Measurement and characterization of mixing time in shake flasks

As yet, investigations on mixing time have been focused on small and large scale stirred tanks. The aim of this study was to develop a new method for characterizing the mixing process and quantitatively measuring the mixing time in shake flasks by introducing a rotating camera for online observation of the fluid flow in combination with a typical colorimetric method using a pH indicator. In this presented scheme, only one drop of sulfuric acid was injected with a peristaltic pump into a bulk solution consisting of either deionized water or a viscous polyvinylpyrrolidone (PVP) solution. In this study, a novel interpretation of mixing time for the colorimetric method was introduced. The macroscopic mixing time is independent of the concentration of added acid. Interestingly, the recorded mixing time was similar irrespective of the shaking diameters (25, 50 mm). In addition, the dimensionless mixing number stayed constant in the regime of high Reynolds number. Our results showed that mixing number of the fluid in the regime of high Reynolds number is independent of the given geometries of flasks.     

Analysis of turbulence anisotropy in a mixing tank

The objective of this paper is to analyze the gap between the local turbulence and the 3D isotropic state in a mixing tank stirred with a Rushton turbine. Experiments were carried out using the PIV technique, and phase average treatment permits the calculation of the six components of the Reynolds stress tensor. In order to quantify the gap between the measured local turbulence and the 3D isotropic state, methods based on tensorial analysis are developed. In a turbulent flow, three representations are able to characterize the turbulence anisotropy: representation based on two eigenvalues (s-t) of the anisotropy tensor; the Lumley-Newman triangle based on two invariants (II -III ) of the anisotropy tensor; a representation based on the axisymmetry invariant A and the two-dimensional invariant G. These three visual methods, that quantify the degree of anisotropy from two independent variables are developed and used in the impeller stream region, and the distribution of the turbulence state is thus described. A parameter is proposed to quantify the anisotropy level.     

An assessment of different turbulence models for predicting flow in a baffled tank stirred with a Rushton turbine

This work presents a comprehensive study of different turbulence models, including the k–ε, SST, SSG–RSM and the SAS–SST models, for simulating turbulent flow in a baffled tank stirred with a Rushton turbine. All the turbulence models tested predict the mean axial and tangential velocities reasonably well, but under-predict the decay of mean radial velocity away from the impeller. The k–ε model predicts poorly the generation and dissipation of turbulence in the vicinity of the impeller. This contrasts with the SST model, which properly predicts the appearance of maxima in the turbulence kinetic energy and turbulence energy dissipation rate just off the impeller blades. Curvature correction improves the SST model by allowing a more accurate prediction of the magnitude and location of these maxima. However, neither the k–ε nor the SST model is able to properly capture the chaotic and three-dimensional nature of the trailing vortices that form downstream of the blades of the impeller. In this sense, the SAS–SST model produces more physical predictions. However, this model has some drawbacks for modelling stirred tanks, such as the large number of modelled revolutions required to obtain good statistical averaging for calculating turbulence quantities. Taking into consideration both accuracy and solution time, the SSG–RSM model is the least satisfactory model tested for predicting turbulent flow in a baffled stirred tank with a Rushton turbine.     

CFD analysis of turbulence in a baffled stirred tank, a three-compartment model

Three-compartment model was used to study non-homogeneity of mixing in a fully baffled stirred tank. Multiple reference frame (MRF) technique was used for calculations. Calculations were performed to study the effects of agitator speed, impeller diameter, baffle width and distance of impeller from bottom of the tank on turbulent flow field. Three different zones of the vessel, that were a small zone near the impeller, another zone around the baffles, and a relatively large zone far from the impeller and baffles, named circulation zone, were investigated. Boundaries of these zones were determined using two different methods. The first method used gradient of energy dissipation rate while the other method used cumulative energy dissipation rate to determine the zone boundaries. Zone boundaries determined by both methods were comparable. The turbulent kinetic energy dissipation rate gradient was the preferred method due to its simplicity. Turbulent kinetic energy dissipation rate increased with agitator speed in all zones. Both turbulent kinetic energy dissipation rate and turbulent kinetic energy showed considerable change with impeller diameter at impeller zone, while no remarkable change was observed at baffle and circulation zones. Three-compartment model parameters, impeller and baffle energy dissipation ratios λ_i, λ_b, impeller and baffle volume ratios μ_i, μ_b and impeller and baffle exchange flow rates Q_i, Q_b were obtained from CFD simulations. Impeller energy dissipation ratio, impeller exchange flow rate and baffle exchange flow rate increased while baffle volume ratio decreased with agitation rate and impeller diameter. Baffle energy dissipation ratio and impeller volume ratio showed no considerable change with agitation rate and impeller diameter.     

