A multiphase SPH framework for solving the evaporation and combustion process of droplets

Abstract

Purpose This paper aims to introduce a two-dimensional smoothed particle hydrodynamics (SPH) framework for simulating the evaporation and combustion process of fuel droplets. Design/methodology/approach To solve the gas–liquid two-phase flow problem, a multiphase SPH method capable of handling high density-ratio problems is established. Based on the Fourier heat conduction equation and Fick’s law of diffusion, the SPH discrete equations are derived. To effectively characterize the phase transition problem, inspired by volume of fluid method, the concept of liquid phase mass fraction of the SPH particles is proposed. The one-step global reaction model of n-hexane is used for the vapor combustion. Findings The evaporation and combustion process of single droplet conforms to the law. The framework works out well when the evaporation of multiple droplets involves coalescence process. Three different kinds of flames are observed in succession in the combustion process of a single droplet at different inflow velocity, which agree well with the results of the experiment. Originality/value To the best of the authors’ knowledge, this is the first computational framework that has the capability to simulate evaporation and combustion with SPH method. Based on the particle nature of SPH method, the framework has natural advantages in interface tracking.

An incompressible smoothed particle hydrodynamics‐finite volume method coupling algorithm for interface tracking of two‐phase fluid flows

“…The interface curvature $$$ \kappa $$$ is calculated by $$$$ \kappa =-\left(\nabla \cdot \hat{\boldsymbol{n}}\right), $$$$ and the unit normal is derived from normal vector $$$$ \hat{\boldsymbol{n}}=\frac{\boldsymbol{n}}{\mid \boldsymbol{n}\mid }. $$$$ The component of normal vector n can be solved by the discretization formulation of SPH method, 77 as follows $$$$ {n}_{\alpha i}=\left[\sum \limits_{j=1}^N\left({\overline{c}}_j-{\overline{c}}_i\right){\nabla}_{i,\beta }{W}_{\mathrm{ij}}\frac{m_j}{\rho_j}\right]{\left[\sum \limits_{j=1}^N\left({r}_j^{\alpha }-{r}_i^{\alpha}\right){\nabla}_{i,\beta }{W}_{\mathrm{ij}}\frac{m_j}{\rho_j}\right]}^{-1}, $$$$ $$$$ {\overline{c}}_i=\sum \limits_j\frac{m_j}{\rho_j}{c}_j{W}_{\mathrm{ij}}, $$$$ …”

“…The component of normal vector n can be solved by the discretization formulation of SPH method, 77 as follows…”

The simulation of droplet impact on liquid film evaporation in horizontal falling film evaporator based on smoothed particle hydrodynamics

“…Here r is the fluid density, v is the fluid velocity, p is the fluid pressure, g is the gravitational acceleration, m is the dynamic viscosity, f s is the surface tension, T is the temperature, h v is the latent heat of vaporization, m"' is the volumetric mass evaporation rate, C p is the specific heat at constant pressure, OE is the thermal conductivity, Y is the vapor mass fraction and D is the mass diffusivity of the vapor. Noted that the energy equation does not consider the heat energy produced by viscous dissipation because of the relatively small magnitude HFF 34,6 Turns, 2012). The time step Dt is determined by advection constraint Dt # CFLh/c.…”

Numerical simulation of drop deformation under simple shear flow of Giesekus fluids by SPH

“…One of the most promising meshless methods is the smoothed particle hydrodynamics method (SPH) (Kulasegaram et al , 2004; Aly et al , 2022). The SPH demonstrates its capabilities for multiphase flow simulations (Grenier et al , 2009; Aly, 2015; Fonty et al , 2019; Wang et al , 2020; Saghatchi et al , 2020; Rahmat and Yildiz, 2021). The performed simulations are not limited to Newtonian cases but include non-Newtonian ones (Ren et al , 2012; Zainali et al , 2013; Sadeghy and Vahabi, 2016).…”