[american institute of aeronautics and astronautics 43rd aiaa aerospace sciences meeting and exhibit...

American Institute of Aeronautics and Astronautics

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AIAA 2005-0300

Penetration, Mixing and Turbulent Structures of Circular and Non-Circular Jets in Cross Flow

Irene M. Ibrahim*, S. Murugappan† and Ephraim J. Gutmark‡ Department of Aerospace Engineering and Engineering Mechanics

University of Cincinnati, Cincinnati, Ohio 45221-0070

Particle Image Velocimetry (PIV) was used to investigate penetration, mixing and turbulent structures of a jet injected perpendicularly into a free stream through several circular and non-circular shaped orifices. The two controlling parameters were the geometry of the jet exit and the blowing ratio. Both the shape and orientation of the nozzle was found to have a prominent effect on the jet spread and penetration. Compared to the baseline circular nozzle, the slot major highest penetration where as the triangle flat penetrates the least. Each nozzle has a distinctive region of reverse flow which affects its entrainment and mixing in the cross stream. The jet trajectory was scaled using r, rd, r2d parameters in an attempt to collapse the jet trajectory with existing data from PIV, Hot wire, PLIF and numerical computation. All the three scaling laws showed a large spread. A fourth scaling law which includes the initial condition of the jet was found to provide a better collapse

I. Nomenclature A = wetted nozzle area AR = aspect ratio of nozzle

LDAR =

Cm = proportionality constant d = hydraulic diameter of nozzle

PAd 4

=

dj = effective diameter computed for a scaling parameter D = cross-stream dimension of nozzle h = height of jet before bending L = streamwise dimension of nozzle P = nozzle perimeter r = square of the momentum flux ratio s = jet centerline trajectory x,y,z = streamwise, transverse and spanwise coordinate directions Rej = Reynolds number for the jet Re∞ = Reynolds number for the free stream

ju = mean velocity of the jet Vj = jet velocity at the jet injection location V∞ = velocity of the cross flow δ = boundary layer thickness of the cross stream * Graduate Student, Member AIAA † Graduate Student, Member AIAA ‡ Ohio Eminent Scholar, Associate Fellow AIAA

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-300

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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ρ = density of the fluid (subscript j for jet and ∞ for free stream) µ = viscosity of the fluid (subscript j for jet and ∞ for free stream)

II. Introduction N some aspects, a jet in cross flow exhibit similar behavior to that of viscous flow around a bluff body. The jet is impacted by the motion of the free stream surrounding it. Once the jet enters the cross flow, the fluid on the

surface of its circumference comes into contact with the free stream fluid which is moving perpendicular to it. Viscous layers develop in these contact regions as a result of the friction between the two flow fields. Depending on the momentum flux ratio the jet initially would penetrate into the free stream which is eventually bent by the cross flow.

Overall, there are four important vortical structures which have been well established in the studies of jets in cross flow. These are: (a) Horse shoe vortices [1,2 & 3] which form upstream of the jet exit and wrap around the jet column, (b) Jet shear layer vortices [1] which form at the interface between the jet and the cross flow, (c) Wake vortices [3] which form on the lee-side of the jet and persist far downstream, (d) Counter-rotating vortex pair [4] which forms after the jet has been turned by the cross stream.

The horseshoe vortex system is a result of the interaction between the wall boundary layer and the transverse jet [1,2&3]. The adverse pressure gradient formed at the injection wall forces the wall boundary layer to separate and form the horseshoe vortex. This vortex system is then convected and stretched around the jet periphery like a necklace. This is analogous to the vortex system formed when an approaching boundary layer interacts with a cylinder mounted on a wall [4]. [1,2&3] have also identified that the horseshoe vortex system has oscillating modes which correlate with the periodic motions of the upright wake vortices. The upright wake vortices have been identified by Fric and Roshko [1] by means of smoke wire visualization. The boundary layer of the cross flow has been observed to provide the main source of vorticity in the wake vortices. Fric and Roshko [1] have also identified separate events where the wall boundary layer forms vortices which attach themselves to the lee-side of the jet and eventually form the wake vortex system. This finding is called an upright wake vortex system since one end of the vortex string is connected to the jet and follows the jet trajectory whereas the other end stays close to the cross flow wall, positioning the vortex in an upright orientation. The counter-rotating vortex (CVP) pair has been observed to be the dominating structure in the far field region of the jet cross section [5] with evidence of its initiation in the near field [6,7]. Knowledge of the origin and growth of the CVP are critical to the control of vorticity generation and evolution which are primary factors in the mixing of a transverse jet with cross flow. It is generally accepted that the fold and rollup of the jet shear layer near the jet exit contributes to the formation of the CVP [3]. Also, tilting and folding of the vortical structures contributes to the vorticity in the far field which causes, on a time average basis, the formation of the counter rotating vortical structures.

