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This work gives a rheological study of the flow structure generated by an anchor agitator completely submerged in a cylindrical tank with a flat bottom. To better understand the phenomenon of the fluid mechanics that takes place in the agitated medium, several geometric configurations of anchor have been realized. The investigation of the flow generated was made by using the CFX.12 calculation code, which provides a very good visualization of the phenomenon of fluid mechanics. The results obtained from our work can be very supportive to the existing similar models in the literature, which can mature the knowledge and understanding of researchers on the behaviors of various anchor impellers. [ABSTRACT FROM AUTHOR]

Stirred mixers are ubiquitous in industrial applications, operating optimally to achieve homogeneous mixing of liquids, gases, and solids. Improving mixer performance is critical for attaining high efficiency, low production costs, and high product quality. This review examines three key aspects of mixer optimization: power consumption, mixing time, and impeller geometry. The research aims to summarize a comprehensive review on mixing time and the experimental devices used to measure it. The effect of using impellers and changing their geometry on the power consumption, mixing efficiency, and mixing time. Power usage is a vital metric for evaluating mixer efficiency. Complex interplay between impeller design, operating conditions, and fluid properties governs energy consumption. Understanding and minimizing power requirements are essential for efficient, sustainable mixing operations. Mixing time also significantly impacts efficiency, relating directly to impeller geometry and fluid rheology. Reviewing research on mixing time highlights opportunities to reduce durations, boosting productivity. Impeller geometry, governing mixer design for target applications, represents another major optimization variable. Impeller selection plays a major role in stirred tanks, especially in chemical processing. Elucidating relationships between fluid dynamics and impeller configurations is thus necessary for developing effective, economical mixing solutions. [ABSTRACT FROM AUTHOR]

Present research study analyses the suitability of baffled reactor vessels with large diameter agitated using the Rushton Turbine (RT) impeller maintained at standard clearance condition for the solid-liquid suspension process. The mean and turbulent flow fields associated with reactor vessels of various diameter were simulated using Computational Fluid Dynamics (CFD) approach. The impeller rotation was modelled using Multiple Reference Frame (MRF) technique and entrainment of air was simulated using Volume of Fluid (VOF) method respectively. The increase in the diameter of reactor vessel keeping impeller at standard clearance condition lead to the transition from double to single loop pattern with considerable decrease in the power number. In large reactor vessels, a low pressure zone is developed below the impeller which deflects the discharge streams and trailing vortices towards bottom surface of the reactor vessel causing the formation of single loop down-pumping pattern. The downward propagation of trailing vortices weaken the flow separation region behind the impeller blades which in turn decreases the form drag and power number of the impeller. The development of single loop down-pumping pattern, high magnitudes of axial velocity, vortex and turbulence fields near vessel bottom and inferior entrainment of air makes the large reactor vessels suitable for the solid-liquid suspension process. The high magnitudes of axial velocity developed below the impeller of large reactor vessel with same power consumption as compared to low clearance vessel makes the former vessel configuration more suitable for the solid-liquid suspension process. [ABSTRACT FROM AUTHOR]

Present research study analyses the suitability of baffled reactor vessels with large diameter agitated using the Rushton Turbine (RT) impeller maintained at standard clearance condition for the solid-liquid suspension process. The mean and turbulent flow fields associated with reactor vessels of various diameter were simulated using Computational Fluid Dynamics (CFD) approach. The impeller rotation was modelled using Multiple Reference Frame (MRF) technique and entrainment of air was simulated using Volume of Fluid (VOF) method respectively. The increase in the diameter of reactor vessel keeping impeller at standard clearance condition lead to the transition from double to single loop pattern with considerable decrease in the power number. In large reactor vessels, a low pressure zone is developed below the impeller which deflects the discharge streams and trailing vortices towards bottom surface of the reactor vessel causing the formation of single loop down-pumping pattern. The downward propagation of trailing vortices weaken the flow separation region behind the impeller blades which in turn decreases the form drag and power number of the impeller. The development of single loop down-pumping pattern, high magnitudes of axial velocity, vortex and turbulence fields near vessel bottom and inferior entrainment of air makes the large reactor vessels suitable for the solid-liquid suspension process. The high magnitudes of axial velocity developed below the impeller of large reactor vessel with same power consumption as compared to low clearance vessel makes the former vessel configuration more suitable for the solid-liquid suspension process.

