Simultaneous measurements of velocities and sizes ofparticles in flows using a combined systemincorporating a top-hat beam technique
Gerard Grehan and Gerard Gouesbet
A combined system using laser Doppler velocimetry for velocity measurements and a top-hat laser beam(THLB) technique for simultaneous sizing is described. Measurements have been carried out on varioussprays produced by a TSI-3050 generator. Results are compared with scattering theory, free-fall velocitycomputations, and holography measurements. The conclusion is that the measurement obtained from thecombined system are satisfactory.
1. Introduction
Simultaneous measurements of sizes and velocities(and possibly concentrations) of discrete particlestransported by flows are of increasing interest both forthe researcher wishing to understand and describe thelaws of nature, who is almost inevitably faced withmultiphase problems, and for the engineer who has todesign and control various plants and processes involv-ing heat and mass transfer phenomena. Lack of spaceprevents us from giving examples but readers willreadily find those which correspond to their own fieldsof interest.
Emphasis is put on nonintrusive optical techniqueswhich usually do not disturb the medium under study.In this work, the velocimetry problem is solved bymeans of classical laser Doppler velocimetry (LDV).Ways of simultaneously measuring the diameter of theparticles producing the Doppler bursts have been dis-cussed in review papers.1 2 Briefly stated, using theDoppler bursts, two main techniques have been devel-oped for simultaneous velocimetry and sizing, namely,the visibility technique which correlates the particlediameter and signal visibility3-5 and the pedestal cali-bration method which correlates particle diameter andthe amplitude of the signal pedestal.6-10
Both techniques present advantages and disadvan-tages that we have discussed elsewhere.1 2 The pedes-
The authors are with INSA de Rouen, Laboratoire d'Energetiquedes Systemes et Procedes, UA CNRS 230, B.P. 08, 76130 Mont-Saint-Aignan, France.
tal calibration technique is essentially subject to theso-called trajectory ambiguity: a large particle cross-ing the edge of the control volume is confused with asmall one having a median trajectory. Because of thisambiguity, it is impossible to attach one velocity andone diameter to an observed particle. It is only possi-ble to record velocity and size probability densityfunctions simultaneously, when an assumption of tra-jectory equiprobability is used to perform the mathe-matical inversion scheme discussed in detail by Holveand Self.67 Consequently, this technique does notmeet our aim which is to simultaneously measure sizesand velocities, particle by particle.
The visibility technique has been successful inachieving the above stated aim in some experiments.However, our opinion is that this technique is neitherfully developed nor generally reliable and works onlywhen some very restrictive assumptions are met in theexperimental design. As stated by Ghezzi et al,'1"many ... reliability tests, improvements and modifi-cations are necessary." The main drawback is proba-bly that an exact theory of the visibility concept is stilllacking. Such a theory would enable us to control theconcept precisely but remains to be developed. Apreliminary necessary step toward such a theory is theproduction of a generalized Lorenz-Mie theory wherethe properties of the light scattered by a Mie scattercenter illuminated by a Gaussian beam could be com-puted.1 2-15 Furthermore, ideally, a knowledge of theparticle trajectory is still required to interpret visibili-ty data.
With these considerations in mind we chose to devel-op another approach based on the following threepoints:
(i) Use of monotonic relationships between particlediameters and scattered powers for sizing.
(ii) Use of two different optical probes, one for velo-cimetry which will be a classical LDV probe and anoth-er for sizing. In other words, simultaneous measure-ments of sizes and velocities are not carried out onindividual Doppler bursts but on two separate signalsproduced from two separate optical probes, spatiallysuperimposed but using two different colors.
(iii) Getting rid of the trajectory ambiguity by cor-recting the Gaussian cross-sectional repartition of en-ergy in the sizing beam to a top-hat profile.
When one particle crosses the dual optical probe, itgives birth to a LDV signal from the LDV probe and toa sizing signal from the sizing probe. The sizing signalis a top-hat signal which is a copy of the energy reparti-tion in the sizing probe. Its height is linked to theparticle diameter using the monotonic relationshipspreviously mentioned.
II. Monotonic Relationships
To determine particle diameters from scatteredlight powers, we have to obtain monotonic relation-ships linking these quantities. The Lorenz-Mie the-ory is used to predict the properties of the light scat-tered by a Mie scatter center (diameter d, complexrefractive index m = n - ink) illuminated by a planewave.16,13, 7
Computer programs must be designed to handlenumerical computations. However, when based onclassical algorithms, they usually suffer from limitedranges of application due to numerical instabilities.
