We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient EFT-based two-fluid Navier-Stokes solver, using an algebraic VoF method for the interface representation, and extended with the transport equations of thermal energy and vaporized liquid mass for the single-component evaporating liquid in an inert gas. The conservation of vaporizing liquid and computation of the interfacial mass flux are performed with the aid of a reconstructed signed-distance field, which enables the use of well-established methods for phase change solvers based on level-set methods. The interface velocity is computed with a novel approach that ensures accurate mass conservation, by constructing a divergence-free extension of the liquid velocity field onto the entire domain. The resulting approach does not depend on the type of interface reconstruction (i.e. can be employed in both algebraic and geometrical VoF methods). We extensively verified and validated the overall method against several benchmark cases, and demonstrated its excellent mass conservation and good overall performance for simulating evaporating two-fluid flows in two and three dimensions.

Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics are neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases. 

We perform interface-resolved simulations of finite-size evaporating droplets in wealdy compressible homogeneous shear turbulence. The study is conducted by varying three dimensionless physical parameters: the initial gas temperature over the critical temperature T-g,T-0/T-c, the initial droplet diameter over the Kolmogorov scale d(0)/eta and the surface tension, i.e. the shear-based Weber number, We(S). For the smallest We(S), we first discuss the impact on the evaporation rate of the three thermodynamic models employed to evaluate the gas thermophysical properties: a constant property model and two variable-properties approaches where either the gas density or all the gas properties are allowed to vary. Taking this last approach as reference, the model assuming constant gas properties and evaluated with the '1/3' rule is shown to predict the evaporation rate better than the model where the only variable property is the gas density. Moreover, we observe that the well-known Frossling/Ranz-Marshall correlation underpredicts the Sherwood number at low temperatures, T-g,T-0/T-c = 0.75. Next, we show that the ratio between the actual evaporation rate in turbulence and the one computed in stagnant conditions is always much higher than one for wealdy deformable droplets: it decreases with T-g,T-0/T-c without approaching unity at the highest T-g,T-0/T-c considered. This suggests an evaporation enhancement due to turbulence also in conditions typical of combustion applications. Finally, we examine the overall evaporation rate and the local interfacial mass flux at higher Wes, showing a positive correlation between evaporation rate and interfacial curvature, especially at the lowest T-g,T-0/T-c.

We propose an analytical model to estimate the interface temperature $\Theta_{\Gamma}$ and the Nusselt number $Nu$ for an evaporating two-layer Rayleigh-B\'enard configuration in statistically stationary conditions. The model is based on three assumptions: (i) the Grossmann-Lohse theory for thermal convection can be applied on the liquid and gas layers separately, (ii) the vapour content in the gas can be taken as the mean value at the gas-liquid interface and (iii) the bulk gas temperature can be determined neglecting the contributions of the thermal boundary layers. The resulting model can accommodate non-Oberbeck-Boussinesq effects in the liquid and the gas phases, as well as the variation of the liquid height due to evaporation. To obtain a simplified scaling between $Nu$ and the Rayleigh number $Ra$, we specify the model for the case of an Oberbeck-Boussinesq liquid and a gas phase with uniform properties except for the gas density and the vapour diffusion coefficient, which are functions of thermodynamic pressure, local temperature and vapour composition. We validate this simplified setting using direct numerical simulations for $Ra=10^6, 10^7$ and $10^8$ and for four values of the temperature differential $\varepsilon=0.05,0.10,0.15$ and $0.20$, which modulates the change of state variables in the gas layer. The proposed model agrees very well with the numerical simulations in the entire range of $Ra-\varepsilon$ investigated.

This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In contrast to the classical conservative four-equation model formulation, the adopted set of equations features volume fraction, temperature, velocity and pressure as the primary variables. The model includes the effects of viscosity, surface tension, thermal conductivity and gravity, and has the ability to incorporate complex equations of state. Additionally, a Gibbs free energy relaxation procedure is used to model mass transfer. A key characteristic of the proposed methodology is the use of high performance and scalable solvers for the solution of the Helmholtz equation for the pressure, which drastically reduces the computational cost compared to analogous density-based approaches. We demonstrate the capabilities of the methodology to simulate flows with large density and viscosity ratios through extended verification against a range of different test cases. Finally, the potential of the methodology to tackle challenging phase change flows is demonstrated with the simulation of three-dimensional nucleate boiling. <comment>Superscript/Subscript Available</comment

We present the Fluid Transport Accelerated Solver, FluTAS, a scalable GPU code for multiphase flows with thermal effects. The code solves the incompressible Navier-Stokes equation for two-fluid systems, with a direct FFT-based Poisson solver for the pressure equation. The interface between the two fluids is represented with the Volume of Fluid (VoF) method, which is mass conserving and well suited for complex flows thanks to its capacity of handling topological changes. The energy equation is explicitly solved and coupled with the momentum equation through the Boussinesq approximation. The code is conceived in a modular fashion so that different numerical methods can be used independently, the existing routines can be modified, and new ones can be included in a straightforward and sustainable manner. FluTAS is written in modern Fortran and parallelized using hybrid MPI/OpenMP in the CPU-only version and accelerated with OpenACC directives in the GPU implementation. We present different benchmarks to validate the code, and two large-scale simulations of fundamental interest in turbulent multiphase flows: isothermal emulsions in HIT and two-layer Rayleigh-Bénard convection. FluTAS is distributed through a MIT license and arises from a collaborative effort of several scientists, aiming to become a flexible tool to study complex multiphase flows.