Experimental investigation of Elliptical jet in coflow.

Abstract

The objective of the present study is to investigate systematically the mixing characteristics of an Elliptical jet with varying large aspect ratio in a co-flow current using experimental technique. Laser-Induced Fluorescence (LIF) technique is employed to measure the quantitative time-averaged and turbulent concentration fields of an elliptic jet issuing into a co-flowing current and then get compared with the previous experimental results of a round jet in the present work. The spreading and mixing characteristics of an elliptical jet in a co-flow including centerline concentration, centerline dilution decay, turbulence intensity and axis-switching ... etc are discussed and compared with circular jet. The experimental results with varying large aspect ratio (AR=3, 6 and 10) at different downstream distance indicate that: i) when x/D> 1.33 in the major axis plane and x/D> 1 in the minor axis plane, the mean concentration, the turbulence intensity, are self-similar and the mean concentration field appear to be Gaussian, ii) axis switching phenomena happens at about x/D [approximately equal to] 7; iii) The experimental results using LIF further verify that the Elliptic jet with varying large aspect ratio has also much higher dilution in a co-flow than an equivalent round jet under the same flow conditions (same momentum flux Me and same flow rate Q).

Keywords: Elliptical jet, Coflow, Laser Induced Fluorescence (LIF), Centerline Dilution, Centerline Concentration, Axis Switching, Aspect ratio.

Introduction

Jets are common configuration used in various mixing and thrusts producing devices and several extinctive investigations have been made on axisymmetric jets (e.g. Meslem, Nastase and Martin 2006 [1]; Gaskin and Wood 2001 [2]; Hua Ming and Tang 2001 [3]) and plane jets (e.g. Kechiche and Benaissia 2004 [4]; Daeyoung, Ali and Joseph Lee 2003 [5]). Studies on three dimensional jets (elliptic or rectangular jets) have not been completely neglected but certainly have been insufficient (e.g. Ho and Gutmark 1987 [6]; Kuang and Lee 2001[7]). Many studies have been carried out in the past; they were usually focused on the study of circular jets, however, there are other jet geometries available (elliptic or rectangular), which may prove to be advantageous over circular jets in term of mixing process.

Elliptical jet is an intermediate configuration between the two simple, and extensively, asymptotic geometries circular and plane jets, although the existence of two geometrical length scales (major and minor axis planes) make it more complicated. Elliptical jet is lip-shaped three-dimensional jet; the cross section area and velocity vary nonlinearly with flow.

The elliptical jets mixing has important applications in the design of combustors and the design of propulsion system (Papanikalaou and Wierzba (2001) [8]). They have been studied in unforced and cold flow studies. In addition elliptical jets have been used extensively as a means of rapid dilution of a concentrate fluid discharge into the environment (Husain and Hussain (1993) [9]). A considerable amount of experimental investigations is available in the literature to define the mixing entrainment and development of the flow fields of elliptic jets [6], [9]. Their studies were limited, because they only focused on the velocity measurements to scrutinize the mixing process of the elliptical jets. Their results revealed that the flow field of elliptic jet was characterized by the presence of the phenomenon of axis switching. Moreover, it is found that a small aspect ratio elliptic jet entrains surrounding fluid more effectively than a circular jet [6].

Despite the use of such nozzles by practitioners over the past decade, there has been only limited research on the mixing characteristics of elliptical coflowing jets in terms of the concentration approach, which may provide a better understanding of these phenomenons. In view of this reason this study is thus carried out. A series of laboratory measurements by Laser Induced Fluorescence technique (LIF) were applied to give concentration data that allows an accurate determination of the jet properties. Moreover, this work is also carried out to prove that even elliptic jet with varying large aspect ratio can produce much higher dilution than circular nozzle.

