determination of the particle size and soot volume

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1. Introduction

Soot particles emitted through engine combustion have a negative impact on both human health and the environment. Therefore, the effective control of soot formation is essential. A variety of studies have been conducted on the mechanism of soot particle formation, and its physicochemical properties have been investigated for many years [1-4]. Laser-based diagnostics has been widely applied to investigate the characteristics of soot particles [5-20], such as, the laser-induced incandescence (LII) method [6-8], the laser diffraction (LD) method [9], the light extinction method (LEM) [10-11], and the dynamic light scattering (DLS) method [12,13]. LII is applied widely in determining the soot volume fraction and primary particle size [6-8]. This technique is capable of spatially and temporally resolving soot measurements and may

be applied to practical combustion systems. However, the equipment required is relatively expensive. In addition, for particle sizing a theoretical model is needed [8]. The upper limit of the light diffraction (LD) method [9] can reach on the order of 100 μm at maximum, and the lower limit of measurement is on the order of 0.1 μm [5]. Thus, the diffraction method is capable of measuring only larger particles and has many difficulties measuring particles whose mean diameters are less than 1 μm. The development of the light extinction method (LEM) is premised on the attenuation of the transmitted light intensity relative to the incident light intensity instead of the scattered light intensity signal [10-11]. The technique is widely used for the determination of the soot volume fraction. In the dynamic light scattering (DLS) method [12-14], the measurable range is from 1 nm to 1 μm order [5]. This method has been used for ultrafine particle measurement in various applications. DLS measurements are very sensitive to * Corresponding author. E-mail: [email protected]

■ORIGINAL PAPER■

Determination of the Particle Size and Soot Volume Fraction in a Butane Laminar Coflow Diffusion Flame by the Multi-Wavelength Polarization Ratio Method

CHENG, Long*, ARAKI, Mikiya, KOIZUMI, Yuichi, KIRIBAYASHI, Seibu, ODA, Shotaro, and IKEDA, Kazuki

Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515, Japan

Received 22 August, 2019; Accepted 23 March, 2020

Abstract: The feasibility of a newly developed particle size distribution, complex refractive index and soot volume fraction determination method in a butane laminar coflow diffusion flame at atmospheric pressure is evaluated based on Mie scattering theory. The polarization measurements were performed using multi-wavelength light sources. The scattered light intensities were obtained by analyzing the soot particles images taken by polarization CCD cameras under a scattering angle of 60°. The flame height is set at z = 30 mm. Through calculation, information regarding the particle number, geometric mean diameter, geometric standard deviation and complex refractive index can be determined simultaneously. The experimental results show that the geometric mean diameters increase, and the particle numbers decrease as moving downstream of flame. Polystyrene standard particles of 46 nm and 269 nm in pure water under five different number densities are used to validate the accuracy of MPR method. The soot volume fraction was calculated and compared with the data obtained using the light extinction method (LEM). At z = 20 mm, the two results showed good agreement. At z = 25 mm, the soot volume fraction obtained by two methods had a difference. The reason is considered due to coagulation and aggregation of soot particles. The particle size distribution is also compared with the results obtained using a portable aerosol mobility spectrometer (PAMS). The particle size measurement obtained from the MPR method is underestimated in comparison with that of the PAMS. The possible reason considered that PAMS system is a sampling method to measure particle size distribution and it may influence the soot formation.

Key Words: Polarization, Mie scattering theory, Particle size distribution, Particle number, Refractive index, Soot volume fraction

日本燃焼学会誌　第 62巻 201号（2020年）249-258 Journal of the Combustion Society of JapanVol.62 No.201 (2020) 249-258

