Despite the widely acknowledged significance of turbulence-driven clustering, a clear topological definition of particle cluster in turbulent dispersed multiphase flows has been lacking. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to distributions of heavy particles in direct numerical simulations of homogeneous isotropic turbulence, with and without gravitational acceleration. Clusters show self-similarity already at length scales larger than twice the Kolmogorov length, as indicated by the fractal nature of their surface and by the power-law decay of their size distribution. The size of the identified clusters extends to the integral scale, with average concentrations that depend on the Stokes number but not on the cluster dimension. Compared to non-clustered particles, coherent clusters show a stronger tendency to sample regions of high strain and low vorticity. Moreover, we find that the clusters align themselves with the local vorticity vector. In the presence of gravity, they tend to align themselves vertically and their fall speed is significantly different from the average settling velocity: for moderate fall speeds they experience stronger settling enhancement than non-clustered particles, while for large fall speeds they exhibit weakly reduced settling. The proposed approach for cluster identification leverages the Voronoi diagram method, but is also compatible with other tessellation techniques such as the classic box-counting method.

Coherent clusters of inertial particles in homogeneous turbulence

Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle-fluid interaction

We study the case of inertial particles heated by thermal radiation while settling by gravity through a turbulent transparent gas. We consider dilute and optically thin regimes in which each particle receives the same heat flux. Numerical simulations of forced homogeneous turbulence are performed taking into account the two-way coupling of both momentum and temperature between the dispersed and continuous phases. Particles much smaller than the smallest flow scales are considered and the point-particle approximation is adopted. The particle Stokes number (based on the Kolmogorov time scale) is of order unity, while the nominal settling velocity is up to an order of magnitude larger than the Kolmogorov velocity, marking a critical difference with previous two-way coupled simulations. It is found that non-heated particles enhance turbulence when their settling velocity is sufficiently high compared to the Kolmogorov velocity. Energy spectra show that the non-heated particle settling impacts both the very small and very large flow scales, while the intermediate scales are weakly affected. When heated, particles shed plumes of buoyant gas, further modifying the turbulence structure. At the considered radiation intensities, clustering is strong but the classic mechanism of preferential concentration is modified, while preferential sweeping is eliminated or even reversed. Particle heating also causes a significant reduction of the mean settling velocity, which is caused by rising buoyant plumes in the vicinity of particle clusters. The turbulent kinetic energy is affected non-monotonically as the radiation intensity is increased due to the competing effects of the downward gravitational force and the upward buoyancy force. The thermal radiation influences all scales of the turbulence. The effects of settling and buoyancy on the turbulence anisotropy are also discussed.

Settling of heated particles in homogeneous turbulence

The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas-liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. In order to investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been carried out. The turbulent dissipation is shown to be highly demanding on mesh resolution compared to other terms in TKE budget. The results obtained with the finest mesh are shown to be not far from converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability

We present direct numerical simulation (DNS) of a stationary turbulent hydraulic jump with inflow Froude number of 2, Weber number of 1820 and density ratio of 831, consistent with ambient water–air systems, all based on the inlet height and inlet velocity A non-dissipative geometric volume of fluid (VOF) method is used to track the detailed interactions between turbulent flow structures and the nonlinear interface dynamics Level set equations are also solved concurrent with VOF in order to calculate the interface curvature and surface tension forces The mesh resolution is set to resolve a wide range of interfacial scales including the Hinze scale Calculations are compared against experimental data of void fraction and interfacial scales indicating, reasonable agreement despite a Reynolds number mismatch Multiple calculations are performed confirming weak sensitivity of low-order statistics and void fraction on the Reynolds number The presented results provide, for the first time, a comprehensive quantitative data for a wide range of phenomena in a turbulent breaking wave using DNS These include mean velocity fields, Reynolds stresses, turbulence production and dissipation, velocity spectra and air entrainment data In addition, we present the energy budget as a function of streamwise location by keeping track of various energy exchange processes in the wake of the jump The kinetic energy is mostly transferred to pressure work, potential energy and dissipation while surface energy plays a less significant role Our results indicate that the rate associated with various energy exchange processes peak at different streamwise locations, with exchange to pressure work flux peaking first, followed by potential energy flux and then dissipation The energy exchange process spans a streamwise length of order jump heights Furthermore, we report statistics associated with bubble transport downstream of the jump The bubble formation is found to have a periodic nature Meaning that the bubbles are generated in patches with a specific frequency associated with the roll-up frequency of the roller at the toe of the jump, with its footprint apparent in the velocity energy spectrum Our study also provides the ensemble-averaged statistics of the flow which we present in this paper These results are useful for the development and validation of reduced-order models such as dissipation models in wave dynamics simulations, Reynolds-averaged Navier–Stokes models and air entrainment models

Direct numerical simulation of a turbulent hydraulic jump: turbulence statistics and air entrainment

We have developed a fully parallel C++/MPI based simulation code for variable-density particle-laden turbulent flows. The fluid is represented through a uniform Eulerian staggered grid, while particles are modeled using a Lagrangian point-particle framework. Spatial discretization is second-order accurate, and time integration has a fourth-order accuracy. Two-way coupling of the particles with the background flow is considered in both momentum and energy equations. The code is fully modular and abstracted, and easily can be extended or modified. We have considered two different boundary conditions. We have also developed a novel parallel linear solver for the variable density Poisson equation that arises in the calculation.

Parallel variable-density particle-laden turbulence simulation

This study addresses the optical performance of a plasma adaptive lens for aero-optical applications by using both axisymmetric and three-dimensional numerical simulations Plasma adaptive lenses are based on the effects of free electrons on the phase velocity of incident light, which, in theory, can be used as a phase-conjugation mechanism A closed cylindrical chamber filled with Argon plasma is used as a model lens into which a beam of light is launched The plasma is sustained by applying a radio-frequency electric current through a coil that envelops the chamber Four different operating conditions, ranging from low to high powers and induction frequencies, are employed in the simulations The numerical simulations reveal complex hydrodynamic phenomena related to buoyant and electromagnetic laminar transport, which generate, respectively, large recirculating cells and wall-normal compression stresses in the form of local stagnation-point flows In the axisymmetric simulations, the plasma motion is coupled with near-wall axial striations in the electron-density field, some of which propagate in the form of low-frequency traveling disturbances adjacent to vortical quadrupoles that are reminiscent of Taylor-Gortler flow structures in centrifugally unstable flows Although the refractive-index fields obtained from axisymmetric simulations lead to smooth beam wavefronts, they are found to be unstable to azimuthal disturbances in three of the four three-dimensional cases considered The azimuthal striations are optically detrimental, since they produce high-order angular aberrations that account for most of the beam wavefront error A fourth case is computed at high input power and high induction frequency, which displays the best optical properties among all the three-dimensional simulations considered In particular, the increase in induction frequency prevents local thermalization and leads to an axisymmetric distribution of electrons even after introduction of spatial disturbances The results highlight the importance of accounting for spatial effects in the numerical computations when optical analyses of plasma lenses are pursued in this range of operating conditions

Milad Mortazavi

Papers

Direct numerical simulation of a turbulent hydraulic jump: turbulence statistics and air entrainment

Parallel variable-density particle-laden turbulence simulation

Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses