Ind. Eng. Chem. Res. 2004, 43, 4149-4158
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Mixing in Unbaffled High-Throughput Experimentation Reactors Jonathan F. Hall,† Mostafa Barigou,† Mark J. H. Simmons,*,† and E. Hugh Stitt‡ Department of Chemical Engineering, The University of Birmingham, Edgbaston, Birmingham, B15 2TT U.K., and Johnson Matthey Catalysts, P.O. Box 1, Belasis Avenue, Billingham, Cleveland, TS23 1LB U.K.
With the increasing implementation of high-throughput experimentation techniques within research laboratories throughout the chemicals industries, it is important that the flow regimes in such unbaffled vessels be fully characterized and the implications on mixing performance be understood. Particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques are used in this work to study the mixing and hydrodynamic behavior of low-viscosity fluids in small stirred vessels with diameters 60 and 88 mm. Baffled and unbaffled vessels are considered, and the difference in efficiency is quantified at a constant power input per unit volume. Positioning the impeller into an eccentric configuration is adopted as a means toward improving mixing efficiency in unbaffled vessels. Results show that the eccentric configuration provides equally efficient mixing as the traditional baffled vessel in terms of mixing time and turbulent kinetic energy distribution. PIV and PLIF measurements show that the distribution of turbulent kinetic energy is more evenly spread in smaller vessels, leading to the conclusion that such vessels are better mixers. 1. Introduction For applications requiring the mixing of one or more fluids plus any additional phases, the stirred vessel remains the primary choice throughout industry. This time-honored method has been the subject of extensive research in the past, and the deceptively complex nature of the fluid behavior in such vessels ensures that much current research is also devoted to the subject. Previous research has generally focused on the ability to scaleup processes from the laboratory scale, where vessel volumes are on the order of ∼10-3 m3, to the industrial scale, where vessel volumes can range over several orders of magnitude from ∼1 to ∼103 m3. High-throughput experimentation (HTE) is a revolutionary new procedure that allows for rapid screening of new compounds using massive parallel arrays of robotized batch stirred-tank reactors. To obtain information on the reaction kinetics, as might be needed for the development of novel catalysts, understanding is needed of the mixing characteristics of these HTE vessels, where typical volumes are on the order of 10-510-4 m3. For equipment at this scale, there is a dearth of published information available in the literature. Although many empirical rules for scale-up exist,1 it is not clear a priori whether the same rules remain valid for scale-down, and hence, new work is needed at these smaller scales to determine whether the classical approaches to the problem are suitable when applied to the most modern mixer designs. Determination of the macromixing effects involves characterization of the bulk flow structures and largerscale eddies such as impeller discharge loops2,3 and mixing times. Previous work4,5 has characterized such flow structures using the particle image velocimetry (PIV) technique to obtain measurements of the velocity * To whom correspondence should be addressed. Tel.: +44 (0)121 4145371. Fax: +44 (0)121 4145324. E-mail:
[email protected]. † The University of Birmingham. ‡ Johnson Matthey Catalysts.
