## 4 Characteristics of Flame and Its Combustion
### Ignition Delay Time  
The ignition delay time is defined as the time required for the transition from the initial state to sudden temperature rise when the combustible material has reached the ignition condition. In the field of gas-phase combustion, controlling the relative magnitude of ignition delay time and residence time determines whether the flame can be produced and whether the combustion is thorough or not. Shorter ignition delay time means that the reactor is more portable, and the start-up process is safer. According to [PERSON] [104], the ignition delay time as a very important function of all experimental parameters reflected the interactions among the factors of reactant diffusion, heat production and heat dissipation. In fact, there is no difference between SCWO and SCHC, so the free radical chain mechanism used for explaining the SCWO reaction process is also suitable for the delay analysis in the ignition process. Such an autocatalytic mechanism will yield an S-shaped conversion-time curve as opposed to the exponential curve observed first-order kinetics [81]. In hydrothermal combustion, the ignition delay stage corresponds to the induction stage of the chain mechanism. [PERSON] et al. observed the ignition delay of hydrothermal flame in a semi-batch reactor, and pointed out it was the consequence of the combination of component mixing and chemical reaction delay [50]. However, the ignition delay time under specific conditions was not clearly stated in this literature, and only the delay of 10-15 s was observed. Moreover, for every 50 \({}^{\circ}\)C increase in air temperature, the delay time will be shortened by 1-2 s. [PERSON] et al. supplemented the calculation of ignition delay time of methanol with a specific range of concentrations (2-15 mol%) at a preheating temperature (350-550 \({}^{\circ}\)C), with an oxidant coefficient of 1 [40]. The results showed that as the preheating temperature increased, the ignition delay time decreased exponentially, which was similar to the variation trend of the ignition delay time in conventional gas phase combustion. At the same time, by comparing with the experimental results of [PERSON], [PERSON] also found that their calculated value (4-11 s) was smaller than the experimental value (10-15 s). [PERSON] believed that the reason for this difference was that the reactants were assumed to be completely mixed in the calculation process, while the experimental values included the effects of the component mixing process. [PERSON] et al. studied the ignition characteristics of the n-propanol laminar reverse diffusion flame in a semi-batch reactor with experimental parameters including reactor temperature, oxidant temperature and n-propanol concentration [60]. Results showed that with the other parameters keeping the same, the ignition delay time significantly reduced with the increase of temperature in the reactor. In addition, it was worth noting that the ignition of laminar diverse diffusion flame proved that strong buoyancy caused by density difference had positive effects on ignition. More information about the influence of buoyancy on hydrothermal flame was in NASA's experiments in Section 4.5. Subsequently, [PERSON] et al. further studied the effects of oxidant flow rate (0.5-3 mL/s) on ignition delay time under subcritical (380 \({}^{\circ}\)C, 20.5 MPa) and supercritical (400 \({}^{\circ}\)C, 22.5 MPa) conditions, while comparing their differences [44]. In the first case, the oxidizer flow rate of 1.5 mL/s corresponded to the shortest ignition delay time and was extremely beneficial to spontaneous ignition. While in the second case, the ignition delay time decreased monotonously with the growth of oxidant flow rate. Combined with numerical simulations, the researchers found that the generation of hydrothermal flame under subcritical conditions mainly depended on thermal diffusion and buoyancy, which promoted the mixing of n-propanol and oxygen.