An extended mixture model for the simultaneous treatment of small‐scale and large‐scale interfaces

Abstract

SUMMARYThe aim of this work is to present a new model based on the volume of fluid method and the algebraic slip mixture model in order to solve multiphase gas–fluid flows with different interface scales and the transition among them. The interface scale is characterized by a measure of the grid, which acts as a geometrical filter and is related with the accuracy in the solution; in this sense, the presented coupled model allows to reduce the grid requirements for a given accuracy. With this objective in mind, a generalization of the algebraic slip mixture model is proposed to solve problems involving small‐scale and large‐scale interfaces in an unified framework taking special care in preserving the conservativeness of the fluxes. This model is implemented using the OpenFOAM® libraries to generate a tool capable of solving large problems on high‐performance computing facilities. Several examples are solved as a validation for the presented model, including new quantitative measurements to assess the advantages of the method. Copyright © 2014 John Wiley & Sons, Ltd.

Lagrangian versus Eulerian integration errors

“…In order to emphasize the differences between the errors introduced in the spacetime integration for large time-steps using a Lagrangian or an Eulerian frame, the current case was also simulated with a large range of time-steps using PFEM-2 and comparing with results obtained by the widely known OpenFOAM code. The solver InterFOAM was chosen, which implements a Volume of Fluid (VoF) algorithm for multi-fluid flows [36] [37]. Another relevant feature to take into account when comparing both algorithms is that similar CPU times are required to solve a time-step.…”

Simulation of Reinforced Reactive Injection Molding with the Finite Volume Method

“…The models are implemented in OpenFOAM 4.1, using C++ as the program language and finite volume theory for the numerical solution [13][14][15]. In principal, the Navier-Stokes equations can be solved on structured and unstructured meshes.…”

“…This solver uses the Volume-of-Fluid-Method (VoF) for modeling multiphase flows. VoF separates the different phases using the dimensionless scalar α, which is equal to one in cells completely filled by phase 1, zero in cells filled with phase 2 and 0 < α < 1 in the interface regions [13,15]. In this work, α = 1 means that a control volume is completely filled with polymer resin, and α = 0 if it is filled with air.…”

“…On the other hand, Finite-Volume-based solvers, representing the state of research, focus on thermoplastic injection molding using incompressible and isothermal models [12]. In this study, the Finite-Volume-Method (FVM) is used, resolving the flux at the cell faces and using an Eulerian approach [13][14][15]. Due to this flow modeling, FVM provides a more realistic multiphase flow with physical significance on the fluxes, which is not possible in FEM by solving a Lagrangian mesh at the nodes.…”

“…Due to this flow modeling, FVM provides a more realistic multiphase flow with physical significance on the fluxes, which is not possible in FEM by solving a Lagrangian mesh at the nodes. For implementation and simulation, the open source Computational-Fluid-Dynamics (CFD) toolbox OpenFOAM 4.1 (OpenCFD Ltd., Bracknell, UK) [7,[12][13][14][15]] is used and well-known viscosity, curing and fiber orientation models are implemented to model the reinforced reactive injection molding process. A solver for compressible, non-isothermal multiphase flow is extended, using a phase depending boundary condition, defined to enable mold-filling simulation, by separating and interpolating boundary conditions for polymer and air.…”