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

NUMERICAL AND EXPERIMENTAL STUDIES OF LIQUID-LIQUID MIXING IN A KENICS STATIC MIXER

Zdzislaw Jaworskia, Halina Murasiewicza,

aInstitute of Chemical Engineering and Environmental Protection Processes, West

Pomeranian University of Technology, Szczecin, Aleja Piastow 42, 71065 Szczecin, Poland

zdzislaw.jaworski@zut.edu.pl, hmurasiewicz@zut.edu.pl

Abstract. A successful attempt to investigate the mixing of immiscible fluids in a Kenics mixer by using the large eddy simulation (LES) technique was undertaken. The CFD simulations were performed for three levels of the Reynolds number ranging from 5,000 to 18,000 with the volumetric ratio of 99 % of water to 1 % of oil. The goal of this work was mainly achieved by determining values of the coefficient of concentration variation, CoV, and comparing it with the experimental results available in the literature. First of all, the single–phase flow field was simulated and compared with experimental data obtained by means of Laser Doppler Anemometry (LDA) measurements. The mean axial and tangential velocities, calculated from the LES approach agreed quite well with those from LDA. Furthermore, the turbulent liquid-liquid flow was investigated by means of CFD simulations. The simulated values of mixing homogeneity were determined. With increase in the L/D ratio a faster decrease in CoV, i.e. a faster increase of the homogeneity level in the system was achieved. Keywords: liquid-liquid system, CFD, LDA, turbulent mixing, static mixer, LES model.

1. INTRODUCTION Mixing is the most fundamental process among all industrial chemical processes, ranging

from simple blending to mixing of complex multiphase reaction systems. Improper mixing often results in lower product quality and non-reproducible processing conditions. Consequently, it is then necessary to repeat the procedure of mixing or to use advanced treatment processes, which increases the cost of waste disposal. In many cases static or dynamic mixers are widely used for mixing immiscible liquids [1]. However, static mixers are applied more often than stirrers due to lower operating costs. Among all static mixers the Kenics mixer is regarded as the most efficient mixer in a wide range of flows and scales, ranging from micro- to macro-scale. The subject literature shows many investigations of Kenics static mixer with the following main aspects considered: pressure drop [2], optimization of the mixer geometry [3] and determination of the quality of mixing [1].

A liquid-liquid dispersion in static mixers is achieved by passing two immiscible liquids concurrently through the mixers. The open literature shows results of numerical and experimental studies of liquid-liquid systems that focus mainly on the analysis of the effect of the dispersed phase viscosity on the mean drop size and drop size distribution (DSD) [4-5], the Sauter mean drop diameter [6], the drop break-up process in intermittent turbulence [6-7]. Studies of mixing of liquid-liquid dispersions in a Kenics mixer were performed by Rauline at all. [8] or Guo at all. [9].

An important factor in dispersed systems is the droplet size distribution whose character depends on the flow. Elements of the dispersed phase can change their identity as a result of break-up or coalescence processes, which depend on flow conditions. Detailed knowledge of hydrodynamics in such devices is therefore necessary and it is also vital for the control of the mixing process in the most efficient way. Experimental study of the two-phase flow field is

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difficult because intrusive techniques can disturb the flow, while for the dispersed phase the availability of modern, non-invasive measurement techniques like LDA and PIV is limited. These techniques were successfully used in single-phase systems [10] while for the two-phase systems a limited number of investigations was published [11]. Limitations of numerical methods involved in investigations of two-phase systems led to simplifications that treat the two-phase systems as if they were homogeneous.

In addition to experimental approaches, enormous capability of Computational Fluid Dynamics (CFD) codes has been exploited in modern investigations of two-phase liquid-liquid flow. The numerical tool allows for computing flow structure, local flow and turbulence of both phases and their interaction. However, despite of the high potential of CFD and increasing number of papers on liquid-liquid flows, the flows are yet not sufficiently studied. This is due to the complexity of two-phase liquid-liquid flows.

