Impeller Reynolds Number Research Articles

Electrical resistance tomography-assisted analysis of dispersed phase hold-up in a gas-inducing mechanically stirred vessel

Tomographic analysis of the hydrodynamic attributes of the gas–liquid–solid mixing in a 1-l capacity stirred-tank equipped with a 4-blade gas-entrainment impeller has been used to obtain the dispersed phase hold-up distribution as a function of stirring speed (impeller Reynolds Number, Re I ) and solid particle loading. Although the liquid phase stirring was turbulent, both gas and solid flows went through different hydrodynamic regimes and experienced radial hold-up gradient over the range of impeller speed employed. Global solid phase hold-up profile exhibited a sigmoid-shape with respect to the impeller Reynolds number indicative of three solid suspension regimes across the stirring range (1.0≤Re I ≤6.25×10 4) investigated. The solid phase hold-up distribution was adequately captured by, ε s = ε s,max [1−exp(− τ spp Re I )] γ with ε s,max and γ dependent on solid loading. An analogous expression was also obtained for the radial solid phase hold-up distribution and has enabled the proposition of a criterion for existence of radial transport gradient in gas-induced stirred tanks (GIST). Additionally, correlations for estimating the mixing time and power number for gas-induced mechanical agitators also gave good agreement with the empirical data.

Experimental Study and Detached Eddy Simulation of the Macro-Instability in an Eccentric Stirred Tank

The turbulent flow in stirred tank is highly complicated and anisotropic, especially when the macro-instability (MI) are involved. In this work, the numerical simulation method of the eccentric agitation was established based on the detached eddy simulation (DES) model to study the MI in an eccentric stirred tank. The turbulent flow in the eccentrically located Rushton turbine stirred tank was numerically investigated. The rotation of the impeller was simulated by the transient sliding mesh (SM) method. The effect of eccentricity, impeller Reynolds number and impeller-tank diameter ratio were studied in order to quantify the MI frequency. PIV experiments were performed to validate the DES results and frequency analyses were applied to the obtained time series of the velocity recordings. It was found that the flow field in eccentrically stirred tank are highly unsteady and is subject to MI with varying period less than 10 blade passage period. Good agreements have been found between the DES and PIV results, both indicate that the dominant frequency of MI increases linearly with the Reynolds number, increases with the impeller-tank diameter ratio and decreases with the eccentricity. According to the agreements between the experimental and simulation results, it can be concluded that the combination of DES and SM is suitable for the prediction of the MI phenomenon in stirred tanks.

A Method for Determining the Representative Apparent Viscosity of Highly Viscous Pseudoplastic Liquids in a Stirred Vessel by Numerical Simulation

It is difficult to determine the representative apparent viscosity of a pseudoplastic liquid in a stirred vessel because the viscosity of the liquid varies with on the shear rate in the vessel. Until now, the method proposed by Metzner and Otto has exclusively been applied to the determination of this value. In this study, we proposed a new method for determining the representative viscosity, ηa, by averaging the viscosity distribution in the vessel using a weight of dissipation function on the basis of numerical simulation results, without any power correlation with a Newtonian liquid. Further, we calculated the representative shear rate, Γ, from ηa using a rheological equation presenting the pseudoplasticity; then, we found that Metzner's constant, B, can be expressed as the function of the impeller Reynolds number, Red. The reliability of this method was ascertained by comparing the results with those obtained when using the conventional Metzner's method: better conservation of flow similarity was achieved when scaling up the vessel using the proposed method than when employing the conventional method.

Flow structure and the effect of macro-instabilities in a pitched-blade stirred tank

Turbulent flow inside a dished bottom baffled stirred tank reactor (STR) with a 45° pitched blade impeller is studied numerically and experimentally. Three different impeller rotational speeds are studied corresponding to impeller Reynolds numbers of 44,000, 88,000 and 132,000, respectively. The numerical study is based on a large-eddy simulation (LES) technique with a fixed body-fitted curvilinear mesh. The moving impeller geometries are modeled using an immersed boundary method (IBM). The experiments consist of particle image velocimeter (PIV) measurements of the flow field. The instantaneous as well as the time-averaged flow field suggests the formation of trailing vortex structures which are associated with higher levels of turbulent kinetic energy relative to the remaining flow field. Instabilities occurring at a frequency lower than the frequency of impeller rotation are identified from the time signal of the velocity components. The role of these lower frequency macro-instabilities (MI) is explored by observing changes in the three-dimensional circulation pattern within the stirred tank. The growth and dissipation of trailing edge vortices are shown to be appreciably influenced by the macro-instability. A significant amount of kinetic energy (velocity fluctuations) is observed to be associated with the low frequency dynamics of the trailing edge vortices during an MI cycle.

