uc (%) u0p=Uc (%)0 0.45 0.054h 0.030h 1.80 551 2.0 16.80.90 0.068h 0.035h 1.95 642 1.9 8.11.80 0.127h 0.052h 2.44 955 1.9 5.5

3.60 0.151h 0.061h 2.48 1120 1.5 3.9

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 5 10 15 20

r/h = 00.450.901.803.60

Quinn [10]orifice-plate (rectangular)

x/h

Uc/Uo,b

Quinn [11], orifice-plate(rectangular) nozzle

r/h 00.45

0.90

1.80

3.60

Fig. 3. Near-field evolution of the normalized centerline mean velocity,Uc/U0,b for various cases of investigation.



8/15

velocity spectra Uu

(f*) within the potential core region mea-sured at x/h = 3, a location typically known to produceKelvinHelmholtz vortices in plane jets. Here, the normal-ized vortex shedding frequency, f* fh/U0,b and the inte-gral

RUufdf 1.

The spectra (Fig. 5) reveal that there are clear differencesin the underlying flow structure of all five jets. Each jetexhibits a broad peak in Uu(f*), revealing the periodic pas-sage of primary vortices in the near-nozzle region. The pro-cesses of vortex formation and growth in the near region ofplane jets are well established. For instance, it is well-known that 2-D roller-like counter-rotating vortices domi-nate the shear-layers which bound the potential core [36].

Thus the present spectra clearly confirm the regular occur-rence of primary vortices from all the tested nozzles. Simi-larly, flow visualizations of a round jet from a sharp-edgedorifice-plate by Mi et al. [13] revealed well-defined coherentvortices along their potential core region. In their smokevisualization experiments, Tsuchiya et al. [32] noted axiallysymmetric vortices within 04 nozzle widths downstream.

The mechanism leading to vortex formation immediatelydownstream from the nozzle exit is a known feature [37]as is the roll-up of the unstable laminar shear-layers to pro-duce the primary vortices. During their streamwise propa-gation, the vortices convect the irrotational ambient fluidinto the jet. Early observations of plane jets by Brown

[38] and Beavers and Wilson [39] found that the symmetri-cal vortices occur on alternate sides of a plane jet. Theirsuccessive growth into larger and larger vortices throughcoalescence with adjacent vortices [40] causes them to even-tually breakdown as they propagate downstream. The pro-cess of coalescence typically depends on the exit conditions,as can be seen from the work of Sato [41], who found thatan externally driven noise at a frequency close to that of thenatural vortex shedding frequency, causes vortices to growand coalesce closer to the nozzle exit. The dependence ofvortex dynamics on initial conditions is also well-known,e.g. [14]. Collating from the past and present work, itbecomes apparent that as the exit conditions are varied

by changing r/h from 3.60 to 0, the normalized vortex shed-ding frequency, Sth increases from approximately 0.24 to0.39. Recall from Fig. 2 and Table 1 that the boundarylayer gets thicker as r/h increases. Therefore, a thinnerboundary layer, with more concentrated vorticity, resultsin a higher formation rate of the primary vortices for thecase r/h % 0 [13]. As evidenced, different nozzle-exit-geo-metric profiles probably generate structurally different vor-tices, which convect downstream at different rates. Alsonote that the exit and near-field centerline turbulence inten-sity is higher for smaller values of r/h (Figs. 2 and 12 shownlater). This indicates that a higher formation rate of the pri-

mary vortices (found for smaller r/h), is associated with lar-ger velocity fluctuations. However, a higher frequency istypically associated with a smaller scale of the vortexmotion, indicating that the higher turbulence intensityresults, at least in part, from a greater variability in theinstantaneous location of the vortex cores.

Table 2 assembles the f* data from previous investiga-tions of round and plane nozzles. Also listed in Table 2are the key initial conditions. The present measurementoff* = 0.39 using r/h % 0 is in good agreement with the val-ues f* = 0.43 and 0.40 measured by Beavers and Wilson[39] and Tsuchiya et al. [32] using plane and rectangularnozzles, respectively. This close comparison provides fur-ther support that the geometry of r/h % 0 produces a flowstructure similar to those from other sharp-edged orifice-plates. However, all the f* values are significantly higherthan a value of 0.23 measured by Sato [41] for a channel(analogous to a pipe). This difference reflects the key rolethat a nozzles geometry plays in vortex formation. Impor-tantly, the values of 0.27 and 0.24 measured by Namar andOtugen [37] using smoothly contracting nozzles and thepresent value for r/h = 1.80 and 3.60 are in good agreementtoo, confirming that they closely approximate other typesof smoothly contoured plane nozzles.

