R. 1. Adrian· D. F. G. Durao . F. Durst M. Maeda· 1. H.Whitelaw (Eds.)
Applications of Laser Techniques to Fluid Mechanics 5th International Symposium Lisbon, Portugal, 9-12 July, 1990
With 358 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Professor R. 1. Adrian University of Illinois Talbot Laboratory 216 104 Wright Street Urbana IL 61801 USA
Professor D. F. G. Durao Instituto SuperiorTecnico A v. Rovisco Pais Lisbon Portugal
Professor F. Durst University ofEriangen-Niirnberg Dept. of Fluid Mechanics CauerstraBe 4 8520 Erlangen Germany
Professor M. Maeda Keio University Mechanical Engineering Dept. 3-14-1 Hiyoshi Kohoko-ku Yokohama 223 Japan
Professor 1.Whitelaw Imperial College Mechanical Engineering Dept. Exhibition Road London SW7 2BX England
ISBN-13:978-3-642-64763-5 e- ISBN-13:978-3-642-61254-1 DOl: 10.1007/978-3-642-61254-1
Library of Congress Cataloging-in-Publication Data International Symposium on Applications of LaserTechniques to Fluid Mechanics (5th: 1990 : Calouste Gulbenkian Foundation) Applications of laser techniques to fluid mechanics 5th international symposium, Lisbon, Portugal, 9-12 July 19901 R. J. Adrian ... [et al.l. "Papers selected from the proceedings of the Fifth Internation Symposium on Applications of LaserTechniques to Fluid Mechanics, held at the Calouste Gulbenkian Foundation in Lisbon from 9 to 12 July 1990"--Pref. ISBN-13:978-3·M2-M763-5 I. Fluid dynamic measurements--Congresses. 2. Lasers--Congresses. I. Adrian, R.1. (Ronald 1.) TA357.5.M43I58 1990 681'.2--dc20 91-26951
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Preface
This volume consists of papers selected from the proceedings of the Fifth International Symposium on Applications of Laser Techniques to Fluid Mechanics, held at the Calouste Gulbenkian Foundation in Lisbon from 9 to 12 July, 1990. Relative to previous meetings in the Lisbon series the scope of this symposium was broadened by expanding the topical coverage to include all laser techniques used in fluid mechanics. This change recognized the trend amongst experimental fluid dynamicists to employ laser techniques for the mea­ surement of many different quantities, including concentration, temperature, particle size, and velocity, and the need for researchers to have a forum in which to communicate their work and share their common interests. The Fifth Symposium contained twenty-three sessions of formal presentations and a lively Open Forum ses­ sion. In addition, Dr. H. J. Pfeiffer organized a special Workshop on the Use of Computers in Flow Mea­ surements which contained five sessions on frequency domain processors, correIa tors, special detectors, and biasing.
The Editors of this volume were assisted in organizing the Symposium by members of an Advisory Committee, listed on the following page, whose valuable services as referees of abstracts and as chairmen of technical sessions are greatly appreciated. We are also grateful to the authors and to the other participants of the Symposium for the contributiQns they made. Financial support of the Symposium, which was essential to its success, was provided by the following organizations:
Centro de Termodinamica Aplicada e Mecanica dos Fluidos da Universidade Tecnica de Lisboa
Commission of the European Communities
Direccao Geral de Turismo
European Research Office: United States Army, Navy and Air Force
Fundacao Luso-Americana para 0 Desenvolvimento
Fundacao Calouste Gulbenkian
Instituto Superior Tecnico
Sociedade Estoril Sol, SARL
TAP-Air Portugal
The organization of this volume reflects coherent areas that were prominent at the symposium: scalar transport, two-phase flow, instrumentation, and whole field techniques. We wish to thank all of the authors for contributing their papers and for their efforts in preparing the manuscripts.
Urbana, April 1991 The Editors
Advisory Committee
A. Boutier, ONERA, Chantillon, France
V. Brederode, Instituto Superior Tecnico, Lisbon, Portugal
A. Coghe, CNPM-CNR, Milano, Italy
D. Dopheide, Physikalische-Techn. Bundesanstalt, Germany
L. E. Drain, Reading, England
R. V. Edwards, Case Western Reserve University, OR, USA
H. Eickhoff, DRL, Koln, Germany
M. P. Escudier, University of Liverpool, England
A. F. de O. Falcao, Instituto Superior Tecnico, Lisbon, Portugal
L. M. Fingerson, TSI, Inc., MN, USA
G. Gouesbet, Laboratoire de Thermod., Universite de Rouen, France
K. Hanjalic, University of Sarajevo, Yugoslavia
M. V. Heitor, Instituto Superior Wcnico, Lisbon, Portugal
D. Hirleman, Arizona State University, AZ, USA
J. A. C. Humphrey, University of California, Berkeley, USA
R. Karlsson, Swedish State Power Board, Alvkarleby, Sweden
L. Lading, Danish Atomic Energy Research, Riso, Denmark
B. Lehmann, DLR, Berlin, Germany
A. Melling, A VL-LIST, Graz, Austria
W. Merzkirch, Universitat Essen, Germany
J. F. Meyers, NASA-Langley Research Center, V A, USA
A. Muller, Eidgnossiche Technische Hochschule, Zurich, Switzerland
N. Nakatani, Osaka University, Osaka, Japan
M. N. R. Nina, Instituto Superior Tecnico, Lisbon, Portugal
K. Ohba, Kansai University, Osaka, Japan
T. Obokata, Gunma University, Kiryu, Japan
J. C. F. Pereira, Instituto Superior Tecnico, Lisbon, Portugal
H. J. Pfeifer, Ins. Franco Allemand de Rech. de Saint-Louis, France
P. A. Pfund, Babcock & Wilcox, OH, USA
A. Restivo, Universidade do Porto, Porto, Portugal
W. C. Reynolds, Stanford University, CA, USA
M. L. Riethmuller, Von Karman Inst. Fl. Dyn., Rhode-St.-Genese, Belgium
R. L. Simpson, Virginia Polytechnic Inst. and State Univ " VA, USA
X. Shen, Tsinghua University, Beijing, China
W. L. Stevenson, Purdue University, IN, USA
N. S yred, University College, Cardiff, Wales
A. M. K. P. Taylor, Imperial College, London, England
C. Tropea, Universitat Erlangen, Erlangen, Germany
J. T. Turner, University of Manchester, England
C. Wigley, AVL-LIST, Graz, Austria
P. O. Witze, Sandia National Laboratories, CA, USA
Table of Contents
Planar Laser-Induced Fluorescence Scalar Measurements in a Turbulent Jet A. Lozano, I. J. van Cruyningen and R. K. Hanson .............................................................................. 19
Simultaneous Measurement of Velocity and Temperature of Water Using LDV and Fluorescence Technique T. Nakajima, M. Utsunomiya, Y. Ikeda and R. Matsumoto .................................................................. 34
Simultaneous, Real-Time Une Measurements of Concentration and Velocity in Turbulent Flows K. C. Muck, J. M. Wallace and W. M. Pitts .......................................................................................... 54
Digital Particle Image Thermometry and Its Application to a Heated Vortex-Ring D. DabiO and M. Gharib ......................................................................................................................... 81
Temperature Measurement in a Asymmetric Thermal Flow Field by Laser Holographic Interferometry S.-M. Tieng and H.-T. Chen ................................................................................................................. 102
Chapter II - TWO-PHASE FLOW, SIZE AND VELOCITY
LDA Measurements of Plastic and Elastic Collisions of Small Particles with Metal Surfaces S. R. Martin, T. M. Pinfold and G. R. Wallace-Sims .......................................................................... 125
The Influence of Swirl on the Particle Dispersion in a Pipe Expansion flow M. Sommerfeld, H.-H. Qiu and D. Koubaridis ...............................•.................................................... 142
flow Measurements in a Uquid Fuelled Burner D. F. G. Durao, M. V. Heitor and A. L. N. Moreira ........................................................................... 163
Fringe Count Umitations on the Accuracy of Velocity and Mass flux in Two-Phase flows Y. Hardalupas, A. M. K. P. Taylor and J. H. Whitelaw ...................................................................... 183
Measurement of Size and Velocity Distributions of Droplets Produced by Bubbles Bursting M. Ramirez De Santiago and C. Marvillet ........................................................................................... 203
Sensitivity of Dropsize Measurements by Phase Doppler Anemometry to Refractive Index Changes in Combusting Fuel Sprays G. Pitcher, G. Wigley and M. Saffman ................................................................................................ 227
LDA Measurement of Gasoline Droplet Velocities and Sizes at Intake-Valve Annular Passage in Steady flow State H. Kawazoe, K. Ohsawa and M. Kataoka ........................................................................................... 248
Measurement of Fuel Injector Spray flow of I. C. Engine by FFT Based Phase Doppler Anemometer - An Approach to the Time Series Measurement of Size and Velocity K. Kobashi, K. Hishida and M. Maeda ................................................................................................ 268
VIII
Improved Optical Systems for Velocimetry and Particle Sizing Using Semiconductor Lasers and Detectors J. Domnick. F. Durst. R. Miiller and A. Naqwi ........•.........................••••............................................. 317
A Photothermal Velocimeter Using an Optical Fibre Heterndyne Interferometer with Phase Differentiation at Two Points N. Nakatani. T. Oshio, J. Inagaki, T. Kataoka and K. Kishida ....•••.....•..•..••.•..................................... 331
rvg~~~~£at~:':n~\~ U~~~.~~.~~~~~~.~~ ................................................................ 347
Velocity Measurement Using Fibre Optic Sagnac Interferometers R. McBride. D. Harvey. J. S. Barton and J. D. C. Jones .........•.......................................................... 364
~~~hl~.oa~t~~.~~~u:~~~~~~¥~~: ~.~~.~~~.~.~~~~.~.~~.~~~.~~~~~~ ............. 385
An Experimental Evaluation of a Novel Method of Using Localized Laser Heating in the Determination of Wall Shear Stress W. E. Carscallen, P. H. Oosthuizen and F. J. Arthur ...................................•••.................................... 400
Chapter IY - WHOLE-HELD VELOCIMETRY
Application of Particle Image Velocimetry to Transonic Hows R. Hocker and J. Kompenhans ............................................................................................................. 415
