PDPA System

Particle (water droplets) sizing is an important part of this program since the particle sizes and their distribution play an essential role in determining mist film heat transfer and cooling effectiveness. A large number of particle sizing methods have been developed in the past (a review can be found in the paper by Swithenbank, 1991). A Phase Doppler Particle Analyzer (PDPA) system, invented by Bachalo in the 1980's (Bachalo, 1980; Bachalo and Houser, 1984), is used in this study. t=1.5d L=3d d=1/4 in θ=30deg Secondary flow

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Figure 2.16 Film injection hole details

The Phase Doppler Method is based upon the principles of light scattering interferometry. Two collimated, monochromatic, and coherent laser beams are made to cross at a point

(measurement point), where they interfere and generate light fringes. A particle moving across the fringes will reflect light, which is picked up by a receiving lens located at a certain off-axis collection angle. A set (usually 3) of detectors in the receiver is used to capture the signals. The temporal frequency of the signal is used to determine the particle velocity, and the spatial

frequency can be used to calculate the particle size.

Based on geometric optics, the relative phase shift for any incidental light passing through a spherical droplet can be calculated by the following equation (Bachalo and Houser, 1984):

)

'

sin

(sin

2α

τ

τ

φ

=

⋅

−m

,where φ is the relative phase shift between any light passing through the droplet and a theoretical, reference light undergoing no phase shift; α is the non-dimensional size parameter, πd/λ , in which d is the droplet diameter, and λ is the wavelength of the incident light; τ is the angle formed by the incident light and the surface tangent of the droplet; τ′ is the angle formed by the first refracted light and the surface tangent of the droplet; m is the relative (to air) index of refraction for the droplet.

The measurement volume is the body bounded by the ellipsoidal surface shown in Fig. 2.17, and it corresponds to the surface on which the light intensity of the fringes is 1/e2 of the maximum intensity, which occurs at the center of the measurement volume. This width definition

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is also called the D86 width. If the light intensity profile follows a circular Gaussian profile, when it is integrated down to 1/e2 of its peak value, it contains 86% of its total power. Fringe spacing decreases with increasing angle κ.

NFR = number of fringes

V = volume of measurement volume df = fringe spacing

dm = diameter of the measurement volume lm = length of the measurement volume f= focal length of the lens

λ= laser wavelength

Figure 2.17 Film injection hole details

It is noted that one distinguished feature of Phase Doppler measurement, compared with conventional interferometric techniques such a Laser Doppler Anemometry (LDA), is that the change in phase is independent of the incident intensity or scattering amplitudes of light, but is directly proportional to the droplet diameter. PDPA measures the relative phase shift of the Doppler signal directly as a linear function of the droplet diameter. As such, PDPA measurements

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are dependent on the wavelength of the scattered light, which is not easily affected by environmental conditions. This feature gives PDPA measurement a clear advantage over the conventional intensity based measurement method which is sensitive to background noise.

Another noted feature of the PDPA system is that its detector is commonly placed off the

plane of the transmitting beams at an angle close to 30o. This is because the intensity of the scattered light, which affects the Signal-to-Noise Ratio (SNR), can vary by several orders of magnitude depending on the receiving angle and the droplet concentration. Figure 2.18 shows the variation of the scattered light intensity as a function of receiver position for polarization

perpendicular to the beams. The intensity values are obtained from the Mie scattering calculations.

Generally, within the angle of 0º-20º off the transmitting axis, light is scattered primarily by

diffraction, which contains no information for the PDPA process. At an angle between 20º-90º, which is called the forward-scattering region, the scattered light, mostly by refraction for

non-opaque droplets, has the highest SNR, thus the size sensitivity is the best.

For some conditions, this forward-scattering configuration is difficult to traverse and the optical accessibility is poor because the transmitting and receiving optics are on the opposite side

of the flow. For angles between 90º-180º, which is called the back-scattering region, most light will be scattered by reflection, which has an SNR higher than the forward-scattering. However, the optical accessibility and traversibility of the back-scattering configuration are better since all the optics are on one side of the measuring point, requiring only one window and providing easier traversing arrangement of the LDV system. In this case, the same lens is used for focusing the two beams and for collecting and collimating the scattered light. For PDPA application, the forward-scattering method must be used due to the special need to receive the strongest signal at about 30o from light refraction caused by particle sizes.

The existing PDPA system has a fiberoptic probe with a focal length of 350 mm and a beam waist diameter of 115 µm. The beam spacing for the probe is 50 mm. The focal length of the receiver for the PDPA system is 500 mm. The laser system is an Argon-Ion type water cooled system with 4 watt maximum power output.

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Figure 2.18 Film injection hole details

57 (b)

(c)

Figure 2.19 PDPA system overview (a) a schematic of complete PDPA system (b) a schematic of PDPA transimmitng and receiving layout (c) Photoes of the PDPA system for this study Photodetectors Receiving Optics Transmitting Optics Fringes Move Signal Processor F SA Laser Fiberoptic C B A Receiving Angle FireWire PDM FlowSizer

58 (a)

(b)

Figure 2.20 PDPA bragcell (a) Outisde look (b) Inside structure (TSI manual, 2007)

59 (a)

(b)

Figure 2.21 PDPA coupler (a) Connection with other parts (b) Adjusting knobs detail (TSI manual, 2007)