The aim of this work is shedding more light on the mixing process and turbulent flow of liquid-liquid systems in a Kenics static mixer. Based on review of the literature and our earlier experience, a study of a dispersed system was carried out in three stages. In the first step, experimental data obtained for single–phase flow in a Kenics static mixer with six inserts by means of Laser Doppler Anemometry (LDA) measurements were compared with CFD simulation data. The mean values of axial and tangential components of velocities were the subject of extended analysis. The simulation step of single-phase allows ascertaining whether a CFD simulation method is capable to adequately describe the flow field. In the second stage, a CFD analysis of the flow structure of liquid–liquid mixtures was performed by using Eulerian approach together with the LES method. In particular, average and RMS velocities have been determined in parallel. Furthermore, the computations of the coefficient of concentration variation, CoV, as a measure of the mixing process, were carried out and compared with experimental data available in literature.

2. NUMERICAL AND EXEPERIMENTAL METHODS

Dispersion of immiscible liquid-liquid system was numerically investigated for a Kenics static mixer with 10 standard inserts (Figure1) located in the mixer tube. The symbols D [m] and h [m] denote the diameter and length of the Kenics insert equal to 25·10-3 [m] and 37.5·10-3 [m], respectively. The total length of the static mixer, L, was 515·10-3 [m]. A detailed description of the tube and inserts has been presented in an earlier paper [12].

Figure 1. Scheme of the Kenics mixer geometry. The mixer’s numerical mesh was created with the help of a specialized preprocessor Gambit 2.0. The total number of control volumes (cells) was about 900 thousand, denoted by (900 k). The numerical modelling was performed for three cases using the commercial ANSYS 13 package. Two immiscible liquid streams formed two phases with the dispersed-to-continuous phase volumetric ratio of 1:99, analogously to the experimental conditions applied elsewhere [20]. Water was used as the continuous phase (index c) whereas silicon oil was used as the dispersed phase (index d). Such a small contribution of dispersed phase allowed ignoring the coalescence process. Physical and rheological properties of the liquids used are shown in Table 1. The first case mimicked the literature experimental conditions [13]. A Perspex Kenics mixer with six black-painted inserts was used in LDA measurements to meet the requirement of optically transparent vessel. Main dimensions of the mixer tube and inserts were as follows: internal diameter of pipe D=0.074 [m], total length L=1.152 [m], height of single inserts h=0.113 [m]. Water of temperature 20ºC was used as the process liquid with density of ρ=998 [kg m-3]. The evolution of the hydrodynamic conditions was monitored for consecutive time steps at the region of the 5th insert of the Kenics static mixer.

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Table 1. Physical properties of the working fluids

Case 1, ρc > ρd 2, ρc = ρd 3, ρc < ρd

Fluids water oil phase “c” phase “d” phase “c” phase “d”

ρ [kg m–3] 998.2 900 900 900 900 998.2

μ · 103 [Pa s] 1.003 0.900 1.003 0.900 1.0037 0.900

avρ [kg m–3] 997.2 900 901

In our study we used simplification that at such a low concentration of the dispersed phase this two-phase system can be well described as a single-phase system. Therefore, simulations of single-phase flow were carried out to compare and confirm the agreement between simulations and experimental data. This assumption is useful for validation of CFD numerical simulations. The numerical method will be described in the next chapter.

