[american institute of aeronautics and astronautics 46th aiaa aerospace sciences meeting and exhibit...

American Institute of Aeronautics and Astronautics 092407

1

Flow analysis of a jet emanating from a flexible membrane

nozzle using particle image velocimetry

R. R. Lakhamraju1*, S. Murugappan

2†, E. J. Gutmark

1‡, and S. Khosla

2†

1Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH-

45219 2Department of Otolaryngology-Head and Neck Surgery, University of Cincinnati, Cincinnati, OH-45267

The study of flow control using pulsatile jets has been a prominent area of research in the recent

years due to its many applications. The current study aims to study the near-field characteristics of flow field

associated with an incompressible circular jet generated by a self oscillating flexible membrane nozzle. The

jet was self-excited and produced a pulsatile flow due to the motion of the flexible membrane. The dynamic characteristics of the jet are studied using time-averaged and phase-locked 2D PIV measurements in different

planes relative to the flexible membrane nozzle in an attempt to study the complex three dimensional features

of the jet. As illustrated in Reference 1, two different kinds of flow could be excited depending on the tension

applied to the flexible nozzle that is pointed as nozzle parameter or strain % (change in length/original

length) of the flexible nozzle and mass flow through it. The first was a flapping mode that is related to the

alternate shedding of vortices and the second was a symmetric mode that is related to the generation of

counter rotating vortex pairs. The first mode initiates a strong steering of the jet to either side and turbulence

was much larger in the measured plane for the first mode compare to the second mode. The experiments were

conducted by attaching strings at the flexible nozzle’s exit to impart tension to the nozzle. This allows a

certain length of the flexible nozzle upstream of the string location to conform flexibly to the jet. In the

current study, focus has been on the three dimensionality of the jet in the near field of a symmetric mode. The

formation of counter rotating vertical structures is symmetrical in the middle plane compared to the other

planes as the flow is extremely sensitive to the initial conditions at the exit of the nozzle.

Nomenclature

St = Strouhal number (=fD/U) Re = Reynolds number (=ρUD/μ)

f = frequency

D = Diameter of the jet

x,y,z = Streamwise, transverse and spanwise coordinates respectively

U, V = Streamwise and transverse velocities respectively

|V| = Absolute velocity ))VU(( 22

ρ = density of fluid

μ = dynamic viscosity of fluid

r = radial coordinate

W = Weight attached to the strings at the edge of the flexible nozzle

V = Volume flow rate of air passed through the flexible nozzle

De = Equivalent diameter based on maximum opening of the nozzle

Ae = Equivalent area based on maximum opening of the nozzle

= Phase angle in a cycle

UMax = Maximum streamwise velocity at the exit of the measurement plane

UCL = local mean centerline velocity in streamwise direction U' = Streamwise root mean square velocity component

U'V' = Reynolds stress

*Graduate Student, Student member AIAA †

Assistant Professor ‡

Professor and Ohio Regents Eminent Scholar, Associate Fellow AIAA

46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada

AIAA 2008-308

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

r1/2 = Jet half-width

AR = Aspect ratio (length of major axis/length of minor axis)

I. Introduction

he study of turbulence is of great practical importance due to enhanced mixing rates that can be achieved by

turbulence2. However, the non-linear governing equations and the interaction of many degrees of freedom over

broad ranges of spatial and temporal scales make the study difficult. The experimental discovery of the presence of

organized structures known as coherent structures in fully developed turbulent flows provided some reduction in complexity and an improved understanding of the flow physics

2. An increased understanding of turbulence and its

control can be achieved by studying these coherent structures in the flow.

The study of the dynamics of pulsed jets has received huge interest due to a large number of its applications in

flow control. The shear layer emerging from the nozzle develops instability waves that lead to the creation of

coherent structures. These structures combine as they are convected downstream. Shear layer spreads due to this

merging and several vortex mergings occur between the nozzle and the end of the potential core. Crow and

Champagne3 demonstrated the presence of jet column instability at the end of potential core that is characterized by

a normalized frequency (Strouhal number-St) defined as fD/U where f is the frequency at the end of the potential

core, D is the diameter of the jet and U is the exit velocity. They found that the instability was excited at St=0.3.

