Size and Velocity Measurements of Large Drops ... - Wiley Online Library

63

Part. Part. Syst. Charact. I1 (1994) 63-72

Size and Velocity Measurements of Large Drops in Air and in a Liquid-Liquid Two-Phase Flow by the Phase-Doppler Technique Per Haugen *, Edward I. Hayes *, Hans-Henrik von Benzon ** (Received: 19 November 1993)

Abstract Particles comparable in size to or larger than the measurement volume need extra consideration when measured by a phaseDoppler system. The phase of the Doppler burst received when such particles traverse the measurement volume depends not only on the size of the particle but also on its trajectory, since the particle is not uniformly illuminated. This paper presents a strategy for securing correct measurements even under such conditions, taking advantage of the three-detector receiving optics of the Dantec Particle Dynamics Analyzer. The effec-

1 Introduction The Dantec implementation of the phase-Doppler anemometric technique, the Particle Dynamics Analyzer (PDA) [l, 21, is now a well established instrument for measuring size and velocity of individual particles in flows such as sprays [3-91, solid-liquid two-phase flows [lo, 111and bubbles [2,12]. In these applications the relative refractive index, i. e. the refractive index of the particles relaitive to that of the medium, is typically below 0.8 or above 1.2. The purpose of this work was twofold: (i) to test a scheme for securing correct measurements of particles larger than the laser beam diameter and (ii) to explore the reliability of the phase-Doppler technique in liquid-liquid two-phase flows where the relative refractive index is close to unity. Preliminary reports of the work were presented at the 3rd International Congress on Optical Particle Sizing in Yokohama, 1993 [13, 141. 1.1 Basic Principles

The practical implementation of phase-Doppler anemometry was originally based on the assumptions that the particles to be sized are spherical and traverse a uniform field of plane waves and that the scattering angle is selected such that a single mode of scattering dominates the scattered light collected by the receiving optics. The scattering angle, p, is defined as the angle of the optical axis of the receiving optics relative to direct forward scattering (Figure 1). In this case the phase difference between two detectors forming a pair is linearly related to the diameter of the particle. The uniform field is a good approximation when the particles are much smaller than the measurement volume generated by ~

*

Dr. f! Haugen, Dr. E. I. Hayes, Dantec Measurement Technology A/S, Tonsbakken 16-18, DK-2740 Skovlunde (Denmark). ** Mr. H.-H. von Benzon, Physics Department, Technical University of Denmark, DK-2800 Lyngby (Denmark).

0 VCH Verlagsgesellschaft mbH, D-69469 Weinheim, 1994

tiveness of the approach is demonstrated for sizing drops in liquid-gas and liquid-liquid two-phase flows: water drops in air, water drops in FC72 and FC72 drops in water. The combination of water and FC72 is also of interest because the relative refractive index is close to unity. Measurements of drop size were made on a monodisperse stream of drops about 2 mm in diameter, i. e. substantially larger than the measurement volume, and polydisperse distributions of drops ranging in diameter from below 0.2 mm to about 1 mm.

i

Fig. 1: Definition of the angles 9, y~ and 19 for the centre of gravity of the aperture of one detector.

the two intersecting laser beams. Then the scattered light can be described by conventional Lorenz-Mie theory for light scattering (LMT). For a spherical particle substantially larger than the wavelength, the light received by the detectors and the diameterphase relationship can be given to a good approximation by geometrical optics (GO). The range of scattering angles (p) where each mode dominates the scattering and also the scattering intensity depends on the relative refractive index between the particles and the scattering medium. In Figure 2 the intensities for reflection (0) and the seven first modes of refraction (1-7) have been calculated for a water droplet (50 pm in diameter) in air, small enough that it can be considered to be uniformly illuminated. The diagram shows these intensities for two polarizations : perpendicular (upper halo and parallel (lower half) on a logarithmic scale (8 decades) in a polar plot. From such a diagram, the scattering angle can be chosen so that a single mode of scattering dominates. This gives an analytically simple solution which is implemented in the PDA software. Thus, the phase difference @i, between the Doppler bursts received by two photo-detectors (i, j ) becomes linear with a slope depending on the scattering mode and the angular posi0934-0866/94/0102-0063 $5.00 + .25/0

64

Part. Part. Syst. Charact. I 1 (1994) 63-72 1.2 Large Particles in Gaussian Beams

Fig. 2: Polar plot of the intensity (log scale, 8 decades) of reflected light (0) and seven first modes of refiraction (1-7) as functions of scattering angle for a uniformly illuminated water droplet.

tion of the detector apertures. For first and higher orders of refraction, the phase also depends on the relative refractive index [l, 151. Mathematically, the phase of a Doppler burst received at detector i can be expressed as the product of a size parameter and a geometrical factor :

