The document summarizes an experiment examining the zone of flow establishment (ZFE) in turbulent jets. Key points:
1. Planar laser-induced fluorescence (PLIF) visualization was used to measure the geometric characteristics of the jet core as a function of initial velocity and nozzle diameter within 10 jet diameters of the nozzle.
2. The ZFE length was estimated based on the absence of turbulent intensity fluctuations using time-averaged and root-mean-squared concentration images.
3. Results showed the ZFE shape is conical in time-averaged images and ballistic in RMS images. Turbulence initiation occurred at the nozzle elevation in RMS images.
4. As Reynolds number increased, measured Z
Large eddy simulation of the flow over a circular cylinder at high reynolds n...Jesús Martínez
The issue of numerical study of turbulent flow over a circular cylinder for different Reynolds numbers has been studied over almost 20 years. During those two decades, there have been successes and failures in the numerical models. This paper presents the implementation of the method of large eddy simulation (LES) to solve the problem of the external flow over a cylinder under a subcritical Reynolds number (Re = 1.4E +5). The purpose is to evaluate the performance of a computational method and complement experimental and numerical data presented in the literature, this as part of a research work which attempts to explain a method of passive drag reduction.
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
We follow "Rigorous Publication" model - means that all articles appear on IJERD after full appraisal, effectiveness, legitimacy and reliability of research content. International Journal of Engineering Research and Development publishes papers online as well as provide hard copy of Journal to authors after publication of paper. It is intended to serve as a forum for researchers, practitioners and developers to exchange ideas and results for the advancement of Engineering & Technology.
The current study examines the generation and propagation of a Third order solitary water wave along
the channel. Surface displacement and wave profi le prediction challenges are interesting subjects in the
fi eld of marine engineering and many researchers have tried to investigate these parameters. To study the
wave propagation problem, here, fi rstly the meshless Incompressible Smoothed Particle Hydrodynamics
(ISPH) numerical method is described. Secondly,
Effect of Turbulence Model in Numerical Simulation of Single Round Jet at Low...ijceronline
Single axi-symmetric round jet flow was analyzed using computational techniques and validated with experimental results to establish the suitable turbulence model for simulation of low Reynolds number jets exiting from fully developed pipe. This work is performed as an initial study before computationally simulating multiple impinging jets. To this end a single round jet at Reynolds number of 7500 exiting from a fully developed pipe and entering into stationary air was modeled. Velocity and turbulence profiles were extracted from the simulation and validated with in-house experimental results. It was observed that although all the four turbulence models studied were able to closely predict the mean velocity field, they were not able to accurately predict the turbulence intensity distributions. From the models studied, it was concluded that SST k- ω model was the best turbulence model for simulating low Reynolds number jet flow exiting from fully developed pipe.
Large eddy simulation of the flow over a circular cylinder at high reynolds n...Jesús Martínez
The issue of numerical study of turbulent flow over a circular cylinder for different Reynolds numbers has been studied over almost 20 years. During those two decades, there have been successes and failures in the numerical models. This paper presents the implementation of the method of large eddy simulation (LES) to solve the problem of the external flow over a cylinder under a subcritical Reynolds number (Re = 1.4E +5). The purpose is to evaluate the performance of a computational method and complement experimental and numerical data presented in the literature, this as part of a research work which attempts to explain a method of passive drag reduction.
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
We follow "Rigorous Publication" model - means that all articles appear on IJERD after full appraisal, effectiveness, legitimacy and reliability of research content. International Journal of Engineering Research and Development publishes papers online as well as provide hard copy of Journal to authors after publication of paper. It is intended to serve as a forum for researchers, practitioners and developers to exchange ideas and results for the advancement of Engineering & Technology.
