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6.4.0MEASUREMENT TECHNIQUES FOR DROPLET TEMPERATURE

Droplet temperature is of interest in practical spray processes since it influences the associated heat and mass transfer, chemical reactions, and phase changes such as evaporation or solidification. Various forms of Rayleigh, Raman and fluorescence spectroscopies have been developed for measurements of droplet temperature and species concentration in sprays.[647] Rainbow refractometry (thermometry), polarization ratioing thermometry, and exciplex method are some examples of the droplet temperature measurement techniques.

In the rainbow thermometry, a linear CCD array is used to determine the location of the primary rainbow that is formed when a droplet is illuminated by a laser beam. The refractive index of the droplet is obtained by measuring the rainbow location assuming that the droplet is spherical. Since the refractive index varies with temperature, the droplet temperature is then inferred from a relationship between the refractive index and temperature if the relationship is known a priori. For accurate measurements of droplet temperatures in spray flames, the information of droplet sizes is required because rainbow angles also depend on droplet sizes. Accordingly, a rainbow thermometer should be integrated with an independent particle sizing instrument, such as the well established and widely used phaseDoppler interferometer, for simultaneous, accurate measurements of individual droplet size, velocity and temperature (refractive index) in complex sprays. Such an integrated system has been developed by Aerometrics, Inc. at Mountain View, CA.[655] The accuracy of the rainbow method may be limited by non-uniform heating of droplets and when measuring temperatures of multi-component fuel droplets. However, the rainbow method appears to have the most potential for accurate measurements of droplet temperatures via the refractive index in a combustion environment as well as in a wide range of applications.

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Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy’s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huygen’s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory.

A critical review of the rainbow method for droplet temperature measurement has been presented by Massoli et al.[710] They conducted a light-scattering analysis based on the Lorenz-Mie theory and showed that the size and refractive index of transparent droplets can be determined by measuring the polarized components of the scattered light at two angles in the forward direction. The horizontally polarized cross section CHH(33°) depends exclusively on the droplet diameter, whereas the ratio CHH(33°)/CHH(60°) is a sensitive function of the refractive index and hence of the droplet temperature. On the basis of the light scattering in the forward and rainbow regions, these researchers developed a new optical system for measuring the temperature, size, and velocity of individual transparent droplets. This system is capable of determining droplet temperatures with a resolution of a few degrees Centigrade. The techniques have been applied to vaporizing tetradecane droplets (D0 = 72 µm), which were heated up in a tube furnace with a temperature range of 20–200 °C.

Polarization ratioing thermometry has been proposed as a means of measuring the refractive index of a droplet and relating it to the droplet temperature. However, this approach does not have the

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potential resolution of the rainbow method whereas it has the similar limitations.

Exciplex method has also been proposed for droplet temperature measurement. In an oxygen environment, however, the fluorescence from the exciplex is quenched by the oxygen. In addition, fuel droplets may contain aromatic hydrocarbons that can produce fluorescence emissions, masking the fluorescence spectrum of the dopants used for the temperature determination.

A two-color pyrometer has been used along with the phaseDoppler anemometer to simultaneously measure the local velocity and size of kerosene droplets and the temperature of burning soot mantle in a swirl burner.[648] The measurements were conducted within the flame brush that develops in the shear layer of a swirlstabilized, gas-supported kerosene flame with a swirl number of about 0.19 and potential heat releases of 10.6 and 15.5 kW, respectively. The results showed that the maximum burning fraction of the droplets occurs adjacent to the region denoted as gas flame but the value ranges from 20±5 to 40±5% depending on the axial station, and decreases sharply across the shear layer. The flame mantle temperature was found to be independent of droplet diameter, which agrees with previous results in the literature.

A non-invasive infrared (IR) method has been developed for the measurement of temperatures of small moving fuel droplets in combustion chambers.[711] The IR system is composed of two coupled off-axis parabolic mirrors and a MCT LWIR detector. The system was used to measure the temperature variations in a chain of monosized droplets generated with equal spacing and diameter (200 µm), moving at a velocity of >5 m/s and evaporating in ambient air. The system was also evaluated for droplet temperature measurements in flames under combustion conditions.

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6.5.0MEASUREMENT TECHNIQUES FOR DROPLET DEFORMATION ON A SURFACE

Experimental observations of the spreading of a liquid droplet impinging on a flat surface were first reported by Worthington[337] in the late nineteenth century. In his experiments, Worthington designed an ingenious inductor circuit to produce an electric spark for illumination at different stages of droplet spreading and to sketch artistically the various forms assumed by a droplet during its impact on a surface.

