Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session Z16: Interface Modeling II |
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Chair: Suhas Jain, Stanford University; Ali Mani, Standard University Room: 143 |
Tuesday, November 22, 2022 12:50PM - 1:03PM |
Z16.00001: Assessment of Localized Artificial Diffusivity and Interface Sharpening for Modelling a Two-Phase Mixing Layer zoe barbeau, Sanjiva K Lele Atomization occurs when a liquid jet from a nozzle is discharged into a stagnant or moving gas causing the gas-liquid interface to become unstable and break up into a collection of droplets. The objective is to simulate a simplified problem of a 3D, planar two-phase mixing layer between a co-flowing liquid and high-speed gas stream in a compressible regime, relevant to rocket propulsion. Localized artificial diffusivity (LAD) method is a diffuse interface method that combines explicitly adding artificial fluid properties to physical transport properties in regions around the two-phase interface and shocks with high-order compact finite difference schemes to produce stable, low-cost, and high accuracy simulations. The addition of interface-sharpening treatment allows the two-phase interface to remain sharp. This extended LAD method has potential to accurately simulate the two-phase mixing layer with substantial density differences, but its performance in basic flows related to the two-phase mixing layer must be determined. The present work evaluates the performance of the extended LAD method in treating basic phenomena related to the breakdown of the gas-liquid interface through a series of model problems, including shear-induced breakdown of a temporal two-phase shear layer. |
Tuesday, November 22, 2022 1:03PM - 1:16PM |
Z16.00002: Assessment of WENO and TENO spatial discretizations for diffuse interface simulations of compressible two-phase flows, and their interplay with regularization terms Henry Collis, Shahab Mirjalili, Suhas S Jain, Ali Mani In this work, two popular ENO-like discretization schemes are evaluated for their applicability to simulation of compressible two-phase flows using a diffuse interface method. WENO and TENO have been previously shown to be robust for shocks and other flow discontinues - including material interfaces. In this work, in the framework of the four-equation two-phase model in conjunction with the stiffened gas equation of state, we assess the performance of WENO and TENO schemes for simulations of compressible two-phase flows. A particularly unique aspect of this work is in assessment of the WENO and TENO schemes coupled with recently developed conservative diffuse interface regularization terms. Recent studies using central-difference schemes have demonstrated that these regularization terms can maintain a constant interface thickness while guaranteeing boundedness of volume fraction and conservation properties that result in robustness of the two-phase flow solver even at large density ratios. Using multiple 1D and 2D test cases, WENO and TENO are evaluated with and without coupling to the diffuse interface regularization terms. |
Tuesday, November 22, 2022 1:16PM - 1:29PM |
Z16.00003: Satisfying conservation and pressure equilibrium in compressible multi-component flow simulation: a novel discretely compatible scheme Yuji Fujiwara, Yoshiharu Tamaki, Soshi Kawai The mixing of fluid components is a crucial physical phenomenon in engineering applications. While the pressure equilibrium at the fluid interface is the physics of inviscid flows without surface tension, the conventional conservative schemes generate spurious pressure oscillations at the interface, thus violating the physics of pressure equilibrium. In this study, we propose a fully conservative and pressure-equilibrium preserving scheme for compressible multi-component flows. We first derive the compatibility condition that describes a condition for implicitly satisfying the pressure equilibrium at the discrete level. Then, we propose a novel scheme that satisfies the compatibility condition. Unlike conventional non-conservative or over-specifying equilibrium preserving schemes, the proposed scheme satisfies both the primary conservation (i.e., the conservation of mass of each species, momentum, and total energy) and pressure-equilibrium preservation. To the authors' knowledge, there is no scheme proposed that maintains the pressure equilibrium by solving only the conservative equations without an additional overspecified equation. |
Tuesday, November 22, 2022 1:29PM - 1:42PM |
Z16.00004: Adaptation of Phase-Field methods to compressible multiphase flows Ziyang Huang, Eric Johnsen Thanks to the consistency of mass conservation and consistency of mass and momentum transport, a general model is derived to adapt the Phase-Field methods to multiphase compressible flows, without any prior assumptions on the formulation of the Phase-Field methods. The second law of thermodynamics, isolated interfaces under a uniform flow, Galilean invariance, and consistency of reduction are analyzed and illustrate the physical constraints that need to be satisfied by the formulation of the Phase-Field methods. Then, the proposed model is implemented in the two-phase Eulerian system, and a general numerical strategy is developed to tackle the added terms due to the Phase-Field methods. The numerical strategy guarantees the boundedness of the volume fraction and positivity of the mass, independent of the formulation of the Phase-Field methods. As a specific example, the conservative Allen-Cahn Phase-Field formulation is applied, and canonical problems are investigated to demonstrate the effectiveness and improvement. |
Tuesday, November 22, 2022 1:42PM - 1:55PM |