The current study examines the generation and propagation of a Third order solitary water wave along
the channel. Surface displacement and wave profi le prediction challenges are interesting subjects in the
fi eld of marine engineering and many researchers have tried to investigate these parameters. To study the
wave propagation problem, here, fi rstly the meshless Incompressible Smoothed Particle Hydrodynamics
(ISPH) numerical method is described. Secondly,
Effect of Turbulence Model in Numerical Simulation of Single Round Jet at Low...ijceronline
Single axi-symmetric round jet flow was analyzed using computational techniques and validated with experimental results to establish the suitable turbulence model for simulation of low Reynolds number jets exiting from fully developed pipe. This work is performed as an initial study before computationally simulating multiple impinging jets. To this end a single round jet at Reynolds number of 7500 exiting from a fully developed pipe and entering into stationary air was modeled. Velocity and turbulence profiles were extracted from the simulation and validated with in-house experimental results. It was observed that although all the four turbulence models studied were able to closely predict the mean velocity field, they were not able to accurately predict the turbulence intensity distributions. From the models studied, it was concluded that SST k- ω model was the best turbulence model for simulating low Reynolds number jet flow exiting from fully developed pipe.
Seismic data Interpretation On Dhodak field PakistanJamal Ahmad
I (Jamal Ahmad) presented this on 21 Feb, 2009 to defend my M.Phil dissertation in Geophysics at QAU, Islamabad, Pakistan. For more information about this, you may contact me directly at jamal.qau@gmail.com.
The oxford dictionary defines an attribute as, “a quality ascribed to any person or thing”. We have extended this definition to: “seismic attributes are all the information obtained from seismic data, either by direct measurements or by logical or experience based reasoning
In reflection seismology : aseismic attributes is a quality extracted or derived from seismic data that can be analyzed in order to enhance information that might be more subtle in a traditional seismic image , leading to a better geological or geophysical interpretation of the data
Over the past decades, we have witnessed attribute developments track breakthroughs in reflector acquisition and mapping, fault identification, bright spot identification, frequency loss, thin bed tuning, seismic stratigraphy.
Experimental flow visualization for flow around multiple side-by-side circula...Santosh Sivaramakrishnan
This paper deals with Flow visualization of multiple side by side circular cylinders of varying cross sections at Reynolds numbers from 50-200. An experimental setup for this purpose has been designed and described in the paper.
Caliper tools measure hole size and shape.
The simple mechanical caliper measures a vertical profile of hole diameter.
The more sophisticated geometry tools records two simultaneous calipers and give an accurate borehole shape and orientation.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Field and Theoretical Analysis of Accelerated Consolidation Using Vertical Dr...inventionjournals
Mumbai is the region consisting of soft compressible marine clay deposits. There are several construction problems on such soils and thus ground improvement is need to be carried out. Vertical drains is generally preferred technique as accelerated settlement is achieved during the construction phase itself if planned accordingly. The concept of vertical drains is based on the theory of three dimensional consolidation as described by Terzaghi (1943). Based on this concept, a consolidation programme is developed and an attempt is made to determine the field to laboratory coefficient of vertical consolidation ratio by Taylor’s Square Root of Time Method and Casagrande’s Logarithm of Time Fitting Method for this region. Based on this, the rate of consolidation and time required for consolidation in the field can be determined knowing the consolidation parameters. Equations are developed by using output of the programme and it is explained.
Time-Frequency Representation For Estimating Young’s Modulus And Poisson’s Ra...IJERA Editor
The present paper examines a new procedure for estimating Young‘s modulus and Poisson‘s ratio of homogeneous materials constituting the one-layer thin tubes. The work is done from the use of the timefrequency representation. Spectrogram and its reassigned version have been chosen to analyze experimentally acoustic signals backscattered by air-filled tubes immersed in water. For reduced frequencies ranging from 0.1 to 500, time-frequency images have shown the presence of the Symmetrical and the Antisymmetrical waves. Satisfactory resolution and good localization in the time-frequency plane have been observed in the case of concentrated spectrogram. Reduced cutoff frequencies of A1 and S1 waves have also been extracted from Spectrogram and concentrated Spectrogram time-frequency images. A good agreement has, therefore, been observed. Comparisons with results obtained by experiment indicate that mechanical parameters such as Young‘s modulus and Poisson‘s ratio of aluminum and copper are evaluated accurately
Seismic data Interpretation On Dhodak field PakistanJamal Ahmad
I (Jamal Ahmad) presented this on 21 Feb, 2009 to defend my M.Phil dissertation in Geophysics at QAU, Islamabad, Pakistan. For more information about this, you may contact me directly at jamal.qau@gmail.com.
