The effect of a cylinder on the velocity field at the outlet of a circular jet
measured by PIV and PTV.
B. Mauti*, W. Faber**, G.P. Romano*
* Dept. Mechanics and Aeronautics, University "La Sapienza", Roma, Italy
** J.M. Burgers Centre, Delft University of Technology, Delft, the Netherlands
ABSTRACT
Measurements of the velocity field in the near field of a circular jet are performed by Particle Image Velocimetry (PIV) and
Particle Tracking Velocimetry (PTV). One of the aim of the paper is to investigate the effect of inserting a cylinder
(orthogonal to the mean velocity) on the degree of mixing of the jet with the ambient fluid. As shown in figure 1, the
instantaneous velocity field is affected by the large scale vortices developing in the shear layers of the free jet and of
the jet with cylinder. For the jet without the cylinder (on the left in figure 1), ejections of jet flow into the ambient fluid
and injections of ambient fluid into the jet are observed where the large scale Kelvin-Helmholtz vortices are located (as
in the vorticity colour map in figure 1 for x/D ≈1.5, x/D ≈2.5 and x/D ≈3.5 (x and D being the axial co-ordinate and the jet
nozzle diameter)). On the other hand, for the jet with cylinder (on the right in figure 1), four shear layers are observed
(two for the jet and two for the cylinder) which quickly merge and loose their identity. Large-scale vortices are not
observed further downstream (except for a weak couple of counter-rotating vortices at x/D ≈3) and an overall larger
spreading is observed in comparison to the jet without cylinder (in figure 1 compare the vector profiles at x/D ≈3.5 for
the two conditions). In this paper, the velocity measurements are used to derive information on the growth of the shear
layers and on the degree of mixing by computing the momentum thickness at each distance from the outlet. In the near
field, the jet with cylinder allows a mixing degree much higher than the simple jet, whereas the two velocity fields are
almost identical when moving towards the far field (x/D >5). The PIV results, in terms of mean fields, are also compared
with the PTV data in order to assess the quality and the reliability of these techniques in the different regions of the flow
field. It appears that the PTV measurements describe better than PIV the average flow field in the regions where strong
gradients are present, whereas instantaneous data and velocity fluctuations are described much better by PIV.
1
0.5
y /D
y /D
0.5
0
-0.5
-0.5
-1
-4
0
-1
-3.5
-3
-2.5
-2
x/D
-1.5
-1
-0.5
0
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
x/D
Fig.1. Velocity (arrows) and vorticity (colours) fields from instantaneous images of the jet (on the left) and of the jet
with cylinder (on the right). Flow from right to left. Data from PIV at Re=8000.
1. MOTIVATION AND OBJECTIVES
Several efforts have been spent in recent years to characterise the flow field at the outlet of a jet both using refined
numerical simulations and detailed experiments. This flow configuration has fundamental engineering applications in
devices related to turbulent mixing, combustion and environmental studies (usually the axysymmetric circular shape is
adopted). For all these topics, it is very important to enhance as much as possible the entrainment of the ambient fluid
into the jet. This can be accomplished by considering different possibilities:
-
by forcing the jet at a frequency close to one of its natural frequencies by using acoustic or electromagnetic devices
(Zaman & Hussain, 1980, 1981; Husain et al., 1988);
by adding secondary flow and/or swirl through injections of fluid (upstream of the nozzle) both along the radial and
the azimuthal directions (Martin & Meiburg,1988);
by changing the shape of the nozzle from circular to elliptical, rectangular or even triangular (Krothapalli et al., 1981;
Vandersburger & Ding, 1995; Tam, 1998; Gutmark & Grinstein, 1999);
by inserting a body in the near field of the jet (Tong & Warhaft, 1994; Rajagopalan & Antonia, 1998, Olsen et al.
1999).