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日本燃焼学会誌　第 62巻 201号（2020年）

temperature and solvent viscosity. Therefore, the temperature must be kept constant and solvent viscosity must be known for a reliable DLS experiment. DLS is also restricted to transparent sample preparation [14]. There are many intrusive measurement methods, such as transmission electron microscope, the centrifugal sedimentation method, and the electrostatic classification method [5]. By using of these methods, it is possible to measure particle size on the order of 1 nm [5]. However, the sampling is necessary in the measurement, the spatial distributions of the particle size and time variations are lost. Understanding the soot formation in a combustion process requires in situ measurement techniques which can provide important characteristics of particles in combustion, such as the soot volume fractions and particle sizes, under a variety of conditions [15]. The polarization ratio method [16-20] is a well-known in situ measurement method for submicron particles. However, single wavelength polarization ratio method [16] cannot distinguish the width of the particle size distribution due to nature of single wavelength of the laser source. In this research, multi-wavelength light sources are applied to investigate the characteristics of soot particles simultaneously, such as the geometric mean diameter, the geometric standard deviation, the particle number and the complex refractive index in a butane laminar coflow diffusion flame [21-23]. This new method, the multi-wavelength polarization ratio (MPR) method, is capable of obtaining the information of soot particles non-intrusively [17-20]. Compared with previous study [17-18], the measurement object is standard particles in the pure water. Therefore, diameter, geometric standard deviation and complex refractive index are known parameters. The accuracy of MPR method was validated. The measurement upper limit of diameter was expanded to 1 μm order. In the present study, the measurement object is soot particles in the flame. Therefore, geometric mean diameter, geometric standard deviation and complex refractive index are unknown parameters. By using MPR method, these unknown parameters could be determined. The authors also expanded the measurement lower limit of diameter to 1 nm order. Polystyrene standard particles of 46 nm and 269 nm in the pure water under five different number densities were used to validate the accuracy of MPR method. The results from MPR were also compared with two other measurement methods. The soot volume fraction is calculated and compared with the data obtained using the LEM. The particle size distribution is compared with the data measured by a portable aerosol mobility spectrometer (PAMS) [24].

2. Nomenclature

α Particle size parameterλ Wavelength of the incident lightD Particle diameterf(D) Function of lognormal distributionlog σg Geometric standard deviationDg Geometric mean diameterτ Exposure timeI1, λ1 Perpendicular components of theoretical scattered light

intensities having wavelength of λ1

I2, λ1 Parallel components of theoretical scattered light intensities having wavelength of λ1

I1, λ2 Perpendicular components of theoretical scattered light intensities having wavelength of λ2

I2, λ2 Parallel components of theoretical scattered light intensities having wavelength of λ2

IM1, λ1 Perpendicular components of measured scattered light


IM2, λ1 Parallel components of measured scattered light


IM1, λ2 Perpendicular components of measured scattered light


IM2, λ2 Parallel components of measured scattered light


Cλ Optical constantn Particle numberm Complex refractive indexθ Scattering angleεI1,λ1 Residual between measured value and theoretical value

of perpendicular components having wavelength of λ1

εI2,λ1 Residual between measured value and theoretical value of parallel components having wavelength of λ1

εI1,λ2 Residual between measured value and theoretical value of perpendicular components having wavelength of λ2

εI2,λ2 Residual between measured value and theoretical value of parallel components having wavelength of λ2

ε Sum of residualsz Flame height above the burnerr Lateral measurement distanceR Fuel nozzle radiusMPR Multi-wavelength polarization ratio methodLEM Light extinction ratio methodTEM Transmission electron microscopePAMS Portable aerosol mobility spectrometer

3. Formulation

The Mie scattering theory which describes the scattering and absorption of light by a homogeneous spherical particle is widely

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CHENG, Long et al., Determination of the Particle Size and Soot Volume Fraction in a Butane Laminar Coflow Diffusion Flame by the Multi-Wavelength Polarization Ratio Method

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adopted. Figure 1 shows the light scattering of a single particle for the incident light of random polarization. The observation plane is defined by the incident light axis and the observer (camera). The scattered light includes component i1 and component i2. The component i1 is perpendicular to the observation plane, and the component i2 is parallel to the observation plane. The intensity functions depend upon both complex refractive index m and particle size parameter α. The value of m could be determined by calculation. The size parameter α is calculated as follows.

