Cylindrical Mixing Vessel Research Articles

Correlation of Power Consumption in a Cylindrical Mixing Vessel with a Spherical Bottom

Correlation of Power Consumption in a Cylindrical Mixing Vessel with a Spherical Bottom

Analysis of particle cloud height dynamics in a stirred tank

Local and temporal variations of the particle cloud formed in a cylindrical mixing vessel were investigated experimentally. Different particle sizes (0.5, 1, and 2 mm) and volumetric concentration up to 20 vol % were evaluated at different impeller speeds. The time‐averaged cloud height was linear with impeller frequency and with volume concentration. Suspensions with larger particles had a lower average cloud height, while the standard deviation for the temporal cloud height variation was larger. Two strong periodic phenomena were identified to be dominating the particle cloud height variations. The frequencies were linear with impeller speed, resulting in dimensionless frequencies of S1=0.02–0.03 and S2=0.05–0.06. The frequencies were affected by neither the particle size nor the volumetric concentration. The amplitude showed no dependency on the particle size, but the S2 amplitude significantly decreases and S1 increases with increasing solid concentration. The results were compared to LES/discrete element method simulations and showed a fair agreement. © 2015 American Institute of Chemical Engineers AIChE J, 62: 338–348, 2016

Using Tomography to Characterize the Mixing of Non‐Newtonian Fluids with a Maxblend Impeller

AbstractThe flow field inside a cylindrical mixing vessel was visualized by electrical resistance tomography (ERT), a non‐intrusive measurement technique. Six tomography planes, each containing 16 sensing electrodes, measured the mixing time in the agitation of pseudoplastic fluid exhibiting yield stress. The effects of various parameters such as impeller types, impeller speed, fluid rheology, power consumption, Reynolds number, and absence of baffles on the mixing time were investigated. The Maxblend impeller was able to improve the mixing performance of non‐Newtonian fluids in a batch reactor. The mixing quality could be further enhanced by decreasing the xanthan gum concentration and using baffles in the mixing vessel.

Modeling Erosion Wear Rates in Slurry Flotation Cells

In processes using slurry as the working fluid, wear due to solid particles impinging on elements of the process units is a serious reliability issue. This study considers modeling wear damage in flotation cells, which are widely used in mineral processing. Flotation cells are typically cylindrical vessels where an impeller is used to agitate the fluid, enabling the liberation of the minerals from the slurry. Some solids, particularly those entrained in the impeller stream, can impact on the wall of the cell, leading to material loss and eventually to loss of structural integrity. The problem of predicting the remaining life of the unit due to erosion requires understanding of various sub-processes: flow modeling, particle–fluid interaction, energy interactions at the surface, and the mechanism of erosion itself. In this study, empirically developed equations for the flow field of cylindrical mixing vessel with a Rushton turbine are used in formulating a model relating and the damage accumulation rate to a simple set of measurable variables. To validate a model, a PIV technique was used to measure velocities in the flow field and near the wall on a physical model of the cell with transparent walls and particles that match the refractive index of the fluid. An Eulerian–Langrangian approach has been used to determine the particle trajectories and the effect of a squeeze film is incorporated into the model to modify the velocity distribution of particles prior to impacts. An analytical model based on equations of impulse and momentum for a particle of any shape striking a flat massive surface has been used to describe the energy lost at the walls. Finally, a damage model is developed that takes into account impact velocity, attack angle, properties of the impinging particles and the surface. This model is verified against a second physical model that measures material loss rate at different locations within the cell.

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.

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.

Large Eddy Simulations of a Brine-Mixing Tank

Abstract Traditionally, solid–liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing, and contacting related to power draw. One important application of solid–liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as in the Barents Sea. In this paper large-eddy simulations, of a turbulent flow in a solid–liquid, baffled, cylindrical mixing vessel with a large number of solid particles, are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the sliding mesh. The simulations are four-way coupled, which implies that both solid–liquid and solid–solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.

