## 2 Numerical Details
It should be noted that, in the present work, the GRI-MECH 3.0 detailed chemical reaction mechanisms, with includes 325 reaction steps and 53 chemical species [56], was implemented to formulate the flamelet library for the strained laminar flamelet model, with ethylene (C\({}_{2}\)H\({}_{4}\)) selected as parental fuel. The presented approach of the modelling turbulence-chemistry interaction has been validated in previous studies to provide a reasonable result with moderate computational burden [50,56,57]. This approach has been validated in previous numerical studies for modelling turbulence chemistry interaction, and has been proved to provide a reasonable result with moderate computational consumption [50,57,58]. It should be highlighted that alcohol-based fuel methanol (CH\({}_{3}\)OH), is deliberately selected as the parent fuel to constrain the coupling between radiative energy feedback and the combustion process, due to its feature of clean and soot-free burning behaviour [45]. For the same reason, the concentration of the key building structure unit of soot formation, acetylene (C\({}_{2}\)H\({}_{2}\)), in the gas mixture produced by this very parent fuel, is proved to be negligible. The most commonly adopted soot models formulated on C\({}_{2}\)H\({}_{2}\) precursor-based inception and surface growth mechanism are not applicable in this study [59,60,61,62]. As a result, a primitive and computational lightweight two-step soot model is integrated, for concept verification purpose only. With respect to the boundary conditions, a set flow rate of 0.0216 ms\({}^{-1}\) in the direction normal to the fuel surface is applied on the fuel pan. The applied injection velocity is determined on the basis of the cross-sectional area of the fire pan, the density of the parent fuel at a reference temperature, and the heat of combustion of the parent fuel in order to match the targeted heat release rate reported in the experimental study. The constant injection rate ensures an evenly distributed burning profile, regardless of the intensity of flow circulation and energy feedback. The fuel surface is set at an elevated height according to the experimental setup. The top and the periphery of the domain is set as the opening to allow naturally convected air entrainment in and out of the system. The base of the domain is set as a non-slip adiabatic wall, across which no heat or matter is allowed to pass. The simulation is initiated with standard temperature and pressure replicating the ambient conditions for the combustion process to proceed. For convenience, the case with one side entrainment slit is referred to as the Slit 01 case, case 1, or the baseline case/model, and that with two side entrainment slits is referred as the Slit 02 case, case 2, or the comparison case/model, in the following sections. It should be noted that the simulation result is validated against experimental data and achieve good comparison in temperature profile as well as the incoming velocity at the entraining slits at various HABs (height above burners), which is explained in detail in the co-published work [49]. For the sake of brevity, the validation process is not presented in this work.