Adaptive coarse graining method for energy transfer and dissociation kinetics of polyatomic species

Abstract

A novel reduced-order method is presented for modeling reacting flows characterized by strong non-equilibrium of the internal energy level distribution of chemical species in the gas. The approach seeks for a reduced-order representation of the distribution function by grouping individual energy states into macroscopic bins, and then reconstructing state population using the maximum entropy principle. This work introduces an adaptive grouping methodology to identify and lump together groups of states that are likely to equilibrate faster with respect to each other. To this aim, two algorithms have been considered: the modified island algorithm and the spectral clustering method. Both methods require a measure of dissimilarity between internal energy states. This is achieved by defining "metrics" based on the strength of the elementary rate coefficients included in the state-specific kinetic mechanism. Penalty terms are used to avoid grouping together states characterized by distinctively different energies. The two methods are used to investigate excitation and dissociation of N (Σg+1) molecules due to interaction with N(Su4) atoms in an ideal chemical reactor. The results are compared with a direct numerical simulation of the state-specific kinetics obtained by solving the master equations for the complete set of energy levels. It is found that adaptive grouping techniques outperform the more conventional uniform energy grouping algorithm by providing a more accurate description of the distribution function, mole fraction and energy profiles during non-equilibrium relaxation.

Principal component analysis acceleration of rovibrational coarse-grain models for internal energy excitation and dissociation

“…The error on the molar fraction of single nitrogen is shown in Figure 6c and has a value of 10 % for the score model and 17% for the URVC (20) scores model is significantly lower than the one obtained using the URVC (20) representation. Comparing these results with the error of advanced binning techniques as presented in the works of Sahai et al [42], we can conclude PCA performs better in terms of accuracy for the test case investigated here.…”

“…Retrieving the populations of the energy bins with such a high precision is a unique property of the method compared to the coarse grain models. The relative error between the full model and the PCA-based reduction shows higher accuracy for the results at a lower computation cost than recently published work using advanced lumping techniques [42].…”

“…This is possible as the scores or principal components are a linear combination of the original variables. We are able to retrieve the same detail on the distribution function as the 100 bins at a reduced cost with respect to alternative methods such as the spectral methods [42] as can be seen in Figure 5b where the populations have been plotted for the URVC(10) model. This unique property of PCA stresses its suitability for reducing large plasma mechanisms.…”

“…The vibrational kinetics of CO 2 has been reduced by using an adaptive binning scheme by Sahai et al [41] maximizing the entropy in each bin. As a follow-up on this method, they reduced the NASA database for N 2 ( 1 Σ + g )-N( 4 S u ) combining a spectral clustering algorithm with the maximum entropy principle reducing the 9391 species in the mechanism to 15-20 bins [42]. Multiple research has been published on the N 2 ( 1 Σ + g )-N( 4 S u ) database developed by the Computational Quantum Chemistry Group at NASA Ames Research Center [31][32][33] to gain insight on molecular dissociation and internal energy excitation in hypersonic flows [34][35][36].…”

Coupling of state-resolved rovibrational coarse-grain model for nitrogen to stochastic particle method for simulating internal energy excitation and dissociation

“…The second approach has been to develop so-called coarse-grain models 22,[51][52][53][54][55] to reduce the size of the state-resolved reaction mechanism. The details of the reduction differ for each model, but the basic concept is always to approximate the behavior of the full set of levels with a much smaller number of suitably defined internal energy groups (often called "bins"), whose properties are weighted averages over the properties of the individual constituting levels.…”