Damir Juric

Numerical simulation of Faraday waves

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier-Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, p. 49). The finite-amplitude results are compared with the experiments of Kityk et al. (Phys. Rev. E, vol. 72, 2005, p. 036209). In particular, we reproduce the detailed spatio-temporal spectrum of both square and hexagonal patterns within experimental uncertainty. We present the first calculations of a three-dimensional velocity field arising from the Faraday instability for a hexagonal pattern as it varies over its oscillation period.

High Order Level Contour Reconstruction Method

Complex interfacial physics arising from geometric curvature associated with surface tension as well as phase transformation make it a formidable task to design an accurate, reliable, and yet simple method for direct computation of multiphase flows. Hybrid methods mixing conventional, Volume-of-Fluid, Level Set, Phase Field, and Front Tracking methods have recently become popular in an attempt to overcome the shortcomings of each method alone. We developed the Level Contour Reconstruction Method (LCRM) as part of a hybrid method for treating the complex interface geometry associated with general three-dimensional multiphase flows. The main idea in that work focused on a simple and robust algorithm especially suited for dynamic interfaces in the three-dimensional case by combining characteristics of both Front Tracking and Level Set methods. In this article we describe a modification to the LCRM which introduces a high order interpolation kernel during the course of the interface reconstruction along with a new hybrid surface tension formulation. With this we can essentially eliminate any mass redistribution between regions of differing curvature and reconstruct the interface accurately and smoothly. The improvement with high order reconstruction is also noticeable vis a vis spurious currents which are further decreased by two orders of magnitude over the previous linear reconstruction method. Moreover, there is no disturbance concurrent with reconstruction and the solution fidelity is not influenced by the reconstruction time step. This High Order Level Contour Reconstruction Method retains the simplicity of the original LCRM and avoids complicated interface smoothing procedures.

The Local Front Reconstruction Method for direct simulation of two- and three-dimensional multiphase flows

We present a new interface reconstruction technique, the Local Front Reconstruction Method (LFRM), for incompressible multiphase flows. This new method falls in the category of Front Tracking methods but it shares automatic topology handling characteristics of the previously proposed Level Contour Reconstruction Method (LCRM). The LFRM tracks the phase interface explicitly as in Front Tracking but there is no logical connectivity between interface elements thus greatly easing the algorithmic complexity. Topological changes such as interfacial merging or pinch off are dealt with automatically and naturally as in the Level Contour Reconstruction Method. Here the method is described for both two- and three-dimensional flow geometries. The interfacial reconstruction technique in the LFRM differs from that in the LCRM formulation by foregoing using an Eulerian distance field function. Instead, the LFRM uses information from the original interface elements directly to generate the new interface in a mass conservative way thus showing significantly improved local mass conservation. Because the reconstruction procedure is independently carried out in each individual reconstruction cell after an initial localization process, an adaptive reconstruction procedure can be easily implemented to increase the accuracy while at the same time significantly decreasing the computational time required to perform the reconstruction. Several benchmarking tests are performed to validate the improved accuracy and computational efficiency as compared to the LCRM. The results demonstrate superior performance of the LFRM in maintaining detailed interfacial shapes and good local mass conservation especially when using low-resolution Eulerian grids.

Alternating hexagonal and striped patterns in Faraday surface waves.

A direct numerical simulation of Faraday waves is carried out in a minimal hexagonal domain. Over long times, we observe the alternation of patterns we call quasihexagons and beaded stripes. The symmetries and spatial Fourier spectra of these patterns are analyzed.

A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows

We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 262144 threads or more (limited only by the availability to us of more threads). The code is wholly written by the authors in Fortran 2008 and uses a domain decomposition strategy for parallelization with MPI. The fluid interface solver is based on a parallel implementation of the LCRM hybrid front tracking/level set method designed to handle highly deforming interfaces with complex topology changes. We discuss the implementation of this interface method and its particular suitability to distributed processing where all operations are carried out locally on distributed subdomains. We have developed parallel GMRES and Multigrid iterative solvers suited to the linear systems arising from the implicit solution of the fluid velocities and pressure in the presence of strong density and viscosity discontinuities across fluid phases. Particular attention is drawn to the details and performance of the parallel Multigrid solver. The code includes modules for flow interaction with immersed solid objects, contact line dynamics, species and thermal transport with phase change. Here, however, we focus on the simulation of the canonical problem of drop splash onto a liquid film and report on the parallel performance of the code on varying numbers of threads. The 3D simulations were run on mesh resolutions up to 10243 with results at the higher resolutions showing the fine details and features of droplet ejection, crown formation and rim instability observed under similar experimental conditions.

Effects of Surface Evaporation and Condensation on the Dynamics of Thin Liquid Films for the Porous Wetted Wall Protection Scheme in IFE Reactors

ABSTRACT A numerical investigation has been conducted to analyze the fluid dynamic aspects of the porous wetted wall protection scheme for IFE reactor first walls. A level contour reconstruction method has been used to track the three-dimensional evolution of the liquid film surface on porous downward facing walls with different initial film thickness, liquid injection velocity through the porous wall, surface disturbance amplitude, configuration and mode number, liquid properties, and surface inclination angle. Here, we report on the effects of evaporation and condensation at the liquid film surface on the dynamics of film flow, the free surface topology, the frequency of liquid droplet formation and detachment, the minimum film thickness between explosions, and the equivalent diameter of detached droplets. Generalized charts, which allow designers of conceptual IFE reactors to identify appropriate “windows” for successful operation of the wetted wall protection concept for different coolants are presented.

Fluid Dynamic Aspects of the Porous Wetted Wall Protection Scheme for Inertial Fusion Energy Reactors

A numerical and experimental investigation has been conducted to analyze the fluid dynamic aspects of the porous wetted wall protection scheme for inertial fusion energy (IFE) reactor first walls. A level contour reconstruction method has been used to track the three-dimensional evolution of the liquid film surface on porous downward-facing walls with different initial film thickness, liquid injection velocity through the porous wall, surface disturbance amplitude, configuration and mode number, liquid properties, and surface inclination angle. Generalized charts for the computed droplet detachment time, detached droplet equivalent diameter, and minimum film thickness during the transient for various design parameters and coolant properties are presented. In order to validate the numerical results over a wide range of parameters, an experimental test facility has been designed and constructed to simulate the hydrodynamics of downward-facing porous wetted walls. Nondimensionalization of the model shows that water can be adequately used as a simulant to validate the numerical results. Preliminary experimental results show good agreement with model predictions. The results of this investigation should allow designers of conceptual IFE reactors to identify appropriate “windows” for successful operation of the porous wetted wall protection concept for different coolants.

A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant

Abstract A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu and Tryggvason (JCP 274 (2014) 737–757) [17] is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753–778, [8] ) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.

A numerical model for the simulation of low Mach number gas‐liquid flows

This work is devoted to the numerical simulation of gas‐liquid flows. The liquid phase is considered as incompressible, while the gas phase is treated as compressible in the low Mach number approach. We present a model and a numerical method aimed at the computation of such two‐phase flows. The numerical model uses a lagrangian front‐tracking method to deal with the interface. The model being validated with a 1‐D reference solution, results in the 2‐D case are presented. Two air bubbles are enclosed in a rigid cavity and surrounded with liquid water. As the initial pressure of the two bubbles is set to different values, an oscillatory motion is induced in which the bubbles undergo alternate compression and dilatation associated with alternate internal heating and cooling. This oscillatory motion can not be sustained and a damping is finally observed. It is shown in the present work that thermal conductivity of the liquid has a significant effect on both the frequency and the damping time scale of the osci...