MIXING TIME IN UNBAFFLED STIRRED TANKSmixing14.eu/p/mixing14eu_07.pdf · however a general lack of information on their mixing performance, that needs to be addressed in order to

14th European Conference on Mixing Warszawa, 10-13 September 2012

MIXING TIME IN UNBAFFLED STIRRED TANKS

A. Busciglioa, F. Grisafia, F. Ippolito, F. Scargialia, A. Brucatoa

a University of Palermo, Dipartimento di Ingegneria Chimica, Gestionale, Informatica e Meccanica, Viale delle Scienze, Ed. 6, 90128 Palermo (Italy)

[email protected]

Abstract. Unbaffled stirred tanks, despite their poorer mixing performance with respect to baffled vessels, are gaining a growing industrial interest as they provide significant advantages in selected applications, including a number of biochemical, food and pharmaceutical processes. There still is however a general lack of information on their mixing performance, that needs to be addressed in order to fully exploit their application potential. The present work is aimed at providing experimental information on mixing rates in an unbaffled vessel operated without top-cover (Uncovered Unbaffled Stirred Tank, UUST). The planar laser induced fluorescence (PLIF) technique was adopted for measuring the dispersion dynamics of a passive tracer over a vertical section of the vessel. In agreement with the scant literature information available for these systems, results confirm the existence of two well defined, partially segregated, zones that give rise to a double mixing dynamics behavior. A suitable mixing time definition is proposed and results are finally compared with literature information. Keywords: Mixing time, unbaffled stirred tanks, planar laser induced fluorescence, PLIF.

1. INTRODUCTION One of the main drawbacks of unbaffled stirred tanks is the poorer mixing performance

with respect to baffled vessels, due to the smaller pumping rate generated by the impeller. As a consequence limited attention has been devoted so far to the fundamental mixing characterization of these devices. Nevertheless, unbaffled stirred tanks are gaining interest as they may provide significant advantages in a number of applications, including biochemical, food and pharmaceutical processes.

Mixing time (tmix) is the main parameter commonly employed to assess the mixing performance of single phase stirred tanks. It is defined as the time required to obtain a given level of homogeneity in an initial non-homogeneous mixture. Several mixing time measuring techniques have been proposed over the years. A comprehensive review may be found in [1]. In practice the experimental techniques employed can be generally classified into two groups: observation and transducers methods [2]. In the first group the initial liquid in the vessel contains a dissolved species which colors the solution and the added tracer combined with the solution leads to decolorization [3, 4], in the second group the tracer is typically a dissolved species whose concentration can be measured by a probe, e.g. conductivity [5, 6, 7]. Techniques belonging to the latter group have the advantage of providing information on both circulation time, tc, and mixing time, tmix,, but have the disadvantage of being intrusive. In practice the tracer is suddenly added in some point of the vessel while tracer concentration

43

time dynamics is read by suitable sensors located in one or more other places inside vessel volume. Tracer data dynamics are then suitably processed to extract the mixing time, typically defined as the time required for tracer concentration to reach within 95% of the completely mixed value.

Due to their greater industrial importance, significant attention has been devoted to baffled vessels so that experimental information on mixing time and relevant correlations are available for these systems [1, 2, 8, 9]. More limited information is presently available for unbaffled vessels [4, 6, 7, 10]. In some of these works [4, 10] the main focus is on micromixing issues and only limited information is provided on macromixing time. Other papers [6, 7] concern the case of unbaffled tanks stirred by suitably offset impellers, a case where the strongly swirling motion that characterizes unbaffled tanks is more or less efficiently suppressed. Not many papers are significantly devoted to macromixing in vortexing unbaffled vessels (see [6] and references therein).

In the present work mixing times in an unbaffled vessel operated without top-cover (Uncovered Unbaffled Stirred Tank, UUST) are obtained using the planar laser induced fluorescence (PLIF) technique to characterize dispersion dynamics of a passive tracer.

2. EXPERIMENTAL SET UP AND METHODS The technique here employed is based on the analysis of images obtained by laser sheet

excitation of a solution containing a fluorescent dye (Rhodamine-B). As such, it overcomes some of the limitations of other measurement techniques. In fact, apart from being quantitative and totally non-intrusive, a feature particularly desirable in unbaffled vessels, it allows the simultaneous measurement of tracer concentrations over most of the investigated diametrical plane.

