## 5 Ignition Process and Mechanisms
### Ignition Mechanism
#### 5.2.3 Mixing  
As mentioned earlier, buoyancy mixing is mainly due to the spatial difference in fluid density and the variation extent of the density with temperature. The effect of density is usually expressed by the thermal expansion coefficient and Froude number. The peak of the thermal expansion coefficient near the critical point theoretically reflects the important contribution of density to the buoyancy mixing that occurs during transcritical processes. [PERSON] pointed out that the transcritical process was a sign of the emergence of a large scale of buoyancy convections, and even small temperature differences (-1 \({}^{\circ}\)C) was to cause strong buoyancy effects [59]. They observed that the strong buoyancy convection started at 370 \({}^{\circ}\)C and disappeared at the temperature exceeding 400 \({}^{\circ}\)C, reflecting the strong temperature-dependent nature of density during the transcritical process. [PERSON] investigated the variation of the water state with the temperature at supercritical pressure, and found that before 374 \({}^{\circ}\)C, it was still clearly liquid and the same as the water at normal temperature and pressure; once the temperature reached the critical point, water suddenly lost its transparency and turned black, which presented the characteristic of critical water; as the temperature continued to rise, the black became gray; when it reached 400 \({}^{\circ}\)C, the water became completely transparent again, and there was no visible phase separation after 400 \({}^{\circ}\)C. The above results also support the dramatic physical changes in the transcritical process (Figure 10a) [49]. To evaluate the effects of buoyancy on the flow and temperature fields [69; 111], [PERSON] et al. removed the exothermic chemical reaction and obtained a temperature map by simulation under both normal gravity and zero gravity. With gravity, entrainment and high velocity could be clearly seen near the central axis, and the zone of temperature spread was obviously narrower due to the buoyancy. With zero gravity, the mixing away from the nozzle was insufficient, and the inertia force was dominant only in the position near the nozzle, the normal gravity and zero gravity were similar (Figure 10b). By controlling the existence of gravity, the results showed the influence of the buoyancy caused by the density gradient on the mixing. Furthermore, based on existing simulation works, [PERSON] experimentally observed the effect of buoyancy on the mixing process in three scenarios, which were subcritical jet injected into subcritical water, supercritical jet injected into supercritical  
Figure 10: (**a**) Influence of temperature on the water flow at 25 MPa (50 mL min\({}^{-1}\) water and 1 nL min\({}^{-1}\) air) (adapted from [49]); (**b**) Illustration of buoyancy effects showing non-reacting axisymmetric jet of heated fluid injected into the body of cooler fluid (adapted from [59]). water, and supercritical jet injected into subcritical water [57]. They found that the first two scenarios had similar results, and that with the increase of Reynolds number (_Re_), the position where the flow transferred to the turbulent flow was getting closer and closer to the nozzle. However, in the third scenario, the buoyancy mixing induced by the density difference was very strong, and even if the jet's _Re_ was low, the distance required for the transition to turbulence was short. Therefore, by combining the definition of the intrinsic characteristic vorticity and the Froude number of turbulence, the author proposed the effective Froude number \(F^{2}_{\mathit{eff}}\). In case of \(1/\,F^{2}_{\mathit{eff}}>>1\) and small Reynolds number, the jet exhibited a turbulent plume behavior, which also corresponded to the third scenario. In case of \(1/\,F^{2}_{\mathit{eff}}\)-O (1), the _Re_ determined the behavior of the jet, that was, the flow was laminar with small _Re_ and would change into turbulent flow when the _Re_ was greater than 2000.