Fortunately, a very efficient algorithm for comput-ing Bessel function ratios has been established byLentz.18 Using it, we built a new computer program,the so-called SUPERMIDI19 which, in its more recentversion, is able to compute scattered intensities, thephase angle between perpendicular scattered compo-nents, cross sections, efficiency factors, turbidity,pressure radiation, and some of the quantities relevantto the study of multiple scattering problems.2 0
The SUPERMIDI computer program has been used, inconnection with accessory programs, to compute thepowers which are scattered and collected in a givendirection of observation and for a given solid angle ofcollection, according to the typical scattering geometrysketched in Fig. 1.
Computations for several materials have been pub-lished elsewhere, for diameters ranging from 1 to 300Arm (typically), with emphasis on scattering anglesnear 90°, and for particles made of glass, aluminum,fuel, water and alcohol in air, or air bubbles in wa-ter. 9 21 -25 In all cases, monotonic relationships havebeen obtained when the solid angle of collection is largeenough to smooth the lobe pattern inherent to Lorenz-Mie scattering. Although a direction of observationdefined by 0 = 0 = 90° is a good choice in any caseexamined, it is not always the best choice. For waterdroplets in air, a direction 0 = 600, 0 = 900 could berecommended while, in the case of fuel, a direction 0 >1000 is preferable.
For near-forward scattering and transparent parti-cles, computations can also be achieved with reason-
x
(electric field ct 9v~~(scatteringcincident right
QŽ: solid angle ofy collection
-enter)
direc onof propagation
Fig. 1. Scattering geometry for the INTIMI or GENMIE program
able accuracy by means of a simplified version of geo-metrical optics.2 3 26
Examples of computations will be given in the dis-cussion of experimental results.
Ill. Dual Optical Probe
The idea of using two different probes, one for LDvelocimetry and the other for sizing, was apparentlyintroduced for the first time by Durst and Umhauer.27
It is also described and developed in Refs. 28-30. Thesizing light source was a white light source. The ad-vantage of white light is to smooth out the complicatedlobe structure associated with the Lorenz-Mie scatter-ing pattern. The optical sizing setup was designed toproduce a probe volume of uniform illumination,avoiding the trajectory ambiguity. Nevertheless, sucha system suffers from limitations when used in hostileenvironments, such as in flames or plasmas. In thesesituations, the collected light must usually be filteredto remove stray or background photons in order to get agood SNR. When the optical filtering bandwidth issmaller than the light source bandwidth, the use of awhite light is of no interest. Furthermore, it seemsdifficult to project the white light control volume atarbitrary distances from the focusing optics, thus lim-iting the potential range of applications.
We consequently decided to produce a similar com-bined system where the sizing light source would be alaser beam instead of a white source. A similar ap-proach was also chosen more recently by Hishida etal., 3 1 Bates et al., 32 and Hess.33
IV. Gaussian Beam Correction to a Top-Hat Profile
When a scattering particle travels through a Gauss-ian beam, the scattered signal depends on the time,according to the particle trajectory, giving rise to theso-called trajectory ambiguity: a large particle pass-ing through the edge of the control volume is confusedwith a small one having a median trajectory.
When the Gaussian beam is corrected to a top-hatprofile, the trajectory ambiguity disappears since thecollected signal now also has a top-hat shape. Fur-thermore, the scattering response can easily be com-puted in the framework of the Lorenz-Mie theory.
Consequently the use of an incident top-hat laserbeam enables us to take simultaneous advantage of theproperties of the laser light (high luminance, directiv-ity, monochromaticity) and of the white light source
system with uniform illumination and removal of thetrajectory ambiguity. Such a combination of advan-tages is useful in many fields: photolithography, in-formation storage, laser projection printing, laser etch-ing, which is why a lot of work is devoted to thecorrection of Gaussian beams to top-hat beams (seeRefs. 34-41 among others).
As far as our work is concerned, we have used eitheran anti-Gaussian metal-coated absorbing filter or aholographic filter produced according to the Quintan-illa and de Frutos technique.42 Advantages and disad-vantages of these two correcting techniques are de-scribed elsewhere.2 5 The holographic filter is a singlecomponent which is easy to adjust but which does notwithstand the laser power and is significantly de-stroyed after a few hours of operation time. For thisreason the first correcting device will be used in thiswork.
It is also interesting to compare the production of atop-hat beam as recommended here and another possi-bility which assimilates the central part of a sizingGaussian beam to a region of constant illumination.When the sizing beam is enlarged to ensure that itscentral region has constant illumination with goodapproximation, the procedure results in a systemwhich is very poor in terms of energy efficiency.Hess,3 3 however, for example, does not enlarge hissizing Gaussian beam (which has a i/e2 diameter ofabout do = 1 mm) and selects the central part with theaid of a smaller LDV probe. If we consider a particle ofdiameter d, it is possible to evaluate the modificationsin the scattered intensities due to the Gaussian charac-ter of the beam with respect to the plane wave case vsdido. For this we can use the localized approxima-tion15 to the generalized Lorenz-Mie theory. 2-14 Thislocalized approximation is not yet published but rele-vant results are worth presenting here. Figure 2 showsthe differences in scattered intensities computed ei-ther by Lorenz-Mie theory or by our localized approxi-mation (error in percent) vs the ratios ddo of theparticle diameter d over the 1/e2 beam diameter do.For particles with diameters of 200 btm in a beam of700-bum diameter (dido 0.3), the error reaches -10%.Conversely, similar errors are not expected using top-hat profiles when the diameter of the corrected top-hatpart of the probe is larger than about twice the particlediameter.
