Andreas Lehwald 1, Stefan Leschka 1,2, Katharina Zähringer 3, Dominique Thévenin 4. Introduction

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1 Fluid dynamics and mixing behavior of a static mixer using simultaneously Particle Image Velocimetry and Planar Laser-Induced Fluorescence measurements Andreas Lehwald 1, Stefan Leschka 1,2, Katharina Zähringer 3, Dominique Thévenin 4 1: Lab. of Fluid Dynamics and Technical Flows, Otto-von-Guericke-University, Magdeburg, Germany, andreas.lehwald@ovgu.de 2: now at Hydraulic & Coastal Engineering, DHI-WASY GmbH, Syke, Germany, sle@dhi-umwelt.de 3: Lab. of Fluid Dynamics and Technical Flows, Otto-von-Guericke-University, Magdeburg, Germany, katharina.zaehringer@ovgu.de 4: Lab. of Fluid Dynamics and Technical Flows, Otto-von-Guericke-University, Magdeburg, Germany, thevenin@ovgu.de Abstract The mixing behavior around a SMX-type static mixer segment has been investigated experimentally by using Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF) simultaneously. To quantify mixing, velocity fields and concentration fields have been measured for different Reynolds numbers along vertical and horizontal sections directly behind the mixer. The experimental data have been post-processed. A spectral analysis of the simultaneous PIV and PLIF measurements has been carried out, in order to determine the characteristic frequencies induced by the mixer and correlations between velocity and concentrations. Furthermore, the mixing efficiency has been quantified by considering the segregation index. Introduction In the past, the mixing behavior of static mixers has been investigated in a global manner for various mixer configurations, but usually without relying on non-intrusive optical diagnostics. For example Pahl and Muschelknautz (1982) have compared 12 different static mixer types, but considering only global properties, like pressure drop and overall mixing efficiency. Recently, static mixers have been also characterized using Planar Laser-Induced Fluorescence (PLIF) to determine the concentration fields and the concentration variance, a characteristic parameter to quantify macro-mixing. A few generic configurations (Wadley and Dawson, 2005) and commercial static mixers (Pust et al., 2006) have been investigated in this manner. This is an essential step, but an isolated PLIF measurement cannot deliver information concerning the flow structure. In the present project Particle Image Velocimetry (PIV) and PLIF have been combined and used simultaneously to quantify experimentally the fluid behavior around a static mixer, in particular to determine the flow and mixing conditions behind an isolated mixer segment. The considered configuration is a SMX-type static mixer (fig. 1). These extensive experimental measurements are additionally employed to check and improve numerical mixing models and to validate computational simulations relying on Large-Eddy Simulations (LES). Such LES computations should ultimately be able to characterize in an accurate manner the properties of industrial static mixers

2 Experimental set-up and measurement methods In order to obtain laminar conditions at the inlet of the mixer, a gravity-driven flow channel installation is used (fig. 2). For that, a pump delivers the fluid from a lower tank to an upper tank, whose water level lies roughly 10 m above the channel axis. A diffuser is installed, which is used after the down-pipe to adapt the cross-section from circular to square. This square shape has been chosen for the whole measurement section in order to increase the quality of all optical measurements by limiting refraction, laser beam divergence and image distortion. After the diffuser, a 2.45 m long inflow section leads the fluid to the static mixer. The mixer consists of seven rectangular lamellas with an individual width of 13 mm, as illustrated in figure 1. Four lamellas are turned against the flow; between them, three are turned in the direction of the flow. The straight outflow section behind the mixer also has a length of 2.45 m. Inflow, outflow and mixer consist of acrylic glass and have a cross section of 91 x 91 mm². A flow meter is installed at the end of the test section. The required flow-rates are adjusted using a precision control valve. From there, the fluid goes to a damper. For simultaneous PIV and PLIF measurements, the water contains not only PIV tracers but also the fluorescence dye. It is sent to a purification process, so that the dye does not recirculate in the installation (open loop). A schematic view of the experimental set-up developed for the present investigation is shown in figure 2. Further details can be found in Leschka et al. (2006). Figure 1. SMX-type static mixer considered in this study, a) top view: horizontal (x-y) plane, b) side view: vertical (x-z) plane. Figure 2. Schematic view of the experimental set-up. For PIV measurements tracer particles are injected into the upper tank (fig. 2). Spherical hollow glass balls (Type 110 P8 CP00) with a mean diameter of d 50 = 10.2 µm (d 10 = 2.9 µm, d 90 = 21.6 µm), a mean density of 1.1 g/cm³ and a bulk volume between 2.22 l/kg and 2.85 l/kg have been used. Depending on the fluid velocities, the tracer concentration is adapted to obtain 30 to 40 particles in a 32 x 32 pixel interrogation area of the PIV image. This results in a typical volume - 2 -

