Induction Time Definitions

The concept of induction time presupposes that the shocked-heated reactants will have a well-defined period of nearly isothermal reaction followed by a very rapid exothermal event (explosion). The end of the induction period is typically marked by a very sharp increase in pressure, temperature, and product species. This supposition is reasonable for most cases because almost all combustion reactions initially consist of thermally-neutral, chain-branching processes that create the intermediate and radical species that ultimately combine to form products. Under some conditions, for instance at very high or very low temperature, an induction time does not exist. At low temperature, it may be effectively infinite. At high temperature, the equilibrium state may not contain significant quantities of product, but rather may be largely dissociated. At some intermediate conditions, the induction time may be weakly defined, because the transition from reactants to products may be smooth and continuous.

Supposing that an induction time can be used to characterize a combustion event, the question arises of exactly how to define it. The definition is unimportant if all variables (temperature, pressure, reactant, product, and species concentrations) change rapidly at the same time. This is not always the case for the mixtures of interest to the present study. We generally use the definition that the end of the induction zone is the point where the rate of increase of temperature is maximum. This is convenient because it does not involve arbitrary reactant consumption fractions (for instance when 50% of reactant A is consumed), and it coincides with the point of maximum heat release. Table 3 gives a list of measures used in the literature to indicate the end of the induction zone.

 

Table 3: Induction time definitions used in the literature

[Asaba et al. (1963)]	Sudden end wall pressure rise.
[Bhaskaran et al. (1973)]	Large increase in optical emission (photomultiplier) and end wall pressure.
[Blumenthal et al. (1996)]	Multiple induction time definitions were used, and two events were sometimes observed: an initial small change (``first kernel'') followed by a more rapid change (DDT). The ``first kernel'' was variably measured by detection of a density gradient (shadowgraph), sudden OH emission, or a slight pressure rise. A sudden pressure jump defined the DDT. In cases where no detonation occurred, a first kernel was reported by the shadowgraph technique.
[Borisov et al. (1977)] and [Borisov et al. (1978)]	In ``static experiments'', induction time was defined as the delay between stopping the flow and the observation of a sharp pressure increase. In shock tube experiments, absorption spectroscopy of N2O at 253.6 nm was used to detect a sudden decrease in N2O concentration.
[Bradley et al. (1968)]	Appearance of OH by absorption at 306.7 nm and NH3 emission at 3000 nm.
[Burcat et al. (1971)]	Sudden level or slope change in pressure and heat flux.
[Cheng and Oppenheim (1984)]	Extrapolated from reflected wave trajectories (pressure increase).
[Craig (1966)]	Sudden pressure rise.
[Drummond (1969)]	Maximum OH absorption at 307 nm and end wall pressure rise.
[Drummond (1972b)]	Absorption by OH at 307 nm, NH2 at 570 nm, and NH at 336 nm.
[Hidaka et al. (1985b)]	tm was defined by the point of maximum OH emission intensity at 305.5 nm.
[Hidaka et al. (1985a)]	t20, t50, and t80 are times to 20, 50, and 80 percent consumption of N2O measured by infrared emission at 4.68 $\mu m$. $\tau$ indicates a rapid decrease in N2O concentration.
[Miyama and Endoh (1967a)]	Appearance of nitric oxide emission at 430.5 nm.
[Miyama and Endoh (1967b)]	Variation of NH3 absorption at 224.5 nm.
[Miyama (1968b)]	Variation of NH3 absorption at 224.5, 230, and 240 nm.
[Miyama (1968a)]	Variation in nitric oxide emission at 430.5 nm.
[Pamidimukkala and Skinner (1982)]	Induction time was defined at maximum O concentration by atomic resonance absorption spectroscopy. Another time was reported as the point where the reaction was 65% complete, by an unknown method.
[Petersen et al. (1996)]	Time of maximum rate of OH formation as indicated by absorption spectroscopy.
[Seery and Bowman (1970)]	Most rapid increase in pressure, OH absorption, and emission of OH (306.7 nm), CH (431.5 nm), CO (220.0 nm) and C2 (516.5 nm).
[Skinner and Ringrose (1966)]	Time of maximum OH emission.
[Soloukhin (1971)]	Interferograms, emission of N2O at 4.5 $\mu$, and of OH at around 300 nm were interpreted to derive induction times.
[Takeyama and Miyama (1967)]	Variation in NH3 absorption at 224.5 nm.
[Takeyama and Miyama (1965)]	Variation in OH emission.