Experiments using top-hat laser beams have beenpublished for a pure sizing system23-25 and parts of thedevelopment of a combined system for simultaneousvelocimetry and sizing are discussed in Refs. 29 and 43.The development has been fully completed in collabo-ration with the German company OEI (Opto-Elek-tronische Instrumente) to produce a prototype whichis described and discussed in the rest of this paper.
V. General Presentation of the Optical Setup
The overall setup is formed by a laser Doppler velo-cimeter combined with a top-hat laser beam sizingsystem (Fig. 3). The source is a Spectra-Physics 168-
10
9
8
7
6
5
4
3
2
Fig.2.
error
0.06 0.12 0.17 0.23 0.3 d/doPercentage of error on the scattered intensities for a particle
lighted by a plane or a Gaussian wave.
LD-0.701
LD-0.610/1LD-OK-501
beam-turningreflector
~ taser- I-L..... lli
/D-O-10 D-o-3o24o2A/4
LD-OG -10 LD-01K-302/402 A/4'
Fig. 3. Overall setup.
04 argon-ion laser working in the TEMoo multilinemode. To reduce the length of the device, the laserand the optical setup are parallel, the direction of thelaser output beam behind modified by 1800 with theaid of a beam-turning reflector. All the elements aremounted on a ground plate ensuring good rigidity andadjustment stability.
The optical setup is made of optical and optoelec-tronic modules. The modules can be easily assembledand are connected with the aid of ring connectors.
The laser beam, forming the optical axis, is firsttreated by a (X/4) retarder plate. The LD-OK-302/402 (OEI reference number) module contains a colorseparator, a beam splitter (302 part), and a doubleBragg cell module which is required for some veloci-metry applications (402 part). The central sizingbeam is corrected to a top-hat beam by the LD-OG-10module. The last component of the transmitter opticsis the LD-0-610/1 front lens. The LD-OK-501 mod-ule is only used for LDV backward collection. TheLD-0-701 is the sizing collecting optics.
VI. Module Discussion of the Optical Setup
A. Beam-Turning Reflector
The beam-turning reflector is made of two mirrorsoriented at 450 to the main system directions. Theexact horizontal and vertical adjustments of the laserbeam into the optics are ensured by the beam-turningreflector mirrors. A beam expander can also be fixed
E flik, A F ~~~~~~~~blueI~~ /Fig. 4. Module LD-OK-302.
at the entrance of the beam-returning system to modi-fy the dimensions of the dual optical probe.
B. The (X/4) Retarder Plate
The plate is used to transform the linear polarizationof the beam to circular polarization. The utility of thiscomponent will be made clear later.
C. Module LD-OK-302/402
The LD-OK-302/402 module is connected to the (X/4) retarder plate support by a ring connector allowingfor complete rotation of the module.
The first part of the module (302) produces a centralblue beam (X = 488 nm) and two green beams ( =514.5 nm) which are parallel, have equal intensities,and are separated by a distance of 50 mm. These twogreen beams propagate symmetrically with respect tothe optical axis defined by the blue beam. This spatialand frequency separation is described in Fig. 4.
A second (/4) retarder plate is fixed with respect tothe color separator SC and transforms the circularpolarization of incoming light into linear polarization.Under these circumstances, the color beam splitterand the following components are constantly illumi-nated by the same incoming waves (same intensities,same polarizations) whatever the module orientation,ensuring a constant quality of the dual optical probe.This is why the first retarder plate is essential.
Since the color beam splitter is not perfect, an addi-tional interferential filter Fl had to be incorporated onchannel A to avoid color crosstalking between the two(green and blue) channels A and B.
The green beam is divided into two parallel beams ofequal intensities by the beam splitter SF. A rhombicprism, identical to the color separator, relocates theblue beam on the optical axis.
The 402 part of he module permits a frequency shiftof each green beam with the aid of two Bragg cells,useful for certain LDV applications, e.g., removal ofdirectional ambiguity.
The LDV green beams then propagate to the frontfocusing lens LD-0-610/1 without further modifica-tion.