Studies of Liquid Turbulence Using Double-Pulsed Particle Correlation R. J. Adrian. P. W. Offutt. T. J. Hanratty. z.-c. Liu and C. C. Landreth ................................................................................................................................ 435
Turbulent Intensity Evaluation with PlY A. Cenedese. G. Palmieri and G. P. Romano ...................................................................................... 451
Instantaneous Particle Image Velocimetry with Electronic Speck1egram E. Okada. H. Enomoto. Y. Fukuoka and H. Minamitani ..................................................................... 464
Measurement of Dynamics of Coherent How Structures Using Particle Image Velocimetry J. Westerweel, F. T. M. Nieuwstadt and 1. B. Hor ................................................................................ .476
Two-Phase How Velocity Measurements Using Automated-Based Imaging Pulsed Laser Velocimctry Y. Hassan and T. Blanchat ................................................................................................................... 500
Mixing How in a Cylindrical Vessel Agitated by a Bubbling Jet -Application ofImage Processing Velocimetry T. Uemura. K. Ohmi and F. Yamamoto ............................................................................................... 521
Visualization and Measurement of Detailed Velocity Field in U-Bend and Branched Tube Using Laser-Induced fluorescence Method K. Ohba. A. Sakurai. M. Sato and S. Sakaguchi ................................................................................. 537
Photobleaching flow Visualization K. F. Sollows. C. R. Dutcher, A. C. M. Sousa and J. E. S. Venart .................................................... 553
Scalar Transport
Werner J.A. Dahm, Kenneth B. Southerland and Kenneth A. Euch
Department of Aerospace Engineering The University of Michigan Ann Arbor, Michigan, USA
Abstract
We deal with conserved scalar mixing in turbulent flows, and present a newly developed laser imaging diagnostic for obtaining highly detailed, four-dimensional measurements of the full space and time varying conserved scalar field S(x,t) and tbe associated scalar energy dissipation rate field VS· VS(x,t) in a turbulent flow. The method is based on high-speed, high-resolution, successive planar laser induced fluorescence imaging of a synchronized raster swept laser beam, combined with high-speed data acquisition of gigabyte-sized data sets using very fast computer disk ranks. The measurement resolution reaches down to the local strain-limited molecular diffusion scale in the flow, so tbat the resulting four-dimensional data are directly dif­ ferentiable in all three space dimensions and in time. These data spaces are numerically ana­ lyzed to determine the time evolution of all three components of the instantaneous scalar gradi­ ent vector field VS(x,t) and the resulting instantaneous scalar energy dissipation rate field. Typical results are presented in the form of spatial sequences of adjacent two-dimensional data planes within a particular three-dimensional data volume, as well as temporal sequences of spa­ tial data planes from three-dimensional data volumes acquired successively in time, allowing the evolution of the true scalar dissipation rate to be examined in detail throughout the four­ dimensional data space.
Introduction
The problem of mixing of conserved scalar quantities in turbulent flows can be formally posed
in terms of a conserved scalar field S(x,t) which satisfies the advection-diffusion equation
[i.+U.V-_1_V2]S(X,t) = o. at ReSc (1)
The associated scalar energy per unit mass 1/2S2(x,t), defined analogous to the kinetic energy
per unit mass 1/2U2(x,t), where u == lui, can then be shown from Eq. (1) to follow the exact
transport equation
(2)
4
in which the instantaneous rate of scalar energy dissipation per unit mass (ReSc)-l V~· V~(x,t)
gives the rate at which non-uniformities in the scalar energy field are reduced by molecular dif­
fusion at any point in the flow. In this sense, the scalar dissipation field V~·V~(x,t) gives the
local instantaneous rate of molecular mixing in the flow. Sometimes the scalar gradient magni­
tude I V~(x,t) I is adopted as an alternative definition for the local instantaneous molecular mix­
ing rate, though in terms of the logarithm of the mixing rate field these two definitions of course
differ only by a constant scale factor.
In the context of the above discussion, the structure of the scalar energy dissipation rate field in
turbulent flows is of direct interest in problems involving the mixing of dynamically passive
scalar quantities in such flows. However, even in chemically reacting turbulent flows, under
certain conditions simultaneous measurements of the conserved scalar field ~(x,t) and the asso­
ciated scalar energy dissipation rate field V ~. V ~(x,t) allow determination of the structure of the
chemical reaction rate field using a formulation first noted by Bilger (1976). In particular, the
mass fraction of any chemical species Y follows an advection-diffusion-reaction equation of the
form
(3)
where w.<x,t) is the local instantaneous reaction rate field of species i, and where ReSc is the
temperature dependent diffusivity of this species. If the relevant chemical reaction time scales
involved in Wi(X,t) are sufficiently short in comparison with the local fluid dynamic time scales
of the flow, so that the relevant forward and backward reactions involving Y i remain essentially
in equilibrium, then Y i can be related to an appropriately defined conserved scalar quantity (e.g.
the fuel atom mixture fraction) as Yi(x,t) = Y i elJ[ ~(x,t)]. In that case, Eq. (3) yields
-' -+u·V-V·--V C(x,t) - --VC·VC(x,t) -'- = w(x,t). {( dYeq )[ a I]} { 1 (d2y
e Q )}
dC at ReSci ReSci dC2 ' (4)
If, furthermore, the diffusivities of the scalar ~ and the species i are the same, then from Eq. (1)
the first term on the left in Eq. (4) will vanish. The reaction rate field Wi(X,t) is then given by
1 (d2y e
ReSc dC (5)
namely as the product of the instantaneous scalar dissipation rate fieldV~·V~(x,t) and the sec­
ond derivative of the equilibrium relation evaluated at the local instantaneous scalar value ~(x, t).
Correspondingly, the concepts of scalar energy and its dissipation rate playa central role in
many approaches for understanding and modeling both molecular mixing and chemical reac­
tions in turbulent flows. However, direct measurements of instantaneous scalar dissipation rate
5
fields in turbulent flows have been difficult to obtain. This has been principally due to two ob­
stacles. First, detennination of the true scalar gradient vector field VC(x,t) and the associated
scalar energy dissipation rate field V~· V~(x,t) requires measurement of the conserved scalar
field C(x,t) in all three spatial dimensions. Second, since the dissipation rate is obtained by dif -
ferentiation of the measured conserved scalar field, the spatial and temporal resolution of the
original scalar measurements must be high enough to accurately resolve the fillest local scales
on which spatial gradients in the scalar field are present in the flow. Beyond this, the signal
quality of the original scalar field measurements must also be high enough to allow accurate dif­
ferentiation to determine the scalar dissipation rate field.
Previous Work
A number of different approaches have been used in recent years to obtain accurate measure­
ments of conserved scalar fields in turbulent flows. Almost all of these have made use of vari-
0us planar laser imaging techniques; a good review of many of these is given by Hanson
(1986). Relevant to the present work, Long & Chu (1981) and Escoda & Long (1983) ad­
dressed the relatively simple large scale features in the transition region of a turbulent jet using
single-plane two-dimensional laser imaging measurements. In a similar laser imaging effort
aimed at obtaining the additional information in a third dimension from such measurements,
Fourguette & Long (1983) and Yip, Long & Fourguette (1986) used acoustic excitation to pro­
duce a phase-locked flow which could then be selectively advanced either in space or in time.
Bowman, Lewis, Cantwell & Vandsburger (1988) have used a similar forcing technique in con­
junction with laser imaging to examine large scale mixing in the near field vortical structures of
an excited jet. This technique of artificially phase-locking the large structures in the jet transi­
tion region has also been used by Kychakoff, Paul, Cruyingen & Hanson (1987) to obtain
three-dimensional measurements in a topologically simple forced flow. Also of relevance here,
Hesselink et al (1983) and Agiii & Hesselink (1988) have digitized cine frames obtained with a
rapidly swept laser sheet to obtain qualitative three-dimensional visualizations of the coarse
structure of isoscalar surfaces in the transition region of a coflowing turbulent jet.
These previous measurements have all been primarily aimed at the topologically simple large
scale features of transitional flows. The spatial and temporal resolution achieved in them has
not been adequate to resolve the fine scale structure of the conserved scalar fields typical of fully
developed turbulent flows. As a result, while such measurements have produced useful infor­
mation about the largest flow scales, they have been unable to yield information with sufficient
resolution to allow accurate detennination of the scalar gradient field and the resulting molecular
mixing process in turbulent flows. Yip & Long (1986) have attempted to extend their measure­
ments based on two-dimensional planar laser imaging to yield three-dimensional scalar gradient
6
infonnation by imaging from two parallel and closely spaced laser sheets. However, both the
sheet spacing and the pixel separation were significantly larger than the local molecular diffu­
sion scale in the flow. Following a somewhat different approach, Yip, Lam, Winter & Long
(1987) and Yip, Schmitt & Long (1988) have swept a laser sheet at very high speed through a
turbulent flow, in conjunction with very high speed image acquisition over a short duration, to
obtain measurements in up to 16 closely spaced parallel planes. Nevertheless, even in these
measurements the resolution was sufficient only to yield data at comparatively coarse scales of
the flow.
