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18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Analysis of scalar mixing and turbulent flow in a continuous stirred tank by simultaneous PIV and PLIF

Michela Marino1, Antonio Busciglio2, Giuseppina Montante2, Alessandro Paglianti1,* 1: Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Italy

2: Department of Industrial Chemistry “Toso Montanari”, University of Bologna, Italy * Correspondent author: [email protected]

Keywords: PIV, PLIF, Continuous stirred tanks, Turbulent Scalar Transport

ABSTRACT

This work deals with the velocity field of the liquid and the scalar transport of a passive tracer in a continuously fed standard configuration stirred vessel under turbulent impeller Reynolds number. The aim of the investigation is twofold. The influence of a liquid jet entering the vessel from the top lid on the fluid flow patterns is assessed first. Afterwards, a finer analysis of the turbulent characteristics of the flow and of the scalar concentration fluctuations is performed. As fed-batch and continuous stirred tanks are widely adopted in chemical and bio-chemical processes, the results of this work provide useful indication for assessing to what extend the current knowledge on batch stirred tanks can be applied to continuous systems. Besides, the results on the turbulent mixing of the tracer provide a very useful benchmark for the Reynolds-averaged scalar transport equations, which are widely adopted for the industrial Computational Fluid Dynamics (CFD) simulation of stirred vessels, but their reliability would be significantly improved by quantitative validations of the turbulent fluctuations modelling. The data are collected by 2D Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF). The results of the first part of the investigation show that the inlet jet affects the fluid flow field with respect to batch conditions. As expected, the variations of the flow field in the upper zone of the vessel are significant, while the impeller pumping action is slightly affected by the liquid jet, as the impeller speed is higher than that of the liquid feed stream. The simultaneous PIV and PLIF measurements in the vertical plane passing through the inlet jet axis allow the evaluation of the Reynolds fluxes and the Reynolds stress components in the axial and radial directions. The results provide insight into the interaction between the jet and the flow features due to the mechanical agitation.

1. Introduction Fed-batch and continuous operations in stirred chemical and bio-chemical reactors are common in industrial practice, though significantly less investigated so far with respect to batch stirred tanks (Liu, 2012). Traditional design methods rely on simple global parameters, namely the blend time and the residence time, and their comparison to establish the significance of the non-ideal mixing on the reactor performances (Roussinova and Kresta, 2008). Besides, it is well know that the feed location and turbulent intensity have a major effect on yield (Patterson et al., 2004). In many industrial applications, the feed location is placed on the vessel top for easier operations with respect to submerged pipes, but the relationship between the jet characteristics and the


reactor performances is not straightforward (Bhattacharya and Kresta, 2006), particularly for mixing sensitive reactions. Since the local fluid dynamics characteristics of the reactors depends on the combination of geometrical and operational parameters, the results relevant to each specific condition cannot be extended for obtaining general design guidelines. Instead, the detailed determination of the fluid dynamic variables in combination with the turbulent transport of scalar properties can ultimately support the development of fully predictive modelling methods. Important contributions in this field have been already given in the investigation of different systems, such as confined liquid jets (Feng et al., 2007; 2010) and cross flowing gas jets (Su and Mugal, 2004), while to the best of our knowledge the simultaneous application of PIV and PLIF for the determination of the relevant flow statistics in stirred tanks has never been performed. In this work, we adopt Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) for the determination of the turbulent dispersion of a passive scalar and of the turbulent flow field in a stirred tank provided with a continuous feed stream. Since the investigation is carried out under steady state conditions, for our system the Reynolds Averaged transport equations read as: (1)

(2)

where the symbols have the usual meaning. Of the flow statistics that require closure models in the realm of the Reynolds Averaged formulation of the momentum (eqn. 1) and scalar conservation equations (eqn. 2), that are the Reynolds stress tensor, , and the Reynolds flux tensor, , those including the radial and the axial velocity components are discussed in the

following. 2. Experimental The investigation is carried out in a 9.8 litre stirred tank of standard configuration made of Perspex. The cylindrical flat-bottomed tank has diameter T equal to 23.2 cm and height, H, equal to T. Mechanical agitation is carried out by a standard Rushton turbine of diameter D=T/3 placed at an impeller off-bottom clearance, C=T/2. The vessel is closed on top with a flat lid provided with one 20 mm hole for the liquid outlet and two 8.1 mm holes (inlet # 1 and inlet #2) for the feed stream entrance. Inlet #2 consists of two concentric tubes, the inner diameter of the internal tube is equal to 4.2mm and its thickness is equal to 0.6mm. The vessel is placed in a


square Perspex container filled with the working liquid for the reduction of the laser light refractive effects at the curved vessel surface. A schematic view of the stirred tank, including the lid, the position of the outlet and inlets holes and the measurement set-up are shown in Fig. 1.