The first possibility is within the ensemble of the so-called active control devices, which require external energy to be
supplied to the flow in different form. This complicates the experimental set-up, makes difficult the comparison with
numerical results and need for a detailed energy budget balance to determine possible advantages. Adding fluid
through injectors is, in a certain sense, also a form of active-control using mechanical energy. Also in this case the flow
field is strongly modified (for example by the presence of a swirl) and it is still difficult to evaluate and to compare the
improvements. The simplest and more economic way to control a jet is to adopt a passive-control which mainly consists
of the last two possibilities. The change in shape was considered in the past, but still requires further investigations
especially for what concerns three-dimensional effects (Gutmark & Grinstein, 1999).
Among the different bodies, which can be placed in the near field to increase the amount of mixing, the use of a cylinder
was recently considered. Usually the symmetry of the configuration is maintained. For example Tong & Warhaft (1994)
placed a circular ring in front of a circular jet, while Rajagopalan & Antonia (1998) used a linear cylinder in front of a
plane jet. The diameter of these devices (d) is usually much lower than the nozzle diameter (D) (d/D ≤ 0.01) and they are
placed close to the nozzle (x/D < 0.3, where x is the axial distance from the nozzle).
Rajagopalan & Antonia (1998) proposed a simple model in which the growth of the Kelvin-Helmholtz large-scale vortices
(usually observed in jet flows) is partially suppressed by the counter-rotating Von Karman vortices in the cylinder wake.
This model is supported by the spectral measurements, which reveal a main line at Strouhal numbers approximately
equal to 0.3 for the jet without the cylinder and a suppression of this line with a simultaneous appearance of a line at
Strouhal numbers equal to about 0.1 for the measurements on the jet with the cylinder. The former is a value typical for
the shear layer of a jet, whereas the latter is obtained in the wake of a cylinder (the Strouhal number is defined as St =
fD/U0 for the shear layer of the jet and St = fd/U0 for the wake of the cylinder, U0 being the mean stream velocity). The
conclusion of the paper is that the shear layer increment (measured by the momentum thickness) along the axial
direction is smaller for the jet with the cylinder, thus indicating a smaller amount of mixing in comparison to the jet
without cylinder. On the other hand, Tong & Warhaft (1994) noticed an increased mixing with the cylinder in their
circular jet configuration.
The question seems far to be solved and it must be also considered that the small size of the cylinders used in the
previous investigations is largely inadequate for industrial applications where larger cylinders would be simpler to
design and to set-up. Moreover, a non-symmetric configuration, with a linear cylinder in front of a circular jet, could be
easily optimised by changing the axial and radial positions of the cylinder in respect to the nozzle (which was not
possible for the ring of Tong & Warhaft, (1994)).
In this paper, the near velocity field at the outlet of a circular jet with and without a linear cylinder in front to the outlet
was investigated experimentally to determine if the shear layer is increased or not by the presence of the cylinder. The
techniques, which are employed, are the Particle Image Velocimetry (PIV) and the Particle Tracking Velocimetry (PTV).
Another aim of the paper is to compare the results on instantaneous and time-averaged velocity fields obtained by the
two techniques to determine if, and eventually in which regions, they differ.
2. EXPERIMENTAL SET-UP
The experimental set-up consists of a water jet flowing through a circular nozzle into a large tank as shown in figure 2.
The circular water jet develops downstream a strong contraction (50:1 in area) into a tank where measurements are taken.
Detailed Laser Doppler (LDA) measurements are performed at the outlet of the jet to ensure that disturbances from the
circuit are not present and that the velocity profile has a top-hat shape (without the cylinder) with a turbulence intensity
equal to 5% (the momentum thickness measured at x/D = 0.2 for Re = 8000 is θ/D ≈ 0.02). This rather high turbulence
level was considered to match those usually observed in industrial applications. The Reynolds number, based on the jet
diameter (D=2 cm), ranges from 2000 to 10000 and the cylinder diameter (d) is equal to 0.4 mm (d=D/5). The axes are
selected as follows: x for the streamwise direction, y for the vertical and z spanwise (the origin is at the centre of the
nozzle). The cylinder extends along z from –8D to 8D and can be displaced along x and y (for the present measurements
it is positioned at x=0.3D and y=0). The infrared radiation of a Laser diode array (maximum power equal to 15 W) is
focused on a region of the (x, y) plane which extends streamwise from the nozzle (x = 0) to about x = 5D and from y = –2D
to y = 2D along the vertical (the thickness of the laser sheet is about 1mm).
