Modeling of spark ignition in gaseous mixtures using adaptive mesh refinement coupled to the thickened flame model

Abstract

In standard LES of spark ignition using the thickened flame model (TFM) and a static mesh, in other words without the use of adaptive mesh refinement (AMR), a progressive increase of the thickening factor F from unity to the nominal value is a consequence of the progressive increase of the cell size away from the spark plug. If the refined mesh is limited to a small region around the spark plug, the computational cost is limited but F will increase very rapidly as soon as the flame leaves the spark region, leading to an erroneous prediction of the total heat release rate as shown in this study. Conversely, using a large refined mesh region will allow such a progressive increase of F but at the cost of a strongly increased computational cost. To solve this issue, two new spark ignition models called TFM-AMR-I and TFM-AMR-I-Ftrans are proposed for TFM. These models are based on TFM-AMR Mehl et al.(2021) which employs AMR to ensure the desired thickening level and a constant number of grid points across the flame. It also uses a realistic spark plug energy model as in Colin et al.(2019). To avoid the aforementioned issue, a physical criterion is proposed to start the increase of F only when the flame kernel can be considered self-sustained. As this criterion is given by a model transport equation, the possible convection of the kernel outside the spark region doesn’t prevent the model to work properly. Secondly, in both models the increase of F is no more dictated by the cell size of the static mesh but it is given by an additional transport equation that controls the growth rate of F in time.These models are applied to the laminar propane/air ignition experiment presented in Colin et al.(2019). It is first shown that the experimental MIE is correctly recovered when using a DNS type resolution, that is, F=1 at any time. Then both proposed LES ignition models are applied to the same case: they recover correctly the MIE of the DNS provided the stretch correction of Quillatre (2014) is applied, which confirms the need to correct the effect of stretch with TFM. At the same time, TFM-AMR-I under-predicts the total heat release rate, which is attributed to the jump of the thickening factor at each AMR level removal. On the contrary, TFM-AMR-I-Ftrans compares better with the DNS, which is attributed to the continuous evolution of F with this model. Finally, it is shown that both models lead to a computational time reduction of a factor between 2 and 6 compared to static mesh TFM simulations.