Session G35: Multiphase Flows: Computational Methods II

A novel phase field method for droplet freezing

Simulations of dynamic freezing of liquid droplets have applications in both natural and industrial processes. In this work, a novel phase field method--based on the accurate conservative diffuse interface method (Jain et al., J. Comput. Phys., 111529, 2022)--is presented for the simulations of droplet freezing and melting. This method is compared against the analytical solutions and the state-of-the-art Allen-Cahn model in two dimensions (2D) based on computational cost, conservation behavior, and accuracy using Stefan problems. Additionally, an order estimate for the interface kinetic coefficient--that is typically arbitrarily chosen--is proposed and verified. A new semi-implicit, iterative time advancement method is presented, which results in a constant coefficient pressure Poisson system for variable density incompressible flows. This method leads to a consistent formulation for the pressure projection method in the presence of phase change. Finally, 2D simulations of droplet impact on a wall and subsequent freezing will be presented.   

Consistent and conservative numerical approach with Phase-Field mechanism for compressible N-phase flows

Multiphase flows including shocks are ubiquitous in natural phenomena and engineering processes, while reliable numerical approaches to accurately simulate problems with an arbitrary number of phases are still in demand. Simply repeating numerical approaches for two-phase flows to individual phases of N-phase flows produces unphysical behaviors that are not observed in two-phase simulations, such as fictitious phases, local voids, or overfilling, which are sources of numerical instability. To resolve the issue, a consistent and conservative approach is developed to solve the N-phase Euler/Phase-Field model. The proposed method is general in the sense that it admits N different phases and is not restricted to a specific Phase-Field formulation. Not only is the volume fraction bounded and the mass non-negative, the volume fractions also sum up to unity, preventing the production of fictitious phases, local voids, or overfilling. Kinematic, mechanical, and thermal equilibria are maintained across material interfaces. High-order implementation of the approach is straightforward. The Phase-Field mechanism produces controllable interface thickness, thus effectively preventing the numerical mixing of different phases due to numerical diffusion in shock-capturing schemes. Various numerical examples are provided to demonstrate the approach.   

A difference-free conservative phase-field method for two-phase flows

We propose an innovative difference-free scheme that combines the one-fluid lattice Boltzmann method (LBM) with the conservative phase-field (CPF) LBM to effectively solve large-scale two-phase fluid flow problems. The difference-free scheme enables the derivation of the derivative of the order parameter and the normal vector through the moments of the particle distribution function (PDF). We further incorporate the surface tension force in a Korteweg stress form into the momentum equations by modifying the equilibrium PDF to eliminate the divergence operator. Consequently, the entire computation process, executed without any inter-grid finite difference formulation, demonstrates an improved efficiency, making it an ideal choice for high-performance computing applications. We conduct simulations of a single static droplet to evaluate the intensity of spurious currents and assess the accuracy of the scheme. We then introduce the density or viscosity ratio and apply an external body force to model the Rayleigh-Taylor instability and the behavior of a single rising bubble, respectively. Finally, we employ our method to study the phenomenon of a single bubble breaking up in a Taylor-Green vortex. The comparison between the difference-free scheme and the finite difference method demonstrates the scheme's capability to yield accurate results. Furthermore, based on the performance evaluation, the current scheme exhibits an impressive 47% increase in efficiency compared to the previous method.   

Numerical uncertainty due to parallelization in an unsteady cloud cavitation

Cavitation is the formation of vapor bubbles in a liquid when the pressure drops below the vapor pressure of the liquid. This can happen when a liquid is accelerated to high speeds, such as in the impeller of a pump or the propeller of a boat. Experimental studies of cavitation can provide valuable insights into the flow dynamics, but they can be expensive and time-consuming. Numerical simulations are a more economical way to study cavitation, and they can be used to obtain preliminary designs for devices that are susceptible to cavitation damage. In this study, cloud cavitation was studied in a venturi geometry using the incompressible solver from OpenFOAM. Due to the presence of different bubble sizes and time scales, the homogeneous transport equation model was used to reduce the computational effort. The Merkle model was used to model the phase transition due to cavitation. The flow is very complex in the presence of cloud cavitation, and there are many uncertainties involved in the calculations. One source of uncertainty is unavoidable due to parallelization, which is needed to decompose the domain to reduce simulation time. It was observed that the shedding behavior varies when different numbers of processors are used. This study shows that the uncertainty coming from parallelization can be reduced by increasing the sampling rate.   

Unstructured Finite-Volume Arbitrary Lagrangian / Eulerian Interface Tracking computational framework for incompressible two-phase flows with surfactants

We present an open-source computational framework that implements the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian (ALE) Interface Tracking method for incompressible two-phase flows with surfactants. The framework implements the Interface Tracking ALE method for incompressible two-phase flows using a segregated solution algorithm for solving coupled Navier-Stokes equations with interfacial jump conditions. The Finite Area method discretizes transport equations on curved and evolving fluid interfaces. The open-source implementation as an OpenFOAM module also contains the Sub-Grid-Scale (SGS) model for handling extremely narrow boundary layers of passively transported scalars with very small diffusivity. The SGS model significantly reduces resolution requirements for species transport across the fluid interface. The surface and bulk transport of surfactants and the SGS model are verified using (semi-)analytical verification cases. We also discuss complex setups, e.g., of a rising bubble at high Peclet-numbers under the influence of soluble surfactants.