Later Gutmark and Ho4 showed that for subsonic jets, the most amplified frequency or the preferred mode occurs at

a St in the range of 0.25-0.5 based on the experimental test facility. By exciting a jet at a frequency that is lower than

the preferred mode, vortices tend to coalesce together in a process called collective interaction. This leads to a

further enhancement of the spreading rate in subsonic jets5. Manipulation of the large vertical structures in the near

field of the jet is the key to flow control.

Reynolds et al.6 used a combination of axial and helical excitations to generate a class of flows known as

bifurcating and blooming jets. Enhanced spreading and mixing has been shown for both bifurcating and blooming

jets. Noncircular jets have been used in passive flow control to produce much better entrainment and mixing rates compared to the axisymmetric jets

7. Gutmark and Grinstein

7 provided a comprehensive review of flow control using

noncircular jets. The mechanisms of vortex evolution and interaction, flow instabilities, interactions due to self

induction and fine-scale turbulence augmentation are the flow patterns associated with the noncircular jets. For the

current study, a discussion of rectangular and elliptic jets is more relevant. In rectangular and elliptic jets,

interactions between azimuthal and axial vortices lead to axis switching in the mean flow field which in turn causes

higher large scale mixing rates compared to circular jets. Gutmark and Grinstein7 indicated that the mechanism of

self induction is more important in an elliptic and rectangular jet than vortex interaction and merging as in a circular

jet. Husain and Hussain8 studied controlled excitation of elliptic jets. In their studies, near field turbulence, jet spread

and locations of switching of major and minor axes were found to be greatly altered by forcing. „Preferred mode‟ of

the elliptic jet with moderate aspect ratio was found to scale with exit equivalent diameter. Schadow et al9 performed

studies on elliptic ducted air jets in which they excited elliptic jets with acoustic resonant pressure waves of the duct.

They determined that by reducing the forcing frequency to the range of preferred mode frequency, maximum mixing

can be achieved. A 2:1 aspect ratio self-excited whistler elliptic jet in the studies of Husain and Hussain10

did not

display axis switching phenomenon, but the near field mass entrainment was found to be 70% higher than a non-

whistler elliptic jet. This was attributed to the evolution of the secondary counter rotating vortex pair that cause

tearing of the primary vortices, increasing the jet spread and mixing that could not be achieved in circular or elliptic

jets without a collar. In order to improve mixing, growth rates and entrainment, shear layer characteristics have to be efficiently

manipulated. As flow modulation, axial, helical or a combination of both is found to achieve this goal, pulsatile jets

have received considerable attention in the recent decades.

The current study explores the flow dynamics of a flexible membrane nozzle that is stretched at its exit by

applying uniform tension. The flow emanating from the flexible membrane nozzle is a special case of unsteady

pulsatile jets in which the nozzle shape is allowed to deform as the operating fluid flows inside the flexible walls of

the nozzle. The flow is self excited and the pulsations are generated by the periodic deformation of the nozzle. The

association of the wall deformations with the flow dynamics in the flexible nozzle has applications in engineering

and medical fields. Some of the engineering areas where flow over flexible walls is studied are summarized below.

Greenhalgh et al11

and Lorillu et al12

studied aerodynamics properties of a two dimensional flexible airfoil that

has application in aerodynamic wing, sail and parachute design. The prime focus has been on improving

aerodynamic efficiency, extending stall margin for low speed high angle of attack operations and on validating

computations with experiments. Bhat et al13

used flexible filaments to control mixing and noise characteristics in jet

T


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noise applications. The turbulence intensity and centerline velocity were decreased by up to 25% with flexible

filaments. Their acoustic results indicate that the filaments reduced low and mid-frequency noise at all measured

angles. Thaokar and Kumaran14

performed stability analysis of laminar flow in flexible tubes and channels and

observed three different instability modes that are governed by Reynolds number (Re).

Most channels in a biological system that carry fluids are flexible and interactions between the internal flow and

wall deformation often influence the biological functionality. These interactions comprise of a wide range of fluid-

mechanical phenomena such as nonlinear pressure-drop/flow-rate relations, self-excited oscillations of single-phase

flow at high Reynolds numbers and capillary-elastic instabilities of two-phase flow at low Reynolds numbers. A

comprehensive review of flexible tubes in the area of biomechanics is provided by Grotberg et al15

. The present study is an extension to the investigation conducted by Murugappan et al

1 in order to look closely at

the dynamics of the flow in the near field of the jet exiting from a flexible membrane nozzle.

