Using computational fluid dynamics modeling to study the mixing of pseudoplastic fluids with a Scaba 6SRGT impeller

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Abstract

The 3D flow field generated by a Scaba 6SRGT impeller in the agitation of xanthan gum, a pseudoplastic fluid with yield stress, was simulated using the commercial CFD package. The flow was modeled as laminar and a multiple reference frame (MRF) approach was used to solve the discretized equations of motion. The velocity profiles predicted by the simulation agreed well with those measured using ultrasonic Doppler velocimetry, a non-invasive fluid flow measurement technique for opaque systems. Using computed velocity profiles across the impeller, the effect of fluid rheology on the impeller flow number was investigated. The validated CFD model provided useful information regarding the formation of cavern around the impeller in the mixing of yield stress fluids and the size of cavern predicted by the CFD model was in good agreement with that calculated using Elson's model.

Introduction

Mixing is among the most common processes in chemical, biochemical, pharmaceutical, polymer, mineral, food, and wastewater treatment industries [1]. Understanding mixing mechanisms, which is crucial to industrial scale-up [2], still remains difficult especially in the case of non-Newtonian fluids. Shear-thinning fluids with yield stress are an important class of non-Newtonian fluids, which are commonly encountered in industrial mixing operations. Many slurries of fine particles, certain polymer and biopolymer solutions, wastewater sludge, pulp suspension, and food substances like margarine and ketchup exhibit a yield stress [3]. Mixing of such fluids result in the formation of a well mixed region (the so called cavern) around the impeller and essentially stagnant and/or slow moving fluids elsewhere in the vessel. The prediction of the cavern size is important in the mixing of shear-thinning fluids with yield stress, so one can be sure that the whole fluid is in motion (good mixing) and there is no undesirable poor mixing region in the tank. For instance, when the stagnant zones exist, poor heat and mass transfer rates, high temperature gradients, and if aerated, the possibility of oxygen starvation during fermentation will occur [4].Wichterle and Wein [5] were the first to study cavern in extremely shear thinning suspensions of finely divided particulate solids, coining the term cavern to describe the well-mixed region near the impeller. Several studies have been conducted using various impellers to evaluate cavern size as a function of the power drawn by yield stress fluids including those by Elson [6] for marine propeller, pitched blade turbine, disk turbine, and a two bladed paddle; Galindo and Nienow [7], [8] for Lightnin A315 and Scaba 6SRGT impeller; Underwood [9] for the axial flow Prochem Maxflo impeller; Amanullah et al. [10] for axial flow SCABA 3SHPI impeller; and Serrando-Carreon and Galindo [11] for four different impellers (Rushton turbine, Chemineer He-3, CD-6 and Scaba 6SRGT) in individual and dual arrangements.

The mathematical models have also been developed in order to predict the cavern volume as a function of the power input. Solomon et al. [4] developed a mathematical model for a spherical cavern centered upon an impeller mixing a fluid with a yield stress based on the assumption that the predominant motion of the fluid within the cavern is tangential. Using X-ray flow visualization technique, Elson [3] and Elson et al. [12] developed a cylindrical model, which predicts the behaviour of the cavern with diameter less than the tank diameter. This model indicates that the dimensionless cavern diameter is proportional to the product of the power number and the yield stress Reynolds number. Although both models (spherical and cylindrical) predicted the cavern diameter well, Amanullah et al. [13] reported that the cylindrical model is a better representation of the cavern shape. Amanullah et al. [10] found that once the cavern reached the wall, impeller type had little influence on the vertical expansion of the fluid. A torus-shaped cavern is another approximation as visualized using dye tracers in transparent fluids [7]. Amunallah et al. [13] developed a mathematical model for the torus-shaped cavern. This model considers the total momentum imparted by the impeller as the sum of both tangential and axial shear components, with these forces transported to the cavern boundary by the pumping action of the impeller. Wilkens et al. [14] proposed an experimental approach to determine the cavern dimensions (diameter and height) for an opaque Bingham fluid by injecting glitter, freezing the fluid and dissecting the frozen solid. They also developed an elliptical torus model without accounting axial force to predict the cavern diameter and height with the cavern boundary defined by the yield stress of the fluid. Besides all works done to determine the cavern size, some researchers focused on the nature of the flow in the cavern region such as Amanullah et al. [13], Moore et al. [15], Mavros et al. [16], and Jaworski and Nienow [17], [18].

