Solids suspension in stirred tanks with pitched blade turbines

In view of developing a universal correlation for critical speed of suspension, extensive suspension experiments were conducted with tank scales in the range of 15-, D/T from 0.083 to 0.625, using four different sizes of spherical glass beads and employing Pitched Blade Turbines with four and six blades as the impellers. The periphery of the tank bottom was modified to include a permanent fillet in order to eliminate the effect of induced recirculation loop, which account for the formation of peripheral fillets of unsuspended solids. The critical speed of suspension N_c and power P_c were observed to vary independently both with D and T to give two correlations for each of the variables, N_c and P_c; one for the close proximity impeller operation where both N_c and P_c remained invariant with off-bottom impeller clearance and the second for the region where N_c and P_c were affected significantly by the impeller position. The effects of the physical characteristics of the solids were also included in the four correlations so proposed. It was clearly noticed that the correlations were valid up to a critical value of D/T beyond which the trapped particles in the stagnant zone below the impeller needed extra energy to be raked out and suspended, thus breaking the log-linear relationship between N_c (or P_c) and D/T hitherto maintained. Comparisons of the suspension speed and power have been made with open literature. More importantly, the reasons why the earlier studies differed with each other in N_c-predictions have been identified.     

On POD analysis of PIV measurements applied to mixing in a stirred vessel with a shear thinning fluid

P.O.D. technique is applied to 2D P.I.V. data in the field of hydrodynamics in a mixing tank with a Rushton turbine and a shear thinning fluid. Classical eigen-value spectrum is presented and phase portrait of P.O.D. coefficients are plotted and analyzed in terms of trailing vortices. A spectrum of dissipation rate of kinetic energy is introduced and discussed. Length scales associated to each P.O.D. modes are proposed.     

Development of a networks-of-zones fluid mixing model for an unbaffled stirred vessel used for precipitation

Reactive acid-alkali tracers have been deployed to capture the macromixing and partial segregation behaviour in an unbaffled stirred vessel. This configuration is often used in precipitators to avoid inadvertent solid accretions on vessel internals. The macromixing behaviour for semi-batch addition with visualisation of reactive (acid-alkali) tracers has been acquired via video images which are rendered visible using phenolphthalein as indicator. By means of visual reality modelling, in which computer graphics are used to reconstruct and closely mimic the experimentally visualised fluid mixing “scenes”, the parameters for a networks-of-zones mixing model for the unbaffled semi-batch case have been established. The model can then be used for predicting precipitation behaviour for single-jet and other modes of operation. Some illustrative examples for barium sulphate, showing the underlying supersaturation fields in 3-D and the consequent time evolving particle size distributions, are presented and discussed for a single jet case.     

Numerical simulation of a dissolution process in a stirred tank reactor

A dissolution process of solid particles suspended in a turbulent flow of a Rushton turbine stirred tank is studied numerically by large eddy simulations including passive scalar transport and particle tracking. The lattice-Boltzmann flow solver and the Smagorinsky subgrid-scale model are adopted for solving the stirred tank flow. To the LES a finite volume scheme is coupled that solves the convection-diffusion equation for the solute. The solid particles are tracked in the Eulerian flow field through solving the dynamic equations of linear and rotational motion of the particles. Particle-particle and particle-wall collisions are included, and the particle transport code is two-way coupled. The simulation has been restricted to a lab-scale tank with a volume equal to . A set of 7×10⁶ spherical particles in diameter are released in the top part of the tank (10% of the tank volume), resulting in a local initial solids volume fraction of 10%. The particle properties are such that they resemble those of calcium chloride beads. The focus is on solids and scalar concentration distributions, particle size distributions, and the dissolution time. For the particular process considered, the dissolution time is found to be at most one order of magnitude larger than the time needed to fully disperse the solids throughout the tank.     

Drag models, solids concentration and velocity distribution in a stirred tank

Drag force influences both the particle suspension and solids concentration distribution in a stirred tank. The influence of drag models on the prediction of solids suspension in a tank stirred by a hydrofoil impeller was studied in the present work using computational fluid dynamics (CFD) and experimental techniques. A comparison was made between the drag models based on Reynolds number only and those that take solid volume fraction into account or those that account for the effect of the free stream turbulence. One of the drag models investigated was a function of the energy dissipation rate, and therefore, the influence of the methods of determining the energy dissipation rate on the prediction of solids suspension was investigated. It was shown that a better agreement between the CFD simulation and experimental results can be obtained using drag models based on solids volume fraction than those that are based on Reynolds number only.     

