Solutions of the spray flamelet equations in a non-monotonic mixture fraction space

TL;DR

This paper introduces an analytical method to determine the maximum mixture fraction in spray flames, enabling more effective solutions of the spray flamelet equations in complex combustion scenarios.

Contribution

An analytical solution for the maximum mixture fraction in spray flames with quadratic evaporation profiles is proposed, enhancing the ability to solve spray flamelet equations.

Findings

The approach accurately determines $Z_{max}$ in tested cases.

The method effectively covers the solution space of spray flamelet equations.

Flexibility in evaporation profile definition allows for future parametric studies.

Abstract

Solving the spray flamelet equations in composition space is very challenging, which is attributable to the fact that the maximum value of the mixture fraction, $Z_\mathrm{max}$, is a priori unknown in such flames. In this work, an analytical solution for this quantity is proposed, which allows its determination in spray flames subject to imposed quadratic evaporation profiles. It is then illustrated how the proposed approach allows to effectively cover the solution space of the spray flamelet equations. The employed strategy works very well for the considered cases and the generality of the evaporation profile definition provides flexibility for explorations of other parametric choices in the future.