# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
In addition to the comparisons between hydrogen- and methane-based flames, the impacts of fuel mixing were studied as well, where the combustion characteristics of different fuel mixture (H\({}_{2}\) + CH\({}_{4}\)) compositions were analyzed and compared (see Figure 14). They reported that the fraction of hydrogen in the fuel mixture has a controlling impact on the burner flame temperature, which was found to be attributed to the reaction rate of H + O\({}_{2}\) + M \(\rightarrow\) HO\({}_{2}\) + M as it is suppressed by reactions involving intermediate species such as CH\({}_{3}\) and CH\({}_{2}\)O in methane consumption. With that, they suggested that the combination of methane and hydrogen can be considered a good alternative to prevent the potential thermal damages to the chamber. Figure 1:5 Experimental and numerical study of the dry-low-NOx hydrogen micro-mix combustion chamber by [PERSON] et al. [24]. Calculated reaction rates in comparison with visual flame structure. [PERSON] et al. continued their investigations by conducting a numerical study of micro-jet diffusion flames using different fuels for several operating conditions by varying the inlet jet velocities and burners proprieties. The objective of this study was to prove the importance of the heat-recirculation impact on the flame stabilization at near-extinction conditions [28]. They used different fuels such as hydrogen, methane and dimethyl ether (DME), and employed a chemical kinetics mechanism with 17 species and 58 reactions. The first part of the study consisted of the analysis of the heat recirculation, \(Q_{re}\), and the heat losses through the burner surfaces, \(Q_{loss}\), by varying the thermal conductivities, \(k_{b}\), from 1 to 100 W/m-K, and the wall thicknesses, \(c_{b}\), from 0.2 to 0.8 mm. To evaluate the global thermal effect on the burner, an effective excess enthalpy was defined, \(H=(Q_{re}-Q_{loss})/M\), where \(M\) is the mass flow rate (kg/s). They reported that the ratio between \(Q_{re}\) and \(Q_{loss}\) increases monotonically as the jet velocity increases. This results in a critical fuel velocity, where \(Q_{re}\) overcomes \(Q_{loss}\), i.e., the heat recirculation can shadow the impact of the heat losses. Correspondingly, as \(k_{b}\) and \(c_{b}\) decrease at near extinction conditions, the flame temperature increases, i.e., the extinction limit for a specific heat Reynolds number \(\
u_{b}\), and the heat Reynolds number \(\
u_{b}\). Figure 1:6 Numerical study of micro-jet hydrogen/methane diffusion flames by [PERSON] et al. [27]. **Top**: Computed temperature contours and heat release rate (HRR) isopleths for CH\({}_{4}\) flames at fuel jet velocity of 0.4 m/s for (**a**) \(T_{b}~{}=~{}1800\) K (**b**) \(T_{b}=300\) K, and for H\({}_{2}\) flames at 1.0 m/s for (**c**) \(Tb~{}=~{}1800\) K (**d**) \(T_{b}=300\) K; **Bottom**: Computed temperature contours and HRR isopleths at the thermal conductive burner condition (the thermal conductivity of burner wall is 16 W/m-K) for (**a**) H\({}_{2}\) flame at 2.0 m/s, (**b**) H\({}_{2}\)/CH\({}_{4}\) 80%/20% flame at 1.2 m/s, (**c**) H\({}_{2}\)/CH\({}_{4}\) 20%/80% flame at 0.6 m/s, (**d**) CH\({}_{4}\) flame at 0.5 m/s. Here the flame temperatures range between 2028 K and 2034 K.  
fuel jet velocity can be extended. Figure 15 (left) represents the effective excess enthalpy, \(H\), and the maximum flame temperatures of a micro-jet methane combustion, for different burners, over fuel jet velocities ranging from 0.1 m/s to 3.2 m/s. It is evident that the heat-recirculation can assist the combustion regime for positive values of \(H\). In second part of the work, simulations were performed for the same burner proprieties, \(k_{b}=6\) W/(m-K) and \(c_{b}=0.2\) mm, and using different fuels to analyze the impact of the effective excess enthalpy, \(H\). Results of this analysis are presented in Figure 15 (right).