Session L46: Particle-Laden Flows: Modeling and Theory II

Euler-Lagrange scheme for modeling particle-laden flows in medical image-based geometries

We describe the implementation of a coupled computational fluid dynamics - discrete element method (CFD-DEM) approach for modeling particle-laden biological flows in patient-specific geometries. There have been significant advances in the Euler-Lagrange modeling paradigm in recent years, but this has been largely restricted to studying engineering problems on structured grids. Here, we extend the CRIMSON cardiovascular flow framework to model Lagrangian particles that interact with each other and are coupled with the fluid. The incompressible Navier-Stokes equations are solved using a stabilized finite-element method on an unstructured grid. Rigid particle collisions are modeled using a damped soft-sphere approach. We employ an efficient hash-table based cell-list to accelerate particle collision detection in complex domains. Particle-fluid coupling is performed using a two-stage procedure that decouples the particle sizes from the mesh element size. The resulting process is a consistent, conservative and convergent method that naturally handles complex geometries. These improvements contrast with prior approaches on unstructured grids. The method developed here is used to study benign paroxysmal positional vertigo which is caused by particles settling in the semi-circular canals of the inner ear.   

Filtered volume fraction fluctuations: a measure to model clustering in dilute, non-collisional particle-laden flow

Turbulent particle-laden flows are known to give rise to spatial heterogeneity (e.g. clustering) characterized by two-point statistics. However, most coarse-grained models only solve for one-point moments, challenging their ability to accurately reproduce important two-phase flow statistics. In this talk, we present a new set of equations describing the evolution of these flows that include fluctuating components of filtered fields that describe the level of clustering present in these flows. We demonstrate that for dilute heavy particles settling in homogeneous isotropic turbulence, the averaged filtered drag and filtered Reynolds-stress like term that dictates enhanced settling is correlated to this description of volume fraction fluctuation. A data-driven approach that efficiently traverses parameter space in direct numerical simulations to inform closures is proposed, providing both descriptive insights and directions for future modeling. The evolution of the fluctuation of filtered volume fraction is shown to be valuable in that it may enable better fits for unclosed quantities related to particle drag and particle-phase momentum flux in coarse-grained simulations.   

Chaotic Behaviour of Multiple Immersed Ellipsoids

Building on previous work (Essmann et al, 2020) exploring the complex dynamics of a single immersed ellipsoid, we investigate the dynamics of multiple immersed ellipsoids under both inviscid and viscous environments. Earlier, using our in-house fully-coupled 6DoF solid-fluid DNS solver, GISS (https://github.com/eessmann/GISS, Essmann et al 2020), we showed that a single body can present chaotic motions even under viscous environments under certain conditions due to vortex shedding. Here, we extend Kirchoff’s equations to multiple bodies under inviscid conditions, using Lamb (1932) as a starting point. Analytical solutions for added mass and inertia are no longer available for multiple bodies, and so we solve for the potential flow using boundary integral equations (BIE), and resolve for the forces on the bodies by evaluating the flow using a regularisation of the hypersingular BIE (Toh et al, 1994). Calculations are carried out in Rust and are parallelised with a high degree of efficiency. Rotational motion is represented using quaternions. Using recurrence quantification and cross-correlation analyses (Marwan et al, 2007), we will present how we can characterise chaos and how the number of solids affects chaos.   

Determination of the probability of randomly forced point-particle tracers

A method is proposed that determines the probability of the location and velocity of a randomly forced, Lagrangian point-particle trace. Randomness naturally describes deviations from the exact Stokes drag law of a spherical shaped point-particle for different shapes and physical conditions. A hyperbolic PDE model is derived that propagates this randomness into its joint PDF solution that governs the particle phase. A Method of Characteristics (MoC) solves the PDE locally and thus determines the probability of a single trace. The traces seeded at a tensorial grid of Jacobi quadrature points at initial time and computed over a finite time yield a high-order flow map. This flow map is used to determine marginals and moments of the PDF. The MoC approach is not subject to grid based numerical inaccuracies and instabilities in the solution of Eulerian form such as spatial approximation errors and Gibbs oscillations. We validate this novel framework with several tests and show that the MoC is accurate and computationally more efficient than the Eulerian method and Monte Carlo (MC) based methods.   

