Review Article

Rate-Controlled Constrained-Equilibrium Application in Shock Tube Ignition Delay Time Simulation

[+] Author and Article Information
Guangying Yu

Mechanical and Industrial
Engineering Department,
Northeastern University,
Boston, MA 02115
e-mail: yu.g@husky.neu.edu

Fatemeh Hadi

Department of Mechanical and
Manufacturing Engineering,
Tennessee State University,
Nashville, TN 37212
e-mail: fhadi@tnstate.edu

Hameed Metghalchi

Mechanical and Industrial
Engineering Department,
Northeastern University,
Boston, MA 02115
e-mail: metghalchi@coe.neu.edu

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 31, 2018; final manuscript received August 13, 2018; published online September 26, 2018. Special Editor: Reza Sheikhi.

J. Energy Resour. Technol 141(2), 020801 (Sep 26, 2018) (5 pages) Paper No: JERT-18-1594; doi: 10.1115/1.4041288 History: Received July 31, 2018; Revised August 13, 2018

The rate-controlled constrained-equilibrium (RCCE), a model order reduction method, assumes that the nonequilibrium states of a system can be described by a sequence of constrained-equilibrium kinetically controlled by relatively a small number of constraints within acceptable accuracies. 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 the constraints. Regardless of the nature of the kinetic constraints, RCCE always guarantees correct final equilibrium state. Ignition delay times measured in shock tube experiments with low initial temperatures are significantly shorter than the values obtained by constant volume models. Low initial temperatures and thus longer shock tube test times cause nonideal heat transfer and fluid flow effects such as boundary layer growth and shock wave attenuation to gradually increase the pressure (and simultaneously increase the temperature) before ignition. To account for these effects, in this paper, the RCCE prescribed enthalpy and pressure (prescribed h/p) model has been further developed and has been applied to methane shock tube ignition delay time simulation using GRI-Mech 3.0. Excellent agreement between RCCE predictions and shock tube experimental data was achieved.

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Smooke, M. , and Giovangigli, V. , 1991, “ Premixed and Nonpremixed Test Problem Results,” Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, Springer, Berlin, pp. 29–47.
Bodenstein, M. , and Lind, S. , 1907, “ Geschwindigkeit Der Bildung Des Bromwasserstoffs Aus Seinen Elementen,” Z. Für Phys. Chem., 57(1), pp. 168–192.
Rein, M. , 1992, “ The Partial-Equilibrium Approximation in Reacting Flows,” Phys. Fluids A: Fluid Dyn., 4(5), pp. 873–886. [CrossRef]
Maas, U. , and Pope, S. , 1992, “ Simplifying Chemical Kinetics: Intrinsic Low-Dimensional Manifolds in Composition Space,” Combust. Flame, 88(3–4), pp. 239–264. [CrossRef]
Pope, S. B. , and Maas, U. , 1993, “ Simplifying Chemical Kinetics: Trajectory-Generated Low-Dimensional Manifolds,” Mechanical and Aerospace Engineering Report, Ithaca, NY, Report No. FDA 93--11. https://tcg.mae.cornell.edu/pubs/Pope_Maas_93.pdf
Nahvi, S. , Nabi, M. , and Janardhanan, S. , 2012, “ A Quasi-Linearisation Approach to Trajectory Based Methods for Nonlinear MOR,” International Conference on Modelling, Identification and Control, Wuhan, China, June 24–26, pp. 217–222.
Bykov, V. , and Maas, U. , 2007, “ The Extension of the ILDM Concept to Reaction–Diffusion Manifolds,” Combust. Theory Modell., 11(6), pp. 839–862. [CrossRef]
Bykov, V. , and Maas, U. , 2009, “ Problem Adapted Reduced Models Based on Reaction–Diffusion Manifolds (REDIMs),” Proc. Combust. Inst., 32(1), pp. 561–568. [CrossRef]
Lebiedz, D. , 2004, “ Computing Minimal Entropy Production Trajectories: An Approach to Model Reduction in Chemical Kinetics,” J. Chem. Phys., 120(15), pp. 6890–6897. [CrossRef] [PubMed]
Lam, S. , and Goussis, D. , 1994, “ The CSP Method for Simplifying Kinetics,” Int. J. Chem. Kinetics, 26(4), pp. 461–486. [CrossRef]
Løvås, T. , 2009, “ Automatic Generation of Skeletal Mechanisms for Ignition Combustion Based on Level of Importance Analysis,” Combust. Flame, 156(7), pp. 1348–1358. [CrossRef]
Schwer, D. , Lu, P. , and Green, W. , 2003, “ An Adaptive Chemistry Approach to Modeling Complex Kinetics in Reacting Flows,” Combust. Flame, 133(4), pp. 451–465. [CrossRef]
Van Oijen, J. , and De Goey, L. , 2000, “ Modelling of Premixed Laminar Flames Using Flamelet-Generated Manifolds,” Combust. Sci. Technol., 161(1), pp. 113–137. [CrossRef]
Lu, T. , and Law, C. , 2005, “ A Directed Relation Graph Method for Mechanism Reduction,” Proc. Combust. Inst., 30(1), pp. 1333–1341. [CrossRef]
Keck, J. , and Gillespie, D. , 1971, “ Rate-Controlled Partial-Equilibrium Method for Treating Reacting Gas Mixtures,” Combust. Flame, 17(2), pp. 237–241 [CrossRef]
Keck, J. , 1990, “ Rate-Controlled Constrained-Equilibrium Theory of Chemical Reactions in Complex Systems,” Prog. Energy Combust. Sci., 16(2), pp. 125–154. [CrossRef]
Law, R. , Metghalchi, M. , and Keck, J. C. , 1989, “ Rate-Controlled Constrained Equilibrium Calculation of Ignition Delay Times in Hydrogen-Oxygen Mixtures,” Symp. (Int.) Combust., 22(1), pp. 1705–1713. [CrossRef]
Ugarte, S. , Gao, Y. , and Metghalchi, M. , 2005, “ Application of the Maximum Entropy Principle in the Analysis of a Non-Equilibrium Chemically Reacting Mixture,” Int. J. Thermodyn., 8(1), pp. 43–53.
Hamiroune, D. , Bishnu, P. , Metghalchi, M. , and Keck, J. C. , 1998, “ Rate-Controlled Constrained Equilibrium Method Using Constraint Potentials,” Combust. Theory Model., 2(1), pp. 81–94. [CrossRef]
Janbozorgi, M. , Gao, Y. , Metghalchi, M. , and Keck, J. C. , 2006, “ Rate-Controlled Constrained-Equilibrium Calculations of Ethanol-Oxygen Mixture,” ASME Paper No. IMECE2006-15667.
Hadi, F. , and Sheikhi, M. , 2016, “ A Comparison of Constraint and Constraint Potential Forms of the Rate-Controlled Constraint-Equilibrium Method,” ASME J. Energy Resour. Technol., 138(2), p. 022202. [CrossRef]
Hadi, F. , Janbozorgi, M. , Sheikhi, M. R. H. , and Metghalchi, H. , 2016, “ A Study of Interactions Between Mixing and Chemical Reaction Using the Rate-Controlled Constrained-Equilibrium Method,” J. Nonequilibrium Thermodyn., 41(4), pp. 257–278.
Bishnu, P. S. , Hamiroune, D. , Metghalchi, M. , and Keck, J. C. , 1997, “ Constrained-Equilibrium Calculations for Chemical Systems Subject to Generalized Linear Constraints Using the NASA and STANJAN Equilibrium Programs,” Combust. Theory Modell., 1(3), pp. 295–312. [CrossRef]
Safari, M. , Hadi, F. , and Sheikhi, M. , 2014, “ Progress in the Prediction of Entropy Generation in Turbulent Reacting Flows Using Large Eddy Simulation,” Entropy, 16(10), pp. 5159–5177. [CrossRef]
