Refined Level Set Grid Research Articles

Subgrid-scale Capillary Breakup Model for Liquid Jet Atomization

ABSTRACT A subgrid-scale capillary breakup model has been developed by coupling a Eulerian interface-capturing approach to a Lagrangian point particle method. At the fully resolved scale, the evolution of phase interface is captured by the Refined Level Set Grid method (RLSG), while the under-resolved, small-scale liquid structures are represented by Lagrangian point particles. To couple the level-set method with the Lagrangian approach, a numerical algorithm is developed to identify the under-resolved structures and compute their shape metric. The capillary instability theory is then applied to predict the sizes and number of post-breakup drops needed to replace them with Lagrangian drops. The secondary atomization of the Lagrangian drops is modeled by the stochastic breakup model. To validate the present model, numerical simulations are performed for the breakups of a single liquid filament and a round liquid coaxial jet. Grid-convergence studies for the drop-size distribution of the resulting spray are conducted and compared to the experimental data. The numerical results show good agreement with the experimental data. The present subgrid-scale capillary breakup model reduces the computational cost by relaxing the stringent grid resolution required for multi-scale atomization simulations.

An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets

We present a Runge–Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method [18,19]. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid [9] and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann [9]. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.

Geometry‐Aware Volume‐of‐Fluid Method

AbstractWe present a new framework to simulate moving interfaces in viscous incompressible two phase flows. The goal is to achieve both conservation of the fluid volume and a detailed reconstruction of the fluid surface. To these ends, we incorporate sub‐grid refinement of the level set with the volume‐of‐fluid method. In the context of this refined level set grid we propose the algorithms needed for the coupling of the level set and the volume‐of‐fluid, which include techniques for computing volume, redistancing the level set, and handling surface tension. We report the experimental results produced with the proposed method via simulations of the two phase fluid phenomena such as air‐cushioning and deforming large bubbles.

A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics

This paper presents a novel model for the sub-filter surface tension induced motion of interfaces separating immiscible fluids. A key feature of the proposed Sub-Grid Surface Dynamics (SGSD) model is to take the sub-filter interface dynamics fully into account by employing a dual-scale approach. Instead of modeling the sub-filter interface geometry, it is resolved on an auxiliary grid using the Refined Level Set Grid approach. The required sub-filter velocity field on the auxiliary grid is reconstructed solving a PDE in a narrow band surrounding the interface. With the fully resolved interface geometry available, the previously unclosed surface tension term in the filtered Navier–Stokes equations can be directly closed using explicit filtering. The novel model shows excellent results for different test cases, including sub-grid oscillations of drops, the sub-grid Rayleigh–Plateau instability, and the viscous capillary breakup of a ligament.

Primary atomization of a liquid jet in crossflow

In this fluid dynamics video, we present a visualization of the primary atomization of a turbulent liquid jet injected into a turbulent gaseous crossflow. It is based on a detailed numerical simulation of the primary atomization region of the jet using a finite volume, balanced force, incompressible LES/DNS flow solver coupled to a Refined Level Set Grid (RLSG) solver to track the phase interface position. The visualization highlights the two distinct breakup modes of the jet: the column breakup mode of the main liquid column and the ligament breakup mode on the sides of the jet and highlights the complex evolution of the phase interface geometry.

The Impact of Density Ratio on the Liquid Core Dynamics of a Turbulent Liquid Jet Injected Into a Crossflow

