430Science and Engineering of Droplets

6.2.0MEASUREMENT TECHNIQUES FOR DROPLET VELOCITY

In sprays, droplet trajectories in the Lagrangian reference frame are probably one of the most interesting quantities to be measured. To optimize atomizer design, it is necessary to obtain spray characteristics such as droplet size and velocity. The primary methods for simultaneous measurements of droplet size and velocity may include high-speed photography,[706] cinematography, holography,[650] and phase-Doppler particle analyzer.[686][689][690] Bachalo[655] has presented a brief description of a variety of optical measurement techniques, and reviewed the capabilities and limitations of these methods along with discussions on the range of reliability, accuracy, and droplet number density considerations.

High-speed photography techniques can be used to measure droplet velocity. During a measurement, two light pulses are generated in rapid succession, yielding a double image of a single droplet on the photographic plate. The droplet velocity can be then determined from the image by measuring the distance traveled by the droplet and dividing it by the time interval between the two pulses. The direction of the velocity vector can also be directly determined from the image as an angle of flight with respect to the central axis of spray. From a series of such instantaneous measurements of individual droplets, time-averaged and space-averaged velocities as well as standard deviations can be obtained.[457][671][672] High-magnifica- tion double-pulse laser photography techniques can be used to measure both droplet size and velocity simultaneously. However, the measurement range may be limited.[706]

To extract spatial and temporal information on 3-D trajectories of droplets, high-speed photography, cinematography and/or holography should be used together with a digital image analyzer. Ante et al.[651] combined a double pulse holographic system with digital image processing to measure droplet velocities and number densities in the injection spray of a model diesel engine. The model engine consisted of a conventional injection pump and a rest

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chamber that could be operated at high pressures and temperatures to simulate the conditions in an operating diesel engine. The holographic images were reconstructed and fed into a PC by means of a CCD camera. Up to 30 image sections were necessary to store the information of a whole hologram. A software package was developed for the segmentation of droplets and the determination of droplet velocities.

In imaging methods, droplet velocity is generally determined by measuring the displacement of droplet images over a known time interval. This family of techniques is commonly referred to as particle image velocimetry (PIV), although a number of other terms are also often used to describe various subsets of the wide range of similar techniques.[707] The PIV can generate information of instantaneous velocity vectors across planes, from which vortex and cluster structures can be discerned. In a measurement with the PIV, droplets in a spray are illuminated with a sheet of light, normally provided by a pulsed laser, and scatter light to an imaging device. The droplet images may be recorded photographically on films or electronically using a CCD or CID camera. High resolution (>25 million pixels per image mark) CCD and CID cameras eliminate the need for both the chemical processing of films and the subsequent digitization of images. Alternatively to the 2-D recording with CCDs, holographic recording may be used to obtain 3-D components of droplet velocities over an entire flow volume. To obtain reliable velocity information using the PIV, the time between exposures must be selected so as to obtain a sufficient displacement for an acceptable velocity resolution, but not so large that the droplet moves out of the field of view or the plane of illumination. A variety of techniques have been used for the analysis of images from the

PIV.[655]

The phase-Doppler method is capable of accurately measuring particle size distribution and velocity.[655] The most recent models of phase-Doppler particle analyzer (PDPA) can generate data of droplet size and velocity simultaneously as a function of time, from that droplet drag can be calculated and clustering phenomenon can

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be studied. PDPA is now recognized as the most successful and advanced instrument for simultaneous measurements of droplet size and velocity.[686][689][690][708] A phase-Doppler anemometer (PDA) and associated instrument for simultaneous measurements of droplet size and velocity are shown in Fig. 6.6. The mathematical formulations for droplet size and velocity have been discussed in detail by Manasse et al.[689] and the measurement results have been compared to the Mie theory in Ref. 690.

Figure 6.6. Experimental setup of a PDA and associated instrument for simultaneous measurements of droplet size and velocity. (Courtesy of Prof. Dr.-Ing. Klaus Bauckhage at University of Bremen, Germany.)