Images of the scattering tracers (pollen particles with a density equal to 1.05 times that of water and an average size
equal to 40 µm) are recorded using a high speed video-camera (frame rate up to 2000 Hz, but for these measurements
used at 250 Hz with 440×420 resolution) and transferred to a PC. The tracer particles are supplied upstream of the
contraction and in the tank to seed both the jet and ambient flows. The infrared filter of the videocamera was removed to
allow the collection of the scattered light. The velocity field on the plane (x, y) is determined using two methods based
on Image Analysis, which are usually considered complementary: Particle Tracking Velocimetry (PTV) and Particle Image
Velocimetry (PIV). The experimental set-up is exactly the same for both methods (the videocamera was maintained
exactly in the same position) except for the tracer concentration (which is appropriately selected for each one before
starting the image acquisition) and for the image analysis procedure.
y, V
nozzle
y
d
D
x, U
d
D
x
Fig.2. Experimental set-up and co-ordinate system for the water jet. The exploded part shows the nozzle (diameter D)
and the cylinder (diameter d).
For PTV, a frame by frame tracking algorithm is employed (Querzoli & Cenedese, 1994; Romano 1996, 1998). On the
average it enables to validate about 100 tracer images per frame and to follow them for at least 10 consecutive frames. As
typical for PTV, data are obtained at random positions in space and interpolation algorithms are required to derive
results on a regular grid and to compute statistical moments (Eulerian frame of reference). About 15 sequences of 512
frames were acquired at each Reynolds number. Therefore, the Eulerian grid is the same used for PIV. On the other hand,
PTV can give the statistics on a Lagrangian frame, following tracers along the travelled path.
For PIV, cross-correlations between two consecutive frames are performed: the use of a high-speed video camera
enables to follow the time evolution with a high resolution (∆t = 0.004 s, ∆tUmax /D ≈ 0.1). The PIV algorithm contains
recent improvements for image analysis by cross-correlation functions as the window-offset, the sub-pixel Gaussian
interpolation and the Hart iterative method (Cotroni et al., 1999). The image analysis was performed using 32 pixel ×32
pixel windows with 60% overlapping which results in about (60×40) grid elements in the acquired region. Also for PIV,
about 15 sequences of 512 images were averaged to compute the mean values.
3. FLOW VISUALIZATIONS
Preliminary flow visualisations using Laser Induced Fluorescence (LIF) have been performed. An example in shown in
figure 3 for the two configurations for Re = 6000. The well-known Kelvin-Helmholtz large-scale vortices are observed in
the jet without the cylinder. They grow in size from x/D ≈ 0.5 to x/D ≈ 2.5 and then break with a strong injection of
ambient fluid towards the centreline. The situation changes drastically for the jet with the cylinder where vortices of
smaller size (in comparison to the previous ones) are observed only around x/D ≈ 1. Downstream these vortices
disappear and the overall spreading of the jet (say the aperture) is larger than for the jet without the cylinder even if the
ambient fluid doesn’t attain the centreline. This picture must be confirmed by measurements.
4. RESULTS: THE EFFECT OF THE CYLINDER
A sequence of instantaneous velocity and vorticity plots obtained by PIV is given in figure 4 for the condition of the jet
without the cylinder. The interval between successive images is 8 frames which correspond to about 0.032 s in time.