Fig. 1 Simplified view of the stirred tank and measurement set-up. The dimensions on the lid

sketch are in mm Two different measurement planar sections are investigated, namely P1 and P2 in the following, passing through the axis of inlet #1 and of inlet #2, respectively, as shown in Fig. 1. For a general characterization of the flow field (by PIV), the vertical diametrical plane P1 placed mid-way between two baffles is considered with the feed entering from the inlet #1 with a flow rate of 10.5 mL/s, whose axis is located at a radial distance from the vessel axis of 71mm. In this case, the demineralized water, that is working liquid, is stored in a reservoir and recirculated by a single peristaltic pump. A finer characterization of the turbulent flow and of the scalar concentration fluctuations, by the simultaneous PIV and PLIF measurements, is performed on a portion of plane P2 close to the feed from inlet #2. As a difference with plane P1, on P2 the laser light does not to meet the shaft and the impeller, thus the disturbance due to the laser light reflections is reduced. The total feed flow rate is equal to 10.45 mL/s. It consist of the two streams: 5.06 mL/s of water solution of Rhodamine-6G of concentration equal to 0.08mg/L and 5.39 mL/s of demineralized water, entering from the internal tube and the annular space of inlet #2, respectively. Talc powder is


adopted for seeding the liquid, for cheaply obtaining a good laser light scatter at a different wavelength with respect to that emitted by the tracer. In order to achieve quickly and maintain steady-state conditions, the stirred tank is filled with a demineralised water solution of Rhodamine-6G of concentration equal to 0.041 mg/L. It matches the final concentration corresponding to the complete dye homogenization. Two reservoirs are adopted for the two inlet streams, which are fed to the stirred tank by two separate peristaltic pumps, while the outlet stream is stored in a single reservoir before disposal. The pulsed Nd:YAG laser (λ=532 nm, 15 Hz, 65 mJ) and the two digital cameras (resolution of 1344×1024 pixels) are handled by a Dantec Dynamics system. The two cameras are equipped with appropriate filters for discriminating between the light scattered by the liquid seeding (λ=532 nm) and the light emitted by the fluorescent dye (peak emission λ=560 nm). The area viewed from the two cameras are identical, enabling an accurate overlap of the PIV and PLIF data. A double-frame mode is selected for the PIV camera for the measurement of the instantaneous velocity vectors by cross-correlation. The time interval between the two laser pulses is set to 800 µm, the total number of image pairs is 2000, that are acquired at a frequency of 6 images/s. A vector spacing of 0.3 mm is obtained by applying the cross-correlation on an interrogation area size of 16×16 pixels with on overlap of 50%. Subsequently, two validation algorithm are applied, one based on the evaluation of the peak heights in the correlation plane and the other on the velocity magnitude. A single frame mode is selected for the PLIF camera and the exposure time is set to 1 ms. The raw instantaneous PLIF images are processed for eliminating the effect of the non-uniformity of the laser light. To this end, the mean of 50 images collected with the seeded water only is subtracted to each instantaneous PLIF image. The image resulting from this operation is normalized by the difference between the mean value of 50 images collected at the dye concentration corresponding to complete homogenization (0.041mg/L) and the mean of the 50 images collected without dye. Since the vector spacing is three time bigger than the concentration spacing, the concentration is resampled on a coarser grid for obtaining the same resolution of the velocity vectors. The comparison of the measurement resolution with the Kolmogoroff and Batchelor lenght scale is not performed here, since the local dissipation rate is not estimated. Preliminary tests were performed for the identification of the optimal measurement parameters and their mutual effects on the results’ accuracy (seeding quantity, Rhodamine 6G concentration, time delay between one laser pulse and the other, number of instantaneous measurements, shot-to-shot laser power variation effect, etc.) particularly in the case of the simultaneous measurements, for which the effect of the liquid seeding particle on the PLIF measurements and


of the fluorescent dye on the PIV measurements has to be minimized. The following results are found: − the maximum dye concentration for obtaining a linear relationship between local intensity

of fluoresced light and local dye concentration is equal to 0.0816 mg/L; − the absorption of Rhodamine 6G on the talc particles for contact time of 30 minute is found

to decrease the emitted light intensity of 4%. Since each measurement lasted less than 6 minutes, the absorption is negligible;