Atomizing liquids by injecting them into crossflows is a common approach in gas turbines and augmentors. Much of our current understanding of the processes resulting in atomization of the jets, the resulting jet penetration and spray drop size distribution have been obtained by performing laboratory experiments at ambient conditions. Yet, operating conditions under which jets in crossflows atomize can be far different from ambient. Hence, several dimensionless groups have been identified that are believed to determine jet penetration and resulting drop size distribution. These are usually the jet and crossflow Weber and Reynolds numbers and the momentum flux ratio. In this paper, we aim to answer the question of whether an additional dimensionless group, the liquid to gas density ratio must be matched. We perform detailed simulations of the primary atomization region using the refined level set grid (RLSG) method to track the motion of the liquid/gas phase interface. We employ a balanced force, interface projected curvature method to ensure high accuracy of the surface tension forces, use a multiscale approach to transfer broken off, small scale nearly spherical drops into a Lagrangian point particle description allowing for full two-way coupling and continued secondary atomization, and employ a dynamic Smagorinsky large eddy simulation (LES) approach in the single phase regions of the flow to describe turbulence. We present simulation results for a turbulent liquid jet (q=6.6, We=330, and Re=14,000) injected into a gaseous crossflow (Re=740,000) analyzed under ambient conditions (density ratio 816) experimentally by Brown and McDonnell [2006, “Near Field Behavior of a Liquid Jet in a Crossflow,” Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems]. We compare simulation results obtained using a liquid to gas density ratio of 10 and 100. The results show that the increase in density ratio causes a noticeable increase in liquid core penetration with reduced bending and spreading in the transverse directions. The post-primary atomization spray penetrates further in both the jet and transverse direction. Results further show that the penetration correlations for the windward side trajectory commonly reported in the literature strongly depend on the value of threshold probability used to identify the leading edge. Correlations based on penetration of the jet’s liquid core center of mass, on the other hand, can provide a less ambiguous measure of jet penetration. Finally, the increase in density ratio results in a decrease in wavelength of the most dominant feature associated with a traveling wave along the jet as determined by proper orthogonal decomposition.

ON SIMULATING PRIMARY ATOMIZATION USING THE REFINED LEVEL SET GRID METHOD

The atomization process of turbulent liquid jets is as of this day not well understood. Detailed numerical simulations can help study the fundamental mechanisms in regions where experimental access and analysis is difficult. This paper presents simulation results of the primary atomization of round turbulent liquid jets injected into stagnant high-pressure air under diesel engine conditions using the refined level set grid approach. A balanced force approach is used to accurately account for surface tension forces using an interface projected curvature method to minimize erroneous spurious currents. Broken off, small-scale nearly spherical drops are transferred into a Lagrangian point particle description allowing for full two-way coupling. The physical mechanisms resulting in the initial breakup of the jet are discussed. We analyze the impact of finite grid resolution on the phase interface geometry of the injected liquid core and discuss the impact of the automatic topology-change length scale inherent in the fixed grid interface, capturing methods like the level set method. Drop size distributions resulting from primary atomization are presented, showing that grid-independent drop sizes can be achieved for liquid structures resolved by at least six grid points.

Modeling Wall Film Formation and Breakup Using an Integrated Interface-Tracking/Discrete-Phase Approach

We propose a computationally tractable model for film formation and breakup based on data from experiments and direct numerical simulations. This work is a natural continuation of previous studies where primary atomization was modeled based on local flow information from a relatively low-resolution tracking of the liquid interface [Arienti and Soteriou, 2007, “Dynamics of Pulsed Jet in Crossflow,” ASME Paper No. GT2007-27816]. The submodels for film formation proposed here are supported by direct numerical simulations obtained with the refined level set grid method [Herrmann, 2008, “A Balanced Force Refined Level Set Grid Method for Two-Phase Flows on Unstructured Flow Solver Grids,” J. Comput. Phys., 227, pp. 2674–2706]. The overall approach is validated by a carefully designed experiment [Shedd et. al., 2009, “Liquid Jet Breakup by an Impinging Air Jet,” Forty-Seventh AIAA Aerospace Sciences Meeting. Paper No. AIAA-2009-0998], where the liquid jet is crossflow-atomized in a rectangular channel so that a film forms on the wall opposite to the injection orifice. The film eventually breaks up at the downstream exit of the channel. Comparisons with phase Doppler particle analyzer data and with nonintrusive film thickness point measurements complete this study.

