Fundamentals of Rate-Controlled Constrained-Equilibrium Method

2018 ◽  
pp. 237-266 ◽  
Author(s):  
Fatemeh Hadi ◽  
Guangying Yu ◽  
Hameed Metghalchi
Keyword(s):  
Equilibrium Method ◽  
Constrained Equilibrium ◽  
Rate Controlled

Development of the Rate-Controlled Constrained-Equilibrium Method for Modeling of Ethanol Combustion

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Ghassan Nicolas ◽  
Hameed Metghalchi
Keyword(s):  
Ignition Delay ◽  
Stable Equilibrium ◽  
Combustion Process ◽  
Detailed Chemical Kinetics ◽  
Equilibrium Method ◽  
Constrained Equilibrium ◽  
Ethanol Combustion ◽  
Rate Controlled ◽  
Detailed Chemical

The rate-controlled constrained-equilibrium method (RCCE) has been further developed to model the combustion process of ethanol air mixtures. The RCCE is a reduction technique based on local maximization of entropy or minimization of a relevant free energy at any time during the nonequilibrium evolution of the system subject to a set of kinetic constraints. An important part of RCCE calculation is determination of a set of constraints that can guide the nonequilibrium mixture to the final stable equilibrium state. In this study, 16 constraints have been developed to model the nonequilibrium ethanol combustion process. The method requires solution of 16 differential equations for the corresponding constraint potentials. Ignition delay calculations of ethanol oxidizer mixtures using RCCE have been compared to those of detailed chemical kinetics using 37 species and 235 reactions. Agreement between the two models is very good. In addition, ignition delay of C2H5OH/O2/Ar mixtures using RCCE has been compared with the experimental measurements in the shock tube and excellent agreement has been reached validating the RCCE calculation.

Modeling of Combustion of Mono-Carbon Fuels Using the Rate-Controlled Constrained-Equilibrium Method

2004 ◽  
Author(s):  
Sergio Ugarte ◽  
Mohamad Metghalchi ◽  
James C. Keck
Keyword(s):  
Combustion Process ◽  
Chemical Species ◽  
Second Law Of Thermodynamics ◽  
Equilibrium System ◽  
Equilibrium Method ◽  
Ignition Delay Times ◽  
Constrained Equilibrium ◽  
Rate Controlled ◽  
Induction Times ◽  
Non Equilibrium

Modeling of a non-equilibrium combustion process involves the solution of large systems of differential equations with as many equations as species present during the process. The process of chemical reaction and combustion is complicated since it may be governed by hundreds, sometimes thousands of microscopic rate processes. Integration of these equations simultaneously becomes more difficult with the complexity of the combustible. In order to reduce the size of these systems of equations, the Rate-Controlled Constrained-Equilibrium method (RCCE) has been proposed to model non-equilibrium combustion processes. This method is based on the Second Law of Thermodynamics, assuming that the evolution of a complex system can be described by a small number of rate-controlling reactions which impose slowly changing constraints on all allowed states of the system, therefore a non-equilibrium system will relax to its final equilibrium state through a sequence of rate controlled constrained equilibrium states. Oxidation induction times and concentration of species during a combustion process are found in a less complicated way with this method, as equations for constraints rather than for species determine the composition and evolution of the system. The time evolution of the system can be reduced since the number of constraints is much smaller than the number of species presents, so the number of equations to solve. The RCCE method has been applied to the stoichiometric combustion of mono-carbon fuels using 29 chemical species and 139 chemical reactions at different sets of pressure and temperature, ranging from 1 atm to 100 atm, and from 900 K to 1600 K respectively. Results of using 8, 9, 10 and 11 constraints compared very well to those of the detailed calculations at all conditions for the cases of formaldehyde (H2CO), methanol (CH3OH) and methane (CH4). For these systems, ignition delay times and major species concentrations were within 5% of the values given by detailed calculations, and computational saving times up to 50% have been met.

Rate-controlled constrained-equilibrium method using constraint potentials

1998 ◽  
Vol 2 (1) ◽  
pp. 81-94 ◽  
Author(s):  
D. Hamiroune ◽  
P. Bishnu ◽  
M. Metghalchi ◽  
J.C. Keck
Keyword(s):  
Equilibrium Method ◽  
Constrained Equilibrium ◽  
Rate Controlled

Combustion modeling of mono-carbon fuels using the rate-controlled constrained-equilibrium method

2009 ◽  
Vol 156 (10) ◽  
pp. 1871-1885 ◽  
Author(s):  
Mohammad Janbozorgi ◽  
Sergio Ugarte ◽  
Hameed Metghalchi ◽  
James. C. Keck
Keyword(s):  
Combustion Modeling ◽  
Equilibrium Method ◽  
Constrained Equilibrium ◽  
Rate Controlled

Methanol Oxidation Induction Times Using the Rate-Controlled Constrained-Equilibrium Method