II. Experimental Setup

A flexible nozzle is constructed by placing a tube-shaped thin latex segment on a circular rigid pipe that is 406

mm long with 26.7 mm outer diameter. The diameter of the nozzle employed in the current study is 25.4 mm. The

length of the flexible tube that extends above the circular pipe is 30.5 mm. A narrow slot is formed at the exit of the

flexible nozzle by placing strings at two diametrically opposite points of the tube‟s edge (see figure 3). A calibrated

tension is applied to the nozzle‟s edges by connecting weights through pulleys to the strings. The weights applied to

the strings control the length and tension at the slot edges.

The flow entering the flexible membrane nozzle from a rigid tube is fed by a compressor that can produce a

maximum flow rate of 2500 cc/sec at 35 psi. x, y and z refer to the streamwise, transverse and span-wise directions

(Refer figures 1 and 2) respectively. The origin is located at the center of the nozzle (x=0, y=0, z=0). Pressure

regulator, thermocouple, electronic pressure gages, an electronic control valve and a coriolis mass flow meter were

mounted upstream to monitor and regulate the flow. The nozzle assembly is mounted on a 3D traverse system that

facilitates the motion of the observation plane relative to the nozzle exit during the experiments. 2D PIV, as shown in Figure 2 was used in this study to make non-intrusive measurements of the two velocity

components projected in the laser plane. In this experimental technique, two successive and discreet images of the

flow are recorded at a described time interval and a cross-correlation algorithm is applied in order to obtain velocity

information. With the help of pulsed laser, it is easy to study the unsteady complex flow occurring at the exit of the

flexible nozzle. The LaVision Imager Intense camera used to capture the images has 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 bandpass filter with a Nikon 105 mm

F/2.8 lens for all the cases. A dual Pentium 4 processor with a 1GB RAM was used to control the data acquisition.

Flow seeding is one of the most important aspects of PIV measurements since the PIV technique actually

measures the displacement of the particles following the flow. In this study, the intake air is seeded with droplets of

olive oil of diameter 1-5 μm. These are generated in an atomizer by passing air through a bath of olive oil. The

particles are illuminated by a frequency double Nd-YAG laser with dual cavity (New wave Research Solo-PIV). The

output of the laser source was 50mJ/pulse at 532 nm at a pulse rate of 10Hz. The time delay between the two laser

pulses was kept constant at 8 μsec. The arrangement of the laser and the camera is shown in figure 3. The observation plane (xy) was aligned at the nozzle‟s exit in the flow direction. Each of the images is divided into

interrogation windows of size 64×64 pixels. Post-processing of the images is done by DAVIS (PIV data processing

software from LaVision). The velocity vectors are extracted by calculating the average displacement of the particle

pairs in each window using a cross correlation algorithm and passed through the complete PIV recording with a

specified window shift. The evaluation yielded one velocity vector for each interrogation window. From the

mentioned processing, 47×36 vectors are obtained in the computational domain. For a detailed description of the

extraction technique, refer to Kompenhans et al.16

Time-resolved and phase-locked PIV images are acquired during the experiment at a particular flow condition.

For phase-locked PIV images, a microphone sensor was placed at 150 mm upstream to the exit of the flexible nozzle

(Figure 2). The microphone signal is inputted to a Dspace (Model DS1104) real time signal processor. The signal is

bandpass (Type: 4th

Order Butterworth) filtered with a lower and upper cut off frequencies of 60 and 400Hz. The

filtered signal is then amplified before being sent to a threshold detector which outputs a square wave (-5 to 5 Volts)

depending on the input signal. It is positive if the input is greater than the threshold and negative if the input is lower

than threshold. The threshold is set such that the trigger is not generated due to noise. This trigger signal is then sent

to the Davis software. One entire microphone cycle is scanned by generating different delays in the synchronizer

based on the number of phases needed in a cycle. In the current study, 100 images were acquired at each phase for a


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total of 10 phases. Time-averaged images are obtained by separately acquiring 500 images for each case. There is no

time correlation between these images.