(1)

Where D is particle diameter and λ is wavelength of the light. The probability distribution function, f(D), is assumed that particle size distribution obeys a lognormal distribution, which is expressed as [25]:

(2)

Where log σg is geometric standard deviation and Dg is geometric mean diameter. Two different wavelengths laser sources were used. Therefore, two pairs of equations describing the scattered light intensities can be obtained. In multiple particles, the scattered light components are shown as follows.

(3)

(4)

Herein, I1, λ1, I2, λ1, I1, λ2 and I2, λ2 are the theoretical scattered light intensities of MPR method which are used to describe the

perpendicular components and parallel components under two different wavelength lights, respectively. The parameters τλ1 and τλ2 are the exposure times of the polarization CCD cameras, λ1 and λ2 indicate two different wavelengths of incident lights, Cλ1 and Cλ2 are the optical constants which the factors are depending on the particle number concentration and on the instrument constant, n is the particle number, fI1 and fI2 are Mie scattering intensity functions. The parameter θ is the scattering angle. The residuals between theoretical values of the scattered light intensities and the measured values are expressed as follows.

(5)

(6)

Where IM1, λ1, IM

2, λ1, IM1, λ2 and IM

2, λ2 are the measured values of the scattered light intensities. The power M represents the measured value. Insert Eq. (3) and Eq. (4) into Eq. (5) and (6) as follows.

(7)

(8)

Sum of residuals ε is shown by the following equation.

(9)

The optical constants Cλ1 and Cλ2 can be determined using polystyrene standard particles with diameters of 22 nm. Particle number n, geometrical mean diameter Dg, geometric standard deviation log σg, and complex refractive index m are unknown parameters. While ε reaches minimum, the iterative calculation has converged. In the meanwhile, the corresponding unknown parameters can be determined simultaneously.

4. Experimental Setup

4.1. Butane Laminar Coflow Diffusion Flame An axisymmetric, laminar, coflow, diffusion flame was used, which is shown in Fig. 2. The burner consists of a fuel nozzle having an inner diameter of 5 mm and a co-annular air nozzle having a diameter of 50 mm. Hereafter, the fuel nozzle radius is designated as R. The flame height is set at 30 mm. The z- and r-axes are set along the center axis and the lateral direction of the flame, respectively. Measurements have been done at two

Fig. 1 Light scattering from a single particle for incident light of random polarization.

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different heights above the fuel nozzle at z = 20 mm and z = 25 mm. The whole burner system is set on a stage and it can be scanned in the vertical and horizontal directions. The test fuel is butane stored in a fuel bottle in liquid phase. The fuel bottle is settled in a constant-temperature water bath set at 5 °C to keep the vapor pressure of fuel constant. The gas phase fuel is supplied via a pipeline. The fuel flow rate is measured using a thermal flow meter (KOFLOC, Model 3760). In order to adjust the mass flow rate, a precision needle valve was employed. For the purpose of keeping the fuel density constant, the fuel temperature is set at 35 °C using a silicon cord heater and a temperature controller. In order to keep the shape of the flame stable, the surrounding air flow is used. The air flow rate was also measured using a thermal flow meter (KOFLOC, Model 3105).

4.2. Optical Setup A schematic of the optical setup is shown in Fig. 3. Two diode lasers having wavelengths of 405 nm and 488 nm are used. These are emitted simultaneously and on the same axis. Two polarization CCD cameras (4D-Technology, Polar Cam 7001-00161) are set symmetrically at 60° with respect to the laser axis. Interference filters centered at 405 nm and 488 nm are set in front of the two cameras; 405 nm corresponds to the camera 1 and 488 nm to the camera 2. A polarizer was used to make the incident light linearly polarized. The orientation of the polarization is set at 45° with respect to the observation plane. By setting the orientation at 45°, the incident light intensities of perpendicular and parallel components become the same. Figure 4 shows the polarization camera and its micro polarizers attached on each pixel. The resolution of the camera is 648 × 488 and the bit depth is 12 bits. The scattered light from soot particles contains the perpendicular and parallel components of polarization depending on their size distribution. The polarizers on the CCD elements have four different orientations, and two polarization components can be obtained from a single image.

