Rate-controlled constrained equilibrium for large hydrocarbon fuels with NTC

Abstract

The rate-controlled constrained equilibrium (RCCE) method is a thermodynamic-based dimension reduction method that enables the representation of a reactive system involving $n_{\mathrm{s}}$ chemical species in terms of a smaller number, $n_{\mathrm{c}}$, of constraints and thus reduces the computational burden imposed by detailed chemical kinetics. The application of RCCE for large hydrocarbon fuels like n-heptane has rarely been reported due to the challenges in the specification of constraints. In this study, a systematic approach of constraint specifications for hydrocarbon fuels with negative temperature coefficients behaviour has been proposed. Specifically, the bimolecular species lumping consistent with partial equilibrium assumption (PEA) makes the thermodynamics-based constrained equilibrium manifolds a good approximation to the actual kinetics-controlled slow invariant manifolds in reactive systems. Sensitivity-aided optimisation for species constraints has been formulated to improve the prediction of two-stage ignition. Two sets of optimised constraints for high- and low-temperature ignitions e.g., High-T C and Low-T C with 47 and 48 constraints have been developed from an 88-species n-heptane skeletal mechanism. The method has been successfully demonstrated in the two-stage auto-ignition of n-heptane/air mixture over a wide range of pressures and temperatures. The results show that the dynamics predicted with RCCE agree well with that from the full description. The one-dimensional laminar flame propagation simulation demonstrates that the constraints from auto-ignition can be applied for flame simulations and the RCCE reduced description of flame is less sensitive to the selection of constraints. Moreover, a more compact RCCE description with only 16 species constraints is capable of accurate prediction of the flame propagation process.

Keywords:

• dimension reduction
• constrained equilibrium
• partial equilibrium
• species lumping
• negative temperature coefficient

Acknowledgment

Simulations are performed with the computational resources of the Tsinghua National Laboratory for Information Science and Technology.

Additional information

Funding

The work is supported by National Natural Science Foundation of China [grant numbers 51476087 and 91441202].