cfd characteristics of variable-density jets in cross flow.pdf

8/21/2019 CFD Characteristics of Variable-density Jets in Cross Flow.pdf

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45th

AIAA Aerospace and Sciences Meeting Exhibit AIAA 2007-13158-11 January 2007, Reno, Nevada

Characteristics of Variable-density Jets in Cross Flow

Raghava R. Lakhamraju*,Shanmugam Murugappan,Steven J. Coppess,and Ephraim J. Gutmark

Department of Aerospace Engineering and Engineering Mechanics

University of Cincinnati, Cincinnati, Ohio 45221-0070

Subsonic wind tunnel experiments are conducted to investigate the behavior of a circular

jet injected perpendicularly into a uniform cross flow. In particular, the jet trajectory and

penetration, velocity decay along the trajectory, windward and leeward jet spread, area of

recirculation, vorticity are used for characterizing jet behavior. The utility of the jet

diameter and blowing ratio as similarity parameters is investigated over a range of

conditions, in which the velocity ratio and density ratio of jet are independently controlled to

determine the influence of each. In particular, the density ratio is controlled via a mixture of

gases of differing densities, thereby providing a range of density conditions independent of

temperature variations. The impact of these parameters upon time-averaged flow field is

characterized. Results demonstrate that the variable density jet trajectory collapses better

using the scaling parameter r2

D rather than the more common scaling parameter rD usedfor air jets.

Nomenclature

A, B = jet trajectory constants

Aj = area of jet injector

Ar = area of recirculation flow region in jet centerplaneCO2 = Carbon-dioxide

D = diameter of the injector nozzle

He = Helium

mdot = mass flow ratemdotj = mass flow rate of the jet at injection

mdote = mass flow rate entrained from the crossflow streamMwj = molecular weight of the jet fluidMwfs = molecular weight of the freestream fluid

p = pressure

E = density ratio of the jet relative to the freestream; E=

fs

j

r = square root of the momentum flux ratio (i.e., blowing ratio);2

fsfs

2

jj

V

Vr

=

Rej = Reynolds number of the jet flow;

j

jj

j

DVRe

=

R = velocity ratio of the jet relative to the freestream; R=

fs

j

V

V

*Doctoral Student, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati.Research Assistant Professor, Department of Otolaryngology-HNS, University of Cincinnati, Member AIAAGraduate Student, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati,Member AIAAProfessor & Ohio Regents Eminent Scholar, Department of Aerospace Engineering and Engineering Mechanics,

University of Cincinnati, Associate Fellow AIAA

45th AIAA Aerospace Sciences Meeting and Exhibit8 - 11 January 2007, Reno, Nevada

AIAA 2007-131

Copyright 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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s = coordinate measured along the jet centerline trajectory

T = temperature

TKE = turbulent kinetic energy in the xy-plane; )'v'u(4

3TKE 22 +=

u', v' = streamwise and transverse root mean square velocity components

VCL = local mean centerline velocity along jet trajectory

V = jet speedx, y, z = streamwise, transverse, and spanwise coordinates respectively

w = windward spread of jet measured perpendicular to jet centerline trajectoryl = leeward spread of jet measured perpendicular to jet centerline trajectory = deflection angle of jet with respect to normal = densityc = swirling strength

Subscripts

j = jet-exit property

x, y, z = streamwise, transverse, and spanwise properties respectivelyfs = freestream (cross-flow) property

I. Introduction

JETS in cross flow (JICF), or transverse jets, constitute a classical flow field that may be encountered in a widevariety of natural environments and engineering applications. A few examples of the latter include cooling jetsand fuel injection in a multitude of propulsion system components; active fluidic control mechanisms on airfoils,

and on missiles; thrust vectoring and V/STOL (vertical and/or short takeoff and landing) technology for modernaircraft; and a variety of other uses in the aerospace industry. Notably, transverse jets provide one of the most

effective methods to mix two streams in a limited space. Characterization of mixing properties of transverse jets, in

a wide range of flow environments, are therefore of significant scientific and practical importance.

Pratte and Baines [1] showed that the jet discharging transversely into a cross stream exhibits three sequentialpatterns of development: 1) a potential core which exists before the turbulent shear region developed alongside the

jet boundary reaches the centerline of the jet; 2) a zone of maximum deflection in the near field where rapidentrainment of the free stream into jet fluid occurs causing the jet to bend in the direction of freestream; 3) a vortexzone in the far field where the flow is governed mainly by the dynamics of a turbulent vortex pair formed following

the bending over. The critical vortex pair was experimentally identified to be the counter-rotating vortex pair (CVP)

[2] that dominates the cross section of the jet especially in the far field.

Several flow parameters and concepts are of interest in this discussion. The first and most basic parameter is thejet trajectory defined by the location of the jet centerline. The centerline is the curve defined by the loci of maximum

velocity magnitude as a function of the axial and transverse locations (x, y). The parameters specifies the position

relative to the jet exit as measured along the trajectory, while the angle of the trajectory to the transverse direction, at

a given height, is denoted by . Also of importance are the windward and leeward boundaries of the jet, which forthe present study are defined as the locations at which the velocity magnitudes are 40% of the corresponding peak

magnitude at the centerline. The distances from the centerline to the windward and to the leeward boundaries

measured perpendicular to the centerline are wand l respectively. An illustration of these geometric definitions is

provided in Figure 1.One of the goals of JICF research is to determine similarity parameters, for which experimental data over a wide

range of conditions will collapse upon the same jet trajectory curves. As established by Pratte and Baines [1], amongothers, the most widely accepted scaling parameters is the product of the jet diameter, D, and the blowing ratio, r,

where the latter is defined as the square root of the momentum flux ratio. Hence,2

1

2

fsfs

2

jj

V

Vr

= where is the

density, V is the velocity, and the subscripts j and fs denote the jet and the freestream conditions, respectively.