Present Work
Here we present a laser imaging diagnostic for obtaining highly detailed, four-dimensional mea­
surements of the full space- and time-varying conserved scalar field t,;(x,t) and the associated
scalar energy dissipation rate field in turbulent flows. The method is based on high-speed, high-
Two-Dimensional Data Planes
Three-Dimensional Data Volumes
Four-Dimensional Data Space
..........
<% ", ...--.--
Fig. 1. Structure of the four-dimensional conserved scalar data space t,;ex,t) as a temporal progression of three-dimensional spatial data volumes, each consisting of a sequence of two­ dimensional spatial data planes, each of which consists of a 256 x 256 array of data points. The spatial and temporal resolution achieved is sufficient to allow direct differentiation of the conserved scalar data in all three space dimensions and in time, allowing the evolution of the true molecular mixing rate field Vt,;· Vt,;(x,t) to be directly determined.
7
resolution, successive planar laser induced fluorescence imaging of a synchronized raster swept
laser beam, combined with high-speed data acquisition of gigabyte sized data sets using very
large fast computer disk ranks, to produce a four-dimensional data space structured as shown in
Figure 1. Each such measured spatio-temporal data space consists of a rapid progression of
individual three-dimensional spatial data volumes, each of which is composed of a sequence of
two-dimensional spatial data planes, each consisting of an array of 256 x 256 individual data
points. The spatial separations between adjacent points within each data plane, and also be­
tween the adjacent data planes within each data volume, are smaller than the local molecular dif­
fusion scale in the flow. Similarly, the temporal separation between adjacent data planes within
each data volume, and between the same data plane in successive data volumes, are shorter than
the local molecular diffusion scale advection time. This resolution, together with the high signal
quality attained, allows accurate differentiation of the measured conserved scalar data in all three
space dimensions and in time. The resulting four-dimensional data volumes are then numerical­
ly analyzed to determine the evolution of all three components of the instantaneous scalar gradi­
ent vector field V~(x,t) and the resulting true instantaneous scalar energy dissipation rate field
V~·V~(x,t). Here we concentrate principally on describing the technique we have developed
for acquiring such four-dimensional measurements. A technical discussion of results pertinent
to mixing in turbulent flows, obtained from these four-dimensional measurements, is given by
Dahm, Southerland & Buch (1990).
Measurement Technique
The technique used and the measurements obtained are an extension of our earlier work (Dahm
& Buch 1989, 1991) in developing very high resolution three-dimensional (2563) spatio-tempo­
ral measurements of the conserved scalar concentration field and the resulting scalar energy dis­
sipation rate field in turbulent flows. The present measurements are also based on successive
high-speed planar laser induced fluorescence imaging in the self-similar far field of a turbulent
shear flow in water. The mixture fraction, in this case determined by the concentration of a pas­
sive laser fluorescent dye (disodium fluorescein) carried by one of the fluids, is a conserved
scalar in the flow. Here this mixture fraction is measured repeatedly in time throughout a small
three-dimensional volume in the flow by imaging the laser induced fluorescence from dye-con­
taining fluid in the path of a laser beam rapidly swept through the volume onto a planar photodi­
ode array. The conserved scalar field ~(x,t) can then be obtained from the measured
fluorescence intensity through a simple transfer function and attenuation integral as described by
Dahm & Buch (1989).
Key elements of the imaging and data acquisition system assembled for these four-dimensional
measurements are shown schematically in Figure 2. A pair of very low inertia, galvanometric
8
mirror scanners are used to synchronously sweep a collimated laser beam in a raster scan fash­
ion through the desired volume in the flow field. The horizontal and vertical sweep angles are
typically quite small (1'}h = 0.125° and 1'}v = 4.26° for the results presented here). The resulting
laser induced fluorescence intensity is measured with a 256 x 256 imaging array, having a cen­
ter-to-center pixel spacing of 40 ~m. The array is synchronized to the same clock that drives
the scanners, and is driven at variable pixel rates up to 11 MHz, allowing measurement of suc­
cessive data planes at a continuous rate in excess of 140 planes per second. The fluorescence
data from the array is serially acquired through a programmable digital port interface, digitized
to 8-bits digital depth, then ported into a 16 MB high-speed, dual-ported data buffer from which
it is continuously written in real time to a 3.1 gigabyte high-speed parallel transfer disk rank.
The overall sustained data throughput rate to the disks, deducting all the line and frame overhead
1--.... ------------
781MB ....
781MB .... 781MB .... 781MB ....
Fig. 2. Key elements of the high-speed, variable-rate (non RS-170) imaging and data acquisition system for obtaining highly-resolved, four-dimensional, laser induced fluorescence measurements of conserved scalar mixing in turbulent flows. Two low-inertia galvanometric laser beam scanners are slaved to the imaging array timing as outlined in Fig. 3 to rapidly sweep the beam in a successive raster fashion through the flow field. The data acquisition system can achieve a sustained throughput rate to the disk bank of up to 9.3 MB/sec for data volumes as large as the full 3.1 GB disk capacity.
9
FEN
~ MMCLK
mil
Fig. 3. Schematic overview of the drive and timing electronics for the two laser beam scanners. Each successive vertical sweep of the beam scans through one spatial data plane, while each successive sweep of the horizontal scanner corresponds to one spatial data volume. Acquisition of the data occurs while frame enable (FEN) from the imaging array is high. The scanners are in turn slaved to the imaging array by triggering each of their driver waveforms with the rising edge of FEN and its N z-period filtered version (FEN/Nz). To accomodate the minimum scanner flyback times, the master clock (MCLK) is temporarily expanded when FEN is low.
cycles, is up to 9.3 MB/sec. The 3.1 GB disk capacity can accommodate more than 50,000
such measured 256 x 256 spatial data planes within the four-dimensional data space.
Programmable gain and offset on the digital port interface allow the resulting data to span the
full 8-bits of digital depth. The rms noise levels achieved are in all cases less than ± 1 digital
signal level out of the 256 levels spanned by the scalar measurements.
Figure 3 shows the timing arrangement used to synchronize the scanners with the imaging
array. Aside from obvious synchronization objectives, the principal concern involves accom­
modating the minimum flyback times for the scanners within the frame overhead cycles between
acquisition of successive data planes, so that each plane will correspond to a single sweep of the
beam. Briefly, data acquisition proceeds while frame enable (FEN) from the imaging array is
high. FEN goes low during the frame overhead time (nominally 4 line times), which at these
clock rates is too short to complete the beam flyback. This requires modifying the original
master clock (MCLK) so that, while FEN is low, the clock period is expanded as required for
10
the frame overhead time to match the minimum flyback time. This modified master clock
(MMCLK) then drives both the imaging array and the AID converter. The resulting FEN and
(FENIN) then respectively drive the vertical (fast) and horizontal (slow) mirror scanners by re­
peatedly triggering an appropriate ramp waveform for each.
Spatial and Temporal Resolution
Since the principal interest in these measurements is in obtaining the scalar dissipation field
from the measured conserved scalar field via direct differentiation of the data, the central issue is
the spatial and temporal resolution achieved by the measurements. From the measured thick­
ness of the imaged portion of the laser beam, together with the pixel size and the image ratio of
the measurements, the volume in the flow (~·~y·~z) imaged onto each pixel can be deter­
mined. Furthermore, for the pixel clock rates used, the time ~t between acquisition of succes -
sive data planes within each spatial data volume, and the time ~T between the same data plane
in successive data volumes, can also be determined.
To assess the resulting relative resolution achieved, these smallest spatial and temporal scales
discernible in the data must be compared with the finest local spatial and temporal scales on
which gradients in the conserved scalar field can be sustained in the flow. For diffusion of vor­
ticity in the presence of a time-varying strain rate a(t), the competing effects of strain and diffu­
sion establish an equilibrium strain-limited vorticity diffusion layer thickness Av - (via) 1/2,
closely related to the Kolmogorov scale, giving the finest scale on which spatial gradients in the
strain rate and vorticity fields can be locally sustained in the flow (e.g. Burgers 1948; Corcos
and Sherman 1984). A similar competition between the effects of strain and molecular diffu­
sion of the conserved scalar establishes a local strain-limited molecular diffusion layer thickness
AD - (5)la) 1/2, related to the Batchelor scale and giving the smallest scale on which spatial gra­
dients in the conserved scalar field can be sustained by the flow (e.g. Carrier, Fendell and
Marble 1975; Marble 1985). The ratio of the vorticity and scalar diffusivities, v and D respec­
tively, establishes the relation between these two scales as AD - Av·Sc-1/2, where Sc :; (vID) is
the Schmidt number and, due to the similarity of the two strain-diffusion equilibrium processes,
the proportionality constant should be approximately one. Note that with the highest strain rates
occurring locally in the flow scaling as a - (u/o)·Re 1/2, the strain-limited diffusion scale in the
conserved scalar field is (ArJO) - Sc -1/2 Re-3/4• Measurements by Dowling (1988) give indica­
tions that the resulting proportionality constant is roughly 25. Here Re :; uO/V is the local
Reynolds number of the shear flow, with o(x) and u(x) denoting the local length and velocity
scales which characterize the shear at that stage in the flow.