Although mixing in stirred tanks is common in the chemical and process industry, it is complex and not fully understood. In recent years, computational fluid dynamics (CFD) simulations with large eddy simulation turbulence models have become an important modeling tool. In this study, its current state for applicability to stirred tanks was evaluated. First, the power characteristics of different impellers were simulated and compared with experimental data. Second, Rushton and pitched blade turbines were validated in terms of the local velocity components, dissipation rates, and the trailing vortex. Finally, mixing times for different viscosity ratios were obtained from the CFD results and compared with a literature study. Hydrodynamics can be well predicted. However, mixing times for viscosity ratios larger than 1:100 are error‐prone. [ABSTRACT FROM AUTHOR]

Stirred tanks are often used in industrial applications to store and process liquids and solids. However, these systems have become an increasing challenge to improve and optimize these processes. Computational Fluids Dynamics (CFD) simulation predicts complex phenomena as hydrodynamics system performance. An optimal solution is found using an effective mesh scheme and selecting appropriate boundary conditions. This work aims to validate and describe the distribution velocities inside the tank using a rigorous turbulence model. Stirred tank with a diameter of 27 cm and an oval cone tip using a Rushton impeller (radial impeller) and a 4-blade impeller inclined at 45° (axial impeller) are performed. For both cases, hydrodynamics in the bottom tank is analyzed. In addition, the power and the pumping numbers for each impeller are studied. The overall results show that at the tip of the oval cone, the asymmetry in the mesh is improved, and the divergence in the solution is avoided. Also, the cone designer increased the turbulent kinetic energy, which can enhance the mixture process. A decrease in power impeller is shown when the axial type is applied at low Reynolds numbers; however, when the cone is introduced inside the tank and a radial impeller type is used, the impeller power values are increased. The overall results of CFD simulation are compared to experimental data and provide similar values with an absolute deviation below 4.46 %.

Stirred tanks are often used in industrial applications to store and process liquids and solids. However, these systems have become an increasing challenge to improve and optimize these processes. Computational Fluids Dynamics (CFD) simulation predicts complex phenomena as hydrodynamics system performance. An optimal solution is found using an effective mesh scheme and selecting appropriate boundary conditions. This work aims to validate and describe the distribution velocities inside the tank using a rigorous turbulence model. Stirred tank with a diameter of 27 cm and an oval cone tip using a Rushton impeller (radial impeller) and a 4-blade impeller inclined at 45° (axial impeller) are performed. For both cases, hydrodynamics in the bottom tank is analyzed. In addition, the power and the pumping numbers for each impeller are studied. The overall results show that at the tip of the oval cone, the asymmetry in the mesh is improved, and the divergence in the solution is avoided. Also, the cone designer increased the turbulent kinetic energy, which can enhance the mixture process. A decrease in power impeller is shown when the axial type is applied at low Reynolds numbers; however, when the cone is introduced inside the tank and a radial impeller type is used, the impeller power values are increased. The overall results of CFD simulation are compared to experimental data and provide similar values with an absolute deviation below 4.46 %. [ABSTRACT FROM AUTHOR]

Computational Fluid Dynamics (CFD) is a tool frequently used for the optimization and improvement of industrial processes. In this work, the CFD simulation is used for analyzing the appropriate power in stirred-tank systems with three different types of cones at the bottom of the tank and with two types of impellers: 45° pitch 4- bladed turbine (axial impeller) and Rushton standard turbine (radial impeller). The simulation was carried out in a stirred tank with a diameter of 27 cm and with different cone diameters and height ratios are analyzed. Also, 4 rotation speeds (50, 100, 300, and 600 rpm) were evaluated to describe the transition to turbulent states. Reynolds Stress Model (RSM) and the Moving Reference Frame are used. The results show that the power decrease with the axial impeller when this is operated at low Reynolds number values meanwhile the radial impeller presented an increase in the values of power when the cone is introduced inside the tank. By increasing the Reynolds number an exponential increase in the power volume of each impeller is made. Also, the inclusion of a 4-impeller blade inclination between laminar and transition shows a significant saving in power consumption and for turbulent regimes, the inclusion of geometries in the bottom of the tank affects power consumption. Finally, the results are validated using experimental data and show that the absolute deviations are below 4 %. [ABSTRACT FROM AUTHOR]

