numerical and experimental analysis of particle strain and breakage in turbulent dispersions

S. Maaß et al.; Numerical and experimental analysis of particle strain and breakage in turbulent dispersions, Chemical Engi-neering Research and Design, Volume 87, Issue 4, 2009, p. 565-572 , doi:10.1016/j.cherd.2009.01.002

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NUMERICAL AND EXPERIMENTAL ANALYSIS OF PARTICLE STRAIN AND BREAKAGE IN TURBULENT DISPERSIONS

S. Maaßa*, S. Wollnyb, R. Sperlingb, M. Kraumea a Chair of Chemical Engineering, TU Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany, e-mail: [email protected] b Department of Fluid Mechanics, Anhalt University of Applied Sciences, Bernburger Straße 55, 06366 Köthen, Germany Abstract: This study deals with particle stress and breakage in turbulent flow. To estimate the particle stress, experimental set-up and computational fluid dynamics (CFD) are combined. The experimental set-up is used to examine the single drop breakage around a stirrer blade. The configuration of the breakage cell permits a study of particle break-up under variation of the mother droplet size and/or the flow velocity. CFD is used to investigate the flow pattern in this breakage cell. The CFD results are used to verify the flow field in the breakage cell as an acceptable model of a stirred tank. The results of the experimental investigations show that particle breakage takes place behind the stirrer blade. Referring to CFD simulations this region is clearly dominated by the highest energy dissipation rates. The shear gradients, which were calculated by CFD, show also a major impact on the particle break-age. Key words: single drop breakage, CFD, stirred vessel, Rushton turbine

1. INTRODUCTION

High energy dissipation rates are necessary for fast and high quality turbulent mixing in a stirred ves-sel. There is also a need for gentle mixing in many biochemical, pharmaceutical and food industry processes. The key factor for optimizing such processes is to fulfil both needs. Therefore the predic-tion of particle strain is of major importance for these industries. Computational fluid dynamics (CFD) is a useful tool to obtain the three-dimensional velocity fields in agitated vessels. This analysis can be used to predict flow patterns like turbulent shear rate, turbulent kinetic energy and turbulent energy dissipation rates. It is broadly known that different stirrer types create different particle strain for the same energy input (P/V). Primarily the differences between axial and radial stirrers are obvious and well described in literature [Gandhi and Kumar 1990, Henzler and Biedermann 1996, Langer and Deppe 2000, Wille et al. 2001, Wollny and Sperling 2007, Wollny et al. 2007, Gabriele et al. 2009]. The reason for these differences has not been analysed yet. Therefore Langer et al. [Langer and Deppe 2000] carried out investigations in a self developed measuring section to analyse the different phenomena of shear and strain. Their results show that clearly for the same energy input, the particles become much smaller by strain forces then by shear forces. The same results are expected to occur in a stirred vessel. To verify these estimations a distinction is necessary between shear flow and strain flow resulting from different stirrer types. Therefore an experimental set-up was developed and operated to show the clear influence of different stirrer types on single drop breakage. Concluding from 2D particle image velocimetry – measurements, Wille et al. [Wille et al. 2001] as-sume that the ratio of strain to shear forces is higher for axial agitators compared with radial agitators. With this work we want to establish a base to analyse the different shear and strain forces created by different stirrer types in an in-house developed breakage cell. Therefore the flow pattern will be simu-lated and analysed using CFD, Ansys-CFX 11.0, to calculate the mean velocity field in the breakage


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cell and to compare the location of the particle break-up from the experimental results with numerical parameters like local velocity and energy dissipation rate. The results proof that the breakage cell is an appropriate experimental set-up to mimic single drop breakage in stirred tanks.