D. Module LD-OG-10 (Fig. 5)
The LD-OG-10 module transforms the Gaussianblue beam to a top-hat sizing probe. An afocal system(converging lenses Li and L2 of 20- and 250-mm focallengths, respectively, with a spatial filter SF which is a15-Am diam pinhole) expands the blue beam in theratio of the focal lengths. Such an expansion is neces-sary to limit the thermal stresses produced later in the
Ll
B
L4
Fig. 5. Module LD-OG-10.
1
A
Pc-7mm Pmm
Fig. 6. Absorption law of the Gaussian filter.
L 3
Fig. 7. Module LD-OK-501.
anti-Gaussian correcting filter (AGCF) by laser irra-diation.
The AGCF is obtained by a metal coating depositedon a glass plate of high optical quality. Absorption Aof the filter vs distance p to the axis is shown in Fig. 6.It transforms the Gaussian profile (Fig. 5, Sec. A) to atop-hat profile (Fig. 5, sec. B). The dimension of thetop-hat beam is reduced to the final dimension of thesizing probe ( 800-gm diameter) by another afocalsystem made with a converging lens of focal length L3= 350 mm followed by a diverging lens of focal lengthL4 = 20 mm.
The LD-0-610/1 front lens is pierced at its center bya 5-mm diam hole which lets the sizing beam passwithout any modification.
E. Backward Module LD-OK-501 (Fig. 7)
The backward module is used for LDV backwardcollection. The scattered light is collected by the LD-0-610/1 lens. The scattering particle being adequate-ly located in the focal plane of the front lens, thecollected light forms a parallel beam which is focusedby lens L'1 on a spatial filter SF2 (100-Mm diameter)which can be adjusted in the transverse directions to
minimize optical noise. Lens L'2 produces anotherparallel beam whose axis is displaced by mirrors Mland M2 and which is focused by lens L'3 on the photo-multiplier PM1 entrance pinhole.
In this setup, the blue sizing beam, whose axis isdisplaced by a rhombic prism added to the LD-OG-10correcting module, travels below the collecting opticsand is relocated by another rhombic prism RP.
F. Collecting Optics of the Sizing Channel (Fig. 8)
The collecting optics of the sizing channel is the LD-0-701 module. It collects the scattered light at 900from the direction of propagation of the blue beam andat 900 from the polarization plane (defined here as theplane containing the direction of propagation and theincident electric field). The angle between the inci-dent beam and the direction of observation can beadjusted to within 200 in this standard version.Lens Li of 150-mm focal length and 63-mm diameterconjugates the control volume and the photomultiplier(PM2) entrance pinhole with a magnification unity.The solid angle of collection can be modified with thediaphragm. Its diameter may be adjusted between 5and 60 mm. The components shown in Fig. 8 are notin the same plane. To produce a more compact sys-tem, the direction LiM' is actually perpendicular tothe direction M 20'
VIl. General Presentation (Fig. 9) of the Electronics
The light scattered by a particle passing through thedual optical probe is collected by the LD-OG-601/1lens (velocity channel) and produces an electronic sig-nal behind the photomultiplier PM1. This LDV sig-nal is filtered by a filter bank VBF which removes thepedestal and high-frequency noise. It is afterwarddigitized by a DM 901 transient recorder. After vali-dation by the box OXD, the digital information is fedinto the microcomputer.
The blue sizing light is collected by lens Li of theLD-0-701 module and produces an electronic signalbehind photomultiplier PM2. This signal is digitizedby the DM 305 transient recorder (with the necessarycondition that the DM 901 velocity transient recordermust be activated) and fed to the microcomputer.
VII. Component and Operation Discussion of theElectronics
A. Photomultipliers
The PM1 system contains the photomultiplier itself,the voltage divider chain, and an amplifier. The pho-tomultiplier tube is an EMI 9871B with an S20 photo-cathode. The bandwidth of the photomultiplier isfrom 0 to 20 MHz. The photomultiplier entrancepinholes are provided with diameters of 100, 200, 300,400, and 500 Am. They are transversally adjustablewithin a 3-mm diam circle. Between the entrancepinhole and the photocathode, there is an interferen-tial filter at = 514.5 nm to remove the blue lightcoming from the sizing probe. The PM2 system issimilar to the PM1 system, except for the following
D
Fig. 8. Module LD-0-701.
Fig. 9. General presentation of the electronics.
points: (i) the protecting interferential filter is set at488 nm to remove the green light coming from the LDVprobe and (ii) the diameter of the entrance pinhole is 1mm.
The high voltage supply of the photomultipliers is adouble supply, having different characteristics accord-ing to the channel. The LDV channel supply can beadjusted by eleven 50-V steps, from 850 to 1350 V,while the sizing channel supply can be adjusted byeleven 50-V steps, starting from 600 V.