Recently, experimental investigations of droplet spreading processes have received increasing attention. A variety of techniques have been used to record and measure the dynamic shapes of a droplet during its interaction with a surface. These include, for example, (a) high-speed film camera,[334][357][395][411] high-speed digital video system,[371][400][409] electronically controlled short-du- ration flash light photography, and holography[368] for recording droplet deformation details, and (b) high-speed two-color pyrometers[406] and high-speed thermal imaging systems[410] for recording and measuring both spreading and solidification. The clarity of pictures has been greatly improved by using single-shot flash illumination.[357][411] In the single-shot method, only one image of a droplet is recorded at one instant of the droplet impact process. By recording successive stages of the impact of several different droplets, the entire impact process can be pieced together from individual images.[411] Key parameters describing a droplet spreading process, such as splat-substrate contact area, splat diameter, and splat thickness, may be measured subsequently from the recorded pictures.

Generally, visualization methods record deforming droplet shapes at discrete stages of a continuous deformation process. The splat size is usually measured from visualization images with an accuracy on the order of 10 microns.[411] The visualization methods, while providing pictures of droplet spreading events at different stages, have certain limitations[368] For example, high-speed cinematography is expensive to implement and records multiple images of a

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single deforming droplet at the cost of reduction of image clarity so that it is difficult to make quantitative measurements. Single-shot flash photography can produce high clarity images of deforming droplets, but only one image can be rendered for each impinging droplet. Some details of the entire droplet spreading and possibly recoiling process may be skipped due to insufficient information at certain stages.

Efforts have been made to search for alternative experimental methods that do not involve direct visualization. Senda et al.[335] presented a simple method for the measurement of heat flux and heat transfer coefficient between a droplet and a hot surface on which it impinges. Shi et al.[336] developed simple experimental devices and measurement methods for the instantaneous diameter of a spreading droplet and the transient surface temperature of a solid substrate to assess cooling rates during droplet impingement without resort to photographic interpretation. In the work of Shi et al.,[336] the instantaneous diameter of a spreading water droplet was measured using an electrical resistance probe method. In their experimental set-up, a glass plate was coated with a 10-µm thick aluminum layer. A gap of 0.2 mm in width and 0.01 mm in depth was scribed across the center, separating the conducting surface into two halves. An electrical DC voltage was applied to each half of the conducting surface. As a water droplet spreads at the center of the gap, the gap is bridged and the voltage across the gap decreases. By monitoring the voltage change across the gap, the temporal change of the splat radius may be obtained. The calibration was performed by measuring the final splat area vs. the output signal voltage for an impacting water droplet of known initial radius. While this method is of considerable merit, it has certain limitations. For example, different droplet sizes require different calibration curves. The recoiling of the splat may result in loss of data in high-speed impact calibration. The gap is intrusive and may affect the spreading and recoiling dynamics, particularly for small droplets. In addition, an off-center droplet spreading may cause measurement errors.

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In an effort to invent fast, reliable and affordable measurement techniques, Zhao et al.[368] developed a simple and accurate non-intrusive photoelectric method to measure the transient splat diameter and the entire evolution of the maximum splat diameter during the collision of a droplet on a substrate. In this measurement system, a collimated laser beam and a linear response photodiode are used, as schematically depicted in Fig. 6.8. As a droplet spreads out on a horizontal quartz plate, the splat area increases and blocks more laser light. Thus, the light intensity collected by the photodiode decreases as the spreading proceeds. By recording the output signals from the photodiode, the transient splat diameter can be measured. In the experiments of Zhao et al.,[368] the probe beam was provided by a 15-mW He-Ne laser. The laser beam was focused and passed through a 20-µm diameter spatial filter in order to produce a smooth irradiance across the expanded and collimated probe beam. An iris was used to improve the system sensitivity for small droplets. After intercepting the splat, the partially blocked beam was collected onto the sensor area of the photodiode by a focusing lens. A Si-photo- diode (E2RUV passive silicon photo detector of type S 1226-5BQ, Spindler and Hoyer Inc.) was chosen to detect the laser light due to its fast response and high linearity. The photo detector rise time is 0.5 µs and the sensitive area is 2.4×2.4 mm2. A 100-MHz oscilloscope (HP 54601 A Oscilloscope, Hewlett-Packard Co.) was used to record the output voltage signals. The angle between the probe beam axis and the vertical direction was 8.5°. The measurement system was calibrated by placing successively opaque circular disks of known area on the clear quartz to block the probe beam. The sample disks were precisely manufactured from a black cardboard using a com- puter-operated CO2 laser (C-80 Laser System, Laser Machining, Inc.). The system output signals are a linear function of the sample areas. The measurement uncertainty of this technique is directly related to the sensitivity of the oscilloscope and the measurement system calibration. The uncertainty of splat area measurements was estimated to be less than 6.6×10-3 mm2, corresponding to uncertainties less than 2 µm and 1 µm for splat diameters larger than 2.1 mm