The key parameter governing the flow field of a jet in cross flow is the square of the momentum flux ratio

defined as 2

2

∞∞

=VV

r jj

ρ

ρ. Other relevant parameters include the jet and the free stream Reynolds numbers (Re)

carrying the subscripts j and ∞ for jet and free stream, respectively. Re is defined generically as µρVd

=Re based

on the hydraulic diameter of the nozzle shape. To scale the local velocity maxima [5], local temperature maxima [5] and local concentration maxima [6], a

dimensionless parameter chosen to be the product of r and d was used. For r ranging from 5 to 35, Pratte and Baines [8] have identified this rd length scale to collapse the centerline trajectory of circular jets following the empirical relation:

m

rdxA

rdy

= (1)

where A = 2.05 and m = 0.28. Several other researchers [5,6] have used these same values of A and m to scale their data. Although this data showed a power-law trend, both A and m were found to vary based on the experiments and the rd-scaled trajectories did not collapse the data for the blowing ratios, r. Another length scaling parameter, r2d, was proposed by Keffer and Baines [9] to collapse trajectories for r = 6, 8 and 10. Again, a third length scaling parameter has recently been proposed by Suman and Mahesh [10] which incorporates the effect of cross flow boundary layer thickness together

I


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with the initial profile of the jet. Their computations were carried out for r = 1.5 and 5.7. They observed that the inclusion of the relative inertias of the jet and the cross flow improves the scaling in the jet trajectories. Also recently, Particle Image Velocimetry (PIV) has been used to study the flow field of a jet in cross flow. Su and Mungal [11] used simultaneous planar laser induced fluorescence (PLIF) and PIV to investigate an incompressible jet in subsonic cross flow. They identified that both the scalar and velocity fields showed a strong similarity in growth rates and centerline decay rates when scaled by the jet centerline coordinate. Their velocity field indicates a jet-like scaling in the near field and a wake-like scaling in the far field. There have been numerous studies of jets in cross flow conducted over the past 60 years, the above list is by no means an exhaustive one and the reader should refer to a review article by Margason [12] for a complete overview of the problem until 1993.

Although the majority of the above studies have dealt with circular jets in cross flow, there has also been additional interest in the development of innovative techniques to improve mixing between the jet and the cross stream. For instance, some of these techniques involve forcing the jet [13,14], employing non-circular geometries such as elliptical nozzles [15,16], slotted nozzles [16] and swirling nozzles [17, 18]. Research showed that the use of non-circular jets in cross flow is an effective means by which to enhance jet mixing with the cross flow in both cold and reacting environments. A good review of flow control for non-circular jets is provided by Gutmark and Grinstein [19]. The current study is an effort to investigate the flow field of two different non-circular jets in a cross flow. PIV is used to evaluate the flow structure, velocity field and turbulence of the various non-circular jets for two different blowing ratios, r. The impact of a non-circular jet nozzle shape on the flow structures and its dynamics is discussed along with its impact on penetration and mixing. Results are compared with the baseline circular jet which has the same equivalent area as the other non-circular geometries

III. Experimental Facility and Methods 1. Wind tunnel and jet air supply system

The jet in cross flow experiments were carried out in a subsonic wind tunnel at the University of Cincinnati Fluid Mechanics and Propulsion laboratory. The wind tunnel has a square Plexiglas test section measuring 61 cm x 61 cm. The jets are mounted 20.32 cm downstream of a leading edge and flush with a metal plate in the test section as can be seen in Fig 1. The cross flow at the inlet of the wind tunnel is laminar based on pitot tube velocity profile measurements which were done in the wind tunnel without the presence of the leading edge. A laskin nozzle was used to seed the jet. The free stream flow was not seeded in these experiments.