2. MATERIAL AND METHODS

2.1 Experimental investigations The difficulty in the use of stirred vessels is that the influence of the turbulence on the transient drop size distribution can only analysed combining both relevant physical effects coalescence and drop breakage as they take place in parallel. For systematic analysis and quantitative understanding of par-ticle strain and drop breakage is a special experimental set-up for the investigation of single drop brea-kage necessary. Some efforts have already been made to analyse single bubble break-up in a fully developed turbulent pipe flow [Hesketh et al. 1991, Martinez-Bazan et al. 1999]. The turbulence field is well analysed in these investigations, but it is achieved by a jet stream through a nozzle. Similar flow conditions are used in the workgroup of Masbernat [Galinat et al. 2005, Galinat et al. 2007] for single drop and drop swarm investigations. The dispersed phase is n-heptane and it is used pure and also coloured with a non-water soluble red dye. The results of these research projects allow a valuable insight into the dependency of particle break-up on particle diameter and on energy dissipation rates, but the flow conditions are not comparable with those in the stirred tank. Andersson and Andersson [Andersson and Andersson 2006] show in their study about fluid particle break-up that not only the micro scale turbulent eddies but also the macro scale vortices have a significant influence on particle strain and particle break-up. Taken these results into account an experimental set-up for analysing single drop breakage under stirred tank flow condition is needed. With these difficulties in mind, the objective of the present study is, therefore, a quantitative analysis of particle strain and single drop breakage under conditions comparable to a stirred vessel [Maaß et al. 2007] and to proof these as-sumption with CFD simulations. The used dispersed phase for this investigation is toluene (99.98 % purity) blended with a non-water soluble black dye, which decreases the interfacial tension between water and toluene. The chemical data for the used system are listed in Table 1. Table 1 – Listing of the data on used chemical media

γ ]m/mN[ γ ]m/mN[ with dye ρ ³]m/kg[ at 20°C η ]smPa[ ⋅ dyec ]L/g[

36 32 870 0.55 0.075 A single blade representing a section of a Rushton turbine (d = 0.08 m) is fixed in a rectangular chan-nel (□ 30 x 30 mm). A single droplet, called mother drop, of a certain diameter between 300 – 3000 µm is introduced into a continuous water flow (see Fig. 1 – left) by a Hamilton® dosing pump. Pictures of the breakage event and the resulting daughter drops are taken with a high-speed camera using frame rates up to 1000 frames per second (fps). Automated image recognition (commercial software ImagePro-Plus®) is used to analyse the drop pictures resulting in number, size and centre of mass position of all objects on a picture. The first step of picture analysis is the subtraction of a refer-ence picture from the picture with drops. To get a binary picture a threshold is set. The final picture only contains black particles (see Fig. 1 – right). Automatic data treatment is necessary to obtain statis-tically relevant results. More than 1000 events are recorded for one parameter set-up (constant drop diameter and flow velocity).


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V&

camera

stirrer bladestirrer diskdroplet

dropletstirrer diskstirrer blade

4 mm

V&dosing pump

Fig. 1 – Experimental set-up: single drop breakage cell (left) and high-speed photography of a breaking 1 mm mother droplet, original photos and post processed images (right)

The high accurate dosing pump produces mother drops with standard deviation of the diameter less than 0.003 mm. Exemplary results of a mother drop distribution of a targeted diameter of 1.0 mm are shown in Fig. 2 from a population of 200 mother drops. All mother drops left the nozzle as one piece, so no early breakage was observed. In Fig. 2 the relative number of mother drops is plotted as a func-tion of different dimensionless size classes. Each size class describes an interval of a three percent fraction of the dimensionless diameter ration of the measured diameter (dreal) and the expectation value (dgoal= 1.0 mm). The mother drop distribution is a normal distribution with around 60 percent of the drops with less deviation of the expectation value than one percent. Another 30 percent of the popula-tion have a deviation of less than ±4 percent. So in sum of these three size classes around 90 percent of the population have a deviation less than ±4 percent. For volume conservation reasons the entering droplet volume (see Fig. 1 – right) is controlled at every run. If the deviation of the volumes is more than 15% the breakage event is neglected and not counted.

18.59

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≤83 84-86 87-89 90-92 93-95 96-98 99-101 102-04 105-07 108-10 111-13 ≥114dreal/dgoal [%]

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tive

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ber

of m

othe

rdro

ps [%

]

m/s 1.5 velocity flow

mm 1.0 ddroplets toluene

goal

=

=

Fig. 2 – Mother droplet distribution for 1.0 mm toluene droplets at a flow velocity of 1.5 m/s.


