Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session P26: Multiphase Flows: Computational Methods I 
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Chair: Spencer Bryngelson, Georgia Tech Room: North 226 ABC 
Monday, November 22, 2021 4:05PM  4:18PM 
P26.00001: Accurate conservative diffuseinterface method for the simulation of twophase flows Suhas S Jain, Parviz Moin We present a novel phasefield model for the simulation of twophase flows that is accurate, conservative, bounded, and stable. The proposed model conserves the volume/mass of each of the phases, and results in bounded transport of the volume fraction. We present results from the canonical test cases of a drop advection and a drop in a shear flow, showing the improvement in the accuracy over the commonly used secondorder conservative phasefield method. Furthermore, we also derive consistent momentum transport equation for the proposed phasefield model and show that the proposed model when coupled with the consistent momentum transport equation results in discrete conservation of kinetic energy, which is a sufficient condition for the numerical stability of incompressible flows, in the absence of dissipative mechanisms. To illustrate the robustness of the method to simulate highdensity ratio turbulent twophase flows, we present the numerical simulation of an infinite Reynolds number highdensity ratio dropletladen isotropic turbulence. 
Monday, November 22, 2021 4:18PM  4:31PM 
P26.00002: A DualScale Modeling Approach for Turbulent Interfaces with Finite Weber Numbers Dominic Kedelty, Marcus Herrmann Direct Numerical Simulation remains a prohibitively expensive task, especially for cases involving atomization. Instead of DNS, a dualscale modeling approach (Gorokhovski and Herrmann, 2008) that describe turbulent phase interface dynamics in a Large Eddy Simulation spatial filtering context is proposed. Spatial filtering of the equations of fluid motion introduce several subfilter terms that require modeling. Instead of developing individual closure models for the interface associated terms, the dualscale approach uses an exact closure by explicitly filtering a fully resolved realization of the phase interface. This resolved realization is maintained using a Refined Local Surface Grid approach (Herrmann, 2008) employing an unsplit geometric Volumeof Fluid method (Owkes and Desjardins, 2014). Advection of the phase interface on this DNS scale requires a reconstruction of the fully resolved interface velocity. In this work, results from the dualscale LES model employing subfilter velocity reconstruction by combined approximate deconvolution and nonlinear spectral enrichment (Bassenne et al. 2019) including a subgrid surface dynamics model (Herrmann 2013) are compared to DNS results for a phase interface in a homogeneous isotropic turbulent flow at several Weber numbers. 
Monday, November 22, 2021 4:31PM  4:44PM 
P26.00003: Computing foaming flows: from microfluidic crystals to breaking waves Petr Karnakov, Sergey Litvinov, Petros Koumoutsakos Foamy flows are critical in numerous natural and industrial processes and remain notoriously difficult to compute as they involve coupled, multiscale physical processes. The simulation of foamy flows, involving noncoalescing bubbles, presents a number of formidable challenges, in addition to those associated with resolving the bubble interactions with the fluid flow and the solid boundaries. We present a novel multilayer simulation framework (MultiVOF) that advances the state of the art in simulation capabilities of foamy flows. The framework introduces a novel scheme for the distinct handling of multiple neighboring bubbles and a new regularization method that produces sharp interfaces and removes spurious fragments. MultiVOF is verified and validated with experimental results and complemented with open source, efficient scalable software. We demonstrate capturing of bubble crystalline structures in realistic microfluidics devices and foamy flows involving tens of thousands of bubbles. 
Monday, November 22, 2021 4:44PM  4:57PM 
P26.00004: A Numerical Formulation to Study Interactions Between Fluids and Deformable Solid in Extension to Thin Film Geometries Jiazhen Qiao, Amir Riaz, Elias Balaras In the present work, we use a fully Eulerian Level set method to track locations of the solid, solid strain, and calculate solid stress on the Eulerian grid. Stressstrain relationship of the solid is governed by the NeoHookean solid model. A unified framework of equation of motion is used to solve for both fluid and solid dynamics. FluidStructure Interaction is accounted for by adding a volumetric body force term in the solid region and the solid force is diffused into the fluid by a Heaviside function. Linear extrapolation has been used to reconstruct the solid strain field at the solidfluid interface in prevention of the discontinuities. We first Validated our implementations by fully resolving the solid and comparing with existing literature results. We have then extended our implementations to thin film geometries by defining a thin region of solid of an order of a few computational cells where solid shear modulus quickly goes from solid value to zero. Numerical results are shown in this presentation. 