Next we assess the influence of nozzle-exit contraction

profiles on the far-field flow of the present plane jets.

0.8

1.0

1.2

1.4

1.6

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

present data

Quinn [11]

r/h

Um,c

/Uo,b

Fig. 4. Dependence of the ratio of mean centerline velocity maximum,Um,c and exit bulk mean velocity, U0,b on r/h obtained at x/h = 3.

0.00001

0.0001

0.001

0.01

0.1

0.5 1.0 1.5

(1.80, 0.24)(r/h,f*) (3.60, 0.24)

(0.90, 0.26) (0.45, 0.28)

(r/h,f*) (0, 0.39)

f =f h / Uo,b

u

(f)*

*

Fig. 5. Power spectra, Uu(f*) of the centerline velocity fluctuations

measured at x/h = 3.



9/15

Fig. 6 presents the far-field mean centerline velocity, Uc,normalized by the exit bulk mean velocity U0,b.

3 It isrevealed that in the self-similar region, Uc $ x1/2, leadingto the well-known relationship of the form

U0;b

Uc

2 Ku x

hx01

h

1

where Ku represents the velocity decay rate and x01 is its

virtual origin. As with the near-field case, the decay ratesof the far-field mean centerline velocity reveal a consistentdependence on r/h, with the nozzle ofr/h % 0 exhibiting the

highest far-field velocity decay. The velocity decay rates,shown explicitly in Fig. 7, exhibit an asymptotic-like con-

vergence toward a single curve as r/h approaches 3.60.While the differences between the cases of r/h = 1.80 and3.60 are within experimental uncertainty, the trend is con-sistent, both internally and with other data presented later.

Fig. 8 presents the lateral distributions of the normalizedmean velocity at selected downstream locations for r/h % 0,r/h = 0.45, 0.90 and 3.60. The mean velocity profilesbecome approximately self-similar at x/h = 20 forr/h % 0, which is significantly further downstream thanthe equivalent x/h = 5 for r/h = 3.60. The largest distanceis required for the. case r/h % 0. That is, the downstreamdistance required for the lateral profiles of the mean veloc-ity to achieve self-similarity decreases as r/h is increased.All the self-similar profiles conform closely to a Gaussianrelation, Un = exp[ln2(yn)2]. Likewise, the streamwisevariations (Fig. 9) of the normalized velocity half-widths,y0.5/h, conform to the far-field relationship

y0:5h

Ky xhx02

h

2

0.15

0.17

0.19

0.21

0.23

0.25

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

r/h

Ku

Fig. 7. The decay rates of the centerline mean velocity for r/h = 03.60.

Table 2The normalized vortex shedding frequency, f* for previous jets of round, rectangular and plane configurations

Investigation Geometry Nozzle profile Re AR f*

Beavers and Wilson [39] Plane Orifice-plate 5003000 0.43Tsuchiya et al. [32] Rectangular Orifice-plate 3500 5 0.40Satoa [41] Plane Channel 15008000 1067 0.23Namar and Otugen [37] Rectangular Contoured 10007000 56 0.27

Present, r/h % 0 Planar Orifice-like 18,000 72 0.39Present, r/h = 1.80, 3.60 Planar Radially contoured 18,000 72 0.24

Beavers and Wilson [39] Round Orifice-plate 5003000 0.63Johansen [42] Round Orifice-plate 2001000 0.60Mi et al. [13] Round Orifice-plate 16,000 0.70Ko and Davis [43] Round Contoured 0.20Crow and Champagne [44] Round Contoured 10,50030,900 0.30Mi et al. [13] Round Contoured 16,000 0.40

a Note: Sato [41] used a contoured planar nozzle with an upstream channel of length between 300 and 1100 mm.

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90

r/h 00.45

0.901.803.60

x/h

(Uo,b/Uc

)2

Fig. 6. The normalized profiles of centerline mean velocity for differentvalues of r/h.

3 We have also checked the normalization by the momentum-averagedexit velocity (Um-a), not shown, and found the relative results between thedifferent cases being similar to those normalized by U0,b. Note that thecharacteristic velocity

Um-a 1h

Zh=2h=2

U2dy

!1=2

since the exit momentum is M0 qwhU2m-a qw

Rh=2

h=2 U2dy. Obviously,

the normalization by Um-a takes into account the different mean momen-

tum flux rates with different exit mean velocity profiles.



