Session ZC20: Numerical Simulation of Multiphase Flows

Verification of PLAID Phase Change Algorithm Applied to Direct Numerical Simulation of Condensation Phenomena

A new algorithm developed for flexible, regime-independent phase change simulations has been developed and is undergoing verification. The Parallel Lattice Algorithm for Interphase Dynamics (PLAID) is designed to resolve spatial variations in phase change rate within the Level-Set interface tracking framework. It has been implemented in the massively parallel multiphase CFD flow solver PHASTA and represents a major advance in versatility over the previous phase change algorithm implementation. The previous phase change algorithm was a Lagrangian based approach that was intended for application to bubbly flows. As such, each vapor mass was treated independently and assumed to be spherical. PLAID makes no assumptions on the shape of the interface and offers a purely Eulerian approach to phase change phenomena. It works by overlaying a coarse cartesian lattice on the computational mesh and computes the net heat flux toward the interface independently within each lattice cell. PLAID has previously undergone verification for simple boiling, however robustness demands that verification for the reverse process is completed as well. In this work the application of PLAID to simple condensation cases with known solutions is presented, including the Stefan and Scriven problems for interphase transfer. Additionally, the effects of mesh and lattice refinement on the results are investigated.   

Simulating mass transfer with interface capturing schemes

Interface-capturing schemes with a non-conservative volume fraction advection equation have been used in various multi-component problems, such as bubble collapse and aerodroplet breakup. For some flows, such as fuel droplet combustion in detonation waves, mass transfer (diffusion) in the gaseous phase requires source terms in the species continuity equations. Such source terms are described using mass fractions rather than volume fractions. Thus, a consistent framework relating the mass and volume fraction equations must be derived that applies to both single-fluid and mixture regions. In this preliminary work, we derive a consistent source term for the volume fraction equation in our interface-capturing model. While this procedure is expected to work with any source term, it is tested with mass transfer problems via binary diffusion using the stiffened gas equation of state.   

Simulations of High-Speed Droplet Impingement with a Dispersed Phase Model

Accurately simulating high-velocity droplet impingement at hypersonic speeds is a challenging task as it creates extreme flow conditions characterized by (likely) negative to gigapascal pressure regimes. Another aspect that has drawn less attention is the challenge of dealing with the different phases that are created during impact, notably not only liquid, vapor and gas phases. It has been theorized that, during impingement, the ejected mass atomizes, generating a dispersed phase which alters the fluid dynamic behavior drastically. Characterization of each individual micro-droplet in the dispersed phase is not computationally feasible, hence a specific variant of the 7-equation model, the dense-dilute model by Saurel et al. 2017, has been implemented and validated for shock-liquid/dispersed phase interactions and proposed as a way to model high-speed droplet impingement. A hypervelocity droplet impingement simulation is showcased, demonstrating how velocity non-equilibrium is of paramount importance to accurately capture the splashing dynamics observed in experiments.   

A Variable Density and Viscosity Solver for Acoustic Streaming

Acoustofluidics, the merger of acoustics and microfluidics, has shown significant promise for lab-on-a-chip applications. Fluid response in acoustofluidic systems is characterized by a harmonic component and a time-averaged acoustic streaming component. Typical numerical models either consider fluid-only systems or assume the immersed objects (e.g., bubbles, cells, particles, etc.) to have same density/viscosity as the surrounding fluid.), which omits interesting physics concerning acoustic response of variable density and viscosity media.

 

We present a numerical formulation that considers spatially and temporally varying density and viscosity in an acoustofluidic system. Using a perturbation approach, we split the problem into a harmonic first-order and a second-order acoustic streaming system. The former is a hyperbolic system solved using a sparse direct solver while the latter resembles a steady low-Mach Stokes system, with forcing terms arising from the first-order solution. The second-order system is solved using the FGMRES solver with a matrix-free implementation and a projection method-based preconditioner. In both first- and second-order systems, we achieve O(2) accuracy. Furthermore, we adapt the variable viscosity and density formulation to model rigid immersed objects in acoustofluidic flows via a Brinkman penalization method and provide the details of implementation within the open-source Immersed Boundary Adaptive Mesh Refinement (IBAMR) framework.   

