Simulation of Dilute Acetone Spray Flames with LES-CMC Using Two Conditional Moments

Abstract

Large-eddy simulations (LES) have been coupled with a conditional moment closure (CMC) method for the computation of a series of turbulent spray flames. An earlier study by Ukai et al. (Proc. Combust. Inst. 34(1),1643–1650, 2013) gave reasonable results for the prediction of temperature and velocity profiles, but some limitations of the method became apparent. These limitations are primarily related to the upper limit in mixture fraction space. In order to enhance the applicability of the LES-CMC model, this paper proposes a two-conditional moment approach to account for the existence of pre-evaporated fuel by introducing two sets of conditional moments based on different mixture fractions. The two-conditional moment approach is first tested for a non-reacting test case. The results indicate that the spray evaporation induces relatively large conditional fluctuations within a CMC cell, and one set of conditional moments might not be sufficient. The upper limit of the mixture fraction space is dynamically selected for the solution of the second set of conditional moments, and the corresponding CMC solution in a CFD cell is estimated by interpolation between the two conditional moments weighted by the amount of vapour emitted within the domain. The cell-filtered value is given by integration of the conditional moment across mixture fraction space using a bounded β-FDF for the distribution of the scalar. As a result, the fuel concentration profiles given by LES and the two-conditional moment approach are shown to agree well. Then, the two-conditional moment approach is applied to four different flame configurations. The comparison of LES cell quantities and conditionally averaged moments indicates that the two sets of conditional moments are necessary for accurate predictions in zones where gas phase mixture fraction is significantly increased by droplet evaporation within the computational domain. The unconditional temperature profiles clearly show that the new approach improves the predictions of mean temperature especially along the centerline. Also, the better predictions of the temperature field improve the accuracy of the predicted mean axial droplet velocities. Overall, good agreement with the experimental results is found for all four cases, and the methodology is shown to be applicable to flames with a relatively wide range of fuel vapour concentrations.