Search for: All records

Abstract A novel methodology is developed to extract accurate skeletal reaction models for nuclear combustion. Local sensitivities of isotope mass fractions with respect to reaction rates are modeled based on the forced optimally time-dependent (f-OTD) scheme. These sensitivities are then analyzed temporally to generate skeletal models. The methodology is demonstrated by conducting skeletal reduction of constant density and temperature burning of carbon and oxygen relevant to Type Ia supernovae (SNe Ia). The 495-isotopes Torch model is chosen as the detailed reaction network. A map of maximum production of⁵⁶Ni in SNe Ia is produced for different temperatures, densities, and proton-to-neutron ratios. The f-OTD simulations and the sensitivity analyses are then performed with initial conditions from this map. A series of skeletal models are derived and their performances are assessed by comparison against currently existing skeletal models. Previous models have been constructed intuitively by assuming the dominance ofα-chain reactions. The comparison of the newly generated skeletal models against previous models is based on the predicted energy release and⁴⁴Ti and⁵⁶Ni abundances by each model. The consequences ofy_e≠ 0.5 in the initial composition are also explored wherey_eis the electron fraction. The simulated results show that⁵⁶Ni production decreases by decreasingy_eas expected, and that the⁴³Sc is a key isotope in proton and neutron channels toward⁵⁶Ni production. It is shown that an f-OTD skeletal model with 150 isotopes can accurately predict the⁵⁶Ni abundance in SNe Ia fory_e≲ 0.5 initial conditions. 

A dynamical low-rank approximation is developed for reduced-order modelling (ROM) of the filtered density function (FDF) transport equation, which is utilised for large eddy simulation (LES) of turbulent reacting flows. In this methodology, the evolution of the composition matrix describing the FDF transport via a set of Langevin equations is con- strained to a low-rank matrix manifold. The composition matrix is approximated using a low-rank factorisation, which consists of two thin, time-dependent matrices repre- senting spatial and composition bases, along with a small time-dependent coefficient matrix. The evolution equations for spatial and composition subspaces are derived by projecting the composition transport equation onto the tangent space of the low-rank matrix manifold. Unlike conventional ROMs, such as those based on principal com- ponent analysis, both subspaces are time-dependent and the ROM does not require any prior data to extract the low-dimensional subspaces. As a result, the constructed ROM adapts on the fly to changes in the dynamics. For demonstration, LES via the time-dependent bases (TDB) is conducted of the canonical configuration of a tempo- rally developing planar CO/H2 jet flame. The flame is rich with strong flame-turbulence interactions resulting in local extinction followed by re-ignition. The combustion chem- istry is modelled via the skeletal kinetics, containing 11 species with 21 reaction steps. It is shown that the FDF-TDB yields excellent predictions of various sta 

A local-sensitivity-analysis technique is employed to generate new skeletal reaction models for methane combustion from the foundational fuel chemistry model (FFCM-1). The sensitivities of the thermo-chemical variables with respect to the reaction rates are computed via the forced-optimally time dependent (f-OTD) methodology. In this methodology, the large sensitivity matrix containing all local sensitivities is modeled as a product of two low-rank time-dependent matrices. The evolution equations of these matrices are derived from the governing equations of the system. The modeled sensitivities are computed for the auto-ignition of methane at atmospheric and high pressures with different sets of initial temperatures, and equivalence ratios. These sensitivities are then analyzed to rank the most important (sensitive) species. A series of skeletal models with different number of species and levels of accuracy in reproducing the FFCM-1 results are suggested. The performances of the generated models are compared against FFCM-1 in predicting the ignition delay, the laminar flame speed, and the flame extinction. The results of this comparative assessment suggest the skeletal models with 24 and more species generate the FFCM-1 results with an excellent accuracy.