## 4 Characteristics of Flame and Its Combustion
### Flame Propagation Speed  
In gas-phase combustion, the flame propagation speed featuring the moving velocity of the flame front in space during the combustion is an important parameter for the evaluation of flame stability. It depends on many factors, including the nature of the combustible material itself, pressure, temperature, oxygen excess, flow state and heat dissipation. If it is larger than the fluid flow velocity, the front end of the flame will move to the nozzle, while if it is smaller, the hydrothermal flame will be blown out. Only when both items are equal to each other can stable flames be obtained. Comparing with gas-phase combustion, many scholars have found that the propagation speed of hydrothermal flame is one order of magnitude lower than that of gas-phase combustion. Therefore, special attention should be paid to this difference in the design of reactors and the determination of operating parameters.  
The stability of the hydrothermal flame depends on the deceleration of reaction flow and the acceleration of flame propagation speed. The reason why the flame stability in the volumetric reactor is better than that in the tubular reactor is that the flow rate of reactants can be significantly reduced in the large flow area. As to how to improve the flame propagation speed, [PERSON] believed that strengthening the injection temperature of reactants was a practical measure to maintain flame at a high velocity. In order to get a clear picture, it is necessary to determine the flame propagation speed. In describing the relationship between temperature and flame propagation speed, [PERSON] [33] adopted the expression deduced by [PERSON]. The results showed that the speed increased with injection temperature. In comparison with a higher flame propagation velocity (0.4-3 m/s) in gas phase combustion, the hydrothermal flame propagation velocity varied from 0.01 to 0.1 m/s in the volumetric reactor, which was also consistent with the experimental results by [PERSON] [59]. However, it should be noted that due to the fact that the properties of the mixture in the supercritical state cannot be calculated accurately, there is still a deviation for the calculated value. Based on the above conclusions, [PERSON] gave some suggestions to guide the scale-up design of the reactor. For example, the fluid velocity in a volumetric reaction chamber must be between 0.1-0.01 m/s. In addition, it was also found that the flame propagation velocity changed little at a low fuel concentration, but whether a high concentration fuel had an effect on the flame propagation velocity was not clear.  
With visualization apparatus, [PERSON] obtained the propagation velocity of axial laminar diffusion of hydrothermal flame at both low air velocity condition (50 vol% ethanol of 2 mL/min, air of 2 mL/min) and high air velocity condition (50 vol% ethanol of 2 mL/min, air of 7 mL/min) [59]. At a low air velocity, the flame propagation velocity was basically stable, with average value about 4.6 cm/s. While at a high air velocity, the variation of flame propagation velocity along the axis was not monotonous with a minimum value of 5 cm/s. By comparing the generation process of the flame kernel, [PERSON] believed that the minimum value appeared near the extinction point of the flame kernel on the nozzle side, because of insufficient combustible reactants. Due to the supplementation of reactants by mixing and the heat released by reaction, the speed of the flame away from the nozzle continued to increase. This study revealed that the complete mixing of fuel and oxidant help improve the flame propagation speed and the stability of the hydrothermal flame.