Experiments in Fluids 31 (2001) 45±55 Ó Springer-Verlag 2001
Evaporating and combusting droplet temperature measurements
using two-color laser-induced fluorescence
P. Lavieille, F. Lemoine, G. Lavergne, M. LeboucheÂ
Abstract The paper presents a new technique based on
laser-induced ¯uorescence, allowing droplet temperature
measurement of evaporating and combusting droplets to
be performed. The liquid spray is seeded with a low
concentration of rhodamine B. The ¯uorescence, induced
by the green line of an argon laser, is measured on two
separated color bands. It is demonstrated that two color
bands can be selected for their strong difference in the
temperature sensitivity of the ¯uorescence quantum
yield. The determination of the ¯uorescence ratio between the ¯uorescence intensity corresponding to each
color band allows the tracer concentration and the
droplet size dependences to be eliminated. The technique
was applied on a monodisperse spray: the effect of a
thermal impulse on the distribution of the droplet
temperature is studied and, the temperature of
combusting droplets is investigated.
List of symbols
C
molecular concentration of the tracer
D
droplet diameter
f
piezoceramic frequency
I0
incident laser beam intensity
If
¯uorescence intensity
K
fuel thermal conductivity
Kopt optical constant
Kspec spectroscopic constant
L
distance parameter (de®ned just after the jet
break-up)
r
radial position in the droplet axis system
R
droplet radius
Rf
¯uorescence ratio
T
absolute temperature
Ti
injection temperature
T0
reference temperature
Vi
injection velocity
Vc
probe volume
Received: 16 June 2000/Accepted: 10 November 2000
P. Lavieille, F. Lemoine (&), M. LeboucheÂ
Laboratoire d'EnergeÂtique et de MeÂcanique TheÂorique et
AppliqueÂe, 2, Avenue de la ForeÃt de Haye, BP 160
54504 Vandoeuvre-les-Nancy Cedex, France
G. Lavergne
ONERA/DMAE, 2, Avenue Edouard Belin, BP 4025
31055 Toulouse Cedex 4, France
Greek symbols
b
temperature sensitivity coef®cient
ef
extinction coef®cient for the ¯uorescent emission
el
extinction coef®cient for the laser radiation
F0
injector aperture diameter
k
wavelength
Subscripts
1 ®rst spectral band k Î[525 nm:535 nm]
2 second spectral band k > 590 nm
1
Introduction
Experimental spray combustion investigations require the
development of challenging measurement techniques.
Spray combustion concerns automotive engines with direct injection of the fuel in the combustion chamber and
also turbojet and rocket engines, where fuel is injected on
a droplet form. The thermal characterization of a spray
should allow better understanding of the physical phenomena involved in spray combustion and may contribute to saving fuel and to reducing global CO2 emissions.
A spray is a two-phase ¯ow where transport phenomena
of heat and mass are strongly related. Heat and mass
transfer occur in the wakes generated by the velocity
difference between the liquid droplets and its gaseous
surrounding. Furthermore, the internal vortex within the
droplets contributes to enhancing the heat conduction in
the liquid phase. One of the key points which needs to be
investigated is the thermal budget between the droplet
and its gaseous surrounding in the evaporation and
combustion phases. This involves a reliable experimental
technique able to measure the droplet temperature. The
most usual technique for determining moving droplets
temperature is the rainbow refractometry technique
(Walker 1976). A laser beam is focused into a droplet and
the multiple re¯exions within the droplet produce a
rainbow ®gure. The angular position of the rainbow,
which may be detected by a photomultiplier (Van Beeck
and Riethmuller 1997) or by a CCD array (Van Beeck and
Riethmuller 1995), depends on the refractive index of the
liquid, related to temperature. The technique is applicable
for providing information about the drop size and mean
temperature in the case of isothermal droplets. However,
the method falls down in the presence of strong temperature gradients within the droplet, for example in the
evaporation phase. The other strategy used to determine
the droplet temperature is to measure and analyze its
45
46
infrared emission (Ravel et al. 1997). The main dif®culty
is to determine the liquid emissivity, and one of the
serious problems is that only the surface temperature
is determined, where the in¯uence of the vapor phase
radiation must be carefully examined.
