Comparison between phase-Doppler anemometry and
shadowgraphy systems with respect to solid-particle size
Ralf Kapulla*, Mathias Trautmann** , Salih Güntay* , Abdel Dehbi* and
Laboratory for Thermal Hydraulics, Paul Scherrer Institut, 5232 Villigen, Switzerland
Stusdsvik SINA Industrieservice GmbH & Co. KG, Hauptstrasse 1B, 76297
Simple experiments with 5 different batches of certiﬁed Latex spheres covering the range
from 5 to 70 µm dispersed in water have been conducted in order to compare PDA and
shadowgraphy systems with respect to the measured mean diameter and the size distribution.
It was found that all the PDA-measured mean diameters agreed with the reference diameters
within ±6 % while the shadowgraphy-measured diameters agreed to better than ±5 %.
However, to achieve these PDA results, it was necessary to heavily correct the input-off-
axis angle used from DANTECs BSA ﬂow software to calculate correct phase conversion
factors while the physical off-axis angle was kept constant. This off-axis angle correction
renders subsequent particle ﬂux calculations with DANTECS software impossible. All of
the PDA-measured distributions are considerably broader than the shadowgraphy-measured
distributions; the latter ones coincide for larger diameters very well with the ones guaranteed
by the manufacturer.
In order to determine the decontamination factor for different aerosol species in a steam gen-
erator (SG) in the framework of the ARTIST project (Güntay et al. 2004), the aerosol size
distribution has to be determined within the SG components. Consequently the available opti-
cal measurement systems, i.e. a phase Doppler anemometer (PDA) and a shadowgraphy system
need to be inter-compared. Very simple experiments with 5 different batches of certiﬁed Latex
spheres covering the range from 5 to 70 µm dispersed in water have been conducted in order to
compare the measured size distribution of both systems with the manufacturer-guaranteed size
Both measurement series for PDA and shadowgraphy were carried out in a small, square Per-
spex pool, with a wall thickness of 2 mm, an edge length of 80 mm and a height of 80 mm.
For every measurement the clean pool was ﬁlled with 250 ml of demineralized water and a
deﬁned amount of latex spheres were injected by means of a pipette. To avoid sedimentation
of the spheres at the bottom of the pool, a magnetic stirrer was used to generate a vortical ﬂow.
Characteristics of the ﬁve different batches of particles with the certiﬁed nominal mean diame-
ter, dm , the nominal standard deviation, σ m , together with the measurement system used by the
manufacturer to determine these values, can be found in Table 1.
particle manufacturer label dm [µm] σ m [µm] measured with
micro particles GmbH P S − ST − 5.0 5.045 0.078 COULTER Multisizer III
BS-Partikel GmbH T e1000 − 25 10.4 0.2 Single optic particle sizing
micro particles GmbH P S − ST − 30.0 29.63 0.35 COULTER Multisizer III
micro particles GmbH P S − ST − 50.0 48.9 0.6 COULTER Multisizer III
micro particles GmbH P S − ST − 70.0 70.6 1.2 Olympus light microscope, with
image analysis software
Table 1: Five different batches of certiﬁed Latex spheres used for the measurements. Information
according to the manufacturer.
The phase-Doppler measurements have
been performed by means of three-detector,
standard DANTEC PDA which is pictured
in Fig. 1. The operation principle of the
PDA can be found elsewhere, (Albrecht et
al. 2003). The parameters of the PDA set-up
are given in Table 2.
Under certain circumstances, particle size
measurements using a PDA instrument can
Figure 1: Optical arrangement of a three-detec- be erroneous due to the so-called ’Gaussian
tor, standard PDA. Picture adopted from (Al- beam effect’, see (Araneo et al. 2000). A
brecht et al. 2003) general rule of thumb recommends applying
standard PDA techniques only up to particle
diameters which do not exceed 1/3 to 1/2 of the beam waist diameter. With the probe vol-
ume given in Table 2, ≈ 60 µm is an approximate limit for the particle diameter above which
the Gaussian beam effects becoming important. Consequently, the Gaussian beam effect might
become an issue for one batch (70 µm) but not below this size.
Laser ArIon − focal length, receiver 310 mm
wavelength 514.5 nm physical∗ off-axis angle Φ 30 ◦
laser power 20 mW/beam aperture mask type A −
focal length, transmitter 800 mm signal level validation −2 dB
intersection angle Θ/2 2.765 high voltage level 700 − 1200 V
beam expander ratio 1.950 − Dominating scattering order refraction −
probe volume dx 0.122 mm
probe volume dy 0.122 mm
probe volume dz 2.578 mm explained in the text
Table 2: Optical parameters used for the measurements.
Since operation parameters such as laser power, photomultiplier ampliﬁcation voltage and
signal gain, can signiﬁcantly inﬂuence the results, i.e. the measured mean diameter and the
broadness of the distribution, these parameters have been determined for each particle batch
individually in the asymptotic range as recommended in (Kapulla and Najera 2006), to ensure
that the result is independent of the operation parameters.