The period for the flow pattern to be convected over a fixed point (the convection velocity of the large-scale vortices is
about 0.35 U0) is slightly larger than 32 consecutive frames (corresponding to the displayed images). It is about 0.15 s,
resulting in a Strouhal number of the jet shear layer equal to 0.33 very close to those in the literature (Cohen &
Wygnanski, 1987). The sequence in figure 4 clearly shows the roll-up process which forms the Kelvin-Helmholtz
vortices in the shear layer. Strong ejections and injections of jet into ambient fluid and viceversa are associated to these
large-scale vortices (the vertical velocity has maximum values equal to ± 2 U0).
y/D 2
x/D
4
3
2
1
y/D
2
1
1
-1
-1
-2
x/D 4
3
2
1
-2
Fig.3. Flow visualizations using LIF for the jet without the cylinder (on the left) and with the cylinder (on the right)
for Re=6000. Shutter speed 250 Hz. Flow from right to left.
0.5
y/D
0
-0.5
-1
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0.5
0
y/D
vort
0.40
0.34
0.29
0.23
0.17
0.11
0.06
0.00
-0.06
-0.11
-0.17
-0.23
-0.29
-0.34
-0.40
-0.5
-1
-4
0
-3.5
-3
-2.5
-1.5
-1
-0.5
0
0.5
0
0
-1.5
-1
-0.5
0
y/D
y/ D
0.5
-0.5
-0.5
-1
-4
-2
x/D
x/D
-1
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
-4
x/D
-3.5
-3
-2.5
-2
x/D
1
1
0.5
0.5
y/D
y/D
Fig.4. Sequence of four instantaneous velocity vectors and vorticity (colours) plots measured by PIV. Time interval
between consecutive plots equal to 0.032 s. Jet without cylinder at Re=8000. Flow from right to left.
0
0
-0.5
-0.5
-1
-1
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
-4
-3.5
-3
-2.5
1
1
0.5
0.5
0
-0.5
-1
-1
-3.5
-3
-2.5
-2
x/D
-1.5
-1
-0.5
0
-1.5
-1
-0.5
0
0
-0.5
-4
-2
x/D
y/D
y/D
x/D
-1.5
-1
-0.5
0
-4
-3.5
-3
-2.5
-2
x/D
Fig.5. Sequence of four instantaneous velocity vectors and vorticity (colours) plots measured by PIV. Time interval
between consecutive plots equal to 0.016 s. Jet with cylinder at Re=8000. Flow from right to left.
1
0.5
y/ D
y/ D
0.5
0
-0.5
-0.5
-1
-4
0
-1
-3.5
-3
-2.5
-2
x/D
-1.5
-1
-0.5
0
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
x/D
Fig.6. Streamlines of the velocity field and vorticity map (in colours) from an instantaneous image processed by PIV
for the jet without cylinder (on the left) and the jet with cylinder (on the right) at Re=8000. Flow from right to left.
Fig.7. Overlapping of 100 frames measured by PTV (time interval equal to 0.4 s) for the jet without cylinder (on the
left) and the jet with cylinder (on the right) at Re=8000. Flow from left to right.
The same plot is given in figure 5 for the jet with the cylinder at the same Reynolds number (in this case the time interval
between images is about 0.016 s). Four vorticity maxima of alternating sign are observed only very close to the nozzle
(x/D < 1): they represent the two shear layers from the jet (y/D ≈ ± 0.5) and the two shear layers from the cylinder which
are already moving sideways (y/D ≈ ± 0.2) from their initial positions (y/D ≈ ± 0.1). The interaction between these
counter-rotating layers allows the Kelvin-Helmholtz vortices to be smoothed very rapidly and to disappear due to the
opposite induced velocities. Even so, the flow for the jet with cylinder seems to spread in the ambient more than for the
jet without cylinder (the vertical velocity in this case is not larger than ±0.5 U0). This is confirmed by the same type of
plots of figures 4 and 5 presented in figure 1 (with less grid elements): instantaneous velocity profiles for the jet with the
cylinder show that the cylinder wake influences the velocity field still for x/D > 3.