Monday, November 22, 2021 4:57PM  5:10PM 
P26.00005: Level Set Modeling of Supersonic Liquid Breakup Using The Method of Characteristics Abdullah Al Muti Sharfuddin, Foluso Ladeinde Numerous studies have been carried out that model the breakup of liquid jets by subsonic air flow. However, its supersonic equivalent has not received enough attention due to computational complexities involved. In this study, a Method of Characteristics (MOC) based algorithm is proposed to simulate the breakup of liquid jets under supersonic conditions. A special version of the Level Set method is required to track the gasliquid interface in the system. In the MOCbased approach, firstorder hyperbolic Euler equations in the gaseous phase are reduced to the characteristic form and then compatibility relations, which do not contain derivatives in the direction normal to the characteristic surfaces, are obtained. Since the MOC reduces dimensionality of the problem by one, faster, yet accurate, solutions can be achieved in comparison to finite difference or finite volume methods. Preliminary results from our ongoing investigations will be presented. 
Monday, November 22, 2021 5:10PM  5:23PM 
P26.00006: High fidelity single framework simulations of acoustic wavebubble cloudelastic solid interactions JeanSebastien A Spratt, Mauro Rodriguez, Spencer H Bryngelson, Shunxiang Cao, Tim Colonius Highfidelity simulations of interacting acoustic waves, bubble clouds and elastic or viscoelastic materials are challenging. Indeed, these simulations typically require two separate numerical frameworks for compressible fluids and solids. The addition of cavitating bubble clouds further complicates the problem by introducing a wide range of spatiotemporal scales. However, such simulations are of particular interest in the development of ultrasound therapies (e.g. lithotripsy and histotripsy) and in understanding traumatic brain injury prediction. We introduce a single framework method to simulate these physics. It is based on a subgrid model for the cavitating bubble clouds and a hypoelastic solid material valid for small strains. These were implemented in our opensource Multicomponent Flow Code (MFC) (Bryngelson et al., Comp. Phys. Comm., 2020). This hypoelastic solid model enables the introduction of elastic and viscoelastic solids into these simulations, as long as we remain in the linear (small strain) regime. We demonstrate the capabilities of the solver for these problems, with example 3D simulations of burstwave lithotripsy including cavitating bubble clouds. Furthermore, we present the computational advantages of the most recent GPUenabled version of the solver. 
Monday, November 22, 2021 5:23PM  5:36PM 
P26.00007: A robust approach for numerical modeling of nonisothermal multiphase flows Ramakrishnan Thirumalaisamy, Amneet Pal S Bhalla Several manufacturing processes such as casting, welding, and additive manufacturing are inherently multiphysics problems with a wide range of thermophysical properties. These processes involve fluid flow, heat transfer, solidification/melting, and fluidstructure interaction. Numerical simulation of these multiphysics problems is quite challenging due to several length and time scales. In this presentation, we present a robust approach for the numerical modeling of nonisothermal multiphase flows with phase change. To ensure the numerical stability of the scheme in presence of highcontrasting thermophysical properties, we consistently treat the mass, momentum, and energy transport in the conservative form of discrete equations. We combine the phasefield model with a levelset advection equation to track the solid, liquid, and gas phases in the computational domain. The proposed model discretely satisfies mass, momentum, and energy conservation, which is tested and presented in our problems. We also present results for several benchmarking cases, including the Stefan problem, melting of ice in water, and thermocapillary droplet migration in liquid metal. 
Monday, November 22, 2021 5:36PM  5:49PM 
P26.00008: A segregated algorithm for the solution of the CahnHilliard equation in multiphase flows Federico Municchi, Matteo Icardi, Mirco Magnini A segregated algorithm for the solution of the CahnHilliard equation in multiphase flowsPhase field methods are gaining momentum in science and engineering to model multicomponent and multiphase systems thanks to their thermodynamically consistent formulation and the general smoothness of the fields. In fact, they provide a framework to include complex physical processes (such as phasechange) and result in less spurious oscillations when dealing with surface tension, compared to other methods like the volume of fluid. The CahnHilliard equation is the principal governing equation in the phase field method as it results from a minimization of the free energy functional and thus includes all the relevant physical phenomena such as phasechange and surface tension forces. However, its solution is not straightforward as it is a fourthorder non linear partial differential equation. A number of explicit methods have been proposed in literature together with an implicit mixed formulation. Segregated implicit algorithms are seldom used due to stability issues.In this work, we present a novel segregated algorithm for the solution of the CahnHilliard equation based on the incomplete blockSchur preconditioning technique. Performance and accuracy of the algorithm are compared against a blockcoupled mixed formulation for a number of cases. We also illustrate several applications of the method to multiphase flows with phase change. 