3 fraction of V p /V f = , low enough to avoid any influence of the particles on the flow. For mixing measurements using PLIF, the fluorescence tracer (99% pure Rhodamine 6G) is injected along the centerline, 39 mm in front of the mixer segment, with the same velocity as the main fluid and with a Rhodamine concentration of 20 µg/l. The PLIF images have been acquired using an intensified CCD camera (LaVision NanoStar, 1280 x 1024 pixels) during the first of two PIV laser pulses (Nd:YAG, 532 nm, 80 mj per pulse), while the CCD camera (LaVision Imager Intense, 1600 x 1186 pixels) used for PIV takes double images, used to calculate the twodimensional velocity fields. To separate PIV and PLIF signals, the cameras are equipped with two different filters. For recording PIV images a laser-line filter BP532/10 nm and for recording PLIF images a high-pass filter LP580 nm have been used, respectively. The outlet of the central LIF tracer injection system has a square section of 25 mm². Before entering the test-section, the injected mixture of water and fluorescing dye flows through a thermostat (Haake Phoenix 2 P1-C25P), which is used to control the temperature of the injected fluid and keep the difference with the main fluid temperature within the channel below 0.5 K. The temperatures typically lie around 17 C in all experiments presented here. This very accurate temperature control was observed to be absolutely necessary, in order to avoid a rapid stratification between the injected mixture and the main flow, due to buoyancy. The static over-pressure in the test-section is bar. The Reynolds numbers are always calculated using the hydraulic diameter of the channel and the mean streamwise velocities. The resulting values of the Reynolds number Re together with the corresponding total flow rate and the flow rates Q 1 of main fluid and Q 2 of the injected mixture, their ratio and the mean streamwise velocities are summarized in table 1 for the two main cases (Re = 562 and Re = 1000) discussed in this paper. Static mixers are usually employed for highly viscous fluids and thus very low Reynolds numbers. The present experiments use water as a main fluid but keep the analogy by considering the same typical Reynolds numbers (similarity conditions), thus leading to very low velocities. Table 1. Reynolds numbers, flow rates and resulting mean axial velocities. Re [-] Q [l/h] Q 1 [l/h] Q 2 [l/h] u x [mm/s] Q2 Q + Q [-] The PIV data has been post-processed and evaluated using an adaptive multi pass cross-correlation with decreasing size over interrogation areas of 128 x 128, 64 x 64 and 32 x 32 pixels, each with 50 % overlapping. Furthermore, a Gaussian low-pass filter has been applied. In the interrogation area, values lying within the range of 120 % of the second highest value have been accepted. For PLIF a concentration calibration is necessary. In the literature different specifications can be found concerning the linear part of the fluorescence behavior of the employed dye. Therefore several tests have been conducted in order to find an appropriate range for the present optical and flow conditions. As recommended by Law and Wang (2000), a concentration range of 0 µg/l to 20 µg/l has been finally found to be suitable for these experiments. The Nd:YAG-laser has been systematically combined with an energy monitor, which allows to correct laser energy fluctuations during post-processing. This correction is necessary to obtain accurate quantitative concentrations from PLIF. Post-processing masks have been defined to exclude non-evaluable areas due to locally insufficiently good optical conditions, resulting from the lamellas, shadows of mounting screws, etc. (see also fig. 1). In addition, background images have been acquired. In this manner negative effects like background scattering (reflection, diffraction and refraction) can be eliminated

