PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine 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 k–ε, renormalization group k–ε, 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 k–ε 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:where the overbars denote the large scales obtained from grid filtering. The effect of the subgrid scales appears through the subgrid scale stress tensorwhich 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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