B. Filter Bank
The filter bank is composed of seventeen Chebyshevfilters of the seventh order, with slopes of 60-65 dB peroctave: nine high-pass filters with nominal frequen-cies of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, and 20 MHz, andeight low-pass filters with nominal frequencies of 0.2,0.5,1,2,5,10, 20, and 50MHz. The proper choice of abandwidth by selecting one high-pass filter and onelow-pass filter enables us to remove the pedestal and toimprove the SNR.
C. Transient Recorders
The LDV transient recorder is an Iwatsu DM 901.Signals are digitized in 1024 words of 8 bits. The rateof digitizing is adjustable from 10 ns to 0.5 s per word in24 steps.
The sizing transient recorder is an Iwatsu DM 305.Signals are again digitized in 1024 words of 8 bits, butthe rate of digitizing is smaller: from 1 s to 1 s perword in 19 steps. The signal acquisition of the DM 305is triggered by the presence of a LDV signal on the DM901. Consequently, the existence of a LDV signal isrequired to obtain sizing information (this point will bediscussed again later).
The logic box OXD contains a microprocessor Z80and performs the LDV signal validation. It providesthe microcomputer with the information required tocompute the velocity of the scatter center, namely, theduration of the signal and the numbers of zero cross-ings. A noise protection procedure is also incorporat-ed in the box.
E. Production and Processing of a Dual Signal
The dual optical probe is formed with a blue sizingprobe of constant illumination, of -- mm diameter,surrounding a smaller LDV green probe having a typi-cal diameter of -200,4m (Fig. 10).
A particle having a trajectory of type A does nottrigger the LDV transient recorder and is consequentlyignored by the electronic device. For a trajectory oftype B, as soon as the LDV transient recorder begins todigitize the filtered LDV signal, an order is given to thesizing transient recorder to start operating. A corre-sponding dual signal is sketched in Fig. ii. The begin-ning of the sizing plateau is obviously lost in the pro-cess. Figure 12 shows an example of a top-hat sizingsignal digitized in 1024 words of 8 bits on 127 levels.
The sizing signal must be validated. In particular, itmust be checked that only one particle is present in thecontrol volume. Afterward, the height of the plateau
Fig. 12. Digitized size signal.
is measured. All these operations are at the presenttime carried out by a FORTRAN program. In anotherversion of this combined system, they will be incorpo-rated in a logic box similar to the OXD.
The FORTRAN program starts by reading the wordsfed from the DM 305 transient recorder. IBUF(i) isthe value of the first word. The program checks thevalue; if it is either too small or too large a logicalcounter is incremented by one. This operation en-ables us to define more precisely an amplitude spec-trum when the signal dynamics is larger than the ad-mitted processing dynamics, defined by theacceptance of the values corresponding, for example,to the levels between 5 and 125.
The program then defines the acceptable quality ofthe plateau which must be constant within a ± (delta)value. Then it looks for the end of the plateau definedby time I for which the signal decreases below[IBUF(i) - delta]. Length I of this plateau is com-pared to a preset criterion ILONG and the signal isrejected when I < ILONG. Finally, the steepness ofthe decreasing slope must be high enough. In otherwords, the quality of the plateau is validated usingthree criteria involving (i) the constancy of the plateauamplitude, (ii) its length, (iii) the steepness of its de-creasing slope.
When a signal is validated, the height of the plateauis computed as the arithmetic mean of all the pointsIBUF (K), K from 1 to I. At this stage, the microcom-puter contains the dual information velocity/ampli-tude attached to the particle which has crossed thedual probe.
IX. Results and Discussion
A. Medium Under Study
To examine the proper operation of the combinedsystem described above, systematic measurementshave been carried out on clouds of droplets producedby means of a TSI-3050 particle generator (Fig. 13).The droplet generation is consequently quite similar tothat used in previous works.23-2 5 However, the piezo-electric ceramic of the TSI generator has beenchanged, with the result that we observe a smallernumber of satellite droplets.
The liquid orifice assembly is located at the top ofthe standard exit column in such a way that the drop-lets flow downward. The flow rate of the dispersion
air is 1500 cm3 min-'. Since we wanted the particles tofall freely downward, no dilution air was used. This isnot the standard method of generating the particlesbut has been chosen because it is more convenient forlarge particle investigations (typically for diametersfrom 80 to 300 ,um). Particles are produced usingnominal orifice diameters of 100, 50, and 35 ,m withsyringe pump gear positions 11, 13, and 15, and opera-tion frequencies set to 7, 17, and 22.1 kHz, correspond-ing to nominal diameters of 195, 115, and 85 ,im, re-spectively.
Measurements have been carried out for two differ-ent liquids: water and methanol. These liquidspresent the advantage of having different densities(that is to say different free-fall velocities for the samediameters) but the same refractive indices (1.3372 and1.3331, respectively), i.e., the same scattering respons-es.
B. Scattering Geometry
The dual optical probe is located on the axis of theTSI exit column (Fig. 13), 3 cm below the exit section.The incident electric field vibrates in the verticalplane.