The resolution requirements that ~x, ~y and ~z must be small compared to AD to allow differ­
entiation in all three space directions within each three-dimensional spatial data volume, and that
11
the time ~ T between the same data plane in successive data volumes must be small in compari­
son with Ar/U to allow differentiation in time between successive data volumes, ultimately place
a limit on the highest Reynolds numbers at which such fully-resolved four-dimensional mea­
surements are possible. Note that while the resolution ~ and ~y within each spatial data plane
can in principle be made very small by simply reducing the image ratio, the resolution ~z is
nominally determined by the laser beam thickness, and there are clear limitations associated with
the Rayleigh range of the laser beam which determine how fme this can be made over the entire
extent of the image volume. In general, the resulting minimum laser beam thickness is signifi­
candy larger than the desired spatial separation between successive data planes. However, if
the time ~t between successive planes is small enough so that the scalar field is effectively
frozen, as is the case in all of our measurements, then the overlap in the measured scalar field
between adjacent planes represents a convolution of the true scalar field with the laser beanl pro­
file, as indicated in Figure 4. The measured scalar field can then be deconvolved with the mea­
sured beam profile shape to produce an effective resolution ~z comparable to the spatial separa­
tion between adjacent data planes, which is set by the horizontal scanner and can in principle be
made arbitrarily small. In the measurements presented here, significant overlap extends only to
the next adjacent data plane on either side of each plane, so that the effect of this deconvolution
is noticeable but relatively small.
~PI
~b-l ~P2 ~I ~2 =
b = 1. beam thickness ~pn gnl ~ ~n e
Fig. 4. Schematic showing deconvolution of the measured conserved scalar field between overlapping parallel adjacent spatial data planes to reduce the laser beam thickness resolution limitation, thereby producing an effective z-resolution within each spatial data volume that is comparable to the interplane separation distance, which can be controlled by the scanner driver.
12
From the resulting discrete deconvolved scalar field values in the four-dimensional data space
~ijk1 == ~(Xi,y.rZ",tl)' the scalar energy dissipation rate field (V~.V~)ijk1 is then obtained by direct
differentiation of the data using linear central difference approximations. While any particular
choice for the local x-y-z coordinate frame at each point in the volume would make use of only
6 of the 26 scalar values surrounding that point, including other coordinate orientations involves
the scalar information at up to all 26 of the surrounding points. Here the scalar dissipation at
each point ijkl is computed as shown in Figure 5.
Figure 5. Scalar dissipation algorithm for computing V~· V~(x,t) at any point (i,j,k) from the measured conserved scalar field ~(x,t). Here the values of the dissipation obtained in each of four coordinate orientations achieved by ro­ tations in the (x-y) and (x-z) planes are equally weighted, with no particu­ lar orientation being preferred.
Example Measurement
As an example, we present here results for the conserved scalar and resulting scalar dissipation
rate fields in the self-similar far field (x/d = 235) of an axisymmetric turbulent jet at R e = 6,000.
In this relatively simple case, the four-dimensional data space consisted of 50 successive three­
dimensional spatial data volumes, each consisting of 5 parallel spatial data planes. The (lIe)
laser beam thickness was measured as 380 !lm, while the resolution ~z between spatial data
planes was 220 !lm. With an image ratio of 2.89, the in-plane resolution was ~x = ~y = 116
!lm. These values can be compared with the strain-limited diffusion scale estimate of AD'" 407
13
o 0.8 1.6
Fig. 6. The measured Sc » 1 conserved scalar field ~(x,t) in three typical adjacent 256 x 256 spatial data planes (x,y) from a typical three-dimensional spatial data volume (x,y,z) from a measured four· dimensional data space (x,y,z,t). The measurements shown were obtained at Re = 6,000 in the fully­ developed self-similar far field (x/d = 235) of an axisymmetric turbulent jet The scale indicates the spatial extent of the data relative to}v The 256 different colors identify the local 8-bit value of the measured scalar field, with the color bar giving the conserved scalar values relative to the local mean value ~m. The three spatial data planes are shown in order of increasing Z (and therefore increasing t) in the clockwise direction, beginning at the upper left. The spatial resolution (fu(, liy) within each data plane and (liz) between adjacent data planes, as well as the temporal resolution between adjacent three-dimensional data volumes, is sufficiently fine relative to the local strain-limited molecular diffusion scale estimate to allow accurate differentiation of the data in all three spatial dimensions and in time. This allows determination of the true local instantaneous scalar energy dissipation rate field V~· V~(x,t) in Eqs. (1) and (2) through the four-dimensional data space, as shown in Fig. 7.
14
I-lm. Note that the resulting pixel image volume was nearly 23 times smaller than the estimated
local strain-limited molecular diffusion volume A.D3, with its maximum dimension nearly 2
times smaller than A.D. Similarly, the time between successive data planes was Llt = 9.0 msec
while the time lapse between the same data plane in successive data volumes was LlT = 45
msec, both of which are significantly less than the estimated local diffusion scale passage time
(A.rlu) '" 100 msec.
Figure 6 shows the 8-bit conserved scalar data in three typical parallel adjacent 256 x 256 spa­
tial data planes from the same data volume. The color levels denote the local conserved scalar
value ~(x,t) at each point, with pure blue corresponding to pure ambient fluid and increasing
uniformly to pure red, corresponding to the highest scalar values in the data. Note that, for the
conditions in this particular measurement, the data planes shown span approximately 1/17 of the
local flow width o(x) in each direction. This suggests that the fine scale mixing process seen
within the measured data space will likely display features that are generic to mixing in turbulent
shear flows in general, and not specific to just this one particular flow. In Figure 7 we show
the true scalar dissipation rate field loge V~· V~(x,t) obtained from the data in the three adjacent
scalar planes in Figure 6, where the logarithmic form is used simply to allow increased contrast
at low dissipation values. In this case, the 256 different color levels denote increasing values of
the mixing rate. The first level, colored black, denotes zero and very low mixing rates, while
the remaining levels range uniformly from pure blue through pure red and denote logarithmical­
ly increasing values of the local instantaneous scalar dissipation rate in the flow. To examine the
time evolution of the true molecular mixing rate field, Figure 8 shows the scalar dissipation rate
field in the same spatial data plane from four temporally successive three-dimensional data vol­
umes. Note that a technical discussion of some of the implications of results from these four­
dimensional measurements for the fine structure of mixing in turbulent flows is given by Dahm,
Southerland & Buch (1990).
While this ability to study the evolution of the mixing process is itself very insightful, perhaps
the most important difference between these four-dimensional data and the earlier three­
dimensional spatio-temporal data of Dahm & Buch (1989,1990) is the ability to include the
third component of the scalar gradient vector in forming the scalar dissipation rate field. In par­
ticular, in a two-dimensional approximation of the scalar dissipation, molecular diffusion layers
oriented largely parallel to the data plane are not discernible. By comparison, the three­
dimensional spatial nature of the present data should capture the complete topology of the dissi­
pation field. Notice also that in Figures 7 and 8, both isolated as well as interacting dissipation
layers can be seen. The earlier measurements of Dahm & Buch (1990) have shown that the in­
ternal structure of the isolated layers closely matches the self-similar solution for the evolution
15
(xf"A.y)
Fig. 7. The true scalar energy dissipation rate field loge VI;· VI;(x,t) in a typical spatial data plane, obtained by direct differentiation of the measured conserved scalar data I;(x,t) in the three adjacent spatial data planes shown in Fig. 6 using linear central difference approximations. The scales show the spatial extent of the plane, and the 256 different colors denote the numerical value of the logarithm of the local dissipation rate, as indicated on the color bat: The scalar dissipation field in this same data plane is shown in Fig. 8 at four successive time steps from the measured four-dimensional data space.
16
Fig. 8. The time evolution of the scalar energy dissipation rate field vt;· vt;(x,t) in a typical spatial data plane, showing the same plane as in Fig. 7 but from four temporally successive data volumes. Time increases in the clockwise direction, beginning at the upper left. Data such as these allow detailed examination of the molecular mixing process within the four-dimensional data space.
17
of a strained laminar diffusion layer in a spatially uniform (though possibly time-varying) strain
rate field. Gradients in the strain rate field should occur on the scale Ay on which gradients in
the vorticity field can be sustained. Since this is a factor of Sc 1/2 larger than the diffusion layer
thickness scale, at large values of Sc, as is the case here, the strain rate would be expected to be
uniform over regions of the order of the diffusion layer thickness. As a result, in retrospect it is
not entirely surprising that the uniform strain solution accurately describes the structure of these
layers. This also suggests that at least the isolated layers in such turbulent mixing problems
may be amenable to a relatively simple type of modeling. The issue of how much of the mixing
occurs in isolated layers versus interacting layers is still an important open question, and this
too can in principle be addressed from data such as these.
Conclusions
A laser imaging technique for obtaining fully-resolved four-dimensional measurements of con­
served scalar mixing in turbulent flows has been developed. Such measurements produce a
four-dimensional spatio-temporal data space within which the conserved scalar field ~(x,t) is di­
rectly differentiable in all three spatial dimensions and in time, allowing the detailed fine struc­
ture of the scalar gradient field V~(x,t) and the scalar energy dissipation rate field V~· V~(x,t) to
be investigated. The resulting scalar dissipation field structure shows that the molecular mixing
in turbulent flows occurs in thin strained laminar diffusion layers.
Acknowledgements
We are grateful to Gerry Faeth for originally suggesting the deconvolution approach for increasing the cross-plane spatial resolution. The work presented here is supported, in part, by the Air Force Office of Scientific Research (AFOSR) under AFOSR Grant No. 89-0541, by the Gas Research Institute (GRI) under Contract No. 5087-260-1443, and with funds provided by The University of Michigan.