Conventional large agricultural machinery or implements are unsafe and unsuitable to operate on slopes >6∘ $\gt {6}^{\circ }$ or 10%. Tractor rollovers are frequent on slopes, precluding farming on arable hills, uneven or highly sloped land. Therefore, a fleet of autonomous ground vehicles (AGV) is proposed to cultivate highly sloped land (>6∘ $\gt {6}^{\circ }$). The fleet aims to expand agricultural land to the slopes and to strengths the human‐robot collaboration in an unsafe sloped environment. However, the fleet's success largely depends on vehicle behavior models regarding traction, mobility, and energy consumption on varying slopes. The vehicle intelligent behavior models are essential and would solve multiple objectives ranging from simulations to path planning & navigation. Therefore, this study aimed to build a deep learning‐based vehicle behavior models on sloping terrain. A standard drawbar test was performed on a single AGV operating on an actual sloped field at varying speeds and load conditions. The drawbar test quantified the AGV's behavior on slopes in metrics related to traction (traction efficiency), mobility (travel reduction), and energy consumption (power number). Deep learning‐based models were developed from the experimental data to predict the AGV's behavior on slopes as a function of vehicle velocity, drawbar, and slope. A special model called the proposed model, which combined multiple deep neural networks with a mixture of Gaussians, was developed and trained with a hybrid training method. The proposed model consistently outperformed the other well‐known machine learning models. This study explored the capabilities of machine learning algorithms to simulate the behavior of small‐track vehicle or AGV on sloping terrain. The fleet aims to provide safer agriculture keeping human safety in focus, and the developed predictive vehicle behavior models would empower the fleet's operation on currently unsafe sloped terrain by assisting in vehicle path planning, route optimization, and decision making. [ABSTRACT FROM AUTHOR]

This paper presents new results for the dynamic behaviour of fluid around a rotating turbulator in a channel. The turbulator has a propeller form which is placed inside a flat channel. The research was carried out using 3D numerical simulation. The rationale of the experiment was as follows: we put a propeller-turbulator inside a flat channel, and then we insert a water flow inside the channel. The turbulator rotates at a constant and uniform speed. The main points studied here are the effect of the presence of turbulator and its rotational direction on the flow behaviour behind the turbulator. The results showed that the behaviour of flow behind the turbulator is mainly related to the direction of turbulator rotating. Also, the studied parameters affect coefficients of drag force and power number. For example, when the turbulator rotates in the positive direction, the drag coefficient decreases in terms of rotational speed of the turbulator, while the drag coefficient increases in terms of rotational speed when the turbulator rotates in the negative direction. [ABSTRACT FROM AUTHOR]

The mixing of granular materials in an agitated drum can be characterized by the dimensionless power equation. The equation was created by dimensional analysis, for which the parameters affecting the mixing power requirement were collected based on the literature. The most important of these are the rotational speed, the drum loading factor, the geometric and physical properties of the mixing drum and the granular materials. The dimensionless power equation is used to estimate with reasonable accuracy the Power number within the given range of applicability (0.48 1 𝑠 ≤ 𝑛 ≤ 1.58 1 𝑠; 10% ≤ 𝑙 ≤ 25%), which has been validated by measurements. From the Power number, the mixing power requirement of the mixed granular material can be calculated, which can be used as operational data for selecting the mixing motor. [ABSTRACT FROM AUTHOR]

Double- to single-loop pattern transition and a significant reduction in the power number with a decrease in the clearance of the Rushton turbine impeller in a baffled reactor was elucidated in earlier research works. The present work investigates the physical reasons behind these phenomena using the computational fluid dynamics approach. The Reynolds Averaged Navier–Stokes equations with standard turbulence model closure were used to model the turbulent flow conditions in the reactor vessels. The Multiple Reference Frame (MRF) approach was adopted to model the impeller baffle interactions in the reactor vessels. The implicit Volume of Fluid (VOF) method was employed to simulate the aeration process in the reactor configurations considered. The development of a low pressure region below the impeller of a low clearance vessel deflects the discharge streams downward, leading to the formation of a single-loop pattern. The downward movement of the discharge streams reduces the vortex activity behind the impeller blades, leading to weaker form drag and a decrease in the power number of the impeller. Similarly, a high clearance vessel provides a low pressure region above the impeller which deflects the discharge streams above the impeller, resulting in a single-loop pattern and a considerable increase in the air entrainment due to superior vortex and turbulence activity present near the free liquid surface. The standard reactor vessel was found to provide superior bulk mixing of fluid as the overall turbulent dissipation rate is 35% more than that associated with low and high clearance vessels.

The mixing of granular materials in an agitated drum can be characterized by the dimensionless power equation. The equation was created by dimensional analysis, for which the parameters affecting the mixing power requirement were collected based on the literature. The most important of these are the rotational speed, the drum loading factor, the geometric and physical properties of the mixing drum and the granular materials. The dimensionless power equation is used to estimate with reasonable accuracy the Power number within the given range of applicability , which has been validated by measurements. From the Power number, the mixing power requirement of the mixed granular material can be calculated, which can be used as operational data for selecting the mixing motor.

