Elsevier

Chemical Engineering Science

Volume 66, Issue 6, 15 March 2011, Pages 1219-1231
Chemical Engineering Science

PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine stirred tanks

https://doi.org/10.1016/j.ces.2010.12.024Get rights and content

Abstract

The single-loop flow fields in Rushton turbine stirred tanks with clearance C=0.15T (T is tank diameter) were investigated by using particle image velocimetry (PIV) experiments and large eddy simulation (LES) methods. The velocity and turbulent kinetic energy (TKE) were carefully measured and resolved with high resolution camera. The regions with high TKE are affected by the movement of the trailing vortices generated behind the impeller blades. The effects of both geometrical configuration and Reynolds number were discussed. It is found that the Reynolds number has little effect on the mean flow for the configuration of impeller diameter D=T/3, C=0.15T. However, the single-loop flow pattern is changed into a double-loop one if D is increased from T/3 to T/2. The LES results were compared with the PIV experiments and the laser Doppler anemometry (LDA) data in the literature. The effect of the grid was validated, and the levels of local anisotropy of turbulence near the impeller discharge regions were investigated. Both the phase-averaged and phase-resolved LES results are in good agreement with the PIV experimental data, and are better than the predictions of the kε model. The agreement shows that the LES method can be used to simulate the complex flow fields in stirred tanks.

Introduction

Stirred tanks are widely used in the chemical process industry. Fundamental knowledge of the flow fields in stirred tanks, such as the velocity and turbulent kinetic energy (TKE) distributions, is urgently needed for optimizing engineering design as well as evaluating practical performance. Up to now, a large number of studies on the flow field in a single Rushton turbine stirred tank have been carried out (Yianneskis et al., 1987, Wu and Patterson, 1989, Stoots and Calabrese, 1995, Sharp and Adrian, 2001). However, these works are mainly focused on the traditional double-loop flow pattern. Montante et al. (1999) experimentally observed that as the off-bottom clearance of the Rushton turbine is reduced from T/3 to 0.15T, the flow pattern undergoes a transition from a double loop to a single loop. Low-clearance configurations are commonly used in the design of pump-mix mixers in the nuclear industry to satisfy both the pumping and mixing requirements (Srilatha et al., 2008), and the mixing efficiency has been evaluated and compared with the standard configuration (Ochieng et al., 2008, Ochieng and Onyango, 2008). Montante et al., 2001a, Montante et al., 2001b simulated the transition and the single-loop flow patterns using the standard kε, renormalization group kε, and Reynolds stress models in their subsequent works, but none of these turbulence models can give good quantitative predictions of velocity and TKE near the impeller region. They suggested that these flow patterns can be considered as benchmark to evaluate simulation approach and turbulence modeling.

Experimental investigation is the fundamental method to reveal the flow characteristics in stirred tanks. Mavros (2001) reviewed in detail the flow visualization techniques used in stirred tanks including Pitot tube, hot-wire anemometer, laser Doppler velocimetry (LDV), laser induced fluorescence (LIF), and particle image velocimetry (PIV). For the single-point measuring techniques, a coarse grid consisting of measurement points was insufficient to resolve the details of the vortex structures behind the impeller (Stoots and Calabrese, 1995). PIV techniques are now widely used in the measurement of stirred tanks, and it is convenient to obtain the full field flow characteristics in a specified region. Escudie and Line (2003) experimentally analyzed the hydrodynamics in a standard stirred tank using PIV measurements, and the trailing vortices behind the blades of a Rushton turbine were clearly resolved (Escudie et al., 2004). The small scale flow structures, such as the Reynolds stress and energy dissipation, were recently investigated by a few researchers (Sharp and Adrian, 2001, Baldi and Yianneskis, 2003). However, the hydrodynamics in a low-clearance stirred tank has not been resolved by PIV techniques until the present work.