The oxford dictionary defines an attribute as, “a quality ascribed to any person or thing”. We have extended this definition to: “seismic attributes are all the information obtained from seismic data, either by direct measurements or by logical or experience based reasoning
In reflection seismology : aseismic attributes is a quality extracted or derived from seismic data that can be analyzed in order to enhance information that might be more subtle in a traditional seismic image , leading to a better geological or geophysical interpretation of the data
Over the past decades, we have witnessed attribute developments track breakthroughs in reflector acquisition and mapping, fault identification, bright spot identification, frequency loss, thin bed tuning, seismic stratigraphy.
Experimental flow visualization for flow around multiple side-by-side circula...Santosh Sivaramakrishnan
This paper deals with Flow visualization of multiple side by side circular cylinders of varying cross sections at Reynolds numbers from 50-200. An experimental setup for this purpose has been designed and described in the paper.
Caliper tools measure hole size and shape.
The simple mechanical caliper measures a vertical profile of hole diameter.
The more sophisticated geometry tools records two simultaneous calipers and give an accurate borehole shape and orientation.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Field and Theoretical Analysis of Accelerated Consolidation Using Vertical Dr...inventionjournals
Mumbai is the region consisting of soft compressible marine clay deposits. There are several construction problems on such soils and thus ground improvement is need to be carried out. Vertical drains is generally preferred technique as accelerated settlement is achieved during the construction phase itself if planned accordingly. The concept of vertical drains is based on the theory of three dimensional consolidation as described by Terzaghi (1943). Based on this concept, a consolidation programme is developed and an attempt is made to determine the field to laboratory coefficient of vertical consolidation ratio by Taylor’s Square Root of Time Method and Casagrande’s Logarithm of Time Fitting Method for this region. Based on this, the rate of consolidation and time required for consolidation in the field can be determined knowing the consolidation parameters. Equations are developed by using output of the programme and it is explained.
Time-Frequency Representation For Estimating Young’s Modulus And Poisson’s Ra...IJERA Editor
The present paper examines a new procedure for estimating Young‘s modulus and Poisson‘s ratio of homogeneous materials constituting the one-layer thin tubes. The work is done from the use of the timefrequency representation. Spectrogram and its reassigned version have been chosen to analyze experimentally acoustic signals backscattered by air-filled tubes immersed in water. For reduced frequencies ranging from 0.1 to 500, time-frequency images have shown the presence of the Symmetrical and the Antisymmetrical waves. Satisfactory resolution and good localization in the time-frequency plane have been observed in the case of concentrated spectrogram. Reduced cutoff frequencies of A1 and S1 waves have also been extracted from Spectrogram and concentrated Spectrogram time-frequency images. A good agreement has, therefore, been observed. Comparisons with results obtained by experiment indicate that mechanical parameters such as Young‘s modulus and Poisson‘s ratio of aluminum and copper are evaluated accurately
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Radio signal from extensive air showers EAS studied by the CODALEMA experiment have been detected by means of the classic short fat antennas array working in a slave trigger mode by a particle scintillator array. It is shown that the radio shower wavefront is curved with respect to the plane wavefront hypothesis. Then a new tting model (parabolic model) is proposed to fit the radio signal time delay distributions in an event-by-event basis. This model take
into account this wavefront property and several shower geometry parameters such as: the existence of an apparent localised radio-emission source located at a distance Rc from the antenna array of and the radio shower core on the
ground. Comparison of the outputs from this model and other reconstruction models used in the same experiment show:
1)- That the radio shower core is shifted from the particle shower core in a statistic analysis approach.
2)- The capability of the radiodetection method to reconstruct the curvature radius with a statistical error less than 50 g.cm−2 .
Finally a preliminary study of the primary particle nature has been performed based on a comparison between data and Xmax distribution from Aires Monte-Carlo simulations for the same set of events.