Effect of shaft eccentricity on the laminar mixing performance of a radial impeller

AbstractThe effects of impeller eccentricity and Reynolds number on the mixing performance were studied for Rushton turbine stirred tank systems operated in the laminar regime (Re < 10). A digital image analysis of an acid–base decolourization reaction was used to characterize the mixing efficiency. Results show that both parameters have remarkable effects on the destruction of the toroidal segregated regions surrounding the Rushton turbine in laminar flow. Criteria are given to prevent the formation of these segregated regions in a tank. It is also shown that shaft eccentricity does not impact on the impeller power consumption.

Measuring Mixing Time in the Agitation of Non‐Newtonian Fluids through Electrical Resistance Tomography

AbstractElectrical resistance tomography (ERT), which is a non‐invasive and robust measurement technique, was employed to visualize, in three dimensions, the concentration field inside a cylindrical mixing vessel equipped with a radial‐flow Scaba 6SRGT impeller. The ability of ERT to work in opaque fluids makes this technique very attractive from an industrial perspective. An ERT system with a 4‐plane assembly of peripheral sensing rings, each containing 16 electrodes, was used to measure the mixing time in agitation of xanthan gum solution which is a pseudoplastic fluid with yield stress. An image reconstruction algorithm was used to generate images of the tracer distribution within the sensing zone. In this study, the effect of impeller speed, fluid rheology, power consumption, and Reynolds number on the mixing time was investigated.

Scale Up Parameter for Surface Aeration Systems

Based on the scale up parameter, X (theoretical power per unit volume = F4/3 R1/3, where F is the impeller Froude number and R is the impeller Reynolds number), it is presented that the said parameter is useful in scaling up the micromixing time in surface aeration systems. Scale up equations correlating X with micromixing time have been presented for the geometrically similar circular surface aeration systems.

CFD analysis of several design parameters affecting the performance of the Maxblend impeller

A CFD characterization of the hydrodynamics of the Maxblend impeller with experimental validations has been carried out with viscous Newtonian and non-Newtonian inelastic fluids. The mixing cases investigated were the non-baffled configuration with Newtonian and shear-thinning fluids, and the baffled configuration with only Newtonian fluids. The study focused on the effect of the impeller bottom clearance and the Reynolds number on the power characteristics, the distribution of shear rates and the overall flow conditions in the vessel. It was found that the bottom clearance plays a significant role on the power consumption, and that the value of the Reynolds number and the power law index strongly affect the axial pumping efficiency and the shear rate profile. The best performance was obtained when the impeller Reynolds number is superior to 10.

Factors affecting protein refolding yields in a fed‐batch and batch‐refolding system

The refolding of recombinant protein from inclusion bodies expressed in Escherichia coli can present a process bottleneck. Yields at industrially relevant concentrations are restricted by aggregation of protein upon dilution of the denatured form. This article studies the effect of five factors upon the dilution refolding of protein in a twin impeller fed-batch system using refold buffer containing only the oxidized form of the redox reagent. Such a buffer is easier to prepare and more stable than a buffer containing both reduced and oxidized forms. The five factors chosen were: bulk impeller Reynolds number, mini-impeller Reynolds number, injection rate of denatured protein, redox ratio, and guanidine hydrochloride (GdHCl) concentration. A 2(5) factorial experiment was conducted at an industrially relevant protein concentration using lysozyme as the test system. The study identified that in the system used, the guanidine hydrochloride concentration, redox ratio, and injection rate were the most important factors in determining refolding yields. Two interactions were found to be important: redox ratio/guanidine hydrochloride concentration and guanidine hydrochloride concentration/injection rate. Conditions were also found at which high refolding yields could be achieved even with rapid injection and poor mixing efficiency. Therefore, a comparative assessment was carried out with minimal mixing in a simple batch-refolding mode of operation, which revealed different behavior to that of fed-batch. A graphical (windows of operation) analysis of the batch data suggested that optimal yields and productivity are obtained at high guanidine hydrochloride concentrations (1.2 M) and redox ratios of unity or greater.