A. Operating condition In the present study, the flexible membrane nozzle is excited by placing calibrated weights of 23 gms on each

side and applying air at a volume flow rate ( V ) of 600 cc/sec through the nozzle. The consequent tension applied to

the nozzle corresponds to a nozzle strain (l/l) percentage of 36%. The strain is calculated from l, length of the exit

opening when there is no stress at the exit and l, increase in length that is obtained by applying uniform stress at

the edges of the tube‟s exit in the form of weights. The frequency of excitation of the nozzle is stable at 167 Hz corresponding to a St=0.15 (St=fD/U is calculated by inserting equivalent diameter (De) which is explained below

and streamwise velocity (U) at the exit). At this particular flow condition, PIV measurements are conducted at three

different planes (with a spacing of 6mm) parallel to the minor axis (as shown in Figure 3) and in one plane along the

major axis. Planes 1, 2, and 3 correspond to measurement planes parallel to the minor axis and plane 4 correspond to

the measurement plane along the major axis. Plane 2 corresponds to the center location on the major axis. The

portion of the flexible tube that directly interacts with the PIV laser sheet is coated with a fluorescent paint

(Rhodamine 6G) that absorbs light at 532 nm to avoid saturation of the CCD pixels due to reflection of the laser

light from the flexible membrane. Figure 3 shows an image of the top surface of the flexible nozzle that is captured

by Vision Research high-speed camera (Phantom, Ver 7.1) capable of taking 48000 frames per second. The images

acquired by this camera provide information about the shape of the nozzle at different phases in a cycle.

An equivalent diameter (De) was defined based on maximum open equivalent area of the flexible nozzle at the

exit. In order to determine the equivalent diameter for the particular flow condition, the image with the largest

opening was chosen from high-speed data by visual inspection and from image processing software, using contrast

detection tool, an outline representing the equivalent area (Ae) was drawn. From the number of pixels in this

enclosed area and the scaling factor, the area in the physical domain was obtained and hence the equivalent

diameter, De=

)4

(

A e

. This has been used as a normalization factor for the plots discussed in section 3.

III. Results and discussion

A. Time averaged flow field The time-averaged flow fields are obtained by acquiring 500 PIV images in each plane. Figure 4a-d shows the

time-averaged flow fields for the four planes (three across the major axis and one along the major axis). During the

experiments, the first 3mm from the exit has some reflection from the flexible tube and hence it is not considered for

data analysis. The equivalent diameter (De) that is explained in section 2 is used as a normalizing factor in all the

plots. At the present operating condition (W=23 gms, V =600 cc/sec), the flow field is symmetric along the minor

axis. The flow fields in planes 1, 2 and 3 show a coherent nature below x/De=1 and a slight increase in the jet spread

above x/De =1. However, the flow field in plane 4 shows a reduction in the jet spread with increase in x/De above

x/De =1. In the current experiments, measurements are restricted to 2 equivalent diameters in the streamwise

direction for planes 1, 2 and 3 and to 4 equivalent diameters for plane 4. Figure 5 shows the variation of jet half

width (r1/2) with streamwise location. Both the coordinates of the plot are normalized by the equivalent diameter, De.

As seen from the time-averaged flow field, planes 1, 2 and 3 show a noticeable increase in slope beyond x/De=1.

This is due to the presence of symmetrical counter rotating vortex pairs in the flow field. Figure 5 also shows plots

from published data for 2:1 and 4:1 aspect ratio (AR) elliptic jet along minor axis from Hussain and Husain17

,

subsonic circular pulsed jet from Bremhorst and Hollis18

, 2:1 and 5:1 AR slotted jets along minor axis from Quinn19

and a 4:1 AR excited elliptic jet (St = fD/U = 0.4) along the minor axis from Hussain and Husain17

. In the present

study, the shape of the nozzle varies over a cycle from a thin slit to a high AR elliptic jet with squeezed corners.

Hence, it is difficult to compare the current jet growth with other fixed AR jets. However, as can be seen from figure

5, the growth rate in the current flexible nozzle case has comparable magnitudes to excited elliptic jets. The near field growth rate of the jet depends on the shape of the nozzle exit and inlet conditions. The excited 4:1elliptic jet

shows a 3.7 times increase compared to an unexcited 4:1 elliptic jet at 2.5 jet diameters in the streamwise direction.