American Institute of Aeronautics and Astronautics

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However, for cases in which the jet density is equivalent to the free-stream density such as air jet entering an air

stream, at nearly equal temperature and pressure the above blowing ratio simplifies to the velocity ratio, i.e.,

r = R = Vj/ Vfs, when j=fs.In fact, a majority of the existing literature has focused upon this simplified case, and numerous studies

have yielded useful relations for predicting and characterizing JICF trajectories. For example, Pratte and Baines [1]

obtained the following relation for a circular JICF, for fluids of equal density:

B

rD

x

ArD

y

=, where A=2.05 and

B=0.28. This correlation was deemed applicable for blowing ratios (or velocity ratios) from 5 to 35. Other studies

have produced similar results, with some variation in the empirical coefficients, A and B [1-5]. Cumulatively, these

studies suggest a power law trend of the form

B

rD

xA

rD

y

= , for which the established variation in experimental

studies generally falls within A = 1.5 2.2, and B = 0.25 0.38.

Ibrahim et al. [6-8] demonstrated the utility of scaling by r and D, by corroborating the results of earlier studies

regarding circular jets, as well as by showing similar behavior for non-circular jets [6]. Furthermore, the use of

tandem jets was investigated [7], and again the blowing ratio and jet diameter were used as similarity parameters,

providing a meaningful comparison of tandem jet and single jet performance. However, as useful as the blowingratio and jet diameter may be for scaling, the data from different test facilities and over different test conditions do

not collapse entirely indicating that the above relationship is not sufficient to describe the JICF behavior.

Although most investigators used rD as a standard scaling parameter for comparison between studies, some haveinvestigated a number of alternative scaling methods. Keffer and Baines [9] employed r2Das a scaling parameter,

when comparing data for blowing ratios between 6 and 10. More recently, Muppidi and Mahesh [10] have proposed

a scaling parameter which includes the effect of the jet inlet profile as well as the boundary layer thickness of the

cross flow as it encounters the jet. Ibrahim [8] showed that the latter provides a better scaling rule for comparisonbetween various researchers data sets.

Despite these extensive and longstanding efforts, though, a completely reliable similarity parameter for a

generalized JICF has not been determined. Moreover, the range of blowing ratios in the majority of available

literature is generally between 2 and 10. Outside of this range, the aforementioned scaling methods have been less

successful. The physical basis for this disparity was demonstrated by the work of Gopalan, Abraham, and Katz [11],who used PIV measurements to study the dynamics and structure of round jets in cross flow. In this research, cases

at low blowing ratios demonstrated characteristically different behavior, in comparison to higher blowing ratios.

Specifically, for 2V

V

fs

j < , Gopalan et al. [10] identified a semi-cylindrical vortical shell, which enclosed a region of

slow, reversed flow behind the jet. In contrast, for cases where 2V

V

fs

j > , wall vortices originating from the boundary

layer dominated the leeward region and these vortices resembled a Von-Karman vortex street. A detailed

explanation of the development and progression of these vortical structures was provided by Fric & Roshko [11],

among others [12-14]. For a more thorough discussion of the historical developments in this area of research, up to1993, refer to Margason [15].

However, the aforementioned studies were largely restricted to air jets injected into cross stream air at the same

density. In order to determine the validity of the aforementioned scaling parameters to jet to free-stream density ratio

variations, data from jets of varying density must also be examined. Early work on this topic was performed by

Callaghan and Ruggeri [16], who used thermocouples for temperature measurements to obtain an empirical relation

for a JICF trajectory, as follows:

D

x

V

V91.2

D

y

fs

j

fs

j

65.1

=

. Note that this relation features essentially the same

quantities of interest, albeit in a significantly different formulation. Similarly, Kamotani and Greber [2] measuredvelocity and temperature distributions for JICF, using heated and unheated jets to provide a range of jet densities.

According to a latter study [17], the jet trajectories were primarily determined by the momentum flux ratio and the

density ratio.

Although the impact of jet density due to temperature differences was examined in the preceding studies [2],[16], the measurements did not isolate the effect of the density ratio from the possible effects of temperature

variation. This serves as the motivation for the current study. The primary goal of this paper is to investigate the

effect of varying the density ratio on the behavior of isothermal JICF. The current study utilizes a mixture of gases


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to supply jet flows of variable densities, e.g. Helium is used to provide a low-density jet while carbon dioxide for

higher density jets.

Notably, other researchers have adopted a similar approach, albeit in significantly different flow environments.

An example of this is the work of Ben-Yakar, Mungal, and Hanson [17-18], who were primarily interested in the

behavior of transverse jets in supersonic cross flows. In a supersonic flow environment, compressibility effects areclearly of great importance, whereas in the current study the flow regime was restricted to low subsonic flow, M =

0.18, below the threshold of significant compressibility effects. In their studies, Ben-Yakar et al. examined the

differences between hydrogen, ethylene, methane, and nitrogen jets injected into air. In agreement with prior studies,it was determined that the momentum flux ratio and the velocity ratio were key parameters. They also found that

increasing the relative molecular weight of the injected gas, even while maintaining a constant momentum flux ratio,

could increase the jet penetration. These results serve to motivate the current study, both in terms of the subject ofvariable density flows, and in the experimental approach of using various gases to provide the different test cases.

