Marianne M. Francois

A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework

A new balanced-force algorithm is presented for modeling interfacial flow with surface tension. The algorithm is characterized by a pressure-correction method with the interfaces represented by volume fractions. Within this flow algorithm, we devise a continuous (e.g., continuum surface tension model) and a sharp (e.g., a ghost fluid method) interface representation of the surface-tension-induced interfacial pressure jump condition. The sharp interface representation is achieved by temporarily reconstructing distance functions from volume fractions. We demonstrate that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients. This balance holds for both continuous and sharp representations of interfacial surface tension. The algorithm design eliminates one of the elusive impediments to more accurate models of surface tension-driven flow, the remaining of which is accurate curvature estimation. To validate our formulation, we present results for an equilibrium (static) drop in two and three dimensions having an arbitrary density jump across the interface. We find that the sharp surface tension method yields an abrupt pressure jump across the interface, whereas the continuous surface tension method results in a smoother transition. Both methods, however, yield spurious velocities of the same order, the origin of which is due solely to errors in curvature. Dynamic results are also presented to illustrate the versatility of the method.

Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability

A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach (Li et al., 2013). The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid–vapor phase change. Using the model, the liquid–vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numerically reproduced in the LB community for the first time. The numerical results show that the basic features and the fundamental characteristics of boiling heat transfer are well captured, such as the severe fluctuation of transient heat flux in the transition boiling and the feature that the maximum heat transfer coefficient lies at a lower wall superheat than that of the maximum heat flux. Furthermore, the effects of the heating surface wettability on boiling heat transfer are investigated. It is found that an increase in contact angle promotes the onset of boiling but reduces the critical heat flux, and makes the boiling process enter into the film boiling regime at a lower wall superheat, which is consistent with the findings from experimental studies.

Efficient simulation of surface tension-dominated flows through enhanced interface geometry interrogation

In this paper, three improvements for modelling surface tension-dominated interfacial flows using interface tracking-based solution algorithms are presented. We have developed an improved approach to curvature estimation for incorporation into modern mesh-based surface tension models such as the Continuum Surface Force (CSF) and Sharp Surface Force (SSF) models. The scheme involves generating samples of curvature estimates from the multitude of height functions that can be generated from VOF representations of interfaces, and applying quality statistics based on interface orientation and smoothness to choose optimal candidates from the samples. In this manner, the orientation-dependence of past schemes for height function-based curvature estimation is ameliorated, the use of compact stencils for efficient computation can be maintained, and robustness is enhanced even in the presence of noticeable subgrid-scale disturbances in the interface representation. For surface tension-dominated flows, the explicit capillary timestep restriction is relaxed through timescale-separated slope limiting that identifies spurious modes in curvature evolution and omits them from contributing to surface force computations, thus promoting efficiency in simulation through the use of less timesteps. Efficiency in flow simulation is further promoted by incorporating awareness of interface location into multigrid preconditioning for Krylov subspace-based solution of elliptic problems. This use of interface-cognizance in solving problems such as the Helmholtz equation and the Poisson equation enables multigrid-like convergence in discontinuous-coefficient elliptic problems without the expense of constructing the Galerkin coarse-grid operator. The key improvements in the surface tension modelling and the numerical linear algebra are also applicable to level-set-based interfacial flow simulation.

A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations

A new, second-order accurate, volume conservative, material-order-independent interface reconstruction method for multi-material flow simulations is presented. First, materials are located in multi-material computational cells using a piecewise linear reconstruction of the volume fraction function. These material locator points are then used as generators to reconstruct the interface with a weighted Voronoi diagram that matches the volume fractions. The interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells. Convergence tests are shown demonstrating second-order accuracy. Static and dynamic examples are shown illustrating the superior performance of the method over existing material-order-dependent methods.

