The external structure of the spray-flamelet can be described using the Schvab–Zel'dovich–Liñan formulation. The gaseous mixture-fraction variable as function of the physical space, $Z\left(x_i\right)$, typically employed for the description of gaseous diffusion flames leads to non-monotonicity behaviour for spray flames due to the extra fuel supplied by vaporisation of droplets distributed into the flow. As a result, the overall properties of spray flames depend not only on Z and the scalar dissipation rate, χ, but also on the spray source term, $S_v$. We propose a new general coordinate variable which takes into account the spatial information about the entire mixture fraction due to the gaseous phase and droplet vaporisation. This coordinate variable $Z_C\left(x_i\right)$ is based on the cumulative value of the gaseous mixture fraction $Z\left(x_i\right)$ and is shown to be monotonic. For pure gaseous flow, the new cumulative function, $Z_C$, yields the well-established flamelet structure in Z-space. In the present manuscript, the spray-flamelet structure and the new equations for temperature and mass fractions in terms of $Z_C$ are derived and then applied to the canonical counterflow configuration with potential flow. Numerical results are obtained for ethanol and methanol sprays, and the effect of Lewis and Stokes numbers on the spray-flamelet structure is analysed. The proposed formulation agrees well when mapping the structure back to physical space thereby confirming our integration methodology.

喷洒式小火苗的外部结构可以使用Schvab–Zel'dovich–Liñan配方进行描述。气体混合物的分数随物理空间而变化，$ž（X_{\mathrm{一世}}）$通常用于描述气态扩散火焰的气体，由于分布在气流中的液滴的汽化而提供了额外的燃料，因此导致喷雾火焰具有非单调性。结果，喷射火焰的整体特性不仅取决于Z和标量耗散率χ，还取决于喷射源项，${\mathrm{小号}}_v$。我们提出了一个新的通用坐标变量，该变量考虑了由于气相和液滴蒸发而导致的整个混合物组分的空间信息。这个坐标变量${ž}_C（X_{\mathrm{一世}}）$ 基于气体混合物分数的累积值 $ž（X_{\mathrm{一世}}）$并且显示为单调的。对于纯气体流，新的累积函数${ž}_C$，在Z空间中产生完善的小火焰结构。在本手稿中，喷雾火焰结构以及温度和质量分数的新方程式${ž}_C$推导得出这些值，然后将其应用于具有潜在流的规范逆流配置。获得了乙醇和甲醇喷雾的数值结果，并分析了路易斯和斯托克斯数对喷雾火焰结构的影响。当将结构映射回物理空间时，建议的公式非常吻合，从而确认了我们的集成方法。