Momentum transfer in an agitated vessel with off-centred impellers

AbstractMomentum transfer was investigated in an unbaffled agitated vessel of inner diameter 0.3 m equipped with different off-centred impellers. The distribution of the shear rate on the tank wall as a function of the impeller type and Reynolds number was studied in the turbulent regime of the Newtonian liquid flow. The dependences of the averaged dimensionless shear rate, friction coefficient, and dissipated energy on the Reynolds number and eccentricity ratio were approximated using four-parameter equations.

Force Effects of the Macro-Instability of Flow Pattern on Radial Baffles in a Stirred Vessel With Pitched-Blade and Rushton Turbine Impellers

Experimental data obtained in a flat-bottomed cylindrical mixing vessel stirred with pitched blade impellers (four or six blades) or with a Rushton turbine impeller by measuring the tangential force affecting radial baffles are analysed. The presence of the macro-instability (MI) related component of the force was detected by spectral analysis of measured data. A single MI-related component occurring with a frequency of about 0.07 4N (N is the impeller speed) was detected for the pitched blade impellers. Two distinct frequencies, both directly proportional to the impeller speed, were detected for the Rushton turbine impeller: a lower frequency of approximately 0.025N and a higher frequency of about 0.085N. The upper frequency occurred only at low ReM values. The lower frequency component occurred over the entire ReM range. The dimensionless frequencies were independent of the stirring speed, the vertical position along the baffle, the number of impeller blades, and liquid viscosity. The relative magnitude (KMI) of the MI-related component of the total force was evaluated by a combination of proper orthogonal decomposition (POD) and spectral analysis of experimental time series. The magnitude kMI varied in the interval from approximately 0.2 to 0.5. The dependence of the kMI on the impeller Reynolds number, the vertical position in the vessel, the number of impeller blades, the impeller off-bottom clearance and liquid properties is discussed.

Residence Time Distributions in a Stirred Tank: Comparison of CFD Predictions with Experiment

Residence time distributions (RTD) are measured for both a baffled and an unbaffled laboratory reactor of the same size with several internal pipes and a Rushton turbine operating at different feed flow rates and impeller rpms. Ideal behavior as determined by the mean and the variance of the RTD was observed at an impeller Reynolds number of 2327 for the baffled tank and 3878 for the unbaffled tank both in the turbulent transition range. The experimental results for the baffled tank are compared to computational fluid dynamics (CFD) predictions of the RTD using the k−e turbulence model in Fluent for transitional flow regime in the tank, i.e., impeller Reynolds number between 10 and 10 000. All the qualitative aspects of the predicted RTDs are similar to those measured experimentally. The mean residence times as well as the variances of the residence time are accurately predicted by CFD in the transition flow regime.

Reynolds number and impeller diameter effects on instabilities in stirred vessels

AbstractFlow instability phenomena in stirred vessels were studied with laser anemometry and flow visualization. The effects of fluid density and viscosity, impeller Reynolds number (Re), impeller design, diameter, and off‐bottom clearance were investigated in order to quantify the frequencies (f) of the macroinstabilities stemming from precessional motions. The instabilities are characterized by two frequencies, one present at low Re, and another at high Re values. For intermediate Re values, both frequencies were present. In all cases, f was proportional to the impeller speed (N). The parameter f′ = f/N was shown to be linearly related to the impeller diameter in the low Re range; f′ was not affected by impeller clearance. At constant Re, a change in fluid density and viscosity did not affect f′. The energy contained in the instability frequencies was shown to vary across the vessel. The implications of the results mixing practice are discussed. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2050–2063, 2004

On the Direct Measurement of Turbulence Energy Dissipation in Stirred Vessels with PIV

The mean flow and turbulence fields and the turbulence energy dissipation rate (ε) in a vessel stirred by a hydrofoil impeller were studied using particle image velocimetry (PIV). The vessel diameter was 100 mm, and it was stirred by an impeller of diameter D = T/3. The impeller Reynolds number was 40 000 to ensure fully turbulent flow in the vessel. Particular attention was paid to the effect of spatial resolution on the estimation of ε, which was determined directly from its definition, i.e., by measuring the instantaneous spatial gradients of the Reynolds stresses. The data provide new information on the quantification and distribution of ε in stirred vessels and indicate that estimates of dissipation based on a constant length scale across the vessel and the distribution of the turbulence levels may underestimate the maximum and overestimate the minimum levels of ε present in a stirred vessel.