The sizing observation direction is located in thehorizontal plane at 900 from the incident sizing beam.The scattered light is collected by the collecting lens,with maximal aperture of the associated diaphragm(6.3-cm diameter). For LDV it was not necessary touse the backward collection module since the opticalaccess was free in all directions. The direction of LDVobservation was at 800 to the incident sizing beam andthe light was collected by a lens of 150-mm focal length,with a 60-mm diameter.
C. Dual Measurements
Table I shows a typical presentation of results ob-tained for water droplets, with the following TSI oper-ating conditions: orifice diameter: 100 gm, syringepump gear position: 11, operation frequency: 7 kHz,
Table I. Typical Water Droplet Measurementsa
IPET = 0 IGRO = 0 INVAL = 502
J= 1 N=O U= S=J= 2 N=3 U= 74 S = 8J = 3 N = 26 U = 77 S = 7J = 4 N = 29 U = 83 S = 10J = 5 N= 18 U= 104 S = 10J= 6 N= 12 U= 112 S= 8J = 7 N= 10 U= 118 S = 13J= 8 N= 1 U= S =J=9 N=O U= S=J=10 N=O U= S=J= 11 N=O U= S=J=12 N=O U= S=J= 13 N=O U= S=
a IPET represents the number of counts corresponding to anamplitude smaller than the background noise level; IGRO repre-sents the number of counts corresponding to an amplitude largerthan the admitted dynamics; INVAL is the number of particleshaving produced a valid LDV signal but a nonvalid sizing signal.
which correspond to a nominal diameter value equal to195 m.
It displays (i) the number J designating the class ofamplitude (digitizing is carried out with 127 levels anda class width is equal to 10 levels), (ii) the number N ofparticles in each class, (iii) the arithmetic mean veloci-ty U of the particles in the class, and (iv) a (crude)estimator S of the rms velocity. The data can also bedisplayed as a histogram. IPET is the number ofcounts corresponding to an amplitude smaller than thebackground noise level and IGRO is the number ofcounts corresponding to an amplitude larger than theadmitted dynamics. INVAL is the number of parti-cles having produced a valid LDV signal but a nonvalidsizing signal. In the present experiments, five out ofsix signals were rejected. This rate of validation obvi-ously depends (among other things) on the user de-mand in defining the validation criteria. In all theresults presented in this paper, the constancy of theflat signals had to be better than ±6%. This presenta-tion is statistical, although dual measurements werecarried out particle by particle. Ninety-five percent ofthe signal amplitudes are in the range of classes 3-7with mean velocity values ranging from 77 to 117 cm/s,and increasing monotonically with the class number.Assuming that the particle velocities are equal to theStokes free-fall velocities (a point to be discussed morefully later), the velocity range (77, 117 cm/s) corre-sponds to diameters ranging from 170 to 205 ,um.These diameter values agree with the TSI nominaldiameter value (195 m) if we assume a 10% dispersionas observed in our previous works.25
Figure 14 shows a 3-D presentation of the same data,emphasizing the fact that dual measurements are car-ried out particle by particle.
The V axis corresponds to the particle velocities bysteps A V of 2 cm/s and the A axis corresponds to thesignal amplitudes by steps A A of 5 levels of digitizing.N is the number of signals in a class (A V, A A). Thisgives a direct visualization of the correlation betweensignal amplitudes and particle velocities. These ex-periments have been repeated many times and would
200Fig. 15. Signal amplitude vs the measured velocity: water experi-
ment 1.
lead to figures similar to Fig. 14. They are not givenhere for the sake of conciseness. Although the detailsof the results are not exactly the same, they can beconsidered as statistically equivalent due to the limit-ed size of the samples.
Another kind of presentation is shown in Fig. 15,again for the same data set. This figure gives thesignal amplitude level vs the measured velocity, eachpoint corresponding to one particle. The number N ofparticles is given in the figure. The best straight lineobtained from a linear regression technique with re-spect to the ordinate direction44 is drawn and slope S isindicated in the figure as well as ordinate Z at zerovelocity. As mentioned above, these experimentshave been repeated many times in the same conditions.Table II gives the values of N, S, and Z for all theseexperiments, leading to a satisfactory agreement be-tween values which should ideally be identical.
Similar experiments have been carried out on meth-anol droplets produced with the same TSI operationconditions as previously. Methanol has a density of0.79 and a refractive index of 1.3331 (Ref. 45) whichcan be considered identical to the water refractiveindex equal to 1.3372.45 Consequently, for a given
Table II. Summary of Results of Various Experiments for Water DropletsWhere N Is the Number of Particles, S is the Slope of the Distribution, and
Fig. 17. Linear regression for five experiments with water and fiveothers with methanol.
amplitude level corresponding to a given diameter, wemust expect a smaller velocity (as long as the velocity isassumed to be equal to the free-fall velocity). Thisstatement is exemplified in Fig. 16 to compare withFig. 14. Again, these experiments have been repeatedmany times in the same conditions, the results beingsummarized in Table III to compare with Table II.