5

Also, the jet growth for the slotted jet of AR=5 from Quinn19

is 50% lower than the unexcited elliptic jet of AR=2 up

to a streamwise distance of around 3.5 jet diameters. The jet growth rate for the slotted jet with AR=2 is analogous

with the flexible nozzle‟s growth rate. The jet spread in the plane 2 is slightly higher compared to the jet spread in

planes 1 and 3 at a streamwise distance of 2 jet diameters. This is due to the maximum opening of the nozzle that

occurs in plane 2. Also, there is a decrease in the jet spread of 0.3De in plane 4 over a streamwise distance of 3.5De.

The trend in the jet spreads from planes 2 and 4 suggest the occurrence of axis switching phenomena. There is a

clear indication that the jet spreads converge over a sufficient streamwise distance. It was observed that the

development and growth of the shear layer is affected by the inlet mean and turbulence profiles, spectral

characteristics of the boundary layer and the shape of the inlet nozzle.20

Centerline mean velocity decay along the centerline is shown in Figure 6. UCL is the local streamwise centerline

velocity and UMax is the maximum velocity at the exit of the particular measurement plane. The maximum velocities

for the planes 1, 2 and 3 are 14.5, 14.9 and 14.8 m/s respectively. The centerline decay shows identical trend in all

the planes considered. As in Figure 5, data from literature for elliptic, excited elliptic, slotted and pulsed circular jets

have been added to the present data. The centerline velocity decay rate of slotted jet with AR =5 shows a closer

resemblance to the current results.

The normalized mean streamwise velocity profiles are presented in Figure 7a-c for the three planes along the

minor axis. U is the streamwise velocity. The profiles are plotted at three streamwise distances, x/De=0.3, 1 and 2.

The radial distance (r) from the centerline is normalized by the jet half-width. As the jet is symmetric along the

minor axis, the plots are shown along one radius. The present data in plane 2 is compared to an excited elliptic jet of

AR=4 at 2 jet diameters17

, a slotted jet of AR=5 at 2 jet diameters19

and a subsonic circular pulsed jet at 1 jet

diameter.18

Due to the symmetrical mode of flexible nozzle oscillation, the streamwise velocity components collapse

onto a single curve. The slight falling apart of the plots in plane 3 beyond r/r1/2=1.5 is due to initial conditions in the

jet that leads to a slight asymmetry of the flow along the major axis. The normalized mean velocity profiles in plane

2 are closer to the profile of the slotted jet of AR=5.

The normalized radial profiles of turbulence (U‟) at various streamwise locations are plotted in Figure 8a-c for

the three planes along the minor axis. The centerline turbulence for all the planes was found to be below 30% of the maximum mean velocity up to 2 jet diameters in the streamwise direction. The data in plane 2 is compared to an

excited elliptic jet of AR=4 at 2 jet diameters. It can be observed that the turbulence profile at x/De=2 attain similar

levels to that of the elliptic jet through a different radial distribution.

Figure 9a-c shows the Reynolds stress (U'V') for planes 1, 2 and 3. The current data in plane 2 is compared with

an excited elliptic jet of AR=4 at 2 jet diameters. Present data show a two times higher U'V' levels compared to the

excited elliptic jet at 0.7 jet half widths in the radial direction. Higher levels of U'V' at 2 jet diameters is due to large

fluctuations in the streamwise turbulence at x/De=2.

Figures 10 and 11 illustrate the normalized streamwise velocity profiles and streamwise turbulence in plane 4 at

various x/De respectively. It is clear from Figure 10 that there is a slight asymmetry in the spanwise (along the major

axis) direction. This is due to the initial conditions during the excitation of the nozzle. From Figure 11, it can be

noticed that there is a clear increase in turbulence along the centerline with increase in streamwise distance. It can be

observed that the turbulence levels scale well with the turbulence levels in the plane 2 (Figure 8b).

