Unsteady solutions of the spray flamelet equations

Abstract

Solutions of the spray flamelet equations reported in the literature during the last decade have been limited to very specific situations presenting steady evaporation profiles only. In contrast, intrinsically unsteady interactions between the liquid and gas phases have received little attention so far. In this work, the spray flamelet equations are closed by means of a Lagrangian description of the liquid phase in mixture fraction space, which allows solving them for unsteady situations. The resulting formulation is then employed to conduct parametric analyses of the effects of initial droplet radius and velocity variations on ethanol/air non-premixed gas flamelets perturbed by sprays generated with different droplet injection strategies. Special emphasis is given to the differences between continuous and discontinuous droplet injection. The results illustrate how the latter can considerably increase the temperature and stability of flamelet structures, provided the spray parameters are appropriately selected.

Figures (8)

• Figure 1: Schematic of the pathways of droplet size groups dynamic in flamelet space over time. The thickness of the lines represents the instantaneous droplet radius.
• Figure 2: Profiles of $R/R_0$, $\dot{S}_v$ and $\chi$ for flamelets C$_0$, C$_1$ and C$_2$. The vertical gray line represents $Z_\mathrm{st}\approx0.1$.
• Figure 3: Temperature (left) and scalar dissipation rate (right) at stoichiometry, over time for flamelets C$_0$, C$_1$ and C$_2$.
• Figure 4: Budgets of the $g_Z$ equation, Eq. \ref{['eq:gz']}, for flamelets C$_1$ (left), and C$_2$ (right) over time at stoichiometric point. For the readers' convenience the equation is shown at the top of the figure.
• Figure 5: Budgets of the decomposition of the strain and diffusion terms, Eq. \ref{['eq:diff-deco']} (left), and the evaporation-related term, Eq. \ref{['eq:evap-deco']} (right), for flamelet C$_2$ over time at stoichiometric point.