# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
The investiagotrs concluded that for fuels with Schmidt number (Sc) \(>1.0\), such as DME (Sc = 1.2), the flame is lifted, resulting in a negligible flame-burner interaction (H \(\approx 0\)). Such behavior was the opposite for fuels with Sc \(<1.0\), such as methane (Sc = 0.7) and hydrogen (Sc = 0.2), where the chemical kinetics is dominant in the flame base structure, and higher values of \(H\) are expected. [PERSON] et al. investigated the mixing performance and the diffusion combustion characteristics in a 2D planar micro-combustor using hydrogen and air separated by a plate [7]. This study was conducted through numerical simulations and consisted of various boundary conditions and burner geometries. Analyzing the mixing performance, flame stability limits and the combustion efficiency, they confirmed that the separating plate improved the mixing performance for lower inlet velocities and channel heights (see Figure 16 (left)), which is attributed to the extended residence time and shortened diffusion distance. They also reported that due to the improved mixing process, the combustion efficiency increased by reducing the combustor height, for the same inlet air velocities (see Figure 16 (right)). Figure 1:7 Numerical study on heat-recirculation assisted combustion for small scale jet diffusion flames at near-extinction condition by [PERSON] et al. [28]. **Left**: Effective excess-enthalpies (**a**) and flame temperatures (**b**) over fuel jet velocities range from the extinction limits to 3.2 m/s for different burners: Burner-A with \(c_{b}=0.2\) mm and \(k_{b}=1\) W/(m-K). Burner-B with \(c_{b}=0.2\) mm and \(k_{b}=6\) W/(m-K) and Burner-C with \(c_{b}=0.8\) mm and \(k_{b}=6\) W/(m-K); **Right**: Effective excess-enthalpies (**a**) and flame temperatures (**b**) as a function of Re number for H\({}_{2}\), CH\({}_{4}\), and DME flames. The burner wall thickness is and the thermal conductivity is \(c_{b}=0.2\) mm and \(k_{b}=6\) W/(m-K). In a most recent paper on this topic, [PERSON] et al. [29] conducted a numerical study to reproduce the \"flame-street\" phenomenon described in the experimental work of [PERSON] et al. [30]. The \"flame-street\" is a phenomenon observed in diffusion flames, and is used to describe a separated flame into a discrete series of flame segments. Typically \"flame-street\" phenomenon has been reported in experimental studies, but this work by [PERSON] et al. seeks to understand its characteristics with the help of numerical simulations. Using a reacting flow solver on the open-source software OpenFOAM [31], and with a chemical reaction mechanism of 21 species and 84 reactions, they simulated a 3D geometry channel with 30 mm in length, 5 mm in width and 0.75 mm in height. They used methane and oxygen as fuel and oxidizer, with inlet flow rates of 100 sccm and 200 sccm, respectively. To consider the heat external losses through the wall, a conjugate heat transfer model was considered, with wall material proprieties identical to the experimental work. The flame-street behavior consisting of a bibrachial, presented a long diffusion tail, a weaker fuel-lean premixed branch, and consecutive downstream \"new moon\"-like flamelets each with a fuel-lean and a fuel-rich premixed branch (see Figure 17 (left)), where \(Z_{st}\) is the fuel mass fraction for an unburnt fuel/oxidizer mixture at stoichiometric conditions. Also, the effects of wall thermal conditions and species mass diffusion on the formation of the flame-street were analyzed, and verified that the flame-street structure was formed at a moderate wall heat loss range, between 800-1100 K wall temperatures (see Figure 17 (right)). Figure 1:8 Numerical investigation on mixing performance and diffusion combustion characteristics of \(H_{2}\) and air in planar micro-combustor by [PERSON] et al. [7]. (**Left**): Required mixing distance versus inlet air velocity for micro-combustors with different heights; (**Right**): Variations in combustion efficiency versus inlet air velocity in three micro-combustors with different heights.