The objective of the current work is to investigate the effect of the density ratio and blowing ratio on the

evolution of a jet in crossflow. The characteristics of the jet such as the trajectory and penetration, windward and

leeward spread, deflection of the jet, mean centerline velocity decay, area of the recirculation region leeward of each

jet, vorticity and the Reynolds stress (net momentum transfer across the surface) are studied in order to understandthe influence of the density ratio (E) and the blowing ratio (r) on the jet behavior.

II. Experimental Methods and Apparatus

The experiments were conducted in the subsonic wind tunnel in the Gas Dynamics & Propulsion Laboratory at

the University of Cincinnati. Quantitative measurements of the flow field were obtained via Particle Image

Velocimetry (PIV). The variation in test conditions was provided by the use of air mixed with either one of twogases; an air-helium mixture provided low-density jet flows, and a mixture of air and carbon dioxide produced

relatively high-density jet flows. Each of the components of the test apparatus are detailed separately below.

1. Subsonic Recirculating Wind tunnel

The subsonic wind tunnel is a closed-loop tunnel, as illustrated in Figure 2a. The recirculating flow is impelledby an electric turbofan, and a series of flow straighteners provide a uniform incoming flow into the test section. The

walls of the test section are made of Plexiglas, for optical access, with a length of 244 cm and a square cross section

of 61 by 61 cm. For this experiment, a flat splitter plate was installed within the aft portion of the test section (referto Figures 2b and 3a), with the 45 leading edge positioned 1.6 m from the inlet. The jet injector was mounted in this

flat plate, oriented normal to the free stream flow direction. The confinement above the plate was approximately 305mm.

A Pitot probe was used to measure the free-stream velocity of the wind tunnel, which was set at a constant value

of 50 m/s for all of the test cases. The turbulence intensity of the free stream was


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MHz, and an energy efficiency of 65% at a wavelength of 532 nm. Magnification was provided by a 50mm Nikon

lens. A 532nm band-pass filter was also installed with the lens. Furthermore, the test section and PIV equipment

were shrouded in opaque paper, thereby shielding the measurement region from extraneous light sources.

The PIV data acquisition and analysis process was as follows. Using the double-frame CCD camera, the

positions of the seeding particles were recorded in each frame and relayed to accompanying software. Therewith, across-correlation analysis was employed to determine the instantaneous velocity vector field from each pair of

images. Additionally, time-averaged velocity fields are obtained from accumulated measurements, and vorticity,

turbulence, etc. are computed from the data statistics.For each test case, 500 samples were recorded, in which each sample consisted of a pair of images separated by

the time interval dt. The value of the latter was adjusted according to the velocities present in the flow field,

although most of the data were taken with dt= 2-5 sec, near the limits of the system capabilities. When processingthe PIV data, the raw particle images were processed multiple times, first with an interrogation window size of 128

by 128 pixels, then with a 64 by 64 pixel window; in both cases, a 50% overlap was employed. Alternate analysis

settings were also employed for comparison, however the aforementioned settings were deemed to be the best.

3. Jet ApparatusThe single jet injector was mounted 203.2 mm downstream from the leading edge of the plate (Figure 3a). The

mounting hardware is adaptable to numerous jet types; however the experiments for the current study were limited

to a circular geometry with a diameter of 4.83 mm. As shown in Figure 3b, two lines were used to supply gases tothe jet; the first line was used for pure air, while the second was used for either of two gases, namely helium and

carbon dioxide. The source of the airflow was a facility compressor, whereas pressurized gas cylinders provided theother gases. A pressure regulator and a manual control valve independently adjusted the flow in each line. An

additional loop was connected to the airline, in order to provide seeding to the jet flow in the form of olive oilparticles. These particles were produced through a particle generator, identical to the one described above; the

seeded air line fed back into the main airline. The two lines were then fed into a larger mixing chamber, where the

impingement of the two streams was used to mix the gases of differing densities. From the mixing chamber, a short

line led directly to the jet injector.

Two mass flow meters were utilized, both of which rely upon the Coriolis effect as a means of measurement.One meter was used for the airflow line, positioned after the introduction of olive oil seeding to the line. A similar

meter, sized for a higher flow rate, was employed to measure the total mass flow of the mixed gas supplied to the jet.

Immediately prior to the jet exit, the flow conditions were measured by the means of a type-T thermocouple and aDruck piezo-resistive pressure transducer. These instruments provided the temperature and pressure of the mixture,

necessary for determining the density of the gas. The temperature and pressure of the freestream were also

measured, providing the reference density.

Hence, the density ratio of the jet was determined as follows:

fsfsfs

jjj

fs

j

T/Mwp

T/MwpE =

= where p and T

represent the pressure and temperature, respectively. In this equation, the molecular weight of the injected gas wasdetermined from the ratio of mass flows of the respective constituent gases supplied to the jet.

4. Test Matrix

A series of density ratios were obtained via a mixture of differing gases. Specifically, a mixture of helium and air

was employed to produce low-density cases, in which the density ratio of the jet was less than 1. Conversely, a

mixture of carbon dioxide and air was used for cases in which the density ratio was greater than 1. In addition, arange of blowing ratios was tested. Seven cases were investigated; the conditions of each are summarized in Table 1.


