Experimental Study of Mixing at the External Boundary of a Submerged Turbulent Jet

1
Experimental Study of Mixing at the External
Boundary of a Submerged Turbulent Jet

• A. Eidelman, T. Elperin, N.Kleeorin, G.Hazak,
  I.Rogachevskii, S.Rudykh, O.Sadot, I.
  Sapir-Katiraie

2
Outline

• Motivation and objectives
• Experimental setup
• Instrumentation and data processing
• Velocity parameters of the jet flow
• Measurements of the phase function of mixing
• Determination of the phase function PDF
  parameters
• Results and conclusions

3
Motivation and objectives

• An important property of mixing is a sharp
  increase of mixing rates observed by Konrad
  (1976). It is attributed to the onset of
  small-scale turbulence within large-scale
  coherent motions. Studies of this effect (i.e.,
  Hussain Zaman, 1980 Huang Ho, 1990 Moser
  Rogers, 1991 Dimotakis, 2000 Meyer, Dutton
  Lucht, 2006) have demonstrated complex nonlinear
  dynamics of this phenomenon .
• However, it is not clear how such mixing states
  are attained. The uncertainty is strengthened by
  the differences in experimental results obtained
  in gaseous and liquid flows (Miller and
  Dimotakis, 1991). The difference in behavior is
  attributed to a Schmidt number effect that is
  high in liquid and low in gaseous flows.
• We investigate the mixing in the submerged air
  jet using the incense smoke characterized by a
  significantly larger Schmidt numbers than
  employed in the previous studies of gas flow
  mixing. In the present study we focus on the
  internal structure of the fluid mixing before the
  molecular effect predominates. It is a first
  stage of the study.
• In our study we use the approach used by Hazak et
  al. (2006). It was based on the phase function
  measurements, suggested by Drew (1983) for mixing
  studies, and determination of its characteristics.

4
Background
The study of Hazak et al. (2006) have revealed
that PDF of the sizes of the regions
occupied by the heavy fluid can be described by
the Gamma function distribution in a flow with
Rayleigh-Taylor instability in the linear
electric motor experiments and in DNS
where , and
are parameters characterizing the length scale
and a deviation from the exponential PDF,
accordingly. Ratios of the PDF moments
define a characteristic scale , where
is a number of a statistical moment, and a
property of a ratio equality
was used for the determination of the PDF
parameters in their study.
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Experimental setup
1 Nd-YAG laser, 2 trajectory of the laser
beam, 3 light sheet optics, 4 CCD camera, 5
system computer.
Test section.
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Scheme of a jet flow and measurements
1 channel with transparent walls, 2 tube with
a jet nozzle, 3 submerged jet, 4 light sheet
optics, 5 laser light sheet, 6 image area, 7
CCD camera.
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Jet velocity field
Parameters
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Measurements in a jet flow
Jet coordinates and a range of measurements
Binary jet image averaged over an ensemble
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PDF of light intensities
Blue line in the jet. Red line in the
surrounding fluid.
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Determination of a jet boundary

• Normalization of images in order to eliminate
  fluctuations of an initial concentration of
  particles.
• Defining of a threshold for image binarization
  with histograms of light distributions inside a
  jet and in an external fluid.
• Images conversion into a binary form.
• Ensemble averaging over 50 binary images.
• Determination of a jet boundary and of an angle
  of the jet expansion with a threshold 0.5 that
  means an equal probability of a jet fluid and of
  an external fluid over the boundary.

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Phase function
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Determination of a phase function parameters

• Turn of binary images on different angles.
• Measurement of phase functions of an ensemble of
  images for each turn angle.
• Determination of a homogeneity range of the phase
  functions for all set of the angles.
• Plotting of the histograms of the phase
  functions obtained over each line.
• Fit of the histograms of the phase functions with
  the Gamma function distribution

13
Mean phase function across a jet
Circles Re10000 Triangles Re8400 Measured in
a range centered at
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Normalized histograms do not show universal
property of power dependence
z/D 0.36
z/D 0
z/D - 0.36
z/D - 0.91
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Normalized histograms do not show an exponential
behavior
z/D 0.36
z/D 0
z/D - 0.36
z/D - 0.91
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Fit of the phase function PDF
Blue circles PDF of jet fluid, Red circles PDF
approximation Magenta circles exponent part of
PDF Green circles power part of PDF
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Ratios of PDF moments are equal, if
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Power r vs. distance from the jet boundary
Circles Re10000 Triangles Re8430
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Scale ? vs. distance from the jet boundary
Circles Re10000 Triangles Re8430
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Conclusions

• PDF of the phase function of jet mixing can be
  described with the Gamma distribution that is
  similar to the PDF of a phase function during
  mixing induced by Rayleigh-Taylor instability.
• The parameters of Gamma distribution can be
  determined using a fit of the measured histogram
  of the phase function. A method of an equality of
  the PDF moments can be applied, if fragments
  sizes is larger than 10?1.
• The measured power r is close to 1, and the
  characteristic scale ? increases from 0.05 to 1 D
  from a periphery to an internal part of a jet.
• There is no evident dependence of both parameters
  on Re number at Re 104, although the range of
  Re was not large.
• There is a difference in the parameters of Gamma
  distribution for mixing induced by
  Rayleigh-Taylor instability and for mixing at the
  external boundary of a turbulent jet caused,
  probably, by the different physical mechanisms of
  mixing in these two cases.

21
References

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