Sparse-Lagrangian PDF Modelling of Silica Synthesis from Silane Jets in Vitiated Co-flows with Varying Inflow Conditions

Abstract

This paper presents a comparison of experimental and numerical results for a series of turbulent reacting jets where silica nanoparticles are formed and grow due to surface growth and agglomeration. We use large-eddy simulation coupled with a multiple mapping conditioning approach for the solution of the transport equation for the joint probability density function of scalar composition and particulate size distribution. The model considers inception based on finite-rate chemistry, volumetric surface growth and agglomeration. The sub-models adopted for these particulate processes are the standard ones used by the community. Validation follows the "paradigm shift" approach where elastic light scattering signals (that depend on particulate number and size), OH-and SiO-LIF signals are computed from the simulation results and compared with "raw signals" from laser diagnostics. The sensitivity towards variable boundary conditions such as co-flow temperature, Reynolds number and precursor doping of the jet is investigated. Agreement between simulation and experiments is very good for a reference case which is used to calibrate the signals. While keeping the model parameters constant, the sensitivity of the particulate size distribution on co-flow temperature is predicted satisfactorily upstream although quantitative differences with the data exist downstream for the lowest coflow temperature case that is considered. When the precursor concentration is varied, the model predicts the correct direction of the change in signal but notable qualitative and quantitative differences with the data are observed. In particular, the measured signals show a highly non-linear variation while the predictions exhibit a square dependence on precursor doping at best. So, while the results for the reference case appear to be very good, shortcomings in the standard submodels are revealed through variation of the boundary conditions. This demonstrates the importance of testing complex nanoparticle synthesis models on a flame series to ensure that the physical trends are correctly accounted for.

Population balance modelling and laser diagnostic validation of soot particle evolution in laminar ethylene diffusion flames

“…The UV laser sheet is 700 µm thick and 58 mm tall to avoid exceeding the OH saturation intensity (10 mJ/cm 2 [30]) with a shot energy of no more than 3.5 mJ, thus ensuring operation within the linear LIF regime. In an unrelated experiment using the same set-up [31], the OH-PLIF signal was found to correlate linearly with the concentration of silane doping (0-3000 ppm) added to a vitiated co-flow burner with an R 2 coefficient of 0.9994, further confirming linearity.…”

“…The second one is a systematic error incurred by the value of the absorption function E(m) in Eq. (31). The instrumentation error originates from the intrinsic uncertainty in the measurement of light intensity.…”