A generalized partially stirred reactor model for turbulent closure

Supervised Clustering for Optimal Sub-model Selection in Reactor-Based Models

“…These findings confirm that a singleformulation model for κ is not capable of predicting the entire spectrum of fast and slow species chemical source terms, further discussed in Refs. Quadarella et al, 2022). However, accepting this model form and targeting an overall predictive accuracy, it evidently follows that different time scale formulations are fit to specific flame zones, mostly depending on mixture fraction in the case of non-premixed flames, where distinct species source terms are dominantly active.…”

“…On the contrary, a species-based error metric would yield an ensemble of N sp − 1 (nitrogen N 2 is withdrawn) optimal chemical time scale maps from the minimisation of species-wise distances. The closing of the species transport equations with arbitrary species dependent κ i in the PaSR model may not assure mass balance and remains a great challenge (Iavarone et al, 2019;Quadarella et al, 2022).…”

“…This suggests that the choice of a single formulation of the chemical time scale in the PaSR model is sub-optimal and specific combinations of multiple κ may account for the multi-scale nature of reacting flows through species-specific chemical time scales. However, the inclusion of multiple fractions comes with modelling challenges, as illustrated in the work of Quadarella et al (Quadarella et al, 2022), where the concept of the fine structures is abandoned to provide closure from a modal decomposition of the Jacobian matrix of the chemical source terms. quantified the inadequacy of using a single cell reacting fraction κ in the standard PaSR model by using several chemical time scale definitions.…”

Model identification in reactor-based combustion closures using sparse symbolic regression

“…where ρ is the Reynolds-averaged density, τ * represents the residence time in the fine structures. In the original model [15], the residence time in the PaSR model was estimated using the mixing timescale only, but other works [20,18,12,22] demonstrated improved model prediction capabilities when τ * equals the minimum between the mixing and the chemical timescales. Therefore, the present work follows the latter definition of the reactor residence time, defined as:…”

“…The PaSR model has been tested for various types of flames [11,12,13,14], sprays [15], and non-conventional combustion regimes [16,17,18,19]. Alternative formulations of the PaSR model have been investigated in RANS and LES simulations [20,21,22], and the effect of the mixing and chemical timescales estimation on the reacting fraction has been assessed in [18].…”