2. Particle Image Velocimetry (PIV)

Non-intrusive measurements of the velocity field were made using stereoscopic particle image velocimetry (PIV). The LaVison cameras used to capture the images have a resolution of 1537 (H) and 1034 (V) pixels with size 6.45 x 6.45 µm and a maximum frame rate of 10Hz. It has 65% quantum efficiency at 532 nm with a 12-bit digital output. The camera was fitted with a 532 nm narrow band pass filter with a Nikon 50 mm f/1.4 lens for all the cases. A 2x tele converter was used in the top views. It was used to magnify the flow field so that a better spatial resolution could be obtained. A dual Pentium 4 processor with a 1GB RAM was used to control the data acquisition. 250 images were acquired for each case at full resolution.

To illuminate the flow field a frequency-double Nd-YAG laser with dual cavity (New Wave Research Solo-PIV) was used. The output was 120mJ/pulse at 532 nm at a pulse rate of 15 Hz. The time ∆t, between the two laser pulses was kept between 5 and 15 µsec. Two different setups were used in the current study.

3. Nozzle Configurations

Two non-circular nozzles and one circular nozzle were tested in this study. The non-circular nozzles were a triangle geometry and a slot geometry. The dimensions of these are given in table 1. The effective area for all the nozzle geometries, 18.56 mm2, was kept constant ensuring the same mass flow rate will be generated for all cases at any given velocity condition. Two different orientations with respect to the cross flow were studied for each of the non-circular cases. The orientations are also illustrated in table 1. The slot geometry was aligned in two different orientations: one having the major axis aligned with the cross flow which is referred to as slot major, and the second having the minor axis aligned with the cross flow which is referred to as slot minor. Also, the triangle geometry was aligned in two different orientations: one having the apex inline with the free stream which is referred to as triangle apex, and the second having the flat side aligned with the free stream which is referred to as triangle flat. Nozzle geometry is defined by two parameters as given in table 1: the hydraulic diameter, d, and the aspect ratio AR which is the ratio of the cross-stream dimension D to the streamwise dimension L of the nozzle. In the case of configurations B and C, the cross-stream dimension is measured at the geometric center of the shape. The design of


4

the triangular and the slotted nozzles incorporated a converging section before transitioning to the desired nozzle exit geometry. The free stream velocity (V∞) was kept constant at 20 m/sec. Two different blowing ratios of r = Vj/V∞ = 2 and 5 were studied; Vj refers to the bulk jet velocity. The origin x=y=z=0 corresponds to the origin of the jet. All the contours and line plots presented in this paper are normalized by the appropriate hydraulic diameter and blowing ratio.

(a) (b) Fig. 1 (a) Vertical and (b) Horizontal experimental setup to obtain side view and top view PIV measurements, respectively. x,y, z refer to the streamwise, transverse, and spanwise coordinate

Table 1. Nozzle Configurations (cross-flow from left to right)

Configuration Nozzle geometry D mm

L mm

AR (D/L)

d mm

A Circular

4.83 4.83 1.00 4.83

B Triangle flat

5.17 5.97 0.87 4.32

C Triangle apex

5.17 5.97 0.87 4.32

D Slot major

2.29 8.61 0.27 3.69

E Slot minor

8.61 2.29 3.76 3.69

L

D

L

D

Cross-Flow

Leading Edge

Jet Exit

Air and Atomized Olive Oil

Double PulsedLaser

CCD Cameray

z

x

Cross-Flow

Leading Edge

Jet Exit


Double PulsedLaser

CCD Cameray

z

x

y

z

x

Cross-Flow

Leading Edge

Jet Exit


Double PulsedLaser

CCD Camera

Cross-Flow

Leading Edge

Jet Exit


Double PulsedLaser

CCD Camera

y

z

x

y

z

x


5

IV. Results and Discussion The paper has been broadly divided into two sections. The first section deals with the top views (x-z plane) taken

at two transverse locations, y=12.3mm and 30.3mm. The second section discusses the side views (x-y plane) taken at z=0. Both instantaneous and time averaged velocity fields were used to evaluate the performance of the injector. Sectional top view analysis of near field Fig. 2 a-c shows the time averaged velocity vectors and the streamlines for the circular, apex triangle and slot major at y=12.3mm. The free stream is from left to right. Both x and z coordinates have been normalized by rd. The viewing area spans approximately 1.6 rd and 1.5 rd along the streamwise and in the spanwise direction. According to Pratte and Baines [8], the far field region begins at the location where y=3.2rd which is the axial distance above the jet injection plane. In this investigation, 3.2rd would correspond to y=77.2, 69.2 and 59.0 mm for the circular, triangle apex and slot major jet respectively. Most of the previous research [6,8] indicate a fully developed CVP in the far-field, hence both y=12.3 and 30.3 mm should be used as a near field.