The shadowgraphy system (LaVision) consists of a pulsed laser backlight and a diffuser
which illuminate the particles passing the system between the light source and camera. The
camera is equipped with a far-ﬁeld microscope and optional magniﬁcation lenses, Fig. 2. The
shadow-pictures , Fig. 3, consists of dark spots representing the size of the dispersed latex
spheres. After calibration, i.e. relating the dimension of one pixel to a physical size, the shadow-
pictures are treated with an image analysis software (DaVis from LaVision) which determines
the diameters of the dark spots in the ﬁeld of view.
Fluorescence plate Farfield microscope
Figure 2: Backlight illumination and camera set-up for for the shadowgraphy system used.
To give an order of magnitude, us-
30 µm ing a camera (PCO Sensicam qe, 12
bit) with a resolution of 1376x1040
pixel, each pixel represents a physical
area of 1x1 µm2 . Laser-based pho-
50 µm tographic recordings such as the shad-
Out of plane
owgraphy system under consideration
are often characterized by a high con-
trast granulation pattern which is super-
imposed on the image. Due to the ran-
dom nature of this process, small dark
and bright grains of speckles can be
70 µm found on the image plane. Since the
image of small-particle shadowgraphy
Figure 3: Example of a raw shadowgraphy picture pictures will also result in dark clus-
taken from a mixture of all latex batches used for the ters of a few pixels, clusters originating
current experiments. from speckle patterns and those from
small particles might become indistin-
guishable from each other, resulting in a bias of the measured size distribution towards smaller
sizes. A second ﬂuorescence plate mounted at the front of the diffuser reduces the background
The comparison of the measured size distributions obtained by means of the PDA and shad-
owgraphy systems for latex sphere sizes of 5, 10, 30 and 70 µm can be found in Fig. 4.P dis-
tributions have been normalized to one. Whereas the count mean diameter D(1, 0) = di /N
(with i = 1, ..., N ) coincides for the PDA and the shadowgraphy system with the manufac-
turer guaranteed value very well, see also Fig. 5, the size distributions exhibit some interesting
Whereas the PDA-system measured size distribution is always considerably broader than
the manufacturer-guaranteed distribution for the size range considered here, the distribution
measured with the shadowgraphy system is only broader for the smallest diameter (5 µm). Since
one pixel corresponds to an area of ≈ 1x1 µm2 in the ﬂuid, the shadow image of a spherical
particle having a diameter of 5 µm is represented by ≈ 5 dark pixels. This is deﬁnitely the
lower limit the analysis routines as well as the optical system can handle. Therefore, although
ﬁltered, randomly contributing noise in the image, might add or subtract a few pixel to the dark
pixel clusters representing the small particles, which immediately shifts the results towards
lower or larger sizes, resulting in a broadened distribution, Fig. 4 a). The other shadowgraphy-
measured size distributions coincide with the manufacturer distributions very well, except for
nominal particle diameter 5.045 µm nominal particle diameter 10.4 µm
0.4 Shadowgraphy 0.4 Manufacturer
0 5 10 15 20 0 10 20 30 40
diameter [µm] diameter [µm] b)
nominal particle diameter 29.63 µm nominal particle diameter 70.6 µm
1.0 1.0 Manufacturer
0.6 PDA 0.6
20 25 30 35 40 50 60 70 80 90
diameter [µm] diameter [µm]
Figure 4: Comparison of measured size distributions for the nominal mean diamters indicated;
PDA, shadowgraphy and manufacturer.
the systematic skew of the distribution towards smaller sizes, Fig. 4 Mark A, which becomes
less severe for larger sizes.
It should be however noted, that it was necessary to heavily correct the diameter conversion
factors β 12 (β 13 ) which relate linearly the measured phase difference Φ12 (Φ13 ) between detec-
tors 1 − 2 and 1 − 3, Fig. 1, to the particle diameter dp : Φ12 = β 12 dp and Φ13 = β 13 dp to
obtain the correct mean particle by means of the PDA measurements. Using simply the physi-
cal off-axis angle of 30 ◦ together with the physical refractive index for latex spheres of 1.59 as
input parameters for DANTECs BSA Software (V4.0) results in diameter conversion factors of
β 12 = 4.384 (β 13 = 2.192) which would have increased the mean diameters by a factor of 2, i.e.
without correction, we measured a mean particle diameter of dp = 20.8 µm when dispersing
particles with dp = 10.4 µm in water. The DOS-based software SizeWare (V2.4) provides a
module which accounts for the geometry of the transmitting and receiving optics relative to the
window and the experimental facility if a window exists between the measurement volume and
the receiving optics, as well as for the refractive index of the ﬂuid which contains the particles.