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Table 1. Summary of test matrix and conditions

Test

CaseGas

Composition

Jet

Density,

Density

Ratio, E

Velocity

Ratio, R

Blowing

Ratio, r

[kg/m3] j/ fs Vj/ Vfs

Case 1 Helium & Air 0.30 0.252 3.19 1.60

Case 2 Helium & Air 0.30 0.252 4.18 2.10

Case 3 Helium & Air 0.46 0.387 2.25 1.40

Case 4 CO2& Air 1.68 1.41 2.31 2.75

Case 5 CO2& Air 1.68 1.41 2.74 3.25

Case 6 CO2& Air 2.28 1.91 2.23 3.09

Case 7 CO2& Air 2.61 2.20 2.30 3.41

III. Results and Discussion

A. Jet Trajectory and Penetration

The jet centerline trajectory is denoted by s and is the locus of points at which the velocity is maxima in the

centerplane of the flow field. However, near the nozzle jet exit, due to the presence of the potential core in which

the velocity is almost uniform, the definition of trajectory as the locus of maximum velocity may not be suitable.

Some researchers in the past, e.g. Yuan and Street [3], came up with mean streamline as the jet trajectory to evadethis problem. It should be pointed out that the data in the first 0.5 jet diameter was eliminated due to laser light

reflection. Hence all the analysis was done beginning from about 0.5 jet diameters above the nozzle exit.

Various effects act on the jet to determine its trajectory in the transverse (y) and crosssflow (x) directions. The

transverse motion of the jet is attributed to the initial momentum and direction of the jet. Deflection of the jet in the

crossflow direction is mainly due to mass and momentum entrainment of the freestream into the jet [1]. The dragforce due to the wake region that is formed by the flow separation behind the jet influences the deflection of the jet

to a lesser extent. Since the momentum of the jet relative to the freestream is a dominant contributor to the jets

transverse motion, the blowing ratio (r) which is the square root of the ratio of momentum fluxes of the jet to the

freestream is a major controlling parameter of the penetration of the jet into the freestream. The higher the blowingratio, the higher is the momentum of the jet and this makes it more resilient to the shear stress effects incurred due to

the oncoming crossflow. Hence, the jets with higher blowing ratios do not bend easily in the freestream and exhibits

higher penetration in the transverse direction.This feature can be seen clearly in Figure 4 where the trajectory of the jet is drawn for increasing blowing ratios

from r = 1.4 to 3.41. Note that the scaling parameter used in the above figure is diameter, D in order to emphasize

the effect of r on the penetration of the jet. These results are in agreement with the findings of many researchers who

concluded that the jet trajectories penetrate deeper into the cross stream with increasing blowing ratio or momentumflux ratio [2-3], [6-7]. The less dense gas mixture has a tendency to diffuse quickly into the freestream due to the

jets lower momentum and hence penetrate lesser than the heavier density jet for the same velocity ratio. This may

have effect on the trajectory since the zone of maximum deflection [1] is characterized by rapid entrainment of thefreestream into the jet. From Figure 4, He and air mixture jets (Cases 1 to 3) owing to their low densities attain the

freestream direction within a few jet diameters in the crossflow direction (x/D~3). In the low density regime, for the

cases with E=0.39 and 0.25, blowing ratio seems to have the major influence on the penetration since a smallvariation in the blowing ratio has a significant effect on the penetration. The difference in the penetrations of thelower density jet (E=0.25) with that of a higher density jet (E=1.41) is ~0.5 jet diameters at a streamwise distance of

3 jet diameters. Comparing the cases with E=1.41 and 2.2 with similar blowing ratios, the reasoning that higher

density jets has higher penetration seems to hold good though to a smaller extent. Comparing the cases with E=0.25

and 1.41, CO2and air mixture, due to its higher density ratio, appears to have more penetration than the low density

He and air mixture jets with comparable velocity ratios.Figure 5a shows the comparison of the current results with jet velocity trajectories from other publications for

different blowing ratios and density ratio of unity since both jet and crossflow fluids are air. The scaling parameter

used here is rD as is commonly done in the JICF related publications. The blowing ratios of 1.5, 2.5 and 3.5 with air


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as the injectant, measured in the same facility described in this paper, is also plotted in this figure. Shown in the

same figure are published data from Han et al. [19] for an air jet injected normally into the freestream at r=5,

Ibrahim et al. [6] at r=3 and lower and upper bounds from a collection of previously published data of various

transversely injected JICF experiments [10]. The wide bounds indicate that there is a large scatter in the data and the

rD scaling does not account for possible differences in the inlet boundary condition, Reynolds number, turbulencelevel and geometry of the jet of different experiments. Shown in Figure 5b are the trajectories of the test conditions

taken into account in Figure5a that are normalized by r2D. This scaling parameter provides a much better collapse

for the different flow conditions including both density and blowing ratio variations.Figure 6 illustrates the change of deflection angle of the jet from the normal as is defined in Figure 1. The

somewhat irregular nature of the plots is attributed to the limited number of data points in the flow regime. The rate

of deflection of the jet trajectory is measured in terms of the increase in angle . It can be seen from the trajectoryplots that for low penetration jets, increases within fewer jet diameters in the transverse direction and then slowly

approaches 900 as the jet is completely mixed with the freestream whereas for jets with higher blowing ratio,

slowly increases in the near field due to higher penetration and then accelerates as the jet bends and mixes with the

free stream. This trend was also explained from jet trajectories, Figure 4. From Figure 5a, it can be clearly seen that

for low density jets of He and air mixture, the growth in the deflection angle starts very close to the jet exit whereasfor the higher density jets, there is a region of up to x/D~2 wherein the jet resists bending and this gives an

indication to the length of the potential core. Again this plot conveys qualitatively the trend of higher r cases having

more penetration and hence reaching the asymptotic value of 900deflection angle over a longer trajectory length.From the plot, it can be noticed that the case of E=0.25 with r =1.6 follows the freestream direction within s/D=5. As

discussed earlier, the ability of this lower density jet to diffuse more quickly into the freestream is responsible forthis accelerated mixing.