− the shot-to-shot laser power variations are monitored and a steady signal is found, thus confirming the suitability of the laser for the PLIF measurement;

− a concentration of 0.00612 g/L for the seeding particles is adopted. It resulted as the best compromise for having accurate PIV results, based on the number of valid instantaneous velocity vectors after applying a suitable validation procedures, and a negligible contribution of the laser light scattered by the seeding out the measurement plane on the PLIF measurements;

− with the above specified seeding and tracer concentrations, the effect of the seeding particles on the PLIF camera images was found negligible.

The operating conditions investigated by the PIV measurements on P1 and by the simultaneous PIV/PLIF measurements on P2 are summarized in Table 1.

P1 P2

Impeller speed, N [rpm] 100 0, 100 Feed superficial velocity [m/s] 0.2 0.25 Impeller Reynolds number 1.03×104 0; 1.03×104 Velocity vector spacing [mm] 3 0.3 Concentration resolution [mm] 0.1

Tab. 1 Measurement conditions. In the following the origin of the coordinate system is placed on the center of the tank bottom. The radial coordinate, r, is positive if directed toward the vessel wall, the axial coordinate, z, is positive if directed upwards. Following the classical nomenclature adopted in fluid mixing research, U and V are the mean axial and radial velocity components, u’ and v’ are the axial and radial velocity fluctuations. The variations of velocity and concentration along the tangential coordinate, θ, are not measured.


3. Results The turbulent flow field of batch standard geometry single-phase stirred tanks is very well known. Both the mean flow field and the turbulent characteristics have been widely and accurately determined by LDA (e.g. Lee and Yianneskis, 1998) and PIV (e.g. Baldi and Yianneskis, 2004) mainly on the vertical plane located between two consecutive baffles, providing insight into the local ensemble averaged and phase resolved features of the flow. The axial, U, and radial, V, mean velocity components normalized by the impeller tip speed, Vtip, reported in Fig. 2 show that with the continuous feed provided through inlet #1 the main characteristics of the impeller discharge stream are not modified with respect to the batch conditions. Instead, the axial velocity in the upper half of the tank is much higher with respect to batch vessels. As a result, the tank performances for mixing sensitive processes, such as fast chemical reactions and phase dispersion, are expected to be significantly different, due to the variations of the local characteristics and of the global parameters such as the mixing time (Busciglio et al., 2015)

Fig. 2 Dimensionless axial (left) and radial (right) mean velocity on P1.

The mean velocity components normalized by the inlet jet velocity, Vjet, in the inlet stream region measured on P2 are shown in Figs. 3 and 4, for the case of still and rotating impeller. As can be observed, with the feed on this location the impeller action affects both the axial (Fig. 3) and the radial (Fig. 4) mean velocity components close to the vessel top, deviating the inlet jet vertical flow pattern. The axial and the radial normal stresses divided the V2

jet are shown in Figs. 5 and 6, respectively.


Fig. 3 Dimensionless axial mean velocity on P2. N=0rpm (left); N=100rpm (right).

Fig. 4 Dimensionless radial mean velocity on P2. N=0rpm (left); N=100rpm (right).

Both with the still and rotating impeller, the normal stresses are higher in the axial than in the radial direction, being their maximum value of the former approximately doubled with respect to the latter. The dimensionless shear stress, shown in Figs 7, exhibits opposite sign with respect to the axis of the jet and its sign is the same of that of the radial gradient of the mean axial velocity. In all cases, the Reynolds stress components are clearly affected by the impeller action.

Fig. 5 Axial normal stress on P2. N=0rpm (left); N=100rpm (right).


Fig. 6 Radial normal stress on P2. N=0rpm (left); N=100rpm (right).