@=a.p where the size parameter is *I

a=n-D

A

nl is the refractive index of the scattering medium, I is laser wavelength in vacuum and D is the particle diameter. The geometrical factor p depends on the scattering mode and the three angles 4, a, and v (Figure 1). The angle between the two incident beams 4 determines the fringe separation, while a, and define the direction towards the (centroid of the ) photo-detector from the measurement volume. The angle of intersection between the two incident beams, 4, is determined by beam separation (S,) and focal length of the front lens (Ft).Thus, for the ithdetector pi is the scattering angle measured from the axis of the transmitting optics (the bisector of the two incident beams; the Z-axis, i. e. the axis of the transmitting optics); vi is the azimuth angle giving the rotational position about the Z-axis. The dependence on the refractive indices of the phase of a Doppler burst at the detectors is expressed most clearly in the case of (first-order) refraction. Then the geometrical factor is pi=2

[fm /

1

If the particles are comparable to or larger in diameter than the measurement volume, the situation is more complicated. The particle can no longer be considered as uniformly illuminated, and the trajectory of the particle becomes important for the intensity balance between the different scattering modes and hence for the phase of the Doppler bursts. Only particles following trajectories where the dominating scattering mode is the same as that dominating under uniform field conditions will be correctly measured. Particles having other trajectories must be rejected in order not to give rise to incorrect values, as discussed by Saffman in 1986 [16] based on geometrical optics. Recently Gdhan et al. [17, 181 have studied the phenomenon for a two-detector PDA system using the generalized Lorenz-Mie theory (GLMT). This paper reports on an ongoing study exploring the application of PDA to large particles. The results show that for particles substantially larger than the measurement volume, particles which could be misinterpreted, can be effectively discriminated against by using a three-detector PDA system and the appropriate validation check.

1.3 Relative Refractive Index Close to Unity Up to now the technique has been used mainly in situations where the relative refractive index is about 1.2 or higher [3-111 or 0.8 or lower [2, 121. In these experiments on a liquid-liquid two-phase flow situation, the refractive index of the drops was only a few per cent from that of the medium. Our results show that with an appropriate choice of scattering angle reliable results can be obtained at least down to a relative refractive index of 1.06 and up to 0.94.

2 Nature of Trajectory Dependence in Terms of Geometrical Optics To give an accurate physical description of this trajectory dependence, known as the Gaussian beam effect, the most accurate approach would be using the GLMT. To obtain a qualitative and more intuitive approach, however, we have chosen to resort primarily to geometrical optics. In Figure 3 ray traces are shown for a series of six rays giving rise to light scattering at a scattering angle of 73 O : reflection, first to fifth order of refraction calculated for a drop of water in air. Each ray represents a single scattering mode. Secondorder refracion does not exist at this angle and fifth-order refraction has two contributions. The important point to note here is that the six rays have different impact points. In the case of a particle much smaller than the measurement volume, each impact point will receive nearly the same light intensity and the far-field intensity of each of the scattering modes can be calculated accordingly. In the case of water droplets in air with a scattering angle of 73 the Brewster effect reduces the intensity of parallel-polarized reflected light leaving refraction as two or three orders of magnitude stronger than reflection (cf. Figure 2). Refraction will therefore account for very nearly all of the power calculated by a Lorenz-Mie analysis. Therefore, refracted light at the combination of 73 and parallel polarization is a good angle for measuring small water droplets [16]. If the particle is very much larger than the diameter of the measurement volume, the impact points will not receive the O,

where

fi*

=

4

1 +sin2

4 2

. sinpi . sinyli + Cos- . cospi

O

and nrel= n2/nlis the relative refractive index of the particle, where n, = refractivc index of the medium and n2 = refractive index of the particle.

65

Part. Part. Syst. Charact. I 1 (1994) 63-72

same light intensity. The position of the centre of the particle relative to the measurement volume will determine the intensity at each impact point. Hence in the far field the balance between the different modes of scattering may be different from that calculated for a uniform field situation.

the drop when the impact point for first-order refraction is at the centre of the measurement volume. Such an interpretation would also be supported by the phase. It would be tempting to associate the two central peaks with the fifth and third orders of refraction, which would agree with the sign of the phase (to be described later) and also roughly with the diagram of scattering angle vs. impact position in Figure 3 and with the relative intensities in Figure 2. This, however, would be an oversimplification since all the modes receive light and will therefore interfere. This interference is most evident in the phase shifts during the fourth peak. During most of the first peak of d. c. power (negative y-values) the phase is negative, as would be expected for refraction. Around the two minor peaks in the trough between the major two peaks, the phase rises in with two oscillations and reaches a maximum before returning to the initial negative level. This maximum occurs during the rising phase of the second peak and corresponds roughly to the level expected for reflection.

Fig. 3 : Ray traces for modes scattering light at 73": reflection (0), first- (l), third- (3), fourth- (4), and fifth-order (5, two contributions) of refraction (drop of water in air).

To each impact position corresponds a scattering angle for each mode of scattering. This dependence of scattering angle is shown on the left in Figure 4 for reflection and for the five first orders of refraction as calculated for a drop of water in air (nrel= 1.33). On the right in Figure 4 the definitions of the corresponding variables are illustrated for the third order of refraction.