This seminal experiment addresses the issue of the generalization of Fick’s Law in the case of a spatially inhomogeneous diffusion coefficient. In Finance this is akin to the problem of a volatility dependent on the price of the underlying asset. We demonstrate deviation from the Stokes-Einstein law. In particular this relates to the Ito versus Stratonovitch controversy in stochastic calculus.
Application of DRP scheme solving for rotating disk-driven cavityijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Time-Frequency Representation For Estimating Young’s Modulus and Poisson’s Ra...IJERA Editor
The present paper examines a new procedure for estimating Young‘s modulus and Poisson‘s ratio of homogeneous materials constituting the one-layer thin tubes. The work is done from the use of the time-frequency representation. Spectrogram and its reassigned version have been chosen to analyze experimentally acoustic signals backscattered by air-filled tubes immersed in water. For reduced frequencies ranging from 0.1 to 500, time-frequency images have shown the presence of the Symmetrical and the Antisymmetrical waves. Satisfactory resolution and good localization in the time-frequency plane have been observed in the case of concentrated spectrogram. Reduced cutoff frequencies of A1 and S1 waves have also been extracted from Spectrogram and concentrated Spectrogram time-frequency images. A good agreement has, therefore, been observed. Comparisons with results obtained by experiment indicate that mechanical parameters such as Young‘s modulus and Poisson‘s ratio of aluminum and copper are evaluated accurately.
Wavelet estimation for a multidimensional acoustic or elastic earthArthur Weglein
A new and general wave theoretical wavelet estimation
method is derived. Knowing the seismic wavelet
is important both for processing seismic data and for
modeling the seismic response. To obtain the wavelet,
both statistical (e.g., Wiener-Levinson) and deterministic
(matching surface seismic to well-log data) methods
are generally used. In the marine case, a far-field
signature is often obtained with a deep-towed hydrophone.
The statistical methods do not allow obtaining
the phase of the wavelet, whereas the deterministic
method obviously requires data from a well. The
deep-towed hydrophone requires that the water be
deep enough for the hydrophone to be in the far field
and in addition that the reflections from the water
bottom and structure do not corrupt the measured
wavelet. None of the methods address the source
array pattern, which is important for amplitude-versus-
offset (AVO) studies.
Wavelet estimation for a multidimensional acoustic or elastic earth- Arthur W...Arthur Weglein
A new and general wave theoretical wavelet estimation
method is derived. Knowing the seismic wavelet
is important both for processing seismic data and for
modeling the seismic response. To obtain the wavelet,
both statistical (e.g., Wiener-Levinson) and deterministic
(matching surface seismic to well-log data) methods
are generally used. In the marine case, a far-field
signature is often obtained with a deep-towed hydrophone.
The statistical methods do not allow obtaining
the phase of the wavelet, whereas the deterministic
method obviously requires data from a well. The
deep-towed hydrophone requires that the water be
deep enough for the hydrophone to be in the far field
and in addition that the reflections from the water
bottom and structure do not corrupt the measured
wavelet. None of the methods address the source
array pattern, which is important for amplitude-versus-
offset (AVO) studies
CFD and Artificial Neural Networks Analysis of Plane Sudden Expansion FlowsCSCJournals
It has been clearly established that the reattachment length for laminar flow depends on two non-dimensional parameters, the Reynolds number and the expansion ratio, therefore in this work, an ANN model that predict reattachment positions for the expansion ratios of 2, 3 and 5 based on the above two parameters has been developed. The R2 values of the testing set output Xr1, Xr2, Xr3, and Xr4 were 0.9383, 0.8577, 0.997 and 0.999 respectively. These results indicate that the network model produced reattachment positions that were in close agreement with the actual values. When considering the reattachment length of plane sudden-expansions the judicious combination of CFD calculated solutions with ANN will result in a considerable saving in computing and turnaround time. Thus CFD can be used in the first instance to obtain reattachment lengths for a limited choice of Reynolds numbers and ANN will be used subsequently to predict the reattachment lengths for other intermediate Reynolds number values. The CFD calculations concern unsteady laminar flow through a plane sudden expansion and are performed using a commercial CFD code STAR-CD while the training process of the corresponding ANN model was performed using the NeuroShellTM simulator.