Laboratory Experiment

Experimental Setup And Apparatus

A series of experiments were carried out in a 6m long, 0.2m wide by 0.3m deep arm field tilting re-circulating flume with toughened transparent glass side walls (figure 1.a), to study the mixing characteristics of elliptical coflowing jet. The jet was discharging along the centerline of the flume through a 12mm internal diameter circular pipe (D=12mm) fitted with an elliptical nozzle at mid-depth (~ 0.14m) of the ambient coflow water. The jet fluid was fed from a bucket of well mixed tap water and known concentration (~ 0.1mg/1) of the dye tracer, rhodamine 6G ([C.sub.28][H.sub.3][N.sub.2][O.sub.3]C1). The jet fluid was pumped to the jet nozzle by a submersible pump, and a rotameter was used to adjust and monitor the rate of discharge. The flow was visualized using Laser-Induced Fluorescence (LIF) technique. A laser sheet, produced by the beam of an argon-ion laser machine, illustrated the measurement section which was at right angle to the axis of the jet (see figure Lb). The laser induced fluorescent images of the jet was captured by a Micro Nikkor 60mm CCD camera, which was fixed at a distance of about 0.5m from the illuminated cross section. The visualized images were digitized and stored in a Pentium4, 2.8G, and 1G Ram computer. Each digitized image was an 8 bit, 1344 x 1024 pixel image with a grey level intensity value varied within the range of 0 to 255. For each set of experiment, the integration time of each frame of video image was 60ms. Analysis of the time averaged images would enable the determination of scalar concentration of the jet.

[FIGURE 1 OMITTED]

At different runs of the experiment, the jet nozzle, installed on a movable trolley, was moved upstream to allow the fixed position laser sheet and CCD camera to capture LIF images of the jet at different downstream distance locations. The images were obtained for distance ranging from 0 to 30 cm from the nozzle. The discharge of the jet flow and the ambient coflow were measured by an Ultrasonic flow meter (figure La). The velocity of the jet is determined by the relation (Q = A . [U.sub.o]) where Q is the flow rate, A is jet exist area and [U.sub.o] is the exist velocity. A schematic diagram showing the entire experimental setup is shown in figure 1.

Experimental Conditions

The purpose of this work is to study the mixing characteristics of elliptical coflowing jet and hence to determine the range where axis switching of the jet takes place. For the data in the present paper, the velocity of coflow was held fixed at (Ua = 10 cm/s), which correspondent to a jet Reynolds number equal to 6712. The entire experiments were performed for three typical aspect ratios (AR=3, 6 and 10), where the aspect ratio AR can be defined as (AR= major diameter of the nozzle / minor diameter of the nozzle = a / b). The major diameter of the nozzle was a = 6mm and the minor diameter was b = 2, 1 and 0.6mm corresponding to a nozzle exit area (A=37.69911, 18.84956 and 11.30973 [mm.sup.2]) respectively. The run parameters for the Elliptical jet experiments are summarized in Table 1.

Experimental Results and Discussion

Centerline Dilution

Centerline dilution is an important engineering parameter; the dilution at a point is defined as the ratio of the discharge concentration to the concentration at the point. This is a measure of the mixing capacity of discharge. The centerline dilution can be expressed as [S.sub.c] = [C.sub.o] / [C.sub.m](x, y, z), where [C.sub.m] and [C.sub.o] are the mean centerline concentration and initial tracer concentration.

The centerline dilution ratios ([S.sub.c] = [C.sub.o]/ [C.sub.m]) of the elliptic jet (aspect ratios 3 and 6) and the circular jet (aspect ratio = 1) for the same momentum flux ([M.sub.eo] =5 x [10.sup.-4]) are plotted in figure 2 against the normalized downstream distance (x / [l.sub.m]), where ([l.sub.m]) is the momentum length scale, defined as ([l.sub.m] = [M.sub.eo.sup.1/2]/[U.sub.a]). Figure 2 shows that the results are well fitted by a straight line passing through origin for both elliptic and circular jets. The linear relationship between Se and x/l n can be expressed as:

Elliptical jet; [S.sub.c] [approximately equal to] 6 .5014 x x /[l.sub.m]

Circular jet; [S.sub.c] [approximately equal to] 4 .808 x x/[l.sub.m]

The analysis of the centerline dilution indicates that this high aspect ratio elliptical jet undergoes a higher degree of dilution (entrainment of the surrounding fluid) more than that of a corresponding round jet when they are discharged at the same momentum flux ([M.sub.eo]). In previous three dimensional jet studies (elliptical jet); it has been found that elliptical jet with small aspect ratio of 2:1 can entrain 3 to 8 times more surrounding fluid than a circular or plane jet; referring to the work of Ho and Gutmark (1987) [6].

