Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session M10: Computational Fluid Dynamics Methods for Multiphase Flows III |
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Chair: Onkar Sahni, Rensselaer Polytechnic Institute Room: Georgia World Congress Center B215 |
Tuesday, November 20, 2018 8:00AM - 8:13AM |
M10.00001: Solving phase change problems using stabilized finite elements with improved interfacial conditions Anirban Chandra, Assad Oberai, Pawel Keblinksi, Onkar Sahni Here we present a mathematically consistent numerical technique for solving two-phase problems involving phase-change processes such as evaporation and condensation. We use a stabilized finite element method on hybrid meshes for solving compressible Navier-Stokes equations and correctly account for the jump conditions across the interface (derived from conservation laws) using discontinuous interpolations. The interface is tracked explicitly using the arbitrary Lagrangian-Eulerian (ALE) description in which the mesh at the interface is required to move with the interface. A penalty approach is used to weakly ensure continuity of tangential velocity components and to explore various jump conditions for temperature. The rate of phase change is evaluated using thermodynamic variables at the interfaces and kinetic interfacial parameters determined from molecular dynamics simulations. |
Tuesday, November 20, 2018 8:13AM - 8:26AM |
M10.00002: A moment-of-fluid method for diffusion equations on irregular domains in multi-material systems Yang Liu, Mark Sussman, Yongsheng Lian, M. Yousuff Hussaini A new numerical method is developed for the solution of the diffusion problem in a system of several materials. In such a system, the diffusion coefficients are piecewise continuous and jumps in their values can occur across the complex-shaped interfaces between contiguous materials. A moment-of-fluid procedure is employed to re-construct the interfaces. This procedure enables accurate reconstruction of any number of material interfaces in a computational cell. Furthermore, it is capable of capturing thin filamentary regions without the necessity of adaptive mesh refinement. It is demonstrated in a simple canonical case. It has the potential to enable numerical simulation of complex flows of technological importance relevant to materials and manufacturing processes, in that it can capture multiple phase changes that occur in such flows in complex domains. |
Tuesday, November 20, 2018 8:26AM - 8:39AM |
M10.00003: Twophase compressible fluid dynamics with Cattaneo heat transfer Khosro Shahbazi The two-phase compressible fluid dynamics model introduced by Romenski etal. (2009, Journal of Scientific Computing) based on application of extended thermodynamics to continuum mixtures, provides a general and powerful mathematical formulation with many desirable properties. The arising system is conservative and entropy-generating. Moreover, given convex equation of states, the resulting system is hyperbolic, i.e., possessing real eigenvalues. Via relaxation source terms with appropriate time scale, this model also incorporate cavitation, both driven by expansion waves or local thermal irradiation. This work focuses on the single velocity and single temperature limit of this two-phase flow model applicable in very fast inter-phase thermal and momentum relaxation scenarios and considers finite-speed heat transfer modeling using Cattaneo heat conduction. Unlike the more common infinite speed heat condition of Fourier, the Cattaneo heat transfer is more suitable for small spatial scales heat conduction (of order of ~ 100 nm or smaller). The first eigenspectrum analysis of the system with the Cattaneo heat transfer is presented followed by a comparison with Fourier heat conduction. |
Tuesday, November 20, 2018 8:39AM - 8:52AM |
M10.00004: An Arbitrary Lagrangian Eulerian Formulation with Exact Mass Conservation for the Numerical Simulation of a Three-Dimensional Rising Bubble Problem Mehmet Sahin, Cagatay Guventurk An arbitrary Lagrangian Eulerian (ALE) framework has been proposed to solve incompressible multiphase fluid flow problems with exact mass conservation in three-dimensions. The incompressible Navier-Stokes equations are discretized over unstructured moving hexahedral meshes using the div-stable face-centered finite volume method where the continuity equation is satisfied exactly within each element. The pressure field is treated to be discontinuous across the fluid-fluid interface with the discontinuous treatment of density and viscosity. The surface tension term is considered as a force tangent to the interface. For the application of the interface kinematic boundary condition due to the normal displacement of interface, a special attention is given to satisfy both local and global discrete geometric conservation law (DGCL) in order to conserve the total mass of both species at machine precision. The resulting algebraic equations are solved in a fully coupled (monolithic) manner and a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization is utilized within each partitioned sub-domain. The proposed method is validated by simulating a classical single rising bubble in a viscous fluid due to buoyancy in three-dimensions. |
Tuesday, November 20, 2018 8:52AM - 9:05AM |
M10.00005: Interface Curvature Calculations for Rudman Coarse-Fine Conservative Grids Kristopher Olshefski, Mark F Owkes This research extends the standard height function method to include information from a subgrid. This inclusion separates the scheme from traditional height function methods and allows the curvature to respond to subgrid interface perturbations. Height function methods calculate the curvature of a cell by taking information from surrounding cells and building columns. By integrating the volume of fluid within a column, a height is established. Including a subgrid is motivated by the work of Rudman (Int. J. Numer. Meth. Fluids, 1998) who showed using a subgrid allows for both mass and momentum conservation, even in high-density ratio flows. |
Tuesday, November 20, 2018 9:05AM - 9:18AM |