The purpose of this investigation was to develop an initial set of Power number versus Reynolds number results for a family of vertical‐wheel bioreactors. These bioreactors are increasingly being used for the manufacture of cells for cell therapy but have not been characterized according to this approach. A novel gravimetric method to measure power was used, and the validity of this method was assessed by measuring power for a standard stirred tank bioreactor with a Rushton impeller. The results of the gravimetric method were found to closely match those derived from traditional methods. The validated method was then used to measure the power draw and develop an initial set of Power number versus Reynolds number results for a family of vertical‐wheel bioreactors. [ABSTRACT FROM AUTHOR]

Power draw characteristics and scale-up procedures for high-speed sawtooth impellers were introduced by investigating various production sizes, fluids, impellers, and scale-up criteria to obtain the same product properties between different scales. The relationship between dimensionless Power number, Reynolds number, and Froude numbers were found for each impeller type at transitional flow regimes. The effect of Froude number was found to be very little, even though there was a deep vortex formation and no baffles in the mixing tank. Metzner – Otto constant which gives the relationship between rotational speed and shear rate was found as 20.7 and 12.4 for sawtooth impeller with big and small teeth, respectively. Productions were made by equalizing tip speed, shear rate, and power per volume between the commercial production and laboratory scales. In the result of rheological behavior measurement, stability test, and optical color evaluation, it was observed that the equal tip speed method gives a more intense dispersion in smaller batch sizes while the power per volume and shear rate method results in an insufficient particle size reduction performance. [Display omitted] • Scale up for saw tooth impellers used in mixing of non-Newtonian paint products was studied. • Type of fluid and production batch size has no significant effect on dimensionless relation of N P vs. Re and Fr. • Similar Metzner – Otto constants between different rotational speeds and batch sizes were observed. • Calculation procedures for different scale up methods are covered. • Equal tip speed is the closest scale up approach for high shear mixing of paint product. [ABSTRACT FROM AUTHOR]

This paper is concerned with the rotational motion of the impeller and the thermal buoyancy within a mechanical mixer. The task was investigated numerically using the ANSYS-CFX simulator. The programmer is based on the finite volume method to solve the differential equations of fluid motion and heat transfer. The impeller has hot surfaces while the vessel has cold walls. The rotational movement of the impeller was controlled by the Reynolds number, while the intensity of the thermal buoyancy effect was controlled by the Richardson number. The equations were solved for a steady flow. After analyzing the results of this research, we were able to conclude that there is no effect of the values of Richardson number on the power number. Also, with the presence of the thermal buoyancy effect, the quality of the fluid mixing becomes more important. The increasing Richardson number increases the value of the Nusselt number of the impeller. [ABSTRACT FROM AUTHOR]

• Stirring paddles with high Ls / S values have more potential for energy savings. • The number of blades has little effect on the power characteristics of stirring paddles with high Ls / S values. • Higher velocity flow field obtained by spiral stirring paddles. Stirred reactors are widely used in various industries, and the stirring paddle structure has a significant effect on its power consumption. Therefore, in this study, different spiral stirring paddles were investigated. The effects of the ratio of paddle length to leads (Ls / S) design values and number of blades on the power characteristics and internal flow field of the reactor are discussed in detail, and the correlation equation of power number (Np) concerning Re and Ls / S values is fitted. It was found that the Np of stirring paddles increased and then decreased as the Ls / S value increased, and the effect of the number of blades on the Np gradually reduced. When the Ls / S value is equal to 0.6, the high-speed region of the flow field is the largest and the mixing effect is the best. The conclusions obtained can provide a reference for the energy-saving optimal design of spiral stirring paddles. [ABSTRACT FROM AUTHOR]

Double- to single-loop pattern transition and a significant reduction in the power number with a decrease in the clearance of the Rushton turbine impeller in a baffled reactor was elucidated in earlier research works. The present work investigates the physical reasons behind these phenomena using the computational fluid dynamics approach. The Reynolds Averaged Navier-Stokes equations with standard 𝑘 - 𝜀 turbulence model closure were used to model the turbulent flow conditions in the reactor vessels. The Multiple Reference Frame (MRF) approach was adopted to model the impeller baffle interactions in the reactor vessels. The implicit Volume of Fluid (VOF) method was employed to simulate the aeration process in the reactor configurations considered. The development of a low pressure region below the impeller of a low clearance vessel deflects the discharge streams downward, leading to the formation of a single-loop pattern. The downward movement of the discharge streams reduces the vortex activity behind the impeller blades, leading to weaker form drag and a decrease in the power number of the impeller. Similarly, a high clearance vessel provides a low pressure region above the impeller which deflects the discharge streams above the impeller, resulting in a single-loop pattern and a considerable increase in the air entrainment due to superior vortex and turbulence activity present near the free liquid surface. The standard reactor vessel was found to provide superior bulk mixing of fluid as the overall turbulent dissipation rate is 35% more than that associated with low and high clearance vessels. [ABSTRACT FROM AUTHOR]

