# (431a) Assessment of 3D-PTV to Measure Lagrangian Flow Fields in Stirred Tanks

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: North American Mixing Forum
- Session:
- Time: Tuesday, November 12, 2019 - 3:30pm-3:51pm

**Background and objectives**

3D Particle Tracking Velocimetry (3D-PTV) is an alternative technique to Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA) for visualization of flow fields. It is gaining increasing attention in industry and academia because it enables to measure all the three dimensions of the velocity field and it can obviate the need for laser illumination. 3D-PTV has been carried out using multiple or single camera setups for many applications, including turbulence measurements (Luthi et al., 2005; Liberzon et al., 2012), pulsed impinging jets (Hwang et al., 2007), pipe flows (Oliveira et al., 2015), simulated flows (Pereira et al., 2006), flows in a lid-driven cavity (Kreizer et al., 2010), aortic flows (Gulan et al., 2012; Gallo et al., 2014), plane Couette flows (Krug et al., 2014) and industrial burners (Hardalupas et al., 2000). However, today, there is still a deep lack of information in the literature on the use of 3D-PTV to fluid mixing in stirred tanks (Alberini et al., 2017), particularly in the transitional regime.

3D-PTV involves the addition of tracer particles (in the order of 10 â€“ 1000 Âµm) within the fluid under investigation, contained in a transparent geometry. A stereoscopic image acquisition system is used to capture synchronous image sequences of the particles in different image planes. After a calibration routine, the 3D coordinates of the particles are computed. Particles are individually tracked from frame to frame, and a set of Lagrangian trajectories in the 3D space is obtained. Eulerian information can also be obtained via post-processing of the time-resolved three-dimensional velocity vectors (Alberini et al., 2017). This requires reconstructing as many trajectories for as long as possible. However, unavoidable unsolved ambiguities result in a certain probability of interruption of the trajectory at each time step (Willneff and Wenisch, 2011). An exhaustive discussion of the principles of PTV may be found in Maas et al. (1993) and Malik et al. (1993).

This work consists of two experimental parts, conducted with a single camera 3D-PTV setup (see Alberini et al., 2017):

- experiments with artificial trajectories with velocities up to 1.9 m s
^{-1}, to assess accuracy, precision, repeatability and effect of procedural variables; - experiments in a 7 L square tank operated in a range of Re from 6,000 to 36,000, to investigate the effects of particle concentration and frames per second on the distribution of the trajectories time scales. To authorsâ€™ knowledge, this is the first time that a similar analysis is conducted to investigate the tracking performance of 3D-PTV for agitated vessels.

**3D-PTV experiments with artificial trajectories**

A rotating geometry has been designed to produce artificial trajectories. It consists of four cylinders of different diameter with four control dots. When it rotates at a speed , the uniform circular motion of the dots is known, and the 3D-PTV measurements of the dot velocities can be compared with their expected values ().

The experiments were conducted at 120, 200 and 360 rpm, producing a maximum velocity of 1.9 m s^{-1}. Two half revolutions of the geometry were recorded at 3600 fps. Four circular trajectories, one for each control dot, were obtained. The trajectories extended within the angle where the control dots were visible.

The peaks of the measured velocity were individually fitted with a Gaussian curve, defined by the mean, Âµ, and the standard deviation, Ïƒ. The accuracy of the measurements was assessed considering the relative error between Âµ and , while the precision was measured by Ïƒ. The results showed that accuracy and precision are reasonable in the range of velocities investigated.

The repeatability was assessed considering the standard deviation of the mean measurements over three repetitions of the experiment at 360 rpm. The variability of the measurements was satisfactory.

The circular trajectories were divided in three portions. The peaks relative to each portion were fitted individually to assess the effect of the direction of the motion on accuracy and precision. No relevant differences were found.

Two further experiments have been conducted at 360 rpm and the calibration target was placed in two different positions at a distance of 100 mm. The results were then compared in terms of Âµ and Ïƒ. The variability due to the two calibration routines were not relevant.