10/15

where Ky is the spreading rate and x02 is the virtual originof the half-width. Clearly, the different values of r/h pro-duce different values of y0.5/h, confirming that the jet-spreading angles differ for each nozzle geometry. Fig. 10shows that the spreading rate decreases, approximatelyasymptotically, as r/h is increased from 0 to 3.60, with

the highest spreading rate for r/h%

0. This trend, in turn,coincides with the measured trends in the decay of Uc(Fig. 7), and thus shows internal consistency of the presentdata.

The magnitude of the virtual origins, x01 and x02 (eachwith uncertainty of approximately 8%) is found to increaseasymptotically with r/h (Fig. 11), although with greaterscatter as expected. That is, the nozzle of r/h % 0 has thesmallest of these virtual origins, consistent with the pres-ence of a vena contracta (Figs. 3 and 4) for this case. Adependence of virtual origins on initial conditions was alsorevealed by Gouldin et al. [5]. Importantly, Flora andGoldschmidt [45] noted that their virtual origin moved

upstream with a relatively modest increase in exit turbu-lence intensity from 1.06% to 1.28%. This trend again, isconsistent with the present results, where an increase inthe initial turbulence intensity from approximately 1.7%to 2.3% is associated with a translation of the virtual ori-gins from x01/h % 3.9 to x01/h % 0.4 and x02/h % 4.7 tox02/h % 2.0. There is only a small difference between the

0.03

0.05

0.07

0.09

0.11

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0r/h

Ky

Fig. 10. The jet-spreading rates for r/h = 03.60.

0

0.2

0.4

0.6

0.8

1.0

0 0.5 1.0 1.5 2.0 2.5

Un= exp[-ln 2 (y

n)2]

yn=y/y

0.5

Un=U

/Uc

Un=U/Uc

0

0.2

0.4

0.6

0.8

1.0

0 0.5 1.0 1.5 2.0 2.5

x/h = 3510204080

yn=y/y

0.5

yn=y/y

0.5y

n=y/y

0.5

0

0.2

0.4

0.6

0.8

1.0

0 0.5 1.0 1.5 2.0 2.5

0

0.2

0.4

0.6

0.8

1.0

0 0.5 1.0 1.5 2.0 2.5

x/h = 35102040

80

Fig. 8. Lateral profiles of the mean velocity, U/Uc for (a) r/h % 0;(b) r/h = 0.45; (c) r/h = 0.90 and (d) r/h = 3.60.

0

2

4

6

8

10

0 10 20 30 40 50 60 70 80 90

r/h = 00.450.903.60

x/h

y0.5/h

r/h 00.45

0.901.80

3.60

Fig. 9. Streamwise evolutions of mean velocity half-width for different

values of r/h.

0

2

4

6

0 1 2 3 4

-5

-3

-1

1

3

5

r/h

x01

/h

x02

/h

Fig. 11. The jets virtual origins for r/h = 03.60.



11/15

values ofx01 for the cases ofr/h = 1.80 and r/h = 3.60, con-

firming that the flows from these configurations are verysimilar.

Next we consider the dependence of the turbulent veloc-ity field on r/h. Fig. 12 presents the streamwise evolutionsof locally normalized turbulence intensity, u0n;c u0c=Uc,for different values of r/h, where u0c hu2i1=2. As with themean velocity field, the turbulent field exhibits a consistentdependence on r/h. This dependence is, as expected, great-est in near-field but does not vanish in the far-field. In gen-eral, the centerline turbulence intensity decreases as r/h isincreased. The initial rapid increase ofu0n;c is a distinct fea-ture of all plane jets, reflecting the streamwise growth of the

shear-layer instability [46] due to the large-scale structures,perhaps similar to those evidenced from the plane jet flowvisualizations of Gordeyev and Thomas [47] and Shlienand Hussain [48]. It is these large-scale structures whichare responsible for large-scale engulfment of the ambientfluid, higher velocity fluctuations and higher decay of meanvelocity, and thus high turbulence intensity. It is alsodeduced from previous work that the far-field flow is influ-enced by propagation of these structures [37], and the dom-inance of large-scale structures diminish as they convectdownstream due to the generation of a broader range ofsmaller eddies.

The different shape in the evolution ofu0n;c

for jets of dif-ferent r/h implies differences in the underlying large-scalestructures of these jets. A distinct hump in u0n;c is foundat x/h % 13 for r/h % 0. A hump in turbulence intensity isprobably associated with stronger intermittent incursionsof low-velocity, predominantly ambient, fluid at this loca-tion, causing higher velocity fluctuations relative to themean values.