4 Results The results presented in figure 3 exemplify instantaneous simultaneous measurements involving PIV and PLIF directly behind the mixer (x = 50) mm, in the central horizontal and at Re = 562 and Re = White zones in the images correspond to masked areas, in which measurements are not possible. Reynolds number 562 is the reference case for this study. Averaging the velocity measurements over 300 images, velocity ranges of 0.3 mm/s up to 33 mm/s in the and of 0.4 mm/s to 22 mm/s in the are obtained. The maximum velocity is measured, as expected, in-between the mixer lamellas (lowest hydraulic section). At Re = 1000 the flow shows more vertical structures and the velocity magnitudes range between 0.2 mm/s and 57 mm/s in the and between 0.3 mm/s and 42 mm/s in the vertical plane. The differences observed between horizontal and vertical measurements are not surprising, since the single-stage mixer structure is not at all isotropic (fig. 1), with all lamellas positioned in the vertical direction. For such low Reynolds numbers, the influence of the mixer geometry is expected to be very high, leading to different results in the horizontal and. This difference will decrease when increasing the Reynolds number or when considering realistic mixer geometry with several stages, turned one to the other at 90, and thus increasing flow isotropy. The concentration measurements clearly show at Re = 562 small-scale, coherent vortex structures both in the horizontal and in the. The measurements for the higher Reynolds number do not present such clear vortex structures any more. Due to the small quantity of dye injected in the main flow and to the higher dynamics of the flow a large part of the injected fluid is already well-mixed when the fluid leaves the mixer segment. Qualitatively, a high level of mixing is, in particular seen in the just behind the mixer, since the influence of the lamellas is maximal in this plane. In the, elongated vortex filaments are observed. As a whole, mixing homogeneity increases with the Reynolds number, as expected. This will be quantified in what follows. Behind the mixer the flow velocities and concentrations have been analyzed extensively using Nonequidistant Fast-Fourier Transformation (NFFT) in order to identify the characteristic frequencies f of the structures induced by the static mixer both in the velocity and in the concentration fields. During the simultaneous PIV/PLIF measurements, the obtained acquisition frequency is limited to 1.6 Hz at most and is furthermore not constant, due to the limited and different data transfer-rates of the cameras. As a consequence, a classical FFT analysis is not possible any more. For the present post-processing the efficient Lomb-Scargle-Algorithm (NFFT, cf. Press et al., 1995) has been used. The frequency analysis of the PIV data delivers clear peaks and harmonics for Re = 562 and Re = 1000 in the horizontal as well as in the s (fig. 4). The PLIF frequency analysis shows a lower signal-to-noise ratio in the, especially for Re = For Re = 562 the peak frequencies for velocity magnitude, velocity direction and concentration are all equal to 0.36 Hz. This means that the structures induced by the mixer repeat very clearly after 2.78 s, as can also be shown by looking directly at time-sequences. For Re = 1000, a peak frequency of 0.75 Hz (period of 1.33 s) has been found. For both planes and both values of Re the variations of the velocity field correlate very well with the fluctuations of the concentration field

5 14th Int Symp on Applications of Laser Techniques to Fluid Mechanics PLIF measurement: concentration field Re = 1000 Re = 562 PIV measurement: velocity vector field Figure 3. Velocity vector fields (left) and concentration fields (right) measured directly behind the static mixer at Reynolds number 562 (top) and 1000 (bottom) for the central horizontal and s. -5-

6 NFFT of velocity magnitude NFFT of velocity direction NFFT of concentration Re = 1000 Re = 562 Figure 4. NFFT for velocity vector fields considering separately vector magnitude (left) and vector direction (middle), as well as NFFT of concentration fields (right). All measurements have been carried out directly behind the mixer at Reynolds number 562 (top) and 1000 (bottom) for horizontal and s. 2 σ For the quantification of the mixing efficiency the classical segregation index IS =, given by 2 σ max Danckwerts (1952) and based on the normalized concentration variance, has been calculated along the channel axis. The variance of the concentration c(x) of the injected dye is calculated by 2 1 [ ] 2 1 σ = c( x ) µ da A, with the expectation (mean) value µ = c( x ) da A. The maximum computed A A 2 variance σ max, used as a reference value for normalization, is computed by considering independently all individual results (global maximum). For this treatment the measurement area has been divided in regular stripes along the streamwise direction. In each stripe, the local, mean concentration value and variance can be determined. After having determined the global maximum of the variance, a segregation index can be calculated as a function of the streamwise coordinate for each instantaneous PLIF image. The resulting segregation indices have then been averaged over

