# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
The numerical simulations were obtained by solving the typical governing equations of mass conservation, momentum, energy, and species conservation. In these equations, the following physical phenomena are taken into account: multi-component diffusion, wall heat diffusion, radiation between the ceramic tube and combustion gasses, and evaporation to simulate droplets combustion process. Comparisons between numerical and experimental results such as height and width of the flames and maximal temperature showed that the discrepancies become maximum if the liquid droplet radiation heat transfer is not taken into account. Consistent with the findings by [PERSON] et al. [10], the flame height and width increased almost linearly with the volume flow rate of the fuel, but the gradient increases as the tube inner diameter decreases. In addition, the maximal temperature increases first and then decreases after a certain flow rate. Figure 7: Experimental and numerical study of diffusion combustion in a micro channel using liquid n-heptane and air mixture, with and without heat recirculation, by [PERSON] et al. [17]. **Top**: Photos of flame at different Reynolds numbers (**b**); **Bottom**: Temperature contours for various heat loss coefficients: (\(h\) Unit: W/m\({}^{2}-K\)): (**a**) \(h=0\), (**b**) \(h=1\), (**c**) \(h=10\), (**d**) \(h=20\), (**e**) \(h=50\), (**f**) \(h=75\), (**g**) \(h=100\). Following the previous procedure, [PERSON] et al. investigated the diffusion combustion characteristics of liquid bio-butanol at micro scales under an electric field [19]. The electric field was imposed to analyze its impact on the flame structure and investigate the quenching phenomenon, in order to improve the stability and efficiency of liquid fuel micro flames, which are known to become unstable and tend to extinguish easily. They observed that the electric field has significant impacts on the micro scale combustion (see Figure 9). Increasing the DC voltage, the quenching flow rate decreased initially and after reaching its trough value, it started to gradually increase. The flame height, however, showed an opposite behavior: increasing at first and then decreasing. Moreover, the flame reached its maximum height faster in the smaller tube. It was also observed that increasing the fuel flow rate results in an almost linear increase of the highest temperature of flame. In this work, the numerical results were in a good agreement with the experimental measurements. The maximum deviation observed in this work was for the flame height (9.13%). In the case of the maximal temperature, the deviations were less than 2.24%. It is noted that the combustion process in this work was modeled by a simplified two-step reaction mechanism. It was however, one of the first studies to model the gasification process of a liquid fuel by calculating the heat change of the liquid droplets. Figure 8: Experimental and numerical study of a liquid ethanol micro-combustion in ceramic tubes with different inner diameters by [PERSON] et al. [18]. Flame characteristics for tube 1 at flow rate of 1.8 mL/h. To understand the limits of spherical hydrogen diffusion flames, [PERSON] et al. performed a study of one-dimensional spherical laminar diffusion flames, using adiabatic porous burners of various diameters [20]. The combustion reaction was modelled with an emphasis on kinetics of extinction, using detailed H\({}_{2}\)/O\({}_{2}\) chemical mechanism with 9 species and 28 reactions, and transport properties with updated light component diffusivities. They tested two configurations: (1) normal (H\({}_{2}\) flowing into quiescent air) and (2) inverse (air flowing into quiescent H\({}_{2}\)). The flames were simulated using a steady-state laminar flame code with detailed chemistry and transport, initially developed by Sandia National Laboratories for premixed flames [21], and modified to include diffusion flames. For equivalent heat release rates, the inverse flames showed to be smaller and hotter than normal flames.