Surface Ageing of Soot Particles

1. C4E burner University of Cambridge Department of Chemical Engineering 1 Soot Model reaction zone Is t > tstop ? residence time 7th WCCE, Glasgow 2 Stochastic Algorithm (LPDA) Initialize system Wait an exponentially-distributed time step and update current time, t yes no Perform deferred processes for all particles Probabilistically choose an event to perform Stop Particle Inception Pyrene condensation Coagulation We present results for three acetylene flames for which some experimental data is available. One can see that the simulated soot volume fraction has a significant dependence on the decay constant C but that by choosing the value carefully good agreement with the experimental data can be achieved. The data were taken from [1]. Select particle(s) Perform deferred processes on selected particle(s) Fictitious event ? no yes Lines: simulation results Points: experimental data Place updated particle(s) back into ensemble Perform jump • Fictitious events are a technical convenience in which time is advanced and the event selection procedure followed upto and including the simulation of the deferred processes but the updated particle(s) are then replaced without performing the selected event. • The algorithm is described in [3] Update particle ensemble 6 Summary • The decay constant can be used to fit the final soot volume fraction for three different flames. • Surface decay never seems to reach its asymptotic value in some flames which are therefore unsuitable for testing this part of the model. • A detailed chemical model for the surface reactions is needed. R I A Patterson, J Singh & M Kraft Department of Chemical Engineering, University of Cambridge Reactions on the surface of soot are the principal route by which mass is transformed from the gas to solid phase in laminar premixed flames. However, the reactivity of soot particles decreases significantly over time so an accurate model is necessary to predict soot mass. Surface Ageing of Soot Particles • The model we use consists of three main processes • Particle inception – when two pyrene molecules ‘coagulate’ • Coagulation – two particles form a new sphere with the same total mass • Surface events – chemical reactions on the particle surface (4 types) • Pyrene condensation • C2H2 addition • OH oxidation • O2 oxidation 3 Active Sites Model An important part of the model for the rate of C2H2 addition and O2 oxidation is the number of active sites on the surface of the soot particle [1,2]. This is known to decrease over time but little is known about the decay process except that it never reaches 0 so we model the density of active sites, α,on the surface of a particle as an offset exponential decay process in the particle age τ: This exponential decay is calculated along with the deferred processes. When two particles coagulate the age of the new particle is calculated from the surface areas a1, a2 and ages τ1,τ2 of the old particles as 4 Decay constant References: [1] J Appel at al. Kinetic Modelling of soot formation with detailed chemistry and physics: Laminar premixed flames of C2 hydrocarbons. Combust. Flame 121 : 122-136 (2000) [2] M Frenklach and H Wang in:H Bockhorn (Ed), Soot Formation in Combustion - Mechanisms and Models. Springer Verlag, Berlin 1994, 165-192 [3] R I A Patterson et al. The Linear Process Deferment Algorithm: A new technique for solving population balance equations. Technical Report 26, c4e-Preprint Series, Cambridge, 2004