Computer simulations of sodium formate solution in a mixing tank

Traditionally, solid–liquid mixing has always been regarded as an empirical technology with many aspects of mixing, dispersing and contacting were related to power draw. One important application of solid–liquid mixing is the preparation of brine from sodium formate. This material has been widely used as a drilling and completion fluid in challenging environments such as the Barents Sea. In this paper, large-eddy simulations of a turbulent flow in a solid–liquid baffled cylindrical mixing vessel with large number of solid particles are performed to obtain insight into the fundamental aspects of a mixing tank. The impeller-induced flow at the blade tip radius is modeled by using the dynamic-mesh Lagrangian method. The simulations are four-way coupled, which implies that both solid–liquid and solid–solid interactions are taken into account. By employing a soft particle approach the normal and tangential forces are calculated acting on a particle due to viscoelastic contacts with other neighboring particles. The results show that the granulated form of sodium formate may provide a mixture that allows faster and easier preparation of formate brine in a mixing tank. In addition it is found that exceeding a critical size for grains phenomena, such as caking, can be prevented. The obtained numerical results suggest that by choosing appropriate parameters a mixture can be produced that remains free-flowing no matter how long it is stored before use.

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.

The Tangential Force Affecting the Radial Baffles in a Stirred Vessel: Analysis of the Macro-instability Related Component

Experimental data obtained by measuring the tangential component of the force affecting radial baffles in a flat-bottomed cylindrical mixing vessel stirred with a Rushton turbine impeller is analysed. Spectral analysis of the experimental data demonstrated the presence of its macro-instability (MI) related low-frequency component embedded in the total force. Two distinct dimensionless frequencies (both directly proportional to the impeller speed of rotation N) of the occurence of the MI component were detected: a lower frequency of approximately 0.025N and a higher frequency of about 0.085N. The relative magnitude QMI of the MI-related component of the total tangential force was evaluated by a combination of proper orthogonal decomposition (POD) and spectral analysis. The values of magnitude QMI varied in the interval [rom approximately 0.05 to 0.30. The magnitude QMI takes maximum values at low Reynolds number values (in laminar and transitional regions). In the turbulent region (ReM >20000) the QMI value is low and practically constant. The dependence oj the QMI values on vertical position in the vessel is only marginal. The results suggest that the magnitude of the MI component of the force is significantly influenced by the liquid viscosity and density.

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.

Dynamic Effect of Discharge Flow of a Rushton Turbine Impeller on a Radial Baffle

This paper presents an analysis of the mutual dynamic relation between the impeller discharge flow of a standard Rushton turbine impeller and a standard radial baffle at the wall of a cylindrical mixing vessel under turbulent regime of flow of an agitated liquid. A portion of the torsional moment of the baffle corresponding to the region of the force interaction of the impeller discharge stream and the baffle is calculated under the assumption of constant angular momentum in the flow region between the impeller and the baffles. This theoretically obtained quantity is compared with the torsional moment of the baffles calculated from the experimentally determined distribution of the peripheral (tangential) component of dynamic pressure along the height of the radial baffle in pilot plant mixing equipment. It follows from the results of our calculations that for both investigated impeller off-bottom clearances the theoretically determined transferred torsional moment of the baffles in the area of interference between the impeller discharge flow and the baffles agrees fairly well with experimentally determined data and, moreover, that more than 2/3 of the transferred torsional moment of the baffles as a whole is located in the above mentioned interference area.

