Ind. Eng. Chem. Res. 2001, 40, 3829-3834
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Flow of Viscous Shear-Thinning Fluids Behind Cooling Coil Banks in Large Reactors William J. Kelly* and Sundip Patel Department of Chemical Engineering, Villanova University, 800 Lancaster Avenue, Villanova, Pennsylvania 19085
Through the use of a laminar flow loop, an ultrasound pulsed doppler device was found to accurately ((5%) measure the velocity of a viscous, opaque fluid (Xanthan Gum solution), using the entrained air (moving with the liquid) as energy reflectors. This technique was then utilized to measure the axial velocity of Xanthan Gum solutions behind cooling coil banks in two large (300 and 20 000 gal) fermentors, agitated by multiple down-pumping A315 impellers. The results indicate that, at both scales, the fluid in the annular region behind the cooling coil banks becomes completely stagnant at moderate to low agitation power (3.7 HP/1000 gal) when air is not sparged into the tank. Stagnant flow was observed at all airflow rates g0.1 vvm. A computational fluid dynamics (Fluent) model predicted reasonably well the actual liquid flow rate in the annular region behind the coil bank(s) of both tanks for the cases when air was not sparged. The results from an experimental design, using this Fluent model for the 20 000 gal tank, indicate that the axial velocity in the annulus is linearly related to the impeller Reynolds number (500-2000), D/T (0.36-0.48) and the cooling coil bank location relative to the tank wall (B/T: 0.06-0.09) and the tank bottom (Ob/D: 0.45-0.90). 1. Introduction Large reactors can have severe mixing problems. In large fermentors, the combination of large internal structures such as banks of cooling coils together with viscous broth can result in regions inside the vessel being poorly mixed.1,2 During a fermentation, bulk mixing problems expose the fermenting organisms to a heterogeneous environment.3 Such an environment can result in regions of decreased metabolic rate and/or decreased productivity and can also stress the organisms. The yield of any subsequent enzymolysis steps in that same fermentor could also be reduced, as a result of little to no conversion in the stagnant regions of the vessel. Recently, many large fermentors have been retrofitted with multiple hydrofoil impellers, such as Lightnin A315 impellers, because several investigators have reported improved mixing and mass-transfer rates with these impellers.4 The flow patterns emanating from hydrofoil impellers can give rise to slow flow or fluid stagnation near the tank perimeter if the vessel is equipped with bank(s) of helical cooling coils. The closer these coil banks are to the outer wall and the more viscous the fluid, the slower the axial flow up the annular region behind the bank(s) of cooling coils. For a typical large reactor with helical cooling coils, the region between the cooling coil bank and the vessel wall can comprise 2035% of the reactor volume. Hence, the potential exists for a significant reduction in reactor productivity if adequate flow is not maintained in the annular region behind the cooling coil bank(s). Several investigators have measured the profiles of mean velocity and velocity fluctuations in stirred tanks. The most commonly used method of measuring the velocity distribution within a tank is laser Doppler
velocimetry (LDV). The results from the LDV studies have been useful in quantifying the overall threedimensional flow,5 the impeller pumping,6 and the local turbulence and energy dissipation and the local shear rates7,8 inside stirred tanks. The LDV measurement, however, is restricted to transparent fluids with low concentrations of gas bubbles, and most fermentation broths are opaque, highly aerated, and viscous. Other measuring techniques are also not well suited to measure the velocity of such a medium in a stirred tank. For example, hot film anemometry has been used to measure flow in a reactor;9 however, these probes can be quite delicate and may not be durable enough for extensive testing in a mixing tank. Lubbert10 developed a 3D ultrasound velocimeter that effectively measured the velocity patterns of bubbles dispersed within aerated stirred tanks. He noted that, in viscous fermentations, the velocity of the bubbles seemed to be indicative of the velocity of the liquid that carried them. Ultrasound can be transmitted through opaque liquids and can use air bubbles and/or solids particles as energy scatterers (reflectors). Furthermore, ultrasound technology is relatively inexpensive (compared