The effect of impeller pumping and fluid rheology on solids suspension in a stirred vessel

Pumping velocities of different impellers were measured using laser Doppler velocimetry. It was found that there is a link between impeller pumping capacity and the 5 parameter in the Zwietering correlation. Measurements showed that N_js increases with impeller spacing for dual impeller configurations. A dual‐impeller configuration shows less sensitivity to solids loading change than a single‐impeller configuration, and the change in N_js is larger for small impeller spacing than for large impeller spacing. An increase in slurry cloud height and a reduction in N_js resulted at a small increase of non‐Newtonian viscosity.     

Gas dispersion and solid suspension in a three-phase stirred tank with triple impellers

The hydrodynamics is still not fully understood in the three-phase stirred tank equipped with multi-impeller due to the intensive interaction between phases. In this work, the solid critical suspension speed(NJSG), relative power demand(RPD) and overall gas holdup(ε_G) were measured in an air–water–glass beads stirred tank equipped with multi-impeller, which consists of a parabolic blade disk turbine below two down-pumping hydrofoils. Results show that either the NJSGor the specific power consumption increases when increasing the volumetric solid concentration or superficial gas velocity. RPD changes less than 10% when solid volumetric concentration ranges from 0 to 15%. ε_G decreases with the increase of solid concentration, and increases with the increase of both superficial gas velocity and the total specific power consumption. The quantitative correlations of NJSG,RPD and εGwere regressed as the function of superficial gas velocity, specific power consumption, Froude number and gas flow number, in order to provide the reference in the design of such three-phase stirred tank with similar multi-impellers.     

Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank

Laminar mixing in the stirred tank is widely encountered in chemical and biological industries.Isolated mixing regions (IMRs) usually exist when the fluid medium has high viscosity,which are not conducive to mixing.In this work,the researches on IMRs,enhancement of laminar mixing and the phenomenon of particle clustering within IMRs are reviewed.For most studies,the aim is to destroy IMRs and improve the chaotic mixing.To this end,the mechanism of chaotic mixing and the structure of IMRs were well investigated.The methods developed to destroy IMRs include off-centered agitation,dynamic mixing protocol,special designs of impellers,baffles,etc.In addition,the methods to characterize the shape and size of IMRs as well as mixing effect by experiments and simulations are summarized.However,IMRs are not always nuisance,and it may be necessary in some situations.Finally,the present engineer-ing applications are summarized,and the prospect of the future application is predicted.For example,particle clustering will form in the co-existing system of chaotic mixing and IMRs,which can be used for solid-liquid separation and recovery of particles from high viscosity fluid.     

自浮颗粒的搅拌混合

综述了近２０年来自浮颗粒的固液两相悬浮和气液固三相分散的研究结果,并与下沉颗粒体系的规律作了比较,发现自浮颗粒三相分散规律与下沉颗粒的三相分散规律存在奶多差别。前者的悬浮难点在液面,要求搅拌浆能提供液面是上推式的流型,而后者的悬浮难点在釜底,要求搅拌浆能提供釜底是下压式的流型。     

Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank

Up-pumping pitched blade turbines (and similar impellers) have recently been shown to be particularly effective for achieving a variety of mixing duties. Here, their turbulent flow characteristics are analysed by angle-resolved particle image velocimetry (PIV) for the first time and compared with their down-pumping equivalent, the usual time-averaged parameters also being determined for each. The work was conducted in 0.15 m diameter vessel (T) with a 45° impeller of diameter D (=0.45T) in water. The angle-resolved PIV enables a number of novel features to be identified. Firstly, the two pumping directions are shown to give very different vortex structures, even though the flow numbers, Fl, are the same (=0.79). In addition, the ‘spottiness’ of the normalized kinetic energy along a radius as the trailing vortex moved away from each impeller can be identified, which is not shown from time-averaged data. Often, the most important parameter for processing is the local normalized specific energy dissipation rate, and this is estimated using three methodologies: by measurement of the components of the stress tensor directly, ; by dimensional analysis, , with measured integral length scales (ILS); and by the Smagorinsky closure method, , to model unresolved scales (with a Smagorinsky constant used in the literature on stirred vessels). Again, only the angle-resolved results show the spottiness of and also higher values than the time-averaged. Differences in the values obtained by the three methods are discussed and compared with the existing literature. Most importantly, for the first time, the power input in the PIV-interrogated region is calculated from the three methods and compared to the input based on the impeller torque. Both DA and SGS methods are shown to overestimate the true power by a factor of 5 and 2, respectively, whilst the DE method provided a significant underestimate (1/5th) due to the limitation of the resolved length scales. The SGS method shows the greatest promise and by changing the value of the Smagorinsky constant in accordance with recent recommendations, good agreement is obtained. Nevertheless, it is concluded that there is still a need for improved methods for determining the important mixing parameter, .     