Oxygen mass transfer and hydrodynamics in a multi-phase airlift bioscrubber system

The addition of select polymer beads to stirred tank bioscrubber systems has been shown to greatly enhance the removal and treatment of toxic VOCs via the capture and sequestration of poorly soluble compounds such as benzene, and the release of these materials, based on equilibrium partitioning, to microorganisms in the aqueous phase. In this study, oxygen volumetric mass transfer coefficients were determined for an 11 L airlift vessel containing tap water alone, tap water with Nylon 6,6 polymer beads (10% v/v), and tap water with silicone rubber beads (10% v/v), over various inlet gas flow rates, with the aim of initially characterizing a low-energy pneumatically agitated reactor (concentric tube airlift). In addition, oxygen transfer rates into the airlift with and without polymers with high oxygen affinity were determined. To further characterize this reactor system, a residence time distribution analysis was completed to determine hydrodynamic parameters including the Peclet number (Pe), circulation time (t_c) and mixing time (t_m) over various gas flow rates for the airlift containing tap water with and without silicone rubber. It was found that the addition of silicone rubber beads, which has a high affinity for oxygen, reduced the measured volumetric mass transfer coefficient relative to a system without polymers due to oxygen sorption during the dynamic period of testing, but increased the overall amount of oxygen that was transferred to the system during the dynamic period. The addition of Nylon 6,6, which has very low oxygen uptake, allowed for estimation of the physical effect of solids addition on gas-liquid mass transfer and it was found that there was no effect on the measured volumetric mass transfer coefficient relative to a system without polymers. However, hydrodynamic parameters revealed that the addition of silicone rubber into an airlift vessel improves liquid phase mixing. This investigation has defined key operational features of a low-energy three-phase airlift bioscrubber system for the treatment of toxic VOC substrates.     

Measurement of local gas holdup in bubble columns via a non-isokinetic withdrawal method

An inexpensive method was developed to measure local gas holdup based on withdrawal of the air–liquid dispersion in bioreactors under non-isokinetic conditions. The method was tested with several suction probe designs and withdrawal pressures using coalescing and non-coalescing model media as well as during yeast fermentations. Simultaneously, gas holdup was measured manometrically. With a straight end probe and vacuum pressure of 3 kPa, local gas holdup measurements presented a relative error <6% compared to the manometric method, independently of the media composition. This method was used to characterize local gas holdup in a bubble column. Two new parameters are proposed to characterize non-gassed volume and gas holdup homogeneity.     

Lagrangian trajectory model for turbulent swirling flow in an annular cell: comparison with residence time distribution measurements

Knowledge of the flow field can be very useful for reactor design and optimization. Data concerning the displacement and trajectories of reactive elements are of primary interest for a better understanding of process running. Results can be deduced from computational fluid dynamics or experimental measurements. However, numerical simulation is difficult to achieve for complex flow such as swirling decaying flow, and trajectories need to be calculated on the basis of velocity field measurements. This problem can be simplified by using a Lagrangian formulation, in which case the only major difficulty is to express the influence of turbulence on calculated trajectories. Velocity fluctuations can be considered as pure random functions or related to turbulence correlations. These two methods were used to calculate trajectories of elementary fluid particles in a swirling decaying flow on the basis of hydrodynamic characteristics obtained by particle image velocimetry (PIV) studies. Trajectory dispersion was then compared with experimental results obtained by PIV measurements of the instantaneous flow field. This comparison shows the great dependence of velocity fluctuation (and thus of trajectories) on spatial correlations. Finally, the correct mathematical formulation of velocity fluctuation was checked by using the trajectory calculation algorithm to determine residence time distribution (RTD). A comparison with experimental RTD confirmed the efficiency of the method for determining trajectories in swirling decaying flow.     