References
1. Agiil, J.C. & Hesselink, L. (1988) Flow visualization and numerical analysis of a coflow­ ing jet: a three-dimensional approach. f. Fluid Mech. 191, 19-45.
2. Bilger, R.W. (1976) Turbulent jet diffusion flames. Prog. Energy Comb. Sci. 1, 87.
3. Bowman, C.T., Lewis, G.S., Cantwell, B.J. & Vandsburger, U. (1988) An investigation of the structure of a laminar non-premixed flame in an unsteady vortical flow. Proc.22nd Inti. Symp. Comb., 515, The Combustion Institute.
4. Burgers, J.M. (1948) A mathematical model illustrating the theory of turbulence. Adv. Appi. Mech.l, 171-199.
18
5. Carrier, G.P., Fendell, F.E. & Marble, F.E. (1975) The effect of strain rate on diffusion flames. SIAM 1. Appl. Math. 28, 463-500.
6. Corcos, G.M. & Sherman, ES. (1976) Vorticity concentrations and the dynamics of un­ stable free shear layers. 1. Fluid Mech. 73, 241-264.
7. Corcos, G.M. & Sherman, F.S. (1984) The mixing layer: deterministic models of turbu­ lent flow. Part 1. Introduction and the two-dimensional flow. 1. Fluid Mech. 139, 29-65.
8. Dahm, W.J.A. & Buch, KA. (1989) High-resolution three-dimensional (2563) spatio­ temporal measurements of the conserved scalar field in turbulent shear flows. Proc. 7th Symp. on Turb. Shear Flows 1, 14.1.1 - 14.1.6; to appear in Turbulent Shear Flows 7, Springer Verlag, Berlin, 1990.
9. Dahm, W.J.A. & Buch, KA. (1991) Fine scale structure of conserved scalar mixing in turbulent flows. Part I: Sc » 1. To be submitted to 1. Fluid Mech.
10. Dahm, W.J.A. & Buch, KA. (1991) Fine scale structure of conserved scalar mixing in turbulent flows. Part II: Sc '" 1. To be submitted to 1. Fluid Mech.
11. Dahm, W.J.A., Southerland, KB. & Buch, KA. (1990) Direct, high-resolution, four­ dimensional measurements of Sc » 1 molecular mixing in turbulent flows. To appear in Phys. Fluids A 3 (5) Part 2, 1991; also in Proc. IUTAM Symp. on Fluid Mech. of Stirring and Mixing, August 20-24, 1990, DC (San Diego), La Jolla, CA.
12. Dowling, D.R. (1988) Mixing in gas phase turbulent jets. Ph.D. Thesis, Caltech, Pasadena, CA.
13. Escoda, M.e. & Long, M.B. (1983) Rayleigh scattering measurements of the gas concen­ tration field in turbulent jets. AIAA 121, 81.
14. Fourguette, D.e. & Long, M.B. (1983) Optics Letters 9, 270.
15. Hanson, R.K. (1986) Combustion diagnostics: planar imaging techniques. Proc. 21st IntI. Symp. Comb. 1677, The Combustion Institute.
16. Hesselink, L., Pender, J., Jaffey, S.M. & Dutta, K (1983) Proc. 3rd Inti. Symp on Flow Visualization, Ann Arbor, MI, Hemisphere.
17. Kychakoff, G., Paul, P.R., Cruyingen, 1. & Hanson, R.K (1987) Applied Optics 26, 2498.
18. Marble, EE. (1985) Growth of a diffusion flame in the field of a vortex. In Recent Advances in Aerospace Sciences (C. Casci, Ed.), 395, Plenum Press, New York.
19. Yip, B., Lam, J.K, Winter, M. & Long, M.B. (1987) Science 235, 1209.
20. Yip, B. & Long, M.B. (1986) Optics Letters 11, 64.
21. Yip, B., Long, M.B. & Fourguette, D.C. (1986) Applied Optics 25, 3919.
22. Yip, B., Schmitt, R.L. & Long, M.B. (1988) Optics Letters 13, 96.
Planar Laser-Induced Fluorescence Scalar Measurements in a Turbulent Jet
A. LOZANO, I. VAN CRUYNINGEN, P. DANEHY, AND R.K. HANSON
High Temperature Gasdynamics Laboratory Department of Mechanical Engineering Stanford University, Stanford, CA, 94305
ABSTRACT
The planar laser-induced fluorescence (PLIF) technique has been used to measure the concentration of a passive molecular tracer (biacetyl) in a turbulent axisymmetric nitrogen jet. The emitted light was recorded using two low noise, high dynamic range CCD cameras. The acquired images were corrected for experimental artifacts and statistically analyzed. Results are presented for mean concentration, RMS concentration fluctuations, scalar dissipation, and cross-section centered means.
INTRODUCTION
Planar laser-induced fluorescence is a very attractive technique for fluid diagnostics. It
is non-intrusive, instantaneous and can be used to determine different flowfield properties in a
plane without integration along the line of sight. It has been successfully applied to liquids
(Dimotakis et. al. [1]), non-reacting gaseous flows (Kychakoff et. al. [2]), and reacting flows
(Kychakoff et. al. [3]). Some examples of the measured fields are species concentration (Dyer
& Crosley [4]), temperature (Seitzman et. al. [5], Lee et. al. [6]), pressure and velocity (Hiller
& Hanson [7]).
In a typical PLIF experiment, the flow is illuminated by a laser sheet tuned to excite a
particular transition of a molecular tracer, which can be a species naturally occurring in the flow
(e.g. CH, OH, NO), or added for this purpose (e.g. biacetyl, 12, NO, fluorescein). A fraction of
the molecules in the appropriate lower energy level absorbs the incident light and is promoted
to a higher energy state. The excited molecules return to the equilibrium state either by emitting
photons or by transferring the excess of energy through nonradiative decay processes (e.g., col­
lisional quenching). The photons can be spontaneously emitted on short time scales (fluores­
cence), or on much longer time scales after a transition to a metastable electronic state (phos­
phorescence). As shown in van Cruyningen et. al. [8], for unsaturated excitation in an isother­
mal flow, the total light emission per unit sheet area, Ne, is given by formula (1), where
20
tion.
NeQ<-, y, V, t) =
{ Photons InCident} {Photons AbSOrbed} {Photons Emitted } per unit Height per unit Length per Photon Absorbed
{ Ni(y) e-u(v) fC(x,y)dx } {a(v)C(x,y) } {11s(V,t) }
Nb) is the number of photons per unit height incident in the flow.
a(v) is the absorption cross-section of the tracer in cm2;
C(x, y) is the absorbing species concentration in cm-3 in the lower energy level;
(1)
and lls(V, t) is the species 'quantum efficiency' or Stem-Vollmer factor for this transi-
Rayleigh scattering has been neglected as its cross-section is usually much smaller than
a. Below saturation the emitted light depends linearly on both the tracer concentration and the
incident laser energy. The images must be corrected for shot to shot laser energy variations if
quantitative inter-image comparisons are to be done.
For a solid-state camera system, the number of photons reaching each pixel is inversely
proportional to the square of the camera lens f# (assuming there is no other limiting aperture)
and is also inversely proportional to the magnification, m, squared. If the laser sheet fills the
whole field of view, for a fixed laser energy the incident light varies inversely with the sheet
height, and the signal levels scale as m/( 1 +m)2. Due to this dependence, when imaging large
flowfield regions the signal dynamic range is ultimately limited by the low light intensity per
pixel. Different aspects can be optimized in order to increase the recorded intensity:
• Increase the laser intensity crossing the flow
(for example double passing the light with a mirror).
·Select a high efficiency tracer.
·Decrease the system f#.
·Use a low noise camera to improve the SIN ratio.
The approach taken for the largest field of view images in these experiments was to use simul­
taneously two very low noise, high dynamic range cameras to increase the magnification while
keeping constant the total field of view. This solution presents another important advantage: as
the resolution scales directly with the magnification, small flow scales can be studied in the re­
sulting images.
21
EXPERIMENTS
The experimental setup is shown in figure 1. A pulsed XeF excimer laser (Questek 2220,
A. = 351 nm, -85 mJ per 20 ns pulse with stable resonator optics) was used to form the light
sheet. The jet flow issued from a 1.0 cm diameter contoured nozzle at 7.4 rn/s (Re = 5(00) into
a 6Ox60 cm chamber. It was seeded with the molecular tracer biacetyl (2-3 Butanedione) to a
saturation concentration of 40 torr partial pressure (-5% mole fraction) . A uniform nitrogen co­
flow (-10 crn/s) in the chamber prevented recirculation of the jet and quenching of the biacetyl
phosphorescence by oxygen The fluorescence emission is broadband with a lifetime of 50 ns
and a peak at A. = 485 nm. The phosphorescence is also broadband, with a lifetime of 1.1 ms,
and presents a strong peak at 520 nm, a secondary peak at 562 nm, plus a third much dimmer
peak in the red. Integrated over the different wavelengths the phosphorescence signal is -60
times higher than the fluorescence (Okabe & Noyes [9]). Both signals were imaged onto a cryo­
genically cooled CCD array (Photometrics Model 81-S camera with Thomson CSF TH 7882-
CDA array, 14 bit AID converter), and a thermoelectrically cooled tCD Photometrics Star1
Excimer Laser
Timing Electronic
Camera Controllers
22
camera (same Thomson array, 12 bit AID converter). The lenses used were 50mm f# 1.2 in both
cameras. The images were acquired in two PC 386 computers, and transferred to a Sun 3/160
hosting a Pixar Image Computer for processing and analysis.