Y-position (pm)

Y-position (pm)

Y-position (pm)

2!!!!L *1

Definilion of variables 120

8

P

*CD w 5

P

0

$

w

8-30 Y-position (pm)

v)

0

Y-position (pm)

30

Y-position (pm)

120

-20 crm lW1O

-08 -06

020 0 0 2 0 4 Relative impact position y/R-cos(r)-sln(pi)

04

06

08

10

Shown for the third order of refraction

Fig. 4: Scattering angle as a function of impact position (relative to particle radius) for reflection (0) and the five orders of refraction (1-5) along with definitions (water drops in air).

To illustrate the phenomenon of trajectory dependence, the scattering angle of 55 in combination with perpendicular polarization is considered since at this angle, under constant field illumination, the reflection is less than a decade weaker than the refraction, which is the dominant scattering mode. Under these conditions the trajectory dependence becomes very evident. Thus, in Figure 5A, B and C are shown the phase and d.c. power calculated from GLMT for three particles of different diameter: (A) 30, (B) 10 and ( C ) 1 pm. In each case the position of the centre of the particle is varied in the y-direction (perpendicular to the plane of the incident beams; cf. Figure 1) from -30 to +30 pm, i.e. across the measurement volume which has a Gaussian diameter of 20 pm. Under constant field illumination the refracted light would be dominant and the phase would correspond to that seen in the left-hand side of the phase diagrams, i. e. for the lowest y-values. As y is increased the phase remains basically constant at the negative value corresponding to refraction, while the intensity increases. For the 30 pm particle the d. c. power shows four distinct peaks. The first and tallest peak corresponds closely to the position of

30 pm

10 pm

1 Pm

Fig. 5: Phase (top row), d.c. power (middle row) against y-position for three different particle sizes as shown relative to the intensity profile (bottom row).

The interference between the scattering modes is also pronounced in the case of the 10 pm particle. The intensity has basically a Gaussian outline, but two narrow troughs appear, the first beginning roughly at the maximum and the second about midway down the tail. Again, the phase starts at the negative level expected for that diameter under uniform-field conditions. It then rises, and after some irregularities it reaches a maximum corresponding to reflection, whereafter it again returns to the negative level. Also for the 1 pm particle, which is one-twentieth of the Gaussian diameter of the measurement volume, a change of phase in the direction of reflection is seen, although not as dramatic as in the two previous cases. That this effect is seen with even such a small particle is related to the fact that at this suboptimal angle under constant field conditions (Figure 2) refraction is less than a decade stronger than the reflection. The effect would be that even such a small particle will give rise to slightly dif-

66

Part. Part. Syst. Charact. 11 (1994) 63-72

ferent values depending on the trajectory due to the contribution of reflection in the scattered light. Therefore, in general, a scattering angle should be selected where at constant field conditions the intensity difference between the dominating scattering mode (here refraction) and any other mode (reflection) is as great as possible. The slope of the diameter-phase relationship was calculated using geometrical optics for each of the eight first scattering modes corresponding to the intensity curves in Figure 2. The sign of the slope was positive for reflection and for third and sixth orders of refraction, and negative for the first, fourth, fifth and seventh orders of refraction. In addition to the sign, the slope itself also differed between the modes. (The second order of refraction does not scatter light at 73 but beyond the rainbow angle the relqionship has a negative slope.) The diameter-phase relationship calculated from geometrical optics corresponded closely to the relationship calculated using generalized Lorenz-Mie theory when the impact area of a small measurement volume coincided with the impact point of the ray giving refraction as shown in Figure 6. The relative impact point was y / R = 0.995 (where y is the coordinate of the centre of the spherical particle of radius R and the Y-axis is perpendicular to the XZ-plane containing the incident beams such that the origin is the centre of the intersection volume; cf. suboptimal Figure 1). The coincidence indicates that one can expect to measure correctly even very large particles provided that they follow a trajectory where the excited scattering mode is the dominant scattering mode at this angle for an evenly lit particle, i. e. refraction. Particles following other trajectories should be rejected since their size could be misinterpreted. For a particle comparable to or larger than the measurement volume, the relative intensities will not be like the chart in Figure 2, but will depend on the trajectory. The chart, however, will give an expression for the relative maximum intensities of the different scattering modes as obtained when the particle has an optimum trajectory for that mode. For example, at 73 with parallel polarization, the third order of refraction can never become stronger than about of the maximum intensity of the first order of refraction. Even if the particles passed at the trajectory optimum for this mode, they would not all scatter the same amount of light.

not trigger the burst detector. To avoid the Doppler burst from such a particle being acquired, the ideal situation would be if it were possible to select a scattering angle such that the difference in intensity of the normally dominant mode and the other modes at least corresponded to this fraction. By inspection of the intensities in Figure 2 it is immediately seen that there is no scattering angle where the dominant mode is as much as 1600 times stronger than the second strongest mode. Still, intensity alone could be used to discriminate against scattering modes associated with the same slope of the diameter-phase relationship. At 73 ' and parallel polarization, the first-order refraction (negative slope) is about LO' times stronger than the fourthorder refraction. At this scattering angle, however, there are two scattering modes : reflection and third order of refraction, which are stronger than the fourth order of refraction. Both of these are associated with a positive slope of the diameter-phase relationship. If the drop is sufficiently large relative to the measurement volume that the weaker mode is less than 20% [I61 of the stronger of the two, the diameter-phase relationship will be nearly linear, as at the top of Figures 7 and 8.