The general practice for the evaluation of stirred vessels has been done over the years through the experimental investigation for a number of different impellers, vessel geometries, and fluid rheology. Such an approach is usually costly and sometimes is not an easy task. With computational fluid dynamics (CFD), we can examine various parameters contributing in the process in shorter time and with less expense, a task otherwise difficult in experimental techniques. During the last two decades, CFD has become an important tool for understanding the flow phenomena [19], developing of new processes, and optimizing the existing processes [20]. The capability of CFD tools to forecast the mixing behaviour in terms of mixing time, power consumption, flow pattern and velocity profiles is considered as a successful achievement of these methods and acceptable results have been obtained. Kelly and Humphrey [21] developed a CFD model for a large fermentor equipped with hydrofoil impellers and investigated the effect of the impeller speed and the fluid rheology on the flow near the perimeter of the fermentor. Murthy and Jayanti [22] studied the mixing of power-law fluids with an anchor impeller using CFD modeling. They verified the proportionality between the shear rate near the impeller and the rotational speed. They also showed that this proportionality constant is broadly independent of the geometric and rheological properties of the mixing system. Iranshahi et al. [23] investigated the flow and mixing in a vessel equipped with a Paravisc impeller in the laminar regime. CFD techniques were applied to study the evolution of mixing patterns and predict the intensity of segregation, mixing time, mixing efficiency and pumping capability, and the results were compared with those obtained for conventional viscous mixing impellers, i.e., an anchor and double helical ribbon. Arratia et al. [24] presented an experimental and numerical investigation of mixing in shear-thinning fluids with yield stress in stirred tanks. The numerical simulations captured the essential features of the flow such as cavern formation and cavern–cavern segregation for multiple impeller system. They found that the mixing of shear-thinning yield stress fluids is controlled by chaotic flow: lobe formation, stretching, folding, and self-similar mixing patterns. To develop a model for aerated fermenters, Moilanen et al. [25] combined gas–liquid mass transfer, bio-reaction kinetics, and fluid rheology with computational fluid dynamics. They reported that their CFD model can be used for the troubleshooting, design, and scale-up of aerobic fermenters. Using commercial CFD software (Fluent), Ford et al. [26] simulated pulp mixing in a rectangular chest equipped by a Maxflo impeller. Their CFD model was not able to capture the dynamics of the mixing chest quite well in flow situations containing significant bypassing. This was attributed to the rheology of the suspension, which was not fully described by a modified Bingham model. A CFD model of a cylindrical pulp mixing chest equipped with a side-entering axial-flow A-310 impeller was developed by Saeed et al. [27]. They studied the effect of operating conditions and design parameters on the cavern formation, mixing time, and velocity profiles generated by the impeller. Using CFD and ultrasonic Doppler velocimetry, Ihejirika and Ein-Mozaffari [28] studied the effect of the impeller speed, power, yield stress, and impeller pumping direction on the mixing performance of a helical ribbon impeller agitated in a non-Newtonian fluid. Their numerical results showed good agreement with experimental results and correlations developed by other researchers.

A thorough search of the literature suggests that little space has been devoted to the numerical simulation of the mixing of yield stress fluids. Therefore, the objective of the present paper is to employ advanced computational fluid dynamics (CFD) and ultrasonic Doppler velocimetry to study the mixing of pseudoplastic fluids possessing yield stress with a Scaba 6SRGT Impeller. Developed originally for velocity measurements in medical applications (blood flows), ultrasonic Doppler velocimetry (UDV) has been adopted for use in fluid mechanics and fluid flow measurements. UDV utilizes a pulsed ultrasonic echography together with the detection of the instantaneous frequency of the detected echo which gives the spatial information and estimates of the Doppler shift frequency, respectively. It is from the Doppler shift frequency that the magnitude and direction of the velocity vector is obtained [29]. This method has the following advantages [30], [31] over the conventional techniques such as laser Doppler anemometry (LDA): (1) an efficient flow mapping process, (2) applicability to opaque liquids, and (3) a record of the spatiotemporal velocity field (i.e., a velocity field as a function of space and time). UDV method is a non-invasive method of measuring velocity profiles [32] and can therefore be used to monitor the flow in stirred tanks or pipes without obstructing it. Its ability to work in opaque fluids makes it applicable for studies of all liquids, emulsions, and slurries and makes this technique very attractive from an industrial perspective [33], [34].

Section snippets

Experimental setup and procedure

The schematic experimental setup is shown in Fig. 1. The mixing vessel was a flat-bottomed cylindrical tank with a diameter (T) of 0.40 m fitted with four equally spaced baffles at a 90° interval against the tank wall. The width of each baffle was T/10 = 0.04 m. The fluid height in the tank was equal to the tank diameter providing a total volume around 0.05 m3. A Scaba 6SRGT impeller with a diameter (D) of 0.18 m was centrally positioned at an off-bottomed clearance (c) of 0.17 m. Further details

Numerical

In order to study the cavern formation, Fluent V6.2 (Fluent Inc.) was used to simulate the steady-state 3D flow field generated by a Scaba 6SRGT impeller in the laminar regime by solving the conservation of mass and momentum equations. A pre-processor (Gambit 2.0, Fluent Inc.) was used to discretize the flow domain with a tetrahedral mesh (Fig. 2). In general, the density of cells in a computational grid needs to be fine enough to capture the flow details, but not so fine, since problems

Results and discussions

To validate the model, CFD results for the power number and velocity field were compared to experimental data. The power number of the Scaba impeller in xanthan gum solutions as a function of the Reynolds number is shown in Fig. 3. These results show good agreement between calculated power number and the experimentally determined values. The trend in the power number is similar to that reported by Galdino and Neinow [8] for the Scaba 6SRGT impeller. Theory and the experimental studies [8], [13]

Conclusions

Computational fluid dynamics simulations were performed to determine the velocity field within a cylindrical tank equipped with a Scaba 6SRGT impeller for laminar regime in the agitation of xanthan gum. The CFD results were validated using ultrasonic Doppler velocimetry (UDV) experiments. UDV's ability to work with opaque fluids makes it a suitable tool for measuring flow velocity in the mixing of xanthan gum. The CFD calculations picked up the features of the flow field, and the computed power

Acknowledgement

The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

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