From these figures the typical dispersion of the di-ameter results is ±10% for a given velocity. This mustbe compared with the criterion of +6% used to definethe quality of the digitized flat sizing signal. It isexpected that a more severe criterion would'have led toa smaller dispersion but the rate of validation wouldhave been decreased. However, velocity fluctuationswill still occur. In fact, the TSI spray jet was visuallyobserved to wander during an experimental run.
Figure 17 presents the straight lines from the linearregression technique, obtained from the experimentsdiscussed above (Tables II and III), to provide thereader with a synthesis of the set of results. Otherexperiments have been performed for methanol drop-lets with the TSI orifices 50 and 35 m but are notdiscussed in this section to limit the number of figures.
I1lllllll 11l ... .I I l .10 20 30 40 50 60 70 80 90 A
Fig. 19. Histogram for 500 water droplets.
D. Diameter/Velocity Information
The net measurements provide us with an ampli-tude/velocity couple attached to each particle. Toconvert this information to a diameter/velocity couple,some kind of calibration is required. In this paper, thecalibration is obtained from Lorenz-Mie computationsof the scattered powers vs diameters. The calibrationcurve is given in Fig. 18 (the results are the same forwater and methanol because of the identity of refrac-tive indices) for diameters in the 10-250-grm range.The mean slope is s - 2 as expected for large diameters.We also need an additional calibration to define theabsolute location of the calibration profile in the ordi-nate direction. This point is discussed below.
Figure 19 shows the histogram obtained by assem-bling all the data corresponding to water experimentswith the TSI orifice equal to 100 gm. The number ofparticles is 500 and the step A A for the amplitudeclasses is 2 levels. The mean value of the class contain-ing the larger number of particles is associated with thenominal value of the diameter corresponding to theTSI operation conditions (do = 195 Am), leading topoint A in Fig. 18. The measured amplitude corre-sponding to point A is put numerically equal to thecomputed scattered powers for a diameter of 195 Mm,enabling us to fix the absolute scale of the calibrationcurve in Fig. 18. Using the calibration curve (Fig. 18),the diameter associated with the second peak in Fig. 19is found to be 247 gm, which agrees very well with thetheoretical diameter associated with a coalescence sat-ellite doublet diameter equal to 245 gm. Such a dou-blet diameter leads to point A' in Fig.18. Points B andC in Fig. 18 correspond to TSI orifices equal to 50 and35 gim, for which the nominal TSI diameters are 115and 85 gm, respectively. In Fig. 18, the plotted diame-ters correspond to the TSI nominal values while theplotted amplitudes are the measured amplitudes forthe class containing the larger number of particles,point A being used to fix the absolute scale. Thelocation of points A', B, and C with respect to thetheoretical curve show good agreement between Lo-renz-Mie theory and experiments.
In our previous pure sizing measurements,2 3-25 thenumber of comparisons between theory and experi-ments was more numerous because it was possible totake advantage of the presence of satellite droplets
150
100
50
kVff ,cm/s
4A * cor11
nputed with (1)Tiputed with(3)
50 10 Vm,cni/s
Fig. 20. Free-fall velocity vs measured velocity: orifice 100 im.
which were observed much more often than in thiswork.
A similar discussion could be provided for methanoldroplets.
E. Free-Fall Velocities
Another (although indirect) check of the consistencyof our measurements is provided by a discussion of thefree-fall velocities. Knowing the diameter of a parti-cle and its measured velocity, from the amplitude/velocity to the diameter/velocity conversion, it is possi-ble to compute the free-fall velocity vff for the mea-sured diameter and to compare it with the measuredvelocity vm. Figure 20 shows the free-fall velocity vff vsthe measured velocity vm for water droplets and the100-gm diam TSI orifice. The numbers in parenthe-ses or underlined correspond to the number of countsin an amplitude class of 5 levels (corresponding to adiameter class of -10 gm).
The measured velocity is defined as the arithmeticmean velocity, the average being made on all the parti-cles in a diameter class. For the open triangles, thefree-fall velocity is computed according to the Stokesdrag law:
gppd2
18 ' (1)
where g is the gravity module, pp is the specific mass ofthe particle material, d is the particle diameter, and Afis the surrounding air viscosity. Using this expression,we admitted that the fluid particles behave like solidparticles which is justified for liquid droplets flowing
Acomputed with(1)*computed with (3)iputed with (1)
iputed with (3)
10 20 30 40 50 Vm,cm/s
Fig. 21. Free-fall velocity vs measured velocity: orifice 50im.Fig. 22. Free-fall velocity vs measured velocity: orifice 35 um.
in a gas.4647 We observe that the agreement betweenvff and Urn is nearly perfect for the classes containing 23and 25 particles, but there is an increasing discrepancyfor the other classes. Furthermore, the slope of thecurve vff vs Urn is far from being satisfactory.