Figure 5 shows the scattered light images having two different polarization components taken at z = 20 mm. The incident light wavelength is 405 nm. The left image is the perpendicular component I1 and the right one is the parallel component I2. The scattered light intensities for these components are calculated from the images shown in Fig. 6.

4.3. Experimental Conditions The experimental conditions for the butane laminar coflow diffusion flame are presented in Table 1. The specifications of the light sources are shown in Table 2. Aimed at determining the optical constant Cλ , standard particles (MORITEX, 3020A) were utilized, whose properties are presented in Table 3. The values of parameters in the optical constant experiment are shown in Table 4. Polystyrene standard particles in the pure water under five different number densities are used to validate the accuracy of MPR method. The information about contrast standard particles is shown in Table 5.

Fig. 2　Direct image of burner and butane laminar diffusion flame.

Fig. 3　Schematic of optical setup.

Fig. 4　Polarization camera and micro polarizers attached on each pixel.

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5. Results and Discussions

5.1. Determination of the Optical Constant This part introduces how to determine the optical constant C405 in the butane laminar coflow diffusion flame. To determine the optical constant, polystyrene standard particles of 22 nm were employed. Schematic of experiment setup for optical constant measurement is shown in Fig. 7. The experimental conditions and experimental device were almost identical to the MPR system. Two lasers with the wavelengths 405 nm and 488 nm are used and the scattering angle is 60°. The difference is that the burner is replaced by a quartz cell filled with pure water and polystyrene standard particles. The equation which is about the optical constant of soot particles is presented as follows.

(10)

Where C405 and C488 are the optical constants corresponding to the soot particles in the under wavelengths of incident light of 405 nm and 488 nm, respectively. Cp,405 and Cp,488 refer to the optical constants of the standard particles. T405 and T488 are the transmissivities of the two wavelength lights through the flame and can be obtained using the LEM system. The optical constants of standard particles Cp,405 and Cp,488 are defined as:

(11)

Herein, IM1,405 and IM

1,488 are the measured scattered light intensities of standard particles. I1,405 and I1,488 are the theoretical

Fig. 5　Scattered light images for two polarized components.

Fig. 6　Scattered light intensity for two polarized components.

Table 1 Experimental conditions for butane laminar coflow diffusion flame.

Table 2　Specifications of light sources.

Table 3　Standard particles for determining optical constant.

Table 4　Specifications of determining optical constant.

Table 5　Test standard particles.

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scattered light intensities of standard particles obtained by MPR method. Here, the value of Cp,488 is set to 1. Accordingly, the value of Cp,405 can be determined in Eq. (11). In Eq. (10), the value of C488 is also set to 1, and the value of Cp,405 has been obtained from Eq. (11). As a result, C405 can be determined.

5.2. Determination of the Four Unknown Parameters Two different lasers having wavelengths of 405 and 488 nm are used. Two different polarization components of scattered lights, perpendicular to and parallel to the polarization plane, are acquired by use of the polarization cameras. In total, four combinations of equations, namely Eqs. 7 and 8, are obtained. The measured values of the scattered light intensities are substituted into Eqs. 7 and 8. The theoretical values are calculated by substituting temporal values into the four unknown parameters. The residual between the measured and theoretical values changes according to the values for four unknown parameters. By use of an iterative procedure, the values for four

unknown parameters are changed so that the sum of the residuals given in Eq. 9 is minimized, which corresponds to the proper combination of four parameters. Figure 8 shows the four layers of unknown parameters of theoretical scattered light intensities. This consists of the particle number n, the geometric mean diameter Dg, the geometric standard deviation log σg and the complex refractive index m. The range of these values are determined under several constraints. The value of log σg is assumed to be 0.05 < log σg < 0.25 based on previous studies [26-28]. Regarding the complex refractive index, the range of the real part is assumed to be set from 1.5 to 2.0 and the sum of the real and imaginary parts is assumed to be kept at 2.5 based on a previous work of numerical calculations [26]. Figure 9 illustrates the isosurface of ε at z = 20 mm. The values of ε are demonstrated in different grayscale levels. The point in the circle indicates the minimum value of ε . Through iterative calculation, it was found that the sum of residuals was minimum while m = 1.9.0.6i with log σg = 0.23.

