Session J20: Multiphase Mixtures

Weathering process and spreading of low sulfur fuel oil (LSFO) on water surface

We investigated the weathering process (viscosity and rheological characteristics) of low sulfur fuel oil (LSFO) to understand its spreading dynamics on the water surface. First, we find that the viscosity dependency of LSFO on the temperature follows the William-Landel-Ferry (WLF) law. Then, through the emulsion test, we measured that the meso-stable emulsion, whose viscosity is 10-100 times larger than the normal condition, is achieved. On the other hand, the evaporation of LSFO is found to be so small that its effect on the properties is negligible in the tested conditions. In addition, we experimentally examined the spreading dynamics (e.g., the thickness of oil slick and spreading area, rate) of LSFO on the water surface in the circulating water bath, in which the wind speed, water temperature, and initial oil volume are controlled as 2-5 m/s, 5-25ºC, and 100-400 ml, respectively. The spreading speed rapidly increased after a critical viscosity (~ 500 cP) by the imbalance between the viscous retarding force and wind shear stress. Finally, based on the acquired weathering properties, we performed the numerical simulation with a length scale of hundred meters on the spreading of LSFO spills, which will help deal with the marine oil-spill accidents.

    

Drop coalescence simulation using phase field method with discrete exterior calculus discretization

We present two spherical drops coalescence simulations by using the phase field method with

discrete exterior calculus (DEC) discretization. Motivated by the fact that two spherical drops

coalescence phenomena are axisymmetric, we extend our previous work, DEC scheme for

2D two-phase incompressible Navier-Stokes equations (Wang et al., 2022), to axisymmetric

incompressible two-phase flow. In our simulation, two drops are stationary and touch each

other initially, and they coalesce rapidly, due to large interface curvature and surface tension

force in the neck region formed upon coalescence. Several drop coalescence simulations are

presented to investigate its interface evolution under various Ohnesorge numbers Oh. The

evolution of the drop neck radius R yields two well-known power-law scaling in viscous and

inertial regimes, respectively, and our simulations reproduce these two power-law scalings.

For the inertial regime (high Oh), the neck radius evolution has the 1/2 power-law scaling, and

the inertial regime transition to the viscous regime by increasing Oh, in which the neck radius

evolution has linear scaling.   

The Micro-Gravity Sediment Trap: Passive Filtration for Spacecraft Pumped Fluid Loops

A considerable number of thermal and environmental control systems aboard satellites and manned spacecraft, such as the International Space Station, are reliant upon pumped fluid loops (PFLs) for heat and mass transfer. However, recent research has discovered a high failure rate (~17%) of western world spacecraft PFLs in microgravity environments. This has precipitated research into debris and sedimentation removal from PFL systems. Active removal of debris from PFL systems requires the use of sieve type and/or porous filtration components. Over time, these components can become clogged with debris, ultimately incurring considerable cost in terms of pressure drop, which can significantly increase the risk of failure. The micro-gravity sediment trap (MGST) is a novel, high efficiency passive filtration device designed to [ideally] replace active filter components. Unlike active filters, MGST does not have orifices or bypass lines and as a result, has significantly lower pressure drops compared to active systems, has minimal risk of clogging, and can target similar particle size ranges. In addition, MGST is designed to be scalable according to the specifications of the PFL, i.e. modifications for increased or decreased flow rate, working fluid selection, and overall system size. In this current work, a combination of experimental and multiphase modeling analyses are used to quantitatively describe the performance of MGST as a filtration device.   

Numerical methods for phase separation of surface tension dominated immiscible fluid mixtures

Understanding the phase separation dynamics of immiscible fluid mixtures is of great interest for a variety of applications. Diffuse interface models based on minimizing a free energy functional are well established for describing the thermodynamics of such mixtures, however, they feature solutions with large gradients that introduce correspondingly large stresses when coupled with the Navier-Stokes equations. For a low Reynolds number, surface tension dominated flow, the coupled system requires integrating a convection dominated, nonlinear 4th order diffusion equation. Using spectral methods in space, we discuss strategies for accurate and efficient time integration of the stiff equations of motion and observe rich fluid dynamical structure when applied to droplet formation from two immiscible polymer solutions.   

Computational modeling of an egg yolk protein behavior at oil/water interface via atomistic and mesoscopic approaches.

Many food emulsions are stabilized by functional egg yolk biomolecules, which act as surfactants at the oil/water interface. Experimental studies on egg yolk emulsifying properties have been hindered due to the difficulty in isolating individual chemical species. Our work focuses on the molecular modeling of one of the most surface-active proteins from the egg yolk low-density lipoproteins, the so-called Apovitellenin I. We used two approaches to study several aspects of protein adsorption at the oil/water interface: Dissipative Particle Dynamics [1] and atomistic metadynamics simulations [2]. The goal is to outline the protein behavior as a surfactant, extracting the interfacial tension at increasing surface concentration. Results from both methods are in agreement with those of a similar well-known protein, the β-casein. A thermodynamic model of protein adsorption is used together with simulations to predict the surface state equation and adsorption isotherm of Apovitellenin I that are not experimentally measurable. The main finding is to show how different computational methods can be linked together to obtain a deeper understanding of this egg yolk protein behavior.   

A numerical scheme for treating viscous effects in three-fluid flows of Newtonian and non-Newtonian shear thinning fluids

Multi-fluid flows with Newtonian and non-Newtonian fluid interactions are encountered in many applications, including surfactant replacement therapy in prematurely born infants, bubbly flows, and wastewater treatment. Computational simulation of such complex fluid interaction requires solving additional constitutive equations to resolve the non-Newtonian fluid dynamics and capture the interactions with the Newtonian fluids. We present a novel numerical scheme for treating the viscous effects in three-fluid flows of two Newtonian fluids (liquid and gas) interacting with a shear thinning non-Newtonian liquid. In this work, the volume-of-fluid method is used to track fluid volumes, where an additional passive scalar is employed to distinguish between the Newtonian and non-Newtonian fluids. The non-Newtonian fluid viscosity is modeled by the Carreau-Yasuda equation. We demonstrate the accuracy of the proposed scheme and the overall flow solver performance using various test cases.   

