Direct numerical simulation of the turbulent flow in a baffled tank driven by a Rushton turbine

We present a direct numerical simulation (DNS) of the turbulent flow in a baffled tank driven by by a Rushton turbine. The DNS is compared to a Large Eddy Simulation (LES), a Reynolds Averaged Navier-Stokes (RANS) simulation, Laser Doppler Velocimetry data, and Particle Image Velocimetry data from the literature. By Reynolds averaging the DNS-data, we validate the turbulent viscosity hypothesis by demonstrating strong alignment between the Reynolds stress and the mean strain rate. Although the turbulent viscosity ν _T in the DNS is larger than in the RANS simulation, the turbulent viscosity parameter C _μ = ν _Tε{lunate}/k ², is an order of magnitude smaller than the standard 0.09 value of the k-ε{lunate} model. By filtering the DNS-data, we show that the Smagorinsky constant C _S is uniformly distributed over the tank with C _S ≈ 0.1. Consequently, the dynamic Smagorisnky model does not improve the accuracy of the LES.