For the measurements, a PIV apparatus was conveniently employed. It consisted of a Nd -YAG pulsed laser source (50mW per pulse, NewWave Research Solo III, wavelength equal to 532nm), coupled with a 1280*1024 pixel digital camera (Dantec 80C60 HiSense) and the control-synchronization unit Dantec FlowMap 1500. A high-pass filter centered on the wavelength of fluoresced light (570nm) was placed in front of the camera in order to allow only this light to reach the CCD. The laser plane was focused in order to obtain a 0.5mm thin light sheet inside the vessel. The investigated vessel was an unbaffled cylindrical tank (T = 0.19m) stirred by a standard Rushton turbine (D=T/3) placed at T/3 from vessel bottom. The liquid phase was deionized water at 25°C. The cylindrical vessel was immersed in a water filled square tank, in order to minimize optical distortions due to vessel cylindrical geometry. The technique is based on the measurement of the light re-emitted by the fluorescent dye (Rhodamine-B) suitably injected immediately above liquid free surface by means of a hypodermic syringe. In particular, two milliliters of a concentrated solution of Rhodamine (C =12mg/l ) were injected in each run. In this way even after 20 injections the final concentration of Rhodamine within the vessel was always considerably below C = 0.5mg/l, at which photon absorption phenomena result into unacceptable light gradients in the final image even if no more than consecutive 5 injections were used before substitution of water within the vessel. A preliminary masking of the laser plane was found to be advisable, in order to prevent direct laser light from hitting the vortexing liquid free surface, so giving rise to reflection phenomena that would quite strongly affect subsequent measurements.

In Fig.1, a typical snapshot sequence is reported in which, it is possible to observe the darker area related to light masking to avoid the undesired illumination of the free-surface vortex (barely visible in the images due to diffuse illumination).

Some manipulation was needed in order to obtain reliable data on mixing dynamics:

44

• Calculation of a final, steady state, background image in order to dump out image inhomogeneity's due to laser reflections or laser intensity decrease because of photon absorption by the fluorescent dye;

• Calculation of the deviation images as the pixelwise ratio between instantaneous images and final image; pixel values so obtained are proportional to local in-plane concentration;

• Masking: in order to minimize disturbances, by means of a suitable binary mask the analysis of tracer dispersion is restricted to directly illuminated liquid phase only.

Figure 1. Raw images recorded with Rushton turbine at 325rpm (t = 2s, t = 5s, t = 20s after injection of concentrated rhodamine solution).

The result of this procedure is the map sequence reported in Fig.2

Figure 2. Relative intensity images recorded with Rushton turbine at 325rpm (t = 2s, t = 5s, t = 20s after surface tracer injection).

45

3. RESULTS AND DISCUSSION As it can be seen in Figs.1 and 2, after a relatively quick internal homogenization (Fig.1

left and center) two mutually segregated zones clearly form: a highly concentrated small volume in between the stirrer and vortex bottom, hereafter called segregated region, and the rest of vessel volume (accounting for over 95% of total vessel volume) hereafter called main region (Figs.1 and 2, right). This finding is in agreement with previous findings, as the existence of the two regions was firstly observed (in the course of decolorization experiments, [4]) by who also pointed it out as a main feature of unbaffled vessel mixing performance.

In order to assess tracer dispersion dynamics, the deviation image inhomogeneity needs to be quantified. To this end, the commonly employed standard deviation (STD) was adopted as a good indicator of vessel unmixedness. In Fig.3 a typical STD dynamics is shown.

Figure 3. Standard deviation of relative intensity as a function of time, N = 325 rpm. Circles, experimentally measured STD; solid line, fitting curve.

As it can be seen, there are three different time zones, or dynamics behaviors, sequentially occurring after tracer injection:

• in the first time interval (dt1) the STD steeply increases from the initial zero value to its maximum value (normalized to unity in Fig.3), as tracer invades greater portions of the illuminated area.

• In the second time interval (dt2), the liquid phase inside both the segregated region and the main region of the vessel homogenize, therefore resulting in a decrease of the overall STD. Physically, it depends on flow field bulk motion within the two regions (but principally in the main region). It was observed that at low impeller speeds, the relevant STD dynamics is quite well described by an exponential decay. However, because of noisy signal and poor reproducibility (being strongly affected by injection time and modality) only the length of time interval dt2 after which there is a neat change in the decay law (where the final exponential decay starts) was practically assessed. Also, time intervals dt1 and dt2 were added together to obtain the main region mixing time tm= dt1+dt2 ; somewhat tm may be regarded as the mixing time the vessel would exhibit if the segregated region did not exist.

• At the end of the above interval, a large tracer concentration difference still exists between the segregated region and the main region (both being rather uniform). Notably, these differences are rather difficult to capture with probe-based techniques because of: a) intrusivity; b) the homogenization of dye contained in the segregated region leads to rather small concentration changes in the main region, therefore often resulting in inaccurate measurements. In the third time interval, tracer exchange between the two zones, mainly via turbulent diffusion, leads to net transport of dye from the segregated to the main region of the vessel, therefore resulting in a slow homogenization of the liquid phase, that follows quite

46

well an exponential decay law. The time constant of this exponential decay (τs) can therefore be reliably measured from experimental data. The time interval needed to equalize the segregated and main region concentrations, hereafter referred to as ts, was estimated as 3 times the relevant time constant (ts=3*τs).

Figure 4. Mixing time (left) and mixing time factors (right) as a function of Reynolds number.