However, the true story is a little more complicated.For liquid particles of diameter d 200 gim fallingfreely in air, the particulate Reynolds number Red,estimated using the measured velocity
Red = vmdpf (2)'f
where pf is the specific mass of air, is -15. For such aReynolds number, the drag Stokes law is not valid.Instead we should use a drag force IF I given by46
IF I = 3ruldv (1 + 0.15 Reo687), (3)
where v is the particle velocity. Using this expressionto compute the free-fall velocities leads to the starpoints in Fig. 20. There is now an overall discrepancybetween the ff and Urn values while the slope Vfg/Vmagrees with the ideal situation depicted by the bisec-trix line.
The remaining discrepancy is attributed to the factthat the particles do not fall in the ideal free-fall situa-tion of individual particles in an infinite medium atrest. The particles under discussion (diameters -200gM) leave the TSI orifice with a high velocity, mea-sured by LDV to be -3.5 m/s. Furthermore, theseparticles are surrounded by a jet of dispersion air witha much higher velocity, estimated to be -36 m/s fromthe dispersion air flow rate and the orifice diameter.Finally, a character of collective falling exists, at leastin the region after the TSI orifice. Taking into ac-count these elements of discussion, the results dis-played in Fig. 20 are considered to be satisfactory.
Figures 21 and 22 show similar results for methanoldroplets corresponding to TSI orifices equal to 50 and35 gim, respectively (nominal values of the diametersequal to 85 and 115 gm, respectively). As the particlesare smaller, the Stokes law [Eq. (1)] is a better approxi-mation than in the previous case. It is observed, par-ticularly for the smallest particles (Fig. 22), that theresults obtained either from Eq. (1) or from Eq. (3)- arenow closer, and that the star points more closely ap-proach the bisectrix line, confirming our previous dis-cussion.
-pure size system-combined measurements
Kflh/f. f'-
300 diFig. 23. Comparison between histogram obtained with the dual
size/velocity apparatus or the size alone device.
It is to be noted that a relative error of -20% on themeasured diameters would suffice to make the starpoints (in Fig. 22, for example) come to the bisectrixline. Such a relative error is rather small. A simplerapproach for the amplitude/diameter conversion hasbeen used in some results given in Refs. 48 and 49.This simpler approach introduced a bias of typically-20% on the measured diameters. This bias wasenough to produce a perfect agreement between the mvalues and the vff values computed from Eq. (1). How-ever, this agreement was fairly fortuitous. Thepresent discussion is more complete.
F. Holography Measurements
A direct check of the quality of our diameter mea-surements has been produced by Gabor holographymeasurements on methanol droplets. The hologra-phy technique used has been described elsewhere.25
The mean diameters by holography have been found tobe 100 5 m and 115 + 5 im for orifice diametersequal to 35 and 50gm, respectively, these values agree-ing with the values obtained by the combined system(see Figs. 21 and 22).
In our previous work23 we discussed the fct that themeasurements by the top-hat techniques were moredispersed than by holography and we stated that thisdefect could be improved by a combined system whichis less sensitive to edge effects, with a faster rate ofacquisition.
Figure 23 shows two diameter histograms for metha-nol droplets (TSI orifice to 100 gim), one being ob-tained by the present combined system, the other hav-ing been previously published and obtained from apure sizing system.25 Both histograms have been nor-malized to the same count number for easier compari-
son. The expected improvements are observed, theleft-hand tail (mainly attributed to edge effects) beingeffectively reduced with the combined system.
X. Conclusion
A combined system for simultaneous measurementsof velocity and size of particles transported in flows hasbeen presented. The velocity is measured by a classi-cal LDV device and sizing is carried out from an addi-tional optical probe whose main feature is to present aregion of constant illumination which removes the so-called trajectory ambiguity. Measurements havebeen carried out on water and methanol droplets pro-duced by a TSI-3050 generator. Results are exten-sively discussed and found to be satisfactory. Theconclusion is that a new measurement technique nowexists which is expected to be useful to researchers andengineers for a very wide range of applications that wemust now determine.
The combined system has been developed in col-laboration with the German company OEI (nowmerged with TSI). We are particularly indebted to R.Kleine whose assistance, efficient collaboration, andfriendliness are greatly appreciated. The financial aidof the CNRS and of the ANVAR has been essential tothe success of this development operation. We alsoacknowledge the assistance of D. Allano and D. Li-siecki for holography measurements in which they areexperts.
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0
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