to LDV), and the probes have the potential to be sterilized for use in biological applications. Consequently, ultrasound Doppler velocimetry was the method chosen to measure viscous liquid velocities in two large reactors as part of this research. Within the last 10-12 years, some researchers have started to use computational fluid dynamic (CFD) models of mixing tanks to estimate the spatial (and most recently temporal) variation of velocity, shear rate, and energy dissipation rate versus operating conditions and equipment configurations.11,6 In each cell of the numerical grid, the equations of motion (conservation of mass and momentum) are solved by either a finite difference or a finite volume approach. Until recently, this approach had been coupled with the experimental ap-
* To whom correspondence should be addressed. Tel.: (610) 519-4947. Fax: (610) 519-7354. E-mail: william.j.kelly@ villanova.edu. 10.1021/ie000918z CCC: $20.00 © 2001 American Chemical Society Published on Web 07/25/2001
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proach because of the difficulty of modeling the rotating impeller with respect to the stationary baffles on the perimeter of the tank. In the last 3-4 years, however, two numerical approaches12 have been developed, both which allow for the generation of flow in mixing tanks by the rotation of an impeller, the geometry of which is imported into the CFD model. In the first method, commonly referred to as “sliding mesh”, two computational grids are employed: one moving with the impeller and the other fixed to the tank. The moving grid is allowed to slide relative to the stationary grid. The second approach, referred to commonly as “MRF” (or multiple reference frame), requires much less computational time for simulations to converge because the steady-state form of the governing transport equations are solved. These equations are solved in two domains, which are fixed to their respective frames of reference; the outer reference frame is stationary and the inner reference frame rotates with the impeller. The overall configuration and geometry of agitated fermentors studied in this research (i.e., multiple downpumping hydrofoil impellers and helical cooling coil banks) is typical of that used in industry to produce antibiotics and polymers such as Xanthan Gum. The primary goal of this research was to determine what conditions promote poor flow behind the helical cooling coil banks in large tanks so that design engineers can minimize this problem through improvements in agitator and cooling coil design. Another goal of the research was to determine how accurate a three-dimensional CFD model, utilizing a multiple reference frame (MRF) approach, was for predicting flow of a viscous fluid behind the cooling coil banks. 2. Experimental and Methods 2.1. The Ultrasound System. An ultrasound pulsed Doppler velocimeter (UPDV) was designed and used for measuring the flow of viscous solutions in large mixing tanks. For enhanced spatial resolution, and the capability of measuring low velocities, a 2-MHz transmission frequency was chosen with a pulse repetition frequency (PRF) of 20.8 kHz (at 4 cycles/pulse). The probes consisted of a piezoelectric crystal (transducer), ≈5-mm o.d., attached with epoxy to the end of a stainless-steel mounting piece (5-mm o.d. × 2.5-cm long). Tone bursts were amplified to 20 V peak-to-peak and applied via coaxial cable to the ultrasonic transducer where they were converted to sound pulses. The sound energy reflected off the small air bubbles entrained in the viscous fluid and was received back by the same transducer. The return signal was digitized (30 kHz), and real-time fast Fourier transform processing of the signals was performed on a personal computer. Ultimately, a power spectrum was generated, and the mode frequency shift was used to calculate the velocity of the air bubbles (assumed to be moving at the same velocity as the liquid) from the Doppler equation. 2.2. The Laminar Flow Loop. To determine the accuracy of the pulsed Doppler ultrasound system for measuring the velocity of a viscous Xanthan Gum solution (2.5% Xanvis), using entrained air bubbles as energy reflectors, a laminar flow loop was set up. The flow loop consisted primarily of a 40-gal recirculation tank, a positive displacement pump, and interconnecting stainless-steel pipe. The range of flow rates for the experiments was 2.5-40 gpm (centerline velocity: 0.2-3 m/s). The volumetric flow rate was measured with a
Figure 1. 2D depiction of the geometry (configuration) of a 20 000-gal fermentor.