In Fig.4a, the values of tm and ts obtained at the various agitation speeds are reported as a function of Reynolds number. As it can be seen, ts is always larger than tm but at small agitation speeds the former is about one order of magnitude larger than the latter and therefore fully dominates the mixing process, while increasing Re number (i.e. agitation speed) the difference between the two reduces up to vanishing at the highest agitation speeds. Also, as a difference from ts, tm is found to be substantially independent of agitation speed (apart for few data points at the highest agitation speeds), an unexpected finding quite difficult to explain. The only explanation that may be attempted here is that being defined as the start of the next phenomenon rather than the end of the former, it is not fully akin to a mixing time, a consideration that makes it less prone to physical interpretations.

The same data of Fig.4a are reported in Fig. 4b in terms of mixing time factors (tmN and tsN). Here tsN is found to be rather constant, as expected for fully turbulent systems, while ts shows an increasing trend corresponding to the flat zone in Fig.4a.

In order to compare present mixing dynamics with literature data, an overall mixing time tom=tm+ts was computed. This is reported in Fig.5 in terms of scaled overall mixing time [8] as a function of power dissipation. In this way it is possible to compare it with relevant literature data (solid symbols) as well as with baffled tank mixing performance (solid line). As it can be seen, present mixing time data are somewhat larger than literature data obtained with similar apparatuses, a finding probably related to the fact that the measuring technique here adopted is particularly effective in spotting the smallest concentration differences, wherever they are located.

As concerns the comparison with baffled vessels, not surprisingly unbaffled tanks are confirmed to be less effective mixers, with mixing times about four/five times larger than in baffled tanks. It is worth pointing out however that there are many processes for which mixing time is not a limiting factor (e.g. chemical reactions with reaction times of the order of tenths of minutes) that might take advantage from the other features of unbaffled vessels. Finally, it may be observed that at the highest agitation speeds, where vortex bottom approaches the stirrer so that the segregated zone practically disappears, unbaffled tank mixing performance approaches that of baffled tanks, making these working conditions particularly suited for mixing promotion in unbaffled vessels.

47

4. CONCLUSIONS The PLIF technique, coupled with suitable self-developed image analysis routines,

allowed to accurately follow dispersion dynamics in unbaffled stirred tanks. Data obtained fully confirm the existence of two different system dynamics, due to the formation of a segregated region between the central vortex bottom and the stirrer.

Overall mixing times were found to be comparable with literature data for centrally stirred unbaffled tanks and about five times larger than in baffled vessels. However the performance difference can be minimized if the unbaffled vessel is operated at the agitation speed needed for the central vortex bottom to almost reach the impeller.

Figure 5. Scaled overall mixing time factors compared with literature data and relevant baffled vessel correlation: open circles, this work, Rushton c=T/3; black diamonds, [6], PBT-3 e/R=0.57; black squares, [4], Rushton c=T/4; solid line Nienow correlation for baffled vessel [8].

5. REFERENCES [1] Patwardan A. W., Joshi J.B., 1999. “Relation between flow pattern and blending in stirred tanks”. Industrial Engineering Chemical Research, 38, 3131-3143. [2] Lee K.C., Yanneskis M., 1997. “A liquid crystal thermographic technique for the measurement of mixing characteristics in stirred vessels”, Chemical Engineering Research and Design, 75, 746-754. [3] Cronin D.G., Nienow A.W., Moody G.W., 1994. “An experimental study of the mixing in a proto-fermenter agitated by dual Rushton turines.”, Food and Bioproducts Processing, 72, 35-40. [4] Assirelli, M. Bujalski, W. Eaglesham , A. Nienow, A, W., 2008. “Macro and micro mixing studies in an unbaffled vessel agitated by a Rushton turbine”, Chemical Engineering Science, 63, 35-46. [5] Holmes D. B., Voncken R.M., Dekker J.A., 1964. “Fluid flow in turbine stirred baffled tanks, Part 1, Circulation time”, Chemical Engineering Science, 19, 201-208. [6] Szlopik, J. Karcz, J., 2005. “An efficiency of the liquid homogenization in agitated vessel equipped with off-centered impeller”, Chemical Papers, 59 (6a), 373-379. [7] Karcz J., Cudak M., Szlopik, J., 2005. “Stirring of a liquid in a stirred tank with an eccentrically located impeller”, Chemical Engineering Science, 60, 2369-2380. [8] Nienow A.W., 1997. “On impeller circulation and mixing effectiveness in the turbulent flow regime”. Chemical Engineering Science, 52, 2557-2565. [9] Cabaret, F., Rivera, C., Fradette, L., Heniche, M. & Tanguy, P.A., 2007. “Hydrodynamics performance of a dual shaft mixer with viscous Newtonian liquids”, Chemical Engineering Research and Design, 85, 583–590. [10] Russeaux J.M., Muhr H., Plasari E., 2001. “Mixing and micromixing times in the forced vortex region of unbaffled mixing devices”, The Canadian Journal of Chemical Engineering, 79, 697-707.

48