On the main flow features and instabilities in an unbaffled vessel agitated with an eccentrically located impeller

The hydrodynamics of an unbaffled vessel stirred by an eccentrically located Rushton turbine is investigated with both Laser Doppler Anemometry and flow visualisation techniques. The flow field is shown to be characterised by a strong circumferential motion which develops itself around two main vortices, one above and one below the impeller, both inclined with respect to the vertical plane. Such vortices are not steady but move periodically very slowly in comparison to the impeller rotational timescale. Accordingly, two low frequency components, whose values are linearly dependent on the impeller rotational speed, are identified across the vessel. The energetic contribution to the turbulent kinetic energy of such flow instabilities is significant so that they should be taken into account when evaluating micro-mixing information from turbulence quantities. Besides, an additional low frequency component is observed and related to vortex shedding phenomena from the flow-shaft interaction which occur in eccentric agitation operation. The flow discharged from the impeller is also measured and discussed.     

Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements

In this study, the hydrodynamics and turbulence in a square tank stirred with a hydrofoil impeller, a Lightnin A310, is investigated using a large eddy particle image velocimetry (LE PIV) approach. The particle image velocimetry data are used as the large scale part of a large eddy simulation and the small scales are modelled assuming that the turbulent kinetic energy production is limited to the large scale structures, the turbulent energy dissipation is confined to the small scale structures and the transfer of energy takes place in the inertial sub-range. The small scale turbulence was modelled by direct calculation of the turbulent stress tensor using filtered particle image velocimetry data. The spatial distribution of the calculated dissipation rate tensors showed good agreement with previous work.

The macro instabilities of the flow structure were investigated by means of spectral analysis. Low frequency phenomena separated from the mean flow were detected. The cause of these could partly be explained by the circulation time for the tank, which corresponded to the low frequency phenomena found at 0.03N Hz, where N is the rotational speed.     

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

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 k–ε model. The agreement shows that the LES method can be used to simulate the complex flow fields in stirred tanks.     

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.     

折流杆换热器在压缩机级间冷却上的应用

一种新型的Ｕ形管式折流杆换热器已成功地替代了Ｈ２２（Ⅲ）氮、氢压缩机的套管式冷却器。新设备的体积、重量和压降分别为原设备的１／６、１／４和１／３。分析介绍了这一新设备的特性及应用实例     

在热管生物反应器中发酵制备L-苯丙氨酸

用在5L热管生物反应器中实体发酵所产生的大肠杆菌E．coli No．1进行苯丙酮酸转氨制备L-苯丙氨酸过程能达到较高的技术指标。在微生物生长各阶段反应器中发酵液的温度很均匀，其平均温差为0．08℃、最大温差为0．4℃。与用传统的搅拌式生物反应器相比，用热管生物反应器发酵的微生物菌体量(以OD值计)从0．40提高至0．54，其发酵液转化苯丙酮酸制备L一苯丙氨酸的平均得率从70％增加至75％。     

Modelling of droplet breakage probabilities in an oscillatory baffled reactor

The breakage of droplets dispersed in a continuous aqueous phase determines the performance of many mixing devices and reactors that rely on effective contact between two phases, e.g. emulsion mills, liquid-liquid extraction columns, stirred tank reactors and Oscillatory Baffled Reactors. Quantitative knowledge of the mechanisms involved in the breakage provides parameters for design and prediction. In the work presented here, oil was dispersed in water in a continuous OBR, and a High Speed Camera was used to record the events of breakage of individual oil droplets and probabilities of breakage were estimated. It was confirmed that breakage was more sensitive to changes in the amplitude of oscillation than in the frequency of oscillation. A novel integral model was developed based on an analysis of the total work effected on the deforming droplet in order to interpret the results. The quantitative results from direct observation were compared to the model predictions. The model with fitted parameters was finally extrapolated to smaller diameters, in an attempt to predict the critical drop diameter for breakage.     

