7.1.5. Induction Time Model

In the two-step kinetics model, the induction parameter α represents the induction time period and its value varies between 0 and 1. The induction phase ends and the exothermal reaction starts when α = 1. Since the heat of reaction during the induction time is assumed to be zero, the energy conservation equation is not affected during the induction phase. The conservation equation for the induction parameter is given as

The source term, Sα, is given as,

where is the induction time which is a function of mixture composition, pressure P, and temperature T.

Two induction time models are implemented in GASFLOW-MPI. The input parameter to choose the model in $xput is itinduct. The default value of itinduct is 0.

7.1.5.1 Induction Model for H2-O2 Mixtures (itinduct = 1)

where Aα=6.2335×10^10 [Pa S/K], Bα=35.1715 [-], Cα=8530.6 K, Dα=7.22×10^(-11) [-] and Tα=21205 [K]. Pressure and temperature application range is: 0.01-100 atm，900-2000 K. The value of Aα can be changed using the input variable: A_alpha.

Sichel, M., Tonello, N. A., Oran, E. S., & Jones, D. A. (2002). A two-step kinetics model for numerical simulation of explosions and detonations in H2-O2 mixtures. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 458(2017), 49–82.

Gaathaug André Vagner, Vaagsaether Knut, Bjerketvedt Dag, Experimental and numerical investigation of DDT in hydrogen–Air behind a single obstacle, International Journal of Hydrogen Energy, volume 37, issue 22, pages 17606-17615.

7.1.5.2. Induction Model for CH4-H2-O2 Mixtures (itinduct = 2)

The composition of the mixture is determined by

where X_H2 is the mole fraction of H2, X_CH4 is the mole fraction of CH4.

The induction time correlation for methane is

The induction time correlation for hydrogen can be calculated as

The induction time for methane/hydrogen can be given by

Pressure and temperature application range is: 1-3 atm，800-2400 K.

Cheng, R. K., & Oppenheim, A. K. (1984). Autoignition in methane-hydrogen mixtures. Combustion and Flame, 58(2), 125–139.