In the self-similar far-field (x/h > 30), the centerline tur-bulence intensity clearly depends on r/h. This dependenceis highlighted in Fig. 13, which plots u0c;1 against r/h. Despitesome scatter, a consistent trend emerges. As r/h is increasedfrom 0 to 3.60, u0c;

1decreases in an asymptotic-like manner

with r/h. This systematic dependence indicates that the state

of fully-developed turbulent flow is dependent on the noz-zle-exit geometric profile. Further evidence of the depen-dence of the turbulent velocity field on nozzle-exitcontraction profile is given by the lateral distributions of tur-bulence intensity, u0n hu2i1=2=Uc as shown in Fig. 14ad.There are clear differences resulting from changes in the val-ues ofr/h. Consistent with the trends in the lateral profiles of

0.1

0.2

0.3

0 10 20 30 40 50 60 70 80 90

r/h = 00.450.901.803.60

x/h

u'n,c=

u'c/Uc

r/h 00.45

0.90

1.80

3.60

Fig. 12. Streamwise evolutions of locally normalized turbulence intensity,u0c=Uc, for different values of r/h.

0.22

0.24

0.26

0.28

0.30

0 1 2 3 4

u'c,

r/h

Fig. 13. Variations of far-field asymptotic turbulence intensity, u0c;1 withr/h.

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3

0.4

0 0.5 1.0 1.5 2.0 2.5

x/h = 35102040

80

0

0.1

0.2

0.3

0.4

0 0.5 1.0 1.5 2.0 2.5y

n= y /y

0.5y

n= y /y

0.5

0 0.5 1.0 1.5 2.0 2.50 0.5 1.0 1.5 2.0 2.5y

n= y /y

0.5y

n= y /y

0.5

u'n=u'/Uc

0

0.1

0.2

0.3

0.4

u'n=u'/Uc

x/h = 3

5

10

20

40

80

Fig. 14. Lateral profiles of the turbulence intensity, u 0/Uc for (a) r/h

%0;

(b) r/h = 0.45; (c) r/h = 0.90 and (d) r/h = 3.60.



12/15

the mean velocity, the axial distance at which turbulence

intensity profiles become self-similar increases with r/h.For instance, when r/h % 0, the axial distance required toattain self-similarity of u0n is at x/h = 40, whereas forr/h = 3.60, this distance is reduced to x/h = 10. This indi-cates that the development of the large-scale structures inthe outer shear-layers also depends on the nozzle-exit geo-metric profile.

The dependence of the flow statistics on r/h is furtherexamined using the higher order moments of velocity fluc-tuations. Figs. 15 and 16 present the centerline evolutionsof the skewness Su and flatness (kurtosis) Fu factors of allfive jets. These were each determined from a large sample

of approximately 400,000 data points of the instantaneousvelocity, so the convergence of the calculations is good.Further, an appropriate voltage offset was applied to theanalogue-to-digital range ensured that no clippingoccurred [31]. The profiles are here vertically offset byunity, and the ordinate is drawn on a logarithmic scalefor clarity. Both factors evolve from nearly Gaussian val-ues (Su, Fu) = (0,3) at the origin, to highly non-Gaussian

values, around 4 < x/h < 6, consistent with previous work.

For example, Browne et al. [36] found that their passivetemperature fluctuations at the exit of a plane nozzle wereGaussian, while those within the potential core region(between 3 and 5h) were highly non-Gaussian. A departurefrom Gaussian values is typically interpreted to result fromthe presence of coherent, non-random motions due to thegrowth of the large-scale roller-like structures in theshear-layers. The near-field trends of Su and Fu, whichare governed by r/h, reflect a dependence of the underlyinglarge-scale shear-layer structures on source (exit) condi-tions. Also importantly, the absence of potential coresfor cases of small r/h (e.g. r/h = 0, 0.45 and 0.90) implies

the more rapid development of large-scale structuresthrough its shear-layer, increased fluid entrainment andquite possibly, more coherent large-scale structures.

To inspect the variations of the minima Sminu and max-ima Fmaxu of both factors due to changes in r/h, we haveplotted their relative magnitudes in Fig. 17. Despite somescatter, a clear asymptotic-like dependence of both valueson r/h is evident, with the cases r/h = 1.80 and 3.60 possess-ing similar values. The present nozzles of small r/h pro-duces larger values of skewness and kurtosis, indicatingthat the near-field flow encounters higher instabilities, per-haps due to greater incursion of low-velocity ambient fluid,than with nozzles of larger r/h. In the interaction and fully-

developed regions (i.e. x/h > 20), both factors approach,but do not reach, truly Gaussian values. The departureof the moments of higher order statistics from their respec-tive Gaussian values are consistent with Browne et al. [36],whose passive scalar measurements were non-Gaussian inthe self-similar field.

