Session EV: Particle Laden Flows: Simulations I

Is Stokes number an appropriate indicator for turbulence modulation by particles of Taylor-length-scale size?

It has been established both experimentally and numerically (e.g. Ferrante and Elghobashi (Phys. Fluids 2003)), that the Stokes number, $\tau_p/\tau_k$, can be used as an indicator to determine the extent to which small particles, $d_p < \eta$, modify the turbulence structure, for fixed values of their volume fraction, and mass fraction. Here, $\tau_p$, $d_p$, $\eta$ and $\tau_k$ are respectively the particle's response time and diameter, the Kolmogorov length- and time-scales. The objective of the present study is to investigate whether $\tau_p/\tau_k$ can also be used as an indicator for the modulation of turbulence by particles of the Taylor-lengthscale size, i.e. $ d_p \sim \lambda >> \eta$. We employ DNS with an immersed boundary method to fully resolve the flow around thousands of freely moving particles of Taylor-lengthscale size ($d_p \sim \lambda $) in decaying isotropic turbulence with initial $Re_\lambda = 110$ . Our results show that although the particles in different test cases have identical Stokes number and volume fraction, they have different effects on the turbulence kinetic energy, $E(t)$ and its dissipation rate $\varepsilon(t)$. For example, particles with smaller diameter and larger density ratio, $\rho_p/\rho_f$, augment $\varepsilon(t)$, resulting in a faster decay of $E(t)$. Our conclusion is that $\tau_p/\tau_k$ is not an appropriate indicator for determining the extent of turbulence modulation by particles with $d_p \sim \lambda $.   

Direct numerical simulation of dense particle-laden flows - Investigation of the forces acting on the particles

Resolved particle direct numerical simulation of dense particulate flows is used to investigate gas-particle interactions in the case of moving and colliding particles. Numerics are based on an immersed boundary implementation that discretely conserves mass and momentum (Meyer et al., JCP 2010). Geometry is accounted for through fictitious cut cell algorithm. Fluxes are rescaled based on gas face and gas cell fractions, while second order accurate volume and surface calculations are obtained through marching tetrahedra reconstruction of the interface. This approach relaxes flow blockage due to the immersed boundaries and is consistent with the soft sphere model used for particle collisions. A Lagrangian solver describes the particle motion. Conservation of momentum across phases is ensured since the forces applied to the particles are directly derived from the Navier-Stokes source terms. This new tool allows investigating the accuracy of existing drag models for freely moving particles (finite Stokes) and colliding particles (sudden and frequent direction changes).   

Direct numerical simulation of flow including dense solid particles having microscopic arrangements

In the flows including dense solid particles such as gas-fluidized beds, particles take complex arrangements as a result of interactions with surrounding particles, walls and gas flows. This kind of structure formation gives large influence on the overall flow behavior. Due to the existence of dense particles, it is still difficult to investigate the microscopic flows occurring in the narrow gaps in-between particles accurately and it has not been discussed well up to the present. In the present study, a direct numerical simulation by coupling discrete element method (DEM) and immersed boundary method (IBM) is performed. This is the first step of our continuing study and the drag force working on particles and permeability of flows are investigated in fixed bed conditions. In addition to the particle arrangement, the solid volume fraction and Reynolds number are varied and its influence is discussed. The results of a two-dimensional gas-fluidized bed are also presented in the study.   

Particle Dispersal in Rapid Expanding Gas Flow: Importance of Unsteady Force and Heat Transfer

When a highly compressed gas-particle mixture is suddenly released, the particles will be dispersed outward in very high speed driven by the rapid expanding gas. This is a phenomenon which can be observed in nature, such as volcanic eruption, and many industrial applications, such as detonation of multiphase explosives. The unsteady compressible nature of the gas flow coupled with the motion of dispersing particles makes accurate prediction of particle behavior challenging. The unsteady force and heat transfer become very important in the momentum and energy transfer between the gas and particle phases. A multiphase flow model is suggested to simulate this problem by Eulerian-Lagrangian approach. The significance of the unsteady force and heat transfer to the quasi-steady force and heat transfer are first justified by using the presented model to solve the problem of shock-particle interaction. The peak values and the total impulses of different forces and heat transfers show that the unsteady force and heat transfer are important. Then the multiphase model will be used to solve the problem of particle dispersal in rapid expanding flow. This problem can be viewed as an extension of the classic problem considered by Brode H. L. (J.\ Appl.\ Phys., Vol.\ 26, 1955, pp.\ 766-775). One-way coupled simulations are carried out for several initial conditions and particle properties.   

Extension of Basset-Boussinesq-Oseen and Maxey-Riley Equations to Compressible Flows

Viscous compressible flow around a sphere is considered in the limit of vanishing Reynolds and Mach numbers. Using the analytical solution derived in earlier works, an exact expression for the transient force on a sphere undergoing arbitrary motion with the inclusion of compressibility effects is presented. The transient force is decomposed into quasi-steady, inviscid unsteady, and viscous unsteady components. The influence of compressibility on each of these components is examined. Numerical results for the transient force are in excellent agreement with theory. The present formulation thus offers an explicit expression for the unsteady force in the time domain and can be considered as a generalization of the Basset-Boussinesq-Oseen equation to the compressible flow regime that can be used in numerical simulations of compressible multiphase flows. An extension of Maxey-Riley equation for particle motion in non-homogeneous compressible flows is also proposed.   

Tracking Rigid Spherical Particles in Incompressible Flows via Dissipative Hydrodynamics

Solutions for particle trajectories computed using dissipative hydrodynamics (DHD) for rigid spherical particles are discussed. DHD reproduces the many-body hydrodynamics of Stokesian Dynamics (SD), but is more computationally efficient. DHD satisfies the fluctuation-dissipation theorem of Dissipative Particle Dynamics (DPD) and therefore is not hindered by the relaxation-time limitations of Stokesian Dynamics. For a given continuum flow field, the translations and rotations of multiple particles are calculated taking into account both stochastic dissipative effects and deterministic conservative forces. Examples of particle tracking in two-dimensional and three-dimensional flows, computed via spectral element simulations, will be discussed.   

LBM Simulations of 3D Peristaltic Transport with Particles

``It is sometimes necessary to produce a flow through a duct without using internal moving parts such as rotors or pistons. This need may arise when the fluid is corrosive or toxic, or when the fluid carries solid particles for which a passage free of obstacles would be desirable.'' (Hanin, 1968) Peristaltic transport offers a suitable solution by eschewing the use of internal flow drivers. A peristaltic flow occurs when a tube with flexible walls transports the contained material by progressing a series of contraction waves along the length of those walls. The deformation induces pressure gradients which drive the flow. Although significant progress has been made to provide the theory and analysis of peristaltic flows, relatively little research has been performed on the effects of particle transport due to the complexities involved. The Lattice Boltzmann Method provides a means to elucidate the behavior of finite-sized particles in peristaltic flows through numerical simulation. This talk investigates the transport and behavior of particles in a model peristaltic system by varying the relevant dimensionless parameters of the problem. It is found that particle transport is maximized for situations where the peculiar phenomenon of ``trapping'' is realized.