Investigation of in-flame soot optical properties in laminar coflow diffusion flames using thermophoretic particle sampling and spectral light extinction

Abstract

Soot optical properties are essential to the noninvasive study of the in-flame evolution of soot particles since they allow quantitative interpretation of optical diagnostics. Such experimental data are critical for comparison to results from computational models and soot sub-models. In this study, the thermophoretic sampling particle diagnostic (TSPD) technique is applied along with data from a previous spectrally resolved line-of-sight light attenuation experiment to determine the soot volume fraction and absorption function. The TSPD technique is applied in a flame stabilized on the Yale burner, and the soot scattering-to-absorption ratio is calculated using the Rayleigh–Debye–Gans theory for fractal aggregates and morphology information from a previous sampling experiment. The soot absorption function is determined as a function of wavelength and found to be in excellent agreement with previous in-flame measurements of the soot absorption function in coflow laminar diffusion flames. Two-dimensional maps of the soot dispersion exponent are calculated and show that the soot absorption function may have a positive or negative exponential wavelength dependence depending on the in-flame location. Finally, the wavelength dependence of the soot absorption function is related to the ratio of soot absorption functions, as would be found using two-excitation-wavelength laser-induced incandescence.

Appendix 1: Uncertainty analysis

To assess the uncertainty of the TSPD/spec-LOSA-derived soot volume fraction and absorption functions, an uncertainty analysis was conducted. The uncertainty in f _v was determined by propagating uncertainty from the independent parameters in Eq. (3) as shown in Eq. (13). The uncertainty in V _p , σ, Nu _x , T _w , and T _g was taken to be 6, 4, 10, 10, and 3 %, respectively. Since the probe wall temperature is a function of grid exposure, we include a 10 % uncertainty estimate to span the range of possible temperatures with the 385 K measured in Ref. [40] serving as an approximate upper limit due to their longer grid exposure.

$$\delta f_{v} = \sqrt {\left( {V_{p} \frac{{\partial f_{v} }}{{\partial V_{p} }}\frac{{\delta V_{p} }}{{V_{p} }}} \right)^{2} + \left( {\sigma \frac{{\partial f_{v} }}{\partial \sigma }\frac{\delta \sigma }{\sigma }} \right)^{2} + \left( {Nu_{x} \frac{{\partial f_{v} }}{{\partial Nu_{x} }}\frac{{\delta Nu_{x} }}{{Nu_{x} }}} \right)^{2} + \left( {T_{w} \frac{{\partial f_{v} }}{{\partial T_{w} }}\frac{{\delta T_{w} }}{{T_{w} }}} \right)^{2} + \left( {T_{g} \frac{{\partial f_{v} }}{{\partial T_{g} }}\frac{{\delta T_{g} }}{{T_{g} }}} \right)^{2} }$$

(13)

Uncertainty in the TSPD-derived f _v was determined from Eq. (13) and used in Eq. (14) to determine uncertainty in the measured soot absorption function. Equation (14) is arrived at after rearranging Eq. (10) and considering uncertainty in τ, ρ _SA(λ), and f _v to be 1, 10 %, and the result of Eq. (13), respectively.

$$\delta E\left( m \right) = \sqrt {\left( {\tau \frac{\partial E\left( m \right)}{\partial \tau }\frac{\delta \tau }{\tau }} \right)^{2} + \left( {\rho_{SA} \left( \lambda \right)\frac{\partial E\left( m \right)}{{\partial \rho_{SA} \left( \lambda \right)}}\frac{{\delta \rho_{SA} \left( \lambda \right)}}{{\rho_{SA} \left( \lambda \right)}}} \right)^{2} + \left( {f_{v} \frac{\partial E\left( m \right)}{{\partial f_{v} }}\frac{{\delta f_{v} }}{{f_{v} }}} \right)^{2} }$$

(14)