B. Jet Spreading Rate

Figure 1 schematically represents the leeward and windward boundaries of the jet which are defined as the 40%

of the absolute maximum velocity along the jet trajectory. l and w are the spreading rate parameters of the jet in

the centerplane that are obtained from the perpendicular distance between the maximum jet velocity on the

centerline and leeward and windward boundaries respectively as shown in Figure 1. Figures 7 and 8 shows the

evolution of the normalized parameters l and w along the jet trajectory respectively for two scaling parameters.The r2D scaling parameter as shown in Figures 7b and 8b seem to provide a better collapse. In all the cases studied,

the windward spread is lower than the leeward spread of the jet at the same jet trajectory location. This asymmetry

has been observed previously by Su and Mungal [4] who indicated that this could be due to the stripping of fluidfrom the developing region (as described in the introduction, following [1]) of the jet by the freestream and

depositing it again in the wake region.The local momentum ratio of the jet and the freestream fluids has a significant effect on the jet spreading rate.

For jets with lower blowing ratios, the local momentum ratio of the jet with freestream is lower, facilitating

increased entrainment of freestream fluid with a subsequent larger spread. This phenomenon is common for both the

leeward and windward sides. Contrarily, higher blowing ratio jets have high local momentum ratio and they spread

less on both the boundaries in the near field. From Figures 7 and 8, it can be noted that the jet spread is minimal at

the nozzle exit and then grows rapidly or slowly based on higher or lower r jets, respectively. Also, though the effectof density ratio is minimal compared to the blowing ratio, as reasoned earlier, lower density ratio jets spread quickly

within a few jet diameters in y-direction due to increased entrainment of the freestream. Both the figures suggest that

with increase in r, a given spread of the jet occurs at a farther location along the trajectory. The higher density ratiojets as mentioned earlier are able to resist the bending initially by up to s/D of 2-3 on the leeward side and s/D of 1-2

on the windward side.

C. Mean Centerline Velocity DecayWhen the jet bends in the direction of the freestream, its cross-sectional area increases and majority of the initial

jet velocity gets redistributed in the offset planes from the centerplane. This and the mixing with entrained lowervelocity flow results in a gradual decay of the mean velocity that is manifested in the centerplane of the jet along its

trajectory. At the nozzle exit, the mean centerline velocity is at its maximum and stays at this value throughout the

length of the potential core. It then starts to decrease sharply in the zone of maximum deflection.

Figure 9 displays the magnitudes of the mean centerline velocities of a jet in crossflow for the seven testconditions in terms of various ratios. All the plots suggest that initial velocity is equal to the injection velocity and

then decreases to approach the freestream velocity. Figure 9c incorporates the influence of freestream velocity and


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shows a sharp decrease in velocity for all the cases. By considering the two cases with r=2.75 and r=3.25 at the same

E, higher slope can be observed in the case of higher blowing ratio indicating an accelerated velocity decay. A

similar observation could be made for the low density cases corresponding to r=1.6 and 2.1. By examining the four

cases two with E=1.41 and two with E=0.25 an increase in the centerline velocity decay rate could be observed with

the low density cases (E=0.25). This suggests that the low density jet decays faster consistent with earlierobservations regarding penetration and mixing.

D. Recirculation Flow RegionJets in cross flow often induce the formation of a recirculating flow region downstream of the jet column. This

reverse flow is generated by the adverse pressure gradient that exists at the leeward side of the jet, because of the

blockage effect of the jet on the approaching freestream. The recirculation flow acts normally on the leeward surface

of the jet just as the original freestream acts on the windward surface and induces a local upward lifting force to lift

the jet from the wall. The strength of the recirculation flow region depends on the degree to which the jet blocks thefreestream and the resulting rate of deceleration of the freestream. The decelerated flow moves around the jet and

produces a corresponding adverse pressure gradient.

The recirculation flow region generated by a circular jet with He and air mixture conditions is illustrated in

Figures 10 (a-c). The color plots in these figures represent the streamwise component of the mean velocity in the

flow field. The centerline trajectory of the jet and a zero contour encircling the recirculation zone of negativestreamwise velocities are superimposed on the plots. In the current situation, the jets with CO2and air mixture had

more penetration and because of the lift-off nature on the leeward side, there was no negative Vx for the

determination of the recirculation region, hence only cases 1-3, i.e. the low-density jet cases, are shown in Figure 10.The areas of the zero contours on the images are determined and shown in Figure 11 in the form of a bar chart. From

this figure, by considering the two cases with E=0.25, it can be noted that with an increase in r, the magnitude of

recirculation area increases and moreover it seems to elongate and move away from the base of the jet exit.

E. VorticityColored contour plots of vorticity of the jets in crossflow superimposed by the jet trajectories and with

streamlines background are depicted in Figure 12. The leeward and windward sides of the jet are characterized by

opposite rotational sense as indicated by the blue and red colors. The amount of vorticity is related to the amount of

freestream mass entrained by the jet due to its influence in the velocity gradients in the shear layers. From the plots

of CO2 and air mixture jets, it can be seen that with increasing blowing ratio, the vorticity on the leeward sidedecreases thereby indicating a reduction in mass entrainment on the leeward side. Moreover, with increase in

blowing ratio, the vorticity on the windward side near the nozzle exit increases owing to an increase in the shearwith higher r. As mentioned earlier, the lower density ratio jets mix quickly with the freestream, bend faster and

generate a stronger recirculation zone, resulting in stronger vorticity on the leeward side.