The coagulation treatment for the removal of turbidity from tannery industry wastewater using the coagulant protein in Moringa oleifera seeds was investigated in this research work. The natural coagulant was prepared from the seed powder using NaCl and KCl salt solutions each having a concentration of 0.25 M. The effect of coagulant dosage and initial pH on % turbidity removal was investigated for both coagulants. A higher turbidity removal efficiency of 74.11% was achieved with NaCl extracted coagulant at an optimum coagulant dosage of 30 mL and initial pH 9, whereas the coagulant prepared by KCl salt solution exhibited a lower treatment efficiency of 68.52%. The maximum and minimum velocity gradients attained was 1098.8 s−1 at 31 °C and 257 s−1 at 25 °C, respectively. The least residual turbidity was achieved at 440 rpm impeller speed. The relationship between power function and Reynolds number (Re) for unbaffled tank shows that transition zone develops between 30,500 < Re < 56,000. The residual turbidity concentration decreases with increase in settling velocity for different coagulant dosages. The turbidity removal process follows the second-order kinetics model with a rate constant of 0.000158 (mg/500 mL)−1 min−1. The variation of coagulation rate constant with temperature was supported by Arrhenius law (R2 = 0.9645) rather than Transition state theory (R2 = 0.96) and Collision theory (R2 = 0.9624). The exponential decay of concentration ratio with time indicates that Smoluchowski rate equation explains the growth of floc particles governed by fluid motion. This study reveals the successive and optimistic influence of coagulant dose, pH, mixing dynamics, settling mechanism and coagulation rate on turbidity removal from tannery wastewater. [ABSTRACT FROM AUTHOR]

[Display omitted] • Use of Volume of Fluid (VOF) method to model free surface dynamics in UUSTs. • Comprehensive assessment of suitable turbulence models for unbaffled stirred tank analysis. • Study of effects of impeller speed on vortex shape and aeration at different viscosities. • Prediction of Power Number (Np) and vortex shape in non-aerated and aerated conditions. • Prediction of cavities near the impeller blades in super-critical regime. The transition between non-aerated and aerated regimes in uncovered unbaffled stirred tanks (UUSTs) was investigated using computational fluid dynamics (CFD). The Volume of Fluid (VOF) method was employed to model the free surface dynamics under various operational conditions. The simulations were able to predict the peculiar experimentally observed behavior of UUSTs and revealed that at velocities below a critical threshold (N_ < _N crit) , the system remains non-aerated, while exceeding this threshold (N_ ≥ _N crit) induces bubble ingestion, leading to significant changes in power consumption and flow patterns. The CFD simulations accurately predicted the behaviour of the Power Number (Np) as well as the vortex shape inside the tank both in subcritical and supercritical regimes and showed good agreement with original experimental data and correlations from the literature. Additionally, the modeling of the aerated regime successfully predicted the vortex shape, the bubble dispersion within the tank, and the cavities formed behind the blades. [ABSTRACT FROM AUTHOR]

Stirred tank reactors are one of the crucial equipments in the chemical, biochemical, pharmaceutical, and food industries. The design of mechanically agitated vessels contains two main tasks: to find appropriate geometry of the system (such as vessel shape, impeller types, and others) and to choose suitable driving force that would supply required power input for operational conditions reach. The ungassed power input prediction is necessary for the effective industrial design of the engine. The ungassed power input depends on many variables such as tank geometry, used impeller type, and properties of the batch. This work focuses on the influence of the batch composition, impeller type, and impeller diameter on ungassed power consumption. Experiments were performed in laboratory and pilot plant scale vessels while using various operational conditions (such as impeller type, impeller diameter, batch viscosity, and others). Due to a wide range of operational conditions, the obtained results could be transferable to other systems with similar geometry up to industrial conditions. [ABSTRACT FROM AUTHOR]

A comprehensive CFD study was conducted to understand the hydrodynamics characteristics in a top-covered unbaffled stirred tank. The turbulent flow in the tank was described by the Reynolds stress turbulence (RST) model, and the impeller rotation was simulated using a single reference frame (SRF) approach. The flow field and power number in the tank stirred by a Rushton turbine were investigated firstly. It is found that circumferential flow is dominant in the unabffled tank, and the flow field can be divided into forced and free vortex zones. A weak two-loop flow pattern forms in the vertical plane, and would evolve into one single-loop when impeller was equipped very close to the bottom of the tank. In general, impeller off-bottom clearance and blade thickness have small effects on flow field in the unbaffled tank. With increasing of rotational speed, the dimensionless liquid velocity rises, especially near the critical radius of two zones. Critical radius is larger for larger impeller, while the variation range of critical radius to impeller diameter ratio is narrow. The effects of operational and geometric parameters on impeller power number (Np) in unbafffled tank are far different from those in baffled tank. In the unbaffled stirred tank, rotational speed, blade thickness and impeller off-bottom clearance have small effects on power number, while impeller diameter has a significant effect on power number. Under the same operating condition, the larger the impeller diameter, the smaller the power number is. Finally, the hydrodynamics characteristics in the tank stirred by four common impellers were investigated and compared. [ABSTRACT FROM AUTHOR]