Fig. 2 a-c shows the entrainment of the cross flow into the jet fluid for all the configurations. There is a S-shaped structure mapped out by the streamlines in these images. This structure is an indicator of the stage of development of the jet. Eventually, in the far field this structure would become fully developed as the Counter-rotating Vortex Pair (CVP) which has been observed by other studies [2,3,5-10,11,12]. All jets show entrainment of the free stream even in the underdeveloped S-shape case (or the pre CVP formation stage). A similar pattern was also observed in the instantaneous PIV images (not shown).

It could also be observed that the circular jet shows a more well developed S shape structure when compared to the triangle apex and the slot major.

x/rd

y/rd

0 0.5 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.610 m/sec

(a)

x/rd

y/rd

0 0.5 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.610 m/sec

(b)

(c)

Fig. 2 Top view absolute velocity vector fields and streamlines at a y= 12.3 mm above the injection plane of a (a) circular, (b) triangle apex, (c) slot major jet for a blowing ratio r=5

x/rd

y/rd

0 0.5 1-0.6

-0.4

-0.2

0

0.2

0.4

0.6

10 m/sec

z/rd

z/rd z/rd


6

Measurements taken at a plane 30.3 mm above the jet injection plane are shown in Fig. 3 a-c. These show growth of the turbulent structure as the jet evolves in the free stream. For the slot major case the transverse location of 30.3 corresponds to 1.64rd where as it translate into 1.25 and 1.4 rd for the circular and apex triangle case. From the penetration plot (figure 7), the slot major case is almost perpendicular until 1.6rd where as the circular and apex triangle has a curvature indicating the transition to a bent jet. This would indicate that the large scale S structure which dominate the flow-field begin to develop as the jet is bent by the free stream. The other interesting feature is the asymmetric nature of these structures. Similar asymmetry has also been observed by smith and mungal [6] in their PLIF studies. There is also stagnation point forming in Fig. 3(a) and Fig. 3(b). This stagnation point is shifted from the center of the jet and is located approximately at (x/rd, y/rd) = (0.22, 0.1) for the circular configuration and at (x/rd, y/rd) = (0.30, 0.092) for the triangle apex configuration. Fig. 3(a) and 3 (b) shows the strong convolution of the streamlines deep into the axis of the jet. This implies the strongest entrainment of the cross flow fluid compared to the slot major case.

(a)

(b)

x/rd

y/rd

0 0.5 1 1.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.810 m/sec

(c)

Fig. 3 Top view absolute velocity vector fields and streamlines at y=30.3 mm above the injection plane of a (a) circular, (b) triangle apex, (c) slot major jet for blowing ratio r=5

Fig. 4 shows instantaneous raw PIV images and the vectors highlighting some of the vortical structures observed

in each of configurations A, C and D. These images indicate the dynamic nature of the jet in cross flow problem. Some of these structures are similar to those identified by New et al [15] in their studies. For example, WVP (Windward Vortex Pair) were observed in figure 4b. WVP defined as counter-rotating pair occurring as a result of fold and roll ups of the shear layer on the windward side of a jet [15]. These are considerably weaker than the

x/rd

y/rd

0 0.5 1-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8 10 m/sec

x/rd

y/rd

0 0.5 1

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8 10 m/sec

z/rd

z/rd

z/rd


7

dominating CVP and they occur relatively far away from the axis of the jet. Similar flow structures are seen here for the instantaneous triangle apex nozzle configuration (fig. 4b). These WVP maintain their structure unaffected by the presence of the CVP. Primary and secondary CVP could also be observed in 4c as identified by [15] in their low aspect ratio elliptic jets. Figure 4 a shows the growth of the arms of the lee-side vortex filament, identified by [15]

(a)

c

(b)

(c)

Fig. 4 Top view instantaneous raw PIV images and velocity vectors at a y= 12.3 mm above the injection plane of a (a) circular, (b) triangle apex, (c) slot major jet for blowing ratio r=5.

