Modeling laser-induced incandescence of soot: a new approach based on the use of inverse techniques

Analysis of the Influence of the Conduction Sub-Model Formulation on the Modeling of Laser-Induced Incandescence of Diesel Soot Aggregates

“…First, the formulation derived from the work of McCoy and Cha [ 18 ] has been considered since this widespread-used formulation directly applies when the heat conduction is expected to occur in the free-molecular regime, which is generally the case in LII studies conducted at atmospheric pressure. According to References [ 13 , 15 ], then equates as follows: where is the ambient pressure, (83.145 bar·cm 3 ·mol −1 ·K −1 ) and (8.3145 × 10 7 g·cm 2 ·mol −1 ·K −1 ·s −2 ) correspond to the universal gas constant expressed in effective pressure and mass units, respectively, represents the average molecular weight of air (28.74 g·mol −1 ) considered as a surrogate for flame gases, is the molar heat capacity at constant pressure (the expression of which can be found in Reference [ 13 ] based on a fit to data from the NIST-JANAF database [ 35 ]), (8.3145 J·mol −1 ·K −1 ) is the universal gas constant while and stand for the particle and surrounding gas temperatures, respectively. In addition, the updated formulation proposed by Michelsen et al in [ 19 ] has been tested.…”

“…The solving of the system of differential equations specified in Equation (1) leads to infer the variations of the particle temperature , mass , and diameter (considering spherical primary particles) as a function of space and time. LII signals can then be assessed by integrating the Planck function over the spectral range of the detection system, including its spectral response as previously done and explained in Reference [ 15 ]. The normal law derived from the TEM measurements carried out in Reference [ 29 ] has been integrated within the calculations so as to represent the size distribution of the primary particles, which is characterized by a mean diameter = 16.4 nm and a standard deviation = 3.3 at the investigated flame location (i.e., 92 mm HAB).…”

“…This is particularly the case of Michelsen who proposed an absorption sub-model accounting for saturation of linear, single-photon, and multi-photon absorption while also considering phenomena such as thermionic emission, soot oxidation, and non-thermal photodesorption of carbon clusters from the particle surface [ 13 , 14 ]. To rule on the consistency of such wide varied model formulations, Lemaire et al [ 15 ] recently proposed a theoretical analysis focusing on the ability of basic and refined LII simulation tools to predict an extensive set of LII time decays and fluence curves obtained by Goulay et al in a laminar diffusion flame of ethylene [ 16 ]. Using inverse techniques to obtain model predictions merging on a single curve with experimental data, Lemaire et al showed that integrating photolytic mechanisms such as multi-photon absorption and carbon cluster photodesorption was required to reproduce LII signals over a wide range of fluences [ 15 ].…”

“…To rule on the consistency of such wide varied model formulations, Lemaire et al [ 15 ] recently proposed a theoretical analysis focusing on the ability of basic and refined LII simulation tools to predict an extensive set of LII time decays and fluence curves obtained by Goulay et al in a laminar diffusion flame of ethylene [ 16 ]. Using inverse techniques to obtain model predictions merging on a single curve with experimental data, Lemaire et al showed that integrating photolytic mechanisms such as multi-photon absorption and carbon cluster photodesorption was required to reproduce LII signals over a wide range of fluences [ 15 ]. While giving insights regarding the physical processes needing to be included in LII models, this work also led to the conclusion that further developments were necessary to account for the effect of aggregate properties on energy and mass transfer phenomena.…”

“…While giving insights regarding the physical processes needing to be included in LII models, this work also led to the conclusion that further developments were necessary to account for the effect of aggregate properties on energy and mass transfer phenomena. In addition to the inclusion of additional processes such as annealing, an in-depth analysis of the formulation and parameterization of the sub-models currently used in LII studies to represent absorption and conduction fluxes was eventually pointed out as being of major importance for future developments [ 15 ]. In this respect, one should pay particular attention to the rate of energy transferred by heat conduction since this latter directly drives the LII time decays at low-to-intermediate laser fluences, the modeling of which is essential for soot size assessment by time-resolved LII (TiRe-LII).…”