Now we find that even large aspect ratio elliptical jet can produce higher dilution (entrainment) ([approximately equal to] 2 times) than that in circular jet.

[FIGURE 2 OMITTED]

Concentration Characteristics

In order to get more understanding about the mixing characteristics of elliptical jet in co-flow, the Laser Induced Fluorescence (LIF) technique is used to obtain the concentration field of elliptical jet.

A non-dimensional plot of the mean concentration (C) for all three series of (AR) in different positions (x/D [approximately equal to] 0-20) are shown in figures 4, 5 & 6, in which the vertical coordinates is (C /[C.sub.m]) and the horizontal coordinate is (r / [b.sub.gc]); where C is the concentration at a radius (r), [C.sub.m] is the centerline concentration and [b.sub.gc] is a characteristic radius (in this case it is the radius at which the value of C / [C.sub.m] equals to 1 /e (C / [C.sub.m] = [e.sup.-1]) (figure 3 refers)).

It is interesting to see that all the results data points collapse nicely into one curve for both major and minor axis planes. This implies that the concentration distributions profiles of all experimental runs are self similar and they are normally assumed to have a Gaussian concentration distribution [(C = [[C.sub.m].e.sup.-(r/[b.sub.gc])].sup.2].

These results are compared to have a good agreement with the concentration profiles of the Lip-shaped jet, referring to the work of Kuang and Lee (2001) [7]. Figures 4 to 6 show the radial profile of the time-averaged concentration of the elliptical coflowing jet of experimental runs 1, 3 and 5.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Concentration Half-Width and Axis Switching

Elliptical jets are very turbulent in its initial stages in which; it is observed to entrain relatively large amounts of ambient fluid. The experiments also revealed that the elliptical jet undergoes an interesting axis switching in which the major axis becomes the minor axis farther downstream distance from the nozzle. This phenomenon has been observed in many laboratory experiments on non-circular jets (Ho and Gutmark 1987 [6]; Hussain and Husain 1989 [10] ... Etc).

In this study, the concentration half-width ([b.sub.gc]) at each axis plane of every time averaged cross-sectional image is computed from the Gaussian approximation of its corresponding radial concentration profiles. Comparison of the jet half-width for the major axis plane and minor axis plane of the jet enables the determination of the range where axis switching occurs. Figure 8 shows the plot of the concentration half-width with the downstream distance for experimental runs 1 to 4.

It's interesting to see that the effect of axis switching is quite obvious. From the observation of time-averaged cross-sectional images and the jet half-width computation, it is found that the spreading rate in the two axis planes was noticeably different. Larger spreading is observed in the minor axis plane than that in the major axis plane, and this causes the jet to gradually decay from the initial oblong shape to the ultimate circular shape (see figure 7). In the major axis plane, the shear layer mainly spread into the potential core, while the shear layer spread widely into the quiescent surrounding in the minor axis plane. The jet grew almost linearly in the minor axis plane. The jet width in the major axis plane remained constant or slightly decreased until x / a [approximately equal to] 13.5, then, it began growing. Beyond this region, no noticeable difference was observed between the jet spreading in both planes, Ho and Gutmark 1987 found the same trends in there work on small aspect ratio elliptic jet [6].

Only one such switch of the major axis of this jet has been observed in the range of (4 < x / D < 13) at about x / D [approximately equal to] 7 (see figure 7). These results are almost similar to the results given by Ho and Gutmark 1987 [6]. According to the velocity measurement of Ho and Gutmark on elliptical jet; the first axis switching occurred at about x / D [approximately equal to] 5 within the range of their study. Work of Husain and Hussain 1993 [9] have shown that axis switching occurred at x / [D.sub.e] [approximately equal to] 2.5 and could take place up to 100[D.sub.e], [10], where ([D.sub.e] = [(a.b).sup.1/2]). For this work, switching may take place at far downstream distance, but this cannot be studied in this experiment due to the limitation of tracer dye concentration. Figure 7 shows the Cross-sectional concentration images of experimental run 4 (Note the switching of the major axis at the jet flows downstream distance).

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Turbulent Characteristics (R.M.S Concentration Fluctuation Profile)

Turbulent intensities of the elliptical jet in coflow are measured in the experiments. Some results are plotted in figures 9, 10 and 11 for three different runs (run 1, 3 and 5). Figures 9 to 11 show the radial profile of root mean square concentration ([C.sub.rms]) normalized by the centerline maximum [C.sub.m] (turbulent intensity); in which [C.sub.rms] = [square root of [bar.([C - [C.sub.mean])].sup.2].