The instantaneous streamlines (shown in figure 6) clarify that in the jet without the cylinder the majority of the
interaction between the jet and the ambient fluid derives from the large scale Kelvin-Helmholtz vortices, whereas on the
jet with the cylinder the ambient fluid is mainly “attracted” towards the jet boundaries. In this condition, the centreline is
more perturbed in comparison to the jet without the cylinder.
Measurements by PTV confirm this picture. They are given in figure 7, where almost 100 frames are overlapped (total
acquisition time equal to 0.4 s). The larger spreading and the absence of (or much smaller) Kelvin-Helmholtz vortices are
observed when comparing the jet without and with the cylinder.
4
3
3
M /M o
M /Mo
4
2
1
0
-4
2
1
-3
-2
-1
0
x/D
0
-4
-3
-2
-1
0
x/D
Fig.8. Instantaneous mass flow rate derived from PIV measurements of the velocity field for the jet without cylinder (on
the left) and the jet with cylinder (on the right) at Re=8000.
To evaluate the mixing between jet and ambient fluids, the mass flow rate is evaluated from the axial velocity:
∞
M ( x ) = 2π ∫ ρU ( x, y) ydy
0
which by several authors is observed to increase linearly along the axis x: M(x)/M0 ≈ K1 (x/D) + K2, where M0 is the mass
flow rate at the nozzle and K1 ≈ 0.2÷0.3 at Re ≈ 104 (Ricou & Spalding, 1961; Hill, 1972). This is valid for isothermal flow
(ρ constant) and for x/D > 10; for x/D < 10, K1 is lower and not longer constant increasing approximately as x1/2, which
means that M(x) increases non-linearly. Here, the attention is focused on the instantaneous behaviour of this quantity
obtained from PIV measurements, the integral being evaluated between y = ±1.5D. The result is given in figure 8 for the
lower left side velocity field of figure 4 (jet without cylinder) and for the upper right side velocity field of figure 5 (jet with
cylinder). In both cases the mass flow rate increases with oscillations around linearity. For the jet without cylinder, the
amplitude of the oscillations is low and maxima and minima of such oscillations correspond respectively to regions of jet
fluid ejections and injections, which are related to regions in front of and behind the Kelvin-Helmholtz vortices. The
average value for the constant K1 is 0.2, which is in agreement with previous findings. For the jet with the cylinder, the
amplitude of the oscillations is much larger than before and the maxima of M(x) are related to the displacement of the
mean flow from the centreline: close to the nozzle, due to the splitting and acceleration of the jet stream, whereas far from
the nozzle, due to the related wide spreading. The average value of the constant K1 is 0.45, which is much larger than
that for the jet without cylinder, thus indicating an increased amount of mass flow rate along x: this confirms the larger
mixing for the cylinder case.
If the average mass flow rate is computed on the whole PIV image set (mean fields), the result is K1 ≈ 0 for the jet without
cylinder and K1≈ 0.15 for the jet with the cylinder. This indicates that, although in an “integral” sense the results from
instantaneous PIV data seem to be reasonable and in agreement with those in the literature, anyway there is a smoothing
effect to be considered. In the next section, this argument will be investigated in more detail.
5. RESULTS: COMPARISON BETWEEN PIV AND PTV
The velocity fields averaged over the whole PIV and PTV data sets are shown in figure 9 for the two experimental
conditions. The larger spreading for the jet with the cylinder is noticeable also in the mean fields. However, when
comparing the results from PIV and PTV, the former displays very smooth variations in the shear regions of large
velocity gradients (sideways of the jet and of the cylinder), whereas for the latter abrupt changes are observed. This
derives from the different analysis procedure which averages displacements in the PIV window, while derives local
velocity in PTV (although there is still some averaging when performing interpolation on a regular grid).
Fig. 9. Averaged vector plots without the cylinder (figures on the left) and with the cylinder (on the right) obtained
by means of PIV (at the top) and PTV (at the bottom). Flow from right to left (Re=8000).
