## 4 Characteristics of Flame and Its Combustion
### Extinction Temperature  
Extinction temperature refers to the lowest fuel inlet temperature of avoiding extinction, and it is also an important index to measure the stability of hydrothermal flame. The lower the extinction temperature is, the better the stability of the hydrothermal flame becomes and the lower the demand for fuel preheating achieves. Thus, it is necessary to maintain hydrothermal combustion at room temperature to reduce energy consumption and realize the miniaturization and high efficiency of the reactor. Operating parameters and geometric parameters of the reactor can affect the extinction temperature, and both higher fuel concentration and lower injection velocity can decrease extinction temperature according to some works. Different from the ignition temperature, the effect of fuel mass concentration on extinction temperature is extremely significant. The experiments done by [PERSON] showed that with the rise of mass fraction, the extinction temperature obviously decreased from 380 \({}^{\circ}\)C for 12 wt% to 340 \({}^{\circ}\)C for 20 wt% [27]. [PERSON] et al. observed an analogous phenomenon [72]. When the mass fraction was less than 11 wt%, the extinction temperature was still above the critical temperature, and once the mass fraction exceeded 27 wt%, the extinction temperature would be less than 100 \({}^{\circ}\)C, which meant that the injection of cold fluid could also maintain hydrothermal combustion. In the experiments of testing the effects of different tube mixers on the hydrothermal flame in TWR, [PERSON] et al. realized stable flame with injection temperature in the range of 390 \({}^{\circ}\)C to 50 \({}^{\circ}\)C, which referred to extinction temperature [31]. Moreover, according to the isopropanol extinction experiment in the semi-batch reactor, [PERSON] et al. pointed out that the extinction temperature was almost inversely proportional to the fuel concentration [60]. The flow rate and the type of oxidants also affect the extinction temperature. [PERSON] et al. studied the factors influencing extinction temperature in the tubular reactor and TWR at the same time, and found out that in the tubular reactor, the flow rate of the reactants determined the minimum injection temperature maintaining the flame (extinction temperature) [33]. Slower flow velocity in the tube corresponded to lower extinction temperature, which was always close to the critical temperature of the water. Meanwhile, in the TWR, the stability of the hydrothermal flame could be realized when the injection temperature of reactants was as low as 170 \({}^{\circ}\)C. Through analysis, researchers considered that compared to 3-24 m/s in the tubular mixer (reactor), the flow velocity in the main reaction chamber of TWR was basically between 0.1-0.01 m/s. Additionally, by comparing the effects of oxygen and air on hydrothermal flame, they found out that air could achieve lower extinction temperature with the same fuel flow rate. The air took up more space under the condition of the same oxygen content. This might promote the mixing between oxidants and isopropanol during the flow process, resulting in lower extinction temperature. The mixing degree of reactants and the flow-field are the key conditions to determine extinction temperature. [PERSON] pointed out that the size of the nozzle would impact the flow-field in the reactor and the flame stability [27]. Combined with the re-circulation zone near the nozzle obtained by [PERSON] et al. [43] and [PERSON] et al. [29] in the calculation of two-dimensional axisymmetric flow-reaction, we speculate that the backflow of high-temperature reactants can transfer heats and free radicals back to the fuel and oxidant at the inlet, so as to reduce the extinction temperature.