Frequency and Magnitude Analysis of the Macro-instability Related Component of the Tangential Force Affecting Radial Baffles in a Stirred Vessel

Experimental data obtained by measuring the tangential component of force affecting radial baffles in a flat-bottomed cylindrical mixing vessel stirred with pitched blade impellers is analysed. The maximum mean tangential force is detected at the vessel bottom. The mean force value increases somewhat with decreasing impeller off-bottom clearance and is noticeably affected by the number of impeller blades. Spectral analysis of the experimental data clearly demonstrated the presence of its macro-instability (MI) related low-frequency component embedded in the total force at all values of impeller Reynolds number. The dimensionless frequency of the occurrence of the MI force component is independent of stirring speed, position along the baffle, number of impeller blades and liquid viscosity. Its mean value is about 0.074. The relative magnitude (QMI) of the MI-related component of the total force is evaluated by a combination of proper orthogonal decomposition (POD) and spectral analysis. Relative magnitude QMI was analysed in dependence on the frequency of the impeller revolution, the axial position of the measuring point in the vessel, the number of impeller blades, the impeller off-bottom clearance, and liquid viscosity. Higher values of QMI are observed at higher impeller off-bottom clearance height and (generally) QMI decreases slightly with increasing impeller speed. The QMI value decreases in the direction from vessel bottom to liquid level. No evident difference was observed between 4 blade and 6 blade impellers. Liquid viscosity has only a marginal impact on the QMI value.

Dissolution of Finely Ground Limestone Particles in Acidic Solutions

Batch dissolution of fine limestone particles in HCl solutions was studied in a baffled tank reactor stirred with a Rushton turbine using a pH-drift technique. The effects of both acid strength and stirring rate were analyzed by varying the initial pH in the range of 3.7−5 and the impeller Reynolds number in the range of 104−105. The main experimental result is that, after a very fast step that leads to a quick rise of the solution pH, the dissolution rate is strongly affected by CO2 gas−liquid mass transfer, the intensity of which depends on the rate of stirring. A diffusional model based on film theory was used to analyze the data. The model confirmed that, for the operating conditions considered, a very short time is necessary for the first step of the dissolution process to take place. Furthermore, by taking into account the two limiting cases of the absence of CO2 gas−liquid transport and of infinitely fast transport, it was possible to identify lower and upper bounds for the experimental Ca2+ concentration.

Flow of Viscous Shear-Thinning Fluids Behind Cooling Coil Banks in Large Reactors

Through the use of a laminar flow loop, an ultrasound pulsed doppler device was found to accurately (±5%) measure the velocity of a viscous, opaque fluid (Xanthan Gum solution), using the entrained air (moving with the liquid) as energy reflectors. This technique was then utilized to measure the axial velocity of Xanthan Gum solutions behind cooling coil banks in two large (300 and 20 000 gal) fermentors, agitated by multiple down-pumping A315 impellers. The results indicate that, at both scales, the fluid in the annular region behind the cooling coil banks becomes completely stagnant at moderate to low agitation power (3.7 HP/1000 gal) when air is not sparged into the tank. Stagnant flow was observed at all airflow rates ≥0.1 vvm. A computational fluid dynamics (Fluent) model predicted reasonably well the actual liquid flow rate in the annular region behind the coil bank(s) of both tanks for the cases when air was not sparged. The results from an experimental design, using this Fluent model for the 20 000 gal tank, indicate that the axial velocity in the annulus is linearly related to the impeller Reynolds number (500−2000), D/T (0.36−0.48) and the cooling coil bank location relative to the tank wall (B/T: 0.06−0.09) and the tank bottom (Ob/D: 0.45−0.90).

