LDV measurements and numerical modeling of the turbulent flow in a stirred mixer.

Abstract

It is recognized that detailed knowledge of turbulence parameters, as well as velocities, can aid in understanding and modeling mixing rate-dominated phenomena in stirred vessels. Measurements using a laser-Doppler velocimeter and modeling using a k-ε turbulence model and FLUENT, a general-purpose fluid flow modeling program, have been conducted of the flow in a baffled, turbine-agitated vessel. The complex flow patterns and high turbulence intensities explain why flows in stirred vessels are difficult to attack experimentally or numerically. In the measurements, the necessary corrections for the periodic, nondissipative velocity fluctuations in the near-impeller region, which were caused by the periodic passage of the impeller blades, were made by an autocorrelation method. With the contributions of the periodic fluctuations removed, meaningful turbulence data including turbulence intensities, autocorrelation functions, turbulence energy spectra, turbulence scales, and turbulence energy dissipation rates were obtained. Integral scales and energy dissipation rates were a particular objective in this work because of their usefulness in modeling local mixing rates in turbulent flows. An energy balance around a region containing the impeller and the impeller stream showed that 60% of the energy transmitted into the vessel via the impeller was dissipated in the region, and 40% was dissipated in the rest of the vessel. An equation for calculating local energy dissipation rates ε from total turbulence energy and resultant integral scales, ε = A q³/² /L(res), appeared adequate with constant A = 0.85 (where q ≡ uᵢuᵢ/2, L(res) ≡√LᵢLᵢ, and uᵢ and Lᵢ are, respectively, the i-th component of fluctuation velocity and the turbulence integral scale measured in direction i). Both the k-ε model (two-dimensional) and FLUENT (which employed three-dimensional k-ε and Reynolds stress models) obtained mean velocity profiles fairly close to the experimental data, but both predicted k and ε significantly lower than the measured values. The reason for the underestimation of k and ε was not entirely clear, but may have been caused by use of only the random parts of velocities for computing k and ε at the impeller boundary. The objective of modeling complex turbulent flows in stirred vessels has been accomplished, a goal which until recently would have been considered beyond the possibility of computation.