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 D10: Computational Fluid Dynamics Methods for Multiphase Flows II |
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Chair: Stephane Zaleski, Pierre and Marie Curie University Room: Georgia World Congress Center B215 |
Sunday, November 18, 2018 2:30PM - 2:43PM |
D10.00001: Development of a Multi-Plane Interface Reconstruction to Enable Modeling of Atomizing Flows in Volume of Fluid Simulations Robert Chiodi, Olivier Desjardins For simulations of liquid-gas flows that undergo topology changes, the ideal representation of the interface would be capable of conserving mass and be truthful to the structures in the flow. The need to conserve mass has been largely met by geometric Volume of Fluid methods. These methods, however, typically induce erroneous breakup due to numerical errors once the interfacial structures become near the scale of the mesh size. To prevent the numerical method from dictating when structures breakup, we have developed a novel multi-plane reconstruction technique that allows capturing of sub-cell structures while still maintaining discrete mass conservation. With the small structures maintained, physical models can then be applied to address the onset of breakup and the ensuing physics. In this talk, we will compare the new multi-plane reconstruction method to the current de-facto standard, PLIC, for several canonical test cases along with the case of an atomizing liquid jet. Models for the breakup of sub-cell structures will be explored. |
Sunday, November 18, 2018 2:43PM - 2:56PM |
D10.00002: Investigation of direct forcing immersed boundary method Kun Zhou, S Balachandar The direct forcing immersed boundary method (DF-IBM) is very popular in direct numerical simulation of rigid particulate flows. However, most simulations are limited to spherical particles. The current theory relies upon matching the Eulerian mesh (fluid) velocity and the Lagrangian markers (particles) velocity to correctly model the interaction between the fluid and particles. This approach poses two main difficulties in its extension to irregular particles, one to generate Lagrangian markers in accordance to the Eulerian mesh, the other to assign to each marker a proper weight. Here, analyses show that the interaction force modeling in DF-IBM is actually seeking the least-square error solution for the fluid-particle system, which can also been seen as a reflective projection of unperturbed fluid force field over the fluid-particle interface region. Through investigating the projection subspace, an unexpected conclusion is that the marker distribution can be chosen freely to a great extent, without noticeable impact on the results. On the other hand, the weight proves to be a relaxation factor, whose optimal value is the largest limited by a stability condition. Numerical examples are provided to support the new theories. |
Sunday, November 18, 2018 2:56PM - 3:09PM |
D10.00003: Adjoint data assimilation for a two-fluids flow with deformable interface Jie Wu, Lian Shen The aim of data assimilation is to recover more kinematics and dynamics details from observations by combing numerical model and measurement. In this study, we have developed an adjoint data assimilation model for assimilating measurements in two-fluids flow simulation with deformable interfaces. The coupled level-set and volume-of-fluid (CLSVOF) method is used to capture the liquid-gas interface in the simulation. An adjoint solver for the Navier-Stokes equations with the CLSVOF method is developed. In this method, a cost function is defined for the error between simulation and measurement. The cost function is reduced in an optimization process with the gradient information provided by the adjoint solver. Our model is validated by matching the gradients calculated by the adjoint solver with the approximated gradients by the finite difference method. Canonical problems of surface waves and vortices interacting with a free surface are considered as test cases. It is found that the flow structure and interface geometry can be successfully reconstructed by incorporating velocity measurements at several positions into the data assimilation model. |
Sunday, November 18, 2018 3:09PM - 3:22PM |