Boundary-shear velocities and fluxes in the MEERC experimental ecosystems

Diffusion to solid-water interfaces is directly related to shear velocity. Shear velocities at the walls and bottoms of experimental ecosystem enclosures of different sizes and shapes (the Mul- tiscale Experiment Ecosystem Research Center pelagic/benthic (MEERC P/B) tanks at the University of Maryland Center for Environmental Science, Horn Point Laboratory) were measured using hot- film sensors. Spatially averaged bottom and wall shear velocities were related to internal mixing, which was produced by rotating internal paddles and measured using a combination of gypsum dis- solution and direct turbulence measurements. Shear velocities always increased with increasing mix- ing, but relationships between mixing and shear velocity changed with tank volume and shape. Spa- tially averaged bottom shear velocities decreased with increasing tank volume at an internal mixing level of 2 cm s -1 , but average wall shear velocities were similar for most tanks. In contrast, the rate of increase in bottom shear velocity with increasing mixing was similar for most tanks, but the rate of increase in wall shear velocity with increasing mixing was lower for the larger tanks. A bulk impeller Reynolds number captured some, but not all, of the scale dependence of ratios of boundary shear velocity to internal mixing intensity; mixing design and tank geometry were also important. Levels of all shear velocities in the MEERC P/B tanks were lower than levels in natural coastal environments for equivalent internal mixing. Realistic levels of internal mixing in the tanks resulted in unrealisti- cally low boundary shear velocities. As a result, wall diffusive sublayer thicknesses were similar to those found in deep-sea environments, and benthic diffusive sublayer thicknesses were even larger. Most current mesocosm designs are likely to be affected similarly. The artificially low-energy benthic environment may have particularly important consequences for ecosystem processes affected by pelagic-benthic coupling.

Average Shear Rates in the Rapid Visco Analyser (RVA) Mixing System

ABSTRACTThe principle of mixer viscometry was utilized to determine the average shear rate in the mixing system (impeller‐cup combination) of the Rapid Visco Analyser (RVA). A relationship between the impeller Reynolds number and the power number was established with Newtonian standards. Using the matching viscosity technique and non‐Newtonian fluids consisting of various aqueous solutions of guar gum and methylcellulose, the average value of the mixer viscometer constant (k′) was 20.1/rev over speeds of 1.0–3.5 rev/sec (60–210 rpm). Hence, the average shear rate in the RVA can be estimated as 20.1 multiplied by the angular velocity given in revolutions per second. Results show the RVA system has very good potential for characterizing the rheological properties of various non‐Newtonian fluid foods.

Electrostatic charge generation during impeller mixing of used transformer oil

The purpose of this study was to examine the effects of varying conductivity and turbulent impeller mixing intensity on charge generation of used Shell Diala ® transformer oil. The oil was mechanically agitated by a pitched six-bladed impeller in a 1.5 quart fully baffled cylindrical vessel at impeller Reynolds numbers between 5 000 and 10 000. The electrical current generated from the mixing operation was measured on the wall of the mixing tank and also in the internal vapor space on a 1 cm 2 target disk positioned approximately 1.5″ above the free liquid surface. Fluid electrical conductivity was varied using different concentrations of two types of commercially available antistatic additives (Shell ASA-3 and DuPont Stadis 450). A generalized dimensional analysis performed by using the Buckingham Pi theorem showed that a dependent dimensionless group, π 1, which contains the measured wall current and other fluid dynamic and electrical variables was found to be dependent on six independent groups. Four of these groups were related to modified Reynolds numbers based on impeller diameter and width, and tank diameter and fluid depth or tank height. The two remaining independent groups were related to the mass transfer Schmidt number and the impeller rotational speed. The mean particle diameter from a Malvern ZetaSizer and π 1 were plotted versus fluid conductivity to investigate the functional dependence of these parameters. The dimensionless group π 1 was also plotted for different impeller Reynolds numbers. These different plots show results that appear to illustrate inverse dependencies. The current versus conductivity data for different impeller Reynolds numbers also show similar behavior to published data for both laminar and turbulent flow through capillaries (i.e., current first increases with increasing conductivity, hits a maximum and then decreases with further increases in conductivity). This apparently demonstrates that a single charge transport mechanism is responsible for the behavior in two different charge-generation situations for different geometrical conditions.