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The pictures taken have a resolution of 286 x 608 Pixels. This describes an area of 30.25 x 64.25 mm. Therewith the whole breakage event can be analysed systematically by using a high time (1000 fps) and space resolution. The place and time of the breakage is determined precisely. For space analysis the image is divided into squares with a side length of 2.75 mm corresponding to 26 Pixels (see Fig. 3). To avoid interferences with the stirrer blade, the point of origin for the y-axis starts at image pixel 10. Thus the area of interest is divided into 23 x 11 squares with an edge length of 2.75 mm, represent-ing 253 different spatial size classes (magnitudes). All of these magnitudes have four coordinates (xstart, ystart; xend, yend) describing the mounted area of this specific size group. As an example the blanked size group in Fig. 3 is described in mm-coordinates: [(xstart, ystart; xend, yend ) – (24.75, 2.75; 27.5, 5.5) all in mm]. The usable relative velocity between blade and liquid flow in this set-up is approximately 1.0 to 3.0 m/s, a range typical for the flow field around a Rushton turbine. These inves-tigations include two diameters (dp = 644 and 1000 µm) and three flow velocities (w = 1.0, 1.5 and 2.0 m/s) of toluene droplets in a continuous water flow.

y – coordinate [mm]

x –

coor

dina

te [m

m]

0.0 5.5 63.2516.5 33.030.25

0.002.755.50

16.50stirrer blade

stirrer disk

V.

Fig. 3 – Subdivision of the images for space analysis of single drop breakage events; the image is bedded

into a sketch of a Rushton turbine to illustrate the analysed image section

2.2 Numerical investigations By using computational fluid dynamics (CFD) the simplification of the flow field in the breakage cell compared with a stirred tank and the drop breakage itself should be investigated. The commercial sof-tware package ANSYS-CFX, Release 11 and the implemented shear-stress-transport-turbulence model (SST [Menter 1994]) was used for flow analyses. The main advantage of this turbulence model is the combination of the advantages of the k-ε-model (for high Reynolds number in the bulk flow) and the k-ω-model (low Reynolds number near to the wall). This means that close to the wall the SST-turbulence model switches automatically from k-ε to k-ω. Therefore the checking of the dimensionless wall distance (y+) is not necessary.

2.2.1 Stirred tank For validation purposes the flow pattern in the breakage cell was compared with the flow field in a stirred tank. Therefore a 360 degree steady state simulation was carried out with a Rushton turbine (d = 132 mm) installed in a baffled tank (T = 400 mm and H/T = 1.0). The well known k-ε turbulence model and the multiple frame of reference method (MFR) were used for this simulation. The tank was resolved by nearly 4 Mio tetrahedral elements, which led to a mean edge length of 4.6 mm in the who-le tank or a mean edge length of 2.7 mm near to the stirrer. By using inflated boundaries the dimen-sionless wall distance (y+) is determined to nearly 30 for the impeller and tank wall. Excellent ex-perimental results about the flow patterns in a stirred tank are available in literature. For this study the CFD simulations are compared with the work of Schäfer [Schäfer 2001]. To give a brief overview of this comparison all relevant data are listed in Table 2.


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Table 2 – listing of all relevant parameter to compare the CFD simulations with the experimental results of Schäfer [Schäfer 2001]

T [m] H/T [-] h/H [-] d/T [-] P0 [-] exp. results [Schäfer 2001] 0.15 1.0 0.33 0.33 4.5 Num. results [own study] 0.40 1.0 0.35 0.33 4.3

Firstly the numerical results of this simulation were compared with the experimental results. Therefore the power number (P0) is calculated by the simulated stirrer-torque, which means by calculating the pressure and viscous components of force on all boundaries specified as stirrer walls. The simulated power number is P0 = 4.3 which nearly equals (-4%) the experimental power number of Schäfer P0 = 4.5. Trailing vortices behind the stirrer blade are typical for the flow pattern of a Rushton turbine [Stoots and Calabrese 1995, Schäfer 2001]. The numerical simulation not only shows these vortices (see Fig. 4) but even it shows the same development for them like the experiments for the three pre-sented angels (φ = 0°, 5° and 10°). It has to be mentioned that the plotted velocity Vectors of the local velocities (wloc) are dimensionless by dividing them with the stirrer tip speed (wloc/wtip). So it is possible to compare the “absolute” values of the velocities. It can be seen that not only the direction but also the length of the velocity vectors from the CFD simulations (see Fig. 4 – right) are in very good agreement with the experimental results from Schäfer (see Fig. 4 – left).