An experimental method based on the theories for rainbow phenomena has been applied to the measurement of droplet size and velocity and to the detection of non-sphericity.[7] In this method, a comparison between two droplet diameters is deduced from two different optical interference patterns observed in a rainbow that is created by a droplet scattering laser light. Once a rainbow pattern is

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identified as coming from a spherical droplet, reliable droplet velocity and diameter can be derived from the same interference patterns, using the theories for rainbow that are valid only for spherical droplets. Preliminary experiments and validation have been carried out by means of a laser beam along with a photomultiplier and a CCD camera, respectively.

6.3.0MEASUREMENT TECHNIQUES FOR DROPLET NUMBER DENSITY

Droplet number density and volume flux are important quantities in studying droplet dispersion and mixing processes in multiphase flows and sprays. The phase-Doppler particle analyzer has the potential of measuring local droplet number density and volume flux with sufficient accuracy.[655] In addition, it can measure the time varying nature of these quantities that may result from the interaction with large-scale structures in the flows/sprays. The measurement techniques for droplet number density and volume flux have been discussed by Bachalo.[655]

In the phase-Doppler method, the number density, Nd, is determined from:

		1		åti, j (Di )
Eq. (5)	Nd =		å	j
		t		Ω	(D )
			i i		i

where t is the total sampling time, ti, j is the transit time of the ith droplet of size class j, Di is the droplet diameter in each size class i, and Ω(Di) is the sample volume that depends on the probe cross sectional area and the length along the beam axis. The reliable measurement of the number density does not depend on the accurate sizing of droplets but is very dependent on the reliable determination of the measurement volume and the counting of droplets. It requires

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reliable detection of the smallest, most numerous droplets and accurate detection of the transit time of each droplet as it passes the sample volume relative to the total time for accumulating a sample. Such a measurement can be evaluated by comparing to beam extinction measurements and using Beer’s law. In this method, the measured intensity of a beam passed through a spray is compared to the intensity without the spray present that is a measure of the light extinction produced by the spray. The mean droplet size D20 and the number density at points along the extinction beam path are measured using the PDPA. These results are used in the expression of Beer’s law to calculate the effective beam extinction that is then compared to the measured value.

In the phase-Doppler method, the volume flux, Vfx, is obtained from:

		π		D3		N	t
Eq. (6)	V fx =		30
		6		A		t

where A is the probe area normalized to that for the maximum particle diameter and Nt is the total number of particles counted, corrected for probe area variations. The volume flux is not very dependent on the counting of small droplets since they have a minimal effect on D30. However, it is obvious from Eq. (6) that the volume flux is most dependent on the accurate measurement of the size of large droplets in the size distribution. Since the relative population of the large droplets is small in a size distribution, it is important to collect a sufficiently large total number of samples to ensure that the large droplets are statistically representative. Moreover, the sampling cross section must be accurately determined as in the measurement of droplet number density.

Liu et al.[622] used a laser Doppler velocity and size (LDVS) measurement technique to determine the local size, velocity, and number flow density of droplets in the spray cone during spray deposition of a liquid steel. The experimental setup is schematically depicted in Fig. 6.7.[615] The measured results showed that smaller

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particles may be underrepresented due to the rapid solidification typical of the spray deposition processes of molten metals/alloys.

Figure 6.7. Schematic of experimental setup of a LDVS measurement system for local size, velocity, and number flow density of droplets in the spray cone during spray deposition of a liquid steel. (Reprinted from Ref. 615.)

The technique of stimulated Raman scattering (SRS) has been demonstrated as a practical method for the simultaneous measurement of diameter, number density and constituent material of micrometer-sized droplets.[709] The SRS method is applicable to all Raman active materials and to droplets larger than 8 µm in diameter. Experimental studies were conducted for water and ethanol monodisperse droplets in the diameter range of 40–90 µm. Results with a single laser pulse and multiple pulses showed that the SRS method can be used to diagnose droplets of mixed liquids and ensembles of polydisperse droplets.