The recirculation areas are also superimposed on the streamlines for the He and air mixture jets. It could be

observed that reverse zones correspond to regions of sharp turning of the streamlines.

A vortex is defined as a region of concentrated vorticity around which the pattern of streamlines is roughly

circular. In order to identify vortex cores in this study, the swirling strength (or swirl), ci, is used which is shown inFigure 13 at three different transverse locations for case 1. cicorresponds physically to the angular velocity of thelocal swirling motion of the mainstream fluid. Mathematically, it is the imaginary portion of the complex eigenvalue

pair of the local mainstream velocity gradient tensor and is an unambiguous measure of vorticity [21]. The local

velocity gradient tensor for the two-dimensional PIV data is:

y

v

x

v

y

u

x

u

where u and v are the streamwise and

transverse velocity components, respectively. This matrix has two complex conjugate eigenvalues (crici) if thediscriminant of its characteristic equation is negative. The characteristic equation is:

02 =

+

+

x

v

y

u

y

v

x

u

y

v

x

u

and the discriminant D is:

+

+

=x

v

y

u

y

v

x

u

y

v

x

uD 42

22

where if D< 0, then the imaginary part of the complex eigenvalue is ci = (- D)0.5and is always positive. So, the

swirling strength is computed by finding the maximum ci = max (- D, 0).The use of swirling strength is more appropriate for a jet in cross flow because, unlike the conventional vorticityanalysis, it represents only the intensity of the rotating fluid motion and does not involve any contributions from


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shear effects. Figure 13 shows the evolution of normalized swirling strength with transverse distance for case 1. A

shift in the peak of swirl towards the leeward side is noticeable with increased transverse distance. This could be due

to the movement of vortical structures along with the bend of the jet towards the leeward direction. Also, a slight

increase in the swirl strength along with a spread across x/D is observed that may be due to the growth of the

vortical structures along the transverse direction that contribute to the swirl strength.

G. Turbulence (Reynolds Stresses & Turbulent Kinetic Energy)Colored contour plots of Reynolds stresses (v'v') and turbulent kinetic energy (TKE) for the several cases areillustrated in Figures 14-15. Both the transverse and streamwise Reynolds stresses indicate a similarity in behavior,

but the transverse stresses are higher in magnitude, hence are shown. Plotted on these contours is the jet trajectory.These plots identify the regions with intense turbulence activity in the shear layers on both the windward and

leeward sides. The Reynolds stresses and TKE are normalized by the square of freestream velocity (Vfs). Cases 1

and 2 comprising density ratio E=0.25 and cases 5 and 6 with a density ratio of E=1.41 are considered. In all the

cases plotted, the higher Reynolds stress correlate with higher TKE. Also we observe low turbulence production onthe windward side near the jet exit. This corresponds to the low velocity zone just upstream of the jet where the

oncoming free stream comes in contact with the jet. Increasing the blowing ratio for both the high and low density

cases increases the turbulence activity over the entire measurement zone. The distribution of v'v' and TKE areasymmetric across the jet trajectory on the windward and leeward side for the lower density cases, whereas the

distribution is more symmetrical in the high density cases. Higher turbulence levels were found to stretch deeper on

the leeward side in the stream wise direction in the near field of the jet (y/d


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Acknowledgments

The research and experiments conducted for this work were made possible by the funding and technical supportof GE Aircraft Engines. The authors also wish to acknowledge Ms. Irene Ibrahim and Mr. Russ DiMicco for their

advice and assistance on this project.

References[1] Pratte, B. D., and Baines, W. D., Profiles of the Round Turbulent Jet in a Cross Flow, Journal of the

Hydraulics Division of the American Society of Civil Engineers, Vol. 92, Nov. 1967, pp. 53-64.

[2] Kamotani, Y. and Greber, I. Experiments on a Turbulent Jet in a Cross Flow,AIAA Journal, Vol. 10, No.11, November 1972.

[3] Yuan, L. L. and Street, R. L., Trajectory and entrainment of a round jet in crossflow.Phys. Fluids, Vol.

10, 1998, pp. 2323-2335.

[4] Su, L.K. and Mungal, M.G., Simultaneous Measurements of Scalar and Velocity Field Evolution in

Turbulent Crossflowing Jets,Journal of Fluid Mechanics, Vol.513, pp. 1-45, 2004.

[5] Platten, J.L. and Keffer, J.F., Deflected Turbulent Jet Flows,Journal of Applied Mechanics, Vol. 38, No.,4, pp. 756-758, 1971.

[6] Ibrahim, I., Murugappan, S., and Gutmark, E., Penetration, Mixing and Turbulent Structures of Circularand Non-Circular Jets in Cross Flow, 43rd Aerospace Sciences Meeting and Exhibit, No. AIAA-2005-0300, AIAA,

January 2005.

[7] Ibrahim, I., and Gutmark, E., Dynamics of Single and Twin Circular Jets in Cross Flow, 44th AerospaceSciences Meeting and Exhibit, No. AIAA-2006-1281, AIAA, January 2006.

[8] Ibrahim, I., An Experimental Study of Single and Twin Transverse Jets in Subsonic Crossflow, MSThesis, Department of Aerospace Engineering & Engineering Mechanics, University of Cincinnati, Cincinnati, OH,

2006.

[9] Keffer, J.F., and Baines, W.D., The round turbulent jet in cross wind,Journal of Fluid Mechanics, Vol.

15, pp. 481-496, 1963.