0.05 0.10 0.15 0.20 0.25 r/T [-] 0.35

φ = 0°

experimental results [Schäfer 2001] numerical results [own study]

φ = 5°

φ = 10°

φ = 0°

φ = 5°

φ = 10°

0.05 0.10 0.15 0.20 0.25 r/T [-] 0.35 Fig. 4 – Trailing vortices behind the stirrer blade (for φ = 0°, 5° and 10°) the experimental results (left) [Schäfer 2001] and for the CFD-Simulation (right). The vector length describes a dimensionless velocity

(wloc/wTip) to enable the comparability of the two different applications (T = 0.15 and 0.40 m)

Schäfer mentioned a maximum kinetic energy in the tank of k/wTip² = 0.16-0.18 for z/T = 0.349, r/T = 0.197 and φ = 27°. The simulation shows a good quality of the location of the highest kinetic


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energy (see Fig. 5). But the simulated kinetic energy (k/wTip² = 0.073) is more than 50 percent lower than the experimental.

0.400.380.360.340.320.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30

k/(wTip)²

0.380.360.340.320.300.28

z/T [-]

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φ = 30°

φ = 27°0.16

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experimental results [Schäfer 2001]

numerical results [own study]

r/T [-]

z/T [-]

Fig. 5 – Location of high kinetic energy from the experimental results [Schäfer 2001] – above and

CFD-Simulation [own study] – below

2.2.2 Breakage cell

m/s Fig. 6 – CFD flow simulation of the single drop breakage cell (mean velocity and an exemplary 1.0 mm

droplet)

For the numerical investigations the presented breakage cell geometry was divided into three regions. The first block in front of the stirrer blade and the second block behind the stirrer blade were resolved by nearly 285,000 hexahedral elements. The third block, a region near to the stirrer blade (30 mm x 30 mm x 55 mm), was resolved by 1,064,113 tetrahedral elements (resulting in 5·10-5 mL


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per element or mean edge length 0.7 mm). Summarised more than 1,440,000 elements or 550,000 nodes were used for the whole simulated region. A comparison of an imaginary example droplet with dP = 1.0 mm and the fine resolved mesh is shown in Fig. 6.

3. RESULTS

3.1 Comparison of breakage cell flow patterns and flow fields in a stirred tank The aim of the CFD-simulations was to calculate the mean velocity field in the breakage cell and to compare the location of the particle break-up of the experimental results with numerical parameters like velocity and energy dissipation.

0.0 0.3 0.6 0.9 1.2 1.5 wloc/wTip [-] (ffov)

0° 30° f [deg] 60° 0.0 0.2 x/d [-] 0.4

breakage cell (r/T = 0.15)

vectors lengths are normalized: wloc/wTip (rfov) vectors lengths are normalized: wloc/wTip (rfov)

rfov - rotating frame of view (fixed stirrer)ffov - fixed frame of view (rotating stirrer)

stirred tank (r/T = 0.15)

Fig. 7 – Flow velocity in the stirred tank (left) and breakage cell (right). Normalized velocity wloc/wTip as

countor plot for a fixed frame of reference (stirrer rotates) and normalized vectors for a rotating frame of reference (fixed stirrer)

At first results of the simulated flow-pattern around a stirrer blade in the breakage cell are compared with the flow field in a stirred tank. Considering Stoots and Calabrese [Stoots and Calabrese 1995] the breakage cell represents a rotating frame of reference (that means fixed stirrer). So this specific flow is characterized by a wake behind the stirrer blade. This wake flow is characterized by two typically vortices behind the stirrer blade in 2D plot (see Fig. 6 and Fig. 7 – right). Normally stirred tanks are considered by a fixed frame of view (that means rotating stirrer – see counter plot in Fig. 7 – left). To transform the breakage cell from a rotating to a fixed frame of view the local velocities were sub-tracted by the stirrer tip speed wTip. The counter plots in Fig. 7 (left and right) show that the maxi-mum absolute velocity for a Rushton turbine is much higher than the stirrer tip speed. Stoots and Calabrese measured a peak value for the mean tangential velocity of wloc/wTip = 1.43 which corre-sponds with wloc/wTip = 1.5 for the stirred tank simulation and with wloc/wTip = 1.35 for the breakage cell. Both CFD-simulations in Fig. 7 show in general a good agreement between breakage cell flow and flow pattern in stirred tanks. One major difference is obvious: The macro scale vortices behind the stirrer blade, the wake flow, in Fig. 7 are much smaller in the stirred tank than in the breakage cell. These disagreements result from the use of only one blade in the breakage cell (see Fig. 1 – left). The following blade during the rotation compresses the macro scale fluid vortices in the stirred tank but this does not happen in the breakage cell (see comparison of the velocities in Fig. 7). So the flow field