**3D-PTV experiments in a 7 L agitated tank**

Particle trajectories obtained from 3D-PTV have been used to reconstruct the flow field of water in a 7 L square vessel (178 Ã— 178 Ã— 220 mm) equipped with a 60 mm Rushton turbine and operated in a range of Re between 6,000 and 36,000. The effects of the particle concentration and the number of frames per second (fps) on (a) the distribution of the trajectory time scales and on (b) the statistic reliability of time-phase averaged flow fields obtained via post-processing of the Lagrangian trajectories have been investigated. This work is aimed at the development of an appropriate operational window within which the PTV can be optimized for future measurements of transitional flows in agitated vessels.

The flow was visualized using neutrally buoyant microspheres (750 â€“ 820 Âµm). The experimental matrix includes a nine points partial composite central design and two external points. The particle concentration was varied between 0.02 and 0,54 g L^{-1}, the camera frequency between 900 and 3600 fps, and the impeller speed between 100 and 600 rpm, producing a tip speed between 0.3 and 2.5 m s^{-1}. Given the limitations of the camera memory, each experiment was repeated four times to obtain a cumulative time of recording of 4 seconds. The resulting total number of frames went from 3600 to 14400.

At date of writing, the processing of these experiments is ongoing. The outputs will be the three components of velocity in function of the three spatial coordinates and the variable time, grouped in continuous trajectories.

The analysis of the tracking performance at the different operation conditions will consider:

- the total number of trajectories obtained;
- the distributions of the trajectory time scales, namely the population of trajectories tracked for a certain time Ï„;
- the normalized distribution of the time scales, where the number of observations is divided by the total number of events.

In light of some previous results, it is expected that, due to unsolved ambiguities and trajectory interruptions, the total number of trajectories increases with particle concentration and fps, and the distributions exponentially decrease with Ï„.

The statistics of such averaged flow fields will be assessed in some sample regions. In particular, the independence of the ensemble average velocity in those regions with respect to the number of data available will be investigated at the different conditions.

**Cited references**

Alberini, F., Liu, L., Stitt, E.H., Simmons, M.J.H. (2017), *Chem Eng Sci*, 171: 189 â€“ 203.

Gallo, D., Gulan, U., di Stefano, A., Ponzini, R., Luthi, B., Holzner, M., Morbiducci, U. (2014), *J Biomech*, 47: 3149â€“3155.

Gulan, U., Luthi, B., Holzner, M., Liberzon, A., Tsinober, A., Kinzelbach, W. (2012), *Exp in Fluids*, 53: 1469â€“1485.

Hardalupas, Y., Pantelides, K., Whitelaw, J. (2000), *Exp in Fluids*, 29: 220â€“226.

Hwang, T.G., Doh, D.H., Jo, H.J., Tsubokura, M., Piao, B., Kuroda, S., Kobayashi, T., Tanaka, K., Takei, M. (2007), *Chem Eng J,* 130: 153â€“164.

Kreizer, M., Ratner, D., Liberzon, A. (2010), *Exp in Fluids*, 48: 105â€“110.

Krug, D., Holzner, M., Luthi, B., Wolf, M., Tsinober, A., Kinzelbach, W. (2014), *Meas Sci Technol*, 25: 1â€“13.

Liberzon, A., Luthi, B., Holzner, M., Ott, S., Berg, J., Mann, J. (2012), *Phys D*, 241: 208â€“215.

Luthi, B., Tsinober, A., Kinzelbach, W. (2005), *J Fluid Mech*, 528: 87â€“118.

Maas, H.G., Gruen, A., Papantoniou, D.A. (1993), *Exp in Fluids*, 15: 133â€“146.

Malik, N.A., Dracos, T., Papantoniou, D.A. (1993), *Exp in Fluids*, 15: 279â€“294.

Oliveira, J.L.G., Van der Geld, C.W.M., Kuerten, J.G.M. (2015), *Int J Multiphase Flow*, 73: 97â€“107.

Pereira, F., Stuer, H., Graff, E.C., Gharib, M. (2006), *Meas Sci Technol*, 17: 1680â€“1692.