(100f) Influence of the Rotating Domain Size in Simulations of a NORSTONE® Type High-Shear Impeller.

A CFD study of a baffled-stirred tank equipped with a High Shear Impeller was conducted in order to evaluate the effect of modifying the location of the surface separating the RRF and SRF regions on numerical values of local velocity profiles. Modelling of the rotation of the impeller-shaft array was grounded in the MRF approach. The study was conducted considering mixing operations in the laminar and turbulent flow regimes.

1. Introduction

In industrial processes, there are a variety of situations where it is necessary to break particle agglomerates and disperse them in liquids until a certain desired degree of homogeneity is attained [1]. In the pursuit of this end, special devices known as High Shear Impellers (HIS’s) such as the Norstone^® are regularly employed inside stirred-reactors (stirred-tanks) which are then set to spin at a required peripheral velocity.

Improvements in the design, capability and reliability of stirred-reactors may be expected from computational fluid dynamics (CFD) simulation techniques. With these techniques, the actual size of the equipment can be effectively dealt with, avoiding scale-up uncertainties [2]. A requirement for simulating these systems, is modeling the impeller motion, for this, various methods exists, among them, the most commonly employed are the Sliding-Mesh (SM), and the Multiple Reference Frame (MRF). SM is broadly recognized for its capability to yield fully predictive simulations [2], however its computational cost is very high; nonetheless, an alternative exists for concrete applications.

When impeller-baffle interactions are somehow weak (D/T≈0.5, D and T are the impeller and the tank inner diameter, respectively [3]), the MRF methodology can be employed. This methodology has an advantage over SM, for the reason that it conducts steady-state calculations, leading to substantial computational savings [4]. Some studies of stirred-tanks highlights that the location of the surface separating the RRF and SRF regions (MRF components) has to be positioned where flow variables do not change appreciably either through the azimuthal direction or with time, i.e., when an almost steady flow is established at this position [5]; however, no other study was found with a similar recommendation for stirred-systems equipped exclusively with the Norstone^® impeller. The present work is an attempt to address this issue.

2. Methodology

2.1 Experimental

Torque readings for the Norstone-attached stirred-tank system were collected from lab-scale experiments employing a Futek^® TRH300-FSH1980 acquisition system in order to validate the accuracy of the system’s digital replica simulating mixing operations considering 5 Re numbers representing Laminar and/or Turbulent conditions. The laboratory-assembly consisted of a jacketed stainless-steel dish-bottomed cylindrical tank with inner diameter T=132 mm, four distributed baffles of height H=110 mm, width J=13.2 mm, and 1mm thick, thus J/T=1/10. The baffle-tank wall separation was set at 5.72 mm distance. Ratios C/T and D/T, where D is the impeller’s diameter and C is the bottom off clearance measured from the impeller midplane, resulted in 0.3848. Height (Z) corresponding to the liquid interface remaining at rest was equal to T, thus, Z/T=1.

Rotation in the impeller-shaft array was induced by a user-controlled device (Dispermat^® AE01, 0.75 HP). In all experiments, the working fluid temperature was maintained at 23.0±0.5°C by using a thermo-regulated system. The Newtonian fluids considered (Table 1) consisted of two mixed solutions prepared from food grade glucose (45 °Bx) and distilled water at various mass glucose concentrations: 37.5% (fluid 1), 32.21% (fluid 2) and 0% (i.e., distilled water, Fluid 3), respectively. For fluids 1 and 2, viscosity values were gathered from measurements at 23°C using an Anton Paar^® MCR 502 rheometer with concentric cylinder geometry. Their densities were obtained employing a graduated cylinder and an analytical balance. In the case of the distilled water, the data was obtained from [6]. The setup for the equipment can be seen in Figure 1a, whereas the dimensions of the impeller can be consulted in the Figure 1c found in [1].