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is qualitatively the same in both applications, but it is more compact in the stirred tank than in the breakage cell. Anyway CFD-results also include the simulated energy dissipation rate and the turbulence kinetic energy. With rising flow velocity in the breakage cell the local energy dissipation rate increases by εloc/w³ = const. too. The maximum energy dissipation is simulated to be εmax/w³ ≈ 8 m-1. For example a flow velocity of w = 1.5 m/s in the breakage cell should simulate a rotating speed of N = 550 rpm in a stirred tank (T = 0.24 m, d/T = 0.33, Ne = 4.3). This leads to a specific power input of ε = 1.07 m²/s³ in a stirred tank and the energy dissipation ratio can be calculated to εmax/ε = 26 (see Eq. (1)). This energy dissipation rate is well known for a radial impeller [Laufhütte 1986, Schäfer 2001, Baldi and Yianne-skis 2004].

25sm07.1

sm27w8m8w 32

323max1

3max ==

ε⋅

=ε

ε→=

ε − (1)

It is also well known that for turbulent flows drop breakage is usually related to the energy dissipation rate. Nevertheless the deformation rates based on gradients of mean velocity are also helpful to under-stand such processes. Fig. 6 shows a 1 mm droplet, the fine mesh resolution and the simulated mean velocities for a flow velocity w = 1.5 m/s which represents wTip = 2.3 m/s (N = 550 rpm and ε = 1.07 m²/s³). For instance the shear-gradient based on the mean velocity close to the droplet is ne-arly γ& = 1,420 s-1 (∆w = 1.42 m/s and ∆x ≈ dP = 1 mm). This situation leads to a typical drop-breakage-event which is shown in Fig. 1. The calculated shear-gradient mentioned above is equal to γ& / N = 153 or a shear stress of 1.4 Pa. Stoots and Calabrese measured the mean velocity field in a turbulent stirred tank by LDA and calculated deformation rates based on gradients of mean velocity [Stoots and Calabrese 1995]. They locate the maximum deformation rate on the blade edges and quan-tify it to be γ& /N = 150. It is also possible to integrate the kinetic energy over the whole volume of an example droplet. This leads to an input energy ( Ekin = 1.1·10-7 J) which is equal to the surface energy of the droplet (dP = 1 mm; γ = 32 mN/m EP = 1.0·10-7 J). At least the simulated parameters for the mentioned droplet in Fig. 6 are listed in Table 3. Additionally the energy dissipation rates in the breakage cell have been calculated with CFD in a former study [Maaß et al. 2007] and they also have shown good agreement with the values occurring in the stirred tank. Table 3 – Listing of the simulated parameters in the breakage cell for a mother drop dp = 1 mm

maximum local velocity [m/s] 1.74

minimum local velocity [m/s] 0.32

Volume averaged energy dissipation rate [m²/s³] 21

Volume averaged kinetic energy [m²/s²] 0.12

Volume averaged deformation rate based on mean velocity [s-1] 1,025

All explanations in this section should clarify the qualitatively very good agreement between the simu-lated parameters (velocity, deformation rates, energy dissipation) in the breakage cell, the known ex-perimental and the numerical data in a stirred tank. Clearly, the flow pattern in the breakage cell and the flow field in a stirred tank look very similar by using the same frame of reference. This fact is very important for interpreting the experimental results.


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3.2 Single drop breakage results Firstly the location of the breakage events in the single drop breakage cell is analysed. To rate the lo-cal breakage allocation it is necessary to analyse the entrance allocation of the particles. Therefore all breaking droplets are classified by their entry point into the area of interest (see Fig. 3 – left) which is defined as the x-coordinate where the centre of mass is detected at y-coordinates below 36 pixels, equal to 4.0 mm. Fig. 8 shows the results for the so developed relative entrance probability. The rela-tive frequency calculated by the entering number of droplets is plotted against the spatial magnitudes over the width of the images. The investigations include two diameters (644 and 1000 µm) and three flow velocities (1.0, 1.5 and 2.0 m/s) of toluene droplets in a continuous water flow.