Sectional side view analysis Side view time averaged vector plots and streamlines are shown for each of the five cases in Fig. 5. Both the x and y axis are scaled by rd. This scaling also provides insight into the jet penetration for example, slot major shows almost a perpendicular trajectory until y=3.2 rd where as the other cases show some degree of jet bending at this same transverse location. The entrainment of the cross flow fluid into the jet on the windward side could be observed in all the cases. Cross-flow entrainment into the jet on the lee side, however, varies in strength and location amongst the jet configurations. For instance, comparing Fig. 5( a & b) with Fig. 5(d), there is a strong curvature pointing inwards to the jet in the streamline close to the jet (0<x/rd<1, 0<y/rd<1) entraining free stream into the jet in 5 a and b. Two key features to note from Fig. 5 are the nodes at the close to the injection wall on the lee-side of the jets and the open bifurcation of the jet itself. There node is observed by the convergence of the streamlines at approximately y= 0.1rd for all the cases. The position of the node varies slightly from one case to another. The node then bifurcates into two jets. The two jets will be labeled as the primary and the bifurcated streams. The

x

y

Cross flow

Windward-side folds

CVP development

x

z

x

y

Cross flow

Side arms of lee vortex filament

x

z

x

y

Cross flow

Primary CVP Secondary CVP

x

z


8

bifurcated jet is located closer to the injection plane. Bifurcation of the jet has been previously observed by Su and Mungal [11] in their PIV studies for circular jet at r=5.7. It is interesting to note that this feature exist for even non-circular geometries.

x/rd

y/rd

-1 0 1 2 30

1

2

3

20m/sec

(a)

x/rdy/

rd-1 0 1 2 30

0.5

1

1.5

2

2.5

3

20 m/sec

(b)

x/rd

y/rd

-1 0 1 2 30

0.5

1

1.5

2

2.5

3

20 m/sec

(c)

x/rd

y/rd

-1 0 1 2 30

1

2

3

20 m/sec

(d)


9

x/rd

y/rd

-1 0 1 2 30

1

2

3

20 m/sec

(e)

Fig. 5 Center plane absolute velocity vectors and streamlines (a) circular, (b) triangle flat, (c) triangle apex, (d) slot major, (e) slot minor jet for r=5

The centerline trajectories were identified for the different cases and shown in figure 6. The centerline trajectory, referred to as s coordinate is defined here as the path of maximum absolute velocity in the center plane of the jet. It could be clearly seen that the nozzle geometry has an impact on the jet trajectory. The slot major is almost perpendicular in its trajectory until y=1.6rd which is approximately 60% longer than the other nozzles.

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2

x/rd

y/rd

CircularTriangle FlatTriangle ApexSlot MajorSlot Minor

Fig. 6 Jet trajectories for the five nozzle configurations. The triangle flat has the least penetration as the jet bends into the cross-stream where as the slot major has the

highest. The other cases fall in between these and have similar centerline trajectory. Fig. 7 and Fig. 8 show the variation of the normalized parameters δu and δl along the streamline s, respectively.

δu and δl are defined as the difference between the maximum jet velocity at the centerline trajectory and the upper and lower trajectories. Upper and lower boundaries of a jet in cross flow are taken at 40% of the maximum centerline velocity of the jet. All the five configurations have similar upper boundary spread except the triangle flat case. The triangle flat initially has a comparable spread when compared to the other cases but grows rapidly past 1.5 rd.

The lower boundary spread is shown in Fig. 8, data for the five cases. The magnitude of spread was 5-10 times larger than the spread on the upper side for the circular, triangle flat and slot minor cases. Similar to Fig. 7, the triangle flat exhibits the steepest slope indicating the largest spread on the lee-side. Both the triangle apex and slot major has the weakest spread. It should be pointed out that the orientation of the nozzle is an important factor which affects the penetration and mixing. Clearly the apex and flat show contrasting features in jet spread and penetration.


10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3

s/rd

δu/rd


Fig. 7 Upper boundary jet spread for the five nozzle configurations.