U/U0
PIV
PTV
Cohen &
Wygnansky (1987)
U/U0
PIV
PTV
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
-1
-0.8
-0.6
-0.4
-0.2
0
y/D
0.2
0.4
0.6
0.8
1
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
y/D
Fig. 10. Axial velocity profiles (non-dimensional by the outlet velocity) by PIV and PTV for the jet without
cylinder at x/D=0.3 (left) and x/D=2 (right, with also data by Cohen & Wygnanski, 1987). Re=8000.
1
1.6
U/U
U/U00
1.6
U/U0
PIV
PTV
1.4
PTV
PIV
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-1.5
-1
-0.5
0
0.5
1
-0.4
-1.5
1.5
-1
-0.5
0
0.5
1
1.5
y/D
y/D
Fig. 11. Axial velocity profiles (non-dimensional by the jet without cylinder outlet velocity) obtained by
PIV and PTV for the jet with the cylinder at x/D =0.4 (left) and x/D=2 (right). Re=8000.
1.5
1 .5
PIV
PTV
U / U0
PIV
PTV
U/U 0
1
1
0.5
0 .5
0
0
-0.5
0
1
2
x/D
3
4
-0 .5
0
1
2
x/ D
3
4
Fig. 12. Streamwise velocity variation (non-dimensional by the jet without cylinder outlet velocity) along
the axis measured by PIV and PTV at y/D = 0.5 for the jet without the cylinder (on the left) and at y/D = 0
(centreline) for the jet with the cylinder (on the right). Re=8000.
The statement is confirmed by the analysis of the axial velocity profiles at different distances from the nozzle given in
figures 10 and 11. For both the jets with and without cylinder, the regions with large gradients are much better described
by PTV rather than by PIV. For the jet with the cylinder, at x/D = 0.4 the PTV data display negative values at the
centreline corresponding to the reverse flow in the cylinder wake. For the jet without cylinder, even at x/D = 2 the
comparison with the data by Cohen & Wygnanski (1987) (obtained at Re ≈ 104 by Hot Wire Anemometry) is much
favourable for PTV. The data obtained by PIV are usually smoothed due to the window size, to the window-offset and to
the partial overlapping in cross-correlation computations. The computations were repeated with 16 pixel × 16 pixel
windows, without substantial improvements on the results especially in the high gradient regions close to the outlet.
Therefore, the quantities derived by integrating these profiles (as the mass flow rate) using PIV are biased positively
(overestimation) in comparison to those obtained by PTV.
The variation of the streamwise velocity along the axis is given in figure 12 for the PIV and PTV measurements at y/D =
0.5 (jet without the cylinder) and at the centreline (jet with the cylinder). These are the locations where the largest
differences are observed (the velocity plot for the free jet without the cylinder along the centreline is almost unchanged
for both PIV and PTV). The PTV data describe better than PIV the low (and even negative) velocities close to the nozzle
and to the cylinder as well as the downstream acceleration around the cylinder. For x/D > 2.5 the two techniques give
almost the same results.
Another useful quantity for investigating the amount of mixing is given by the growth of the shear layer along the axis
of the jet due to the interaction between the jet flow and the ambient fluid. To this aim, the momentum thickness
∞
1
ϑ ( x) = 2
U ( x, y)[1 − U ( x, y ) ]dy
U 0 ( x) −∫∞
is computed for the measurements by PIV and PTV (U0(x) is the maximum velocity at each distance x from the nozzle). As
for the mass flow rate previously defined, for the free jet, also the momentum thickness was found to increase almost
linearly from the nozzle (Cohen & Wygnanski, 1987; Rajagopalan & Antonia, 1998). As before, the integral was
evaluated between y = ±1.5D. The results are given in figure 13 for the jet with and without the cylinder.