field in stirred vessels with volumes on the order of (515) × 10-3 m3, but no information is available at the HTE scale. However, this technique is ideally suited to bulk flow characterization in HTE vessels, as the whole flow field can be evaluated instantaneously at a spatial resolution that allows accurate determination of the bulk flow structure. Unlike the case with point-by-point techniques such as laser Doppler velocimetry (LDV), information on the turbulence within the flow can be determined from the PIV data without recourse to computationally expensive data-reconstruction procedures. Measurement of mixing times in stirred vessels can be accomplished by a number of different techniques, e.g., conductivity probes to measure concentration of a passive scalar6,7 or methods based on the reaction of two or more chemical species with differing rates of reaction.6,8,9 Planar laser-induced fluorescence (PLIF) is a whole-field flow visualization technique where the objective is to determine the localized concentration of a passive scalar at each point rather than the local fluid velocity. This technique has been employed in previous mixing studies involving stirred vessels10-14 although mainly with respect to continuously or semibatchoperated reactors with premixed tracer feeds. In this work, the PLIF technique is used to determine mixing times for batch-operated reactors at the HTE scale. The application of conventional scaling rules to HTE reactors is complicated by the fact that these vessels are used without the presence of baffles. Use of unbaffled vessels is essential because of the automation of the unit responsible for loading, sampling, discharging, and cleaning the vessel; such tasks are easier for a robot to perform on unbaffled vessels because material can be trapped around baffle plates, especially when viscous materials are involved. Research at the laboratory and industrial scales has generally focused on energy-efficient baffled vessels; the presence of baffles prevents vortex formation at the free surface and breaks the solid-body rotation of the fluid within the vessel. The poor mixing characteristics of unbaffled vessels are
10.1021/ie049872q CCC: $27.50 © 2004 American Chemical Society Published on Web 06/09/2004
4150 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 Table 1. Experimental Conditions T (mm)
D (mm)
D/T
W/D
H/T
Cimp/H
Cw/T
HTE
60
35
0.58
0.18
1
0.33
laboratory
88
48
0.55
0.16
1
0.33
0.5 (U, B) 0.7 (E) 0.5 (U) 0.7 (E)
scale
Figure 1. Vessel dimensions showing baffles (where fitted) plus experimental layout of impeller positions. Grayed lines denote offcenter position.
exacerbated at the HTE scale by relatively low Reynolds numbers (because of the small vessel size and also possibly the use of high-viscosity liquids), which reduce macro- and micromixing performance. Given that conventional unbaffled vessels with the agitator positioned at the vessel centerline are generally unsuitable for effective mixing, an alternative configuration must be sought. To this end, the method chosen for this work was the repositioning of the impeller away from the vessel centerline axis into an off-center or eccentric configuration to reduce the level of solid-body rotation observed and improve the mixing performance. This paper presents an investigation of the flow phenomena observed in vessels at the HTE and laboratory scales using both PIV and PLIF techniques. Determination of the effects of scale-down are made for a number of geometric configurations, namely, conventional baffled, unbaffled centerline and unbaffled eccentric agitation, hereafter referred to as configurations B, U, and E, respectively. Two vessels of 60- and 88mm diameter are examined. The 60-mm-diameter vessel (working volume ) 1.7 × 10-3 m-3) is representative of a large HTE vessel, such as those employed in industry for three- or four-phase slurry catalyst screening. The larger vessel of 88-mm diameter (working volume ) 5 × 10-3 m-3) is comparable to the smallest categories of laboratory-scale vessels that have been used in previous mixing studies.8,15,16 2. Experimental Section 2.1. Vessels and Impellers. A schematic of the two geometrically similar vessels used is given in Figure 1. The experimental and geometric parameters for both
P/V (W‚m-3) 168 168
Re 11 330 (U) 8237 (B, E) 19 280 (U) 13 500 (E)
