Said Elghobashi

On predicting particle-laden turbulent flows

The paper provides an overview of the challenges and progress associated with the task of numerically predicting particle-laden turbulent flows. The review covers the mathematical methods based on turbulence closure models as well as direct numerical simulation (DNS). In addition, the statistical (pdf) approach in deriving the dispersed-phase transport equations is discussed. The review is restricted to incompressible, isothermal flows without phase change or particle-particle collision. Suggestions are made for improving closure modelling of some important correlations.

Direct simulation of particle dispersion in a decaying isotropic turbulence

Results of a numerical investigation of the dispersion of solid particles in decaying isotropic turbulence are presented. The 3D time-dependent velocity field of a homogeneous nonstationary turbulence is computed using the method of direct numerical simulation (DNS). The dispersion characteristics of three different solid particles (corn, copper, and glass) injected in the flow are obtained by integrating the complete equation of particle motion along the instantaneous trajectories of 22-cubed particles for each particle type, and then by performing ensemble averaging. Good agreement was achieved between the present DNS results and the measured time development of the mean-square displacement of the particles. Questions of how and why the dispersion statistics of a solid particle differ from those of its corresponding fluid point and surrounding fluid and what influences inertia and gravity have on these statistics are also discussed.

On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence

The objective of the present study is to analyze our recent direct numerical simulation (DNS) results to explain in some detail the main physical mechanisms responsible for the modification of isotropic turbulence by dispersed solid particles. The details of these two-way coupling mechanisms have not been explained in earlier publications. The present study, in comparison to the previous DNS studies, has been performed with higher resolution (Reλ=75) and considerably larger number (80 million) of particles, in addition to accounting for the effects of gravity. We study the modulation of turbulence by the dispersed particles while fixing both their volume fraction, φv=10−3, and mass fraction, φm=1, for three different particles classified by the ratio of their response time to the Kolmogorov time scale: microparticles, τp/τk≪1, critical particles, τp/τk≈1, large particles, τp/τk>1. Furthermore, we show that in zero gravity, dispersed particles with τp/τk=0.25 (denoted here as “ghost particles”) modify the ...

On the equation for spherical-particle motion : effect of Reynolds and acceleration numbers

The existing model equations governing the accelerated motion of a spherical particle are examined and their predictions compared with the results of the numerical solution of the full Navier–Stokes equations for unsteady, axisymmetric flow around a freely moving sphere injected into an initially stationary or oscillating fluid. The comparison for the particle Reynolds number in the range of 2 to 150 and the particle to fluid density ratio in the range of 5 to 200 indicates that the existing equations deviate considerably from the Navier–Stokes equations. As a result, we propose a new equation for the particle motion and demonstrate its superiority to the existing equations over a range of Reynolds numbers (from 2 to 150) and particle to fluid density ratios (from 5 to 200). The history terms in the new equation account for the effects of large relative acceleration or deceleration of the particle and the initial relative velocity between the fluid and the particle. We also examine the temporal structure of the near wake of the unsteady, axisymmetric flow around a freely moving sphere injected into an initially stagnant fluid. As the sphere decelerates, the recirculation eddy size grows monotonically even though the instantaneous Reynolds number of the sphere decreases.

Three-dimensional flow over two spheres placed side by side

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.

Modulation of isotropic turbulence by particles of Taylor length-scale size

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤d/λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤d/η≤35 and 38≤τp/τk≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φm≤1.0, corresponding to a volume fraction of 0.01≤φv≤0.1 and density ratio of 2.56≤ρp/ρf≤10. The maximum number of dispersed particles is 6400 for φv=0.1. The typical particle Reynolds number is of O(10). The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate (t), its two-way coupling rate of change Ψp(t) and frequency spectra E(ω) are discussed.In contrast to particles with d η, is that E(t) is always smaller than that of the single-phase flow. In addition, Ψp(t) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.

On the physical mechanisms of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles

The objective of this paper is to explain, in as much detail as possible, the physical mechanisms responsible for the reduction of skin friction in a microbubble-laden spatially developing turbulent boundary layer over a flat plate, for

Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer

Re_{\theta} = 1430

On the decay rate of isotropic turbulence laden with microparticles

. Our DNS results with microbubble volume fraction ranging from

Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence

\phi_v = 0.001