[10] Muppidi, M., and Mahesh, K., Study of trajectories of jets in cross flow using direct numerical

simulations,Journal of Fluid Mechanics, Vol. 530, pp. 81-100, 2005.

[11] Gopalan, S., Abraham, B., Katz, J., The Structure of a Jet in Cross Flow at Low Velocity Ratios,Physics

of Fluids, Vol. 16, No. 6, June 2004.

[12] Fric, T. F., and Roshko, A., Vortical Structure in the Wake of a Transverse Jet, Journal of Fluid

Mechanics, Vol. 279, pp. 1-47, 1994.

[13] Smith, S.H. and Mungal M.G., Mixing, Structure and Scaling of the Jet in Crossflow,Journal of Fluid

Mechanics, Vol. 357, pp. 83-122, 1998.

[14] Cortelezzi, L. and Karagozian, A.R., On the Formation of Counter-Rotating Vortex Pair in Transverse

Jets,Journal of Fluid Mechanics, Vol. 446, pp. 347-373, 2001.

[15] Margason, R.J., Fifty years of jet in crossflow research, AGARD symposium on a jet in crossflow,

Winchester, UK, AGARD CP-534, 1993.


10


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[16] Callaghan, E. E., Ruggeri, R. S., Investigation of the Penetration of an Air Jet Directed Perpendicularly to

an Air Stream,NACA, TN No. 1615, June 1948.

[17] Ben-Yakar, A., Mungal, M. G., and Hanson, R. K. Transverse Jets in Supersonic Crossflows, Part 1: Time

evolution and mixing characteristics of hydrogen and ethylene jets,Physics of Fluids, 2005.

[18] Ben-Yakar, A., Mungal, M. G., and Hanson, R. K. Transverse Jets in Supersonic Crossflows, Part 2: The

Effect of Compressibility, Velocity Ratio and Density Ratio,Physics of Fluids, 2005.

[19] Han, D., Orozco, V. and Mungal, M. G., Gross-Entrainment Behavior of Turbulent Jets injected Obliquely

into a Uniform Crossflow, AIAA Journal, Vol. 38, No. 9, pp. 1643-1649, Sept 2000.

[20] Smith, S. H. and Mungal M. G., Mixing, Structure and Scaling of the Jet in Crossflow, Journal of Fluid

Mechanics, Vol. 357, pp. 83-122, 1998.

[21]Christensen, K.T. and Adrian, R. J., The Velocity and acceleration signatures of small-scale vortices inturbulent channel flow,Journal of Turbulence, Vol. 3, No 23, 2002.


11


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Figure 1: Spatial coordinate system and parameter definitions for a generalized jet in cross flow.

Figure 2a: A schematic of the recirculating subsonic wind tunnel.


12


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Cross-F

low

Leading Edge

Jet Exit

Air and Atomized

Olive Oil

PIV

Double Pulsed

Laser

CCD Cameray

z

x

Cross-F

low

Leading Edge

Jet Exit

Air and Atomized

Olive Oil

PIV

Double Pulsed

Laser

CCD Cameray

z

x

y

z

x

Jet Gas Mixture &

Olive Oil Seeding Figure 2b: Illustration of test apparatus for PIV measurements.

350 mm

Field of

View

Figure 3a: Schematic of the jet injector installation, illustrating the field of view used for PIV

measurements.

Olive OilAtomizer

MixingChamber

Jet Flow

Air Line

Gas Line (He or CO2)

Facility AirSupply

GasCylinder

Instruments

(Pressure & Temperature)

Air Mass

Flow Meter

Total Mass

Flow Meter

Figure 3b: Schematic of gas supply lines and test apparatus.


13


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0

1

2

3

4

5

0 1 2 3 4

x/D

y/D

E=0.39, r=1.4

E=0.25, r=1.6

E=0.25, r=2.1

E=1.41, r=2.75

E=1.91, r=3.09

E=1.41, r=3.25

E=2.2, r=3.41

Figure 4: Jet centerline velocity trajectories.

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

0 1 2 3 4

x/rD

y/rD

E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1E=0.39, r=1.4

Air, E=1, r=1.5

Air, E=1, r=2.5

Air, E=1, r=3.5

Han et al. 2000, r=5

Ibrahim 2006, r=3

Upper bound, [10]

Lower bound, [10]

Figure 5a: Comparison of jet centerline velocity trajectories for different blowing ratios.


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0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2

x/r

2

D

y/r2D

E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Air, E=1, r=1.5

Air, E=1, r=2.5

Air, E=1, r=3.5

Han et al. 2000, r=5

Ibrahim 2006, r=3

Figure 5b: Jet centerline velocity trajectories normalized by r2D.

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6

s/D

,deg

E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Figure 6: Jet centerline deflection for various test cases.


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0

0.5

1

1.5

2

2.5

0 1 2 3 4

s/D

l/D

E=1.41,r=2.75

E=1.41,r=3.25

E=1.91,r=3.09

E=2.2,r=3.41

E=0.25,r=1.6

E=0.25,r=2.1

E=0.39,r=1.4

Figure 7a: Leeward spread for various test cases.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8

s/r2D

l/r2D

E=1.41,r=2.75

E=1.41,r=3.25

E=1.91,r=3.09

E=2.2,r=3.41

E=0.25,r=1.6E=0.25,r=2.1

E=0.39,r=1.4

Figure 7b: Leeward spread for various test cases.


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0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

s/D

w/D

E=1.41, r=2.75E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Figure 8a: Windward spread for various test cases.

0

0.2

0.4

0 0.5 1

s/r2D

w/r2D

E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Figure 8b: Windward spread for various test cases.