Single and multiphase CFD approaches for modelling partially baffled stirred vessels: Comparison of experimental data with numerical predictions

Whilst the use of CFD to study mixing vessels is now common-place, there are still many specialised applications that are yet to be addressed. Here we present CFD and PIV results for a hydrodynamic study of a partially baffled vessel with a free surface. The standard k-? and SSG Reynolds Stress turbulence models are used and the numerical predictions of the mean flow field are compared with experimental data for single phase modelling. At low rotation rates a flat free surface is observed and the flow is simulated using a single phase model, whilst at high rotation rates an Eulerian-Eulerian multiphase model is used to capture the free surface location, even under conditions when gas is drawn down to the impeller. It is shown that there are significant transient effects that mean many of the “rules of thumb” that have been developed for fully baffled vessels must be revisited. In particular such flows have central vortices that are unsteady and complex, transient flow-induced vortical structures generated by the impeller-baffle interactions and require a significant number of simulated agitator rotations before meaningful statistical analysis can be performed. Surprisingly, better agreement between CFD and experimental data was obtained using the k-? than the SSG Reynolds stress model. The multiphase inhomogeneous approach used here with simplified physics assumptions gives good agreement for power consumption, and with PIV measurements with flat and deformed free surfaces, making this affordable method practical to avoid the erroneous modelling assumption of a flat free surface often made in such cases.     

Numerical study on the turbulent reacting flow in the vicinity of the injector of an LDPE tubular reactor

Three-dimensional (3-D), transient numerical simulations of the turbulent reacting flow in the vicinity of the initiator injection point of a low-density polyethylene (LDPE) tubular reactor using a large eddy simulation (LES) approach combined with a filtered density function (FDF) technique are presented. The numerical approach allows for detailed predictions of the turbulent flow field and the associated (passive and reactive) scalar mixing. The aim is to study the influence of the injector geometry and initiator injection temperature on the LDPE process in terms of product quality (average polymer chain length, and polydispersity) and process efficiency (such as initiator consumption).     

Modelling Oxygen Transfer and Aerobic Growth in Shake Flasks and Well‐Mixed Bioreactors

Oxygen transfer is an important aspect of aerobic metabolism. In this work, microbial growth on glucose (fast metabolism) and phenol (slow metabolism) have been studied using Pseudomonas putida in shake flasks and a mixed bioreactor considering both substrate and oxygen depletion. Under typical operating conditions, the highest mass transfer coefficient (K_La) for the aerated well‐mixed bioreactor was found to be 50.8 h^?1, while the maximum non‐aerated shake flask K_La was 21.1 h^?1. The presence of media and/or dead cells did not have significant effect on measured values of K_La. A new equation for prediction of K_La in shake flasks with an absolute average deviation of 11.1% is introduced, and a combined model for oxygen mass transfer and microbial growth is shown to fit experimental data during growth on glucose and phenol in both shake flasks and the mixed bioreactor with an absolute average deviation of 19.3%.     

Identification and characterization of flow structures in chemical process equipment using multiresolution techniques

Planar information of velocity from 2D particle image velocimetry (PIV) and large eddy simulation (LES) data have been studied using multiresolution wavelet transform (WT) formalisms, i.e., discrete and continuous WT. Identification of dominant energy containing structures with their characterization in terms of fractal spectra have been carried out for industrially important equipment exhibiting turbulent behavior. These include annular centrifugal contactor, jet loop reactor, ultrasound reactor, channel flow, stirred tank and bubble column reactor. The characterization of their dynamics based on denoising the data and studying the local energy along the WT scales show sensitive variation and this helps in identifying the size and shape of structures. A dependency is seen between mixing time and the higher order moments of length scale distribution, viz., skewness and kurtosis and a generalized correlation has been built up for important types of equipment and associated flow parameters. The correlation is not only based on the knowledge of reactor geometry and operating conditions but also on the flow structures via their statistical parameters. Wavelet transform modulus maxima (WTMM) methodology has been used to study the evolution of structures and their interaction in a reduced dimensionality by evaluating the fractal spectra. Classification studies have been carried out using principal component analysis (PCA) of the fractal spectra. The results obtained show clear classes for the six types of equipments and delineate regimes to obtain benchmark patterns of flow hydrodynamics based on PCA co-ordinates. This methodology offers a generalized way for the optimal design and operation of different types of reactors.