Edoardo Cipriano

    I am a PhD student at Politecnico di Milano, with the CRECK Modeling group. During my PhD, I study the evaporation and combustion of fuel droplets using multiphase CFD. Here you can find my codes. If you would like to discuss a related topic, feel free to email me:


    For a detailed description of the phase change models in this sandbox, please refer to:


    Edoardo Cipriano, Abd Essamade Saufi, Alessio Frassoldati, Tiziano Faravelli, Stéphane Popinet, and Alberto Cuoci. Multicomponent Droplet Evaporation in a Geometric Volume-Of-Fluid Framework. Journal of Computational Physics, 507:112955, June 2024. [ DOI | http | .pdf ]


    Edoardo Cipriano, Alessio Frassoldati, Tiziano Faravelli, Stéphane Popinet, and Alberto Cuoci. A low-Mach volume-of-fluid model for the evaporation of suspended droplets in buoyancy-driven flows. working paper or preprint, May 2024. [ http | .pdf ]

    Source Codes

    The main modules implemented in my sandbox are reported below. The arrow points to the relative tests, where available.

    Phase Change

    • evaporation.h: main phase change module, it must be included in every phase change simulation, together with one of the following phase change mechanisms.
    • fixedflux.h: constant evaporation rate per unit of surface.
    • temperature-gradient.h: evaporation driven by a temperature gradient between the interface temperature and the neighboring phases (suitable for boiling).
    • species-gradient.h: evaporation driven by a gradient of chemical species mass fractions (suitable for isothermal pure evaporation).
    • multicomponent.h: evaporation of a mixture in a non-isothermal environment.
    • multicomponent-varprop.h: extension of the multicomponent model including variable thermodynamic and transport properties.


    • opensmoke.h: interface for the OpenSMOKE++ library, which allows detailed kinetics to be managed.
    • opensmoke-properties.h: use the OpenSMOKE++ library for the calculation of mixture properties.
    • chemistry.h: solve the combustion reactions using the OpenSMOKE++ interface.
    • reactors.h: implementation of the ODE system of equations describing batch reactors.
    • spark.h: activate the chemical reactions using a spark, described as a local increase of temperature (→ spark.c).
    • radiation.h: radiation models for combustion simulation (→ radiation.c).

    Ghost Fluid Method


    • aslam.h: extrapolate a tracer field across the interface using constant or linear extrapolation (based on the levelset approach) (→ aslam.c, aslamvof.c).
    • fsolve-gsl.h: high-level interface to gsl_multiroots, for the solution of non-linear systems of equations (→ fsolve-gsl.c).
    • centripetal.h: suspension of a liquid droplet using a centripetal force applied on the liquid volume (→ centripetal.c).
    • icentripetal.h: suspension of a liquid droplet using a centripetal force applied just on the interface (→ icentripetal.c).
    • pinning.h: suspension of a liquid droplet setting the boundary conditions for the height-function (→ pinning.c).
    • balances.h: automatic calculation of global mass balances.


    The simulation setup for phase change problems, with automatic generation of the results and other test cases, are reported below.

    Phase Change

    • fixedflux.c: evaporation of a droplet with a constant evaporation rate.
    • fixedfluxmac.c: evaporation of a droplet with a constant evaporation rate, using the mac solver.
    • fixedbubblevelocity.c expansion of a bubble with a constant evaporation rate using the velocity potential approach, focusing on the velocity field.
    • stefanproblem.c: evaporation of a liquid plane induced by a temperature gradient.
    • suckingproblem.c: planar boiling configuration.
    • scrivenproblem.c: growth of a bubble in a superheated liquid domain.
    • bubblerisengrowth.c: growth of a bubble in a superheated liquid domain, in normal gravity conditions.
    • filmboiling.c: a possible film boiling configuration.
    • bubblecontact.c: growth of a nucleated bubble on a solid wall, with a fixed contact angle.
    • epsteinplesset.c: isothermal evaporation of a pure droplet in diffusive conditions.
    • pureisothermal.c: isothermal evaporation of a pure droplet.
    • c7pathak.c: evaporation of a n-heptane droplet in a non-isothermal environment.
    • staticbi.c: isothermal evaporation of a binary droplet with different volatilities.
    • forcedbi.c: isothermal evaporation of a binary droplet with different volatilities in forced convective conditions.
    • interfaceregression.c: test for the interface regression velocity, in order to better visualize its behavior.

    Phase Change with Variable-Properties

    • expansion.c: thermal expansion of a liquid droplet.
    • microgravity.c: evaporation of a pure droplet in microgravity conditions.
    • normalgravity.c: evaporation of a pure droplet in buoyancy-driven flows.



    The following list reports known weakness and future steps for the models implemented in my sandbox:

    1. Smoothen velocity field: the point source term in the Poisson equation, related with the density changes in phase change simulations, can lead to oscillations in the velocity field, that disappear using the mac solver. A proper strategy to avoid this phenomena should be developed, without smearing the source term in order to not modify the intensity of the velocity jump.

    2. Velocity Potential: this is the most elegant way to obtain a divergence-free velocity field in phase change simulations. However, this implementation does not work well for strong density ratio or strong vaporization rates, and it should be improved. At the current state, it works when the velocity of the system is higher than the Stefan flow.

    3. Embedded Boundaries: the phase change model cannot be combied with embedded solids yet. This extension should not be too difficult.