The mixing/agitation of time independent non-Newtonian fluids can be a challenge in many technological processes. In the present study, the influence of rheological parameters, K and n, on Reynolds number, power number and power consumption, for different concentration of carboxymethyl cellulose (CMC) solutions, 1%, 2%, 3%, 4 % and 5%, with shear-thinning behaviour, was analysed. The power consumption obtained by theoretical model and by an appropriate curve Po = f(Re) from experimental data, found in literature, was compared. The results have shown good agreement between calculated power number and the graphically determined values, and also minimal power consumption values comparable with those founded for the agitation of non-Newtonian liquids. [ABSTRACT FROM AUTHOR]

In this study, the effect of height/diameter (H/D) ratio and type of impeller on the power consumption of the agitator in the Continuous Stirred Tank Reactor (CSTR) was analyzed. CSTR in the process of producing nitrocellulose from cotton linters with a production capacity of 10,000 tons/year was used as a case study. In designing a CSTR, power consumption is also considered because it is related to techno-economics. The results show that it is necessary to adjust the amount of impeller related to the H/D ratio value because it can affect the level of liquid in the reactor during the stirring process so that it also affects the reaction conversion. This work shows that with the higher H/D ratio, the greater number of impellers needed and increase the agitator power consumption. For specific applications, the number of impellers (NT) must be increased to meet the minimum power consumption. As the result, this work recommends the optimal H/D ratio for CSTR design is the maximum H/D ratio to get the NT-calculation as close as to the NT-taken while satisfying the minimum power consumption required. The optimal H/D ratio can be different depending on the impeller type and application. [ABSTRACT FROM AUTHOR]

Although single‐hole oscillatory columns have been studied since the 1990s, to this day there is an absence of appropriate dimensionless groups to express the hydrodynamic conditions and power requirement for the moving‐baffle oscillatory baffled column (OBC). This paper uses computational fluid dynamic (CFD) software coupled with moving overset meshing to aid in the derivation of the first dimensionless oscillatory power number for OBCs. In terms of the moving‐baffle OBC, this work marks the first time a power density equation has been derived specifically to account for this column's unique hydrodynamic profile. Equations for period‐averaged Reynolds number and period‐averaged Strouhal numbers were developed to better estimate the fluid intensity within these moving‐baffle columns. This work serves as an example of how complex and challenging flow regimes, such as periodically oscillating flow, can be simplified and analyzed to produce appropriate design equations. [ABSTRACT FROM AUTHOR]

• Flow varies between rows of holes in rotor-stator mixers. • Models to predict both power and flow numbers in rotor-stator mixers are proposed. • Proposed models work for various designs of mixing head. • Rotor-stator gap does not have a significant impact on power and flow. The relationship between power and flow characteristics of batch rotor-stator mixers has been studied using CFD simulations with experimental power validation. The mixer studied was the Silverson L5M batch mixer with the standard emulsor head. The size of the holes in the screen and the constriction of the base hole were changed in small increments. The MRF technique was used to model rotor rotation. A model is developed in this study which links the power and flow numbers of the mixer. Since power is easy to measure experimentally, one can use this model to predict the flow number by measuring torque. A second model is also developed which allows one to predict the flow number using solely the geometry of the mixing head. This study greatly enhances our understanding of the relationship between power, flow and mixer geometry in rotor-stator mixers. [ABSTRACT FROM AUTHOR]

A computational fluid dynamics (CFD) simulation was performed to study the hydrodynamics characteristics in a Rushton turbine stirred tank in laminar regime. The effects of operating condition, working medium and geometrical parameter on the flow field and power number characteristics were investigated. It is found that the two-loop flow pattern is formed in laminar regime when the impeller is not very close to tank bottom, while its shape and size vary with Reynolds number and impeller diameter. For a given geometrical configuration, the flow pattern, power number and dimensionless velocity profile are mainly depended on Reynolds number, and do not change with working medium and scale-up for a constant Reynolds number. When impeller off-bottom clearance is too low and Reynolds number is relatively high, the fluid flow would transit from two-loop flow pattern to sing-loop flow pattern as that occurs in turbulent regime. Power number falls for larger impeller in laminar regime. Surprisingly, in laminar regime, power number in the baffled tank with small impeller is almost identical to that in the unbaffled tank. [ABSTRACT FROM AUTHOR]