5. Conclusions

In summary, the statistical properties of the present jetswere found to depend systematically on the nozzle-exit con-traction profiles measured over the range 0 < r/h < 3.60.

The results reveal consistent differences throughout the

1 10

-2

0

-1

1

0

0

0

0

Gaussian

x/h

Su=

/()3/2

100

Fig. 15. Streamwise evolutions of the skewness, Su for different values ofr/h. Note that each profile is shifted vertically by unity relative to itsneighbour for clarity, and symbols are identical to Fig. 12.

1 10 100

3

2

6

3

3

3

4

5

3

Gaussian

x/h

Fu=/()4

Fig. 16. Streamwise evolutions of the flatness, Fu for different values ofr/h.Note that each profile is shifted vertically by unity relative to its neighbour

for clarity, and symbols are identical to Fig. 12.

-8

-6

-4

-2

0

2

0 1 2 3 4

3

4

5

6

7

r/h

Sumin

Fumax

Fig. 17. The dependence of the near-field minima in skewness, Sminu , andmaxima in flatness, Fmaxu , on r/h.



13/15

flow, extending from the exit velocity profiles, through thenear-field, and into the far-field. These differences arededuced to result from differences in the underlying flowstructure that propagates downstream from the differentnozzle-exit geometric profiles. (As shown in the Appendix,any effect of flow separations generated at the junction

between the wind tunnel contraction and the nozzle platesis found to be very small, and would also be consistentlyincorporated in all experiments.)

The exit velocity profiles were found to depend system-atically upon r/h, with a gradual transition from being sad-dle-backed for the case r/h % 0 to closely approximate atop-hat for the cases r/h = 1.80 and 3.60. For the casesr/h 6 0.90, the mean exit velocity profiles exhibit a sad-dle-back, a shape which characterizes sharp-edged ori-fice-plates. Importantly, these configurations exhibit venacontractas, indicating upstream flow separations. Theextent of the departure of these velocity profiles from atop-hat, as characterized by the ratio of the maxima in

Uc, to the exit bulk mean velocity, U0,b, decreased in anasymptotic-like manner with r/h.

Likewise, the thickness of the initial boundary layer wasfound to increase monotonically with an increase in r/h,while its peak turbulence intensity decreased. The powerspectra of the centerline velocity fluctuations revealed thatthe near-field vortex shedding frequency decreases mono-tonically, from a value of f* = 0.39 for r/h % 0 to f* = 0.24for r/h = 1.80 and 3.60. In the self-similar far-field, the ratesof centerline velocity decay and jet spread were found todecrease in an asymptotic-like manner with an increase inr/h, so that the differences between r/h = 1.80 and 3.60 were

small. The streamwise turbulence intensity revealed a dis-tinct hump for the case r/h = 0 near to x/h = 13, while nosignificant hump was found for the radially contoured noz-zles (r/h = 1.80 and 3.60). The far-field values of turbulenceintensity also decreased in an asymptotic-like manner as r/hwas increased to 3.60. However, one would expect that afurther increase in r/h towards infinity would cause the jetproperties to depart from those of a top-hat exit flow, toconverge towards a fully-developed channel flow.

The collective findings from present work, together withthe proposed hypothesis of George [15], experimental workof George and Davidson [49] and recent measurements ofDeo [50] confirm that the downstream development ofany plane jet is dependent upon its exit boundary (i.e. noz-zle-exit profiles) and upstream conditions. In other words,even in the fully-developed state, a plane jet does not for-get its origin. Therefore, the classical theory, which arguesthat all jets should become asymptotically independent ofsource conditions and that the jet properties will dependonly on the rate at which momentum is added and the dis-tance from its source, is not valid for a plane jet.

Acknowledgements

The experimental work for this paper was undertaken by

R.D. at The University of Adelaide (UA), with support by

an international postgraduate funding, UA AchieversScholarship and an ARC Linkage Grant in partnership withFCT-Combustion. Thanks to Dr. Peter Lanspeary for hiscontribution in evaluating the role of the upstream contrac-tion on the flow. We are grateful to Prof. W.K. George forsome valuable discussions. Finally, we would also like to

thank the reviewers for their insightful comments, whichhave strengthened the paper.

Appendix 1.