D10.00004: Towards a mass-conserving volume-of-fluid method for incompressible gas-liquid flows with phase change Antonino Ferrante, Michael Dodd We consider incompressible gas-liquid flows in which the liquid evaporates or condenses. A particular challenge in numerically simulating these flows is to capture or track the gas-liquid interface during phase change while conserving mass. The main computational difficulty is that the fluid velocity is discontinuous across the gas-liquid interface leading to the velocity field having locally non-zero divergence (∇ · u ≠ 0), whereas existing volume-of-fluid (VoF) methods conserve mass only if ∇ · u = 0. In this talk, we will present two general approaches for advecting the VoF function in the presence of phase change: (i) compute the interface velocity explicitly and use it to update the VoF field and (ii) compute a divergence-free extension of the liquid velocity to advect the VoF field, and include a source term in the advection equation to account for the phase change. Our results show that only the latter approach leads to zero-machine mass conservation. |
Sunday, November 18, 2018 3:22PM - 3:35PM |
D10.00005: Stability and robustness of a consistent and mass-conserving dual-grid Volume-of-Fluid method. Sagar Pal, Daniel Fuster, Stephane Zaleski We consider Volume-of-Fluid methods for the Direct Numerical Simulation of the Navier-Stokes equations for multiphase incompressible flow with capillary forces and a large contrast in material properties. These methods are notoriously unstable for high density ratios, further compounded by the presence of large surface tension and small viscosity (as for example with air and water fluid properties). In order to alleviate these difficulties we use as discrete variables the Volume-of-Fluid and the momentum density. We explore the performance of the method on a staggered ``MAC'' grid. The staggered character of the grid makes it difficult to compute the fluxes of mass and momentum in a consistent manner. Thus we use a dual grid with a twice finer resolution for Volume-of-Fluid than for momentum and pressure, in a manner similar to the method of Rudman (1998). We perform numerous tests to quantify the stability and robustness of the method, including a dynamic spurious current tests in which a spherical droplet or bubble is advected at uniform velocity. We explore a large number of regimes for this flow characterized by the Reynolds, Weber and CFL numbers, the density ratio and the grid resolution. The stability limit is determined in this five-parameter space. |
Sunday, November 18, 2018 3:35PM - 3:48PM |
D10.00006: An extended stratified flow model with multiple Riemann solvers for compressible Fluid-Elastic Interactions Liang Tao, Xiaolong Deng In flow-structure interactions (FSI) with strong impact or strong shock wave, compressibility effects often need to be considered. In our earlier works, based on a cut-cell based sharp-interface method (Chang, Deng & Theofanous, JCP 2013), various Riemann solvers have been applied for linearly elastic (Tao & Deng, IJCM 2017) and elastic-perfectly plastic materials. In the current work, to improve the efficiency, flexibility and applicability in solving complex FSI problems, a robust method based on the stratified multiphase flow model (Chang & Liou, JCP 2007) is developed to simulate compressible fluid-elastic interactions in pure Cartesian grid. In this method, a volume fraction is used to differentiate each phase, and the reconstruction of volume fraction is performed on each cell face for flux calculations. A set of equations subjected to this model are solved with the finite volume method and a series of Riemann solvers. The AUSM+-up scheme, the exact linearly elastic Riemann solver, and an exact two-phase Riemann solver are used to calculate the numerical fluxes in fluid, elastic solid, and at the fluid-solid interface, respectively. Validations with several 1D, 2D and 3D problems show the accuracy and robustness of this method. |
Sunday, November 18, 2018 3:48PM - 4:01PM |
D10.00007: The extended Ghost Fluid Method (xGFM): recovering convergence of the fluxes when solving Poisson equations with jump conditions. Raphael Egan, Frederic Gibou Among the various numerical methods that have been developed over the last decades to address the Poisson problem with jump conditions across an irregular interface, the "Boundary Condition Capturing Method" by Liu, et al., 2000 (commonly referred to as the "Ghost Fluid Method") has established itself as a first-choice tool in (sharp) multiphase flow simulations. Its small discretization stencil, its ease of implementation and the symmetric positive-definiteness of its linear system of equations make the method very robust and thus highly suited for large-scale simulations. Nevertheless, the GFM's weakness lies in the lack of convergence for the gradients of the solution (and thus the flux vectors) which may pose serious accuracy issues, especially in the context of projection methods. In this presentation, we show a rather simple fix to recover convergence for the gradient of the solution. The technique does not alter the discretization stencil nor the symmetric positive-definiteness of the linear system of equations. Illustrations (including multiphase-flow simulations) are shown. |
