Investigation of an Inhomogeneous Mixing Model for Conditional Moment Closure Applied to Autoignition

Autoignition of high pressure methane jets at engine relveant conditions within a shock tube \nis investigated using Conditional Moment Closure (CMC). The impact of two commonly \nused approximations applied in previous work is examined, the assumption of homogeneous \nturbulence in the closure of the micro-mixing term and the assumption of negligible radial \nvariation of terms within the CMC equations. In the present work two formulations of \nan inhomogeneous mixing model are implemented, both utilizing the β -PDF, but differing \nin the respective conditional velocity closure that is applied. The common linear model \nfor conditional velocity is considered, in addition to the gradient diffusion model. The \nvalidity of cross-stream averaging the CMC equations is examined by comparing results \nfrom two-dimensional (axial and radial) solution of the CMC equations with cross-stream \naveraged results. \n The CMC equations are presented and all terms requiring closure are discussed. So- \nlution of the CMC equations is decoupled from the flow field solution using the frozen \nmixing assumption. Detailed chemical kinetics are implemented. The CMC equations are \ndiscretized using finite differences and solved using a fractional step method. To maintain \nconsistency between the mixing model and the mixture fraction variance equation, the \nscalar dissipation rate from both implementations of the inhomogeneous model are scaled. \nThe autoignition results for five air temperatures are compared with results obtained using \nhomogeneous mixing models and experimental data. \n The gradient diffusion conditional velocity model is shown to produce diverging be- \nhaviour in low probability regions. The corresponding profiles of conditional scalar dis- \nsipation rate are negatively impacted with the use of the gradient model, as unphysical \nbehaviour at lean mixtures within the core of the fuel jet is observed. The predictions of \nignition delay and location from the Inhomogeneous-Linear model are very close to the \nhomogeneous mixing model results. The Inhomogeneous-Gradient model yields longer ig- \nnition delays and ignition locations further downstream. This is influenced by the higher \nscalar dissipation rates at lean mixtures resulting from the divergent behaviour of the \ngradient conditional velocity model. The ignition delays obtained by solving the CMC \nequations in two dimensions are in excellent agreement with the cross-stream averaged \nvalues, but the ignition locations are predicted closer to the injector.

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