Towards the identification of the primary particle nature by the radiodetecti...Ahmed Ammar Rebai PhD
To contact the author use ahmed.rebai2@gmail.com
Radio signal from extensive air showers EAS studied by the CODALEMA experiment have been detected by means of the classic short fat antennas array working in a slave trigger mode by a particle scintillator array. It is shown that the radio shower wavefront is curved with respect to the plane wavefront hypothesis. Then a new fitting model (parabolic model) is proposed to fit the radio signal time delay distributions in an event-by-event basis. This model take into account this wavefront property and several shower geometry parameters such as: the existence of an apparent localised radio-emission source located at a distance Rc from the antenna array of and the
radio shower core on the ground. Comparison of the outputs from this model and other reconstruction models used in the same experiment show: 1)- That the radio shower core is shifted from the particle shower core in a statistic analysis approach. 2)- The capability of the radiodetection method to reconstruct the curvature radius
with a statistical error less than 50 g.cm−2 . Finally a preliminary study of the primary particle nature has been performed based on a comparison between data and Xmax distribution from Aires Monte-Carlo simulations for the same set of events.
Some possible interpretations from data of the CODALEMA experimentAhmed Ammar Rebai PhD
The purpose of the CODALEMA experiment, installed at the Nan\c{c}ay Radio Observatory (France), is to study the radio-detection of ultra-high energy cosmic rays in the energy range of 10^{16}-10^{18} eV. Distributed over an area of 0.25 km^2, the original device uses in coincidence an array of particle detectors and an array of short antennas, with a centralized acquisition. A new analysis of the observable in energy for radio is presented from this system, taking into account the geomagnetic effect. Since 2011, a new array of radio-detectors, consisting of 60 stand-alone and self-triggered stations, is being deployed over an area of 1.5 km^2 around the initial configuration. This new development leads to specific constraints to be discussed in term of recognition of cosmic rays and in term of analysis of wave-front.
Modeling and simulation of ducted axial fan for one dimensional flow
Zone of flow establishment in turbulent jets
1. Zone of flow establishment in turbulent jets
Dimitriadis P., M. Liveri-Dalaveri, A. Kaldis, C. Kotsalos, G.
Papacharalampous and P. Papanicolaou
Department of Water Resources and Environmental Engineering
National Technical University of Athens
(www.itia.ntua.gr)
European Geosciences Union General Assembly 2012
Vienna, Austria, 22-29 April 2012
Session AS2.2/OS5.3: Turbulence in the atmospheric
and oceanic boundary layers, Vol. 14, EGU2012-12716
2. 1. Abstract
It is well established experimentally that as the Reynolds number increases the core of the jet diminishes and has smaller
effects on the jet’s mean profiles (e.g. concentration, temperature, velocity). The scope of this project is to examine this
relationship based on dimensional analysis and experimental data. For that, spatio-temporal concentration records are
obtained on the plane of symmetry of heated vertical round jets (for a laboratory turbulent scale at the order of mm) using
tracer concentration measurements via a planar laser induced fluorescence technique (PLIF). The investigation area is set
close to the nozzle of the jets (up to 10 jet diameters away), at the zone of flow establishment (ZFE), so as to determine the
geometric characteristics (dimensions and shape) of the core as a function of the initial velocity and nozzle diameter. The ZFE
is estimated through the absence of turbulent intensity fluctuations (assuming a threshold value of 1% of the maximum
intensity).
2. Introduction
The jets are widely used in several engineering fields mainly for wastewater/salt disposal,
gaseous releases etc. Using engineering terms, investigation of the zone of flow establishment
(ZFE) “seems both futile and unnecessary in view of its limited extent” (Jirka, 2004).