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Rel

ativ

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cy [-

]

1,0 m/s (1000 µm)

1,5 m/s (1000 µm)

2,0 m/s (1000 µm)

1,5 m/s (650 µm)

toluene droplets

pH 7

y-coordinate allways

below 2.75 mm

stirrer blade

Fig. 8 – Relative entrance probability (y-coordinate smaller than 4 mm) for all breaking toluene droplets

under variation of mother drop diameter (644 and 1000 µm) and flow velocity (1.0 - 2.0 m/s)

All three investigated flow velocities and both diameters show basically the same behaviour. Many more droplets are entering the analysed area at the right and at the left border than in the centre of the channel, because the water flow is forced around the stirrer blade to the sides. A second difference between relative entrance probabilities of the left and the right side becomes obvious on closer inspec-tion. The summation, of the number and the relative frequency of entering droplets of the first three pixel size groups, is always higher than the sum of the last three size groups (see Fig. 8). This phe-nomenon is especially significant for the experiments with the small diameter of 644 µm and a flow velocity of 1.5 m/s. These permanent errors have to be taken into account for the following analysis of drop breakage places. Fig. 9 and Fig. 10 show the local analysis of all counted breaking events. The coordinates of the loca-tion of the drop breakages are collected and classified after the presented magnitudes (see Fig. 3). A direct comparison for two different velocities (1.0 and 2.0 m/s) is presented in Fig. 9. Both diagrams show the results for 1000 µm toluene droplets. As presented in chapter 2, the allocation of the break-ing droplets into the different pixel size groups, starts for the y-axis at 1 mm (10 pixels). The x-axis starts at 0.0, and therewith the first size group with an edge length of 2.75 mm starts in the upper left corner from [(1; 0) spanned to (3.75; 2.75) all in mm]. The relative frequency of breaking droplets is now plotted against this incremental 2D-area of the range around the stirrer model. The same example area are shown here as the blanked field in Fig. 3 for the lower velocity: The relative frequency of the investigated breaking droplets for the size group [(24.75, 2.75; 27.5, 5.5) all in mm] is a local maxi-mum of approximately 2.2 percent. Such an analysis shows three main results.


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Firstly both diagrams show that the main number of breakages is occurring in the centre of the stirrer range. No breakages occur, due to the no-slip condition at the wall, near the channel walls for magni-tudes with y-coordinates lower than 2.75 or higher than 27.5 mm. This means that, for closer distances than 2.75 mm from the wall, breakage is strongly hindered. Secondly Fig. 9 shows that breakage ends mainly after a distance of 55 mm from the y-coordinate for the lower velocity. That means that after a distance of 0.65·d behind the stirrer blade no breakage is occurring anymore due to the flow patterns. For the higher velocity (Fig. 9 – right diagram) the gradi-ents of the flow are still able to break droplets. So the allocation of breakage events is more homoge-neous for the higher than for the smaller velocity. The same is true for the discussion based on the energy dissipation rates. Thirdly the error shown and discussed in Fig. 8 can also be recognized in the breakage plots. All dia-grams including the following figures show slightly higher values for the smaller x-Pixel classes than for the symmetric higher ones.

Rel

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30.2563.25

33.0

0.04

y [mm]V& V&

dp = 1000 µmw = 1.0 m/s

dp = 1000 µmw = 2.0 m/s

Fig. 9 – Comparison of the location of breakage for toluene drops with a diameter of 1 mm at two differ-

ent flow velocities (1.0 m/s and 2.0 m/s)

In Fig. 10 the comparison of the breakage positions for two different drop diameters (644 and 1000 µm, left and right) are presented for a third flow velocity (1.5 m/s). Both diagrams show the same fundamental behaviour as the analyzed events in Fig. 9. On closer examination the distribution of the right diagram for the 1000 µm droplets with the flow velocity of 1.5 m/s lies exactly between the 1.0 and 2.0 m/s data, presented in Fig. 9.

