A Hybrid Immersed-Boundary/Front-Tracking Method for Interface-Resolved Simulation of Droplet Evaporation

TL;DR

This work presents a hybrid sharp-interface immersed-boundary/front-tracking framework for interface-resolved evaporation in incompressible multiphase flows. By enforcing a Dirichlet boundary condition for the mass fraction at the droplet surface through an image-point/ghost-cell scheme, it achieves overall second-order spatial accuracy in mass transfer while preserving a sharp interface. The method is validated against the $d^2$-law and wet-bulb temperature data, then applied to evaporating droplets in convective environments using a moving reference frame to examine deformation effects on local and average Sherwood numbers, comparing with Abramzon–Sirignano and classical models. The results demonstrate grid-converged, high-fidelity predictions of evaporation dynamics and Stefan-flow effects, indicating the approach as a robust tool for high-fidelity spray combustion and related multiphase applications.

Abstract

A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species mass fraction and energy equations in the entire computational domain with appropriate jump conditions at the interface. An image point and ghost cell methodology is coupled with a front-tracking method to achieve an overall second order spatial accuracy for the mass fraction boundary condition on the droplet surface. The immersed-boundary method is also extended to simulate mass transfer from a solid sphere in a convective environment. The numerical method is first validated for the standard benchmark cases and the results are found to be in good agreement with analytical solutions. The method is shown to be overall second order accurate in space. Employing a moving reference frame methodology, the method is then applied to simulate evaporation of a deformable droplet in a convective environment and the results are compared with the existing evaporation models widely used in spray combustion simulations.

Figures (19)

• Figure 1: Effect of Stefan flow on the vapor mass fraction and flow fields around evaporating droplets including both nearly spherical and deforming cases.
• Figure 2: (a) A schematic representation of the Lagrangian grid cast on the stationary Eulerian grid. (b) The staggered grid arrangement used to solve the field equations.
• Figure 3: Schematic representation of the sharp-interface immersed-boundary methodology used to impose the species mass boundary condition at the interface. GP, BI and IP denote a ghost cell, a boundary-intercept point, and an image-point, respectively. The the image points denoted by 1 and 2 are located partially and totally in the bulk fluid cell, respectively.
• Figure 4: (a) The procedure to find the mass fraction gradient at the interface. (b) A schematic illustration of a front element and its length, $\Delta s_k$.
• Figure 5: Performance of the new restructuring procedure for the Lagrangian grid. The randomly initialized (black dots on left side) and uniformly restructured (red dots on right side) front marker points for various shapes. The solid blue lines show the prespecified interfaces.