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0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

s/D

VCL/Vj

E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Air, E=1, r=1.5

Air, E=1, r=2.5

Air, E=1, r=3.5

Figure 9a: Mean centerline velocity decay.

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6

s/D

Vj/VCL

E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Figure 9b: Inverse mean centerline velocity decay.


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0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

s/D

(VCL-Vfs)/(Vj-Vfs

) E=1.41, r=2.75

E=1.41, r=3.25

E=1.91, r=3.09

E=2.2, r=3.41

E=0.25, r=1.6

E=0.25, r=2.1

E=0.39, r=1.4

Figure 9c: Mean centerline velocity decay.

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

Vx

55

35

15

-5

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

Vx

55

35

15

-5

(a) (b)


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x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

Vx

55

35

15

-5

(c)

Figure 10: Streamwise velocity contours (a) E=0.25, r=1.6, (b) E=0.25, r=2.1,

(c) E=0.39, r=1.4.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

E=0.39, r=1.4 E=0.25, r=1.6 E=0.25, r=2.1

Normalizedarea(Ar/Aj)

Figure 11: Areas of recirculation flow regions.


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x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

Vx

x y

D

Vj

x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

V

x

x y

D

Vj

E=1.41, r=2.75 E=1.41, r=3.25

x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

Vx

x y

D

Vj

x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

Vx

x y

D

Vj

E=1.91, r=3.09 E=2.2, r=3.41

x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

V

x

x y

D

Vj

x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

Vx

x y

D

Vj

E=0.25, r=1.6 E=0.25, r=2.1


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x/D

y/D

-1 0 1 2 3 4 50

1

2

3

4

5

5

2.5

0

-2.5

-5

2V

y

V

x

x y

D

Vj

E=0.39, r=1.4

Figure 12: Vorticity colored contours test conditions are specified below the individual plots.

-2 -1 0 1 2 3 4-0.5

0

0.5

1

1.5

x/D

Swirlstrength

E=0.25, r=1.6, 0.6r2D

-2 -1 0 1 2 3 4-0.5

0

0.5

1

1.5

x/D

Swirlstrength

E=0.25, r=1.6, 0.4r2D

-2 -1 0 1 2 3 4-0.5

0

0.5

1

1.5

x/D

Swirlstrength

E=0.25, r=1.6, 0.2r2D

Figure 13: Line plots of normalized swirling strength for case 1 at three transverse locations.


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x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5 0.0 1.3 2.5 3.8

v'v'/Vfs

2

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

50.00 1.26 2.53 3.79

v'v'/Vfs

2

E=1.41, r=2.75 E= 1.41, r=3.25

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

0.0 1.3 2 .5 3 .8

v'v'/Vfs

2

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

0.0 1.3 2 .5 3 .8

v'v'/Vfs

2

E=0.25, r=1.6 E=0.25, r=2.1

Figure 14: Normalized Reynolds stress contours.

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5 0.0 1.3 2.5 3.8

TKE/Vfs

2

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

50.00 1.26 2.53 3.79

TKE/Vfs

2

E=1.41, r=2.75 E= 1.41, r=3.25


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x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

0.0 1.3 2.5 3.8

TKE/V fs2

x/D

y/D

-1 0 1 2 3 40

1

2

3

4

5

0.0 1.3 2.5 3.8

TKE/Vfs2

E=0.25, r=1.6 E=0.25, r=2.1

Figure 15: Normalized TKE contours.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-2 -1 0 1 2 3 4

x / D

VariablesNormalizedbyVfs

2

Average KE

TKE

v' v'

0

1

2

3

4

5

6

7

8

9

10

-2 -1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

y = 0.2r2D y = 0.2r2D

0

0.5

1

1.5

2

2.5

33.5

4

4.5

5

-2 -1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

0

1

2

3

4

5

67

8

9

10

-2 - 1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

y = 0.4r2D y = 0.4r2D

0

0.5

11.5

2

2.5

3

3.5

4

4.5

5

-2 -1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

0

1

23

4

5

6

7

8

9

10

-2 -1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

y = 0.6r2D y = 0.6r2D

(a) (b)

Figure 16: Line Plots of Average Kinetic Energy, Turbulent Kinetic Energy, and v'v' at three transverse

positions for each case (a) Case 1, E=0.25, r=1.6, (b) Case 2, E=0.25, r=2.1.


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0

0.5

1

1.5

2

2.5

3

-2 -1 0 1 2 3 4

x / D

Variable

sNormalizedbyVfs

2

Average KE

TKE

v' v'

0

1

2

3

4

5

6

-2 -1 0 1 2 3 4

x / D

Variable

sNormalizedbyVfs

2

Average KE

TKE

v' v'

y = 0.1r2D y = 0.1r

2D

0

0.5

1

1.5

2

2.5

3

-2 -1 0 1 2 3 4x / D


2

Average KE

TKE

v' v'

0

1

2

3

4

5

6

-2 -1 0 1 2 3 4x / D


2

Average KE

TKE

v' v'

y = 0.2r

2D y = 0.2r

2D

0

0.5

1

1.5

2

2.5

3

-2 -1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

0

1

2

3

4

5

6

-2 -1 0 1 2 3 4

x / D


2

Average KE

TKE

v' v'

y = 0.3r

2

D y = 0.3r

2

D(a) (b)

Figure 17: Line Plots of Average Kinetic Energy, Turbulent Kinetic Energy, and v'v', at three transverse

positions for each case (a) Case 5, E=1.41, r=2.75, (b) Case 6, E=1.41, r=3.25.

cfd characteristics of variable-density jets in cross flow.pdf

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