A control volume derivation of the energy equation for LII modeling

Laser-induced incandescence: Particulate diagnostics for combustion, atmospheric, and industrial applications

“…Following the earlier modeling work of Weeks and Duley [133], Eckbreth [134], Burakov et al [135], Bukatyi et al [136,137], and Melton [138], Bengtsson et al [172,173], Smallwood et al [121,146,174,175], and Michelsen [176,177] developed detailed models to serve as a means to extend the technique to a wider variety of conditions, including high pressures and low temperatures, by understanding and targeting the largest sources of uncertainties. This work was complemented and followed by a considerable body of work to develop models for predicting LII signals under a wide range of conditions [35,129,132,145,147,154,[178][179][180][181][182][183][184][185][186][187][188][189][190]. Vander Wal et al [13,37,191] performed extensive surveys of experimental parameters for optimizing the application of the technique, used LII coupled with laser-induced fluorescence (LIF) measurements to distinguish soot precursors from mature soot particles in flames [158,160,192], and applied the technique to carbon nanotubes and other materials [193,…”

“…Hiers [184], and Michelsen et al [202] derived a modified expression with an extra term that accounts for the loss of some ability to store sensible heat when the mass of the particle is reduced, but this term is canceled in Eq. (1) by extra terms introduced in similar expansions of terms for sublimation [175,184,202] and oxidation [184,202].The interested reader is referred to the respective papers; in the following discussion, the straightforward version of the balance is used. Substituting Eq.…”

“…The expression given by Eq. (17), however, does not account for the temperature of the incoming O 2 [184,202]. Michelsen et al [202] provided a more detailed expression that explicitly accounts for the incoming O 2 , i.e., .…”