B. Phase locked flow field Phase locked flow fields are acquired at 10 phases in a microphone cycle. A total of 100 images are averaged for

each phase. The velocity vector flow fields in the four planes are presented in different phases along with the nozzle image from the top (taken with high speed camera) in Figure 12a-j. All the length dimensions in these flow fields are

normalized by the equivalent diameter (De) and the range of magnitude of absolute velocity (|V|) is kept constant for

all the plots to make the comparison easier. During the initial stages of a cycle, the plots show a remnant flow from

the previous cycle and the flow field is similar in the three planes along the minor axis. In the current set of

experiments, the flexible nozzle did not close fully at any time in the cycle. Hence, there is flow at all the phases in a

cycle. At = 0 degrees, there is a hint of a large vortex. This is the remaining structure (entrainment vortex) that aroused during the closing of the nozzle. This is responsible for the slight jet spread above x/De=1 in all the three

planes. The presence of this vortex in the three planes suggests the cylindrical nature of the vortex, though there is

an indication of stretching. The formation of counter rotating vortex pairs occurs at two different stages in a cycle.

The first pair can be detected after a delay in the opening between phases 36 and 72 degrees (Refer 12c - plane 2) at

a streamwise distance of 0.7x/De. The second pair is more obvious and occurs when the nozzle is fully open

(between phases 180 and 216 degrees). In plane 2, the formation of this counter rotating vortex pair is symmetric

compared to in the other planes. This pair convects downstream up to a distance of around 1.2 x/De and leads to a


6

slight wavering that results in the formation of an entrainment vortex whose magnitude grows as it proceeds

downstream. A small asymmetry can be noticed in the 3 planes in the phases 216-288 degrees. This is attributed to a

spanwise moving wave at the edge of the nozzle from plane 1 to plane 3. This result in a slight maximum opening at

plane 3 compared to plane 1. This is the reason for the asymmetry in Figure 10. The flow fields in plane 4 show the

variation of velocity at the exit at different phases in a cycle. Maximum velocity seems to be at the shut off

conditions near opening and closing of the nozzle.

The measurements in reference 1 were conducted at the location of plane 2 at various operating conditions. The

symmetrical mode gave rise to nice symmetrical vertical structures pertaining to the counter rotating vortex pairs.

However, the measurements in other planes are extremely sensitive to the initial conditions at the exit of the nozzle. Though some key features can be assessed, the stretching of the vortices that occur during the cycle may vary based

on the initial conditions. Figure 13 shows a 3-D representation of the three planes at a phase angle of 252 degrees

that focuses on the vortex that formed on the right side of the jet. A cylindrical nature of the vortical structures can

be ascertained from this image.

IV. Conclusions

The flow at the exit of a flexible membrane nozzle is studied by the use of 2D PIV. Previous studies indicated

that the oscillation of the flexible nozzle is periodic over a wide range of mass flow rates and various tensions

applied at the nozzle‟s exit. In this study, both time averaged and phase locked PIV measurements were used to

study the near field at a particular flow condition that generates symmetrical mode of oscillation1 by obtaining

measurements across a few planes. Two sets of symmetrical counter rotating vortex pairs are formed at the

beginning of the nozzle exit and also at the maximum opening in the central plane (Plane 2). Though these vortices

are cylindrical in nature, the formation in other planes (Planes 1 and 3) are extremely sensitive to the initial

conditions at the exit of the nozzle.

References 1Murugappan, S., Lakhamraju, R. R., Gutmark, E. J and Khosla, S., “Flow-Structure interaction effects on a jet

Emanating from a flexible nozzle”, 44th AIAA Aerospace and Sciences Meeting and Exhibit, Reno, 2006, AIAA

2006-482. 2Lumley, J. L., Holmes, P and Berkooz, G., Turbulence, Coherent Structures, Dynamical Systems and Symmetry,

Cambridge: Cambridge University Press, 1996. 3Crow, S. C and Champagne, F. H., “Orderly structures in jet turbulence”, Journal of Fluid Mechanics, Vol. 48, pp.

547-591, 1971. 4Gutmark, E. and Ho, C.M., “Preferred modes and the spreading rates of jets”, Physics of Fluids, Vol. 26, pp. 2932-

2938, 1983. 5Ho, C. M. and Huerre, P., “Perturbed free shear layers,” Annual Review of Fluid Mechanics, Vol. 16, pp. 365-424,

1984. 6Reynolds, W.C., Parekh, D.E., Juvet, P.J.D., Lee, M.J.D., “Bifurcating and Blooming Jets,” Annual Review of Fluid

Mechanics, Vol.35, pp. 295-315, 2003. 7Gutmark, E. J and Grinstein, F.F., “Flow Control with Non-Circular Jets,” Annual Review of Fluid Mechanics, Vol.