Cross-code comparisons of mixing during the implosion of dense cylindrical and spherical shells

We present simulations of the implosion of a dense shell in two-dimensional (2D) spherical and cylindrical geometry performed with four different compressible, Eulerian codes: RAGE, FLASH, CASTRO, and PPM. We follow the growth of instabilities on the inner face of the dense shell. Three codes employed Cartesian grid geometry, and one (FLASH) employed polar grid geometry. While the codes are similar, they employ different advection algorithms, limiters, adaptive mesh refinement (AMR) schemes, and interface-preservation techniques. We find that the growth rate of the instability is largely insensitive to the choice of grid geometry or other implementation details specific to an individual code, provided the grid resolution is sufficiently fine. Overall, all simulations from different codes compare very well on the fine grids for which we tested them, though they show slight differences in small-scale mixing. Simulations produced by codes that explicitly limit numerical diffusion show a smaller amount of small-scale mixing than codes that do not. This difference is most prominent for low-mode perturbations where little instability finger interaction takes place, and less prominent for high- or multi-mode simulations where a great deal of interaction takes place, though it is still present. We present RAGE and FLASH simulations to quantify the initial perturbation amplitude to wavelength ratio at which metrics of mixing agree across codes, and find that bubble/spike amplitudes are converged for low-mode and high-mode simulations in which the perturbation amplitude is more than 1% and 5% of the wavelength of the perturbation, respectively. Other metrics of small-scale mixing depend on details of multi-fluid advection and do not converge between codes for the resolutions that were accessible.

An interface reconstruction method based on analytical formulae for 2D planar and axisymmetric arbitrary convex cells

In this paper, we propose a non-iterative interface reconstruction method for 2D planar and axisymmetric geometries that is valid for arbitrary convex cells and intended to be used in multi-material simulation codes with sharp interface treatment for instance. Assuming that the normal vector to the interface is known, we focus on the computation of the line constant so that the polygon resulting from the cell-interface intersection has the requested volume. To this end, we first decompose the cell in trapezoidal elements and then propose a new approach to derive an exact formula for the trapezoids volumes. This formula, derived for both the planar and axisymmetric cases, is used to first bracket and then find the line constant that exactly matches the prescribed volume. The computational efficiency of the proposed method is demonstrated over a large number of reproducible conditions and against two existing methods.

A numerical method for interface reconstruction of triple points within a volume tracking algorithm

A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a triple point is described as the minimum of a constrained minimization problem inside an interfacial cell of the discretization. For given volume fractions of materials in the cell, an interior-point/Newton method is used for the reconstruction of the local geometry and the localization of the triple point. Initialization of the Newton method is performed with a derivative-free algorithm. Numerical results are presented for static and pure advection cases to illustrate the efficiency and robustness of the algorithm.

A hybrid incremental projection method for thermal-hydraulics applications

A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuska-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ? C F L ? 100 . The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos. A new second-order hybrid finite-element/finite-volume projection algorithm for transient viscous flow has been introduced.The hybrid discretization prevents pressure modes without using Rhie-Chow interpolation or a Petrov-Galerkin formulation.A monotonicity-preserving advection method shown to deliver second-order accuracy on mixed element topology meshes.Verification studies demonstrate hybrid projection solver accuracy and temporal stability for super-CFL conditions.

The balanced-force volume tracking algorithm and global embedded interface formulation for droplet dynamics with mass transfer

Understanding the complex interaction of droplet dynamics with mass transfer and chemical reactions is of fundamental importance in liquid-liquid extraction. High-fidelity numerical simulation of droplet dynamics with interfacial mass transfer is particularly challenging because the position of the interface between the fluids and the interface physics need to be predicted as part of the solution of the flow equations. In addition, the discontinuity in fluid density, viscosity and species concentration at the interface present additional numerical challenges. In this work, we extend our balanced-force volume-tracking algorithm for modeling surface tension force (Francois et al., 2006) and we propose a global embedded interface formulation to model the interfacial conditions of an interface in thermodynamic equilibrium. To validate our formulation, we perform simulations of pure diffusion problems in one- and two-dimensions. Then we present two and three-dimensional simulations of a single droplet dynamics rising by buoyancy with mass transfer.Copyright

BALANCED FORCE IMPLEMENTATION OF THE CONTINUUM SURFACE TENSION FORCE METHOD INTO A PRESSURE CORRECTION ALGORITHM

A consistent formulation is presented for modeling surface tension driven flow with the continuum surface tension force (CSF) model within a volume of fluid (VOF) method using a pressure-correction projection method. We show that a flow algorithm whose inherent design is motivated by legislating force balance gives an exact (to round off) balance between surface tension forces and pressure gradients that arise as a result. This design eliminates one of the elusive impediments to more accurate CSF-based surface tension models, the remaining of which is curvature estimation accuracy. To validate our formulation, we present results for an equilibrium (static) drop in two and three dimensions having an arbitrary density ratio and demonstrate in the process that scaling effects within the CSF framework are insignificant.Copyright