Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session T20: Sharp and Diffuse Interface Methods |
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Chair: Ali Mani, Stanford University Room: 250 D |
Monday, November 25, 2024 4:45PM - 4:58PM |
T20.00001: Abstract Withdrawn
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Monday, November 25, 2024 4:58PM - 5:11PM |
T20.00002: Towards a high-order two-dimensional volume-of-fluid method for gas-liquid flow simulations Ashish Dhanalakota, Richeek Dutta, Fabien Evrard It is well known that current geometric volume-of-fluid (VOF) methods are limited to second-order accuracy due to the piecewise linear nature of the cell pre-images and interface approximations used to compute advective fluxes. We present recent work towards the extension of this framework to high-order accuracy in two dimensions. To this end, we provide closed-form expressions for the area of a Jordan curve clipped by a parabola. The Jordan curves we consider are reconstructed as a composite of quadratic Bézier curves and approximate the pre-image of a computational cell for transporting volume fractions in a semi-Lagrangian fashion. The expressions for computing the clipped area are derived from applying the divergence theorem across parameterized intersections between the Jordan curve cell and the parabola. The resulting analytical expressions have been verified using several carefully engineered test configurations and Monte Carlo integration. We also present means to reconstruct cellwise pre-images as composite quadratic Bézier curves that guarantee exact volume conservation. Ultimately, the proposed framework is used to conservatively advect the VOF indicator function with high-order accuracy. It is tested over a range of canonical advection test-cases. |
Monday, November 25, 2024 5:11PM - 5:24PM |
T20.00003: A Momentum-Consistent One-Fluid Formulation of Evaporating Two-Phase Flows in a Sharp Volume-of-Fluid Framework Jordi Poblador Ibanez, Nicolas Valle Marchante, Bendiks Jan Boersma The one-fluid formulation of two-phase flows regularizes the discontinuity at the phase interface as a single fluid with varying properties and adds additional source terms to satisfy jump conditions (e.g., surface tension). While well-suited for non-evaporative flows, analytical and numerical inconsistencies appear if phase change occurs due to the local volume dilatation at the interface, which may cause a momentum imbalance and affect the flow dynamics. Corrections to the momentum jump are implemented in the presence of phase change in the non-conservative one-fluid formulation of the momentum equation for incompressible flows coupled to a sharp Volume-of-Fluid approach: (a) two body forces are added in the context of the Continuum Surface Force model to address the ill-defined convective term; and (b) the flow solver is modified to include a preliminary predictor-projection step to shift the Stefan flow before integrating the momentum equation with a second predictor-projection step. A physically meaningful pressure field is recovered in the limit of low viscosity while using standard discretization schemes in the one-fluid framework. Further, the corrections improve the spatial and temporal smoothness of the pressure field. However, issues remain with the regularization of the viscous term due to the discrete evaluation of the one-fluid velocity gradients. |
Monday, November 25, 2024 5:24PM - 5:37PM |
T20.00004: A density-based sharp-interface method for compressible gas-liquid flows Mira Tipirneni, Lingquan Li, Antonino Ferrante We have developed a novel density-based, sharp-interface method for solving numerically compressible two-phase (gas-liquid) flows that uses the minimum number of governing equations, i.e., four equations: conservation of mass, momentum, energy, and advection of color function. The interface between the gas and the liquid phases is sharply captured in a single computational cell with the volume of fluid (VoF) method. The VoF method is coupled in a consistent manner with a new flux integral method. The methodology is designed to capture sharply the flow discontinuities, i.e., shock-waves and gas-liquid interfaces. The results showing this feature are presented for the test-cases of air-water shock tube, and shock-wave/droplet interaction. |
Monday, November 25, 2024 5:37PM - 5:50PM |
T20.00005: Interface capturing in compressible two-phase flows with non-equilibrium models Luis H Hatashita, Suhas Jain The applications of compressible multiphase flows in aerospace applications are numerous. The target is to develop a robust framework to model two phases and preserve interfaces in a compressible turbulent regime. Non-equilibrium models, namely six- and seven-equation, are of interest here because of more accurate wave transmission across interfaces. One approach to capture interfaces with low-dissipative central schemes is to add interface-sharpening terms; moreover, shock and contact-discontinuity capturing may also be achieved with the use of artificial-viscosity approaches. Analogous formulations already developed for four- and five-equation model approaches are extended to these non-equilibrium models by adding the general conservative interface-capturing term based on the phase-field method in the volume fraction transport equation and consistently incorporating the corresponding terms to the phasic conservation equations. The novel formulation is tested for canonical test cases such as two-phase shock-tube and droplet advection problems. |
Monday, November 25, 2024 5:50PM - 6:03PM |
T20.00006: A Novel Slip Boundary Condition for Contact Angle Modeling Using Phase-Field Methods Lucy J Brown, Suhas Jain, Parviz Moin This work introduces a novel slip boundary condition designed to enforce a given contact angle in phase-field simulations. Unlike traditional methods, which typically alter the mass transport equation or impose an arbitrary Navier-slip boundary condition, this approach is motivated from a momentum balance at the wall. This physics-based boundary condition enables the seamless integration of contact angle physics into phase-field simulations. In this talk, the boundary condition, which takes the form of a PDE that is advanced discretely in time, is derived and results are shown for various static contact angles. Following this, the boundary condition is coupled with various pre-existing models for the dynamic contact angle. Results for a drop sliding down an inclined plane are then shown. |
Monday, November 25, 2024 6:03PM - 6:16PM |
T20.00007: A Six-Equation Multimaterial Method for Compact Finite Differences Steven R Brill, Britton J Olson High-order compact finite difference schemes' spectral-like accuracy is well suited for capturing turbulent mixing, but additional stabilization is needed to capture jumps in material properties in multimaterial flows. Localized artificial diffusivity (LAD) methods have been developed for compact finite differences to stabilize large material property jumps. However, the methods struggle to simulate stiff and complex equations of state due to an inability to enforce monotonic state variables with pressure/temperature equilibrium. We present a novel six-equation model for the compact finite difference method, which addresses these limitations by relaxing the pressure equilibrium requirement and explicitly tracking volume fractions and species energies. The strength of the proposed scheme is validated on a suite of test problems. |
Monday, November 25, 2024 6:16PM - 6:29PM |
T20.00008: Kinetic energy and entropy preserving (KEEP) scheme for compressible multi-component flows Shigetaka Kawai, Aziz F Abidin, Soshi Kawai Flows of multiple species with different properties are important physical phenomena in many engineering applications. Simulations of multi-component flows often lead to numerical instability around the interface due to the steep variations in the flow properties. While this instability can be mitigated by introducing numerical dissipation, it is crucial to minimize (ideally zero) the numerical dissipation in high-fidelity turbulent flow simulations, highlighting the need for non-dissipative and robust numerical methods. This study proposes non-dissipative and robust spatial discretization schemes for discontinuity-free compressible multi-component flows. In addition to the primary conservation for the mass of each species, momentum, and total energy, the secondary preservation of the kinetic energy and entropy is considered, and the kinetic energy and entropy preserving (KEEP) scheme, originally developed for single component flows, is extended to multi-component flows. Based on the entropy conservation error analysis, the entropy conservative numerical fluxes are derived, and their pressure-equilibrium-preservation property is discussed. |
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