2.1 CFD approach Numerical simulations were carried out for both single-phase and two-phase fluid flow in the Kenics mixer. The first step of the analysis of two-phase flow in a mixer with 10 Kenics inserts was studying the flow field resolved by using Large Eddy Simulation, LES, method with Smagorinsky-Lilly (S-L) model. A simplified, pseudo-homogeneous version of the E-E model called the Mixture Model was used to describe the behaviour of dispersed phase and the interaction between phases. The main algebraic equations of this model were presented elsewhere [12]. One of the assumptions of the basic Mixture Model is a constant value of drop diameter irrespective of the flow conditions. The value of the Sauter mean diameter calculated for the Kenics mixer for Re 5 000, 10 000 and 18 000 were 2.357·10-3 [m], 8.33·10-4 [m] and 3.45·10-4 [m], respectively. In the LES modelling, the single time step in iterations was δt=10-3 [s]. Within each time step, 50 SIMPLEC iterations were performed to couple velocities and pressure fields. In the second stage of analysis, the single-phase flow was simulated in the mixer and the same geometry of the Kenics mixer as in experiment was used. The numerical grid consisted of about 1 500 000 computational cells. The CFD modelling was carried out by employing LES with S-L model for the same three levels of Reynolds number as for the two-phase flow. The time step of 0.025 [s] and 100 internal iterations for each time step were assumed. The applied convergence criteria was less than 10-7.

2.2 Experimental technique The LDA instrument used in the experiments was a TSI 1D (one active channel) system and the equipment was controlled by the TSI software FlowSizer. All flows were seeded with PSP-5 polyamid seeding particles delivered by DANTEC. Measurements were taken in the region of the 5th insert downstream the first insert at heights h, set to 1/2 of the total insert height, H, and for five measurement points and angular position, α=90º. The tangential and axial velocities were measured separately in selected points located at different radial positions and for three Reynolds number, Re, 5 000, 10 000 and 18 000.

3. RESULTS AND DISCUSSION The experimental and numerical simulations of the flow and mixing in the Kenics static mixer were performed using a three step procedure. In the first step, the flow velocity of single-phase was computed by using two techniques: LDA and CFD and then they were compared.

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3.1 Comparison of fields for single phase flow In order to describe the turbulent flow and to compare both methods, data obtained from LDA and CFD methods were used to plot the mean axial velocity profiles for the fifth insert of the Kenics mixer at different levels of Reynolds number (Fig. 2). The values of the axial and tangential component of velocity were related to the superficial velocity, v0, for the sake of better readability.

Figure 2. The experimental and numerical profiles of axial and tangential velocities of fifth insert, three Reynolds numbers: 5 000, 10 000 and 18 000, angular positions α=90ºand heights h=1/2 H. The obtained velocity profiles are characterized by evidence of heterogeneity of turbulent flow. Based on the above examples of the distributions of the axial and tangential components of the velocity, good agreement was observed between profiles. Changes in the axial and tangential velocity components shown in Figure 2 confirm similar behaviour for each Reynolds number. No meaningful differences between the velocity profiles of the two components obtained from LDA and CFD were found. The mean differences in tangential components of velocity were approximately 6%, -5% and 1% for Re 5 000, 10 000 and 18 000, respectively. However, for the axial component these values were slightly larger - 13% for Re=5 000, 9 % for Re=10 000 and for Re=18 000 20%. In almost all cases, slightly higher values of the velocity components were obtained from CFD simulations, except for the tangential velocity obtained at Re=10 000. In order to test the agreement between components of velocity for two methods, the Mean Squared Error, MSE, was estimated. The MSE values predicted for the axial velocity amounted to 5% for Re=5 000 and 10 000, 8% for Re=18 000, whereas for the tangential component the MSE were smaller and equalled to 3%, 2.5% and 1% for Re 5 000, 10 000 and 18 000, respectively. The MSE values below 8% confirm good conformity between the LDA measurements and CFD simulations. The obtained agreement was satisfactory and it led to the conclusion that the CFD simulation can be used to reliably predict fluid flow in Kenics static mixer.