31, pp. 239-272, 1999. 8 Husain, H. S., and Hussain, A. K. M. F., “Controlled Excitation of Elliptic Jets,” Physics of Fluids, Vol. 26, pp.

2763-2766, 1983. 9Schadow, K.C., Gutmark, E. J., Wilson, K.J., and Parr, D.M., “Mixing Characteristics of a Ducted Elliptic Jet,”

Journal of Propulsion and Power, Vol. 4, No. 4, pp. 328-333, 1988. 10

Husain, H. S., Hussain, A. K. M. F., “The Elliptic Whistler Jet,” Journal of Fluid Mechanics, Vol. 397, pp. 23-44,

1999. 11

Greenhalgh, S., Curtis, H. C. J. R., Smith, B., “Aerodynamic properties of a two dimensional inextensible flexible

airfoil,” AIAA Journal, Vol. 22, No. 7, pp. 865-870, 1984 12

Lorillu, o., Weber, R., Hureau, J., “Numerical and experimental analysis of two-dimensional separated flows over

a flexible sail,‟ Journal of Fluid Mechanics, Vol. 466, pp. 319-341, 2002. 13

Bhat, T. R. S., Anderson, B. A., and Gutmark, E. J., “Flexible filaments in Jets and the interaction mechanism,”

AIAA Paper 2000-0083, 2000.


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14Thaokar, R. M and Kumaran, V., “Stability of fluid flow past a membrane,” Journal of Fluid Mechanics, Vol. 472,

pp. 29-50, 2002. 15

Grotberg, J.B., Jensen, O.E., “BioFluid Mechanics in Flexible Tubes,” Annual Review of Fluid Mechanics, Vol.

36, pp. 121-147, 2004. 16

Kompenhans, J., Raffel, M., Willert, C., “Particle Image Velocimetry- A practical guide,” Springer, Berlin, 1998.

Hussain, F., and Husain, H. S., “Elliptic jets. Part 1. Characteristics of unexcited and excited jets,” Journal of Fluid

Mechanics, Vol. 208, pp. 257-320, 1989. 17

Hussain, F., and Husain, H. S., “Elliptic jets. Part 1. Characteristics of unexcited and excited jets,” Journal of Fluid

Mechanics, Vol. 208, pp. 257-320, 1989. 18

Bremhorst, K., and Hollis, P.G., “Velocity Field of an Axisymmetric Pulsed, Subsonic Air Jet,” AIAA Journal,

Vol.28, No.12, pp. 2043-2049, 1990. 19

Quinn. W. R., “Turbulent Free Jet Flows Issuing from Sharp-Edged Rectangular Slots: The Influence of Slot

Aspect Ratio,” Experimental Thermal and Fluid Science, Vol. 5, pp. 203-215, 1992. 20

Bradshaw, P., “The effect of initial conditions on the development of a free shear layer,” Journal of Fluid

Mechanics, Vol. 26, pp 225- 236, 1966.


8

Pressure

regulator

x

FIG. 1. Schematic of the flow system.

To flexible nozzle

406 mm I.D of the pipe = 25.4 mm

I.D of flexible membrane

nozzle = 25.4 mm

Length of membrane above

the pipe = 30 mm

Laskin olive oil

seeder

Mixing

Chamber

Digital volume

flow meter

y

P P

Electronic

volume flow

controller

T

Compressor

Control

valve

T - Thermocouple (Type T)

P - Electronic pressure gage

(0-30psi)


9

Figure 2: Schematic of the setup

Figure 3: The planes along which the flow fields have been determined.

y

High speed

camera

Dual cavity

Nd:YAG laser

PIV camera Trigger

Band pass filter

Amplifier

Zero detectors

Synchronizer

Air + Oil seeding

Laser power and control

x

Microphone

Tension

Tension x

x

y

x

Digital signal

processing unit

y

z

3 2 1 2

4


10

Figure 4a

Figure 4b

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s


11

Figure 4c

Figure 4d

Figure 4a-d: Time Averaged flow fields for the four planes 1, 2, 3 and 4 respectively