Z16.00005: Efficient Solution of Exact Riemann Problems for Compressible Multiphase Flow and Fluid-Structure Interaction Simulations Wentao Ma, Xuning Zhao, Shafquat Islam, Aditya Narkhede, Kevin Wang When solving compressible multiphase flow problems, it is often important to account for the discontinuity of the equations of state (EOS) across material interfaces. One method to achieve this, known as FIVER ("FInite Volume method based on Exact multiphase Riemann solvers"), is to construct and solve an exact one-dimensional bimaterial Riemann problem between each pair of neighboring cells separated by a material interface. In this talk, we present a method to accelerate the solution of bimaterial Riemann problems with arbitrary (convex) EOS, based on the idea of storing and reusing previous solutions. The talk will start with a summary of the FIVER framework, including the use of level set method for tracking fluid-fluid interface. Then, the iterative solution of bimaterial Riemann problems will be discussed in detail, focusing on computation efficiency. For an arbitrary EOS, the Riemann invariants associated with rarefaction waves involve ordinary differential equations (ODEs) that cannot be solved analytically. The numerical solution of these ODEs significantly increases the computational cost. To mitigate this issue, we propose an acceleration technique that utilizes the results of previously solved Riemann problems. Specifically, in each simulation, an R-tree is constructed to store the inputs and outputs of bimaterial Riemann problems. When solving a new Riemann problem, a nearest neighbor search is performed using the R-tree to find data points that are closest to the current one. The corresponding outputs are then interpolated to provide an accurate initial guess for the current Riemann problem, thereby reducing the number of iterations required to achieve convergence. Finally, several numerical tests will be presented to demonstrate the acceleration effects of the proposed method in solving challenging multi-physics problems in the contexts of underwater explosion, laser lithotripsy, and hypervelocity impact. |
Tuesday, November 22, 2022 1:55PM - 2:08PM |
Z16.00006: A numerical comparison of 5-, 6-, and 7-equation Baer-Nunziato-based diffuse interface methods Achyut Panchal, Anand Radhakrishnan, Spencer H Bryngelson, Suresh Menon The Baer-Nunziato equations are often used to represent multiphase flows and solve them via the diffuse interface method. These equations solve for phasic volume, mass, momentum, and energy in the most general form (the 7-equation model). Since a pressure and velocity equality is maintained at a multiphase interface, reduced forms such as 5- (one pressure, one velocity) and 6-equation (two pressures, one velocity) models can be appropriate approximations for the full model. These are widely used for resolved multiphase modeling due to their simplicity. However, the 7-equation model offers advantages in handling independent and arbitrary equations of state and its validity in regions with unresolved multiphase entities. We recently developed a numerical method for solving the 7-equation model. Here, we compare this approach to existing ones for the 6- and 5-equation models. Numerical results for a shock-droplet interaction problem (Mach 1.4 and 2.5) are assessed. Simulation results are validated against established experimental data, and theory is used to help describe the observed differences. |
Tuesday, November 22, 2022 2:08PM - 2:21PM |
Z16.00007: A Self-Similar Diffuse Interface Method for a Rotating Ablating Cylinder Emma M Schmidt, J. Matt Quinlan, Brandon Runnels A melting, sublimating, ablating, or deflagrating solid exerts a variety of boundary conditions on the fluid as mass, momentum, angular momentum, and energy are exchanged between the phases. By treating the interface implicitly, Diffuse Interface Methods (DIMs) do not require complex interface tracking or reconstruction; when coupled with adaptive mesh refinement (AMR), which allows sufficient resolution of the interface at minimal computational cost, a diffuse interface approach provides a straightforward framework for modeling multi-phase problems on a single mesh. The introduction of artificial diffusivity naturally comes with the introduction of an artificial numerical length scale. The authors present a robust DIM which preserves self-similarity for phase boundaries between a solid and viscous, compressible flow - that is, a DIM in which the diffuse length scale has no adverse effects. We consider a rotating, sublimating solid cylinder in viscous compressible flow with mass and energy flux across the evolving phase boundary; stability of this method is considered, along with convergence analysis to the equivalent free-boundary problem. A variety of analytic solutions for cylinders in viscous compressible flow are included for verification. |
Tuesday, November 22, 2022 2:21PM - 2:34PM |
Z16.00008: Characterizing turbulence-interface interaction in a two-phase mixing layer Tanjina Azad, Delin Jiang, Yue Ling When two parallel gas and liquid streams meet at the exit of the separator plate, the velocity difference between the two triggers a shear instability at the interface. When turbulence is present in the gas inlet, the interaction between the inlet gas turbulence and the interface will influence the development of shear instability, including the selection of the most unstable mode and the transition from convective to absolute instability. The modified shear instability will in turn influence the formation of longitudinal interfacial waves, the transverse Rayleigh-Taylor instability on the wave crest, and multiphase turbulence statistics downstream. Both direct numerical simulation (DNS) and linear stability analysis have been conducted in the present study to investigate the effect of inlet gas turbulence intensity. In stability analysis, the Orr-Sommerfeld equation was solved to analyze the spatio-temporal viscous modes, and the turbulent eddy viscosity model has been used to represent the effect of inlet gas turbulence intensity. The effective gas viscosity, namely the sum of eddy viscosity and molecular viscosity, increases with the inlet gas turbulence intensity, which will in turn influence two dimensionless parameters, Reynolds number and viscosity ratio, which determine the stability. The effects of these two parameters will be investigated systematically. The results indicated that the modification of Re is dominant. In DNS the mass-momentum consistent volume-of-fluid method has been used to capture the sharp gas-liquid interface, and the pseudo turbulence at the gas inlet is generated by digital-filter approach. The stability model well captured the increasing trend of most-unstable frequency with inlet gas turbulence intensity, as observed in DNS. |
Tuesday, November 22, 2022 2:34PM - 2:47PM |
Z16.00009: Modeling of subgrid-scale interfacial area for turbulent two-phase flows Suhas S Jain, Ahmed Elnahhas Interfacial exchange of mass, momentum, and energy is directly proportional to the amount of interfacial surface area. Hence, an accurate prediction of the interfacial surface area is vital for modeling these transfer processes. However, numerically resolving all the interfacial area corrugations down to the Hinze scale in a turbulent flow is prohibitively expensive due to the large separation of scales. This necessitates an alternate modeling strategy. |
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