Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session J36: Multiphase Flows: Computational Methods III 
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Chair: Zhen Li, Clemson University Room: 202B 
Sunday, November 19, 2023 4:35PM  4:48PM 
J36.00001: Assessment of Numerical Methods for Two Phase Shear Layers zoe barbeau, Sanjiva K Lele Atomization occurs when a liquid jet from a nozzle is discharged into a stagnant or moving gas causing the gasliquid interface to become unstable and break up into a collection of droplets. The objective is to simulate a simplified problem of a 3D, planar twophase mixing layer between a coflowing liquid and highspeed gas stream in a compressible regime, relevant to rocket propulsion. The performance of 6th order staggered, compact finite difference method with the 5equation model, 2nd interface sharpening, and localized continuum surface force method for surface tension modeling is evaluated for basic flows related to the twophase mixing layer. 8thorder filtering is currently used for robustness with the longerterm objective of minimizing numerical dissipation. Surface tension test cases of a highdensity stationary droplet and Laplace number = 24,000 droplet show low spurious current levels and 2nd order convergence of spurious currents with refinement. This combination of methods is robust for high density ratios, showing promise to simulate shearinduced breakdown of a temporal twophase shear layer.
Funded by the US Department of Energy PSAAPIII Program at Stanford University (Award DENA0003968) and by U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship (Award Number DESC0022158).

Sunday, November 19, 2023 4:48PM  5:01PM 
J36.00002: Analysis of interfacial sharpening techniques for upwindbiased shock and interfacecapturing methods in diffuse interface simulations of shockdominated compressible twophase flows Deniz Bezgin, Henry Collis, Shahab Mirjalili, Ali Mani, Nikolaus Adams In compressible twophase flows, WENOtype upwindbiased spatial discretization schemes are a popular choice to provide sufficient numerical dissipation for stabilizing material interfaces and shock discontinuities. In contrast to shocks, material interfaces are not inherently selfsharpening. Thus, in the presence of numerical dissipation, material interfaces will continuously diffuse unless interfacial sharpening is applied. In this work, we investigate the interplay of WENOtype spatial discretization schemes and interfacial sharpening techniques in the fiveequation diffuse interface model. We consider multiple variants of the conservative diffuseinterface method and compare them against the wellestablished THINC scheme and the baseline WENO scheme without interfacial sharpening. We consider 2D and 3D canonical test cases of shockdominated compressible flows with large density ratios. We analyze the interaction between aforementioned interface regularization techniques and the underlying WENOtype discretization and evaluate how the interface regularization affects the temporal interface evolution. 
Sunday, November 19, 2023 5:01PM  5:14PM 
J36.00003: Robust implementation of the four equation model for compressible twophase flows using ENOtype schemes and application to simulation of "cold" combustors Henry Collis, Deniz Bezgin, Shahab Mirjalili, Ali Mani ENOtype schemes provide a general approach to capturing flow discontinuities without adding substantial numerical dissipation. While these schemes have "essentially" nonoscillatory solutions, for highMach flows even small oscillations in flow variables can lead to simulation failure. In particular, the highdensity ratios common in twophase flows demand stricter robustness criteria than singlephase compressible flow. Obtaining robust solutions for highMach twophase flow requires enforcing positivity of pressure, mass, the squared speedofsound, and boundedness of phase volume fraction. In this work, a positivitypreserving framework was constructed for the fourequation twophase model and implemented into the highlyparallel Hypersonic Task based Research (HTR) Solver. The positivitypreserving scheme is conservative and applied locally for minimum degradation of the baseline ENOtype scheme. The positivitypreserving framework was applied to multiple highMach twophase flows including the simulation of a multiphase "cold" combustor on curvilinear grids. 
Sunday, November 19, 2023 5:14PM  5:27PM 
J36.00004: SemiLagrangian Pressure Solver for Accurate, Consistent, and Conservative VolumeofFluid Simulations Julian L Fox, Mark F Owkes In this work, a novel discretization of the incompressible NavierStokes equations for a gasliquid flow is developed. Simulations of gasliquid flows are often performed discretizing time with a predictor > pressure > corrector approach and the phase interface is represented by a volume of fluid (VOF) method. Recently, unsplit, geometric VOF methods have been developed that use a semiLagrangian discretization of the advection term within the predictor step. A disadvantage of the current methods is that an alternative discretization (e.g.~finite volume or finite difference) is used for the divergence operator in the pressure equation. Due to the inconsistency in discretizations, a correction to the semiLagrangian advection term is required to achieve mass conservation, which increases the computational cost and reduces the accuracy. In this work, we explore the idea of using a semiLagrangian discretization for the divergence operators in both the advection term and the pressure equation. The proposed discretization avoids the correction to semiLagrangian fluxes improving the accuracy. Additionally, this method has the potential to reduce the computational cost of VOF simulations for gasliquid flows. 
