Session LK: Multiphase Flows V

An efficient and accurate coupling between Lagrangian front-tracking and unstructured Eulerian grids

Evolution of flow of immiscible fluids under high-shear poses severe challenges to the development of accurate and robust numerical techniques that can maintain a sharp separating interface. The implicit volume of fluid (VOF) advection using High Resolution Interface Capturing (HRIC) scheme offers the advantage of numerical stability at large time steps, but has been observed to cause interface diffusion at high shear. Advection using the standard Piecewise Linear Interface Calculation (PLIC), on the other hand, requires much smaller time steps. We have developed an efficient, accurate coupling approach between a sharp-interface front-tracking library and an \textit{unstructured-grid} implicit flow solver. The high efficiency results from a localized searching algorithm for grid cells close to the interface. The accuracy is obtained from a conservative interfacial force transfer between front and grid that preserves momentum balance and from a novel approach for constructing the density profile across the interface. Validation of the method with tests of drop deformation in high shear will be presented, with attention to efficiency and accuracy. The performance of this stand-alone front-tracking capability on unstructured grids suggests that the coupled approach may be well suited for simulations in complex domains.   

Sharp Interface Cartesian Grid Method for High Speed Multi-material Dynamics Problems

The dynamic response of materials to high-speed and high-intensity loading conditions due to shock waves, detonation waves, high-velocity impact and penetration processes is important in several applications including high-speed flows with droplets, bubbles and particles, and hypervelocity impact and penetration. To simulate such complicated high-pressure physics problems,a fixed Cartesian grid approach in conjunction with level set interface tracking is attractive. In this work, a sharp interface, Cartesian grid-based, Ghost Fluid Method is developed for resolving embedded fluid, elasto-plastic solid and rigid objects in hyper-velocity impact and high-intensity shock loaded environment. The embedded multi-material interface is tracked and represented by virtue of the level set interface tracking technique. The evolving interface and the flow are coupled via the GFM approach by meticulously enforcing the boundary conditions and jump relations exactly at the interface. A reflective boundary condition based approach is used to enforce the conditions on the interface. The subcell position of the interface and the topology of the interface are carefully embedded in the interpolation procedure. In addition, a tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. The broad range of results presented in this work demonstrates the flexibility and robustness of the current approach.   

A level set based method for modeling large density ratio, interfacial flows

We present a numerical methodology in the context of the level set method for modeling interfacial flows characterized by large density ratio. In this method, to advect momentum the conservative form of the momentum equation is solved. Using the level set function, the density of momentum fluxes is calculated based on the interface evolution. The same flux density is used for advecting mass, and thereby a tight coupling between mass and momentum transport is established. We present a set of results in which the density ratio ranges from 650 to 10,000 and demonstrate the capability of the method in handling flows with large interface deformations.   

An Embedded Boundary Method for Solving the Elliptic And Parabolic Interface Problems and Its application to the Stefan Problem

The embedded boundary method (EBM) on a Cartesian grid developed by Johansen and Colella has been extended to solve the elliptic/parabolic problems in 2D with an interior boundary (also called elliptic interface, parabolic interface problem). The method is a finite volume method. 2nd order accuracy in $L_{\infty}$ norm is achieved. As its application, a Stefan problem is solved. Problems with multiple components (3 or 4 components) meeting at a single Cartesian cell was also solved by using this method. The algorithm is implemented in C++. The computational domain is partitioned using Cartesian grid. To reduce the computational memory needed, each cell of the Cartesian grid could change itself to be different type for cells with at most 2 components or more complex cells with 3 or 4 components. Test results for 3D elliptic interface problems also show that it is 2nd order accurate in $L_{\infty}$ norm.   

Dynamics of morphology formation in phase-separation fronts

We discuss the formation of domains in the wake of a phase-separation front in one, two and three dimensions. Perhaps surprisingly, if such a phase-separation front migrates with a constant velocity it will form very regular structures of lamellar domains or cylindrical columns oriented either parallel or orthogonal to the phase-separation front. We show analytical predictions of how the structure, orientation, and size of the formed domains depends on the speed of the phase-separation front (as well as the volume fraction) if the dynamics is purely diffusive and show numerical verification of our theoretical results. When hydrodynamics becomes important, however, the results are more complicated: in more than one dimension the formed structures become more fractal in nature, with structures on many different length-scales.   