Nevertheless, in scientific terms, it is of high importance as it includes the shear layer and
transition to turbulence. The ZFE is defined as the area within the shear layer developed at the
edge of a jet and is known to have a ‘conical’shape, because of the shear layer dispersion
towards the jet axis at the advancing of the jet (Chen & Nikitopoulos, 1979) . The limit of that
dispersion is the axis of symmetry and its distance from the nozzle is considered as the ZFE
length (xe), which is affected by flow instability and thus it is difficult to define. It is generally
observed that as the Reynolds number increases, distance xe decreases. A literature survey is
done along with some measurements of xe in time and space via PLIF visualization to verify this
view. Specifically, three locations are recorded that are based on the time-averaged (TAV) and
root-mean-squared (RMS) images of rhodamine 6G concentration C. The first at the point where
the TAV of C at the jet-axis starts to decay (xe,m), the second where the RMS of C takes values
above a threshold (xe,smin), and the third where the normalized RMS of C (xe,smax) is maximum.
3. 3a. Literature survey (experimental values)
Figure 1a (up): Experimental values of the ZFE length are extracted from the
graphs of the researchers noted above with a certain degree of tolerance. The axes
of the graphs are V/V0 and xe/D, where V is the mean axial jet-velocity and D the
nozzle’s diameter (where the subscript 0 denotes the exit of the orifice).
Figure 1b (left): Several researchers have measured the ZFE length indicating only
the order of the Reynolds number (Re).
Researchers xe/D Re
Type of
the Jet
Albertson et al. (1948) 6,2 large Air
Crow and Champagne
(1971)
5,3 large Water
Pratte and Baines (1967) 6,4 large Air
In the case of Labus & Symons only the
descending branch of the graph is taken
into account due to uncertainties
concerning the validity of ascending
branch.
4. 3b. Literature survey (approximated equations)
• Abramovich (1963) states that for a jet of an incompressible fluid in a co-flowing (V ua, the
cross flow ambient velocity) external stream, the ZFE length is given by the equation :
( ) a
1 /1
/ ,
2 0.27 1 / (0.416 0.13
where minus sign for /
4 / )
1
+
+
>= ±
−
a
e
a a
V u
x D
V u V
V u
u
• Pratte & Baines (1967) report that xe of a jet released from a tube perpendicular to a cross
flow approaches the potential core length for a turbulent free jet with no cross flow, as the
ratio of the jet velocity to the cross-flow velocity (V/ua) becomes large. Although xe is also a
function of the Reynolds number (in the tube), Reynolds number dependence is less
important for large release momentum. Pratte and Baines (largest Reynolds number-
vertically directed jet) data are correlated as:
( )( )e a a e/ 6.4(1 exp 0.48 or/ , f / 60 : .4= − − ==x D V u x Du
• Chen & Nikitopoulos (1979) present some data for xe, derived from a differential model, as a
function of the densimetric Froude number (Fo), for a plume discharging vertically into a
stagnant ambient. Henderson-Sellers (1983) suggest the following empirical fit to these data:
( )
2
0
2
2 2 2
e 0 0 0
2
a0
0
o
4 , 8
3.27 0.26 , 8 128, , where
∆
g
26.2 ,
,
( C) is the temperatur
128
e,
a subscr
α <
= + ≤ ≤ =
>
∆ = −
T
T T T
T
D F
V
x F D F F
D T
TD
T T T
T
F
ipt is for the ambient
and 0 the exit of the nozzle
5. 3c. Literature survey (approximated equations)
• Lee & Jirka (1981) have given a solution of Xe as a function of F0 for a stagnant uniform
waterbody of large horizontal extent. Xe increases rapidly from zero for F0 0, to an
asymptotic value of 5.74 for Fo greater than 25. This is somewhat smaller than the value of 6.2
determined by Anderson et al. (1950).