7 images. The final, average values are shown in figure 5. The fastest mixing is, as expected, obtained at the higher Reynolds number, as can clearly be seen from this figure. The difference between the vertical and the can again be explained by the geometry of the single-state mixer, highly non-isotropic. For a further quantification of the mixing efficiency the mixing length L mix can be defined as the distance from the mixer outlet to the first location after which a given threshold value of the segregation index, usually 5%, is not exceeded any more. Considering the mean velocities u x given in table 1, a characteristic mixing time t mix can then be deduced as t mix = Lmix ux. For the conditions considered here this analysis leads to a characteristic mixing distance of 58 mm and to a corresponding mixing time of 9.3 s for Re = 562. For Re = 1000, L mix = 38 mm and t mix = 3.5 s are found. These are the limiting (slowest) values, obtained in the. In the this criterion leads to a slightly faster mixing process, which is not obvious from a visual, qualitative analysis of the images (see fig.3). This quantitative analysis shows that the mixing is roughly three times faster when doubling the Reynolds number. Re = 562 L mix 58 mm L mix 47 mm t mix 9,3 s t mix 7,6 s Re = 1000 L mix 38 mm L mix 31 mm t mix 3,5 s t mix 2,8 s Figure 5. Segregation index calculated from PLIF concentration fields at Reynolds number 562 (top) and 1000 (bottom) for horizontal and s. Resulting characteristic mixing length and mixing time for Re = 562 and Re =

8 Conclusions and present work Thanks to such simultaneous PIV/PLIF measurements it is possible to characterize quantitatively and in a non-intrusive manner the flow and mixing conditions behind static mixers, in particular to determine characteristic flow frequencies, correlations between velocity and concentration fields and to quantify mixing efficiency. In the near future similar simultaneous PIV and PLIF measurements will be realized for up to four consecutive mixer segments, each of them turned by π/2 compared to the previous one. At present, mixing chemically reacting species in a liquid-liquid system is being characterized experimentally, in order to quantify simultaneously micro-mixing and macro-mixing. For that purpose, a preliminary study has demonstrated that fluorescein disodium salt (Uranine) can be used. This fluorescence dye changes its fluorescence emission depending on the local ph-value, which can be used to track micro-mixing. Figure 6 shows the fluorescence emission I as a function of the ph-value for a range of the ph between 3.5 and 8. 1,0 relativ intensity [counts] = f(ph-value) 0,9 0,8 0,7 I / I max [-] 0,6 0,5 0,4 0,3 0,2 0,1 0,0 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 ph-value [-] Figure 6. Fluorescence emission of fluorescein disodium salt (Uranine) as a function of the ph-value. In this study hydrochloride acid (HCl) mixed with fluorescein disodium salt is injected into the main fluid, which is an alkaline fluorescein disodium salt solution. The resulting acid-base reaction changes the local ph-value and as a consequence the fluorescence properties of the fluorescein disodium salt. Using equal concentrations of fluorescein disodium salt in both liquids, this local ph modification can be quantified by PLIF and is a direct marker of the chemical reaction. PIV is again employed simultaneously to analyze the velocity field. All these experimental measurements will be made freely available to the scientific community through a data-base accessible via Internet, which is already partly available under

9 Acknowledgments The authors would like to acknowledge the financial support of the German Research Foundation (DFG) through the Priority Programme Analyse, Modellbildung und Berechnungen von Strömungsmischern mit und ohne chemische Reaktion (SPP1141). Interesting discussions with H. Nobach (Max Planck Institute for Dynamics und Self-Organization, Goettingen, Germany) concerning the frequency analysis of non-equidistant time-signals are gratefully acknowledged. References Danckwerths PV (1952) The definition and measurement of some characteristics of mixtures. Appl Sci Res A3: Leschka S, Thévenin D, Zähringer K (2006) Fluid velocity measurements around a static mixer usng Laser-Doppler Anemometry and Particle Image Velocimetry. Proceedings of the Conference on Modelling Fluid Flow (Eds Lajos T, Vad J) Vol. 1, pp , Budapest, ISBN Law AWK, Wang H (2000) Measurement of mixing process with combined digital particle image velocimetry and planar laser induced fluorescence. Exp Therm Fluid Sci 22: Leschka S, Thévenin D, Zähringer K (2006) Flow and mixing characterization of a static mixer using Laser-Doppler Anemometry and simultaneous Particle-Image Velocimetry/Planar Laser- Induced Fluorescence. NAMF Mixing XXI Conference, Park City, UT, 2007 Pahl MH, Muschelknautz E (1982) Static mixers and their applications. Int Chem Eng 22: Press W, Teukolsky S, Vetterling W, Flannery B (1995) Numerical Recipes in FORTRAN. Cambridge University Press, ISBN X Pust O, Strand T, Mathys P, Rütti A (2006) Quantification of Laminar Mixing Performance using Laser-Induced Fluorescence. 13th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon 2006 Wadley R, Dawson MK (2005) LIF measurements of blending in static mixers in the turbulent and transitional flow regimes. Chem Eng Sci