Fig. 7 Shear stress on P2. N=0rpm (left); N=100rpm (right).

The mean and fluctuating tracer concentration collected simultaneously and in the same location of the velocity data are shown in Figure 8 for the case of N=100rpm. The local values are made dimensionless by the average concentration of the dye on the measurement area. The dye mean and fluctuating concentration decreases in the radial direction moving far from the axis of the jet, although the effect of the upper impeller recirculation loop is visible. Also the reduction of both e in the axial direction moving downwards is obtained, as expected. Across z/T=0.65, the effect of the radial impeller on the dye concentration fluctuation is noticeable. The axial, , and the radial, , Reynolds fluxes obtained at N=100rpm are shown in dimensionless form in Fig. 9. As can be observed the axial components are higher in magnitude than the radial, as found for the normal Reynolds stresses. While the axial fluxes are always negative, the radial fluxes are negative on the left of the jet axis and positive on the right due to the gradient of the mean concentration. Finally, in Fig. 10 the magnitude and the angle of the Reynolds fluxes are shown. The angle is zero for vertical vectors oriented upwards and the Reynolds flux vectors are superimposed to the color map. It is worth observing that magnitude is higher where the dye concentration is higher


and the direction of the Reynolds flux is clearly consistent with the action of the turbulent dispersion moving the dye far from the jet axis where the concentration is higher.

Fig. 8 Mean (left) and fluctuating (right) tracer concentration at N=100rpm (dimensionless

values).

Fig. 9 Axial (left) and radial (right) turbulent flux at N=100rpm (dimensionless values).

Fig. 10 Dimensionless Reynolds flux magnitude (left) and orientation angle (right) at N=100rpm.


4. Conclusions In this work, the flow field of a stirred tank of standard geometry provided with a continuous feed stream from the top lid was investigated by PIV and PLIF. The simultaneous measurements of velocity and concentration of a passive scalar have led to estimate for the first time the radial and axial components of the Reynolds flux in continuous stirred tank. The measured variables in the additive stream region can be adopted for the evaluation of important parameters, such as the turbulent viscosity and the turbulent diffusivity and for the assessment of the closure models for the CFD predictions of stirred tanks. 5. References Bhattacharya, S., Kresta, S.M., (2006) Reactor performance with high velocity surface feed

Chemical Engineering Science, 61: 3033-3043. Busciglio, A., Montante, G., Paglianti, A. (2015) Flow field and homogenization time assessment

in continuously-fed stirred tanks Chemical Engineering Research and Design, 102: 42-56. Feng, H., Olsen, M.G., Hill, J.C., Fox, R.O. (2007) Simultaneous velocity and concentration field

measurements of passive-scalar mixing in a confined rectangular jet Experiments in Fluids, 42: 847-862.

Feng, H., Olsen, M.G., Hill, J.C., Fox, R.O. (2010) Investigation of passive scalar mixing in a confined rectangular wake using simultaneous PIV and PLIF Chemical Engineering Science, 65: 3372-3383.

Liu M., (2012) Age distribution and the degree of mixing in continuous flow stirred tank reactors, Chem. Eng. Sci., 69:382-393.

Patterson G.K., Paul E.L., Kresta S.M., Etchells A.W. (2014). Mixing and Chemical reactions, Chapter 13 in in Handbook of Industrial Mixing, edited by E.L. Paul, V. A. Atiemo-Obeng, S.M. Kresta, Ch.4, p.782.

Roussinova V., Kresta S.M., (2008) Comparison of continuous blend time and residence time distribution models for a stirred tank, Ind. Eng. Chem. Res., 47:3532-3539.

Lee, K.C., Yianneskis, M. (1998) Turbulence Properties of the Impeller Stream of a Rushton Turbine AIChE Journal, 44: 13-24.

Baldi, S., Yianneskis, M. (2004) On the quantification of energy dissipation in the impeller stream of a stirred vessel from fluctuating velocity gradient measurements Chemical Engineering Science, 59 (13), pp. 2659-2671.

Su, L.K., Mungal, M.G. (2004) Simultaneous measurements of scalar and velocity field evolution in turbulent crossflowing jets Journal of Fluid Mechanics, 513, pp. 1-45.

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