The effect on the jet flow of the inevitable corner separa-tion immediately upstream from the nozzle plate is assessedhere both by dimensional reasoning and by measurement.We note that the shedding frequency of the corner eddiescan be expected to be lower than that of the natural shed-ding of the jet eddies by a factor of the order ( L/h)2, i.e.by three orders of magnitude (here, L is the height of thenozzle plate, Fig. 2a). This is because the natural sheddingfrequency of an oscillation scales directly with the charac-teristic length dimension, and inversely with the character-istic velocity at their respective planes (i.e. upstream fromthe contraction and at the nozzle exit).

On this basis, even though there will be small differencesin the local Strouhal number of the two oscillations, it isclearly impossible for the two types of oscillations to cou-ple directly. Rather, any possible influence would bethrough the generation of a low frequency oscillation ofthe entire jet. The most probable mode can be expectedto be a low frequency flapping motion of the emergingjet, which would arise were the oscillations on either side

of the contraction to be out of phase. Nevertheless, a sym-metrical oscillation is also possible. The extent of such alow-frequency oscillation is determined by the ratio ofthe momentum of the lateral component of the oscillation,M0y, to that of the axial component of the entire jet, Mx.

We firstly characterize the magnitude of velocity fluctu-ations in the corner eddies, u0 and v 0 as being the sameorder as the local mean velocity U. A contraction reducessuch non-uniformities in the velocity field by the followingratios [51]:

u0outUout

hL

2u0inUin

A1

and

v0outUout

hL

1=2v0inUin

A2

where L/h = 34 is the area contraction ratio. Hence thestreamwise components of non-uniformities are reducedby u 0/U% 0.0009, making it negligible, and the spanwisecomponent by v0/U% 0.17.

To obtain the momentum flux of the lateral fluctuations,we note that the extent of such fluctuations can be charac-terized by the thickness of the boundary layer. Its thickness

can be estimated from Schlictings flat plate solution [1],

http://-/?-http://-/?-


14/15

since the flow speed through the contraction is sufficientlylow for the boundary layers to be laminar. On this basis

U

U0 3tanh2 1ffiffiffi

2p y

x

ffiffiffiffiffiffiffiffiU0x

m

r 1:146

! 2 A3

which yields a boundary layer thickness at the edge of the

slot d0.99 % 0.22 mm. This accords well with the measure-ments obtained at x/h = 0.2 (Fig. 2). Assuming constantdensity, the momentum ratio of the lateral fluctuations inthe boundary layer relative to the axial momentum in thejet then reduces to

M0yMx

2dh

ffiffiffih

L

r% 3:3 103 A4

Hence the effect of the corner oscillations on the emergingjet flow can be expected to be negligible. Note that L/h isthe area contraction ratio of the plane nozzle.

The validity of this dimensional reasoning was verified

by measurement of the frequency spectra, since any large-scale oscillation of the jet can be expected to be identifiableby measurement. The record length of our data samples(22 s) is sufficient to capture some 10100 of such oscilla-tions. To assess this, the data at x/h = 0.2 were first low-pass filtered at 100 Hz, 30 Hz and 1 Hz, and then analyzed.No evidence of any low frequency oscillation was found.This confirms that the effect of the corner eddies on theemerging flow is negligible, and any flow separation withinthe corners of the anterior portion of wind tunnel has insig-nificant effect on the emerging flow.

References

[1] H. Schlichting, Laminare strahlausbreitung, Z. Angew. Math. Mech.13 (1933) 260263.

[2] G. Heskestad, Hot-wire measurements in a plane turbulent jet, Trans.ASME J. Appl. Mech. 32 (1965) 721734.

[3] L.J.S. Bradbury, The structure of a self-preserving turbulent planarjet, J. Fluid Mech. 23 (1965) 3164.

[4] E. Gutmark, I. Wygnanski, The planar turbulent jet, J. Fluid Mech.73 (3) (1976) 465495.

[5] F.C. Gouldin, R.W. Schefer, S.C. Johnson, W. Kollmann, Non-reacting turbulent mixing flows, Prog. Energy Combust. Sci. 12 (1986)257303.

[6] M. Stephane, S. Camille, P. Michel, Parametric analysis of theimpinging plane air jet on a variable scaled-down model, in: Proc.

ASME/JSME Fluids Engineering Division Summer Meeting, vol. F-227, Boston, Massachusetts, 2000.

[7] B. Moshfegh, M. Sandberg, S. Amiri, Spreading of turbulent warm/cold plane air jet in a well-insulated room, 2004, Supported by:University of Gavle and K K-Foundation. .

[8] R.C. Deo, G.J. Nathan, J. Mi, The influence of nozzle aspect ratio onplane jets, Expl. Therm. Fluid Sci., 2006. http://dx.doi.org/10.1016/j.expthermflusci.2006.08.009.

