# Numerical Investigations of Micro-Scale Diffusion Combustion: A Brief Review
## 3 Numerical Studies of Micro-Diffusion Flames
**Top**: Photographs and single-pulse LIPF-OH (Laser Induced Predissociative Fluorescence - OH radical) (a pre-dissociation fluorescence technique to collect densities of OH radicals) images of the microscale hydrogen diffusion flames with tube diameters of 0.2 and 0.48 mm; **Bottom**: Comparison of measured mean temperature, major species, and OH mole fraction with calculated radial profile for \(d=0.48\) mm (**bottom-left**) and 0.2 mm (**bottom-right**) flame at \(x=1\) mm. [PERSON] et al. continued the research that was initially pursued by [PERSON] et al. [10] by conducting experimental and numerical analyses of the structure and stabilization mechanism of a micro jet methane diffusion flame at near extinction conditions, especially in the standoff region [13] (see Figure 5). The numerical simulations were conducted by the simulation tool CFD-ACE [14], where the energy balance of conductive, diffusive, and convective fluxes in the gas flow with thermal conduction at the wall are solved to compute the wall temperature profile. Similar to the previous work [8], the radiation heat loss was neglected and non-slip and non-catalytic reaction conditions were applied on the burner surface. The code was validated through initial simulations at different tube diameters (0.148 mm, 0.4 mm and 1.0 mm) and fuel exit velocities. The stoichiometric mixture fraction at the symmetric jet center line was common in all cases. The simulations were able to capture flame heights as measured in the experimental results, where the flame height increased with the increase of the exit velocity, for all tube diameters. In terms of the prediction of the micro-flame  
Figure 4: Experimental (**a** and **b** in both **top** and **bottom** figures) and numerical (**c** in both **top** and **bottom** figures) study of hydrogen micro-diffusion flame for different Reynolds numbers by [PERSON] et al. [8]. (**a**) Photograph, (**b**) single-pulse LIPF-OH image and (**c**) computed OH isopleths of the hydrogen jet diffusion flame, **Top**: \(Re=30\); **Bottom**: \(Re=330\). stabilization characteristics, CH mass fraction isopleths were also in good agreement with those of measurements (Figure 5). They also made a comparison between CH contours of adiabatic and variable wall temperature conditions and observed that, with the adiabatic wall, the flame tends to extend farther upstream to the port and anchor on the tube. However, in the case of variable wall temperature, the flame quenched on the tube wall resulting in a gap. Subsequently, the heat transfer through the wall led to accelerated fuel decomposition and chain-branching reactions. They also suggested that the role of the buoyancy becomes important in flames with larger tube diameters and fuel velocities. On the other hand, for lower tube diameters, \(d=0.186\) mm, and inlet velocities \(<\)3.68 m/s, the buoyancy effect becomes less important and the flame is controlled only by diffusion. The design of micro combustors has always been the main concern in order to increase their efficiency and stability. One of the first attempts to stabilize and enhance a methane diffusion flame in micro combustors was made by [PERSON] and [PERSON] [15]. They simulated different 2D and 3D designs to optimize the mixing fractions of the methane and air streams and obtain the stability conditions for the flame. To do so, they examined various inlet temperatures, multiple chamber inner materials (changing the conductivity), and reducing the external heat losses. With varying the materials inside the chamber, it was verified that the material with higher thermal conductivity allowed for stronger and more stable flames. This is attributed the fact that more conductive materials allow for more heat transfer to the incoming mixtures, which results in increasing their temperature to 100-300 \({}^{\circ}\)C. On the  
Figure 5: Numerical study of a microjet methane diffusion flame near extinction by [PERSON] et al. [13].