Improved Characterization of Mixing for Sludge Conditioning

The dewatering characteristics of polymer conditioned sludges are examined for sludge-conditioning regimes effected by agitation in a baffled, cylindrical mixing vessel using different impellers operated at constant values of \iG¯ and constant mixing time. Dewatering characteristics are evaluated by different laboratory tests, characterizing sludge filterability, settleability, and drainability. Only one type of sludge and polymer was applied for the conditioning experiments. The experimental results suggest that \iG¯ is deficient as the only descriptor of the impact of turbulent mixing intensity on sludge-conditioning performance. Based on the results, it is questioned whether laboratory-scale sludge conditioning performed by impeller agitation in a baffled, cylindrical mixing vessel is comparable to the pipe-flow conditioning taking place at many full-scale sludge-dewatering installations. It is suggested that a more appropriate characterization of mixing regimes for sludge conditioning should take into account how the applied power for mixing is converted into steady flow and turbulent shear, respectively, and which of these conditions is more important at a particular mixing time and polymer dosage. The three parameters: (1) Mixing intensity; (2) mixing time; and (3) polymer dosage need to all be properly accounted for in order to evaluate sludge-conditioning performance.

軸方向ジェットノズルを備えた混合槽内での熱伝達係数及び混合時間

Heat transfer coefficient and mixing time were measured in an axial-jet mixing vessel equipped with a single or combined nozzle of various diameters.The equivalent nozzle diameter de for such a nozzle was defined asde = {(1/2)(4/π)2(pQ3/P)}1/4where Q and P are total jet flow rate and total power input, respectively. The equivalent nozzle diameter was usable for the correlation of heat transfer coefficient and mixing time for the combined jet nozzle.The heat transfer coefficient measured was well correlated with nozzle Reynolds number Ren (≡uedeρ/μ) by using the equivalent nozzle diameter, ashD/κ = 0.27(uedeρ/μ)3/4Pr0.4(μ/μw)0.144.2 × 103 Ren 4The mixing time measured was well correlated with the nozzle Reynolds number, based on the correlation method of Hiby et al. The minimum dimensionless mixing time was obtained at Ren = 1.0 × 104–1.3 × 104, and its value satisfied the correlation equation proposed in our previous paper.

Interdiffusion of gases in cylindrical mixing vessels

A qualitative experimental study has been carried out for the interdiffusion of bromine and air in a cylindrical mixing vessel. A time for complete mixing was derived from the appropriate integral form of Fick's equation, which may be compared to the Einstein equation for linear diffusion in an infinite vessel. Tabulated values for diffusion times in several gases emphasise the importance of allowing sufficient time for mixing prior to gas-phase kinetic studies.

Analytical Studies on the Flow Patterns of Liquid in a Cylindrical Mixing Vessel

Analytical studies were attempted to make clear the flow patterns of the liquid in the cylindrical mixing vessel without baffles, as the experimental results had already been obtained as shown in the previous reports.We could not well explain the details of the liquid flow patterns in the vessel by means of the so-called “Rankine's combined vortex” model (Refer to Fig. 1 and Eq.(1)). Therefore, we studied three important factors contributing to the momentum transfer in the agitated liquid; i.e., the liquid viscosity, the displacement of the liquid by the agitating impeller and the secondary circulation flow which is induced by the discharge flow from the tips of the impeller blades.In the range where Reynolds number was very small, the momentum transfer due to the viscosity effect was found to be predominant, so that the analytical results, obtained upon the assumption that the effects of the two factors other than the liquid viscosity are negligible, had a tendency to show good agreement with the experimental data on the tangential velocity distribution of the liquid in the vessel, as shown in Figs. 4 and 5.On the other hand, in the turbulent flow range where Reynolds number was very large, the secondary circulation flow had considerably important effects on the liquid flow pattern. Considering its contribution to the momentum transfer (Refer to Fig. 6), Eqs.(10) and (13) were analytically derived to express the tangential velocity distribution of the agitated liquid. The comparisons between the experimental data and the calculated results by these equations are shown in Fig. 8. They show good agreement.Furthermore, there were obtained data on the distributions of the turbulent kinematic viscosity and the static pressure in the vessel, as shown in Figs. 9 and 10, respectively.These results are considered to show the utility of the analysis.

