# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
For example, at large flow rates, the peak temperature of inverse flames was 290 K higher than the adiabatic flame temperature of the normal flames, which is attributed to the low Lewis number of the ambient gas for inverse flames fueled by hydrogen. Similar to quenching limits measured in normal gravity on tube burners, the lower quenching limits of normal flames were predicted with a lower bound of 0.25 W, but in case of inverse flames the lower heat release rate increased to 1.38 W. The minimum temperatures at the quenching limits were 1070 K and 903 K for normal and inverse flames, respectively. Some of the aforementioned results are graphically presented in Figure 1:0  
Figure 1:1 Experimental and numerical study of the effects of electric field on micro-combustion using liquid biobutanol by [PERSON] et al. [19]. Experimental micro flame structure (**Top**) and Flame temperature field of numerical simulation (**Bottom**), with the flow rate of 0.9 mL/h for tube 1. (**a**) 0 V; (**b**) 4000 V.  
[PERSON] and [PERSON] conducted a numerical investigation to study the thermal and chemical structures formed in the hydrogen-air jet flames in a micro burner, where the excess heat recirculation through the burner wall has the potential to stabilize the miniaturized jet diffusion flame [22]. In their numerical simulations, they considered an axis-symmetric 2D case, where different burner materials and fuel ejecting velocities were tested to understand their roles on the flame structure inside the combustion chamber. Figure 11 presents a sample of the results obtained from these simulations. The thermal structure of the micro-jet flame under different burner materials (titanium and aluminum) showed that the overall flame shape and height were almost identical. They however behaved differently near the burner port. Here, due to the low conductivity of the materials, the heat recirculation from the flame toward the burner is small and therefore the burner tip and its vicinity were continuously heated up. The incoming fuel was also preheated, which increased the maximum flame temperature slightly. Decreasing the fuel velocity resulted in pushing the stoichiometric mixture fraction towards the burner surface, i.e., the flame height decreased, which was also evident in the OH distribution. It is important to note that even at extremely low Reynolds numbers, the effective usage of the burner wall properties and heat transfer can stabilize a significantly small flame. They also showed that enriching the fuel mixture can modify the flame structure and expand the low stability limit. Figure 1:2 Numerical study of hydrogen-air jet flames in a micro burner by [PERSON] and [PERSON] [22]. 2D temperature and mass fraction of H-atom distributions for different fuel ejecting velocities ((**a**) \(U_{lin}=2.5\) m/s and (**b**) \(U_{lin}=0.25\) m/s) over titanium burner. Figure 1:3 Modeled quenching limits of hydrogen diffusion flames by [PERSON] et al. [20]. Flame structure (**a**) and local heat release rates (**b**) for a large H2/air normal flame on a 5 mm radius burner. In order to investigate the wall thermal interactions with the flame, [PERSON] et al. conducted a numerical and experimental research to study the combustion characteristics of the non-premixed micro-jet hydrogen flame in an air co-flow, while considering the thermal interactions through the solid walls of the micro tube [23]. The experimental results showed how the flame height and shape, and correspondingly the OH-radical distributions would change with fuel flow velocity. Such results were well captured by the numerical simulations (see Figure 12). The evolution of the flame temperature field with the velocity variations was analyzed by post processing the numerical simulations results. Th flame temperature was shown to reach its maximum of 2300 K for the fuel flow velocity range of 5-25 m/s and to decrease smoothly in the fuel velocity range of 1-5 m/s. The fuel velocity could not go below 0.08 m/s, where the flame extinction occurred.