[9] B.G. Van der Hegge Zijnen, Measurements of the distribution of heatand matter in a plane turbulent jet of air, Appl. Sci. Res. A7 (1958)277292.

[10] R.A.M. Wilson, P. V Danckwerts, Studies in turbulent mixing II. Ahot air jet, Chem. Eng. Sci. 19 (1964) 885895.

[11] W.R. Quinn, Development of a large-aspect ratio rectangular

turbulent free jet, AIAA J. 32 (3) (1994) 547554.

[12] J. Mi, G.J. Nathan, Effect of small vortex generators on scalar mixingin the developing region of a turbulent jet, Int. J. Heat Mass Transfer42 (1999) 39193926.

[13] J. Mi, G.J. Nathan, D.S. Nobes, Mixing characteristics of axisym-metric free jets from a contoured nozzle, an orifice plate and a pipe,J. Fluids Eng. 123 (2001) 878883.

[14] E.J. Gutmark, F.F. Grinstein, Flow control with non-circular jets,Ann. Rev. Fluid Mech. 31 (1999) 239272.

[15] W.K. George, The self-preservation of turbulent flows and its relationto initial conditions, in: Recent Advances in Turbulence, Hemisphere,New York, 1989, pp. 3973.

[16] R.A. Antonia, Q. Zhao, Effects of initial conditions on a circular jet,Exp. Fluids 31 (2001) 319323.

[17] J. Mi, G.J. Nathan, Mean velocity decay of axisymmetric turbulentjets with different initial velocity profiles, in: Proc. 4th Int. Conf. onFluid Mechanics, Dalian, China, 2004.

[18] A.K.M.F. Hussain, M.F. Zedan, Effect of the initial conditions of theaxisymmetric free shear layer: effect of initial momentum thickness,Phys. Fluids 21 (1978) 11001112.

[19] J. Mi, G.J. Nathan, R.E. Luxton, Centerline mixing characteristics ofjets from nine differently shaped nozzles, Exp. Fluids 28 (2000) 9394.

[20] A.K.M.F. Hussain, A.R. Clark, Upstream Influence on the near fieldof a planar turbulent jet, Phys. Fluids 20 (9) (1977).

[21] A.J. Chambers, R.A. Antonia, L.W.B. Browne, Effect of symmetryand asymmetry of turbulent structures on the interaction region of aplane jet, Exp. Fluids 3 (1985) 343348.

[22] V.W. Goldschmidt, P. Bradshaw, Effect of nozzle exit turbulence onthe spreading (or widening) rate of plane free jets, in: JointEngineering, Fluid Engineering and Applied Mechanics Conference,ASME, 17, Boulder, Colarado, June 2224, 1981.

[23] A.K.M.F. Hussain, Coherent structures reality and myth, Phys.Fluids 26 (1983) 28162850.

[24] S. Russ, P.J. Strykowski, Turbulent structure and entrainment inheated jets: the effect of initial conditions, Phys. Fluids A 5 (12) (1993)32163225.

[25] J.K. Eaton, J.P. Johnston, A review of research on subsonic turbulentflow reattachment, AIAA J. 19 (9) (1981) 10931100.

[26] S.K. Ali, J.S. Foss, The discharge coefficient of a planar submergedslit-jet, ASME J. Fluids Eng. 125 (2003) 613619.

[27] H.J. Hussain, S.P. Capp, W.K. George, Velocity measurements in ahigh Reynolds number momentum conserving axisymmetric turbu-lent jet, J. Fluid Mech. 258 (1994) 3175.

[28] F.E. Jorgensen, How to measure turbulence using hot wire anemom-eters a practical guide, Dantec Dynamics, Pub. No. 9040U6151,Skovlunde Denmark, 2000.

[29] P.C. Stainback, K.A. Nagabushana, Review of hot-wire anemometrytechniques and the range of their applicability for various flows,ASME Electron. J. Fluids Eng. 167 (1993) 93.

[30] W.K. George, P.D. Beuther, A. Shabbir, Polynomial calibrations forhot wires in thermally varying flows, Exp. Therm. Fluid Sci. 2 (1989)230235.

[31] J. Tan-Atichat, W.K. George, S. Woodward, Use of computer for

data acquisition and processing, in: A. Fuhs (Ed.), Handbook ofFluids and Fluids Engineering, vol. 15, Wiley, NY, 1996, pp. 10981116.

[32] Y. Tsuchiya, C. Horikoshi, T. Sato, M. Takahashi, A study of thespread of rectangular jets: (the shear layer near the jet exit andvisualization by the dye methods), JSME Int. J. 32 Series II (1) (1989)1117.

