Session T20: Particle Laden Flows

High-speed particle-laden flows over double-cone

Extreme weather conditions with active volcano eruptions around the world impose increased uncertainties for flight safety. One of the uncertainties is induced by the multiphase flow system formed by the volcano ash suspended in the air. High-speed vehicles traveling in such particle-laden flows experience significant challenges compared to their travel in the clear air, such as surface erosion, ventilation clog, and increased heat transfer rate. However, the evolution of the particle phase in shock-dominant flows and the impact of particle-laden flow are not well understood. To this end, we apply a one-way coupling Lagrangian approach to model the evolution and impact of solid particles with various diameters in a flow at M=16 over a 25^o-55^o double cone. A DSMC solver is used to simulate gas phases at Reynolds numbers of 9.35x10⁴ to 3.74x10⁵. As the Reynolds number increases, a larger separation region with a secondary vortex structure is formed between two contact cones, and the shock layers become thinner. The study will address the changes in shock structure and separation region that will affect the evolution of solid particles depending on the initial diameters and the impact on the surface of the double-cone.    

Bifurcations in droplet collisions

We study bifurcations in the collision dynamics of micron-sized water droplets in air. Collisions are caused either by differential settling under gravity in a quiescent fluid, electrostatic attractions, or by a straining flow that brings the droplets together. We take into account hydrodynamic interactions between the droplets and the breakdown of the continuum approximation at short distances. We show how bifurcations of equilibria and grazing bifurcations explain the parameter dependence of the collision cross section.

    

Development of an Eulerian Polydisperse Multiphase Flow Model

The effects of polydisperse particle size distributions on the physics of compressible multiphase systems, such as volcanic eruptions and metalized blasts, can have a significant impact on the particle dynamics. For example, in dust explosion scenarios, the smaller particles closely follow the flow and ignite and burn quickly. Larger particles in the size distribution have much longer ignition and burning time scales, which substantially increases the duration of the explosion. Most Eulerian multiphase models do not account for realistic particle size distributions. To overcome these limitations, a polydisperse Eulerian multiphase flow model was developed based on quadrature-based moment methods. The transport equations that couple a compressible gas to a polydisperse mixture of particles was derived using kinetic theory. The gas-polydisperse multiphase model accounts for particle collisions, drag, convective heat transfer, compaction waves, etc. Ongoing work includes using more accurate numerical flux schemes, such as HLLC and AUSM+-up, and adding chemical reactions to simulate dust explosion scenarios.   

Modeling strategies for aerodynamic interaction in dense particulate distributions

Gas-particle multiphase systems in several scenarios have dense particulate distributions. In these regimes, the gas flow modification by near neighbor particles alters the drag and lift forces experienced by the particulate distribution. The average drag force experienced by these distributions is provided using empirical relations modeled based on experimental and numerical investigations. The variability within the particle force distribution is not understood clearly or modeled to the best of our knowledge. In this work, we will use the direct simulation Monte Carlo (DSMC) method to obtain particle resolved force distributions. Neural network architecture informed by the high-fidelity results will be used to develop a model for the particle force distribution.

Particular emphasis is to incorporate a Knudsen number correction for dense particulate flows in dilute gas regimes.   

Automated framework for data-based modeling of filtered drag for coarse-grained simulations of fluidized beds

Data-based approaches relying on Artificial Neural Networks (ANN) have recently been proposed to model the drag correction factor in coarse-grained simulations of fluidized beds, showing excellent agreement with the physics, especially compared to simulations employing crude analytical models. However, the accuracy of ANNs is largely influenced by the chosen architecture and hyperparameters (activation functions, number of epochs, learning rate etc.), and no defined rules are available for the user to set these a priori. Therefore, the prediction accuracy becomes largely dependent on user expertise in hand-tuning hyperparameters via grid or random searches. In this work, an automated framework to train ANN-based models for the correction coefficient of gas-particle drag is proposed and validated a posteriori. A probabilistic model is first constructed via Bayesian optimization to converge, in an unsupervised fashion, to the optimal architecture and hyperparameters for the ANN. Three different acquisition functions for the design space exploration are tested (i.e., probability of improvement, expected improvement, and lower confidence bound), and their influence on the networks' size and accuracy of the simulations is assessed. Finally, a semi-analytical linear formulation to model the dependence of the drag correction factor from the pressure gradient (for different conditions of void fraction and slip velocity) is derived by means of the ANN predictions.   

Comparisons of Explosive Dispersal of High-Volume Fraction Particle Beds in Static and Supersonic Conditions

Explosive dispersal is a rich and challenging topic of research in the multiphase flow community. Curious questions arise when comparing explosive dispersal in different environments such as static and supersonic regimes. We simulate an explosive dispersal of a high-volume fraction particle bed in static, Mach 3 and 6 ambient conditions. This is done using an Eulerian-Lagrangian finite volume code. The geometry of the explosive dispersal is simulated in an axisymmetric barrel with an exit into ambient conditions. A reactive burn model was used to provide the initial conditions of the explosive with the particle bed in between the explosive and the barrel exit. The non-static conditions were setup with a startup simulation that allowed a bow shock to form over the barrel before the explosive and particle bed are released. Flow and particle metrics were captured using three virtual probe plates in three different locations downstream of the barrel exit. These plates capture the incipient flow properties at various times throughout the simulation as they do not interfere with the flow.