Vortex-Damping Outflow Treatment for Multiphase Flows Simulations with Sharp Jumps and Low Weber Numbers

Outflow boundaries play an important role in multiphase fluid dynamics simulations that involve transition between liquid and vapor phases. These flows are dominated by low Weber numbers and a sharp jump in pressure, velocity, and temperature. Inadequate treatment of these jumps at the outlet generates undesirable fluid disturbances that propagate upstream and lead to instabilities within the computational domain. To mitigate these disturbances, we developed a forcing term that can be applied to incompressible Navier-Stokes equations to enforce stability in the numerical solution. The forcing term acts as a damping mechanism to control vortices that are generated by droplet/bubbles in multiphase flows and is designed to be a general formulation that can be coupled with a fixed pressure outflow boundary condition to simulate a variety of multiphase flow problems. We demonstrate its applicability to simulate pool and flow boiling problems, where bubble-induced vortices during evaporation and condensation present a challenge at the outflow. Validation and verification cases are chosen to quantify accuracy and stability of the proposed method in comparison to established benchmarks and reference solutions, along with detailed performance analysis for three-dimensional simulations on leadership supercomputing platforms. Computational experiments are performed using Flash-X, which is a composable open-source software instrument designed for multiscale fluid dynamics simulations on heterogeneous architectures.   

Long-short-term memory (LSTM) prediction of marine oil spreads

We assess the feasibility of utilizing deep learning, particularly the Long Short-Term Memory (LSTM) algorithm, for predicting the spreading of low-sulfur fuel oil (LSFO) under accidental marine spills. Training data was generated through numerical simulations of various artificial geometries, incorporating different configurations of islands and shorelines, as well as varying inlet wind speeds (2.0–8.0 m/s). We performed a three-phase simulation by assuming oil as a liquid at a scale of several hundred meters. Based on these results, we extended the scale to kilometers by assuming oil particles. For simulating the spread of oils over O(10²) km scales, the volume of fluid and discrete phase model were utilized. Key kinematic variables, such as particle location, particle velocity, and water velocity, were collected as input features for the LSTM model. The predicted LSFO spreading pattern showed a strong correlation with the simulation results, exhibiting less than 10% mean absolute error for the untrained data. The model was further validated by applying it to the actual Wakashio LSFO spill accident together with real geometric and weather data, thereby confirming the practical feasibility of the proposed model.   

Effect of Surfactants Preferential Solubility on Droplets Morphology in Turbulence

This study examines soluble surfactants in droplet-laden turbulence using direct numerical simulations of the Navier-Stokes equations coupled to the Phase Field Method in a two-order-parameter formulation. The Cahn-Hilliard equations, where diffusion is driven by a Ginzburg-Landau free energy functional, govern the transport of the parameters. Despite theoretical expectations of symmetry in oil-in-water (O/W) and water-in-oil (W/O) dispersions with matching densities and viscosities, experiments reveal asymmetries attributed to surface-active contaminants that dissolve preferentially in the aqueous phase.

Simulations with droplets matching the carrier fluid's density and viscosity introduce differential solubility by adding a non-symmetrical energy contribution to the surfactant diffusion functional, penalizing dissolution in one phase. Two scenarios are explored: Carrier Preferential Surfactant (CPS), where surfactant dissolution is penalized in the continuous phase, and Droplets Preferential Surfactant (DPS), where it is penalized in the dispersed phase. Results show that surfactant distribution at the interface varies with solubility preference, with higher concentrations in the DPS scenario. This is due to restricted surfactant desorption from the interface in the CPS scenario. Additionally, droplet morphology changes with solubility preference due to differences in surfactant coverage.