Analytical Studies on the Mechanism of Energy Consumption in the Liquid in a Mixing Vessel

Energy balance and energy consumption in an agitating system, consisting of cylindrical mixing vessel and an impeller, are analyzed in this report, as the flow patterns of agitated liquid were made clear in the previous studies.In the first place, based upon the results of the calculation of the energy balance on the cylindrical boundary surface, where the impeller is placed as shown in Fig. 1, it is made clear that the agitating energy loss is greatest in the liquid near the impeller (refer to Table 1).Then, the mechanisms of the energy consumption in the agitated liquid are examined.According to the analytical consideration, the energy consumption in the liquid inside the impeller is caused mainly by the head loss due to abrupt change in the liquid velocity and that outside the impeller, by the energy dissipation due to the turbulent viscosity, under non-baffled condition. However, under fully-baffled condition, the head loss due to the abrupt change in the liquid velocity prevails everywhere in the agitated liquid (refer to Table 2).Furthermore, the general considerations are made on the energy consumption in a simplified model, which shows the flow patterns in the vessel as the combination of so-called compound vortex flow and vertical circulation flow, as given in Fig. 5.In short, it is emphasized in this report that both the liquid-circulating capacity and the turbulencegenerating ability of an impeller are important factors in the performance of an agitator.

Studies on the Flow Patterns of Liquid, in the Cylindrical Mixing Vessel, for the Lamnar and Transitional Flow Range

The flow patterns of agitated liquid in the cylindrical mixing vessel without baffles were measured by the photographic method. for the range extending from the laminar to the so-called transitional flow region.As the authors have already made clear the flow patterns of liquid and the discharging performance of impellers, for the turbulent flow range1), they are now able to discuss these over the wide range of Reynolds Number.Some of the experimental results are shown in Figs. 4, 5 and 6.The results revealed by the authors on the distribution of liquid velocity are as follows:In the range where Reynolds Number is very small, the liquid velocity is considerably high in the neighborhood of the impeller, which, however, rapidly decreases as the distance from the impeller increases. On the other hand, in the range where Reynolds Number is big, the liquid velocity is kept high by the transmission of the momentum, even in a place far from the impeller, since the secondary circulation flow occurs as shown in Fig. 6 (c) and the liquid flow becomes turbulent, keeping the velocity distribution nearly uniform throughout the vessel.Of the discharge flow from the tip of the impeller blades, which causes the secondary circulation, the non-dimensional quantities, Nq1 and NP/Nq1, are defined as in the previous report1). These values have been calculated and the characteristic curves of discharging performance obtained for various types of impellers (Cf. Table 1), as shown in Fig. 7.Furthermore, the relations among flow pattern, discharging performance and power consumption (NP-Re relation) are discussed.

Flow Patterns of Liquid in a Cylindrical Mixing Vessel without Baffles

The velocity distribution of agitated liquid in a cylindrical mixing vessel was measured, using a set of pitot tubes, the composition of which is shown in Fig. 2. Some of the experimental results are shown in Figs. 4, 5, 6 and 8.As a result, the flow patterns in an agitated vessel were made clear and it was ascertained that, besides the primary circulation flow around the agitator axis, there was a secondary circulation of liquid caused by the discharging flow from the tip of the impeller as shown in Figs. 7 and 9. Integrating the measured velocity distributions, the discharging flow rates of the impellers were determined and the discharging performances of various impellers (Cf. Table 1) were compared, relative to the power consumption. Dimensionless factor, Nq1, defined by the author, was called the coefficient of discharge. The ratio, NP/Nq1 in Table 3, shows the relative power required for performing unit quantity of dis-charge.Furthermore, the power consumed in the neighbourhood of the impeller (NPimp), that is in the cylindrical domain (Cf. hatched region in Fig. 9), was calculated and compared with that consumed in the outer region of the vessel as shown in Table 4.From these considerations it is concluded that the improvement in the discharging capacity can be accomplished, to a certain extent, by a properly designed impeller, though we shall have to resort to some other devices for more fundamental improvements.

Flow Patterns of Liquid in a Cylindrical Mixing Vessel with Baffles

Flow Patterns of Liquid in a Cylindrical Mixing Vessel with Baffles