The profiles in general show a double peak off the centerline. The peak occurs at r / [b.sub.gc] [approximately equal to] 0.6 (at about x/D [approximately equal to] 7 to 10), with maximum value equal to 0.23, and the profiles are diminishing gradually towards both ends. The intensity value ranged from 0.04 to 0.23 in the minor axis plane and 0.03 to 0.21 in the major axis around the centerline region. The overall turbulent intensity increases with the downstream distance (x / D), indicating higher turbulence as more ambient fluid is entrained into the jet.

According to the velocity measurements of Ho and Gutmark 1987 [6] on elliptical jets, the velocity fluctuations had a two- peak profiles initially, and evolved into a bell--shaped distribution after (x / D = 10), the peak values occurred at (x / D [approximately equal to] 10). Our experimental results are compared to have a good agreement with the results of Ho and Gutmark 1987.

Table 2 compares the concentration fluctuation statistics of elliptical jet with previous studies on circular jets.

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

Conclusions

In this paper, the mixing characteristics of an elliptical jet with varying large aspect ratio in a co-flow are investigated systematically using laser induced fluorescence (LIF) technique and compared with previous studies of elliptical jet and that of a round jet. The experimental results show;

1. The mean concentration field, which provide the information of the spread and dilution of jet in the ambient current, show that the cross-section distributions of concentration are self-similar and appear to be Gaussian in the ZFE;

2. Growing rates of the jet half-width in the two axis planes are different when x/D is less than 13.5. After x/D is larger than 13.5, jet half-width in two axis planes grow at approximately the same rate. However, the present result suggest beyond a distance of around 13 D, the dynamics of the jet mixing is similar to a round jet in coflow;

3. Only one such switch of the major axis of this jet has been observed within the range of our study (up to about x / D [approximately equal to] 7);

4. The experimental results using LIF further verify that the Elliptic jet with varying large aspect ratio has also higher dilution in co-flow than an equivalent round jet under same conditions (same momentum flux).

Moreover, our laboratory experimental results are compared to have a good agreement with the results of previous studies on elliptical jet in coflowing ambient.

Acknowledgements

The research described herein was supported by Sediment Laboratory of the Water Conservancy and Hydropower Engineering Department at Hohai University (Nanjing City, China).

Special thanks are given to Mr. M. Terfous A, Mr. J.B Poulet at LGECO, INSA Laboratory of Strasbourg (France) and Mr. Tang Hong Wu at Hohai University for their contribution and support in creating this research work.

Abbreviations

R.M.S     Root--mean square

LIF       Laser induced fluorescence

ZFE       Zone of establishment flow

List of Symbols

A              Cross-sectional area of the jet ([mm.sup.2])
AR             Jet aspect ratio (AR = a / b)
[b.sub.g]      Velocity half-width (mm)
[b.sub.gc]     Concentration half-width (mm)
[C.sub.m]      Maximum centerline concentration (mg/l)
[C.sub.rms]    Root mean square concentration (mg/l)
[C.sub.o]      The jet exit Concentration (mg/l)
D              Normalized diameter (D =2.a, where a is the major
               diameter; a=6 mm) (mm)
[l.sub.m]      Momentum length scale (m)
M              Momentum flux
Q              Volume flux ([m.sup.3]/s)
[Q.sub.o]      Jet exit volume flux ([m.sup.3]/s)
r              Radial distance from the jet centerline (mm)
R'             Jet to ambient Velocity ratio
[S.sub.c]      Centerline dilution
[U.sub.o]      Jet exit Velocity (cm/s)
[U.sub.m]      Ambient Velocity (cm/s)
[U.sub.m]      Centerline jet velocity (cm/s)
x, y, z        Co-ordinates

References

[1] Meslem. A, Nastase. I and Martin. O (2006) "Instabilites primaires et secondaires d'un jet d'air turbulent asymetrique et pouvoir de melange", 8th International Meeting on Energetical Physics, November 11-12, Centre Universitaire de Bechar, Algeria.