Sunday, November 18, 2018 4:01PM - 4:14PM |
D10.00008: A momentum-conserving, consistent, Volume-of-Fluid method for incompressible flow on staggered grids Stephane Zaleski, Daniel Fuster, Marco Crialesi Esposito, Yue Ling, Leon Malan, Sagar Pal, Ruben Scardovelli, Gretar Tryggvason The computation of flows with large density contrasts is notoriously difficult. To alleviate the difficulty we consider a partially momentum-conserving discretization of the Navier-Stokes equation. Incompressible flow with capillary forces is considered, and the discretization is performed on a staggered grid of Marker and Cell type. The Volume-of-Fluid method is used to track the interface and a height-function method us used to computed surface tension. The advection of the volume fraction is performed using either the Lagrangian-Explicit / CIAM method or the Weymouth and Yue Eulerian-Implicit method. To improve the stability of the method momentum fluxes are advected in a manner ``consistent'' with the volume-fraction fluxes, that is a discontinuity of the momentum is advected at the same speed as a discontinuity of the density. To find the density on the staggered cells on which the velocity is centered an auxiliary reconstruction of the density is performed. The method is tested for a droplet without surface tension in uniform flow, for a droplet suddenly accelerated in a carrying gas at rest at very large density ratio without viscosity or surface tension, for the Kelvin-Helmholtz instability, for a falling raindrop and for an atomizing flow in air water conditions. |
Sunday, November 18, 2018 4:14PM - 4:27PM |
D10.00009: A novel method to automatically simulate solid fragmentation within fluid flows Francesco Picano, Federico Dalla Barba Fluid-structure interaction (FSI) is a common phenomenon in several scientific and engineering contexts. Nevertheless, analytical solutions are usually impossible and critical difficulties arise also if numerically attacking the problem. A particularly challenging matter deals with the reproduction of solid media fracture due to the action of hydrodynamic forces, e.g. the hydraulic fracture and fracking process. Although different methodologies have been proposed for FSI problems, no recipes exist for automatically handling fragmentation problems. In this context, we propose a novel numerical procedure able to simulate solid fragmentation within fluid flows. The method is based on peridynamics for solid mechanics coupled with Navier-Stokes equations for the fluid phase through an Immersed Boundary Method (IBM). The main advantages of using peridynamics for solid mechanics consist in the natural crack detection and propagation. The proposed FSI method has been implemented into a parallel and several simulations have been performed. We will show tests on simple FSI configurations to benchmark the method. Then, we will present results on complex problems showing the ability of the method to simulate solid fragmentation within fluid flows. |
Sunday, November 18, 2018 4:27PM - 4:40PM |
D10.00010: A sharp interface in-cell-reconstruction volume-of-fluid method for simulating compressible flows with immiscible interfaces Karthik Kannan, Dominic Kedelty, Marcus Herrmann We present a hybrid tracking/capturing scheme using an in-cell-reconstruction technique (Smilijanovski, 1996) coupled to a volume-of-fluid volume tracking method, which is applicable to compressible flows that involve the interaction of shocks with phase interfaces. The proposed method maintains the phase interface as a sharp discontinuity within the continuum limit and avoids the need for small time steps by means of updating the volume averaged states of the cells. This is done by reconstructing the individual phase states from cell average values using the jump conditions across the phase interface and the geometric information provided by the volume-of-fluid method. The update to the volume averaged states is done by means of cell face aperature averaged updates resulting from pure-phase or mixed-face face regions. Effects of surface tension are incorporated directly into the individual phase states by the in-cell-reconstruction method and avoids errors due to discretization in typical surface tension modeling. The method also takes into account effects of viscosity and heat transfer due to heat conduction. A range of test cases is performed to demonstrate the robustness of the method. |
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