# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
**Top**: Simulation results against experimental data of the flame height as a function of the methane inlet velocity, \(u_{e}\); **Bottom**: 2D profiles of the simulation results for \(u_{e}=1\) and \(2\) m/s: (**a**) flow vectors, (**b**) temperature contours, (**c**) methane and oxygen concentrations ratio, and (**d**) reaction contours. extinction behavior, they also showed the existence of a critical minimum flame height and a critical maximum heat release rate, at which the flame can experience extinction, regardless of the burner diameter as presented in the right diagram of Figure 2.  
Using a different fuel, [PERSON] et al. investigated the combustion characteristics of hydrogen diffusion flames at micro-scale, both experimentally and numerically [12]. In their experiments, they implemented non-intrusive techniques to measure all major species concentrations (O\({}_{2}\), H\({}_{2}\)O, H\({}_{2}\), N\({}_{2}\)) and, for the first time, the absolute hydroxyl radical concentration (OH), together with the temperature, at \(Re=30\) with inner diameters of 0.2 mm and 0.48 mm for the tube injector fuel (Figure 3). The OH images illustrated a spherical flame forming with reducing the tube diameter. Furthermore, flames were found to be in the convection-diffusion controlled regime due to the low Peclet (Pe) number, indicating the insignificant effect of Pe number on the flame shape. In the numerical simulations, they applied detailed transport and multi-step reaction mechanisms with 9 species and 21 reactions for hydrogen-air combustion with the following boundary conditions: non-slip, non-catalytic reactions, and constant wall temperature (300 K). These numerical simulations were, however, unable to correctly predict the flame structure for the domains with dominant air entrainment and thermal-diffusive effects. This was later addressed by [PERSON] et al. [13], where the burner was coupled to the computational domain to solve for the properties both inside and outside of the burner wall and to allow for taking the conjugate heat transfer and the back-diffusion of the species into account. More specifically, they obtained the wall temperature distribution by solving the energy balance of diffusive, convective and conductive fluxes into the gas flow and imposed that in their numerical calculations. Figure 2: Numerical study of methane micro diffusion flame to analyze the burner size effects by [PERSON] et al. [11]. (**a**): Size effects on flame shapes and scalar dissipation rate (SDR) evaluated at the location of maximum heat release rate; (**b**): Minimum flame height and corresponding maximum local heat release rate, \(Q_{max}\). Moving forward with their previous work, [PERSON] et al. [8] conducted detailed measurements and assessments of laminar hydrogen jet flames through non-intrusive experimental techniques and compared the findings with computational results. They investigated non-premixed reactive flows with different Reynolds (\(Re\)) numbers (\(Re=30\) and \(Re=330\)). As presented in Figure 4, it was observed that the impact of the thermal diffusion on the flame structure is more pronounced at the case with higher Re number. In addition to varying \(Re\) numbers, [PERSON] et al. examined the flame structure at \(Re=30\) with five different chemical kinetic mechanisms and did not observe any major differences among them. The effects of the burner wall on the flame structure were also studied, using a commercial CFD (Computational Fluid Dynamics) code, CFD-ACE [14], which was found to affect the flows with a lower \(Re\) number more considerably. It was also concluded that a variable wall temperature profile as a boundary condition would result in a better agreement between the computed and measured data. The complete measurements of laminar hydrogen jet diffusion flames in this work can be used as benchmarks for the development and validation of CFD codes. Figure 3: Experimental and numerical study of hydrogen micro-diffusion flame for different tube diameters by [PERSON] et al. [12].