As computers become much faster and more powerful, computational fluid dynamics (CFD) takes on an ever-increasing role in the design and analysis of stirred tanks. The Reynolds averaged Navier–Stokes (RANS) approaches can provide some useful mean flow characteristics and knowledge for engineering design and optimization, but they are not applicable to complex flows, such as the flow in a low-clearance stirred tank (Montante et al., 2001a, Montante et al., 2001b). Direct numerical simulation (DNS) has great potential for the simulation of complex turbulent flow fields; however, resolution of all the fine scales of a high Reynolds number flow requires enormous computing capability, which goes beyond the ability of today's fastest computer. The large eddy simulation (LES) approach, an intermediate method between RANS and DNS, was recently widely used in the simulation of stirred tanks, including the investigations of non-uniform grid (Lu et al., 2002), discretization methods (Eggels, 1996, Derksen and van den Akker, 1999, Revstedt et al., 1998, Yeoh et al., 2004, Yoon et al., 2003, Alcamo et al., 2005, Zhang et al., 2006), subgrid scale (SGS) models (Derksen, 2001, Bakker and Oshinowo, 2004, Hartmann et al., 2004), and the applications in multiphase systems (Derksen, 2003, Zamankhan et al., 2007, Guha et al., 2008, Zamankhan, 2010a, Zamankhan, 2010b). In our previous work on LES (Li and Gao, 2007), the single-loop hydrodynamic characteristics of a Rushton turbine stirred tank was investigated, and the results obtained by LES with a dynamic SGS model are in good agreement with the experimental data from the literature. However, the LES results need further verification since quantitative phase-averaged and phase-resolved experimental data are not available in the literature.

The present work is to investigate the single-loop flow patterns in a Rushton turbine stirred tank by using PIV measurements and LES approaches. With a high resolution camera, both phase-averaged and phase-resolved velocities, TKE, trailing vortices, and their transportations were quantitatively measured. The experimental PIV data are used to carefully validate the CFD results obtained by both the LES approaches and kε model. The effects of the grid and the SGS models on the LES results were also discussed, and the anisotropy of the flow near the turbine was calculated.

Section snippets

PIV experiment

A schematic view of the experimental apparatus is shown in Fig. 1. The stirred tank was a flat bottom Perspex vessel with an inner diameter T=0.476 m. Four equally spaced baffles with width Wb=T/10 were arranged, and the measurement plane was chosen in the middle of two successive baffles. The working fluid was tap water and the liquid height H=T. To minimize optical refraction, the cylindrical tank was placed in a square tank (0.58 m×0.72 m). The impellers were standard Rushton turbines as shown

Large eddy simulations

The basic governing equations of LES for incompressible flows are the filtered Navier–Stokes equations:u¯ixi=0u¯it+u¯iu¯jxj=1ρp¯xi+ν2u¯ixjxjτijxjwhere the overbars denote the large scales obtained from grid filtering. The effect of the subgrid scales appears through the subgrid scale stress tensorτij=u¯iu¯ju¯iu¯jwhich must be modeled. The subgrid scale stresses represent the interaction between the resolved larger scales and the unresolved smaller scales of motion.

In the eddy

Results and discussion

In the following discussion of PIV experimental and CFD simulated results, the radial, axial, and tangential components of mean velocity are represented by U, V, and W, respectively, and the corresponding turbulent components are represented by u′, v′, and w′. All these velocity values are normalized with the impeller tip velocity Vtip. The turbulent kinetic energy is normalized with Vtip2. The origin of the coordinate is located at the center of the bottom of the stirred tank, and the axial

Conclusions

PIV experiments with high resolution were used to obtain the distributions of both the phase-averaged and phase-resolved velocities and turbulent kinetic energy in a low-clearance Rushton turbine stirred tank. Two counter-rotating vortices are generated behind the blade. The vortices gradually move to the bottom of the tank with the rotation of the blade when D=T/3. The regions with high TKE levels are consistent with the trailing vortices, and the energy is transferred by the vortices from the

Nomenclature

    C

    clearance of Rushton turbine (m)

    Cs

    Smagorinsky constant (dimensionless)

    d

    distance from node to the closest wall (m)

    D

    diameter of Rushton turbine (m)

    Ddisk

    diameter of disk (m)

    Dhub

    diameter of hub (m)

    H

    height of liquid in tank (m)

    Himp

    height of the blade of Rushton turbine (m)

    k

    turbulent kinetic energy (m2 s−2)

    Ls

    mixing length of subgrid scale (m)

    N

    rotational speed (s−1)

    p

    pressure (Pa)

    r

    radial coordinate (m)

    Re

    Reynolds number (dimensionless)

    Sij

    strain-rate tensor (s−1)

    t

    time (s)

    tdisk

    thickness of disk of Rushton

Acknowledgments

The authors would like to thank Prof. Hong Xu (School of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China) for the helpful discussion. The financial supports from the National Natural Science Foundation of China (Nos. 20776008, 20821004, 20990224) and the National Basic Research Program of China (973 Program, No. 2007CB714300) are gratefully acknowledged.

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