Experimental Resolution
Following van Cruyningen [10], five parameters are used to characterize the PUP ex­
periments: measuring volume per pixel, spatial dynamic range, temporal resolution, minimum
detectable signal, and signal dynamic range.
The measuring volume per pixel depends on the magnification, and pixel size. The mag­
nifications and measuring volume per pixel for the different data sets are summarized in the ta­
ble included in fig. 2. The CCD array in both cameras was identical, with 384x576 square pixels
23 11m wide. The depth of the measuring volume is determined by the laser sheet thickness.
The smallest detectable scale is twice the measuring volume size, according to the
Nyquist sampling theorem. Assuming that the largest scale is the whole field of view, gives a
spatial dynamic range of 192x288.
The temporal resolution in the present experiments was limited by the emission lifetime.
Collecting fluorescence plus phosphorescence, this limit is - 1.1 ms. This time can be decreased
by adding a suitable quencher, or gating the camera if it is intensified, although in both cases
the collected intensity is also reduced. For an exit velocity of 7.4 mls blurring is negligible after
35 diameters for a 1 mm measuring volume.
The minimum signal that can be detected is that for which the signal to noise ratio SIN is 1. The Star1 camera was operated with a system gain of 4 and a noise floor of 12 e- corre­
sponding to 1.3 digital numbers out of a maximum value of 4096 (12 bits). The gain for the 81-
S camera was 7, and the noise floor was16 e corresponding to 12 digital numbers out ofamax­
imum value of 16384. Knowing the camera and collection optics efficiency, and the incident
laser energy, the minimum detectable biacetyl concentration can be calculated. These values are
given below, and are limited by the large field of view in the experiments.
The maximum signal dynamic range in all these experiments corresponds to the ratio be­
tween the biacetyl saturation concentration (50,000 ppm) and the minimum detectable concen­
tration, as the range imposed by other possible limiting factors (pixel well depth, AID converter)
amply exceeds the biacetyl detectability limit. Note, however, that the biacetyl saturation con­
centration only occurs at the nozzle.
Data Sets
In the same flow conditions, different data sets were acquired, varying the field of view
· · · · · · · ,.~ ..... " .... " .. -...... ~ ........... :.
a.;-M..,!-H-"lt'>r::
0.5xO.5 410
lxl 550
0.18xO.18 40
0.53xO.53 104
OAxOA 80
Fig.2. Schematic of the field of view for the different data sets. The chamber dimensions are 61x61x122 cm.
Axial cuts (1,2):
A data set of 125 images was acquired with the laser sheet illuminating the fIrst 85 diam­
eters of the jet. The initial 30 diameters were imaged with the Starl camera, while the sec­
ond camera imaged the next 60 diameters, thus yielding a ratio of 2: 1 between the respec­
tive fields of view. An overlap of 5 diameters was used to accurately match each pair of
images after a proper rescaling. The laser sheet thickness was 1 mm at the jet axis. The
measuring volumes were 0.5x0.5 mm per pixel in the upper camera and lxl mm for the
lower one. The minimum detectable concentrations were 410 and 550 ppm respectively.
Axial close-ups (3):
To better study the smallest scales, a set of 50 images was acquired at a downstream dis­
tance from 78 to 85 jet diameters, with a fIeld of view of7x1O.5 cm (l80x180 11m per pix­
el), extending horizontally from the jet centerline to 10.5 nozzle diameters. The minimum
concentration was 40 ppm. The mean biacetyl concentration at 82 jet diameters is 0.3%,
which gives an effective dynamic range of 90 (but note that the instantaneous concentra­
tion can be higher than the mean). The average SIN ratio for the jet centerline in these shot
noise limited images was 40. The distance travelled by a fluid element at the centerline
during the exposure time was less than 0.8% of the fIeld of view.
24
Cross-stream cuts (4):
At a distance of 45 diameters the jet was cut horizontally and 110 images were recorded
with a field of view of 30.5x20.3 cm (0.53xO.53 mm per pixel). The minimum detectable
biacetyl concentration was 104 ppm, with an average SIN ratio at the jet center of 33. The
camera was located perpendicular to the laser sheet at the exit of the wind tunnel.
Cross-stream close-ups (5):
These close-ups were taken at 76 diameters with a field of view of 22.9xI5.2 cm (O.4xO.4
mm per pixel), minimum concentration of 80 ppm, and a jet center average SIN ratio of
27. Cross-stream cuts were taken to study solid-body jet displacement and isotropy of ra­
dial and angular components of the scalar dissipation.
Image Corrections
The image corrections will be briefly outlined. For more extensive analysis, see for ex­
ample van Cruyningen et al. [8]. First, a camera dark frame (image taken without external sig­
nal) was subtracted from each jet image. The dark frame was also subtracted from a background
image obtained from the un seeded jet. Then the resulting background image, normalized with
the laser energy, was subtracted from each single-shot image to eliminate possible room light
and reflections in the chamber walls. In the third step, the images were corrected for the laser
sheet profile. Images of the laser sheet profile were obtained using a static cell. The same cor­
rection image was used for each entire data set because of the consistency of the laser profile
from pulse to pulse (RMS -0.5%). The images were finally corrected for shot to shot differences
in the laser energy. Independent energy measurements were taken with a photodiode, although
for the axial cuts the normalization factor can be obtained directly from the intensity of the im­
ages at the nozzle, as we know that at this point the biacetyl concentration is constant corre­
sponding to the saturation value. For the two-camera data sets, the image pairs were converted
to a common scale and matched.
RESULTS
The close-up images give an estimate of the jet small scales. The smallest scale for mo­
lecular diffusion is the Batchelor scale 'llB' which can be defined as the smallest scale over
which a spatial gradient can be maintained in a scalar field (in analogy with the Kolmogorov
scale for vorticity fields). For a turbulent jet
'llB - aRe{3/4Sc-l/2t (2)
where Rei is the Reynolds number based on the local integral scale, I =O.44x is the local diam­
eter (x being the downstream distance), Sc is the Schmidt number, and a is a constant. For the
present jet, the Schmidt number was measured to be -1.1, and Rei = 13500. For a value a = 1,
25
Fig. 3. Axial close-ups from 78 to 85 jet diameters extending horizontally from the jet centerline to 10.5 nozzle diameters. Jet is flowing downwards and the centerline is at the right side of the images. The scale is given in units of Re/-3/4Sc-1!21.
the Batchelor scale spans approximately 1.6 pixels in our close-up images. Measurements by
Dowling [11] indicate that (X is -25, in which case the smallest average structure should span
40 pixels. Figures 3(a) and 3(b) are examples of the close-ups taken from 78 to 85 diameters,
and structures smaller than 40 pixels can be distinguished, although we are looking at planar
cuts of three dimensional structures. No structure smaller than 4 pixels was observed suggesting
that 2 can be a lower limit for (X.
Figure 4 shows a corrected single-shot axial cut of the jet composed from the two camera
images. Figure 5(a) is a 125 frame average. The centerline profile plotted alongside the image
follows the expected turbulent jet lIx decay law, as shown in Tennekes and Lumley [12]. In the
26
Fig. 4. Instantaneous axial cut covering the first 85 jet diameters.
Fig 5. (a) Average of 125 instantaneous axial cuts. (b) Average rescaled for self-similarity.
27
far field region of a turbulent jet, the time averaged concentration values at the centerline follow
the self-similarity expression
(3)
where Xo is the jet virtual origin, Co is the concentration at the jet exit, K is the decay constant
and d is the nozzle diameter. In figure 5(b) the average image has been rescaled for self-simi­
larity allowing direct comparison of pixel values at all downstream locations. This type of res­
caling is possible at the downstream locations because of the high dynamic range of the data; in
these regions the signal is weakest and the correction is the largest. For the rest of the analysis,
all the single-shot images have been self-similarly rescaled.
Because in a PLIF experiment measurements are taken simultaneously for a complete
plane of the flowfield, multi-point operations and statistics can be calculated without having to
invoke Taylor's hypothesis. As an example, figure 6(a) is an instantaneous image of
Fig. 6. (a) Instantaneous scalar dissipation. (b) Average of 125 instantaneous scalar dissipation images.
28
(4)
which is proportional to the scalar dissipation assuming isotropy of the radial and angular com­
ponents of the gradient [13]. The scalar dissipation is a measure of how rapidly concentration
fluctuations are smoothed by molecular diffusion to produce a uniform concentration. The val­
ues are higher for interfaces between the jet and the ambient fluid, so intense lines in the image
indicate preferred directions of fluid entrainment into the jet. Figure 6(b) is an average of the
instantaneous dissipation images. Note the tendency of the maxima to orient along 45 degree
lines corresponding to the direction of maximum strain in the flow.
Figure 7(a) shows a corrected instantaneous cut at 45 jet diameters, while figure 7(b) is
a 110 frame average. The proflle plotted below each image, corresponding to the horizontal di­
ameter, has sharp edges for the instantaneous shot, approaching a gaussian proflle in the aver­
age. The gaussian shape of the average is partly due to the fact that for most of the instantaneous
images the concentration is essentially zero for large values of the radius, that is, the jet is not
present at these space locatiQns. Conditional statistics account for this effect. An indicator func­
tion is defined so that values are only included in the statistics when the concentration is higher
than the indicator value. The resulting mean (fig. 7(c» has higher values in the tails (-30% of
the centerline value), although the convergence is progressively poorer as the radial distance in­
creases. In the central region where the jet is always present, conditioned and non-conditioned
statistics coincide. The RMS shown in figure 7(d) shows a maximum at 6 degrees from the cen­
ter where the fluctuations are approximately 30% of the mean concentration value at the jet cen­
ter. The maxima of the conditioned RMS are smaller, as occurrences with zero value have been
eliminated. These results are summarized in figure 8. In this plot, the variable in the horizontal
axis, 11, is the jet radius nondimensionalized by the downstream distance, r/(x-X{), where Xo is
the jet virtual origin.
