# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
**Top**: Comparison of the measured CH\({}^{\star}\) image (**a**) with computed CH mass fraction isopleths (**b**); **Bottom**: Comparison of CH contours calculated with adiabatic and variable wall temperature conditions (**c**), and Computed 2-D velocity vector coupled with CH isopleths in the standoff region (**d**). other hand, for an adiabatic micro reactor with inlet mixtures at ambient temperature, they observed that the flame could not sustain. As shown in Figure 6, they also suggested that the optimal design to ensure suitable mixing would require a restriction at the inlet of the combustion chamber to help the incoming streams converge while introducing a minor pressure drop. It is noted that the simulations in this work were conducted using the commercial CFD tool ANSYS Fluent [16], where the authors took the thermal diffusion effects into account. To further understand the importance of conjugate heat transfer for the inlet mixture and the negative role of the external heat losses, [PERSON] et al. investigated the diffusion combustion of liquid heptane in a small tube with and without heat recirculation via both experimental and numerical approaches [17]. They demonstrated that it was possible to reach a stable flame even without heat recirculation. Analyzing the impacts of equivalence ratio and the external heat loss coefficient, they observed the reaction zone moving with the variations of equivalence ratio; i.e., the reaction zone moves farther upstream when decreasing the equivalence ratio. The flame position was found to be sensitive to the heat recirculation as well, where no heat recirculation (adiabatic) resulted in the flame formation closer to the tube exit as compared to the cases with the existence of heat recirculation (more details are presented in Figure 7). In terms of the flammability limits, the numerical simulations showed that with the increase of the external heat loss, the flammability limit falls down rapidly if there is no heat recirculation. On the other hand, even for higher values of external heat loss coefficient (e.g., 100 W/m\({}^{2}\)-K), the burner can sustain at the presence of heat recirculation. It is noted that with the heat recirculation, the wall temperature of the inner tube reaches temperatures higher than the boiling point of the liquid n-heptane, which results in the pre-evaporation of the liquid fuel. Otherwise, the liquid fuel would be accumulated in the tube. Numerical simulations in this work were performed by the commercial CFD tool ANSYS Fluent [16], where the effects of solid and gas-phase conduction, solid radiation, solid-to-gas heat transfer, species diffusion, and chemistry were taken into account. To simulate the droplet vaporization, a vaporization and heating model in the ANSYS Fluent package was used. This model follows the mass transfer laws when the evaporation of the droplets takes place at the vaporization temperature. Also, the discrete phase model based on the Euler-Lagrange method was employed to simulate the droplets movement and the atomization of n-heptane. Figure 6: Numerical study of micro-combustor design for optimization of methane and air mixing by [PERSON] and [PERSON] [15]. 3D Temperature contours using aluminum as the conductive material. [PERSON] et al. also studied a liquid fuel (ethanol) by performing experimental and numerical investigations of laminar flow with diffusion combustion in micro scale ceramic tubes of different inner diameters [18]. They employed numerical methods to capture micro flame characteristics as a way around the limitation of measurement tools in experiments. They designed several tests by varying the numerical conditions to examine the model capacity for predicting the micro flame characteristic correctly. As presented in Figure 8, [PERSON]'s group confirmed that the liquid droplet radiation heat transfer and boundary slip had significant impacts on the results and should not be overlooked in modeling.