The influence of density ratio on the primary atomization of a turbulent liquid jet in crossflow

In this paper, we study the impact of density ratio on turbulent liquid jet in crossflow penetration and atomization if all other characteristic parameters, i.e., momentum flux ratio, jet and crossflow Weber and Reynolds numbers, are maintained constant. We perform detailed simulations of the primary atomization region using the refined level set grid method to track the motion of the liquid/gas phase interface. We employ a balanced force, interface projected curvature method to ensure high accuracy of the surface tension forces, use a multi-scale approach to transfer broken-off, small scale nearly spherical drops into a Lagrangian point particle description allowing for full two-way coupling and continued secondary atomization, and employ a dynamic Smagorinsky large eddy simulation approach in the single phase regions of the flow to describe turbulence. We compare simulation results obtained previously using a liquid to gas density ratio of 10 for a momentum flux ratio 6.6, Weber number 330, and Reynolds number 14,000 liquid jet injected into a Reynolds number 740,000 gaseous crossflow to those at a density ratio of 100, a value typical for gas turbine combustors. The results show that the increase in density ratio results in a noticeable increase in jet penetration, change in drop size distribution resulting from primary atomization, change in drop velocities generated by primary atomization in the crossflow and jet direction, but virtually no change in drop velocities in the transverse direction.

Detailed Numerical Simulations of the Primary Atomization of a Turbulent Liquid Jet in Crossflow

This paper presents numerical simulation results of the primary atomization of a turbulent liquid jet injected into a gaseous crossflow. Simulations are performed using the balanced force refined level set grid method. The phase interface during the initial breakup phase is tracked by a level set method on a separate refined grid. A balanced force finite volume algorithm together with an interface projected curvature evaluation is used to ensure the stable and accurate treatment of surface tension forces even on small scales. Broken off, small scale nearly spherical drops are transferred into a Lagrangian point particle description allowing for full two-way coupling and continued secondary atomization. The numerical method is applied to the simulation of the primary atomization region of a turbulent liquid jet (q=6.6, We=330, Re=14,000) injected into a gaseous crossflow (Re=570,000), analyzed experimentally by Brown and McDonell (2006, “Near Field Behavior of a Liquid Jet in a Crossflow,” ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems). The simulations take the actual geometry of the injector into account. Grid converged simulation results of the jet penetration agree well with experimentally obtained correlations. Both column/bag breakup and shear/ligament breakup modes can be observed on the liquid jet. A grid refinement study shows that on the finest employed grids (flow solver 64 points per injector diameter, level set solver 128 points per injector diameter), grid converged drop sizes are achieved for drops as small as one-hundredth the size of the injector diameter.

A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure

This paper presents a parallel Eulerian/Lagrangian multi-scale coupling procedure for two-phase flows. At the fully resolved scale, the dynamically evolving phase interface is tracked using a Eulerian approach. In regions of the flow, where the phase interface geometry can no longer be resolved adequately, separated, small scale liquid structures are described by a Lagrangian point particle approach. The coupling procedure of these two descriptions consists of an efficient parallel algorithm that identifies tracked liquid candidate structures, removes them from the resolved Eulerian description, and inserts them into the Lagrangian description preserving their position, mass, momentum, and lower order shape. While in principle applicable to level set, Volume of Fluid, and marker particle interface tracking methods for the fully resolved scale, this paper focuses on examples from atomization simulations using the refined level set grid method.

A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids

A balanced force refined level set grid method for two-phase flows on structured and unstructured flow solver grids is presented. To accurately track the phase interface location, an auxiliary, high-resolution equidistant Cartesian grid is introduced. In conjunction with a dual-layer narrow band approach, this refined level set grid method allows for parallel, efficient grid convergence and error estimation studies of the interface tracking method. The Navier–Stokes equations are solved on an unstructured flow solver grid with a novel balanced force algorithm for level set methods based on the recently proposed method by Francois et al. [M.M. Francois, S.J. Cummins, E.D. Dendy, D.B. Kothe, J.M. Sicilian, M.W. Williams, A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, J. Comput. Phys. 213 (2006) 141–173] for volume of fluid methods on structured grids. To minimize spurious currents, a second order converging curvature evaluation technique for level set methods is presented. The results of several different test cases demonstrate the effectiveness of the proposed method, showing good mass conservation properties and second order converging spurious current magnitudes.