Modeling particle dispersion in a turbulent puff

In this work we consider particle dispersion in a turbulent pulsed jet. Unresolved subgrid-scale velocity fluctuations in coarse-grained simulations like large-eddy simulation and Reynolds-averaged Navier-Stokes play a significant role in particle dynamics. Stochastic models are commonly used to model the subgrid-scale velocity fluctuations 'seen' by particles as they have proven effective in recapturing one-point and two-time statistics. However, state-of-the-art continuous random walk models lack spatial correlation, leading to the loss of two-point statistics and geometric features such as clustering and preferential concentration. We present a two-point Lagrangian stochastic model designed to capture spatial particle distributions and maintain the one-point and two-time capabilities of classical stochastic models. Model coefficients are chosen to reproduce the correct scaling of particle-pair relative statistics. Comparisons of particle dispersion and preferential concentration between direct numerical simulations, large-eddy simulations, and experimental data demonstrate the utility of stochastic models and the need for a two-point formulation.   

Simulation and validation of a multiphase flow of hydriding ejecta particles

A hydride model for solid ejecta particles has been developed and presented previously with minimal validation [Regele, J. D., Schwarzkopf, J. D., Buttler, W. T., Harrison, A. K., A simple hydride model for cerium ejecta particles, 72nd Annual Meeting of the APS Division of Fluid Dynamics, Seattle, WA 2019]. That model is revisited here with more detailed validation by simulating the experiment which motivated the model's development and analyzing the entire multiphase flow field as is done in the experiment. A detailed comparison of the total ejecta mass produced, particle sizes, velocities and particle temperatures is performed to validate the hydriding particle model. The challenges with temperature validation are highlighted and different techniques for mitigating these issues are discussed.    

Large eddy simulation of turbulent gas-droplet flows using the fully Lagrangian approach

The fully Lagrangian approach (FLA) is a promising means of modelling gas-droplet flows, through its representation of the droplet phase as a continuum in combination with a seeding of Lagrangian trajectories which retain the mesoscopic detail of individual droplet motion. This provides a high resolution of the droplet number density field as it undergoes clustering and segregation in response to the structural behaviour of the carrier flow, and along with the advantages in both accuracy and computational economy that the FLA offers, makes it a suitable methodology for use within turbulent flows. The present work addresses this by developing a formulation of the FLA in the framework of large eddy simulation. In keeping with the continuum representation of the FLA, droplets are tracked in the filtered turbulent velocity field, and the sub-grid scale (SGS) fluid velocity is formally accounted for through the Lagrangian form of the droplet phase continuity equation. This contribution takes the form of an additional unclosed mass flux, and is modelled using a kinetic PDF approach, with the correlations between the droplet number density and SGS fluid velocity fluctuations being closed via a correlation splitting procedure that incorporates the non-local turbulent drift effects on the droplet phase. The evolution of the number density field calculated using this procedure is examined, and compared to the number density based on only the filtered fluid velocity field across a range of values of droplet inertia.   

Comparing turbulent dispersion models for RANS simulations of particle-laden flows

The ingestion of sand-particles into turbomachinery decreases their longevity and performance and can even lead to failure. To address these problems, studying particle deposition and erosion is of high interest in the field. For engineering design, RANS remains an important tool for analyzing turbulent flow behavior, due to low computational cost. RANS simulations solve for the time averaged velocity field. This presents an issue for particle-laden flow analysis since particles are affected by the velocity fluctuations within the flow field. In order to get physical results, RANS simulations are augmented with particle dispersion models that include the influence of small scale velocity fluctuations on particle trajectory.

This work investigates sand particle dispersion due particle dispersion models. The work uses a configuration previously described in [Miranda and Palmore, ASME J. Fluids Eng., vol 145, 2023]. Spherical sand-particles ranginging in size from 1 to 200 microns in diameter are released into a long cylindrical tube and exit to strike a test plate. For all simulations, the commercial CFD software Ansys Fluent is used and the RANS simulations are run with Reynolds-Stress and k-omega SST turbulence models. Variants of both the Discrete Random Walk and Continuous Random Walk dispersion models are used. The accuracy of particle trajectories from RANS simulations are evaluated by comparing to LES results.   

Analysis of Compressible Particle-Particle Interaction in Ejecta Particle Simulations

Ejecta physics play an important role in materials shocked by high explosives. When a shock impacts a surface of a solid material and melts it, the Richtmyer-Meshkov instability grows perturbations on the surface until particles are ejected. After release, the ejecta travel through the post-shock compressible flow. To simulate the large number of ejecta particles, an Euler-Lagrange approach is preferred to model the physics at a subgrid-scale level. If the volume fraction of the particles is high enough, one needs to resolve the particle-particle interaction. In this talk, we review efforts to model such systems, bring different force components of particle hydrodynamics to attention, and examine the relative importance of each term.   

The rise of a sphere along the axis of a rotating container: Revisiting Maxworthy's 1970 experiment on a computer

The flow induced by a rigid particle rising along the axis of a tall cylindrical container set in rigid-body rotation is computed over a parameter range similar to that explored experimentally by Maxworthy in his famous 1970 experiment.