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

s/rd

δl/rd

CircularTriangle FlatTriangle ApexSlot Major Slot Minor

Fig. 8 Lower boundary jet spread for the five nozzle configurations.

Fig. 9 shows horizontal profiles of the y-component of the velocity normalized by the maximum transverse velocity of each jet. Profiles are plotted at the y=0, 4d and 10d. All jets show a fully developed profile as it exits into the cross-stream. As the jet moves downstream, the location of peak velocity along its centerline is shifted to the right due to the cross stream (refer fig. 10). All the cases shift approximately by 0.1 rd. Fig. 11 shows the velocity profiles at y=10 d Both triangle flat and the circular jets shows tow maxima which indicates the jet bifurcation as observed in the time averaged plots in figure 5. This distance is approximately x/rd=0.61 and x/rd=1.67 for the circular and triangle flat nozzles, respectively. The other cases do show the bifurcation phenomena but it is delayed further downstream.


11

0

0.2

0.4

0.6

0.8

1

1.2

-2 -1 0 1 2

x/rd

Vy/V

max

CircularTriangle ApexSlot MajorSlot MinorTriangle Flat

Fig.9 Normalized average transverse velocity at the jet exit for all the five cases.

0

0.2

0.4

0.6

0.8

1

1.2

-2 -1 0 1 2x/rd

Vy/

Vm

ax


Fig. 10 Normalized average transverse velocity at y=4d for all the five cases.


12

0

0.2

0.4

0.6

0.8

1

1.2

-2 -1 0 1 2x/rd

Vy/

Vm

axCircularTriangle FlatTriangle ApexSlot MajorSlot Minor

Fig. 11 Normalized average transverse velocity at y=10d for all the five cases.

The streamwise component of velocity is plotted at two x locations for all the cases and is shown in figure 12-13. The streamwise velocity trends are similar for all five jets along any normal plane. Figure 12 shows the streamwise velocity profile at x=2d. The Vx component is initially positive close to the injection wall, but decays as it is being entrained into the jet. All the cases show different magnitude and location of the first local minima. The circular case shows the largest negative Vx component when compared with other cases. This could also be observed in the streamlines from the side view plot, figure 5a, which show a strong inward curvature around (0<x/rd<1, 0<y/rd<1) The Vx component increases in magnitude there after with the peak corresponding to the location of the jet centerline. It eventually reaches the free stream value. Figure 13 shows the average streamline velocity further downstream at y=5d. It clearly shows the translation of the minima peak found in figure 12. For the circular case there are two maxima, the first one (y/rd=0.7) correspond to the bifurcated jet where as the second (y/rd=3.6) correspond to the primary jet. The peak of the bifurcating stream is roughly 30% of that of the primary stream for the circular case.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

y/rd

Vx/

Vm

ax


Fig. 12 Normalized average streamwise velocity at x=2d for all the five cases.


13

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5y/rd

Vx/

Vm

ax


Fig. 13 Normalized average streamwise velocity at x=5d for all the five cases.

Length Scaling Parameters

It is important to select appropriate normalization variables to be able to scale the jet trajectory. Several studies in the past have selected different scaling to collapse their jet trajectory [5,6,8,9,11]. These parameters include: d, rd and r2d. A recent study by Muppidi and Mahesh [10], indicated the boundary layer thickness, δ, of the cross flow and the inlet velocity profile, uj, of the jet are important in scaling the jet trajectory. The jet trajectory of the baseline circular nozzle from this investigation is scaled by rd, r2d and d and is shown in Fig. 14, 15 and 16, respectively. It is plotted with trajectories from existing data which was obtained using pitot probes [21], hot wire [5], PIV [11], PLIF [6] and computations [10]. It is obvious from all three figures that the jet trajectories do not collapse and there is a wide spread in the data, though the shape associated with different scaling remains unchanged. The data was also scaled according to the power law proposed by Muppidi and Mahesh [10] in Fig. 18 for the circular case at r=2 and 5. h was computed from equations 2 and 3.

