DNS of compressible multiphase flows through the Eulerian approach

In this paper we present three multiphase flow models suitable for the study of the dynamics of compressible dispersed multiphase flows. We adopt the Eulerian approach because we focus our attention to dispersed (concentration smaller than 0.001) and small particles (the Stokes number has to be smaller than 0.2). We apply these models to the compressible ($\text{Ma} = 0.2,\,0.5$) homogeneous and isotropic decaying turbulence inside a periodic three-dimensional box ($256^3$ cells) using a numerical solver based on the OpenFOAM$^{R}$ C++ libraries. In order to validate our simulations in the single-phase case we compare the energy spectrum obtained with our code with the one computed by an eighth order scheme getting a very good result (the relative error is very small $4*10^{-4}$). Moving to the bi-phase case, initially we insert inside the box an homogeneous distribution of particles leaving unchanged the initial velocity field. Because of the centrifugal force, turbulence induce particle preferential concentration and we study the evolution of the solid-phase density. Moreover, we do an {\em a-priori} test on the new sub-grid term of the multiphase equations comparing them with the standard sub-grid scale term of the Navier-Stokes equations.Comment: 10 pages, 5 figures, preprint. Direct and Large Eddy Simulations 9, 201

Application of the exact regularized point particle method (ERPP) to particle laden turbulent shear flows in the two-way coupling regime

The Exact Regularized Point Particle method (ERPP), which is a new inter-phase momentum coupling ap- proach, is extensively used for the first time to explore the response of homogeneous shear turbulence in presence of different particle populations. Particle suspensions with different Stokes number and/or mass loading are considered. Particles with Kolmogorov Stokes number of order one suppress turbulent kinetic energy when the mass loading is increased. In contrast, heavier particles leave this observable almost un- changed with respect to the reference uncoupled case. Turbulence modulation is found to be anisotropic, leaving the streamwise velocity fluctuations less affected by unitary Stokes number particles whilst it is increased by heavier particles. The analysis of the energy spectra shows that the turbulence modulation occurs throughout the entire range of resolved scales leading to non-trivial augmentation/depletion of the energy content among the different velocity components at different length-scales. In this regard, the ERPP approach is able to provide convergent statistics up to the smallest dissipative scales of the flow, giving the opportunity to trust the ensuing results. Indeed, a substantial modification of the turbu- lent fluctuations at the smallest-scales, i.e. at the level of the velocity gradients, is observed due to the particle backreaction. Small scale anisotropies are enhanced and fluctuations show a greater level of in- termittency as measured by the probability distribution function of the longitudinal velocity increments and by the corresponding flatness

Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber number which is varied in the range $We=0.01 - 2.0$. Our numerical simulations show that increasing the deformability of bubbles i.e., $We$ leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder

Eulerian-Lagrangian method for simulation of cloud cavitation

We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The dynamics of the bubbly mixture is formulated using volume-averaged equations of motion. The continuous phase is discretized on an Eulerian grid and integrated using a high-order, finite-volume weighted essentially non-oscillatory (WENO) scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles at the sub-grid scale, each of whose radial evolution is tracked by solving the Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid as the void fraction by using a regularization (smearing) kernel. In the most general case, where the bubble distribution is arbitrary, three-dimensional Cartesian grids are used for spatial discretization. In order to reduce the computational cost for problems possessing translational or rotational homogeneities, we spatially average the governing equations along the direction of symmetry and discretize the continuous phase on two-dimensional or axi-symmetric grids, respectively. We specify a regularization kernel that maps the three-dimensional distribution of bubbles onto the field of an averaged two-dimensional or axi-symmetric void fraction. A closure is developed to model the pressure fluctuations at the sub-grid scale as synthetic noise. For the examples considered here, modeling the sub-grid pressure fluctuations as white noise agrees a priori with computed distributions from three-dimensional simulations, and suffices, a posteriori, to accurately reproduce the statistics of the bubble dynamics. The numerical method and its verification are described by considering test cases of the dynamics of a single bubble and cloud cavitaiton induced by ultrasound fields.Comment: 28 pages, 16 figure

ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes

A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low concentration regimes and small particles Stokes $St<0.2$. When $St < 0.001$ the model reduces to the dusty-gas one. The new model is significantly faster than the Eulerian model while retaining the capability to describe gas-particle non-equilibrium. Direct numerical simulation accurately reproduce the dynamics of isotropic turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration of particles by turbulence, verifying the model reliability and suitability for the simulation of high-Reynolds number and high-temperature regimes. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous properties. The self-similar radial profile and the development of large-scale structures are reproduced, including the rate of entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. Coarse particles partially decouple from the gas within eddies, modifying the turbulent structure, and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the gravity. By these mechanisms, gas-particle non-equilibrium is able to influence the large-scale behavior of volcanic plumes.Comment: 29 pages, 22 figure