Sheikhi, M. , Safari, M. , and Hadi, F. , 2015, “ Entropy Filtered Density Function for Large Eddy Simulation of Turbulent Flows,” AIAA J., 53(9), pp. 2571–2587. [CrossRef]
Beretta, G. P. , Keck, J. C. , Janbozorgi, M. , and Metghalchi, M. , 2012, “ The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics,” Entropy, 14(2), pp. 92–130. [CrossRef]
Bishnu, P. , Hamiroune, D. , and Metghalchi, M. , 2001, “ Development of Constrained Equilibrium Codes and Their Applications in Nonequilibrium Thermodynamics,” ASME J. Energy Resour. Technol., 123(3), pp. 214–220. [CrossRef]
Beretta, G. , Janbozorgi, M. , and Metghalchi, H. , 2016, “ Degree of Disequilibrium Analysis for Automatic Selection of Kinetic Constraints in the Rate-Controlled Constrained-Equilibrium Method,” Combust. Flame, 168, pp. 342–364. [CrossRef]
Yousefian, V. , 1998, “ A Rate-Controlled Constrained-Equilibrium Thermochemistry Algorithm for Complex Reacting Systems,” Combust. Flame, 115(1–2), pp. 66–80. [CrossRef]
Janbozorgi, M. , and Metghalchi, M. , 2012, “ Rate-Controlled Constrained-Equilibrium Modeling of H/O Reacting Nozzle Flow,” J. Propul. Power, 28(4), pp. 677–684. [CrossRef]
Janbozorgi, M. , Ugarte, S. , Metghalchi, M. , and Keck, J. C. , 2009, “ Combustion Modeling of Mono-Carbon Fuels Using the Rate-Controlled Constrained-Equilibrium Method,” Combust. Flame, 156(10), pp. 1871–1885. [CrossRef]
Nicolas, G. , and Metghalchi, H. , 2016, “ Development of the Rate-Controlled Constrained-Equilibrium Method for Modeling of Ethanol Combustion,” ASME J. Energy Resour. Technol., 138(2), p. 022205.
Parsinejad, F. , Keck, J. , and Metghalchi, H. , 2007, “ On the Location of Flame Edge in Shadowgraph Pictures of Spherical Flames: A Theoretical and Experimental Study,” Exp. Fluids, 43(6), pp. 887–894. [CrossRef]
Janbozorgi, M. , and Metghalchi, H. , 2009, “ Rate-Controlled Constrained-Equilibrium Theory Applied to the Expansion of Combustion Products in the Power Stroke of an Internal Combustion Engine,” Int. J. Thermodyn., 12(1), pp. 44–50. http://dergipark.gov.tr/download/article-file/65751
Hadi, F. , Yu, G. , and Metghalchi, H. , 2018, “ Fundamentals of Rate-Controlled Constrained-Equilibrium Method,” Energy for Propulsion, Springer, Singapore, pp. 237–266.
Nicolas, G. , and Metghalchi, H. , 2015, “ Comparison Between RCCE and Shock Tube Ignition Delay Times at Low Temperatures,” ASME J. Energy Resour. Technol., 137(6), p. 062203. [CrossRef]
Cadman, P. , Thomas, G. , and Butler, P. , 2000, “ The Auto-Ignition of Propane at Intermediate Temperatures and High Pressures,” Phys. Chem. Chem. Phys., 2(23), pp. 5411–5419. [CrossRef]
Davis, S. , Joshi, A. , Wang, H. , and Egolfopoulos, F. , 2005, “ An Optimized Kinetic Model of H2/CO Combustion,” Proc. Combust. Inst., 30(1), pp. 1283–1292. [CrossRef]
Chaos, M. , and Dryer, F. , 2010, “ Chemical-Kinetic Modeling of Ignition Delay: Considerations in Interpreting Shock Tube Data,” Int. J. Chem. Kinet., 42(3), pp. 143–150. [CrossRef]
Li, H. , Owens, Z. , Davidson, D. , and Hanson, R. , 2008, “ A Simple Reactive Gasdynamic Model for the Computation of Gas Temperature and Species Concentrations Behind Reflected Shock Waves,” Int. J. Chem. Kinet., 40(4), pp. 189–198. [CrossRef]
Huang, J. , Hill, P. , Bushe, W. , and Munshi, S. , 2004, “ Shock-Tube Study of Methane Ignition Under Engine-Relevant Conditions: Experiments and Modeling,” Combust. Flame, 136(1–2), pp. 25–42. [CrossRef]
Burke, U. , Somers, K. , O'Toole, P. , Zinner, C. , Marquet, N. , Bourque, G. , Petersen, E. , Metcalfe, W. , Serinyel, Z. , and Curran, H. , 2015, “ An Ignition Delay and Kinetic Modeling Study of Methane, Dimethyl Ether, and Their Mixtures at High Pressures,” Combust. Flame, 162(2), pp. 315–330. [CrossRef]


Grahic Jump Location
Fig. 1

A typical prescribed pressure profile of methane/air combustion shock tube experiment

Grahic Jump Location
Fig. 2

Comparison of predicted methane/air ignition delay time of DKM and RCCE constant e/v and prescribed h/p models and experimental data of Huang et al. [41] from 1024 K to 1295 K at pressure of 40 atm and equivalence ratio of ϕ=1

Grahic Jump Location
Fig. 3

Comparison of predicted methane/air ignition delay time of DKM and RCCE constant e/v and prescribed h/p models and experimental data of Huang et al. [41] from 1076 K to 1309 K at pressure of 23 atm and equivalence ratio of ϕ=1

Grahic Jump Location
Fig. 4

Comparison of predicted methane/air ignition delay time of prescribed h/p and constant e/v models for both DKM and RCCE method together with experimental data of Burke et al. [42] from 927 K to 1087 K at pressure of 25 atm and equivalence ratio of ϕ=1



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