    

Particle-laden underexpanded jets: An experimental study

It is well-known that in turbulent two-phase flows with enough mass loading, the added inertial particles can modulate the surrounding flows via momentum transfer and flow interactions with particle wakes. However, most existing work is limited to the incompressible flow regime, with little known about how inertial particles modulate compressible and supersonic flows. In particular, the large slip velocity between the two phases can sometimes lead to the formation of bow shocks around the particles. Although small and local, these shocks can significantly affect the pressure and gas density in the adjacent areas and could merge with other ambient shock structures and lead to flow modulations that are entirely different from the incompressible counterpart. In this work, an experiment was conducted by tracking both the particle and gas phases of a sonic jet. A systematic study was performed to understand particle and gas dynamics as a function of the total pressure ratio, particle diameter, particle volume fraction, and mass loading. These results will be compared with high-fidelity simulations performed at the University of Michigan in the companion presentation titled, "Particle-laden underexpanded jets: A numerical study."   

Particle-laden underexpanded jets: A numerical study

We present numerical simulations of particle-laden underexpanded jets under a wide range of nozzle pressure ratios, particle sizes, and particle mass flow rates. The simulations are performed using a high-order, low dissipation Eulerian-Lagrangian framework and compared to companion experiments performed at Johns Hopkins University (Particle-laden underexpanded jets: An experimental study). The flow configuration allows for direct evaluation of gas-particle dynamics in high-speed flows exhibiting strong gas-phase compressibility. The effect of drag, mass loading on particle velocity and acceleration statistics are reported. Despite the moderately low volume fractions considered (volume loading < 0.2%), two-way coupling between the phases results in significant changes to the Mach disk location and diameter. The extent to which particles modify the Mach disk and the mechanisms responsible are reported.   

A Multiphase Approach in Modeling Heat Transfer from the Assemblage of Firebrands

Wildfire propagation is driven by two main mechanisms that are (1) the spread of local fire front through convection and radiation heat transfer during direct exposure of fuels to flames and (2) firebrand showers, also known as ember attacks. Firebrand showers are the ignition of spot fires as a result of the generation, transport, and deposition of firebrands away from the fire line. It is known that the combustion state of the firebrands, their assemblage patterns, and the reciprocal interactions within the boundary layer influence heat transfer to the recipient surface significantly. However, systematic experimentation on the confluence of these parameters is very challenging. Thus, this work introduces a coupled CFD-DEM approach to modeling the transport and assemblage of firebrands through the boundary layer. A series of numerical simulations are conducted, and the results show the aptitude of the methodology in quantifying the influential factors on heat transfer from the firebrands to the exposed surfaces. In addition, simulations provide insights into forming a preheating zone ahead of the assemblage that may contribute to drying the fuel surface before the arrival of firebrands. This finding may improve our understanding of the time scales involved in spot fire ignition.   

Self-induced velocity disturbance correction in Euler-Lagrange simulations of dense particle-laden flows

When simulating dense particle-laden flows with the volume-filtered Euler-Lagrange (VFEL) method, the flow disturbance caused by the transfer of momentum from a moving point-particle to the underlying fluid is known to introduce an error in the estimation of the fluid forces acting on this particle. This flow disturbance indeed prevents direct access to the local undisturbed fluid velocity, which is needed to estimate fluid-particle forces with reduced models. Over the past years, several models have been proposed so as to correct this error. However, they mostly rely on steady Stokes/Oseen flow solutions, augmented with semi-empirical factors accounting for inertial and/or transient effects. In this work, we present a model that considers both (weak) inertia and transient effects, together with the local volume fraction, for recovering the undisturbed velocity at the location of a point-particle in VFEL simulations. The model is obtained from discretising the linearised governing equations of the particle's self-induced flow disturbance, themselves originating from the governing volume-filtered equations of the Eulerian phase. As such, its convergence in time and space can be proven, and it does not necessitate ad-hoc or empirical parameters. The proposed model is validated with several representative test-cases.   

A neural network-based model for magnetic particle tracking and its application in the study of fluidization

The recently developed magnetic particle tracking (MPT) technology provides a new tool for flow diagnosis in fully opaque environments like those in fluidized bed and sediment transport. The MPT can measure both translation and rotation of a particle, which is crucial to study the particle dynamics. Current reconstruction algorithms in MPT include semi-analytical solver, optimization, and Kalman filter, among others. These methods have certain limitations. For instance, the analytical solver can hardly be extended to multi-particle systems, and the optimization is time-consuming. In this study, a neural network (NN) based model is developed to reconstruct the particle trajectory and orientation. The network architecture uses the multi-layer perceptron for reconstruction and gated recurrent unit for denoising. After initial training, the network model can provide particle trajectories in real time.  More importantly, the NN-based model can simultaneously reconstruct trajectories of several particles, which is a big advantage compared to the existing methods. This progress enables us to study particle collisions, two-point correlations, and other statistical properties. This system has been used to study the dynamics of particles in a fluidized bed.

    

Turbulence modulation by slender fibers in a channel flow

We numerically investigate the turbulence modulation by slender fibers in a turbulent channel flow at shear Reynolds number 300. Our Euler-Lagrangian approach is based on a Direct Numerical Simulation of the flow combined to the rod-chain pointwise representation of flexible fibers (Dotto et al., 2020) together with the ERPP method to account for the momentum exchange between the two phases (Battista et al., 2019). Such an investigation is enabled by a novel algorithm that makes the resolution of dispersed systems of constraint equations (representing the fibers) compatible with a state of the art, GPU-accelerated flow solver. We report a statistical analysis of the interaction between fibers and the flow at moderate concentration phi = 10^(-4), for slender particles of aspect ratio r=100 and dimensionless length L+ = 35 in wall units, which extends up to the inertial range of the turbulent scales. Turbulence modulation is reported for both tracer-like and almost neutrally buoyant fibers, characterized by Stokes number St=0.05, and inertial heavy fibers, characterized by Stokes number St=5, allowing us to focus on the influence of particle inertia on drag reduction (Gillissen et al., 2007; Wang et al., 2021).