Another technique consists in adding ¯uorescent tracers in the liquid phase. Murray and Melton (1985) demonstrate the potential use of exciplex ¯uorescence for
determining the droplet temperature in hydrocarbon fuel
sprays. However, the technique cannot work in a combusting environment. Lavieille et al. (2000) developed a
laser-induced ¯uorescence ef®cient technique in the liquid
phase. A low concentration of a ¯uorescent organic dye
(rhodamine B) is dissolved in the fuel, and the temperature dependence of the ¯uorescence quantum yield is used
to provide a temperature measurement. The technique was
demonstrated to be capable of determining the droplet
temperature within 1 °C in a monodisperse stream, where
size changes due to evaporation were neglected. The major
problem was that the ¯uorescence signal also depended on
the droplet volume, which may change in evaporating or
combusting sprays.
This paper provides an extension of the laser-induced
¯uorescence technique which is able to overcome these
problems ef®ciently. Further information about the drop
volume appears necessary in order to determine the temperature even in the case of strong size changes. An alternative strategy is suggested by the work of Copetta and
Rogers (1998) and Sakakibara and Adrian (1999): a second
¯uorescent, whose ¯uorescence spectral band is well separated from the ®rst one and with a different temperature
sensitivity, can be dissolved in the fuel. The ratio of the
¯uorescence signals measured on the two spectral bands
can eliminate the volume dependence. However, one of the
dif®culties is that the resulting temperature sensitivity
depends on the respective dye concentrations in the
mixture, so that the concentrations must be well known
and maintained constant. The present paper deals with a
new laser-induced ¯orescence technique based on a ratiometric measurement of ¯uorescence signals detected on
two-color bands of a single ¯uorescent dye (rhodamine B).
The technique allows the laser intensity, dye concentration
and drop volume dependence to be eliminated, keeping
the sole effect of temperature. Validation of the technique
is provided on a monodisperse ethanol droplet stream
either in evaporation or combustion. Two droplet sizes
were investigated: D ˆ 100 lm and D ˆ 200 lm.
easily induced by the green line (k ˆ 514.5 nm) of an
argon-ion laser, operating in single-line mode. Lemoine
et al. (1999) have shown that the temperature dependence
of the ¯uorescence emission appears mainly in the ¯uorescence quantum yield, where quenching phenomena are
involved. Expressing the ¯uorescence quantum yield as a
function of the temperature gives the ¯uorescence intensity expression, neglecting Beer's attenuation of the incident laser beam and the ¯uorescence re-absorption:
If ˆ Kopt Kspec Vc I0 Ceb=T
…1†
where Kopt is an optical constant, I0 is the incident laser
intensity, C is the molecular concentration of the ¯uorescent tracer, and T is the absolute temperature. Kspec and b
are two constants depending only on the spectroscopic
and physical properties of the ¯uorescent molecule. The
coef®cient b can be interpreted as a temperature sensitivity coef®cient of the ¯uorescence intensity. The parameter Vc is the measuring volume, corresponding to the
volume of the droplet excited by the laser radiation, captured by the detection device. The principle of droplet
temperature measurement consists in dissolving a very
low dye concentration in the fuel and atomizing the liquid
into droplets. The ¯uorescence resulting from the laser
excitation is collected by an appropriate optical device.