the T ) 60-mm vessel (T60) and the T ) 88-mm vessel (T88) are listed in Table 1. Both vessels were used in the B, U, and E configurations. No wall-baffle gap was present in the baffled vessels. The vessels were constructed of optically perfect borosilicate glass, and to minimize refractive effects distorting the images produced from the PIV, the vessels were enclosed within a square glass box filled with the fluid under investigation, which in this case was distilled water. Experiments for both vessels were carried out at constant power input per unit volume, P/V, of 168 W‚m-3, with the impeller speed controlled via an integrated motor unit (Eurostar PowerVisc, IKA, Bremen, Germany). The impellers used were up-pumping six-bladed pitched-blade turbines (PBTs) that were made of Duraform polyamide powder via a selective laser sintering (SLS) process.17 The angle of the blades was 45° with respect to the impeller axis. The impellers were painted with matte black paint to prevent reflection of incident laser radiation and also to seal the impeller surface. Up-pumping PBTs were chosen to provide versatility with respect to process application; specifically, such turbines exhibit desirable characteristics regarding repression of surface vortex and gas hold-up. 2.2. PIV Experiments. Two mini-Nd:YAG lasers (New Wave Research, Fremont, CA), a synchronizer (TSI LASERPULSE 610030, TSI Inc., Shoreview, MN), and frame-straddling digital 1024 × 1024 pixel chargecoupled device (CCD) cameras (TSI PIVCAM 10-30; TSI Inc., Shoreview, MN) form the basis of the flow diagnostics equipment. Flow seeding is achieved using fluorescent particles of 3-µm nominal diameter (Duke Scientific Corp., Palo Alto, CA): the seeding concentration equals 0.05% v/v, resulting in a particle density of 3.94 × 105 particles per milliliter. A high-pass wavelength filter is fitted to the camera to separate emitted fluorescent light at 602 nm from incident laser radiation at 532 nm (Stokes shift of 70 nm). This feature helps to reduce errors generated from scattered and reflected laser light and minimizes the risk of damage to the CCD array from stray laser beams. The frame-straddling technique used in this work allows for a theoretical minimum laser pulse separation as low as 0.3 µs. In practice, pulse separation must be optimized to ensure that the maximum possible number of particle image pairs can be captured. A reliable method of achieving this optimum is to define the maximum desired particle displacement between pulses as one-quarter of the interrogation volume diameter, LIV. The maximum separation, dTmax, is then given as a function of the magnification of the image and the maximum velocity within the system
dTmax )
0.25LIVM Utip
(1)
where M is the image magnification in micrometers per pixel and Utip is the impeller tip speed in meters per second. All equipment was linked to and controlled by a Dell Precision 620 workstation running INSIGHT 5.1
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(TSI Inc.) software that also performed the preprocessing and validation of the velocity vector fields. The peak search and cross-correlation engines were based on Gaussian and FFT algorithms, respectively.18,19 Particle image definition was further enhanced by application of zero padding to the raw image captures, i.e., subtracting the interrogation-area- (IA-) averaged pixel intensity from each pixel within the IA and padding with zero-intensity pixels, thus improving the particlebackground contrast and reducing noise. Automatic vector validation processing (removal of individual vectors from the global flowmap upon failure of certain criteria, e.g., velocity magnitude greater than 3 times the standard deviation of all neighboring vectors) was kept to a minimum so as to truly capture any peculiarities of the flow, particularly where areas containing significant velocity gradients were concerned. To satisfy this criterion, only vectors of magnitude greater than Utip were removed from the velocity field and any holes, thus created were filled by interpolated vectors of magnitude and direction equal to the mean magnitude and direction of the neighborhood vectors (where the neighborhood is defined as the 5 × 5 array of IAs around the blanked vector). 2.2.1. Time-Averaged Whole-Field Vector Maps. The initial goal of this study was to determine timeaveraged whole-field velocity vector maps for the vessels under investigation. Time-averaged values of the velocity fields were obtained by taking a succession of instantaneous captures. Different schemes were employed to study the centerline (baffled and unbaffled) and the off-center configurations. For centerline configurations, data were evaluated on the basis of a grid covering one-half of the vessel: the light sheet was aligned with the vertical z axis, and the grid covered points 0 e r/R e 1, as it can be safely assumed that the flow will be symmetric about the vessel centerline in the r-z plane. With this convention, radial velocity components take positive values in the direction away from the impeller and vice versa. The asymmetric nature of the off-center configuration means that PIV measurements must be made on both sides of the impeller shaft, with one grid covering the points -0.45 e r/R e +1 and a smaller grid covering the points -1 e r/R e -0.45, all in the r-z plane. With interrogation volumes set at 16 × 16 pixels, between 3000 and 13 000 individual velocity vectors were obtained for each PIV image, depending on image magnification. The grid thus generated is of uniform distribution throughout the vessel; although recent work,20 has studied the use of multiblock grids to define separate spatial resolutions for the impeller region and the bulk fluid, the small size (