One detector pair

Fig. 7 : TWO detectors alone provide no means of distinguishing between refraction and reflection.

Two detector Dairs C

0

Droplet diameter (pm)

0

20

40

60

80

s a

-

5 E Q

a

C

0

p =Q

-401

I

4

I

Geometrical optics

U

kGaussian beam diameter

-60 A

Fig. 6 : Diameter-phase relationship calculated from geometrical optics for refraction (straight line) and from GLMT: 20 pm beam diameter, y / R = 0.995.

The intensity of the scattered light is approximately proportional to the square of the particle diameter. The Dantec PDA is specified as being capable of handling particles in a dynamic range of typically 1 :40. This would correspond to an intensity range of about 1 : 1600. If a large particle scattering light with a mode not dominant under uniform-field conditions scatters less than 1/1600 of the intensity of the dominant mode, it will

Fig. 8: Three detectors forming two pairs permit refraction and reflection to be distinguished.

Figure 7 shows the situation with a two-detector receiver as calculated for a drop of water and a scattering angle of 73 At the top the trajectory of the drop causes the received light to be scattered by refraction. The phase difference points to one diameter value. The lower panel shows when the light is scattered by reflection. (Third-order refraction would have a lower slope.) The same phase difference now points at another diameter value. There is no way of telling from this phase difference alone O.

67


which one represents the true value. In Figure 8 a third photodetector is added and the three detectors (1, 2 and 3) are grouped to form two detector pairs: one more widely separated (1 and 2) and one more closely spaced (1 and 3). The corresponding phase differences are @, and @13.In the upper panel @, points at several different diameter values, one of which coincides with the value indicated by @ 1 3 . In the lower panel there is no such coincidence. From this it is possible to conclude that the two phase differences in this example correspond to refraction. The relationship of and QI3 vs. diameter in Figure 8 corresponds to the typical setting of the detector apertures used with large particles corresponding to the segments of the front lens illustrated in Figure 9.

2 /u2 , 1 \Ul

angle adjustment setting this is 0.4/3.4 = 11.7%. If the ratio 2.5 is selected the corresponding tolerance would be 20%. Not all ratios can be used, however: if the fractional part is zero as for 2.0 or 3.0, any combination of and @ I 3 produced by reflection or third-order refraction will also have a corresponding D' when misinterpreted as refraction.

\ I

/

Fig. 9: Detector apertures shown as segments of the front lens as adjusted for maximum ratio of separation.

The next question is how great a tolerance can be allowed while still maintaining the ability to discriminate between refraction and reflection or third-order refraction. This is illustrated in Figure 10, which is calculated for drops of water and a scattering angle of 73". The drops have a trajectory giving rise to reflection but the signals are analysed as if they were due to refraction. If a particle is to be validated, the two phase differences @, and @13 must correspond within the given tolerances to the same diameter value. It can be seen that if the tolerance is set to 15070 non-sphericity, a small drop of diameter D , will be misinterpreted as a large drop of diameter D;, whereas for the larger drop of diameter D, the phase differences @, and @13 correspond to two different diameters Di,12and Di.13, and the drop will be rejected. If the allowable non-sphericity is set to 10% or less, there will be no misinterpretation. A similar diagram giving exactly the same result in terms of rejection would result if instead of reflection the light received was scattered by third-order refraction. The only difference would be a different scaling of the axis of misinterpreted diameter. The success of this scheme relies on the ratio between the slopes of the phase differences Q12 and @ I 3 vs. diameter, i. e. the phase factors which are proportional to the separation between the centroids of the segments of the front lens corresponding to the photo-detectors U1, U2 and U3. This ratio can be set in the Dantec 57x10 PDA receiving optics. In Figure 10 the ratio is equal to 3.4, corresponding to the angle adjustment setting of 0 [15], i.e. the typical setting one would choose when measuring large particles. Similar results would be obtained with the fibre PDA in combination with the aperture plate for the largest diameter range. The maximum allowable non-sphericity when requiring full rejection is the ratio between the fractional part of the ratio and the ratio itself. For the above

Actual diameter D (relative units)

Fig. 10: Incorrect diameters resulting from misinterpreting the phase difference from scattering by reflection as refraction and tolerances set for the sphericity check.

In contrast, if a scattering angle of 30" had been chosen, the fourth order of refraction would have an intensity only about three orders of magnitude smaller than the refraction in a plane wave field. Therefore, in some cases a large drop could scatter fourth-order refracted light with about the same intensity as the refracted light from about a 30-times smaller drop in a 'good' trajectory. As both scattering modes would have the same sign slope of their diameter-phase relationships, the fourth order can only be discriminated against on the basis of signal intensity. This would mean that this angle could be used only with a limited size range of large particles.