The data are compared with the results obtained by Rajagopalan & Antonia (1998) on the plane jet with the small
cylinder using Hot Wire Anemometry at Re ≈ 2.3 104. As given in the Introduction, they have found a marked decreasing
of the momentum thickness for the jet with the cylinder in comparison to the free jet. This is not confirmed by the
present data (both by PIV and PTV) which show a maximum at x/D ≈ 1 (where the two shear layers from the cylinder start
to merge), a minimum at x/D ≈ 1.5 (where the velocity at the centreline raises the maximum) and an increase for x/D > 1.5
(where the velocity at the centreline decreases). The comparison between figures 12 and right side of figure 13 clarify
these points. The increase of the momentum thickness along the axis is not linear and is much faster than for the jet
without cylinder (the relative difference is about 10% ÷ 15 % for the PTV data). This confirms the previous findings on
the enhance of mixing due to the presence of the large cylinder in this non-simmetric configuration.
The comparison between PIV and PTV reveals that the latter are closer than the former to the free jet data obtained by
Antonia & Rajagopalan (1998). Even for PTV, there is still some overestimation of the momentum thickness obtained by
Antonia & Rajagopalan (1998) which are approached by the single value obtained by LDA (the PTV data also attain
more or less the same value). The increase of the momentum thickness along x is almost linear for all data sets, but the
slope obtained by PTV is quite close to the Hot Wire data, while that from PIV data is largely underestimated.
0.2
0.2
θ/D 0.18
θ/D
PIV
PTV
0.16
PIV
PTV
0.18
0.16
0.14
0.14
0.12
0.12
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0
0
0.5
1
1.5
2
x/D
2.5
3
3.5
4
0.02
0
0.5
1
1.5
2
2.5
3
3.5
4
x/D
Fig. 13. Momentum thickness (non-dimensional by the jet diameter) variation along the axial distance
obtained by PIV and PTV for the jet with and without the cylinder at Re=8000. Open circles show the
results by Rajagopalan & Antonia (1998) at Re=23000. The solid square indicates the result obtained by
measuring the axial velocity profile at x/D =0.2 using LDA.
4.5
6. EFFECT OF THE REYNOLDS NUMBER
The PTV data have been acquired also at different Reynolds numbers and the results for the axial variation of the
momentum thickness are given in figure 14. Although the overall behaviour is very similar for all the data, there is a
Reynolds number dependence for x/D >1.5: the momentum thickness increases as faster the lower the Reynolds number.
However, the larger amplitude of the shear layer for the jet with the cylinder in comparison to the free jet is confirmed
also at the other Reynolds numbers. The values obtained for the jet without cylinder also point out that some of the
difference with the data by Rajagopalan & Antonia (1998) can be attributed also to the different Reynolds number.
7. COMMENTS AND CONCLUSIONS
Velocity measurements using a passive device (a cylinder placed orthogonal to the mean flow) in front of a circular jet
have been performed by means of PIV and PTV to investigate the change in mixing. In comparison to previous
investigations the cylinder is quite large (about 1/5 of the nozzle diameter) and it breaks the axisymmetry of the jet. The
measurements allow the following features to be derived:
-
-
-
a relevant smoothing of the Kelvin-Helmholtz vortices usually observed in circular jets and mixing layers as
confirmed by flow visualisations (figure 3), PIV instantaneous velocity and vorticity plots (figures 1, 4, 5, and 6) and
PTV trajectories (figure 7);
a significative enhancement of mixing (in the order of 15%) due to the larger spreading of the shear layers as
confirmed by the measurements (using PIV and PTV) of the increase in the instantaneous mass flow rate (figure 8),
of the behaviour of the average velocity fields (figure 9) and of the growth along the axis of the shear layer
momentum thickness (figure 13);
a remarkable dependence on the Reynolds number (for the values tested) especially for distances along the axis
larger than 2 nozzle diameters; this dependence does not alter the previous conclusions;
the PIV and PTV methods do not give the same results especially in regions where large velocity gradients are
present (figures 10, 11 and 12): the comparison with the results from other authors and the analysis of the results
suggest that PIV measurements must be considered with care in such regions. On the other hand, preliminary
measurements on velocity fluctuations indicate sensible errors on rms values measured by PTV.