2003 ◽  
Author(s):  
Sergio Ugarte ◽  
Mohamad Metghalchi ◽  
James C. Keck
Keyword(s):  
Methanol Oxidation ◽  
Ignition Delay ◽  
Rate Equations ◽  
Oxygen Mixture ◽  
Free Oxygen ◽  
Equilibrium Method ◽  
Ignition Delay Times ◽  
Delay Times ◽  
Constrained Equilibrium ◽  
Rate Controlled

Methanol oxidation has been modeled using the Rate-Controlled Constrained-Equilibrium method (RCCE). In this method, composition of the system is determined by constraints rather than by species. Since the number of constraints can be much smaller than the number of species present, the number of rate equations required to describe the time evolution of the system can be considerably reduced. In the present paper, C1 chemistry with 29 species and 140 reactions has been used to investigate the oxidation of stoichiometric methanol/oxygen mixture at constant energy and volume. Three fixed elemental constraints: elemental carbon, elemental oxygen and elemental hydrogen and from one to nine variable constraints: moles of fuel, total number of moles, moles of free oxygen, moles of free oxygen, moles of free valence, moles of fuel radical, moles of formaldehyde H2CO, moles of HCO, moles of CO and moles of CH3O were used. The four to twelve rate equations for the constraint potentials (LaGrange multipliers conjugate to the constraints) were integrated for a wide range of initial temperatures and pressures. As expected, the RCCE calculations gave correct equilibrium values in all cases. Only 8 constraints were required to give reasonable agreement with detailed calculations. Results of using 9 constraints showed compared very well to those of the detailed calculations at all conditions. For this system, ignition delay times and major species concentrations were within 0.5% to 5% of the values given by detailed calculations. Adding up to 12 constraints improved the accuracy of the minor species mole fractions at early times, but only had a little effect on the ignition delay times. RCCE calculations reduced the time required for input and output of data in 25% and 10% when using 8 and 9 constraints respectively. In addition, RCCE calculations gave valuable insight into the important reaction paths and rate-limiting reactions involved in methanol oxidation.

Combustion Simulation of Propane/Oxygen (With Nitrogen/Argon) Mixtures Using Rate-Controlled Constrained-Equilibrium

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Guangying Yu ◽  
Hameed Metghalchi ◽  
Omid Askari ◽  
Ziyu Wang
Keyword(s):  
Experimental Data ◽  
Energy System ◽  
Kinetic Mechanism ◽  
Chemical Kinetic ◽  
Oxygen Mixture ◽  
Free Valence ◽  
Wide Range ◽  
Constrained Equilibrium ◽  
Rate Controlled ◽  
Good Agreement

The rate-controlled constrained-equilibrium (RCCE), a model order reduction method, has been further developed to simulate the combustion of propane/oxygen mixture diluted with nitrogen or argon. The RCCE method assumes that the nonequilibrium states of a system can be described by a sequence of constrained-equilibrium states subject to a small number of constraints. The developed new RCCE approach is applied to the oxidation of propane in a constant volume, constant internal energy system over a wide range of initial temperatures and pressures. The USC-Mech II (109 species and 781 reactions, without nitrogen chemistry) is chosen as chemical kinetic mechanism for propane oxidation for both detailed kinetic model (DKM) and RCCE method. The derivation for constraints of propane/oxygen mixture starts from the eight universal constraints for carbon-fuel oxidation. The universal constraints are the elements (C, H, O), number of moles, free valence, free oxygen, fuel, and fuel radicals. The full set of constraints contains eight universal constraints and seven additional constraints. The results of RCCE method are compared with the results of DKM to verify the effectiveness of constraints and the efficiency of RCCE. The RCCE results show good agreement with DKM results under different initial temperature and pressures, and RCCE also reduces at least 60% CPU time. Further validation is made by comparing the experimental data; RCCE shows good agreement with shock tube experimental data.

Comparison Between RCCE and Shock Tube Ignition Delay Times at Low Temperatures

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Ghassan Nicolas ◽  
Hameed Metghalchi
Keyword(s):  
Free Energy ◽  
Shock Tube ◽  
Ignition Delay ◽  
Low Temperatures ◽  
Reduction Technique ◽  
Experimental Measurements ◽  
Ignition Delay Times ◽  
Delay Times ◽  
Constrained Equilibrium ◽  
Rate Controlled

The rate-controlled constrained-equilibrium (RCCE) method is a reduction technique based on local maximization of entropy or minimization of a relevant free energy at any time during the nonequilibrium evolution of the system subject to a set of kinetic constraints. In this paper, RCCE has been used to predict ignition delay times of low temperatures methane/air mixtures in shock tube. A new thermodynamic model along with RCCE kinetics has been developed to model thermodynamic states of the mixture in the shock tube. Results are in excellent agreement with experimental measurements.

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