One of the main dif®culties in determining the droplet
temperature by measuring the ¯uorescence intensity is the
presence of the measuring volume size Vc in Eq. (1), which
may change as the droplet vaporizes. The present paper
demonstrates that this drawback can be overcome by using two spectral bands of ¯uorescence, previously selected
for their strong temperature sensitivity difference. The
ratio of the ¯uorescence intensity measured on each color
band appears to be independent of the measuring volume
Vc. An accurate study of the rhodamine B spectrum has
shown that the temperature sensitivity depended considerably on the wavelength. Rhodamine B spectra measured
in an ethanolic solution (C ˆ 5 ´ 10)6 mol/l) are presented in Fig. 1 at three different temperatures:
T ˆ 24.5 °C, T ˆ 36 °C and T ˆ 57 °C. The spectra were
realized by a spectrometer with a spectral resolution of
2
Two-color laser-induced fluorescence: principles
2.1
Principles
The basis of the technique is to use the temperature dependence of the ¯uorescence of an organic dye dissolved
in the fuel (ethanol here). Rhodamine B is an adequate
tracer, because of its strong temperature sensitivity: this
sensitivity is of the order of 3% of ¯uorescence variation
per K. Rhodamine B is highly soluble in ethanol and its
Fig. 1. Evolution of the rhodamine B ¯uorescence spectrum as
¯uorescence, centered in the red±orange part of the visible a function of the temperature and distribution of the temperature
spectrum, is strong. Furthermore, the ¯uorescence can be sensitivity coef®cient b as a function of the wavelength
0.36 nm. As expected, Fig. 1 shows that the spectrum
amplitude decreases strongly with the solution temperature. This experiment allows the temperature sensitivity
coef®cient b [Eq. (1)] to be calculated as a function of the
wavelength, also reported in Fig. 1. Although the lack of
signal located in the vicinity of 525 nm results in an erroneous determination of b, the spectral band around
525 nm seems to present a very low temperature sensitivity, as high sensitivity is noticed over 590 nm. As far as the
range of the available interferential ®lters and colored glass
®lters is considered, the following two spectral bands were
selected because it is the better trade-off for optimizing the
temperature sensitivity (Fig. 2):
47
± band 2: center frequency, kc ˆ 530 nm, bandwidth,
Dk ˆ 10 nm;
± band 1, k > 590 nm.
In spite of the low energy available on the ®rst spectral
band, the ¯uorescence signal remains largely suf®cient to
be measured by a photomultiplier. It should be added that
the ¯uorescence signal in the band [525 nm; 535 nm] can
be strongly re-absorbed by the medium. This point will be
discussed extensively in Section 2.3.
The ¯uorescence signal detected on the ®rst spectral
band may be written as in Eq. (1):
If ˆ Kopt1 Kspec1 Vc I0 Ceb1 =T
…2†
Fig. 2. Sketch of the two selected spectral bands
in order to eliminate the system dependences, correK
Kspec1
sponding to the ratio Kopt1
. Consequently, the ¯uoresopt2 Kspec2
cence intensity can be written as a function of the
temperature and reference conditions, as follows:
Rf …T†
ˆ …b1
ln
Rf …T0 †
1
b2 †
T
1
T0
…5†
and on the second one as:
2.2
Calibration
An initial calibration of the dye in the two selected spectral
where subscript 1 refers to the ®rst detection band and
bands was performed in a uniformly heated vessel in order
subscript 2 to the second one.
to determine the coef®cient (b1±b2). As shown in Fig. 3,
The calculation of the ratio of the ¯uorescence meathe temperature sensitivity in the ®rst spectral band is
sured on each color bands allows the measuring volume rather low (b2 100 K), and is much higher in the second
dependence and also the laser intensity and the dye con- one (b1 1730 K). Figure 4 shows the ¯uorescence ratio
centration to be eliminated. This ¯uorescence ratio can be ln…Rf …T †=Rf …T0 †† as a function of …1=T 1=T0 †. The effect
written:
of the dye concentration has also been investigated by
using two concentrations, C0 ˆ 5 ´ 10)6 mol/l and
Kopt1 b1 b2
Rf ˆ
e T
…4† C0 ˆ 2.5 ´ 10)6 mol/l. The value of the slope (b1±b2) ˆ
Kopt2
1670 K was found for C0 and (b1±b2) ˆ 1630 K for C0/2. It
A reference temperature T0 and the corresponding ¯u- means that a 1 °C temperature variation corresponds to
about a 2% variation in the ¯uorescence ratio. The 2%
orescence intensity ratio Rf(T0) are previously required
If2 ˆ Kopt2 Kspec2 Vc I0 Ceb2 =T
…3†
Fig. 3. Calibration of the ¯uorescence
intensity as a function of the temperature
in the two spectral bands (C0 ˆ 2.5 ´
10)6 mol/l): second color band,
k Î[525,535]; ®rst color band, k ³ 590
48
Fig. 4. Calibration of the ¯uorescence
ratio as a function of the temperature
and effect of the dye concentration: open
circles, slope b1±b2 ˆ 1,670 K,
C0 ˆ 5 ´ 10)6 mol/l; multiplication signs,
b1±b2 ˆ 1,630 K, C0 ˆ 2.5 ´ 10)6 mol/l
shift between the two values can be attributed to the
random error of the apparatus and, consequently, the
calibration can then be considered as concentration independent if the self-quenching phenomenon remains
negligible, which will be discussed in the next section.