3 Experiments: Materials and Methods 3.1 Drop Generation 3.1.1 Water Drops in Air

The set-up for drop generation is shown schematically in Figure 11A. Drops of purified water (refractive index n = 1.334) were falling freely from the tip of a hypodermic needle. The water was fed at constant rate by a peristaltic pump. To reduce the small amount of pulsation from the pump, an air-filled 20 ml syringe was connected to the output hose via a Y-connector, thus giving an extra compliance (not shown). The drops were monodisperse and the average size did not vary appreciably. 3.1.2 Liquid-Liquid 'Iko-Phase Flow

The two-phase flow used in this work consists of two liquids: purified water and the Freon substitute FC72 (3M Company, Minneapolis, MN, USA; n = 1.251). The two liquids are both fully transparent. They do not dissolve in each other but form nearly spherical drops. When allowed to settle, the water forms a cover on the heavier FC72, preventing this liquid from evaporating. The experimental chamber was a rectangular vessel

68


A

Camera with Bellows extension

x

u

Fig. 12: PDA set-up (top view) showing the scattering angle, 22", used with the water drops in FC72.

3.3 Set-up for PDA Measurements

n

Fig. 11: Set-up for generating (A) water drops in air, (B) water drops in FC72 and (C) drops of FC72 in water.

of 83 x 65 x 30 mm, and was made from optical quality glass (700.002; Hellma, Miillheim, Germany). The vessel was filled with water and FC72. A steady flow of liquid was produced by a peristaltic pump supplied from the reservoir of the vessel and injected back into the vessel by a thin hypodermic needle (Figure 11B and C). Two situations were studied. In the first case, drops of water were released in the FC72 and allowed to rise towards the water ceiling (Figure 11B). The drops had a relative refractive index of nrel = 1.066. In the second case, drops of FC72 were released in water and allowed to drop towards the FC72 floor (Figure 11 C). These drops had a relative refractive index nrel = 0.938, i. e. less than unity. Thus, the FC72 drops behave optically as gas bubbles but, unlike such bubbles, they sink. 3.2 Size Measurements

The drop diameter was measured with the phase-Doppler technique and verified photographically.

The system used for these was a Dantec PDA. Laser light was produced by an air-cooled ILT Model 5490 argon laser (wavelength d = 514.5 nm). The transmitting optics was an optical fibre-based unit: Model 60x82 fibre flow probe, in combination with a Model 55x82 beam translator and 600 mm focal length front lens. The laser light was coupled into the optical fibres by means of the Model 60x40 transmitter, which also generates the 40 MHz frequency shift of one beam. The transmitted light beams were polarized parallel to the scattering plane and emerged from the front lens with a beam separation of 10 mm, producing a measurement volume 0.39 rnrn in diameter. The receiving optics was a 1-D Model 57x10 PDA receiving optics with a 1000 mm focal length front lens positioned at a scattering angle (collection angle) of 73 ' for the measurement of water drops in air. For the water drops in FC72, a 600 mm focal length front lens was used and the receiving optics was set so that the effective scattering angle in the FC72 liquid was 22". The same front lens was used with FC72 drops in water but the effective scattering angle was 45 '. The selection of scattering angle for the liquid-liquid two-phase flow situation will be discussed later. In all three cases the scattering angles corresponded to the values optimized by the method described by von Benzon and Haugen [20]. The angle adjustment for the apertures of the three detectors was set to 0 [IS] to produce the relative aperture sizes and positions shown in Figure 9. For the water drops in air this gave a maximum measurable particle diameter of 5 mm.

3.4 Data Processing The Doppler signals were processed by the Model 58N10 PDA signal processor and analysed on a 386-based PC with the SIZEware software.

3.5 Photographic Measurements To validate the PDA measurements, some drops were photographed exposed by a flash of a stroboscope which was triggered from the burst detector of the Model 58N10 PDA signal processor. In the first experiments a 35 mm camera (Olympus OM1 with a 50 mm macrophotography lens) was used with a bellows extension giving a 4 x magnification. The drops in the photographs were then compared with a photograph of a calibration slide at exactly the same magnification. In later experiments the photographs were made with a digital camera (Videk 50021) with a Nikon 55 mm Micro-Nikkor front lens set to 0.5 x magnification.

69


3.6 Procedure

888 pm and the validation was 31.2% (234 drops) with a validation setting permitting a maximum of 5 070 non-sphericity.

The diameter of the drops was measured when the trajectory was given various positions (0.1 mm intervals) along the Y-axis, i.e. the axis at right-angles to the plane of the two incident beams and crossing this plane at the centre of intersection between the beams. For each position the direction of the receiving optics was finely adjusted to admit the scattered light by making sure that the bright spot on the image of the drop on the spatial filter of the receiving optics coincided with the slit of the spatial filter. Diameter (rnm)

4 Experimental Results 4.1 Water Drops in Air

B

Suboptimal angle adjustment

4.1.1 PDA Measurements The measurements were made with maximum allowable spherical deviation set to 5 %, lo%, 15070, 20% and 25 %.At positions corresponding to refraction the resulting measurements did not vary with the allowable spherical deviation. An example of such a measurement is given in Figure 13. Fig. 14: Incorrect diameter distribution, (A) obtained with too lax a sphericity check and (B) obtained with a suboptimal angle adjustment. Correct values are indicated by broken lines.

