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Energy for Propulsion pp 237–266Cite as

Fundamentals of Rate-Controlled Constrained-Equilibrium Method

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Abstract

The Rate-Controlled Constrained-Equilibrium (RCCE) dimension reduction methodology models complex reacting systems within acceptable accuracy with a number of constraints \(N_c\), much smaller than the number of species \(N_s\), in the corresponding Detailed Kinetics Model (DKM). It describes the time evolution of chemical kinetics systems using a sequence of constrained-equilibrium states specified by the chosen constraints. The comprehensive chemical composition at each constrained-equilibrium state is determined by maximizing entropy (or minimizing Gibbs free energies) given the instantaneous values of the constraints. RCCE guarantees final equilibrium concentrations since Lagrange multipliers of all non-elemental constraints will be zero at final state. In this chapter, RCCE fundamentals, constraint and constraint potential representations, methods of initializing constraint potentials (non-dimensional Lagrange multipliers) as well as a brief discussion of RCCE constraint selection are presented. To show its accuracy against DKM, RCCE method is applied to \({\mathrm{H}_{2}}\)/\({\mathrm{O}_{2}}\) and \({\mathrm{CH}_{4}}\)/\({\mathrm{O}_{2}}\) zero-dimensional, constant energy/volume combustion over a wide range of initial conditions. The results show that both mixture results are in excellent agreement with the DKM predictions.

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Acknowledgements

This paper was made possible by NPRP award 7-252-2-113 from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors. The authors would like to express their appreciation to Dr. Vreg Yousefian for very helpful discussions regarding constraint potentials initialization and RCCE constraint selection.

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, Tennessee State University, Nashville, TN, 37212, USA

    Fatemeh Hadi

  2. Mechanical and Industrial Engineering Department, Northeastern University, Boston, MA, 02115, USA

    Guangying Yu & Hameed Metghalchi

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  1. Fatemeh Hadi
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  2. Guangying Yu
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  3. Hameed Metghalchi
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Correspondence to Fatemeh Hadi .

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Editors and Affiliations

  1. ACRI, The CFD Innovators, Los Angeles, California, USA

    Akshai K. Runchal

  2. Department of Mechanical Engineering, University of Maryland, Department of Mechanical Engineering, College Park, Maryland, USA

    Ashwani K. Gupta

  3. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Abhijit Kushari

  4. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Department of Aerospace Engineering, Kanpur, Uttar Pradesh, India

    Ashoke De

  5. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Department of Mechanical Engineering, Chicago, Illinois, USA

    Suresh K. Aggarwal

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Hadi, F., Yu, G., Metghalchi, H. (2018). Fundamentals of Rate-Controlled Constrained-Equilibrium Method. In: Runchal, A., Gupta, A., Kushari, A., De, A., Aggarwal, S. (eds) Energy for Propulsion . Green Energy and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-7473-8_10

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  • DOI: https://doi.org/10.1007/978-981-10-7473-8_10

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