Experimental and modelling study of gas dispersion in a double turbine stirred tank

Gas dispersion in a double turbine stirred tank is experimentally characterised by measuring local gas holdups and local bubble size distributions throughout the tank, for three liquid media: tap water, aqueous sulphate solution and aqueous sulphate solution with PEG. For all these media, bubble coalescence generally prevails over breakage. Where average bubble size decreases, this can be attributed to the difference in slip velocity between different sized bubbles. Most of the coalescence takes place in the turbine discharge stream.A compartment model that takes into account the combined effect of bubble coalescence and breakage is used to simulate gas dispersion. The model predicts spatial distribution of gas holdup and of average bubble size, with average bubble size at the turbines as an input. Reasonable agreement between experiment and simulation is achieved with optimisation of two parameters, one affecting mainly the slip velocity, the other related mainly to the bubble coalescence/breakage balance. Different sets of parameters are required for each of the three liquid systems under study, but are independent of stirring/aeration conditions. The model only fails to simulate the smaller average bubble diameters at the bottom of the tank.     

CFD simulations of gas-liquid-solid stirred reactor: Prediction of critical impeller speed for solid suspension

In this work, simulations have been performed for three phase stirred dispersions using computational fluid dynamics model (CFD). The effects of tank diameter, impeller diameter, impeller design, impeller location, impeller speed, particle size, solid loading and superficial gas velocity have been investigated over a wide range. The Eulerian multi-fluid model has been employed along with the standard k-ε turbulence model to simulate the gas-liquid, solid-liquid and gas-liquid-solid flows in a stirred tank. A multiple reference frame (MRF) approach was used to model the impeller rotation and for this purpose a commercial CFD code, FLUENT 6.2. Prior to the simulation of three phase dispersions, simulations were performed for the two extreme cases of gas-liquid and solid-liquid dispersions and the predictions have been compared with the experimental velocity and hold-up profiles. The three phase CFD predictions have been compared with the experimental data of Chapman et al. [1983. Particle-gas-liquid mixing in stirred vessels, part III: three phase mixing. Chemical Engineering Research and Design 60, 167-181], Rewatkar et al. [1991. Critical impeller speed for solid suspension in mechanical agitated three-phase reactors. 1. Experimental part. Industrial and Engineering Chemistry Research 30, 1770-1784] and Zhu and Wu [2002. Critical impeller speed for suspending solids in aerated agitation tanks. The Canadian Journal of Chemical Engineering 80, 1-6] to understand the distribution of solids over a wide range of solid loading (0.34-15 wt%), for different impeller designs (Rushton turbine (RT), pitched blade down and upflow turbines (PBT45)), solid particle sizes (120-) and for various superficial gas velocities (0-10 mm/s). It has been observed that the CFD model could well predict the critical impeller speed over these design and operating conditions.     

Influence of solids on macro-instabilities in a stirred tank

Measurements were conducted in a cylindrical tank stirred with a PBT in order to study the effect of varying amounts of suspended solids, up to 11.8% by volume, on the frequency and amplitude of macro-instabilities (MI). Solid glass particles of three different sizes were used in order to investigate the influence of the particle Stokes number. Measurements were made at 18 different locations in the vessel using laser Doppler anemometry (LDA) and were evaluated with the Lomb algorithm to obtain the frequency spectrum of the liquid flow.     

Use of PIV to measure turbulence modulation in a high throughput stirred vessel with the addition of high Stokes number particles for both up- and down-pumping configurations

A refractive index matching technique combined with particle image velocimetry (PIV) was used to measure turbulent properties of solid–liquid suspensions in a small high throughput scale cylindrical vessel of 45 mm diameter agitated with a 45° pitched blade turbine (PBT) for up-pumping (U) and down-pumping (D) configurations. This study analyses the effect of large 1.5 mm diameter particles (Stokes number>1), on liquid mean velocities, turbulent kinetic energy (TKE) and energy dissipation (ε) at particle concentrations of 0%, 1.5% and 5% by volume. Only small changes in the time-averaged liquid velocities were observed with increasing particle concentration. However, maximum TKE near the impeller decreased up to 40% with increasing particle concentration for both configurations. The Smagorinsky SGS method was used to estimate local energy dissipation rate near the impeller and the maximum value was found to decrease by 50% between 0% and 5% concentration for the (U) configuration. A lesser but still significant drop of 30% was observed for the (D) configuration. These data confirm that large Stokes number particles can suppress turbulence, in agreement with some previous experimental studies, but in contradiction with existing theories.     