• Batch and in-line rotor-stators share the same power characterisation. • Pipe flow in In-line rotor-stators is not the true flow through the mixing head. • Stators with larger holes exhibit more recirculation. • Recirculating flow can be modelled using the pipe flow and stator geometry. Rotor-stator mixers are used in many industries to perform emulsification and de-agglomeration processes. Despite previous research, different modes of operation have not been compared in terms of flow and power characteristics. The aim of this study was to use CFD to investigate power and flow characteristics of a Silverson L5M mixer operating in batch and in-line mode. MRF was used along with the standard k - ∊ turbulence model for the simulations. Results suggest that batch mixers can be characterised in the same was as in-line mixers, and for a given mixing head design, the characterisation is independent of the mode of operation. A new way of the calculating flow number is proposed, which explains some discrepant results from previous studies. Overall, this work enhances our understanding of rotor-stator mixers and allows for better design choices of mixer. [ABSTRACT FROM AUTHOR]

Highlights • Flow promoters reduced concentration polarization and improved ion transport. • COMSOL simulations served as a preliminary tool for optimizing spacer geometry. • Helical screw promotes swirling motion in axial direction performed better. • Ion conducting spacers reduced shadow effect during ion transport. Abstract Citric acid transport facilitation in electrodialysis was investigated using different flow promoter geometries e.g. rod, twisted tape (TT), rectangular winglet (RW) shape vortex generator (VG) and helical screws at four different flow rates 5, 10, 15 and 20 LPH. Flow visualization of 39 promoters (shape, spacing and orientation) were performed using 3D simulation (COMSOL Multiphysics® 5.3a). Based on simulation results, 14 best promoters were selected for experimental determination of ion transport and power consumption from Sherwood number, Sh and Power number, Pn respectively. With increase in flow rate and reduced spacing, Sh increased along with Pn. Mesh type TT performed better than mono layer TT but pressure drop increased. Screw promoter placed parallel to flow showed higher Sh and Pn compared to rod, VG and TT. 50% rise in Sh was noted with helical screw (d/h = 1.33, α = 90°) relative to empty channel. 1.5 times rise in LCDs were noted with conducting TT compared to non-conducting TTs with barely 1.5% increase in Pn. LCDs with conducting TTs were 80% higher compared to empty channel. [ABSTRACT FROM AUTHOR]

Oil produced from secondary and tertiary processes is mostly in the form of oil in water emulsions, which is an inherent characteristic of the extraction process itself. An attempt to optimize the factors contributing to the cost of transporting such mixtures from the fields to the processing facilities, seems to be very useful and cost effective. In this work, a thorough investigation of the factors influencing the rheology and transportation of emulsions in circular ducts such as temperature, volume fraction, flow driving pressure and surfactants concentration, is performed using a special Lattice Boltzmann model. A dimensionless power number ratio is presented and used for the assessment of the best practices leading to a more efficient emulsions transportation system. [ABSTRACT FROM AUTHOR]

Numerical simulations were carried out to investigate the turbulent flow with free-surface vortex in an uncovered unbaffled stirred tank. An Eulerian-Eulerian multiphase flow model coupled with a volume-of fluid method was applied to capture the gas-liquid interface and describe the flow field in the tank. Turbulence is computed using a Reynolds stress model with seven equations. The reliability and accuracy of the simulations are verified by comparing the predicted free surface profiles and power numbers with experimental data in the literature. The overall agreements between the simulation results and experimental measurements are obtained. The simulation results show that vortex on the liquid free surface in the uncovered unbaffled tank can be divided into central zone and peripheral zone, and the critical radius of the two zones keeps almost unchanged with enhancing of impeller speeds. At the same impeller speed, vortex becomes deeper and larger with increasing of impeller diameter. However, vortex shape changes not very much with increasing of impeller diameter under the same power consumption. Impeller clearance has no significant influence on the vortex shape. Circumferential flow is dominant in the uncovered unbaffled tank, and the flow field can be divided into forced vortex region and free vortex region. Power numbers in uncovered unbaffled stirred tanks decrease slightly with increasing of the Reynolds number, and are far lower than that in baffled stirred tanks. [ABSTRACT FROM AUTHOR]

Rotor–stator mixers are characterized by a set of rotors moving at high speed surrounded closely by a set of stationary stators which produces high local energy dissipation. Rotor–stator mixers are therefore widely used in the process industries including the manufacture of many food, cosmetic and health care products, fine chemicals, and pharmaceuticals. This paper presents data demonstrating scale-up rules for the key power parameters; laminar power constant, Metzner–Otto constant, and Turbulent power number; for Silverson Batch rotor–stator mixers. Part 2 of this paper explores mixing times, surface aeration, and equilibrium drop sizes. These rules will allow processes involving rotor–stator mixers to be scaled up from around 1 l to over 600 l directly. [ABSTRACT FROM AUTHOR]

