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

Single-phase Large Eddy Simulations (LESs) have been conducted with M-Star CFD software to compute spectra and time scales of the turbulent flow field at positions above the base of a stirred tank as these time scales may be important to the application of solids suspension. Since LESs do not resolve the entire turbulence spectrum with an unknown effect on computing time scales, simulation aspects such as spatial resolution, tank size and the value of the Smagorinsky constant are investigated. The simulations were conducted for the case of a 108 mm diameter axial flow wide blade hydrofoil, Philadelphia Mixing Solutions Ltd. 3MHS39, in a 295 mm diameter vessel at specific power inputs in the range from 0.03 to 0.43 W/kg. These specific power inputs pertain to the energy required to suspend 600 to 10,000 μm glass spheres at 0.9% (v/v). The focus of the study was on the base of the vessel near the vessel corners where solid particles are observed to reside before suspension in solid-liquid mixing application. Integral and Taylor micro time scales as well as 1-D energy spectra were extracted, for all three velocity components, from the temporal autocorrelation function of the resolved velocity traces at various positions. Radial profiles are presented for these 1-D time scales, for the 3-D integral time scale, and for the resolved time scale k/ε.