[2] Gaskin. S.J and Wood. I.R (2001): "The axisymmetric equations for a buoyant jet in crossflow", 12th Australasian Fluid Mechanics Conference, Sydney.

[3] Hua Ming, Tang. H.W and Wang. H.M (2001): "Applying ADV to a round jet flow", IN: XXIX IARH Congress Proceedings, Theme B: Environmental Hydraulics and Eco-hydraulics, Vol. 9, pp. 455-460, Beijing.

[4] Kechiche. N and Benaissia. H (2004): "Experimental characterization of a jet flow type", International Conference on Boundary and Interior Layers-Computational & Asymptotics Methods, July 5-9, Toulouse.

[5] Daeyoung. Y.S, Ali and Joseph. H.W.L (2003): "Experiments on interaction of multiple jets in crossflow", 16th ASCE Engineering Mechanics Conference, July 16-18, University of Washington, Seattle.

[6] Ho. C.M and Gutmark. E (1987): "Vortex induction and mass entrainment in a small aspect ratio elliptic jet", Journal of Fluid Mechanics, 179, pp. 383-405.

[7] Kuang. C.P. and Lee. J.H.W (2001): "Numerical experiments on the mixing of a duckbill valve jet", 3rd International Symposium on Environmental Hydraulics, December 5-8, Arizona, USA.

[8] Papanikalaou. N and Wierzba. 1(2001): "An experimental investigation of the effects of nozzle ellipticity on the flow structure of coflow jet diffusion flames", Journal of Brazilian Society of Mechanical Sciences, Vol. 23, Rio Dejaneiro.

[9] Husain. H.S and Hussain. F (1993) "Elliptic jets. Part 3: Dynamics of preferred mode coherent structure", Journal of Fluid Mechanics, 248, pp. 315-361.

[10] Hussain. F and Husain. H.S (1989): "Elliptical jets. Part 1: Characteristics of unexcited and excited jets", Journal of Fluid Mechanics, 208, pp. 257-320.

[11] Chu. P.C.K (1996): "Mixing of turbulent advected line puffs", PhD. Thesis, University of Hong Kong, Hong Kong, China.

Hakem Mebarka (1), Hazzab Abdelkrim (1), Ghenaim Abdellah (2)

(1) Laboratoire de Modelisation et Methodes de Calcul Centre Universitaire de Saida BP 138 Ennasr Saida 20002, Alegria E-mail: [e-mail] & [e-mail]

(2) Equipe de Recherche en Eau, Sol et Amenagement (ERESA) Institut National des Sciences Appliquees de Strasbourg 24 boulevard de la victoire-67084 Strasbourg, France E-mail: Abdellah.ghenaim@insa-strasbourg fr

Table 1: Experimental Run Parameters

Run No   Aspect Ratio      Ambient             Jet
         (AR=a/b)          Velocity            Velocity
                           [U.sub.a] (cm/s)    [U.sub.0] (cm/s)

1                 3                  10                   3.684

2                 3                  10                   3.50

3                 6                  10                   5.202

4                 6                  10                   3.50

5                10                  10                   6.705

Run No   Velocity Ratio    Nozzle Area         Horizontal
         R'=[U.sub.0]      A ([mm.sup.2])      Distance
         /[U.sub.a]                            X (mm)

1                 36.84            37.69911    0,4,8,12,16,24,32,4
                                               8,80,120,160,240
2                 35.00            37.69911    0,4,8,12,16,24,32,4
                                               8,80,120,160,240
3                 52.02            18.84956    0,4,8,12,16,24,32,4
                                               8,80,120,160,240
4                 35.00            18.84956    0,4,8,12,16,24,32,4
                                               8,80,120,160,240
5                 67.05            11.30973    0,4,8,12,16,24,32,4
                                               8,80,120,160,240

Table 2: Comparison of the Concentration Fluctuation of Elliptical
Coflowing Jet with Previous Studies on Circular Jet

[C.sub.rms]/[C.sub.m]     Run 5        Run 3         Run 1

Centerline Value        0.04-0.21    0.05-0.20     0.03-0.18
Peak Value                0.23          0.23          0.21

[C.sub.rms]/[C.sub.m]   Circular      Circular
                        Coflow *     Stagnant *

Centerline Value          0.18          0.15
Peak Value                0.22          0.20

* Chu (1996) [11].