# Effect of recondensation of sublimed species on nanoparticle temperature evolution in time-resolved laser-induced incandescence

## Abstract

In high-fluence laser-induced incandescence (LII), current LII models significantly overpredict the soot nanoparticle temperature decay rate compared to that inferred from two-color pyrometry at the first 100 ns after the peak laser pulse in atmospheric pressure flames. One possible cause is the back flow of sublimed species, which to date has been neglected in LII modeling. In this study, the transient direct simulation Monte Carlo (DSMC) method has been used, for the first time, to calculate the temperature evolution of soot particles, taking into account recondensation of sublimed species. In this algorithm, the physical time is discretized into a number of time steps called ensemble time steps, and the heat flux is calculated by performing several DSMC runs in each ensemble time step before proceeding to the next ensemble time step until the variance reaches an acceptable value. This heat flux is then used to update the nanoparticle temperature over the ensemble time step. Using the new algorithm, the temperature evolution of the particle can be predicted by the DSMC code, which is an improvement to previous DSMC simulations in which predetermined temperature decay curves must be prescribed. The results show that recondensation of sublimed species on the originating nanoparticle is not significant. Although accounting for condensation of sublimed species originating from neighboring soot particles enhances the role of recondensation of sublimed species in slowing down the soot particle temperature decay, it is still not sufficient to be considered as a plausible cause for the discrepancy between modeled soot temperature and the two-color pyrometry measured one in high-fluence LII.

## Keywords

Heat Transfer Rate Direct Simulation Monte Carlo Soot Volume Fraction Soot Temperature Soot Aggregate## List of symbols

*a*Particle radius (nm)

*c*_{o}Speed of light in vacuum, 2.998 × 10

^{8}(m s^{−1})*c*_{p}Specific heat [J/(kg K)]

*D*_{eq}Equivalent diameter of soot aggregate (nm)

*d*_{p}Primary particle diameter (nm)

*f*_{a}Equivalent sphere scaling prefactor

*h*Planck’s constant, 6.626 × 10

^{−34}(J s)*I*_{λ}Spectral radiation intensity (W/m

^{2}μm sr)*J*_{λ}Spectral incandescence intensity (W/m

^{2}μm sr)*k*_{B}Boltzmann’s constant, 1.38 × 10

^{−23}[J/(molecule K)]*M*Mass of soot particle (kg)

*M*_{v}Average molecular weight of sublimed clusters (kg/mol)

*N*_{p}Number of primary particles in an aggregate

*P*(*a*)Probability density function of particle size

*P*_{g}Gas pressure (Pa)

*P*_{v}Partial pressure of sublimed species (Pa)

*q*_{abs}Laser absorption rate (W)

*Q*_{abs,λ}Spectral absorption efficiency

*q*_{conc}Conduction heat transfer rate (W)

*q*_{evap}Evaporation heat transfer rate (W)

*q*_{rad}Radiation heat transfer rate (W)

*R*Universal gas constant (J/mol K)

*t*Time (s)

*T*_{g}Gas temperature (K)

*T*_{p}Particle temperature (K)

*U*Average velocity of sublimed clusters (m/s)

*α*Thermal accommodation coefficient

*β*Sublimation/condensation coefficient

*ε*_{a}Equivalent sphere scaling exponent

*λ*Wavelength (μm)

*ρ*_{s}Soot density (kg/m

^{3})

## Subscripts and superscripts

- G
Gas

- P
*P*article

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