Time Scales and Turbulent Spectra above the Base of Stirred Vessels from Large Eddy Simulations

A spectral approach of suspending solid particles in a turbulent stirred vessel

“…By obtaining local Eulerian temporal energy spectra above the base of a vessel using LES simulations mimicking actual physical solid–liquid mixing experiments, the local time scale of the turbulent eddies and their respective energies are available to compare with the particle response time. The technique of obtaining and processing Eularian energy spectra from LES is detailed in Giacomelli et al 11 The instantaneous fluctuating component of the resolved velocity field is extracted at discrete sampling locations at a given sampling frequency. The resolved velocity field being three‐dimensional, the energy spectra are computed in the time domain as the sampling points are fixed.…”

“…The model geometry was identical to the physical system from which these impeller speeds were determined and therefore the information given in Tables 1–3 can be referenced. The software used to complete the modeling was M‐Star CFD which uses the Lattice‐Boltzmann technique to solve the Navier–Stokes equations 11 . The subgrid scale viscosity was computed according to the Smagorinsky model with the Smagorinsky constant, C s , set to 0.1.…”

“…The minimum resolution required for this simulation was computed to be T / Δ = 303, where T is the tank diameter and Δ is the lattice size 11,14 . This was based on considering the integral length scale of turbulence, in this case the trailing vortex of the impeller, and C s .…”

“…Therefore, it is of great interest to be able to determine what are the characteristics of the eddy or eddies responsible for interacting with and suspending the particles. To this end, we utilize the work of Giacomelli et al 11 which employs Large Eddy Simulations (LESs) to extract the local turbulence properties on or above the base of a stirred vessel in the location known as the point of last particle pick up. The ultimate goal is to determine which eddies are relevant for suspending.…”

“…The focus is on dilute suspensions with volume concentrations, x v , lower than 1%, in a first attempt to understand suspension of singular particles without accounting for turbulence modification or dampening by particles as in concentrated suspensions. In Giacomelli et al, 11 suspension experiments utilizing glass spheres with a particle diameter, d p , ranging from 500 to 10,000 μm were reported which provided impeller speeds upon which to model single‐phase LES around. The purpose was to develop a technique in which LES could be used to obtain local turbulent properties such as time scales and energy spectra, and to ensure the technique could be carried out on industrially relevant mixing conditions.…”