[33] J. Mi, P.A.M. Kalt, G.J. Nathan, PIV measurements of a turbulentjet from round sharp-edged plate, Exp. Fluids 42 (4) (2007) 625637.

[34] S.B. Pope, Turbulent Flows, Cambridge University Press, London,2000, p. 303.

[35] H. Schlichting, Boundary Layer Theory, McGraw-Hill, 1968 (Chap-ter 7).

[36] L.W.B. Browne, R.A. Antonia, S. Rajagopalan, A.J. Chambers, Theinteraction region of a turbulent plane jet, J. Fluid Mech. 149 (1984)

355373.

http://www.hig.se/tinst/forskning/em/spreading-of-turbulent.htmhttp://www.hig.se/tinst/forskning/em/spreading-of-turbulent.htmhttp://dx.doi.org/10.1016/j.expthermflusci.2006.08.009http://dx.doi.org/10.1016/j.expthermflusci.2006.08.009http://dx.doi.org/10.1016/j.expthermflusci.2006.08.009http://dx.doi.org/10.1016/j.expthermflusci.2006.08.009http://www.hig.se/tinst/forskning/em/spreading-of-turbulent.htmhttp://www.hig.se/tinst/forskning/em/spreading-of-turbulent.htm


15/15

[37] I. Namar, M.V. Otugen, Velocity measurements in a planar turbulentair jet at moderate Reynolds numbers, Exp. Fluids 6 (1988) 387399.

[38] G.B. Brown, On vortex motion in gaseous jets and origin of theirsensitivity in sound, Proc. Phys. Soc. London 47 (1935) 703732.

[39] G.S. Beavers, T.A. Wilson, Vortex growth in jets, J. Fluid Mech. 44(1) (1970) 97112.

[40] D.O. Rockwell, W.O. Niccolls, Natural breakdown of planar jets,Trans. ASME J. Basic Eng. 94 (1972) 720730.

[41] H. Sato, The stability and transition of a two-dimensional jet, J. FluidMech. 7 (1960) 5380.

[42] F.C. Johansen, Flow through pipe orifices at low Reynolds numbers,Proc. Roy. Soc. 126 (1929) 231245.

[43] N.W.M. Ko, P.O.A.L. Davies, The near field within the potentialcore of subsonic cold jets, J. Fluid Mech. 50 (1971) 4978.

[44] S.C. Crow, F.H. Champagne, Orderly structure in jet turbulence, J.Fluid Mech. 48 (3) (1971) 547591.

[45] J.J. Flora, V.W. Goldschmidt, Virtual origins of a free planeturbulent Jet, AIAA J. 7 (12) (1969) 23442446.

[46] R.A. Antonia, W.B. Browne, S. Rajagopalan, A.J. Chambers, Onorganized motion of a turbulent planar jet, J. Fluid Mech. 134 (1983)4966.

[47] S.V. Gordeyev, F.O. Thomas, Visualization of the topology of thelarge-scale structure in the planar turbulent jet, in: Proc. 9thInternational Symposium on Flow Visualization, 13, 2000.

[48] D.J. Shlien, A.K.M.F. Hussain, Visualization of large-scale motionsof a plane jet, flow visualization III, in: Proc. Third InternationalSymposium, Ann Arbor, MI, September 69, Washington DC 498-502, 1985.

[49] W.K. George, L. Davidson, Role of initial conditions in establishingasymptotic behavior, AIAA J. 42 (3) (2004) 438446.

[50] R.C. Deo, Experimental investigations of the influence of Reynoldsnumber and boundary conditions on a plane air jet, Ph.D. Thesis,School of Mechanical Engineering, The University of Adelaide, SouthAustralia 5005, 2005. Available at Australian Digital Thesis Program:.

[51] P.V. Lanspeary, Private communication, regarding the effects of acontraction on flow separation, School of Mechanical Engineering,The University of Adelaide, South Australia 5005, 2007.

http://thesis.library.adelaide.edu.au/public/adt-SUA20051025.054550/index.htmlhttp://thesis.library.adelaide.edu.au/public/adt-SUA20051025.054550/index.htmlhttp://thesis.library.adelaide.edu.au/public/adt-SUA20051025.054550/index.htmlhttp://thesis.library.adelaide.edu.au/public/adt-SUA20051025.054550/index.html

Deo et al 2007 - The Influence of Nozzle Exit Geometric Profile on a Turbulent Plane Jet

Documents

Transcript of Deo et al 2007 - The Influence of Nozzle Exit Geometric Profile on a Turbulent Plane Jet