θ/D
θ/D
0.2
0.2
0.18
0.18
Re=2000
Re=4000
Re=8000
0.16
0.16
0.14
0.14
0.12
0.12
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
Re=2000
Re=4000
Re=8000
0.02
0.02
0
0.5
1
1.5
2
x/D
2.5
3
3.5
4
0
0.5
1
1.5
2
2.5
3
3.5
x/D
Fig. 14. Momentum thickness (non-dimensional by the jet diameter) variation along the axial distance
obtained by PTV for the jet with and without the cylinder at different Reynolds numbers.
4
REFERENCES
Cohen J. and Wygnansky I., The evolution of instabilities in the axisymmetric jet. Part 1. The linear growth of
disturbances near the nozzle. Journal of Fluid Mechanics, Vol.176, pp.191-219, 1987.
Cotroni A., Di Felice F., Romano G.P. and Elefante M., Propeller tip vortex analysis by means of PIV. Accepted in
Experiments in Fluids, 1999.
Gutmark E.J. and Grinstein F.F., Flow control with non-circular jets. Annual Review of Fluid Mechanics, Vol.31,
pp.239-272, 1999.
Hill B.J., Measurement of local entrainment rate in the initial region of axisymmetric turbulent air jets. Journal of Fluid
Mechanics, Vol.51, pp.773-779, 1972.
Husain H.S., Bridges J.E. and Hussain A.K.M.F., Turbulence menagement in free shear flows by control of coherent
structures. In Transport Phenomena in Turbulent Flows, Edts M.Hirata and N.Kasagi, pp. 11-130, Hemisphere (New
York), 1988.
Krothapalli A., Baganoff D. and Karamcheti K., On the mixing of a rectangular jet. Journal of Fluid Mechanics, Vol.107,
pp.201-220, 1981.
Martin J.E. and MeiburgE., Numerical investigation of three-dimensionally evolving jets subject to axysimmetric and
azimuthal perturbations. Journal of Fluid Mechanics, Vol.230, pp.271-318, 1988.
Olsen J.F., Rajagopalan S. and Antonia R.A., Influence of stationary and rotating cylinders on a turbulent plane jet. In
Engineering Turbulence Modelling and Experiments, Edts W. Rodi and M. Laurence, Vol.4, pp.423-442, 1999.
Querzoli G. and Cenedese A., Lagrangian study of a convective boundary layer using image analysis. In 7th
International Symposium on Application of Laser Anemometry to Fluid Mechanics, Lisbon, 1994.
Rajagopalan S. and Antonia R.A., Turbulence reduction in the mixing layer of a plane jet using small cylinders.
Experiments in Fluids, Vol.25, pp.96-103, 1998.
Ricou F.P. and Spalding D.B., Measurements of entrainment by axisymmetrical turbulent jets. Journal of Fluid
Mechanics, Vol.11, pp.21-32, 1961.
Romano G.P., Investigation on time scales in a low Reynolds jet flow using Particle Tracking Velocimetry. Applied
Scientific Research, Vol.56, pp.209-220, 1996.
Romano G.P., Investigation on particle trajectories and Lagrangian statistics at the outlet of a circular jet. Experimental,
Thermal and Fluid Science, Vol.17, pp.116-123, 1998.
Tam C.K.W., Influence of nozzle geometry on noise of high speed jets. AIAA Journal, Vol.8, pp.1396-1400, 1998.
Tong C. and Warhaft Z., Turbulence suppression in a jet by means of a fine ring. Physics of Fluids, Vol.6, pp.328-333,
1994.
Vandersburger U. and Ding C., Self-excited wire method for the control of turbulent mixing layers. AIAA Journal, Vol.33,
pp.1032-1037, 1995.
Zaman K.B.M. and Hussain A.K.M.F., Vortex pairing in a circular jet under controlled excitation. Journal of Fluid
Mechanics, Vol.101, pp.449-491, 1980.
Zaman K.B.M. and Hussain A.K.M.F., Turbulence suppression in free shear flows by controlled excitation. Journal of
Fluid Mechanics, Vol.103, pp.133-159, 1981.