5.3. Geometric Mean Diameter and Particle Number The geometric mean diameter Dg and particle number n distribution in the radial direction at z = 20 mm and z = 25 mm are shown in Fig. 10 and Fig. 11, respectively. The figures present the right half of the butane laminar coflow diffusion flame. When z = 20 mm, the complex refractive index m = 1.9.0.6i and log σg = 0.23 settings are utilized. When z = 25 mm, the complex refractive index m = 1.6.0.9i and log σg = 0.23 settings are utilized. At a flame height z = 20 mm, the geometric mean diameter is approximately 10 nm near the flame centerline. At a flame height of z = 25 mm, the geometric mean diameter is approximately 19

Fig.7　Schematic of experiment setup for optical constant measurement.

Fig. 8　Four layers of unknown parameters of theoretical scattered light intensities.

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nm near the flame centerline. A comparison of the results of z = 20 mm to those of z = 25 mm shows that the geometric mean diameter increases and the particle number decreases moving downstream of the flame. This finding is in sound agreement with that of Zama, Y, et al. [29]. The reason is considered due to the coagulation of soot particles. It is considered that the surface growth reaction of the soot particles plays a leading role within the zone from z = 20 mm to z = 25 mm. Figure 12 shows the comparison of results for the MPR and TEM methods. The horizontal axis indicates the mean diameter obtained by TEM and the vertical axis that for the MPR method. Two kinds of polystyrene standard particles having nominal diameters of 46 and 269 nm (measured by TEM) are used to validate the accuracy of the MPR method. The polystyrene particles are suspended in pure water in a quartz cell. The number density of the polystyrene particles is widely varied as well. For the smaller particle (nominal diameter of 46 nm), the MPR method overestimates the diameter when compared with TEM. The error is around 170 %. For the larger particle (nominal diameter of 269 nm), the error against the TEM becomes much

smaller whereas it still overestimates the diameter. The error decreased to be around 20 to 40 %. For both standard particles, the MPR method overestimates the diameter and with the decrease in the diameter the error increases. This could be attributed to the leak of polarized light at polarizers on each pixel of the CCD sensor. The extinction ratio of the polarizer of this camera is on the order of 1 % and this makes the measured intensities of the two polarization components uniform, which corresponds to the overestimation in the particle diameter in this range. This problem will be solved by applying correction algorithm being in development.

5.4. Validation by Use of the Light Extinction Method (LEM)

To validate the MPR method, the soot volume fraction attained

Fig. 9　Sum of residuals as a function of m and log σg at z = 20 mm.

Fig. 10 Radial distributions of the geometric mean diameter at z = 20 mm and z = 25 mm.

Fig. 11 Radial distributions of the particle number at z = 20 mm and z = 25 mm.

Fig.12　Comparison of mean particle sizes of MPR and TEM.

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by the MPR method is compared with the data obtained by LEM at z = 20 mm and z = 25 mm. Moreover, the Abel transform was used to calculate the soot volume fraction used in the LEM computation. The schematic of LEM system is shown in Fig. 13. The diode laser source with a 638 nm wavelength is applied in the LEM system. Figure 14 shows the comparison of the soot volume fractions

measured by the two methods at z = 20 mm and z = 25 mm. Moving upwards from z = 20 mm to z = 25 mm, the overall soot volume fractions decrease, which suggests that the oxidation is increasingly prominent. In the radial direction, even though the value of the soot volume fraction continues growing near the flame centerline, the value of the soot volume fraction decreases at the radially outward location. At z = 20 mm, the soot volume fractions obtained by the two methods exhibit similar distribution trends and values. At z = 25 mm, a significant difference between the two methods can be found. The reason could be that in the MPR method, it is assumed that the shapes of soot particles are spherical. At z = 20 mm, the coagulation is not obvious, most particles are primary particles and the shapes are closed to spherical, and then MPR method has a good performance. However, at z = 25 mm, coagulation and aggregation are increasingly obvious. The chain and irregular structures of soot particles may produce a significant effect on the calculation model.