4.1.2 Photographic Measurements

Fig. 13: Diameter distribution (mean 2.243 mm) for a trajectory corresponding to first-order refracted light (maximum non-sphericity 5 070 ; 99.2 070, i. e. 1026 samples, validated). When traversing the drop trajectory the positions corresponding the higher order scattering did not trigger the burst detector. With the position set for maximum reflected light the burst detector again triggered and the data validation before the sphericity check was close to 100%. In this position, however, the result depended on the maximum permitted non-sphericity: for 5- 15Yo the validation after the sphericity check was 0%. With the permitted non-sphericity set to a maximum of 20 or 25 %,about 8 070 of the drops were validated as spherical and gave incorrect diameter measurements as shown in Figure 14A (up to 20% nonsphericity admitted; mean 3.97 mm, validated 8.22%, 163 drops). The fact that the drops were monodisperse explains why the validation percentage was the same in the last two cases. In the above measurements the angle adjustment had been set to 0 [15], thereby giving the ratio between the two phase factors a fractional part of 0.4, i. e. close to 0.5. To test the dependence of the angle adjustment setting, some additional measurements were made at a suboptimal setting which according to the theoretical discussion above should give poor discrimination. At this setting the correct size distribution was just contained in the range (maximum diameter 2.35 mm) and the ratio was 2.09, i. e. close to 2.0. In this case with the trajectory selected to elicit reflection (Figure 14B), the measured mean diameter was

A photograph of a drop with a microscope calibration scale superimposed is shown in Figure 15. The drop in this photograph was 2.3 mm in diameter, which is very close to the mean value of 2.243 mm in the PDA measurements of Figure 13 and about 6 x the Gaussian diameter of the measurement volume. The bright vertical line is a reflection of the laser beam exposed as the drop passed the measurement volume.

Fig. 15: Drop and calibration scale (0.1 mm per small division) photographed at the same magnification and superimposed.

4.2 Liquid-Liquid 'Iko-Phase Flow While the PDA measurements reported here were all made with large drops of controlled trajectory, the present technique was also applied with success to a spray of various sized water droplets in the Freon substitute FC72. The drops sizes used in these experiments ranged from about 1/4 to 2 times the Gaussian diameter of the measurement volume. In that case, by


70 reducing the maximum allowed non-sphericity from 20% to 5070, the size distribution became similar to that obtained by analysis from photographs. 4.2.1 Light Scattering Considerations and Choice of Scattering Angle For both the two relative refractive indices the intensity of the scattered light as a function of scattering angle was calculated for each of the first three scattering modes: reflection, refraction and second-order refraction using geometrical optics. The intensity plots which are shown in Figures 16A and B are marked as follows : curve 0 is reflection, curve 1 is refraction and curve 2 is second-order refraction. The intensity plots for Lorenz-Mie theory which encompasses all scattering modes are markedL-M. The intensities are shown on a logarithmic scale in a polar plot against scattering angle (0 O - 180 0' represents forward scattering). The concentric circles are one decade apart. To facilitate the comparison of the two orientations of polarization, the upper half of the polar plots represents polarization perpendicular to the scattering plane while the lower half is for parallel polarization. The Lorenz-Mie curves also reveal effects of higher scattering modes. Thus, the marks (3) and (4) inFigure 16A indicate the peak intensities corresponding to the rainbow angles of the third and fourth order of refraction. Reflected light exists at all scattering angles. First-order refracted light spans an angular range from 0 O (forward scatter) to the critical angle for first-order refraction pc1as indicated by the arcs centred around 0". O,

When nrel= 1.066 > 1 (Figure 16A), the second order of refraction spans a range from 180 down to the second-order rainbow angle p,, where it folds back to give a double contribution in the range pr2-pc2,as indicated by the arcs centred around 180 '. For relative refractive index values n , ~= 0.938 < 1 (Figure 16B), the second order of refraction exists at all angles and has a double contribution corresponding to the range of first-order refraction: pcz= pc.. The useful scattering angles were selected on the basis of a high degree of coincidence between Lorenz-Mie and the dominant geometrical optics mode of scattering as described by von Benzon and Huugen [20]. Thus for the drops of water in FC72 (Figure 16A) the best scattering mode was judged to be refraction at a scattering angle of 22 and parallel polarization. At first glance it would seem that 22" would have been a good choice also for the drops of FC72 in water (Figure 16B). At this angle, however, the dominant mode (refraction) is only about one decade stronger than the second strongest (reflection), which would have interfered. Thus a better choice was 45 O with parallel polarized light giving reflection. Since the drops used in these experiments were relatively large, i.e. with diameters corresponding to about 0.25-5 times the Gaussian diameter of the measurement volume (0.39 mm), precautions were taken to avoid trajectory-dependent errors, as shown for the experiments with water drops in air. Thus, the angle adjustment, which sets the relative position of the detector apertures (implementation of patent-projected feature [I]), was set to a value giving a ratio of 3.4 between the geometrical factors pI2/pl3corresponding to the detector pairs U1 -U2 and Ul-U3 (Figure 9). Likewise, the maximum permitted nonsphericity was set to 5 070 in the SIZEware software to discriminate against reflection in the case of water drops in FC72. O