The effect of the laser power on the ¯uorescence signals
on each color band was investigated in a static vessel
(Fig. 5): the linearity is well checked. The ¯uorescence
ratio is independent of the laser power within 1%, corresponding to an error in the temperature of less than
0.5 °C. The independence of the ¯uorescence ratio on the
measuring volume size was also veri®ed under static
conditions by using a set of different focal lengths in order
to change the measuring volume. No noticeable changes
were observed.
2.3
Absorption and self-quenching
rhodamine B in water by Lemoine et al. (1996). For
the ®rst time, Beer's attenuation of the laser radiation
propagating in rhodamine B dissolved in ethanol was
measured in a static cell (Fig. 6) by varying the laser
beam path, as the concentration is ®xed (C ˆ 5 ´
10)6 mol/l). The measured extinction coef®cient is
el ˆ 7.9 ´ 106 m/mol l. Furthermore, the absorption of
the ¯uorescence itself should be signi®cantly different in
the two selected color bands, since the second one coincides roughly with the maximum of the absorption
spectrum. A similar experiment was performed by varying the ¯uorescence path (Fig. 6). The results on the two
selected spectral bands are:
± ef2 ˆ 1.18 ´ 107/m/mol l for k Î[525 nm, 535 nm] at
T ˆ 22 °C,
± ef1 ˆ 1.5 ´ 106/m/mol l for the band k > 590 nm,
T ˆ 22 °C.
In this experiment, it was shown that ef2 appears eight
2.3.1
times higher than ef1, which may have serious conseAbsorption
The in¯uence of the optical paths in the absorbing me- quences on ¯uorescence reabsorption and may signi®dium must be carefully characterized, which was done for cantly change the ¯uorescence ratio in the case of large
optical paths. However, this problem should be overcome
in a 200-lm droplet diameter, where ¯uorescence absorption should not exceed 1% (0.5 °C) in the worst case.
For larger droplets and in dense polydisperse sprays,
additional measurement of the absorption would be
necessary.
2.3.2
Self-quenching
The in¯uence of the self-quenching phenomenon on the
¯uorescence quantum yield of rhodamine B must also be
seriously considered (Lopez Arbeloa et al. 1989). The ¯uorescence quantum yield, according to Perrin's law (Bruhat 1992; Bazile and Stepowski 1994), evolves as:
U ˆ U0 e
C=C …6†
Fig. 5. Variation in the ¯uorescence intensity and ¯uorescence
ratio as a function of the laser power: open circles, ®rst color band The critical concentration C is about 0.6 mol/l for the
rhodamine B molecule, according to Lopez Arbeloa et al.
(If1); multiplication signs, second color band (If2); crosses, ¯uo(1989). The dye dissolved in the droplets should not varescence ratio (Rf)
49
Fig. 6. Evolution of the ¯uorescence
intensity as a function of the optical path:
1 for the laser beam; 2 for the ¯uorescence
emission in the second spectral band; 3
for the ¯uorescence emission in the ®rst
spectral band
porize as ethanol, since its vapor pressure is many times
lower than ethanol. In order to maintain the ¯uorescence
constant within 1% (F/F0 ˆ 0.99), C/C should not
exceed 0.01. Consequently, when a droplet with an initial
diameter of D0 and an initial dye concentration of
C0 ˆ 5 ´ 10)6 mol/l vaporizes, the maximum allowed size
reduction for maintaining
the ¯uorescence constant within
1=3
C0

0:1,
which is far larger than the size
1% is DD0 ˆ 0:01C
range in the present experiments.
3
Experimental set-up
3.1
Droplet generator
A monodisperse droplet generator device was used
(Fig. 7). The main characteristics of this device are summarized here, and the advantages of using a monodisperse
droplet stream are brie¯y listed (Lavieille et al. 2000). The
injector is fed with ethanol seeded with a low rhodamine B
Fig. 7. Experimental set-up (in combustion con®guration)
50
achromatic lens (focal length, 310 mm). A ®ber coupled
achromatic doublet allows the ¯uorescence emission at a
right angle to be collected. The injector is mounted on a
3D traversing device with 12 lm resolution. The probe
volume, corresponding to the intersection point of the two
laser beams, is adjusted on the droplet stream so as to
reach the maximum ¯uorescence signal. The measuring
volume dimensions for the ¯uorescence signal are given by
the product of the excitation ®eld and the detection ®eld of
view, corresponding to (115 ´ 115 ´ 150 lm). The temporal resolution is determined by the residence time of the
droplet in the space resolved probe volume described
above, so that time integration of the ¯uorescence signal
comes to space averaging over the droplet in the stream
line direction.