The cross-stream images allow study of the importance of solid body jet displacements
versus turbulent mixing, and the isotropy of the angular and radial dissipation values. To isolate
jet flapping from mixing processes, an average was obtained after displacing each instantaneous
image to a common center of mass. The difference between the normal average and the centered
one is shown in figure 9. For our concentration data, with a total jet spreading angle of 22° (be­
tween opposite points where concentration is 1 % of the value at the center), jet solid body mo­
tions account for 2.5°- 4°.
Finally figure 10 shows the squared radial and axial components of the gradient CdC/or)2
and «l/r)aC/a8)2 for an instantaneous image and the average of 110 dissipation images. The
concentric patterns that appear in the single-shot radial component are still preserved in the av­
erage, as are the radially oriented lines of the angular component. This is because the main con­
tribution to the dissipation comes from the jet boundary and the jet surface is distorted by the
entrained ambient fluid creating lobes in the cross sections. The central region of the averaged
29
Fig. 7. Cross-stream cuts at 45 jet diameters, field of view 30.5x20.3 em; (a) instantaneous im­ age, (b) 110 frame average, (c) conditioned average, (d) RMS concentration fluctuation. The values of the RMS image have been multiplied by 10/3.
30
1.25
1.00
Intermittency
11.
Fig. 8. Intermittency, mean and RMS calculated from 110 cross-stream cuts at 45 jet diameters. Hollow symbols correspond to conditioned statistics. Solid symbols correspond to non-condi­ tioned statistics. The variable 11 is the non-dimensional radius r/(x-XfJ). Cc is the concentration at the jet center.
1.25
1.00
11
- .,
Fig. 10. Squared gradient components: (a) radial component, (b) angular component. Average of the squared gradient components: (c) radial components, (d) angular components.
32
images is much more isotropic, as pure ambient fluid seldom reaches the jet centerline. Despite
the differences between the radial and angular averaged images, the profiles plotted below them
are remarkably similar, justifying the above assumption of equivalency between radial and an­
gular gradient components. The same averages were calculated for the axial close-ups at 76 jet
diameters. In this case the isotropy is stronger because the jet edge concentration gradients are
smaller.
CONCLUSIONS
PLIP techniques has been used to obtain high dynamic range quantitative concentration
measurements in a turbulent jet in both single camera and two-cameras experimental set-ups.
Compared to single camera recording, for the same flow region to be imaged, the simultaneous
use of two cameras increases both the resolution and dynamic range of the data. Compared to
single point measuring techniques PLIP data enables the calculation of multiple-point results
including gradients or spatial correlations. Statistical results (mean, RMS and dissipation) have
been presented for 85 cm field of view axial cuts and for cross-sectional cuts.
ACKNOWLEDGEMENT
This research was sponsored by the Air Force Office of Scientific Research, Aerospace
Sciences Directorate.
1. Dimotakis, P.E., Miake-Lye, R.C., Papantoniou, D.A., 'Structure and dynamics of round
turbulent jets', Phys Fluids, 26, (11), 3185, (1983).
2. Kychakoff, G., Paul, P.H., van Cruyningen, I., Hanson, RK., 'Movies and three-dimen­
sional images of flowfields using planar laser-induced fluorescence', Appl Opt, 26, 2498,
(1987).
3. Kychakoff, G., Howe, R.D., Hanson, RK., McDaniel, J.C., 'Quantitative visualization of
combustion species in a plane', Appl Opt, 21, 3225, (1982).
4. Dyer, M.J., Crosley, D.R., 'Two-dimensional imaging of OH laser-induced fluorescence
in a flame', Opt Lett, 7, (8), 382, (1982).
5. Seitzman, J.M., Kychakoff, G., Hanson, R.K., 'Temperature field measurements in com-
bustion gases using planar-laser induced fluorescence', Opt Lett, 10,439, (1985).
6. Lee, M.P., Paul, P.H., Hanson, RK., 'Quantitative imaging of temperature fields in air us-
ing planar laser-induced fluorescence', Opt Lett, 12,75, (1987).
7. Hiller, B., Hanson, R.K., 'Simultaneous planar measurements of velocity and pressure
fields in gas flows using laser-induced flourescence', Appl Opt, 27, 33, (1988).
33
8. van Cruyningen, 1., Lozano, A., Hanson, R.K., 'Quantitative imaging of concentration by
planar laser induced fluorescence', Expt Fluids, 10,(1),41, (1990).
9. Okabe, H., Noyes, W.A., 'The relative intensities of fluorescence and phosphorescence in
biacetyl vapor', JAm Chem Soc, 79,801, (1957).
10. van Cruyningen, 1. 'Quantitative planar laser-induced fluorescence imaging in turbulent
gaseous jets', PhD Thesis in Mechanical Engineering, Stanford University, (1990).
11. Dowling, D.R., 'Mixing in gas phase turbulent jets' , Ph. Thesis, Caltech, (1988).
12. Tennekes, H., Lumley, J.L., A First Course in Turbulence,Cambridge, MA: MIT Press,
(1987).
13. Namazian, N., Schefer, R.W., Kelly, J., 'Scalar dissipation measurements in the develop­
ing region of ajet', Combustion and Flame, 74, (2),147, (1988).
Simultaneous Measurement of Velocity and Temperature of Water Using LDV and Fluorescence Technique
Tsuyoshi Nakajima, Motoyasu Utsunomiya, and Yuji Ikeda
ABSTRACT
Rokkodai, Nada, Kobe 657 Japan
A method of simultaneous measurement of velocity and temperature of water has been developed using a modified laser induced fluorescence of Rhodamine B. The intensity of fluorescence decreased with temperature and its temperature with a coefficient of 3.2 %/K. The dimensionless calibration curve was not affected by laser intensity, concentration of Rhodamine B, laser wavelength and optical configuration. Simultaneous measurement of velocity and temperature was made in a natural convection field.
INTRODUCTION
diffusion, it is important to estimate turbulent heat flux from
the correlations of temperature and velocity which are obtained
simultaneously. The aim of this paper is to introduce a system
to measure temperature and velocity using
fluorescence and laser Doppler velocimetry.
laser induced
measurement of concentration, the fluorescence intensity
on temperature, pH and laser intensity as well
concentration[l]. Fluorescence has the advantages that
depends
of fluorescence is different from that of the excitation laser
beam. Its intensity decreases with increasing temperature
because the fluorescence changes with molecular activity, and
robs the molecule of energy[2]. Although the change in
fluorescence with temperature is normally around 1 %/K, some
35
fluorescent dyes have temperature coefficient of up to 5 %/K.
For concentration measurements. the temperature has been
controlled carefully.
When a thermocouple and an LDV are used for simultaneous
measurements of temperature and velocity. the sampling volume of
the LDV does not coincide exactly with that of the thermocouple.
The simultaneous measurement of temperature and velocity by
thermocouple and LDV make use of the measurement volume of an
argon-ion laser Doppler velocimeter. This paper provides
theoretical considerations of temperature measurement by this
means and describes its application in natural convection of
water.
PRINCIPLE OF TEMPERATURE MEASUREMENT
Figure 1 shows a collimated laser beam of intensity. 10 , and
wavelength. AQ. passing through a fluorescent solution. The
fluorescence of wavelength. Af. is collected and its intensity
is measured by a photodetector.
x
Detector
36
The excitation laser beam is attenuated and the beam
intensity at point x along the beam path is given by
f(x) = fo' exp(-e for C(x)dx) (1)
where e is the extinction coefficient of fluorescent dye and C(x)
is the dye concentration at x. If the concentration is uniform
and given by CO, the intensity of the excitation beam is
expressed as
f(x) =fo·exp(-e·Co·x)
The beam intensity becomes constant and equal to 10 when the
concentration is so thin that attenuation of the incident beam
may be neglected.
molecule and absorbed in about 10-15s , an outer electron jumps
from the ground state to an upper excited singlet state. While
the electron spends about 10-4 s in the excited state, some
energies in excess of the lowest vibrational level of the singlet
state is dissipated until the lowest vibrational level is
attained. Fluorescence then occurs when the electron returns to
the ground state and the emitted wavelength is longer than the
absorbed wavelength. The intensity of the fluorescence received
by the photodetector shown in Fig. 1 is described by [1]
fJ(x)=fo(x)·A·q}.e·L·C(x) (2)
where A is the fraction of the available light collected, ¢ is
the quantum yield of the fluorescence, e is the extinction
coefficient of the fluorescent dye, and L is the length of the
sampling volume determined by the focal length and position of
the receiving lens. It was assumed that the laser intensity was
so low in the present measurement that no saturation of
fluorescence occurred and the fluorescence was considered to be
proportional to the excitation beam intensity. Since the
extinction coefficient at AJ for the fluorescence is usually
smaller than at Ao for the absorbed excitation beam, the
attenuation along the receiving path will be neglected and the
fraction A is mainly
temperature, because molecular motion and collisions are active
and the molecule loses its energy when the temperature is high.