Monday, November 22, 2021 5:49PM  6:02PM 
P26.00009: Assessment of pseudopotential lattice Boltzmann method for multiphase flows with real fluid properties Juan G RestrepoCano, Francisco E Hernandez Perez, Hong G Im The multirange pseudopotential lattice Boltzmann model (PPLBM) for multiphase flows was implemented along with various strategies, including the multirelaxation time collision operator and the socalled ??scheme, to diminish the parasitic currents and enhance numerical stability. The PPLBM predictions show an excellent agreement with the theoretical coexistence curve, given by Maxwell’s equalarea rule, for both CarnahanStarling (CS) and PengRobinson (PR) equations of state (EOS). Increasing the isotropic order of the interaction force has a stronger impact on reducing the magnitude of the spurious velocities, as compared to the implementation of more sophisticated collision operators. Due to a satisfactory representation of the vaporliquid coexistence curve and acentric factor dependence, the PR EOS is chosen to determine real fluid properties such as equilibrium densities and surface tension for a number of compounds, including nalkanes (carbon number up to 10), ammonia, and hydrogen. For such paraffinic hydrocarbons, the average surface tension error lies in a range of 2.36.2%. Although PPLBM suffers to accurately predict experimental equilibrium density values, the error is inherent to the PR EOS, as PPLBM predicts well those given by Maxwell’s equalarea rule. 
Monday, November 22, 2021 6:02PM  6:15PM 
P26.00010: A robust lowMach solver for phasechanging flows Nicolo' Scapin, Luca Brandt We extended a previously developed VoFbased numerical method for phasechanging flows (Scapin N. et al., J. Comput. Physics, 2020) to solve the governing equations in the limit of zero Mach number. Compared to the fully compressible formulation, the proposed methodology has three distinct advantages. First, it is able to relax the assumption of constant thermophysical properties while effectively filtering the acoustic effects and the associated stringent numerical timestep restrictions. Next, the hydrodynamic pressure is still governed by an elliptic equation for which FFTbased solvers can be employed. Finally, the divergence constrain of the velocity field can be imposed up to machine precision provided that the thermodynamic pressure and the thermophysical properties are updated consistently. The algorithm is implemented on top of a second order accurate twofluid NavierStokes solver coupled with an algebraic volume of fluid method (MTHINC), and extended with the corresponding transport equations for the vaporized liquid mass and thermal energy. Finally, the robustness of the method for more demanding simulations is assessed in two configurations: evaporating droplets in homogeneous turbulent flows and evaporating twolayer RayleighBernard turbulence. 
Monday, November 22, 2021 6:15PM  6:28PM 
P26.00011: Reducing volume and shape errors in front tracking Berend van Wachem, Christian Gorges, Fabien Evrard, Fabian Denner Volume conservation and shape preservation are two wellknown issues related to the advection and remeshing in front tracking. To address these issues, we propose a divergencepreserving velocity interpolation method and a parabolic fit vertex positioning method for remeshing operations for three dimensional front tracking. Errors in preserving the divergence of the velocity field when interpolating the velocity from the fluid mesh to the vertices of the triangles of the front are a primary reason for volume conservation errors when advecting the front. The proposed interpolation method preserves the discrete divergence of the fluid velocity by construction and is compared with other common interpolation methods. Additionally, the parabolic fit vertex positioning method for remeshing operations locally approximates the front with a smooth polynomial surface, improving volume conservation and shape preservation. Results of representative testcases are presented, which demonstrate that the proposed methods can conserve the volume and shape of the front up to an order of magnitude better than conventionally used methods. 
Monday, November 22, 2021 6:28PM  6:41PM 
P26.00012: Discrete Exterior Calculus Discretization of Twophase Incompressible NavierStokes Equations with a Conservative Phase Field Method Minmiao Wang, Pankaj Jagad, Anil N Hirani, Ravi Samtaney

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