The optical ®ber of the collection optics is connected to
an optical signal processing device. The optical signal
passes ®rst through a holographic ®lter (Super Notch Plus,
Kayser Optical) in order to block Mie scattering effects due
to the incident laser radiation, which may be considerable
in a spray, and could interfere seriously with the ¯uorescence emission. The notch ®lter has an optical density of
106 in a 5-nm bandwidth centered on the laser wavelength
k ˆ 514.5 nm, which is suf®cient to eliminate the laser
radiation effects.
After passing through the notch ®lter, the ¯uorescence
signal is separated into two parts by means of a neutral
beamsplitter. The ®rst part of the signal is processed by an
interferential ®lter centered at k ˆ 530 nm, with a 10-nm
3.2
bandwidth and is detected by a ®rst photomultiplier tube
Optical device
Two intersecting laser beams issuing from the same source (PMT) (Hamamatsu R2066), particularly sensitive in the
were used in order to create the probe volume. This device emission range of the rhodamine B. The second part
was used in order to perform simultaneous laser Doppler passes through an optical high-pass ®lter (cut-off: 590 nm)
and is detected by a second PMT (Hamamatsu R2066).
velocimetry (LDV) measurements. This optical device
Signals issuing from the PMT are processed via two
(Fig. 8) consists of a beamsplitter and a convergent
concentration. A piezoceramic induces Rayleigh instability
on a liquid jet ¯owing through a calibrated aperture and
breaks into a monodisperse droplet stream (Koenig et al.
1986). The aperture diameter F0 can be adjusted in order
to change the drop diameter. Two aperture sizes are used
in this experiment: a F0 ˆ 100 lm aperture diameter
supplying a droplet diameter of about 200 lm, and a
F0 ˆ 50 lm aperture diameter supplying a droplet diameter of about 100 lm. An appropriate choice of aperture
diameter, the excitation frequency of the piezoceramic and
ethanol ¯ow rate Q allow a monodisperse droplet stream to
be obtained. The main advantage of such a droplet generator is the separation of the parameters: all the droplets
are streaming at the piezoceramic frequency on a line,
have the same size and the same velocity at the injection
point, and are equally spaced. The non-dimensional distance parameter L can be de®ned as the ratio between the
inter-droplet distance (center to center) and the droplet
diameter. In such a jet, the temporal evolution of the
droplets' properties can be obtained by scanning several
streamwise positions on the jet. The fuel temperature can
be controlled at the injection point by means of a thermal
regulation device, and the injection temperature Ti can be
measured by means of a type K thermocouple. An electrically heated coil (length 12 mm) is used in order to
initiate the combustion or to provide a thermal impulse to
the droplet stream.
Fig. 8. Optical arrangement
synchronized rapid data acquisition boards implemented
in a computer.
3.3
Data processing
Data are acquired on the two measuring channels for 1 s,
corresponding to 333,000 samples on each channel. When
the signal is not ®ltered in frequency, it is impossible to
use Eq. (5) in order to determine the temperature. The
arrival process of the photons on the photodetectors, according to a Poisson law, involves important high frequency ¯uorescence signal ¯uctuations. The analogical
®ltering applied to the signal must be a trade-off between
an accurate description of the signal of the moving droplets and ef®cient ®ltering of the Poisson noise. A cut-off
frequency of 80 kHz seems to be a good trade-off (Fig. 9).