M10.00006: A phase-field method for large-eddy simulation of two-phase slug flow in a pipe Zhicheng Wang, Michael Triantafyllou, Yiannis Constantinides, George Em Karniadakis We present a phase-field method that enables large-eddy simulation (LES) of the initialization and development of the two-phase slugs formed in a stratified flow in a long horizontal pipe using realistic values of density ratio, viscosity ratio, Weber number and Reynolds number. The method is implemented in a spectral-element/Fourier code that makes the simulation fast and very accurate. The free interface is represented by the Cahn-Hilliard equation with interface compression that leads to excellent mass conservation. The Entropy Viscosity Method (EVM) is employed as LES subgrid eddy viscosity model. The visualization of the simulation result exhibits the richness of the evolving topology of the slugs, while the predicted slug length and frequency are in good agreement with experimental measurements. |
Tuesday, November 20, 2018 9:18AM - 9:31AM |
M10.00007: An interface-tracking computational infrastructure for compressible multiphase processes Fan Yang, Anirban Chandra, Yu Zhang, Saurabh Tendulkar, Rocco Nastasia, Assad Oberai, Mark Shephard, Onkar Sahni Numerical simulations with interface tracking in a multiphase medium impact many applications. One such example is a combusting solid involving phase change. In these problems interface tracking is crucial to accurately model and capture the interface physics, for example, discontinuous fields at the interface such as density or normal velocity. We present a mathematically consistent and robust computational approach based on interface tracking for multiphase problems involving phase change. A stabilized finite element method is used to solve the compressible Navier-Stokes equations while accounting for the jump conditions across the interface (derived from conservation laws) by using discontinuous interpolations. Interface is tracked using a combination of mesh motion and mesh modification. Mesh motion is applied until mesh deformation leads to undesirable cells, at which point local mesh modification is used to improve the mesh. All steps are done in parallel on distributed meshes. We will demonstrate our approach for problems with multiple interfaces involving large motions (e.g., multiple droplets or grains). Topological changes in the geometry (of any phase) will be considered in the future. |
Tuesday, November 20, 2018 9:31AM - 9:44AM |
M10.00008: A conservative diffuse-interface method for simulation of two-phase compressible flows with acoustics Suhas S Jain, Ali Mani, Parviz Moin Bubble acoustics and liquid fuel injection are example applications in which important dynamical processes involve coupling between flow compressibility and two-phase flow effects. The numerical study of acoustics and turbulent flows require stable, non-dissipative and conservative numerical methods. We have developed a diffuse-interface five-equation model that (a) can be solved using non-dissipative numerical methods (low and high-order central-difference schemes), (b) discretely conserves mass of each phase, total momentum and total energy in the system, (c) maintains mechanical equilibrium (uniform velocity) and thermodynamic equilibrium (uniform pressure) across the interface (d) maintains a steady interface thickness. Results from test cases such as (a) acoustic wave incident on an interface - showing the accuracy in capturing the theoretically predicted transmitted and reflected wave amplitudes (b) oscillating bubble under a driven pressure pulse – showing the capturing of predicted decay of oscillation for very long time integration, will be discussed. |
Tuesday, November 20, 2018 9:44AM - 9:57AM |
M10.00009: Adjoint-based interfacial control of axisymmetric viscous drops Alexandru Fikl, Daniel Joseph Bodony We develop a continuous adjoint theory for the control of the deformation of a clean, neutrally buoyant droplet in Stokes flow. The problem reduces to the dynamics of the free drop surface, but this introduces significant complexity in the optimization process and, in particular, the formulation of necessary optimality conditions and efficient numerical handling. We make use well-known results from the field of topology optimization to derive rigorous adjoint equations and optimality conditions for this class of problems. Boundary integral methods are used to provide efficient and high-order approximations for all the quantities of interest. Finally, our methodology is then tested on axisymmetric droplets controlled by the non-dimensional Capillary number and several tracking-type |
Tuesday, November 20, 2018 9:57AM - 10:10AM |
M10.00010: Multiphase flows of N immiscible incompressible fluids: An outflow/open boundary condition and algorithm Zhiguo Yang, Suchuan Dong In this talk, we introduce a set of effective outflow/open boundary conditions, which is suitable for simulating multiphase flows of N (N≥2) immiscible incompressible fluids in domains involving outflows or open boundaries. These boundary conditions satisfy two properties: energy stability and reduction consistency. They are devised such that their contributions to the N-phase energy balance equation will not cause the total system energy to increase over time. Therefore, these outflow/open boundary conditions are very effective in overcoming the backflow instability. The reduction consistency ensures the inherent equivalence relations between N-phase system and the corresponding smaller system when some of the fluid components are absent from the N-phase system. We also present an efficient algorithm for numerically treating the proposed boundary conditions together with the N-phase governing equations. The proposed algorithm involves only solving a set of de-coupled individual Helmholtz equations in each time step with constant and time-independent coefficients. We present ample numerical examples to confirm that the proposed method produces physically accurate results. |
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