Let us assume that the concentration is uniform and so small
that attenuation of the incident laser beam may be neglected, and
the laser intensity is low so that no saturation of fluorescence
occurs. The fluorescence intensity, If' is then given by
I, = 10 • A . ¢ . t: • L . Co (3)
The fluorescence of dilute solution increases with decreasing
temperature and reach a maximum, I fO . The fluorescence intensity
is related to temperature by the following equation [3]:
(4)
where T is the absolute temperature ( K ), R is the gas constant,
E is the thermal energy related to vibrational energy levels, and
k is the constant of temperature quenching. If the fluorescence
at a standard temperature, TO' is taken to be If(TO)' then Eq.(4)
becomes
E I,(T) k·e- 7P1li +l 1,('1'0) = k· e-Ifr + 1
(5)
Introducing a dimensionless temperature, o = (T-TO)/To and assuming
the temperature difference T-TO be small or 0 «I, we obtain
I,(T) 1 1,(To) ~ 1+aO+,802
(6)
where
a=
38
If the values of Q and fi are determined experimentally, the
temperature of the solution is therefore estimated from measured
value of If(T).
In the present bench measurement the water temperature was
changed from ZO to 70 . C. This temperature range corresponds to
0=0.033 to 0.13Z when TO=303 K.
RIIODl\MINE B
dye from the following reasons:
(1) The fluorescence of Rhodamine B varies greatly with
temperature and its change can be as high as 5 % per K, while the
temperature coefficient is normally less than 1 % per K [Z].
(Z) The quantum yield of Rhodamine B is large, the example, 0.69
or 0.97 when ethanol is used as a solvent[Z].
(3) Water can be used as a solvent. Rhodamine B is soluble in
water and the polarization is negligibly small in water.
(4) Rhodamine B is easy to prepare because it is a powdery dye.
(5) The fluorescence of Rhodamine B is almost independent o~ the
pH of the solution [Z].
(6) The temperature effect on the polarization can be neglected
for Rhodamine B, while it changes normally with temperature
through the change of excitation lifetime of fluorescent dye and
viscosity of solvent[3].
For Rhodamine B, the peak of the absorption spectrum
occurs at Ao=517.5 nm with the peak of the fluorescence spectrum
at Af=590 nm when water is used as a solvent.
EXPERIMENTAL EQUIPMENT AND METHOD
fluorescence relation as shown in Fig.Z. An aqueous solution of
Rhodamine B in the glass vessel of 150 x 150 x ZOO rnm was
irradiated by an argon-ion laser. The irradiated Rhodamine B
glowing with orange is shown in Photograph I, where the
wavelength of the laser was 514.5 nm or 488 nm. The fluorescence
39
in the measurement volume was collected by the receiving optics
consisting of a lens with a focal length of 300 mm , a pinhole of
0.1 mm in diameter and a bandpass filter of 589. 3± 5 nm. The
receiving optics were placed in the same horizontal plane at 45'
in the forward direction to the incident beam.
The current output of the photomultiplier was converted to
voltage and sent to a personal computer through an analog-to­
digital ( AID) converter. The water as a solvent was boiled and
filtered to remove air and impurities. Black masking tape was
put on the glass wall of the vessel to reduce the influence of
the reflected laser beam.
the measurement volume of the laser induced fluorescence which
was located at the center of the test vessel. In order to
obtain a temperature-fluorescence curve, the solution of
Rhodamine B was cooled naturally from 70 . C to 20 . C, and the
fluorescence intensity and the temperature were measured every
ten seconds. The average of the five data was finally recorded
since the rate of the temperature decrease by the natural cooling
was so small that it might range from 0.005 to 0.01 . Cis.
Collecting
P.M.
Thermocouple
AID converter
I/V converter
Fig. 2 Schematic layout of measurement system for bench test
40
We measured the variation of temperature-fluorescence curve
with wavelength of the excitation beam, the laser intensity and
the concentration of Rhodamine B. Two wavelengths of argon-ion
laser, i.e. 488 and 514.5 nm, were chosen so as to study the
effects of laser wavelength on the temperature-fluorescence
curve. The effects of the laser intensity were also examined for
the incident beam intensity of 19.6, 26.4 and 35.8 mW under the
condition of fluorescence concentration of 0.839 g/m3 and
wavelength of 514.5 nm. The beam intensity was determined to be
so small that no saturation might occur. The effects of the
fluorescent dye concentration were studied for the concentration
of 0.139 to 12.39 g/m3 .
Simultaneous Measurement of Temperature and Velocity
The velocity measurements used Mie scattered light from SiC
particles, while the temperature was estimated from fluorescence
of Rhodamine B or electromotive force of the chromel-alumel
thermocouple. Photograph 2 shows orange liquid for the
fluorescence and green particles for Mie scattering, where large
polystyrene particles -100 pm in diameter) were used to
exaggerate the Mie scattering effect.
Figure 3 shows the test section used for the
measurement of temperature and velocity.
41
simultaneous
Water cooler
Laser beam
42
natural convection of the water which contained Rhodamine B for
fluorescence measurements and SiC particles for LDV measurements.
A partition plate, Fig. 3, divided the test section, and the
heater was placed 20 mm above the bottom of one compartment and
the cooler was near the water surface in the other compartment.
This configuration was useful enhanced global natural convection
and maintained steady temperature field.
The simultaneous measurement system is shown in Fig. 4. Two
beams of an argon-ion LDV were incident in the normal direction
to the axis of the electric heater in order to reduce
fluctuations of the measurement volume or disappearance of the
intersecting point caused by refractive index change of the fluid
due to turbulent natural convection or thermal plume. Since the
Mie scattered light .and fluorescence were collected together, the
receiving optical system included a color separator and two color
filters so as to separate temperature and velocity information.
Thermocouple "'====='?,:J
B.P.F. Af=590 nm
and temperature
The filters used in the experiment were 589.3± 5 nm for orange (
i. e. for fluorescence ), and 514. 5± 3 nm for green or 488 ± 3nm
for blue( i.e. for Mie scattering). The fluorescence and Mie
scattered light were collected by a collecting lens of f=300 mm,
separated each other by a color separator, filtered to remove
43
stray light and sent to an individual photomultiplier. A counter
signal processor was used together with a Bragg cell of 40 MHz
frequency shift.
BENCH MEASUREMENT
temperature, we investigated the effects of background noise on
fluorescence intensity, including those of room light, noise
caused by detector and electronic circuit, fluorescence
impurities which may exist in water, scattering particles used
for velocity measurements, and velocity fluctuations. The effect
of the velocity fluctuations was examined since fluorescence in
the path of the beam decreases with time if fluorescence dye is
used with high laser intensity and without fluid motion[l].
These effects are shown in Figs. 5 - 9. Neither the room light
nor the impurities affected the fluorescence intensity. No
effect of the velocity fluctuation was observed for the laser
beam intensity of 20 mW. In Fig. 5, the time-averaged mean
fluorescence intensity in room light ON are the same as that in
room light
measured to check the influence of detector noise
in water. As shown in Figs 6 and 7, the
test results indicate that those influences are
As shown in Fig. 8, an effect of the scattering
particles on the fluorescence intensity was observed since the
average diameter of the scattering particles was 3 J.L m and their
small concentration influenced that the measurement volume did
not include many particles at the same time. The volume ratio of
one particle to the measurement volume was about 1/470000 for 3
{tm in diameter, while 1/13 for 100J.Lm. The output of the
current-to-voltage (I/V) converter fluctuates due to the shot
noise and the noise caused by the detector and the electronic
circuit. This fluctuation is thought to indicate temperature
resolution of the measurement method. The fluorescence
intensity curve measured under the condition of large velocity
fluctuation shows almost constant as shown in Fig. 9. The
deviation was also negligibly small.
44
Q) tJ I=: 100 100c-__ -'----~--
50 Q)>, tJ+" m·M Q) m ,... I=: o Q) ::l+" .--II=: Lx.. ·M
Q)
50
0
Time(14sec/Div.)
(mV) 150 Q)
g 100 Q)>, tJ+" ~.~ 50 ,... I=: o Q) ~~ OF-------------------~--~--- Lx.. ·M
Q) tJ
(rnV) 150
§ >,100 tJ+" ~.~ 50 ,... I=: o Q) ~ ~ Or~-----------~-----­ Lx.. ·M
Time(14sec/Dlv.)
(mV) (mV) 150 150
g 100 Q)>, tJ+" m·M 50 50 Q) m ,... I=: o Q) ::l+" 0 0 .--II=: Lx.. ·M
Time(14sec/Div.) Time(14sec/Div.)
Fig. 8 Influence of LDV seeding particle
45
(mV)
Time(14sec/Div.)
Figure 10 shows a histogram of temperature calculated from
the fluorescence intensity obtained at a fixed temperature of
20.8 ± 0.1 . C. The standard deviation was e-stimated and found
to be 0.13 . C.
higher than that of the thermocouple. but the absolute resolution
can not be obtained in the present experiment because it was very
difficult to keep the water temperature constant within 0.1' C.
The estimated time resolution is 0.1 ms.
Ul (!)
120
90
(J)
30
o
-
the thermocouple temperature at 20.8+0.1' C
46
various values of concentration of Rhodamine B, intensity of
excitation laser beam and wavelength of the laser beam. Each
figure shows decreasing of fluorescence with increasing
temperature, i.e., temperature quenching. Although it is
expected from Eq. (4) that the experimental data describe a S­
shape curve, a curve of second degree was obtained in the
temperature range of 20 - 70 . C. The temperature coefficient
of the fluorescence was 3.2 %/K at its maximum and decreased with
tempera