Unbaffled stirred tanks are increasingly recognized as a viable alternative to common baffled tanks for a number of processes and bio-processes where the presence of baffles is undesirable. Notwithstanding the increasing industrial interest towards unbaffled tanks, available experimental information on their behaviour is still very poor, even for important parameters such as mechanical power drawn and critical impeller speed ( N cr ) at which the transition between non-aerated ( sub-critical regime) and aerated ( super-critical regime) conditions occurs. In this work the influence of Reynolds and Froude numbers on power consumption characteristics of unbaffled stirred tanks is presented for tanks operating both in non-aerated ( sub-critical regime) and aerated ( super-critical) conditions. Influence of scale-up, impeller to tank size, liquid height aspect-ratio and presence or not of a top-cover is investigated in order to provide a general correlation able to assess (i) the critical rotational speed N cr and (ii) the power number N p under any fluid dynamic regime. Experimental results obtained show that the proposed general correlation is fully validated when scaling-up the system. Moreover, the variation of geometrical features such as impeller to tank size, liquid aspect ratio and the presence or not of a top-cover do not modify the functional dependencies of power number on Re and Fr and only different (dimensionless) multiplying shape factors must be adopted. Finally, an overall general correlation for critical rotational speed ( N cr ) assessment is also proposed. [ABSTRACT FROM AUTHOR]

This paper presents the study of the behavior of a stirred tank with hydrofoil impeller, used to mix water with polymetallic particles in the mining industry, through numerical simulation with CFD software. The mixture has an average density of 1.623 kg / m³ and an apparent viscosity of 0.065 kg / m-s, and was modeled as a non-newtonian homogeneous liquid. The homogeneous Euler-Euler model for free surface biphasic flow in steady state is solved in the simulation, using the k-ε turbulence model. The power curve, which correlates the power number (Np) with the Reynolds number (Re), was obtained from the torque curve of the impeller versus its angular velocity between 200 and 700 rpm. It was found that Np asymptotically converges to 0.32 in turbulent regime, a value that is in agreement with experimental results obtained in the present study and those available in the literature. [ABSTRACT FROM AUTHOR]

The determination of the power number as a design parameter is strongly dependent on geometrical conditions. Due to the internal interactions, spacing between impellers is crucial - especially for axial pumping impellers. Furthermore, different baffle geometries influence the power consumption of the impellers. This paper shows a systematic evaluation of an axial multi-impeller system. By varying the baffle configuration, a characterization of the power input as well as the homogenization performance was obtained. [ABSTRACT FROM AUTHOR]

Previous wind-tunnel measurements have shown that fractal-shaped plates have increased drag compared to square plates of the same area. In this study, the power consumption and drag of turbines with fractal and rectangular blades in a stirred tank are measured. Power number decreases from rectangular to fractal impellers by over 10%, increasingly so with fractal iteration number. Our results suggest that this decrease is not caused by the wake interaction of the blades, nor solely by the wake interaction with the walls either. Pressure measurements on the blades' surface show that fractal blades have lower drag than the rectangular ones, opposite to the wind tunnel experiment results. All tested blades' center of pressure radius increases with Re, while their drag coefficient decreases, a possible effect of the solid body rotation expansion with Re. Spectral analysis of the pressure signal reveals two peaks possibly connected to the blades' roll vortices. © 2016 American Institute of Chemical Engineers AIChE J, 63: 843-854, 2017 [ABSTRACT FROM AUTHOR]

Powder agitation experiments in a bladed planetary mixer have been performed with the objective of establishing correlations based on dimensionless numbers. Powders of different kind have been studied: free flowing (semolina) and cohesive (lactose, talc and milled sand). Mixtures of free flowing and cohesive powders have also been studied to get a more complete range of powders of different properties. It has been observed that the gyration motion plays an important role in the power consumption of cohesive powders. The relation between a modified power number ( N pM = P / ρ b u ch 3 d s 2 ) and a modified Froude number ( Fr M = u ch 2 / gd s ) used in several previous publications is adapted and shown to depend on powder cohesion. These dimensionless numbers are built on the basis of a characteristic speed u ch , a characteristic length d s , the bulk density ρ b and the power consumption P . The filling ratio f is also taken in account. For a free flowing powder, of cohesion smaller than 0.3 kPa, N pM = a ( f ) · F rM − 1 while for a more cohesive powder, of cohesion higher than 0.6 kPa the correlation N pM = 6 · F rM b ( f ) is more appropriate. For both equations, a and b are powder-dependent parameters. Their linear dependency on the filling ratio of the blender has been established. [ABSTRACT FROM AUTHOR]