It allows a suf®cient number of photons to be accumulated
in order to average the statistical effect of the photons on
the detector. The signal is then divided into elementary
blocks, corresponding to a duration of about 15 ms, in
order to ensure insensitivity to the low-frequency random
motions of the jet. A Boolean test function allows the
samples for which the droplets coincide with the probe
volume (Fig. 9) to be determined on each measuring
channel. The percentage of the droplets taken up by the
measuring volume can vary from 100% to 10% according
to the turbulence level in the different measurement location. The signal corresponding to each individual
droplets is averaged on each elementary block and integrated, giving two signal values Ai1 and Ai2 for measurement channels 1 and 2 respectively (Fig. 10). The ratio
Rfi ˆ AAi1i2 is then calculated and averaged for each elementary block. The next step consists in calculating the average value of the ¯uorescence ratio Rf for the complete
sample by:
Pm
iˆ1 Ni Rfi
Rf ˆ P
…7†
m
iˆ1 Ni
51
Fig. 10. Principle of the integration on an averaged period and
determination of the ¯uorescence ratio
4
Experimental demonstration
Two kinds of experiments were performed: the ®rst concerns the in¯uence of a thermal impulse on the droplet
stream, and the second is the study of combusting droplets.
4.1
Thermal impulse
The ®rst type of experiment consists of generating a
thermal impulse on the droplet stream by means of an
electrically heated coil. For this experiment, the injection
velocity measured by LDV is ®xed at Vi ˆ 5.15 m/s, the
injection temperature at Ti ˆ 24 °C and the droplet diameter is about D ˆ 100 lm at the injection point, corresponding to a distance parameter of L ˆ 6.3. The
distance parameter is de®ned as the ratio between the
inter-droplet distance (center to center) and the droplet
diameter. The coil is placed between 19 and 23 mm (length
of the heating zone, 4 mm) from the injector exit. The
where Ni is the number of droplets involved in the calculation of the ¯uorescence ratio in each elementary block, inside coil diameter is about 4 mm and the power output
is 20 W. The length of 19 mm between the injector aperand m is the number of elementary blocks.
Fig. 9. Data processing and periodical
averaging process
52
ture and the coil is necessary in order to minimize the
radiation effect on the injection temperature. The temperature of the coil is adjusted so as to reach the inferior
limit of in¯ammation in this experiment. The jet streams
in the gravity direction for practical reasons rather than
for ¯uid dynamic considerations.
A reference is necessary in order to determine the
temperature by measuring the ¯uorescence signal
[Eq. (5)]. The reference is taken very close to the injection
point, where the liquid jet is cylindrical and not atomized
into droplets, at room temperature.
The jet is explored step by step, except in the coil area,
and the temperature measurements are reported in
Fig. 11 as a function of the time elapsed from the injector
exit, which allows the kinetic of heat transfer to be
monitored directly. It should be remembered that, for
such a monodisperse stream, the distance can be converted into time by the relation t ˆ x/Vi (t is the time, x
is the distance), where Vi is measured at each point by
LDV. As shown in Fig. 11, the droplets are pre-heated
before entering the coil area. This can be attributed to the
strong natural convection phenomena caused by the high
temperature of the coil. The effect of the coil on the
droplet stream seems to be rather low, with a 2 °C
temperature increase, in the continuity of the pre-heating
phenomenon. The temperature increases gradually and
attains a maximum about 5 ms after the coil exit, and
then drops to the ambient due to cooling by forced
convection and evaporation. The droplets are not immediately heated by the radiative and convective ¯uxes of
the coil. The question is to know whether this delay can
be attributed to the conductive heat transfer between the
droplet surface and its inner layers or by an additional
energy gain. A simple heat transfer analysis allows one to
determine the time necessary for reaching the equilibrium temperature in the droplet by heat conduction. The
imposed surface heating conditions are the following for
this analysis:
± rÎ[0; 0.9R], T ˆ Ti
± rÎ[0.9R; R], T±Ti ˆ 50 °C
We have selected a 50 °C temperature difference corresponding to a surface temperature close to the boiling
point of ethanol, which is the maximum allowed temperature for the liquid phase. The heat transfer equation was
solved in the spherical coordinates system, assuming that
there are no thermal ¯uxes in the droplet surface. The
ethanol thermal conductivity k is substituted by an effective conductivity keff ˆ 2:72k (Johns and Beckman 1966)
in order to take into account the internal motion of the
¯uid. The calculated results, reported in Fig. 12, show that
the time for reaching a homogeneous temperature distribution is about 1 ms. The equilibrium temperature of the
droplet, assuming a constant thermal capacity, is given by:
Tequilibrium
1
ˆ
4pR3
ZR
T…r†4pr 2 dr
…8†
0
Considering this result, it is also important to note that
the laser-induced ¯uorescence (LIF) technique provides a
temperature measurement naturally weighted by the
droplet volume and by the Gaussian distribution of the
laser energy in the laser beam (Lavieille et al. 2000).