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


12

Figure 5: Jet half-width for different streamwise locations

Figure 6: Centerline velocity decay for different streamwise locations

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5 4

r 1/2

/De

x/De

Plane1

Plane2

Plane3

Plane4

Hussain and Husain, Elliptic

AR=4:1, St=0.4


AR=4:1, St=0

Bremhorst and Hollis, Pulsed

Jet


AR=2:1, St=0

Quinn, Slotted Jet, AR=2:1


0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

UC

L/U

Max

x/De

Plane1

Plane2

Plane3

Plane4


Jet, AR=4:1, St=0.4


Jet, AR=4:1, St=0


Bremhorst and Hollis, Pulsed

Jet


13

a)

b)

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3

U/U

CL

r/r1/2

Plane 1

x/De=0.3

x/De=1

x/De=2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3

U/U

CL

r/r1/2

Plane 2

x/De=0.3

x/De=1

x/De=2

x/D=2, Hussain and Husain, Elliptic Jet, AR=4:1, St=0.4

x/D=2, Quinn, Slotted Jet, AR=5:1

x/D=1, Bremhorst and Hollis, Pulsed Jet


14

c)

Figure 7a-c: Normalized Streamwise velocity at different streamwise locations

a)

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3

U/U

CL

r/r1/2

Plane 3

x/De=0.3

x/De=1

x/De=2

0

0.1

0.2

0.3

0 0.5 1 1.5 2 2.5 3

U' /U

CL

r/r1/2

Plane1

x/De=0.3

x/De=1

x/De=2


15

b)

c)

Figure 8a-c: Normalized streamwise turbulence at different streamwise locations

0

0.1

0.2

0.3

0 1 2 3

U' /U

CL

r/r1/2

Plane 2

x/De=0.3

x/De=1

x/De=2


0

0.1

0.2

0.3

0 0.5 1 1.5 2 2.5 3

U' /U

CL

r/r1/2

Plane 3

x/De=0.3

x/De=1

x/De=2


16

a)

b)

0

0.01

0.02

0.03

0.04

0.05

0 0.5 1 1.5 2 2.5 3

U' V

' /U2

CL

r/r1/2

Plane 1

x/De=0.3

x/De=1

x/De=2

0

0.01

0.02

0.03

0.04

0.05

0 0.5 1 1.5 2 2.5 3

U' V

' /U2

CL

r/r1/2

Plane 2

x/De=0.3

x/De=1

x/De=2



17

c)

Figure 9a-c: Normalized Reynolds Stress at different streamwise locations

Figure 10: Normalized streamwise velocity profiles at different streamwise locations along the major axis

(Plane 4).

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.5 1 1.5 2 2.5 3

U' V

' /U2

CL

r/r1/2

Plane 3

x/De=0.3

x/De=1

x/De=2

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-3 -2 -1 0 1 2 3

U/U

CL

z/De

x/De=0.3

x/De=1

x/De=2

x/De=3


18

Figure 11: Normalized streamwise turbulence at different streamwise locations along the major axis (Plane

4).

0

0.05

0.1

0.15

0.2

0.25

0.3

-2 -1 0 1 2

U' /U

CL

z/De

x/De=0.3

x/De=1

x/De=2

x/De=3


19

Plane 1 Plane 2

Plane 3 Plane 4

a) = 0 degrees

The order of the flow fields is same in the following figures

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s

2 1 2 3

4


20

b) = 36 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


21

c) = 72 degrees

x/De

y/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


22

d) = 108 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


23

e) = 144 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


24

f) = 180 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


25

g) = 216 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


26

h) = 252 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


27

i) = 288 degrees

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


28

j) = 324 degrees

Figure 12a-j: Phase averaged flow field in four planes

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

2

15

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

y/De

x/D

e

-1 -0.5 0 0.5 10

0.5

1

1.5

215

12

9

6

3

0

10 m/s

|V| m/s

z/De

x/D

e

-2 -1 0 1 20

1

2

3

4

15

12

9

6

3

0

|V| m/s

10 m/s


29

Figure 13: A 3-D representation to look at the vortex on the right side of the jet at a phase of 252 degrees. The

3 frames from the front correspond to planes 1, 2 and 3 respectively.

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