2 2 2 2
2 3
2
e
2 4 2
0
e / , the ZFE length normalized around the diameter
0.109, jet spreading angle
1.14, ratio of temperature diffus
4 (1 ) 1
1 , where
12 12 3 8
ion thickness to moλ
π λ λ λ
λ
+
+ + + =
=
=
=
e
e e
e
X є є
X X
x D
F
X
є
є X
mentum diffusion thickness
• According to Jirka (2004) the ZFE length is measured from a linear spread of the shear layer
and estimated about 6.2 D, based on velocity profiles, or about 5D, based on scalar profiles,
due to the typical dispersion ratio, λ > 1 . This fundamental result is generalized for cross-
flow effects using the empirical approach of Schatzmann (1978), and for buoyancy effects
through model formulation by Lee & Jirka (1981). They suggest
( ) ( )02.0( ) 1 2 20
e 0 0 0
a
/ 4.67
0 ,the angle measured counterclockwise from the ambient current direction
to the plane projection of the orifice
sin γ
5 1 3.22 1 e , where γ
ce
sin 1 cos θ sin σ with
/
n
σ
− −
= − − = −
F
x D
V u
0
terline and
,the angle between the orifice centerline and the horizontal plane.θ
( )0 /2. 4.0
e
6
a
7
Note that for 0 : 5 1 e−
= = − F
u x D
6. 4. Experimental set-up
An experiment using planar laser-induced fluorescence (PLIF) visualization is set at the
laboratory of Applied Hydraulics of the NTUA in order to determine the geometric
characteristics (intrusion length and shape) of the core. The experiment is set-up as follows:
• A jet is heated (buoyant) and dyed with a
rhodamine 6G (R6G) substance and then exits
from a nozzle of diameter D to ambient water
of lower temperature.
• A DPSS 1 W laser beam, at 532 nm
wavelength (green), is converted to a thin
laser light sheet via a rotating prism mirror
(at 20 kHz). R6G emits 556 nm light (yellow)
when excited by the 532 nm light making
visualization possible.
• A high resolution video-camera is then used
to videotape the flow field. In this manner,
the light intensity of R6G (measured through
the RGB 8bit frame format of the camera) can
be converted to concentration.
Figure 2: PLIF experimental set-up (NTUA, Laboratory of
Hydraulics)
The camera is set at the plane of symmetry of the jet, at a distance of at least 0.75×D meters from
the nozzle, so as to achieve a window-view height greater than 10 diameters. The width of the
window is chosen to be at least 3 diameters long to capture the jet expansion (at an angle of 12o-
15o with respect to jet axis). Each video lasts around 25 sec, and is recorded at 12 frames per
second (fps), so as to achieve stationarity.
7. 5. Calibration
The initial fluorescence light intensity Io can be assumed to be proportional to the R6G initial
concentration Co for values less than 50 μg/l (Ferrier et al., 1993). A decrease in power and light
intensity occurs as the laser beam enters the water tank and travels through the dyed jet. For this
range of concentrations and over a small path length (of order of 1 cm), the power attenuation
can be assumed to be negligible (Walker, 1987). Thus, only the light intensity attenuation factor is
taken into account and the raw data are modified according to Walker (1987) formula :
Ιη
η η ε
η ε
−∑= = +ix
o I Iw I
i
Iw I
I(x) I e C,
x i i
, with where
is the distance the laser beam travels through water (from pixel -1 to ),
and are the laser beam attenuation coefficients through water and R6G, repsectively.
Figure 3: Light intensity attenuation factor, where εΙ is the
slope (3.1 10-5) and ηΙw the intercept (4.7 10-4) of the trendline.
Measurements within an adequate range (1-60
μg/l) of concentration intensities (fully mixed
into the water tank) are made in order to
determine the attenuation coefficients εΙ and
ηΙw (as shown in figure 3).
The red intensity of the RGB color format and
a shutter speed (SS) of 50 msec are chosen as
the optima, based on image resolution and
data quality criteria.
The image scale Sc and lens’ distortion (pixel
size variation along height) are estimated from
a ruler placed on the nozzle. The average value
of Sc is considered as it only varies ≈2%.
ηI = 3.1E-5 Co + 4.7E-4
R² = 1.0
4.0E-04
8.0E-04
1.2E-03
1.6E-03
2.0E-03
2.4E-03
0 10 20 30 40 50 60
AttenuationfactorηI
Initial Concentration Co (μg/L)
8. 6. Data processing
• Four jet diameters are tested (0.5, 1, 1.5 and 2 cm) for a range of initial discharges (Q) 5 to 40
cm3/s (±0.85 cm3/s) with Reynolds numbers Re = 102 ÷104 and Froude numbers F0 = 1÷200.
