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

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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> , 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 parabolic 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.