EXPLORATORY INVESTIGATION OF MULTIPLE MAPPING CLOSURE AS A MIXING MODEL IN LES-CMC

Abstract The scalar dissipation rate is a key quantity in turbulent combustion modelling, in particular for Conditional Moment Closure (CMC). Within the CMC framework, its conditional average at a particular value of mixture fraction is of special interest. The present study examines the deterministic version of Multiple Mapping Closure (MMC) to evaluate the conditionally filtered scalar dissipation rate in the filtered CMC equations in the context of Large Eddy Simulation (LES). The objectives of the present investigation are (i) to use MMC to model the conditionally filtered scalar dissipation rate needed in LES-CMC and (ii) to determine if MMC is a viable option in the proposed framework. The paper presents our first results and focuses on the MMC equation, the role of each term in the MMC governing equation and the submodels needed. One major scalar is selected, mixture fraction. The MMC transport equation is implemented in a LES code coupled with CMC to simulate a lifted jet flame in a vitiated coflow. At this initial stage of the present MMC study, it is useful to separate the MMC results and investigate the MMC operation and modelling alone before solving LES, CMC and MMC together. Thus, the MMC equation is solved starting from frozen flow, mixing and temperature fields. Discussion is focused on the models of the MMC unclosed terms and their impact on the prediction of the mapping function and the conditionally filtered scalar dissipation rate. The issue related to low levels of predicted subgrid variance in MMC compared to what is predicted in the LES solver is investigated. Introduction The scalar dissipation rate is a key quantity in turbulent combustion modelling, in particular for flamelet, Conditional Moment Closure (CMC) and Probability Density Function (PDF) approaches [1]. The scalar dissipation rate, N, represents the rate of mixing at the molecular level and is proportional to the mean square gradient of the scalar, Z, such as N ≡ D ∇Z ·∇Z, where D is the molecular diffusivity of Z. Within the CMC framework, its conditional average at a particular value, η, of mixture fraction, Z is of special interest with N|η = D∇Z · ∇Z|Z = η . The angular brackets denote a conditional average over an ensemble of realizations of the flow, subject to the condition to the right of the vertical bar. Accurate modelling of the conditional scalar dissipation rate is crucial, as it appears in both the conditional species transport and temperature equations. However, evaluation of N|η is not straightforward. Further, CMC requires solution of the transport equations for the conditional averages to be consistent with that of the PDF transport equatio