4.2.2 Stream of Monodisperse Drops 0"

In the first series of measurements the peristaltic pump was run at relatively slow speed. Drops of a nearly monodisperse size distribution were formed at the tip of the needle and released. These drops were typically just below 2 mm in diameter and well suited for simple photographic size measurements. Diameter histograms are shown in Figure 17A for water drops in FC72 and in Figure 17B for drops of FC72 in water measured with the PDA. The photographic measurements corresponded closely to the PDA measurements. A photograph of FC72 drop in water such as those in Figure 17B is shown in Figure 18 with a calibrating scale superimposed at the same magnification. It is clearly seen that the drop diameter corresponds to the mean diameter of the histogram.

4.2.3 "Spray" of Drops

Fig. 16: Intensity (radius: log scale, 5 decades) against scattering angle for perpendicular and parallel polarization, (A) for drops of water in FC72 and (B) for drops of FC72 in water.

In the next series of experiments, the pump was run at a higher speed, causing the pumped liquid to emerge from the needle as a jet which broke up into a spray of separate drops a few milimetres downstream. These drops were smaller than those in the first series and their relative distribution as measured with the PDA was wider. The exact diameter distribution of these drops depended on the position relative to the tip of the needle and to the pumping velocity. However, these factors were not examined systematically. In Figures 19A and B the PDA measurements and the measurements from the photographs were divided into bins of the same width (0.1 mm) to facilitate comparison of the diameter distribu-


71

Diameter (mm)

5

0

30

-

20

3

8

10

0

0

1 2 Diameter (mm)

3

Fig. 17: Diameter distribution of (A) 1691 water drops in FC72 (mean diameter 1.96 mm, bin width 6.3 pm) and (B) 622 FC72 drops in water (mean diameter 1.83 mm, bin width 8 pm).

ca

0

Fig. 19: Comparison of drop size distribution using the PDA and measuring from photographic recordings. (A) water drops in FC72; (B) FC72 drops in water.

Fig. 18: Photograph of an FC72 drop in water. Calibrating scale (0.1 mm per division) superimposed at the same magnification. The diameter is just above 1.8 mm, i. e. equal to the PDA mean value. tions. In Figure 20 a detail of a photograph of FC72 drops in water is likewise shown. Both for water drops in FC72 (Figure 19A) and for FC72 drops in water (Figure 19B) the two ways of obtaining the diameter distribution yielded very similar results; however, for the photographic results the small drops received a relatively higher count. The PDA measurements represent temporal averages while the photographic measurements represent spatial averages. The difference between the two reflects the fact that whereas the larger drops quickly penetrated the boundary and fused with the bulk of the same liquid, the small drops tended remain suspended in the other liquid for an extended period. (With higher pumping rates than those used in Figures 19A and B and 20 the small droplets would form a mist.) Thus, although their number was high, their rate of passing the probe volume was lower relative to the largest drops emerging from the injected flow. Further, owing to the limited number of particles in the photographs, statistical variations would be expected to produce some divergence in the shape of the distribution compared with that of the PDA measurements.

Fig. 20: Detail of cloud of FC72 drops in water (calibration scale 0.1 mm per division).

5 Conclusions The present theoretical considerations and experimental results have shown a way to measure with reliability the diameter of particles substantially larger than the measurement volume with the three-detector PDA receiving optics produced by Dantec Measurement Technology. The success of this approach relies, first, on a suitable choice of scattering angle so that the non-dominant scattering modes giv-

72 ing rise to a diameter-phase relationship of the same sign slope are of sufficiently low intensity that they will not trigger the burst detector. Second, the angle adjustment should be set to 0 or 0.5 to produce a ratio between the phase factors of the two detector pairs with a fractional part close to 0.5 (i.e. 3.4 or 2.5). Third, the maximum allowable non-sphericity should be set as low as possible, typically 5 - 10070, to achieve an effective discrimination against scattering modes associated with the opposite sign slope of the diameter-phase relationship. It should be pointed out that the possibility of adjusting the ratio between the phase factors is a side benefit of the Dantec implementation of the Dantec PDA patent [l]. Further, the results show clearly that the Dantec PDA also can be used to measure reliably the size of large spherical drops in a liquid-liquid two-phase flow even when their relative refractive index differs by only about 6% from unity.