Sunday, November 19, 2023 5:27PM  5:40PM 
J36.00005: Numerical modeling of an encapsulated microbubble using an immersed boundarylattice Boltzmann method Morteza Garousi, Michael L Calvisi Encapsulated microbubbles (EMBs) are 110 microns in diameter and are used for various biomedical applications, such as ultrasound imaging and intravenous drug delivery. EMBs have a thin encapsulating layer of lipid, protein or polymer to stabilize them against dissolution in the bloodstream. When an EMB is subjected to ultrasound, the high compressibility of its gas core leads to both spherical and nonspherical oscillations. Numerical modeling of an EMB is a challenging problem that requires accounting for fluidstructure interaction (FSI) between a thin viscoelastic solid layer, a viscous incompressible exterior liquid, and a compressible interior gas. In this work, a numerical method is presented for modeling nonspherical, axisymmetric EMBs that uses the lattice Boltzmann method (LBM) to solve the fluid dynamics of the liquid and gas phases and the immersed boundary (IB) method to account for the FSI between the encapsulation and surrounding fluids. The primary advantage of this hybrid IBLBM is its front tracking feature, i.e., the shape of the bubble surface is directly determined without need for its reconstruction. Simulations of the IBLBM of a spherical bubble subjected to acoustic forcing are validated against the RayleighPlesset equation. In addition, the accuracy of the IBLBM model is investigated with respect to the stencil choice for the kernel function used for velocity interpolation and force spreading and the choice of time integration scheme for advecting the bubble surface. 
Sunday, November 19, 2023 5:40PM  5:53PM 
J36.00006: Highfidelity simulations of fluidsolid interactions during liquid metal casting processes Jiazhen Qiao, Amir Riaz, Elias Balaras The preset work focuses on modeling of the initial stages of dross formation resulting from the interaction of the laminar/turbulent jet impinging on a freesurface. In the presence of air, a thin metal oxide layer forms on the surface of the liquid changing the dynamics of the jet as well as the resulting airentrainement. The basis for the proposed formulation is our inhouse, twophase flow solver for incompressible flows, where we included the thin, highly deformable film that is formed on the liquidgas interface. The frequent breakups of this oxidized layer render classical fluidstructure interaction methods where the solid is considered in a Lagrangian reference frame impractical. To address this issue we developed a fully Eulerian approach to model the liquidgassolid interactions. In particular, we use level set formulations to track both fluidsolid interfaces and the strain history of the deformable solid. The latter is accomplished by constructing a dynamic grid using three reference level set functions (one for each dimension) advected by the local velocity field. A unified framework is used to solve the equations governing the fluid and solid dynamics on the same fixed grid. Across the interface the shear modulus transitions smoothly from the bulk shear modulus to zero in a few computational cells. 
Sunday, November 19, 2023 5:53PM  6:06PM Author not Attending 
J36.00007: Abstract Withdrawn

Sunday, November 19, 2023 6:06PM  6:19PM 
J36.00008: A threedimensional adaptive mesh refinement multiphase flow solver for simulating nonisothermal gasliquidsolid flows with phase change Ramakrishnan Thirumalaisamy, Amneet Pal S Bhalla We present a numerical framework for simulating nonisothermal gasliquidsolid flows with phase change. Such flows are commonly found in engineering processes like welding, casting, and metal additive manufacturing. These processes involve fluid flow, heat transfer, solidification/melting, and fluidstructure interaction. Material properties vary vastly in these processes due to the presence of distinct phases in the domain. Moreover, the phases can evolve over time into other phases. As a result, numerical simulations of these engineering processes are quite challenging. We present a robust, scalable, and efficient threedimensional computational framework with adaptive mesh refinement (AMR) for modeling nonisothermal and highdensity contrasting gasliquidsolid flows. The framework combines the level set method with the enthalpy method to track the three phases in the domain. A new low Mach equation is derived to capture volume changes due to phase change. The proposed method discretely conserves momentum, momentum, and energy. We demonstrate the practical utility of the framework by simulating engineering problems like modeling pipe defects during metal casting or porosity defects during metal solidification. 
Sunday, November 19, 2023 6:19PM  6:32PM 
J36.00009: A coupled twolevel set and volumeoffluid method to simulate fluidstructure interaction of an elastic membrane in a viscous fluid Bashir Alnajar, Michael L Calvisi This work presents a fully Eulerian approach to simulate a cylindrical fluidmembrane interaction. The approach is named the coupled twolevel set and volumeoffluid (C2LSVOF) method owing to its use of the volumeoffluid (VOF) method to enforce mass conservation, and twolevel set (LS) functions to determine the interface shape and the elastic membrane forces. The spatiotemporal flow field is discretized by a singlefield, finite difference formulation of incompressible, immiscible NavierStokes equations on a stationary grid. The secondorder operator split method is used to advect the volume fraction and level set functions by alternating the starting sweep direction at each time step. One level set is advected without implementing the reinitialization algorithm so that its gradient, which can be directly related to the membrane stretching, can be preserved. We apply this approach to benchmark problems involving modeling the large deformation of a flexible elastic membrane in viscous incompressible fluids on each side of the membrane with different density and viscosity ratios. The findings are validated using a stretched and pressurized membrane immersed in a test fluid. 
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