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Research Papers: Fuel Combustion

# A Comparison of Constraint and Constraint Potential Forms of the Rate-Controlled Constraint-Equilibrium Method

[+] Author and Article Information

Department of Mechanical
and Industrial Engineering,
Northeastern University,
Boston, MA 02115

M. Reza H. Sheikhi

Department of Mechanical
and Industrial Engineering,
Northeastern University,
Boston, MA 02115

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 10, 2015; final manuscript received September 14, 2015; published online October 15, 2015. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 138(2), 022202 (Oct 15, 2015) (9 pages) Paper No: JERT-15-1249; doi: 10.1115/1.4031614 History: Received July 10, 2015; Revised September 14, 2015

## Abstract

A comparative assessment is made of two implementations of the rate-controlled constrained-equilibrium (RCCE) method. These are the constraint and constraint potential formulations in which rate equations are solved for the RCCE constraints and constraint potentials, respectively. The two forms are equivalent mathematically; however, they involve different numerical procedures and thus show different computational performance. The main objective of this study is to compare the accuracy and numerical efficiency of the two formulations to attain the most effective implementation of the RCCE in turbulent combustion simulations. The RCCE method is applied to study methane oxygen combustion in an adiabatic, isobaric well stirred reactor. Simulations are carried out over a wide range of initial temperatures and equivalence ratios. Performance studies are conducted and RCCE results are compared with those obtained by direct integration of detailed chemical kinetics. The results show that both methods provide very accurate representation of the kinetics. It is also demonstrated that while the constraint form involves less numerical stiffness, the constraint potential implementation results in more saving in computation time.

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## Figures

Fig. 1

Ignition delay simulations for methane oxygen stoichiometric mixture in PSR at initial temperature of 1000 K. (a) Time variation of temperature and (b) percentage of relative difference between the RCCE and DKM prediction of temperature. Solid and dashed lines denote the constraint potential and constraint results, respectively. The symbol (○) denotes DKM predictions.

Fig. 2

Constraints in ignition delay calculations for stoichiometric methane oxygen mixture at initial temperature of 1000 K in PSR. Solid and dashed lines denote the constraint potential and constraint results, respectively. The symbol (○) denotes DKM predictions. Constraints are listed in Table 1.

Fig. 3

Mass fractions in ignition delay calculations for stoichiometric methane oxygen combustion at initial temperature of 1000 K in PSR. Solid and dashed lines denote the constraint potential and constraint results, respectively. The symbol (○) denotes DKM predictions.

Fig. 4

Performance of RCCE in ignition delay calculations for stoichiometric methane oxygen combustion in PSR at initial temperature of 1000 K. (a) Average CPU time in seconds and (b) number of function evaluations. The symbols (□) and (△) denote constraint potential and constraint results, respectively.

Fig. 5

The percentage of relative difference in prediction of (a) temperature and (b) ignition delay time. Constraint potential (right set) and constraint (left set) forms are compared with DKM in stoichiometric methane oxygen combustion simulations in PSR for initial temperatures of 1000–1400 K.

Fig. 6

The percentage of relative difference in prediction of (a) CH4 and (b) O2 mass fractions. Constraint potential (right set) and constraint (left set) forms are compared to DKM in stoichiometric methane oxygen combustion simulations in PSR for initial temperatures of 1000–1400 K.

Fig. 7

Performance of RCCE in stoichiometric methane oxygen combustion simulations in PSR for initial temperatures of 1000–1400 K. (a) Average CPU time in seconds and (b) number of function evaluations. The symbols (□) and (△) denote constraint potential and constraint results, respectively.

Fig. 8

The percentage of relative difference in prediction of temperature. The RCCE is compared with DKM in lean (Φ = 0.6, 0.9) and rich (Φ = 1.2, 1.6, 2.0) mixtures at initial temperature of 1400 K. Constraint potential and constraint forms are the right and left sets, respectively.

Fig. 9

The percentage of relative difference in prediction of (a) CH4 and (b) O2 mass fractions in comparison with DKM. Nonstoichiometric methane oxygen combustion simulations are performed in PSR for lean (Φ = 0.6, 0.9) and rich (Φ = 1.2, 1.6, 2.0) mixtures at initial temperature of 1400 K. Constraint potential and constraint forms are the right and left sets, respectively.

Fig. 10

Performance of RCCE forms in nonstoichiometric methane oxygen combustion simulations in PSR for lean (Φ = 0.6, 0.9) and rich (Φ = 1.2, 1.6, 2.0) mixtures at initial temperature of 1400 K. (a) Average CPU time in seconds and (b) number of function evaluations. The symbols (□) and (△) denote constraint potential and constraint results, respectively.

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