Evaporation of a deformable droplet under convection

TL;DR

The paper tackles evaporation of deformable droplets in convective flows by performing high-fidelity interface-resolved simulations using the IB/FT method and benchmark-ing two low-order models, the classical and Abramzon–Sirignano models, across $20\le Re\le200$, $1\le B_M\le15$, and $1\le We\le9$. It demonstrates that Stefan flow thickens the boundary layer and expands the wake, significantly altering evaporation patterns, especially in the wake where local $Sh$ is poorly predicted by simplified models. Deformation enhances evaporation in proportion to surface area changes, with the Abramzon–Sirignano model more robust under convection but deteriorating for highly deformed droplets; the classical model consistently overpredicts. The work highlights the pivotal role of wake and deformation in spray combustion contexts and suggests integrating surface-area effects into reduced models, while also noting the limitations of axisymmetric simulations and the need for 3D studies.

Abstract

Evaporation of a deformable droplet under convection is investigated and the performance of the classical and Abramzon-Sirignano (A-S) models is evaluated. Using the Immersed Boundary/Front-Tracking (IB/FT) method, interface-resolved simulations are performed to examine droplet evaporation dynamics over a wide range of Reynolds ($20 \leq Re \leq 200$), Weber ($0.65 \leq We \leq 9$), and mass transfer ($1 \leq B_M \leq 15$) numbers. It is shown that flow in the wake region is greatly influenced by the Stefan flow, as higher evaporation rates lead to earlier flow separation and a larger recirculation zone behind the droplet. Under strong convection, the models fail to capture the evaporation rate, especially in the wake region, which leads to significant discrepancies compared to interface-resolved simulations. Droplet deformation greatly influences the flow field around the droplet and generally enhances evaporation, but the evaporation rate remains well correlated with the surface area. The A-S model exhibits reasonably good performance for a nearly spherical droplet but its performance deteriorates significantly and generally underpredicts the evaporation rate as droplet deformation increases. The A-S model is overall found to outperform the classical model in the presence of significant convection.

Figures (23)

• Figure 1: A schematic illustration of the Lagrangian grid cast on the stationary Eulerian grid.
• Figure 2: Sketch of the computational domain and the boundary conditions used in simulations of droplet evaporation in a convective environment.
• Figure 3: Velocity vectors and streamlines (left portion), and mass fraction field (right portion) around a nearly spherical droplet ($We=0.65$) for Reynolds numbers of $Re\in[20,\;50,\; 100,\;200]$ at the mass transfer number of $B_M=5$. Domain: $4d_0 \times 8d_0$; Grid: $512 \times 1024$.
• Figure 4: Velocity vectors (left portion) and mass fraction (right portion) fields around a nearly spherical droplet ($We=0.65$) for the no-Stefan flow (NSF, top row), the moderately evaporating ($B_M=5$, middle row) and the strongly evaporating ($B_M=15$, bottom row) cases at $Re= 50$ (left column), $Re=100$ (middle column) and $Re=200$ (right column). Color bars indicate values of mass fraction. Domain: $4d_0\times 8d_0$; Grid: $512\times 1024$.
• Figure 5: Axial velocity profiles along the symmetry axis behind the droplet at $Re = 100$ and mass transfer numbers of $B_M\in[2,\; 5,\; 15]$. Domain: $4d_0\times 8d_0$; Grid:$512\times 1024$.