RANS and LES of a Turbulent Jet Ignition System Fueled with Iso-Octane

Abstract

The behaviour of a homogeneously charged Turbulent Jet Ignition (TJI) system, fueled with iso-octane was investigated numerically using Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) turbulence models. This study was an attempt to capture the start of autoignition in a lean charge TJI system, numerically, and, validate the results with experimental pressure measurements and OH chemilominescence images recorded during high speed imaging. Experiments were performed in an optically acessible Rapid Compression Machine (RCM) and the effect of auxiliary fuel injection in the prechamber and ignition distribution through various orrifices was investigated in depth through jet induced autoignition analysis. Heat release and pressure trace analysis were completed to capture the onset of autoignition, as well as comparing LES and RANS capabilities in this regard. Results showed that enhanced prechamber fueling leads to an increase in combustion stability while reducing the ignition delay. It was determined that keeping the prechamber mixture near stoichiometric is essential in order to have a more powerful turbulent jet discharged into the main chamber and to enhance ultra-lean main chamber combustion. The predicted flame propagation speed in the lean iso-octane mixtures was found to be slower than that observed in the experimental measurements. Results showed that the LES turbulence model is capable of predicting the start of autoignition more accurately and enhances the accuracy of the calculated peak pressure and burn rates relative to the RANS model. Two detailed iso-octane mechanisms were tested and based on the ignition delay comparisons, the LLNL-v3 mechanism was used in the current study.

Appendix 1

For implicitly-filtered LES, as is the case for the Finite Volume Method (FVM) used in this study, the grid filtering is intertwined with the spatial discretization. Therefore, for this type of LES no grid convergence can be expected, see e.g. [43]. However, the grid resolution is the main error controller of the LES and it must be fine enough to sufficiently resolve active turbulent structures. To quantify such sufficiency and hence assess the quality of LES, different posteriori measures can be utilized. One is the LES-index of quality (LES_IQ) proposed by Celik et al. [75]. This index reads as,

$$ {LES}_{IQ}=1-\frac{\left|{k}_{tot}-{k}_{res}\right|}{k_{tot}}; $$

(8)

where, k_tot is the total turbulent kinetic energy (TKE) that reflects the “true physics” and can be captured by an accurate direct numerical simulation (DNS), and, k_res specifies the portion of TKE that is directly resolved by LES. The difference between these, i.e. (k_tot-k_res) is the effective SGS TKE (associated with unresolved structures) which is modeled and hence is shown by k_mod. According to Pope [43], evaluation of k_mod that represents the TKE due to the residual motions is not straightforward. According to [43, 76], one way for approximating k_mod is to compute $\raisebox{1ex}{$\left\langle {\tau}_{kk}\right\rangle $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$, which is the average of the trace of the SGS stress tensor τ, where ${\tau}_{ij}=\left(\overline{u_i{u}_j}-\overline{u_i}\overline{u_j}\right)$. For a Boussinesq type of SGS modeling, the anisotropic part of τ_ij is modeled as Eq. 1. Clearly from this definition, τ_kk cannot be directly evaluated since it is absorbed in the pressure gradient term in the Navier-Stokes equations. According to Davidson [76], one way of computing τ_kk and hence, approximating k_mod is to use a SGS model which directly solves for k_mod, such as the model proposed by Kim and Menon [74]. However, in the LES reported in the paper we have only used standard Smagorinsky model that does not allow for direct computation of τ_kk.

Another way of evaluating LES_IQ is to directly compare the k_res to a reference highly-resolved k_tot (e.g. from a reference DNS). In our case, this was not however an option, noting the complexity of the geometry and multiphysics nature of the problem which make a DNS computationally intractable.

Nevertheless, the LES_IQ might not be the best technique to evaluate the quality of LES. It has been shown, for instance see [77, 78] that for different combinations of the grid resolution in different directions, the profile of k_res may exceed the k_tot, which is clearly unphysical.

In two extensive studies performed by Davidson [76, 79], several measures for assessing the quality of LES were evaluated. In the end, it was shown that the two-point correlation of velocity is the most reliable one. This has been also confirmed, for instance, in [77]. Employing these techniques for the RCM configuration is non-trivial and may require approximations, since there is no spatial direction over which the flow is statically homogeneous.