A Reformulation of Degree of Disequilibrium Analysis for Automatic Selection of Kinetic Constraints in the Rate-Controlled Constrained-Equilibrium Method

The Rate-Controlled Constrained-Equilibrium (RCCE) is a model reduction scheme for chemical kinetics. It describes the evolution of a complex chemical system with acceptable accuracy with a number of rate controlling constraints on the associated constrained-equilibrium states of the system, much lower than the number of species in the underlying Detailed Kinetic Model (DKM). Successful approximation of the constrained-equilibrium states requires accurate identification of the constraints. One promising procedure is the fully automatable Approximate Singular Value Decomposition of the Actual Degrees of Disequilibrium (ASVDADD) method that is capable of identifying the best constraints for a given range of thermodynamic conditions and a required level of approximation. ASVDADD is based on simple algebraic analysis of the results of the underlying DKM simulation and is focused on the behavior of the degrees of disequilibrium (DoD) of the individual chemical reactions. In this paper, we introduce an alternative ASVDADD algorithm. Unlike the original ASVDADD algorithm that require the direct computation of the DKM-derived DoDs and the identification of the set of linearly independent reactions, in the alternative algorithm, the components of the overall degree of disequilibrium vector can be computed directly by casting the DKM as an RCCE simulation considering a set of linearly independent constraints equalling the number of chemical species in size. The effectiveness and robustness of the derived constraints from the alternative procedure is examined in hydrogen/oxygen and methane/oxygen ignition delay simulations and the results are compared with those obtained from DKM.

Study of the Constraint Selection Through ASVDADD Method for Rate-Controlled Constrained-Equilibrium Modeling on Ethanol Oxidation Without PLOG Reactions

Reduction of the detail chemical kinetic mechanism is important in solving complex combustion simulation. In this work, a model reduction scheme rate-controlled constrained-equilibrium (RCCE) is considered in predicting the oxidation of ethanol. A detail kinetic mechanism by Merinov from Lawrence Livermore National Laboratory (LLNL) is used in modeling this reduction technique. The RCCE method considers constrained equilibrium states which subjected to a lower number of constraints compared to the number of species. It then has to solve a smaller number of differential equations compared to the number of equations required in solving the detailed kinetic model (DKM). The accuracy of this solution depends on the selection of the constraint. A systematic procedure which will help in identifying the constraint at an optimal level of accuracy is an essential for RCCE modeling. A fully automated Approximate Singular Value Decomposition of the Actual Degrees of Disequilibrium (ASVDADD) method is used in this study to derive the constraint for RCCE simulation. ASVDADD uses an algorithm which follows the simple algebraic analysis on results of underlying DKM to find the degree of disequilibrium (DoD) of the individual chemical reactions. The number of constraints which will be used in RCCE simulation can be selected to reduce the number of equations required to solve. In the current work, this ASVDADD method is applied on ethanol oxidation to select the constraint for RCCE simulation. Both DKM and RCCE calculations on ethanol fuel are demonstrated to compare the result of temperature distribution and an ignition delay time for validating the method.

Review of Applications of Rate-Controlled Constrained-Equilibrium in Combustion Modeling

Developing an effective model for non-equilibrium states is of great importance for a variety of problems related to chemical synthesis and combustion. Rate-Controlled Constrained-Equilibrium (RCCE), a model order reduction method that originated from the second law of thermodynamics, assumes that the non-equilibrium states of a system can be described by a sequence of constrained-equilibrium states kinetically controlled by a relatively small number of constraints within acceptable accuracy. The full chemical composition at each constrained-equilibrium state is obtained by maximizing (or minimizing) the appropriate thermodynamic quantities, e. g., entropy (or Gibbs functions), subject to the instantaneous values of RCCE constraints. Regardless of the nature of the kinetic constraints, RCCE always guarantees a correct final equilibrium state. This paper reviews the fundamentals of the RCCE method, its constraints, constraint potential formulations, and major constraint selection techniques, as well as the application of the RCCE method to combustion of different fuels using a variety of combustion models. The RCCE method has been proven to be accurate and to reduce computational time in these simulations.

Rate Controlled Constrained-Equilibrium Simulation of Ethanol Combustion Using SVD Derived Constraints

In this study, the fully automatable Approximate Singular Value Decomposition of the Actual Degrees of Disequilibrium (ASVDADD) method is used for combustion modeling of ethanol. Due to the importance of ethanol as one of the most common type of biofuels, modeling its reaction kinetics and chemical composition evolution during combustion is necessary. The detailed kinetic mechanism (DKM) considered here is generated by authors using reaction mechanism generator (RMG) technique and it consists of 66 species and 1031 reactions. Tracking this number of species and chemical reactions in computational fluid dynamic (CFD) analysis of engineering problems is prohibitive. To alleviate this issue, Rate-Controlled Constrained-Equilibrium (RCCE) model reduction scheme for chemical kinetics is employed. It describes the evolution of a complex chemical system with acceptable accuracy with a number of rates controlling constraints on the associated constrained-equilibrium states of the system, much lower than the number of species in the underlying DKM. Successful approximation of the constrained equilibrium states requires accurate identification of the constraints. One promising procedure is the ASVDADD method that is capable of identifying the best constraints for a given range of thermodynamic conditions and a required level of approximation. ASVDADD is based on simple algebraic analysis of the results of the underlying DKM simulation and is focused on the behavior of the degrees of disequilibrium (DoD) of the individual chemical reactions. In this paper, ASVDADD is used to derive the RCCE constraints and ethanol combustion is modeled using both DKM and RCCE. Comparison of RCCE results with those of DKM shows the effectiveness of the ASVDADD derived constraints which demonstrates the potential of the RCCE method for combustion modeling of heavy and complex fuels.

The Rate-Controlled Constrained-Equilibrium Combustion Modeling of n-Pentane/Oxygen/Diluent Mixtures

Rate-controlled constrained equilibrium (RCCE) is a reduction technique used to describe the time evolution of complex chemical reacting systems. This method is based on the assumption that a nonequilibrium system can reach its final equilibrium state by a series of RCCE states determined by maximizing entropy or minimizing relevant free energy. Those constraints are imposed by some small number of slow reactions. Much research has been done on this method and many RCCE models of C1−C4 hydrocarbon fuel combustion have been established by the previous researchers. Those models show good performance compared with the result of detailed kinetic model (DKM). In this study, RCCE method is further developed to model normal pentane (n-C5H12) combustion with least number of constraints. The chemical mechanism for DKM contains 133 species and 922 reactions. Two sets of constraints were found during the study: (1) 16 constraints for the normal pentane and pure oxygen mixture and (2) 14 constraints for the mixture of normal pentane and oxygen with argon as diluent. Results of the first constraint set were compared with result of DKM and results of the second constraint set were compared with those of DKM and experimental data by calculating their ignition delay times. Comparisons showed that the first set of constraints had relatively good accuracy and the second set of constraints agreed very well with the experimental data.