This module allows the calculation of corrected diameter conversions factors, i.e. β 12 = 2.527
(β 13 = 1.263) for the experiments considered here. DANTECs BSA software does not provide
the diameter conversion factor as a direct input but uses (presumably), (Albrecht et al. 2003):
√ ¡ ¢ ´1/2
∆Φ12 = 2 · 2π dp 2 Θ Θ 1/2
1 + m − m 2 1 + sin ψ r sin 2 + cos ψ r cos φ cos 2
³ √ ¡ ¢ ´1/2
2 Θ Θ 1/2
− 1 + m − m 2 1 − sin ψ r sin 2 + cos ψ r cos φ cos 2
µPDA / µm , [-]
µSch / µm , [-]
± 10 %
0 20 40 60 80 0 20 40 60 80
diameter [µm] diameter [µm]
σPDA / σm , [-]
σSch / σm , [-]
0 20 40 60 80 0 20 40 60 80
diameter [µm] diameter [µm]
Figure 5: Comparison of PDA-measured and shdowgraphy measured count mean diameter with
nominal diameter, as well as measured broadness with nominal broadness
for ﬁrst order refraction, with the elevation angles ψ r = ψ 1 = −ψ 2 , the off axis angle Θ, Fig.
1, and the relative refractive index m = mp /mf , to calculate β 12 (β 13 ). Since Mask A was
chosen to cover the whole range of particles envisaged, i.e. it was decided to leave the elevation
angles ψ r = ψ 1 = −ψ 2 unchanged, we had to tune Θ or m. Since it was not possible to achieve
the corrected diameter conversion factors by solely changing Θ from 30◦ to 88◦ , we changed
additionally mp from 1.59 to 1.50 and obtained ﬁnally β 12 = 2.495 (β 13 = 1.248) as the closest
possible values compared with the suggestion from the SizeWare software.
For a quantitative comparison of the results we approximated all size distributions with
Gaussian distribution according to:
1 1 (x − µ)2
f (dp ) = √ exp − (2)
2πσ 2 σ2
resulting in the count mean, µ = D(1, 0), as well as the standard deviation, σ, describing
the broadness of the distribution. The manufacturer distributions are denoted by index m, the
PDA-measured distributions by index P DA, and the shadowgraphy-measured distributions by
index Sch. Since the manufacturer guaranteed distributions are considered as the reference, we
calculated the fractions µP DA /µm and µP DA /µm , Fig. 5, as well as σ P DA /σ m and σ P DA /σ m .
For all measurements the PDA-measured mean diameter coincides better than ±6 % and for
the shadowgraphy-measured better than ±5 % with the reference diameter, Fig. 5, that is, with
respect to the measured mean diameter both systems have comparable accuracy. The PDA-
measured distribution is 20 times broader for the smallest size (5 µm), Fig. 5. For increasing
particle sizes, this relation becomes increasingly better, but even for the largest size considered
here (70 µm) it is two times broader than the reference. No deﬁnitive statement can be given
to explain this behavior. This is still subject to further discussions with the PDA manufacturer.
The shadowgraphy-measured size distribution, on the other hand, is 10 times broader for the
smallest sizes, Fig. 5, but then decreases quickly and coincides with the reference value in the
range from 30 to 70 µm.
It must be stressed that the above mentioned corrected off-axis angle deeply inﬂuences the
calculated mean particle-volume ﬂux, by means of the BSA-software, since the mean particle-
volume ﬂux is referenced to the projected probe volume, which contains the off-axis angle as
parameter, (Albrecht et al. 2003).
The results can be summarized as follows:
• The PDA-measured (shadowgraphy-measured) mean particle size is in agreement within
±6 % (better than ±5 %) with the one given by the manufacturer for the size range from 5
to 70 µm.
• Since the experimental set-up with latex spheres dispersed in water introduces additional
refraction of the scattered light for the PDA measurements, the diameter conversion factors
must be corrected. This correction can be performed by means of a module in the DOS
based software SizeWare from DANTEC,i.e. one ends up with new diameter conversion
factors. Because the actual (V4.0) PDA software from DANTEC (V4.0) a) does not con-
tain this module and b) calculates the diameter conversion factors from the geometrical
set-up, it was necessary to use an off-axis angle of 88◦ (while having an physical off-axis
angle of 30 ◦ ) as input for DANTECs BSA software in order to obtain the correct mean
• Furthermore, it must be emphasized, that this corrected off-axis angle also deeply inﬂu-
ences the calculated mean particle-volume ﬂux, by means of the PDA software, since the
mean particle-volume ﬂux is referenced to the projected probe volume, which contains
the off-axis angle as parameter. Consequently the attempts to inter-compare also the PDA
and shadowgraphy based ﬂux measurements for the Latex spheres with hand-calculations,
• Additionally, it was found that for each measurement, the PDA-measured size distribution
of the Latex spheres is considerably broader – a factor of 4 over-all in terms of the standard
deviation – than the one obtained by means of the shadowgraphy system as well as the one
certiﬁed by the manufacturer. No deﬁnitive statement can be given to explain this behavior.
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