2.2 Numerical

The replica of the system exhibited in Fig.1 was built within Ansys DesignModeler® module. Implementing the MRF method resulted in both the SRF and RRF domains. Accounting for changes in the location of the separating-surface, the RRF region was then subdivided into seven volumes: the volume swept by the grooves (VSG), volume V1 being the region immediately surrounding VSG and the impeller, and from V2 up to V6, these volumes were successively defined enclosing the previous one, leading to the construction of the RRF domain as follows: RRF1=BSV+V1, RRF2=BSV+V1+V2, straight up to RRF6=BSV+V1+V2+V3+V4+V5+V6. V1 is peculiar in that its surfaces confines VSG and the impeller at a distance of W/3 in all directions (W is the impeller’s width). From V2 to V6 all the corresponding surfaces were located at a distance corresponding to W/4 from the previous one. V1 extension was chosen by trial and error to avoid the formation of non-hexahedral cells within (see Figure 1b).

An independence analysis resulted in the selection of a sufficiently dense mesh with 3050476 cells, obtained based on the refinement of the maximum velocity gradients computed at the highest Re number evaluated in this study (Re=42946). For Re=4.9, 29.4 and 115.9, the laminar model was used, whilst for Re=21473 and 42946, the standard κ-ε model was employed with the QUICK discretization scheme, standard wall functions, standard pressure-velocity scheme and the SIMPLEC algorithm. Non-slippery boundary conditions were applied to all solid surfaces. At the liquid surface, a zero-shear stress condition was specified. The shaft and the impeller were considered solid-moving walls with the same rotating velocity as the RRF, whereas the baffles, vessel walls, tank bottom and the SRF region, were considered static-solid. All steady-state simulations were executed employing Ansys Fluent© 17.1.

3. Results

In order to evaluate the influence of exerting changes in the RRF size over the velocity magnitude () profiles, the distribution of this parameter was studied over a straight line connecting directly the outer edge of the Norstone^® to the inner surface of the baffle (Figure 1c). Measurements of this magnitude were registered over 30 equally spaced points. The values extracted showed no discrepancies for the profiles computed for the case of laminar mixing conditions (not showed here), however in the case of turbulent conditions (Figure 1d), significant discrepancies were observed for extensions of the RRF region from RRF1 up to RRF4, however by declining all the previous at least in favor of RRF5 (corresponding to 1.367 impeller radius in the radial direction and 0.505 impeller radius above and below the impeller midplane) as the recommended extension for RRF, good agreement between both profiles can be obtained.

Velocity profiles computed for the laminar regime, demonstrated that no relevant discrepancies were detected on the numerical approximations when variations in the location of the separating surface were imposed. However, as the Re increases the extension of the RRF region begins to play a relevant role. The RRF-extension depends on the flow regime, i.e., as the Re increases, the location of the separating surface has to be placed further away from the impeller surfaces in order to enhance reliability of the numerical results.

4. References

[1] Martínez-de Jesús et al. (2017). Computational Fluid Dynamics Study of Flow Induced by a Grooved High-Shear Impeller in an Unbaffled Tank. Chemical Engineering & Technology.

[2] Montante, G. et al. (2001). Numerical simulations of the dependency of flow pattern on impeller clearance in stirred vessels. Chemical Engineering Science.

[3] Oshinowo, L. et al. (2000). Predicting the tangential velocity field in stirred tanks using the Multiple Reference Frames (MRF) model with validation by LDA measurements. In H. E. A. van den Akker & J. J. Derksen (Eds.), 10th European Conference on Mixing. Elsevier Science.

[4] Brucato et al. (1998). Numerical prediction of flow fields in baffled stirred vessels: A comparison of alternative modelling approaches. Chem. Eng. Sci.

[5] Sommerfeld, M., & Decker, S. (2004). State of the Art and Future Trends in CFD Simulation of Stirred Vessel Hydrodynamics. Chemical Engineering & Technology.

[6] Perry, R. H., & Green, D. W. (2008). Perry's chemical engineers' handbook. New York. McGraw-Hill