31

4

222

43

=dd

rCdh j

m

δπ when h≤ δ

2

22

432

dd

rCdd

h jm

πδ+= when h≥ δ

(2)

where dj is computed from

222

4 jjjArea

jj dudAu ρπρ =∫ (3)

δ is the cross-flow boundary layer thickness at the nozzle, d is the jet diameter and Cm = 0.05 is proportionality constant. h was computed for the circular jet at r=2 and r=5 using the above equations. Fig. 18 shows the scaling adopted by [10], and it could be observed that the scattering of the data was found to be much smaller and a better collapse of the jet trajectory was observed when compared with the other scaling parameters. This indicates that the initial conditions play an important role in jet trajectory scaling for jets in cross flow.


14

0

1

2

3

4

5

6

7

0 1 2 3 4 5

x/rd

y/rd

Present Data, r=2,5, fully developedSmith & Mungal, 1998, r=5,10,15,20,25Su & Mungal, PLIF, 2004,r=5.7, mean turbulentSu & Mungal, PIV, 2004, r=5.7, mean turbulenty/rd=2.6*(x/rd)^0.4, r=2,5Kamotani and Greber, 1972, r=3.91,7.7Callaghan et al, 1948, r=1.07,1.78Muppidi & Mahesh, 2004, r=1.5,5.7, fully developed & mean tubulentSchetz & Billig, 1961, r=2.2,4Pratte & Baines, 1967, r=5,15,25,35

Fig. 14 Centerline jet trajectories scaled by rd

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5

x/r 2 d

y/r2 d

Present Data, r=2,5, fully developedSmith & Mungal, 1998, r=5,10,15,20,25Su & Mungal, PLIF, 2004,r=5.7, mean turbulentSu & Mungal, PIV, 2004, r=5.7, mean turbulentKamotani and Greber, 1972, r=3.91,7.7, mean turbulentCallaghan et al, 1948, r=1.07,1.78Muppidi & Mahesh, 2004, r=1.5,2.7, fully developed & mean turbulentSchetz & Billig, 1961, r=2.2,4Pratte & Baines, 1967, r=5,15,25,35

Fig. 15 Centerline jet trajectories scaled by r2d


15

0

2

4

6

8

10

12

14

0 2 4 6

x/d

y/d

Present Data, r=2,5, fully developedSmith & Mungal, 1998, r=5,10,15,20,25Su & Mungal, PLIF, 2004,r=5.7, mean turbulentSu & Mungal, PIV, 2004, r=5.7, mean turbulenty/rd=2.6*(x/rd)^0.4, r=2,5Kamotani and Greber, 1972, r=3.91,7.7Callaghan et al, 1948, r=1.07,1.78Muppidi & Mahesh, 2004, r=1.5,5.7, fully developed & mean tubulentSchetz & Billig, 1961, r=2.2,4Pratte & Baines, 1967, r=5,15,25,35

Fig. 16 Centerline jet trajectories scaled by r2d

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2 2.5 3x/rd

(y/rd

)(h/

d)0.

15

Su & Mungal, 2004, PIV r=5.7

Muppidi & Mahesh, 2004, r=5.7, Computations

Muppidi & Mahesh, 2004, Upper Bound, rd-scaling

Muppidi & Mahesh, 2004, Lower Bound,rd-scaling

Present, PIV, r=5

Present, PIV, r=2

Upper Bound

Lower Bound

Fig. 17 Centerline jet trajectories scaled according to [10]. Scaling law incorporates the jet initial

conditions

V. Conclusion PIV study was conducted to evaluate the penetration and mixing of circular and non-circular jets. The slot major

was found to penetrate the highest with low jet spread whereas the triangle flat had the weakest penetration with highest jet spread. The effect of the nozzle shape and orientation was observed to have a dominant effect of the jet spread and penetration. Interestingly the triangle flat and triangle apex, which just vary in the orientation with respect to the cross stream flow show contrasting features in penetration and mixing. The jet was also found to bifurcate in from a node located close to the injection plane in all the cases. S-Shaped structures were found to dominate the top-view. This is found to develop as the jet bends into the cross stream. The S-Shaped structure is the


16

incipient stage of a fully developed CVP. It was also observed that these structures were asymmetric as identified by other studies in the past. A scaling analysis was conducted for the centerline trajectories of the jets. Using the traditional r, r2d and d length scaling parameters a wide spread of the current and previous data was observed. A recent study by [10] indicates that the initial condition could substantially improve the scaling. The current study validates this result.

Acknowledgments The authors would like to acknowledge L. Vallet and Russell DiMicco for their help in setting up and running

the experiments.

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