Indeed, the ¯uorescence ratio is calculated from two
intensities, each corresponding to a space-averaged value
of the ¯uorescence emission over the resolved probe
volume.
Consequently, the temperature given by LIF (TLIF) is
close to the equilibrium temperature. The temperature
TLIF was computed (Fig. 13) for the different times considered in the heat transfer calculation presented in
Fig. 12. The temperature given by the LIF technique
reaches 85% of the equilibrium temperature (Tequilibrium)
within 0.2 ms, and the measurement is therefore quasiinsensitive to the temperature distribution over the
droplet. We can then conclude that the heating time
(5 ms) of the liquid measured by LIF (Fig. 11) is too long
to be attributed to the conductive heat transfer time
(0.2 ms). The heating phase observed after the coil exit
between 5 and 10 ms (Fig. 11) corresponds to an additional energy gain, attributed to the convection heat
Fig. 11. Effect of a thermal impulse on the
droplet stream
53
Fig. 12. Numerical simulation of heat
conduction in the droplet as a function of
time
transfer between the surrounding transported heated vapor and the liquid phase, which should be considerable for
the short distance parameter used (L ˆ 6.3). As a conclusion, it was clearly demonstrated that a low amount of
energy is gained by the liquid phase during its transit in
the coil. An important part of this energy is used to vaporize the liquid phase. The coil heats only the vapor
phase, which is entrained by the stream and heats the
droplets with a signi®cant time lag, by forced convection.
heated and the ethanol in¯ammation temperature (about
1,000 °C) is reached, the ¯ame appears 23 mm after the
injector exit, just after the coil exit (Fig. 14). The ethanol
¯ame is essentially blue with some orange parts. The goal
is to measure the liquid droplets' temperature in the ¯ame
and, consequently, it was previously checked that the interference between the blue emission of the ¯ame and the
¯uorescence signal was negligible. Furthermore, the
4.2
Combustion
The reference is taken similarly to that in evaporation. The
injection temperature Ti is controlled by heating the body
of the injector, and three injection temperatures were investigated: Ti ˆ 23 °C, Ti ˆ 45 °C and Ti ˆ 56 °C. The jet
is now streaming in the opposite direction to the gravity
because of the presence of the ¯ame. The ignition coil is
similar, as it was used in the preceding experiment and is
placed at the same position. When the coil is suf®ciently
Fig. 13. Averaging effects of the technique on the temperature
measurement
Fig. 14. Droplets combustion experiment
54
emission intensity of the orange parts of the ¯ame is far
lower than the ¯uorescence level, and therefore negligible.
For the combustion experiment, the piezoceramic
frequency is ®xed at 12.8 kHz, allowing a monodisperse
stream to be obtained for an injection velocity of around
5 m/s. The injection pressure of the liquid is ®xed, but it is
impossible to maintain the injection velocity constant
when the injection temperature varies, because of the
variation in the fuel viscosity with the temperature. Consequently, the distance parameter is around 2. Table 1
gives the exact characteristics of the combustion experiment, such as the injection temperature Ti, the injection
velocity Vi measured by LDV, and the distance parameter
L (de®ned conventionally just after the break-up zone).
The droplet size is about D ˆ 200 lm at the injection
point for this experiment.
The gas phase temperature was measured by coherent
antistokes Raman scattering thermometry: the gaseous
phase temperature varies from 1,500 K in the jet center to
2,000 K in the edges. In this experiment, we focused on the
phase of the combustion for which the ¯uorescent tracer
concentration increase due to fuel vaporization has no
effect on the ¯uorescence ratio and on the burning
process.
The temperature distribution of the droplets along the
jet is presented in Fig. 15 as a function of the time
elapsed from the injection aperture. The ®rst points located between the injection point and the coil entry exhibit a temperature clearly lower than at the injection.
