Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence

Abstract

Fully resolved simulations of particles suspended in a sustained turbulent flow field are presented. To solve the Navier-Stokes equations a lattice-Boltzmann scheme was used. A spectral forcing scheme is applied to maintain turbulent conditions at a Taylor microscale Reynolds number of 61. The simulations contained between 2 and 10 vol % particles with a solid to fluid density ratio between 1.15 and 1.73. A lubrication force is used to account for subgrid hydrodynamic interaction between approaching particles. Results are presented on the influence of the particle phase on the turbulence spectrum and on particle collisions. Energy spectra of the simulations show that the particles generate fluid motion at length scales of the order of the particle size. This results in a strong increase in the rate of energy dissipation at these length scales and a decrease of kinetic energy at larger length scales. Collisions due to uncorrelated particle motion are observed (primary collisions), and collision frequencies are in agreement with theory on inertial particle collisions. In addition to this, a large number of collisions at high frequencies is encountered. These secondary collisions are due to the correlated motion of particles resulting from shortrange hydrodynamic interactions and spatial correlation of the turbulent velocity field at short distances. This view is supported by the distribution of relative particle velocities, the particle velocity correlation functions and the particle radial distribution function. IntroductionIn industrial processes where solid materials are produced or handled, often dense slurries are processed under highly turbulent conditions. Turbulence is required to maintain the slurry suspended and well mixed. While operating under such conditions, phenomena such as breakage, agglomeration and segregation of particles can occur; these phenomena can be either desired or potential problems in the operation of these processes (Zwietering 1958;Wibowo & Ng 2001).One specific example is industrial crystallization, which deals with the production of solid crystals from a supersaturated liquid. The crystal suspension typically contains between 5 and 20 vol % solids with an average particle size in the range of 100 to 1000 µm, and with a solid to liquid density ratio in the range of 1 to 2.5. The Kolmogorov length scale typically is one order of magnitude smaller than the mean crystal size (Ten Cate et al. 2001). Under the action of the turbulent flow field, agglomeration (Hollander et al. 2001), abrasion, and fracture (Gahn & Mersmann 234 A. Ten Cate, J. J. Derksen, L. M. Portela and H. E. A. Van den Akker 1999) take place. These phenomena have a strong influence on the performance of the crystallization process and hence on the resulting product, and make scale-up a non-trivial exercise.In this paper we study turbulent solid-liquid suspensions under conditions that are comparable to those encountered in industrial crystallization processes (i.e. d p > η, where d p is the particle diameter and η th...

A Novel Approach to Mineral Carbonation: Enhancing Carbonation While Avoiding Mineral Pretreatment Process Cost

“…The systematic increase in the extent of carbonation with increasing wt.% forsterite (particle concentration) demonstrates the importance of particle-particle interactions (abrasion) in exposing fresh olivine reaction surfaces and enhancing carbonation reactivity. In recent simulations of colliding monodisperse spheres in forced isotopic turbulent flow, corresponding closely to the stirred tank conditions in our experiments, Derksen et al 33 identified two distinct collision mechanisms: (i) primary collisions consisting of uncorrelated "kinetic gas"-like random contacts and (ii) highly correlated secondary collision processes, involving a repetitive "chattering" motion on a short time scale, due to short-range hydrodynamic effects (lubricating forces). Elementary geometric considerations deliver a length scale (L) dependence on weight % solids, W, proportional to W -1/3 .…”

Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows

“…Direct numerical simulations of particle-laden turbulent flow with no-penetration and no-slip boundary conditions imposed at the surface of each particle are now feasible for single and even multiparticle systems. [2][3][4] With increasing computational power, using these DNS the boundary layer around each particle can be resolved. We denote these simulations as "true" DNS.…”

“…Two important unclosed terms are the interphase transfer of turbulent kinetic energy, and the dissipation rate of turbulent kinetic energy in the fluid phase. This paper describes a mathematical constraint that models for these terms must obey, so that they can be meaningfully compared with emerging high-fidelity direct numerical simulations [2][3][4] and experiments. 5 For particle-laden flows with non-negligible mass loading, the interphase transfer of momentum must be accounted for, and it manifests itself as the mean interphase momentum transfer term in the averaged equations of the two-fluid theory.…”

Collision model for fully resolved simulations of flows laden with finite-size particles

“…However, when the particle volume fraction is high, additional models are required to account for short-range hydrodynamic solid-solid interactions (lubrication forces) and solid-solid contacts. Otherwise, the realism of the simulation may be compromised by a poor description of these interactions-for instance, by underpredicting lubrication-enhanced clustering of inertial particles, as observed for homogeneous isotropic * p.simoescosta@tudelft.nl turbulent flows [3]. The challenge is to find a model able to reproduce short-range particle-particle and particle-wall interactions with the required realism and with little effect on the computational efficiency of the overall numerical algorithm.…”