Dynamics of chocolate fountains

We present a three-dimensional direct numerical simulation of a heated chocolate fountain using both dynamical and thermal properties of melted chocolate (60 C) flowing in an ambient atmosphere (20 C). We solve both the Navier-Stokes and the energy equation using a front-tracking-based multiphase method that accounts for both the Newtonian (ambient air) and Non-Newtonian (melted chocolate) fluids, and a direct forcing method technique for the rotational motion of a vertical Archimedes screw. Our numerical framework circumvents numerous meshing issues normally associated with constructing complex geometries within typical computational fluid dynamics packages. The considered device in the present work is composed of a static (motionless) chocolate fountain structure with a fast-rotating vertical Archimedes Screw in it; both of these are constructed via a module that defines solid objects by means of distance functions, which are positive for the fluid part and negative for the solid part. The construction combines primitive objects, such as cylinders, planes, and ellipsoids and combined with simple geometrical operations such as union and intersection. Finally, within a single simulation, we will highlight the multitude of classical flows such as falling film, interfacial singularities, and coiling liquid films.   

Probability distribution of ages of the nearest particle pairs

We define the age of a nearest particle pair as the difference between current time and the time when the particles becomes the nearest pair. Such defined age varies from pair to pair. A statistical method is used to study them. Similar to the human society, we then can compute the average age of the nearest particle pairs at a given time in a flow. We can also investigate the life expectancy of the nearest pairs, which is the average age when the nearest particle in the pair is replaced by another particle. Evolution equation of the age included nearest particle probability distribution function is derived. Under the assumption of random destruction of the nearest pairs, we find the age distribution of nearest particle pairs is exponential. As consequences, the average age, the life expectancy, and the decay time of the probability distribution are then the same.

This theoretical prediction is confirmed by particle resolved simulations of sedimentation flow under gravity. The relation between this age distribution of the nearest particle pairs and the well-known drafting-kissing-tumble motion will be discussed.   

Planar Particle Tracking Velocimetry of Soil Erosion in Small Scale PSI Experiments

During the powered descent of a human-class lander onto an extraterrestrial body a supersonic jet impinges on a surface generally conformed of loose regolith. The plume surface interaction (PSI) changes the surface topsoil geometry and causes entrainment of regolith into a complex multiphase flow that extends well above the surface and radially away from impingement. PSI effects have been identified to pose significant hazards throughout the history of manned spaceflight. The primary risks include, the alteration of the landing site surface, the obstruction of crew and sensor visibility during descent, and the damage by ejecta to vehicle instrumentation and nearby assets. High fidelity numerical simulation of plume-surface interactions is hindered by the complexity of accounting for four-way coupling interactions for a realistic number of particles and in a wide range of volume loadings and flow regimes. Lander scale numerical simulations require constitutive models for these multiphase flow interactions, which rely on experimental data. Historically, PSI experiments have relied on half-domain geometries to avoid the challenges of optical diagnostics in optically dense media. To advance the knowledge on PSI through quantitative measurements we have developed a subscale full-domain experiment with the ability to reproduce the main aerodynamic non-dimensional parameters of full-scale landers. Optical techniques such as high-speed schlieren, molecular tagging velocimetry, PLIF and planar particle tracking velocimetry are used to measure the flow and particle dynamics. Results at varying jet expansion ratios and nozzle-to-surface impingement distances highlight the very distinct flow and soil erosion features at conditions representative of Lunar and Martian landings.

    

Adjoint-based particle forcing reconstruction from sparse measurements with uncertainty quantification

The drag law of particles within turbulent environments influences dynamical properties pertinent to many applications such as the mining industry or supersonic aerodynamics. The current study explores the determination of the forcing function for one-way coupled passive particles, under the assumption that the ambient velocity fields are known. When measurements regarding particle locations are available but sparse, direct evaluation of the forcing is intractable. Nevertheless, the forcing for finite-size particles is determined using adjoint-based data assimilation. This inverse problem is formulated within the framework of optimization, where the cost function is defined as the difference between the measured and predicted particle locations. The gradient of the cost function, with respect to the forcing, can be calculated from the coupling between the forward and adjoint particle traces. When measurements are subject to Gaussian noise, samples within the posterior probability distribution of the forcing function can be drawn using Hamiltonian Monte Carlo (HMC). The algorithm is tested in both the elementary Arnold–Beltrami–Childress (ABC) flow and homogeneous isotropic turbulence.   

Radial oscillations and enhanced collision rates of heavy inertial particles in the vicinity of a vortex

Trajectories of heavy inertial particles near a vortex are expected to converge to an outgoing spiral with a short transient wherein the radius increases monotonically. These transients are considered the cause of caustics. We present results on the dynamics and collision rates of inertial particles finitely denser than the surrounding fluid in the vicinity of a vortex, using the Maxey-Riley equation, with and without the Basset-history force. Contrary to conventional wisdom, we find that in the regime of vortex-associated particle Stokes number > 1, heavy particles starting even outside the vortex core can move inward, and proceed to perform several radial oscillations before converging to an outgoing spiral. This gives rise to a rich particle caustics profile, as well as a significantly higher particle collision rate around the vortex than if these transients were ignored. We particularly highlight how the history force makes non-trivial changes to the transients, by significantly altering the duration of transients, collision rates and distribution of locations of caustic events, hence making a case for why Basset history force shouldn't be ignored.