Table 1. Characteristics of the combustion experiment
Ti (°C)
Vi (m/s)
L
23 °C
4.6
1.77
45 °C
5.8
2.23
56 °C
6.1
2.37
This phenomenon shows simply the cooling of the
droplets due to vaporization. The three curves seems to
converge to an equilibrium temperature of about 42 °C in
less than 10 ms after entering the ¯ame area. This equilibrium temperature can be attributed to the equilibrium
between the thermal loss ¯ux required for vaporizing the
droplet, the convective ¯ux, and the radiative ¯ux fed by
the combustion. The ¯ame front is located at a noticeable
distance, corresponding to a few droplets' diameter, from
the droplet stream (Fig. 15). The high convective ¯ux is
due to the temperature difference between the liquid
phase and the extremely hot gaseous surrounding and to
the relative velocity between the two phases. The heat
transfers occur on the liquid surface and the core droplet
temperature is modi®ed by heat conduction within the
droplet enhanced by the internal vortex (Chiang et al.
1992).
Also, there is no signi®cant mean temperature difference between the entry and the exit of the coil. It demonstrates, as in the preceding experiment, that thermal
¯ux of the coil does not heat the droplets directly, but
heats the surrounding vapor. The curve corresponding to
Ti ˆ 56 °C seems to present very few temperature variations in the ®rst period, which can be attributed to the
presence of a large amount of vapor in the vicinity of the
droplet. This hypothesis can be justi®ed by placing the coil
nearer the injection point, for which case the temperature
decrease appears quicker since there is less accumulated
vapor in the vicinity of the droplets. This statement is
con®rmed by the curve corresponding to Ti ˆ 23 °C,
where the increase of the temperature to the equilibrium
occurs quite instantaneously, because of the low fuel mass
fraction present in the gaseous surrounding of the stream,
due to the low vapor pressure at Ti ˆ 23 °C.
When the droplet are injected at Ti ˆ 45 °C, i.e. close to
the equilibrium temperature, very few temperature variations are noticed.
Fig. 15. Temperature distribution of the
combusting droplets in a monodisperse
stream in for three injection temperatures:
open triangles, Ti ˆ 23 °C, Vi ˆ 4.56 m/s,
L ˆ 1.77; open squares, Ti ˆ 45 °C,
Vi ˆ 5.8 m/s, L ˆ 2.23, open circles,
Ti ˆ 56 °C, Vi ˆ 6.1 m/s, L ˆ 2.38
(D ˆ 200 lm)
5
Discussion and conclusions
The ®rst part of this discussion will be devoted to the error
analysis of this technique. Part of the random error can be
attributed to the temperature sensitivity slope, denoted by
(b1±b2), determined within ‹1%, resulting in a systematic
error of ‹0.3 °C. The second error source is located in the
data-processing method. The periodicity of the ¯uorescence intensity, due to the monodisperse behavior of the
stream, was used in order to average the signals and to
smooth the Poisson noise effects. We tested a large range
of data processing parameters, such as the size of the elementary blocks under which the periods of the ¯uorescence signal are averaged. Changes in these parameters
induce a maximum random error of 0.5%. The absolute
accuracy of the technique is probably of the order of 1 °C
in the evaporation case, but the relative accuracy, by
comparison to a reference, is probably better. The accuracy in the combustion situation remains dif®cult to
evaluate.
This new method is of course insensitive to the
Gaussian distribution of the laser energy over the laser
beam and to the lensing effect of the spherical air±droplet
interface, tending to focus the laser intensity. This technique allows the temperature to be determined by averaging the signal corresponding to a droplet travel across
the measuring volume on a period and is detected on the
entire depth of the droplet, resulting in a mean temperature measurement. However, with the use of a small
measuring volume, the technique has potential for detecting temperature gradients within the droplet, if a deconvolution model of the ¯uorescence signal is applied. In
a general overview of the paper, we can conclude that this
new technique has a large potential for measuring the
temperature of heated and combusting droplets. This will
probably provide valuable information about spray combustion for validating existing calculation models and
developing a more ef®cient one. The paper has presented
experiments performed on a monodisperse stream, and
the role played by the heat transfer between the liquid
droplet and its surroundings has been pointed out. In
combustion, the evaporation process occurs at an equilibrium temperature lower than the fuel temperature
boiling point.
The technique could be worth extended in the case of
polydisperse stationary sprays by using appropriate electronic data processing.
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