Fisher-Porter magnetic flowmeter that was calibrated between 0 and 50 gpm. The solution was maintained at 20-30 °C during the experiment through the use of an in-line heat exchanger. 2.3. The 300- and 20 000-gal Tanks. The 300-gal tank (T ) 36 in., H/T ) 1.8) contained three downpumping 18-in. diameter A315 impellers. Curved sections of sheet metal were inserted between each of the baffles to create a “curved-bottom” effect in the tank. These sections extended exactly 6 in. up from the base of the tank and 6 in. into the tank from the outer wall. The annular space (4.5 in.) near the perimeter of the tank was created by inserting a sheet-metal draft tube. This draft tube was used to simulate a helical cooling coil bank. Four baffles (90° apart) connected the draft tube to the tank wall. A maximum rpm for the study was set at 275 rpm, corresponding to a nonaearted power draw of ≈5.5 HP (15 HP/1000 gal). A single 0.5in. PVC pipe was positioned to direct air straight up toward the bottom of the bottom impeller during aeration studies. The configuration of the 20 000-gal fermentor is presented in Figure 1. The fermentor (T ) 12 ft, H/T ) 2) contained three down-pumping, 65 in. in diameter, A315 impellers. The bottom of the fermentor was “domeshaped”. An annular space of 12 in. existed between the helical cooling coil bank and the fermentor wall. Four 12-in.-wide baffles, spaced 90° apart in the annular space, helped to secure the cooling coil banks to the fermentor wall. As shown in Figure 1, there are actually three separate coil bank sections stacked vertically in the fermentor. A maximum rpm for the study was set at 100 rpm (nonaerated conditions) to be consistent with the maximum power per unit volume employed during the measurements in the 300-gal tank. An air sparger was positioned to direct air straight up toward the bottom of the bottom impeller. 2.4. Xanthan Gum Solutions. For the experiments in the laminar flow loop and the 300-gal tank, a 2.5% Xanvis (Kelco Inc.) in DI water solution was used. The rheology of the Xanthan solutions was characterized with a power law model, and measurements with a Brookfield concentric cylinder viscometer determined that K ) 25.5 Pa sn and n ) 0.19. For the experiments in the 20 000-gal fermentor, Xanthan Gum fermentation broth was used. Measurements with a cone and plate
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Figure 3. Centerline velocity in a pipe: ultrasound measurement versus theory (error bars represent (5%).
with the wall shear stress (τw) being defined as
Figure 2. Numerical grid for a 20 000-gal fermentor.
viscometer indicated that the rheology of this fluid could be modeled as a power law fluid with K ) 25.0 Pa sn and n ) 0.2 over a wide range of shear rates (0.01-750 s-1). 2.5. CFD Modeling. Fluent is a computational fluid dynamics software package that uses a control volume technique to discretize the conservation equations.13 Fluent was used in this research to solve the conservation of mass and momentum and generate steady-state flow fields through 3D depictions of a 300-gal and a 20 000-gal tank. The geometry of the A315 impellers was imported into the Fluent models, and a multireference frame solution approach was utilized. Geometric symmetry was employed as one-quarter of the tank geometry was modeled. The elasticity of the fermentation broth and turbulence were not considered in this laminar flow model. The fluid rheology was modeled as a viscous power law fluid (K ) 25 Pa sn, n ) 0.2). The numerical grids consisted of 140 000 cells for the 300-gal tank and 180 000 cells for the 20 000 gal tank. The grid was structured, with lines concentrated near the cooling coil and tank walls (Figure 2). Grid independence was verified by demonstrating that additional grid lines near these walls did not change the calculated average axial velocity behind the cooling coil banks by more than 5%. The solutions were considered converged when the normalized residuals were below 1 × 10-4, and the average axial velocity behind the cooling coils changed by
