Derivation of a temperature-dependent accommodation coefficient for use in modeling laser-induced incandescence of soot

Abstract

This paper presents a derivation of an expression to estimate the accommodation coefficient for gas collisions with a graphite surface, which is meant for use in models of laser-induced incandescence (LII) of soot. Energy transfer between gas molecules and solid surfaces has been studied extensively, and a considerable amount is known about the physical mechanisms important in thermal accommodation. Values of accommodation coefficients currently used in LII models are temperature independent and are based on a small subset of information available in the literature. The expression derived in this study is based on published data from state-to-state gas-surface scattering experiments. The present study compiles data on the temperature dependence of translational, rotational, and vibrational energy transfer for diatomic molecules (predominantly NO) colliding with graphite surfaces. The data were used to infer partial accommodation coefficients for translational, rotational, and vibrational degrees of freedom, which were consolidated to derive an overall accommodation coefficient that accounts for accommodation of all degrees of freedom of the scattered gas distributions. This accommodation coefficient can be used to calculate conductive cooling rates following laser heating of soot particles.

Measurement of soot concentration and bulk fluid temperature and velocity using modulated laser-induced incandescence

“…9 of [17], the derivation of α gave α = 0.37 for d p = 29 nm over the temperature decay range 2900-2200 K. This is very close to our present value of 0.35 measured at 1700 K. Whilst the difference is probably within the combined uncertainty limits of the two measurements, the accommodation coefficient is expected to change with temperature, and Michelsen [20] has shown from compiling data on NO that the accommodation coefficient for NO drops with decreasing gas temperature. The axial flow velocity in the laminar diffusion flame at the 42 mm height is ~190 cm/s [16], and if we take the laser beam 1/e 2 diameter of 1.435 mm as a measure of the sample size in the axial direction, we get a residence time of 0.76 ms, which is considerably more than our measured 0.47 ms. We previously estimated self-diffusion in the laminar diffusion flame at the 42 mm height using simple hard sphere collision theory and the equation x 2 = 2Dt where x is the distance diffused in time t and D is the self-diffusion coefficient [11], and using this hard sphere data we get D = 3.6 × 10 −4 m 2 s −1 .…”

Thermal accommodation coefficients between polyatomic gas molecules and soot in laser-induced incandescence experiments

“…In gas/surface scattering the vibrational energy modes of gas molecules are most often accessed through one of two mechanisms [29][30][31]: gas molecules having a large incident velocity (which is often the case in molecular beam experiments) can have some of their translational kinetic energy redistributed to internal modes through the collision; and alternatively, gas molecules with lower incident energy can follow a trapping/desorption channel, which allows time for the gas molecules to equilibrate with the surface. Neither scenario applies in this system, however, since incident gas molecules effusing from a gas at 300 K have low incident translational energy (and very few of them are vibrationally excited), while the high surface temperature relative to the potential well prevents the gas molecules from becoming adsorbed onto the surface.…”

Investigation of the size of the incandescent incipient soot particles in premixed sooting and nucleation flames of n-butane using LII, HIM, and 1 nm-SMPS

“…Some consensus has been reached that the TAC of mature soot falls in the range of about 0.2 to 0.4 (Snelling et al 2004;Maffi et al 2011;Kuhlmann et al 2006;Michelsen 2009). However, there have been no studies in the literature to investigate the TAC of incipient soot.…”