• Flow instabilities occurring within the ZFE may result in a non axisymmetric jet:
a) Noise from the camera (estimated via recording with the camera lens covered), background
noise (estimated via recording with no jet discharge) and noise from slow motion of ambient
water (observed from suspended particles) is estimated to be less than 1% (fig. 6).
b)A fountain-like periodic movement of the core is observed within the ZFE.
• The length and shape of the core are estimated through the absence of turbulent intensity
fluctuations rather than the presence of a constant initial jet concentration. This is achieved by
the standard deviation image rather than the mean or the instantaneous one. Image and data
processing are done using MATLAB®.
Figure 4: Instantaneous, time-averaged and RMS images (green and gray images, left). Normalized mean and standard
deviation distributions with their maximum values (middle and right figure, respectively) at a distance of 2 cm (within the
ZFE), 5 cm (around the end of ZFE) and 10 cm (outside the ZFE) from the nozzle.
9. 7. Experiments performed
Here, the initial conditions of the conducted experiments as well as the measured xe, are
presented.
10. 8a. Experimental results (geometrical ZFE shape)
Figure 5: Outer limits (red color line) of the ZFE in an instantaneous (left), time-averaged (middle) and RMS (right) images
(here, the inner line is shown as well). These images are taken from the 3rd experiment (D=1.5 cm). Scale is 1:2.
The outline limit of the ZFE is shown below. The geometrical shape of the ZFE is close to a
conical one (for the instantaneous and time-averaged images) and to a ballistic one (for the RMS
image). One can observe from the RMS image, that flow fluctuation (turbulence) is initiated at
jet nozzle elevation. This is not easy to observe from the two other images, therefore one can
erroneously claim that transition to turbulence occurs at higher elevations.
Asymmetricalaxis
≈12o from
the jet-axis
≈15o from
the jet-axis
11. 8b. Experimental results (ZFE length)
The mean and standard deviation distributions of the concentration along the jet-axis are shown
below. The mean concentration should be constant within the ZFE but here is rising probably
due to the fact that the initial concentration of R6G (≈50μg/l) is high for the laser to pass through
in a small area around the nozzle. Also, the distributions of the standard deviation do not show a
successive decrease. This is because they are normalized with the maximum standard deviation
observed within the ZFE which varied (measured 30 to 45% of the Cm,o).
Figure 6: Mean Cm (left) and standard deviation Cst (right) distributions (normalized with their maximum values Cmo and
Cst,max, respectively) along the jet-axis, from the 1st experiment (D=0.5 cm). For Li see section 7.
Probably some
dirt/scratches on the
water-tank glass.
xe,m
xe,smin
xe,smax
Noise ≈ 1%
12. 8c. Experimental results (graphs)
Figure 7: Measurements of the ZFE length versus Reynolds number taken from the experiments described above. Only
values of green and yellow (symbolized with ^) labels are presented.
Graphs with all the measured ZFE lengths are presented below. It is observed that as Re
increases, distance xe decreases (with the exception of xe,m and xe,smax of the 3rd experiment).
Also, the distances xe,smin and xe,smax seem to be anti-symmetrical with respect to xe,m.
13. 9. Conclusions
References
The main conclusions of this work are as follows:
• The RMS image is much clearer than the time-averaged one, concerning the ZFE outer limit.
• The ZFE, defined through maximum RMS, seems to have a ballistic geometrical shape. Also,
transition to turbulence seem to occur at the jet nozzle elevation.
• It is generally observed that as the Reynolds number increases, the ZFE length decreases.
• The present measurements of the ZFE are quite different than those proposed in earlier studies.
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Acknowledgements
We acknowledge the free, collaborative and multilingual Internet encyclopedia Wikipedia (supported by the non-profit
Wikimedia Foundation) for offering us some first scientific glances in several topics (from ISO notations to LIF techniques)
and thus, saving us valuable time.