5.5. Validation by Use of a Portable Aerosol Mobility Spectrometer (PAMS)

For the purpose of validating the MPR method, a PAMS was employed for the measurement of the particle size distribution followed by a comparison with the results of the MPR method. MPR method was used to measure primary soot particles in the flame. Consequently, it is necessary to ensure the measured particles are primary particles. The PAMS system was also used to distinguish primary particles and secondary particles. The PAMS is a sampling measurement instrument for aerosols [24]. A schematic of the soot particle sampling system is presented in Fig. 15. The nitrogen flow rate used for diluting the aerosol was measured by a thermal flowmeter on the upstream side of the sampling probe and a thermal flow meter on the ejector side. The nitrogen flow rate is 1.7×10-5 m3/s from the upstream side and 2.3×10-4 m3/s for the ejector. In addition, the dilution ratio in the flow path system at the flow rate above is 5.6×103. The dilution of nitrogen to the sampling probe is carried out to freeze the soot particle reaction. Figure 16 compares the particle size distribution measured by the PAMS and the MPR method at z = 20 mm. The vertical axis is the normalized particle number, and the horizontal axis indicates the particle size. The PAMS result contains a bimodal particle size distribution that peaks at 42 nm and 129 nm. The distribution on the side of the larger particles results from the soot coagulation inside of the collection tube. In comparison with the PAMS results, the particle sizes obtained by MPR are underestimated. The possible reason considered is that PAMS system is sampling method to measure particle size distribution, it could influence the soot formation,

Fig. 13　Schematic of the light extinction method.

(a) z = 20 mm

(b) z = 25 mm

Fig. 14 Comparison of soot volume fractions (SVF) measured by MPR method and LEM.

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and then the data from PAMS may be imprecise. Therefore, the optimum solutions of the particle sizes obtained by MPR method are smaller than the data measured by PAMS.

6. Conclusions

The MPR technique has been demonstrated for its application and validating in the context of the soot volume fraction and particle size distributions. The results confirmed the feasibility of MPR method and are presented as follows. 1. A comparison of the results measured at z = 20 mm and z = 25 mm indicates that the geometric mean diameters increase, and the particle numbers decrease as moving downstream of flame due to coagulation. It is considered that the surface growth reaction of the soot particles plays a leading role within the zone from z = 20 mm to z = 25 mm. For both standard particles (nominal diameter of 46 and 269 nm), the MPR method overestimates the diameter when compared with TEM and with the decrease in the diameter the error increases. This could be attributed to the leak of polarized light at polarizers on each pixel of the CCD sensor. This problem will be solved by applying correction algorithm being in development. 2. Moving downstream of the flame from z = 20 mm to z = 25

mm, the overall soot volume fractions decrease. In comparison with the LEM results, at z = 20 mm, the soot volume fractions exhibit good agreement. At z = 25 mm, there is a difference between the results of the two methods. It is considered the reason that the coagulation and aggregation are increasingly obvious, the chain and irregular structures of soot particles may produce a significant effect on the calculation model. 3. The particle size measurement obtained from the MPR method is underestimated in comparison with the PAMS measurement. The possible reason considered is that PAMS system is a sampling method to measure particle size distribution and it could influence the soot formation. Therefore, the optimum solutions of the particle sizes obtained by MPR method are smaller than the data measured by PAMS.

Acknowledgments

A part of this research was subsidized by SIP (Strategic Innovation Creation Program) "Innovative Combustion Technology" (Management Corporation: JST) of Council for Science, Technology and Innovation. The authors thank S. Shiga, J. Gonzalez, K. Hagiwara and S. Hoshino of Gunma University for their help for instrumentation and meaningful discussions.

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