Development and application of 3D-PTV measurements to lab-scale stirred vessel flows

Abstract

In this work, guidelines for reliable 3D-PTV measurements of fluid flows in stirred vessels at the lab-scale have been developed. The flow of water at Re=12,000 in a flat bottom cylindrical tank (T=180 mm) stirred with a 6 blades Rushton turbine (c=D=T/3) has been measured at different camera frame rates (125 – 3600 fps) and tracer concentrations (0.001 – 0.010 px−2). The best compromise between the number of measured data, tracking efficiency and CPU time (206 frame-1, 39% efficiency, 0.026 min frame-1) has been obtained at 125 fps and 0.002 px−2. These results can be expressed in terms of the normalized parameters φ∼0.5 and p∼2 and scaled to different experimental conditions. The Savitzky–Golay filter, used to enhance the measurements signal-to-noise ratio, has been optimized by testing different values of the polynomial order (0–3) and filter width (321 data points). A 2nd order, 11-points filter gave the best results, based on considerations regarding the reduced Chi-squared and velocity distributions. With the best conditions and filter, the uncertainty in the measured tracer positions was in the order of 255 μm. Finally, un unbiased distribution of the flow decorrelation time has been determined from the velocity autocorrelation functions along the trajectories longer than 6 impeller revolutions. This method could be used to compare the macro-mixing performance in different flow systems.