Scalar mixing in a turbulent stirred tank with pitched blade turbine: Role of impeller speed perturbation

Mixing of a passive scalar inside a pitched blade turbine (PBT) impeller stirred tank (STR) is studied using large-eddy simulation (LES) coupled with the immersed boundary method (IBM) for resolving moving interfaces. Mixing time is calculated based on the 95% homogenization of the scalar over the entire tank volume. Growth rate of the unmixed tracer volume is observed in order to identify the effects of low frequency macroinstability (MI) oscillations. Mixing time is significantly reduced when the STR flow is perturbed using a step-change in the impeller speed with a specific MI frequency. The enhancement in turbulent kinetic energy and changes in mean flow field due to the perturbation is observed. The spatio-temporal behavior of the large-scale mixing structures for the fixed impeller-speed case and the perturbed case are compared. The mechanism of mixing enhancement is further explored by observing dynamic changes in the concentration distribution and the velocity field over a perturbation cycle. Penalty in power requirement due to perturbation is calculated.     

Theoretical prediction of gas-liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks

A prediction method for calculating the volumetric mass transfer coefficient, k_La, in gas-liquid sparged stirred tanks is proposed. A theoretical equation based on Hibie's penetration theory and the isotropic turbulence theory of Kolmogoroff is used for k_L determination. The values of the interfacial area have been calculated from a hold-up theoretical equation and the mean size of the gas bubble. Both Ostwald-De Waele and Casson models are used to describe the rheological properties of the fluid. The model predicts the mass transfer coefficient and the interfacial area values in stirred tank reactors, analysing the influence of different variables. The values of the volumetric mass transfer coefficient can be calculated for different geometries of the reactor, different physicochemical properties of the liquid and under different operational conditions. The capability of prediction has been examined using experimental data available in the literature for Newtonian and non-Newtonian fluids, for very different vessel sizes, different numbers and types of stirrers and a wide range of operational conditions, with very good results.     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

CFD modelling of a mixing chamber for the realisation of functionally graded scaffolds

Biological tissues are characterised by spatially distributed gradients, intricately linked with functions. It is widely accepted that ideal tissue engineered scaffolds should exhibit similar functional gradients to promote successful tissue regeneration. Focusing on bone, in previous work we proposed simple methods to obtain osteochondral functionally graded scaffolds (FGSs), starting from homogeneous suspensions of hydroxyapatite (HA) particles in gelatin solutions. With the main aim of developing an automated device to fabricate FGSs, this work is focused on designing a stirred tank to obtain homogeneous HA–gelatin suspensions. The HA particles transport within the gelatin solution was investigated through computational fluid dynamics (CFD) modelling. First, the steady-state flow field was solved for the continuous phase only. Then, it was used as a starting point for solving the multi-phase transient simulation. CFD results showed that the proposed tank geometry and setup allow for obtaining a homogeneous suspension of HA micro-particles within the gelatin solution.     

Positron emission particle tracking (PEPT) compared to particle image velocimetry (PIV) for studying the flow generated by a pitched-blade turbine in single phase and multi-phase systems

Positron emission particle tracking (PEPT) is a new technique allowing the quantitative study of flow phenomena in three dimensions in opaque systems that cannot be studied by techniques based on optical methods such as particle image velocimetry (PIV) or laser Doppler anemometry (LDA). It has previously been used for studying solid particle motion in various systems used in particulate processing. Here, for the first time, velocity measurements made using PEPT with a down-pumping pitched blade turbine (PBTD) are compared directly with those made by PIV in water in the same equipment. It is shown that excellent agreement is found between the two methods except just below the impeller in the discharge. However, this difference is attributed to the different type of data collected and the different way of ensemble-averaging in the two techniques. Similar results were found at higher agitator speeds with both the PBTD and an up-pumping PBT (PBTU) where a small amount of surface aeration occurred. Measurements in solid liquid systems with surface aeration at 0.5 wt% solids or higher were not possible with PIV, but excellent results were obtained with PEPT for both the PBTD and PBTU in a 5 wt% suspension. It is concluded that this calibration study shows that the PEPT technique can be used to obtain accurate velocity data throughout all of the complex three-dimensional flow field in a range of mechanically agitated, turbulent, multi-phase systems previously not amenable to quantitative analysis.