3.2 Characterization of the liquid-liquid flow field

In next stage of analysis, the liquid-liquid flow field in the Kenics static mixer was considered. This step concerned the simulated flow field of the axial component of velocity. However, due to the limited space of the description, only the results obtained in the third case, Case C, are briefly presented. In order to help visualize the distributions, contours of the velocity components obtained for the three levels of Reynolds number used in the LES modelling methods were examined. A typical map for the axial component in the mid-cross section of the 5th insert and for Case C is shown in Fig. 3. The performed analyses of local distributions of the axial velocity component within the fifth insert led to the conclusion that the flow fields are strongly heterogeneous. One can see from the comparison of the results that all maps revealed strong velocity fluctuations and a lack of symmetry, what was usually observed in the RANS modelling. With an increase of Reynolds number, also increase of the average value of the axial velocity was observed. Based on the LES maps, similar differences were found for the other velocity components (not show here) and for corresponding cases. However, all of them demonstrate distinct local instabilities of all velocity components reproduced by the large eddy simulation technique.

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Figure 3. Numerical profiles of the axial velocity of the fifth insert, three Reynolds numbers:5 000, 10 000 and 18 000, LES method, distance h=1/2 H, case 3.

3.3 Coefficient of variation, CoV

A widely used measure of uniformity of tracer concentration at mixer’s cross-sections is the coefficient of variation (CoV). The CoV is defined as the standard deviation of concentration, σ, over the mean concentration, x for a given set of data points, CoV x= σ / [1]. The lower the value of CoV, the better is the mixture quality. The value of CoV= 0 indicates perfect mixing process, while CoV≥1 means significant segregation of the two phases. Nevertheless, values of CoV between 0.01 and 0.05 are a reasonable target for many applications. The distribution of CoV for the dispersed phase and for the three levels of Reynolds number simulated with the LES technique were compared with literature data and presented in Fig. 4.

Figure 4. Concentration CoV as a function of distance downstream from the inlet to the Kenics static mixer at three levels of Re for LES and literature data.

The predicted value of CoV obtained in the LES modelling for Case 3 (Case C) is higher for Re=5 000 than for Re=10 000 and 18 000. However, the CoV values below CoV=0.05 were obtained for the two higher Re number, what might be considered as a well mixed system. According to Fig.4, the LES results of CFD modelling of CoV for all cases are usually lower than the experimental data for miscible liquids [14] where more than 10 inserts were used. Comparing to the experiment, the CFD curves for the

immiscible liquids exhibit non-linear variations. As it can be observed, with increase of the Re number the value of CoV decreases. The homogeneity level for all cases downstream the third insert reaches the constant value. Further, after the fifth insert the value of CoV for Re 10 000 and 18 000 increases, whereas for Re 5 000 it decreases. The CoV value obtained for Re 5 000 decreases after the eighth insert, what means that the mixture homogeneity improves. A similar situation is observed for the CoV data for two higher Reynolds number, but growing of the homogeneity is visible already after the sixth insert.

4. CONCLUSIONS The liquid-liquid dispersion in a Kenics static mixer and single-phase were investigated by using two approaches: experimental - LDA and numerical - CFD. In the first step of analysis, single-phase flows in the Kenics static mixer with six insert were analysed by means of LDA and CFD. In the single flow inside the Kenics static mixer, the mean value of axial and tangential velocity have been determined. Generally, the agreement between two techniques

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was confirmed with the values of the mean squared error being less or equal to 8%. Next, the liquid-liquid turbulent flow was analyzed. The axial, tangential and fluctuation components of velocities and the mixing quality, CoV, were considered. The performed analysis of the CoV coefficient showed that the level of heterogeneity for both Re=10 000 and 18 000 grew after leaving the tenth insert. Results of the large eddy modelling revealed relatively high level of fluctuations of the basic local characteristics of the turbulent flow components, such as the axial and tangential velocity inside the Kenics mixer. Information of this kind cannot be obtained from the RANS modelling where only the average values for the whole turbulence spectrum are directly delivered. Therefore LES gives much better insight into the local, instantaneous characteristics of the turbulent two-phase flow.

ACKNOWLEDGEMENTS

This work was financially supported by the Polish Ministry of Science and Higher Education in grant number N 209 200238.

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