Rel

ativ

e fr

eque

ncy

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dp = 1000 µmw = 1.5 m/s

Fig. 10 – Comparison of the place of breakage for toluene drops with two different diameters (644 and

1000 µm, left and right) for a flow velocity of 1.5 m/s.


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Analyzing the different results for the different diameters, it becomes obvious that the larger droplets break more homogeneously over the investigated range. This can be explained with the surface forces of the droplets. The same flow field with the same gradients resulting by the same flow velocity should stress both diameters equally. The smaller diameter is more stable than the larger one and so breakage occurs only in a close range to the stirrer blade. These results shall now be compared with the flow analysis of the CFD results.

3.2 Comparison of experimental and numerical results Fig. 11 compares experimental and numerical results at the same flow velocity of 1.5 m/s. The left side presents experimentally determined breakage positions in the breakage cell. On the right side numerical results are presented, showing isovolumes of energy dissipation with values above 20 m²/s³. The isovolume cuts the mesh using an isosurface of the local energy dissipation with a specified iso level value of εloc > 20 m²/s³. It outputs the portion of the mesh that is above of this cutting isosurface. All three tearing edges of the stirrer blade (all three sides which are not directly in contact with the stirrer disk, see Fig. 11 – right) produce an almost equal distribution of isovolumes with high energy dissipation rates. The distribution starts at the two opposed corners of one edge and these separated regions unite after more than 15 mm behind the blade (region B in Fig. 11 – right). That happens at all of those three edges. That leads to a kind of a hole in the 3D – distribution of the iso-volumes of high energy dissipation (region A in Fig. 11 – right). This hole can also be considered in the experimental results. In the middle of the channel, directly behind the stirrer blade, the number of breakage events reaches only a third of the number of breakage events of the area around it. Furthermore the union of the areas with high energy dissipation rates leads also to an increase of the number of breakage events at the same place. The area of high energy dissipation (εloc > 20 m²/s³) is quite similar to the experimental breakage re-gion with the highest number of breakage events. As mentioned before breakage ends mainly after a distance of nearly 50 mm behind the stirrer blade. The region of high energy dissipation reaches a distance of 50 mm behind the stirrer blade too.

0.0

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0.02

0.0

30.25y [mm]

x [mm]63.25

33.0V& V&

dp = 1000 µmw = 1.5 m/s

A

A

B

B

Fig. 11 – Comparison of experimental (left) and numerical results (right – isovolume of energy dissipation

above 20 m²/s³) for a flow velocity of 1.5 m/s ( wTip = 2,3 m/s)

4. CONCLUSIONS

In this work the experimental set-up to investigate the single drop breakage and particle strain close to a stirrer blade was discussed. The developed breakage cell simplifies the turbulent flow field near the stirrer blade. Accordingly numerical investigations were carried out to judge the simplification of this application. The comparison of the numerical results in the breakage cell and the experimental data in


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stirred tanks [Stoots and Calabrese 1995] show a good agreement with the typical vortices behind the stirrer blade, the maximum velocity, the deformation rate based on mean velocity and the energy dis-sipation ratio. Also the region of high energy dissipation is similar to the experimentally detected re-gion of high single drop breakage probability.

5. ACKNOWLEDGEMENTS

We gratefully acknowledge the financial support from the Bayer Technology Services GmbH and from the Federal Ministry of Education and Research by the AiF–project FKZ 1733X06.

6. NOMENCLATURE d ]m[ - impeller diameter

Pd ]m[ - particle / drop diameter ]E ]J[ - energy

H ]m[ - total liquid depth in vessel h ]m[ - stirrer bottom clearance

0P ][− - impeller power number r ]m[ - radial distance from the axis of the vessel T ]m[ - vessel diameter w ]sm[ - speed

Tipw ]sm[ - tip speed of the stirrer blade

end;startx ]m[ - space coordinate

end;starty ]m[ - space coordinate z ]m[ - vertical coordinate of the measuring volume

Greek letters

max;locε ³]s²m[ - global and local energy dissipation γ ]m/mN[ - interfacial tension γ& ]s1[ - shear gradient η ]smPa[ ⋅ - viscosity ρ ³]m/kg[ - density ϕ [deg] - tangential coordinate of the impeller revolution

Abbreviations ffov fixed frame of view fps frames per second rfov rotating frame of view

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numerical and experimental analysis of particle strain and breakage in turbulent dispersions

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