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and 4.2 mm, respectively. The time and length scales in this technique were on the order of microseconds and micrometers, respectively. This method requires that the droplet to be studied must be opaque to the probe beam. To alleviate this limitation, a special probe beam may be selected such that the droplet fluid is opaque to it. The preferred probe beam wavelength is generally in the range from visible to ultraviolet, and a special wavelength window may be needed to reduce the environmental radiation that could influence the photoelectric measurements.

Figure 6.8. Schematic showing photoelectric method for measurement of splat diameter. (Reprinted with permission from Ref. 368.)

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Zhao et al.[368] also designed a two-reference-beam doublepulse holography system to visualize the deformation process of a droplet during impingement on a substrate. The system can record and reconstruct two holographic images of a droplet from one hologram at two instances of a deformation process. In this experimental method, the field distribution and phase information from the light scattered by a deforming droplet is recorded on a hologram. A wealth of information about the object can be then extracted from the hologram. For example, one hologram can readily generate different real images of a deforming splat that correspond to different viewing angles. The axial symmetry of a droplet can be examined for each exposure. As schematically depicted in Fig. 6.9 (top), the key components in this optical arrangement are the Pockels cell and the polarizing beam splitter. During each experiment, the ruby laser fires two pulses of laser light. The Pockels cell, driven by a high-voltage pulse generator, is electronically switched such that the polarization direction of the second pulse is rotated by 90°. This enables the second beam to pass through the polarizing beam splitter and follow the second reference path. The images of a deforming droplet from both the first and the second pulse are accordingly recorded on the same holographic plate, but with spatially different reference beams. The Pockels cell modulates both the object beam and the reference beam. This optical arrangement enables the polarization directions for the object beam and the reference beam to be used on the hologram plane. Therefore, a high degree of optical visibility is ensured for the holographic images recorded for both pulses. One reference beam at a time is used for reconstruction. Thus, two images of a splat at different stages of spreading can be separately reconstructed with exact information about the order. The separation time between the first pulse image and the second pulse image is the same as the electronically set laser pulse separation time. For the HLS-2 Ruby Laser (Lumonics, Inc.) used in this study, the pulse separation time varied in the range of 1–800 µs with a pulse duration of 20 ns. The maximum laser beam power was 3 joules. Figure 6.9 (bottom) shows the overall experimental setup of the holography system for

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recording images of a deforming droplet at different stages of spreading. In this setup, a droplet is released from the droplet generator and detected by a detector during its free-fall. After a preset time delay, the droplet detector sends a signal to trigger the pulse laser that in turn fires two pulses consecutively with a preset separation time. Two images of a deforming droplet are recorded on the same holographic plate. The images are then reconstructed from the holograms and digitized and stored in a personal computer for image analysis (IMAGE ANALYST® version 8.0, 1992, Automatix, Inc.).

Experimental observations of droplet impact under conditions typical of thermal spray applications are difficult due partly to the difficulties in accurate determination of droplet size, velocity, and energy state prior to impact. In addition, high-temperature properties may not be available, limiting the usefulness of flattening data in determining the proper scaling.[390] Vardelle et al.[712] used two high-speed two-color pyrometers to monitor the flattening, cooling and solidification of droplets on a substrate during plasma spray deposition. In this measurement system, the light emitted by a flattening droplet was collected by one of the pyrometers that was focused on the substrate. The optical signal was then imaged on the entrance slit of a monochromator, and two output signals filtered at 632.8 and 832.8 nm were transmitted to two photomultipliers. After amplification, the signals were recorded by a numerical oscilloscope. Another identical pyrometer was focused on a point 1.8 mm above the substrate to determine the droplet size, velocity and surface temperature prior to impact. A coincidence sensor was focused on the center of the field of view of this pyrometer to ensure that the radiation detected by both pyrometers came from the same droplet in-flight and at impact. Thus, the measurement system can provide data on the deformation and solidification of a droplet during impingement on a substrate surface, along with data on its size, velocity and molten state at impact. The spatial resolution for the in-flight measurement was about 0.015 mm3 and the monitored area on the substrate surface was 0.5 mm2.