Dynamics of particle clusters at fluid/fluid interfaces

This talk is oriented toward research that describes the hydrodynamics of dense (relative to the lower fluid in a gravitational field) rigid particles at fluid-fluid interfaces through Direct Numerical Simulations (DNS). Understanding the factors that control the formation and stability of the complex rag layer (typically encountered during oil-water separation) is a motivation for the current study. The fundamental aspects of the problem at hand bear a connection with the formation of tight clusters of floating particles. Strong capillary forces are thought to promote this behavior. One of the challenges toward realizing the same in a numerical simulation is the implementation of a physically realistic boundary condition for the three phase moving contact line (MCL). To this end, we implement the recently proposed continuum form of the Generalized Navier Boundary Condition (Gerbeau and Lelievre, 2009) in a levelset and fictitious-domain based finite-element scheme and demonstrate its usefulness and accuracy through case studies.   

Theoretical base and numerical tools for modeling transitions between continuous and disperse multiphase motions

Transitions between continuous and disperse multiphase motions happen commonly in nature and in our daily life. The phenomena include dissolving sugar cubes in a cup, formation of rain and hail, shattering a piece of glass. The capability of numerically simulating these phenomena is both important to industrial applications and to the understanding of nature. Relative to other aspects in this topic, theories for disperse multiphase flow is better developed despite many important issues still to be resolved. The theory for continuous multiphase flow is still in its infancy. The study of transition between continuous and disperse multiphase motion is at an even earlier stage of development. In this talk, we describe a possible theoretical framework based on the probability and statistical theory and a useful numerical method in simulating these phenomena. Deficiencies in the theory and in the numerical method are also discussed.   

Role of Weber number in the primary breakup of liquid jets in crossflow

Atomization of liquid fuel controls the combustion efficiency and pollutant emissions from internal combustion engines and gas turbines. A liquid jet injected into a crossflow breaks up by developing liquid surface instabilities and deformations due to aerodynamic sources and liquid jet turbulence, among other causes. There is a pressing need to understand the origin and role of these instabilities in the breakup of a liquid jet. These instabilities can be accurately quantified in detailed numerical simulations of liquid jets. A spectrally-refined interface (SRI) tracking scheme for interface transport coupled to an accurate and robust Navier-Stokes/Ghost-fluid method gas-phase solver is employed to perform large-scale detailed numerical simulations of liquid jets in a laminar crossflow. The liquid Weber number controls the tendency of a liquid jet to break up, while the liquid Reynolds number controls the range of length scales in the liquid jet turbulence. The interplay and role of these phenomena in the primary breakup of liquid jets is quantified through a parametric study. Existing models for turbulent primary breakup of liquid jets in crossflow are reviewed based on the numerical results.   

An identification of coherent structures in an inhomogeneous turbulence

This study proposes a proper scaling of a vortex indicator for practical identification of coherent structures (CS) from an inhomogeneous wall turbulence at the Reynolds numbers of $Re_{\tau}=180$ and $400$. The Laplacian of the pressure, $\Theta$, is scaled by its time-space average $\Theta_{ave}$ and root-mean-square value $\Theta_{rms}$ to obtain a proper scaling for effective identification of CS, $\hat\Theta=\left(\Theta-\Theta_{ave}\right)/\Theta_{rms}$. Numerical turbulent flow realizations with a wall and a gas-liquid interface obtained by a direct numerical simulation technique are employed to confirm suitability of the proposed scaling. The results of this study exhibit that the probability density function (PDF) of $\hat\Theta$ is very similar without respect to the distance from the wall, unlike PDF of unscaled $\Theta$. Because of this statistical similarity, identification of CS based on $\hat\Theta$ is shown advantageous to separate all the essential CS from disorganized turbulent background using a unique threshold level, especially in the region adjacent to the wall and the gas-liquid interface. Several turbulent flow signatures at the gas-liquid interface suggest that a threshold of $1\le\Theta\le 2$ is preferable to identify all the essential CS in the whole of the turbulent flow domain, without ``contamination'' caused by misidentification of meaningless structures.