6 Acknowledgement The program for calculating the light scattering according to the generalized Lorenz-Mie theory was modified from an original source code generously provided by Dr. G. Grehan, INSA de Rouen, France, to whom we express our sincere gratitude.

7 Symbols and Abbreviations D

particle diameter focal length of front lens of transmitting optics Geometrical Optics GO LMT Lorenz-Mie Theory refractive index of the scattering medium nl refractive index of the particle n2 relative refractive index nrel R particle radius beam separation before front lens of transmitting optics st impact position Y size parameter a geometrical factor P laser wavelength in vacuum 1 phase difference between detectors i and j @ij scattering angle P critical angle for first order of refraction Pcl critical angle for second order of refraction Pc2 scattering angle for the ith detector; incident angle Pi rainbow angle for second order of refraction Pr2 azimuth angle w intersection angle 8 Ft

8 References [l] I? Buchhave, % Knuhtsen, E. Olldag: A laser-Doppler apparatus for determining the size of moving spherical particles in a liquid flow. European Patent Specification, Patent No. 0144310; Japan, 1675221; USA, 4701 051.

Part. Part. Syst. Charact. I 1 (1994) 63-72 [2] M. Saffman, I? Buchhave, H. Tanger: Simultaneous measurement of size concentration and velocity of spherical particles by a laser Doppler method. Second Int. Symp. on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 1984, 8.1. [3] % Domnick, K Dorfner, E Durst: Measurement in the spray cone of pressure atomizers using a factorial design. Sixth Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 1992, 37.3. [4] % Domnick, K Dorfner, E Durst: Investigations of liquid sheet disintegration using optical measuring techniques. ILASS Europe Amsterdam, 1992. [5] C. Hassa, E. Bliimcke, H. Eickhoff: Experimental and theoretical investigation of air blast atomizer. ILASS-Europe '89, Bremen, 1989. [6] 7: Hirai, 7:Inamura, 7:Mori, K. Okamoto, N. Nagai: A study on dynamic characteristics of spray droplets. (In Japanese, abstract in English) 16th Conf. on Liquid Atomization and Spray Systems, Tokyo, Japan, 1989. [7] G. Pitcher, G. Wigley: The droplet dynamics of Diesel fuel sprays under ambient and engine conditions. Laser Anemometry, Vol. 2, ASME 1991, Cleveland, Ohio, USA, 1991, pp. 571-586. [8] G. Pitcher, G. Wigley: A study of the breakup and atomization of a combusting Diesel fuel spray by phase Doppler anemometry. Sixth Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 1992, 25.1. [9] A . Coghe, G. E. Cossali: Characterization of unsteady Diesel sprays by phase Doppler anemometry. Laser Anemometry, Vol. 2, ASME 1991, Cleveland, Ohio, USA, 1991, pp. 587-595. [lo] C. Alimonti, A . Cenedese, E Cioffi: Measurement of velocity, dimension and concentration of solid particles in air and in water by phase difference method. ICALEO 87 San Diego, USA, 1987. [11] E Cioffi, E Gallerano: Velocity and concentration profiles in a channel with movable and erodible bed. Int. Conf. on Mechanics of Two-Phase Flows, Taipei, Taiwan, ROC, 1989. [12] H. Tanger, E.-A. Weitendorf: Applicability tests for the phase Doppler anemometer for cavitation nuclei measurements. 3rd Symp. on Cavitation Inception, San Francisco, CA, USA, 1989. [13] I? Haugen, H. H. von Benzon: Phase Doppler measurement of the diameter of large particles - considerations for optimization. Third Int. Congress on Optical Particle Sizing, Yokohama, Japan, 1993, pp. 301-306. [14] I? Haugen, E. I. Hayes: PDA measurements of drop size at near unity relative refractive index. Third Int. Congress on Optical Particle Sizing, Yokohama, Japan, 1993, pp. 285-289. [15] Dantec. User's manual: Particle Dynamics Analyzer. Dantec publication No. 9150A9041. [16] M. Saffman: The use of polarized light for optical particle sizing. Proc. Third Int. Symp. on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 1986, 18.2. [17] G. GrPhan, G. Gouesbet, A. Naqwi, E Durst: Evaluation of phase Doppler system using generalized Lorenz-Mie theory. Proc. Int. Conf. on Multiphase Flows '91, Tsukuba, Japan, 1991, pp. 291 -294. [18] G. GrPhan, G. Gouesbet, A . Naqwi, E Durst: On elimination of the trajectory effects in phase Doppler systems. 5. Europ. Symp. Particle Characterization, Nuremberg, Germany, 1992, Part 1, pp. 309-318. [19] Z Aizu, E Durst, G. GrPhan, E Onofri, T-H. Xu: PDA System without Gaussian beam defects. Third Int. Congress on Optical Particle Sizing, Yokohama, Japan, 1993, pp. 461-470. [20] H. H. von Benzon, I? Haugen: A method for selecting the optimum scattering angle for particle sizing using phase Doppler anemometry. Third Int. Congress on Optical Particle Sizing, Yokohama, Japan, 1993, pp. 443-448.