Momentum transfer in an agitated vessel with off-centred impellers

Momentum 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. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

CFD simulation of floating particles suspension in a stirred tank

Computational fluid dynamics (CFD) simulations were performed to predict the floating particles suspension in a baffled tank stirred by a standard Rushton turbine. An Eulerian multiphase model and a standard k-ε turbulence model with mixture properties were used in the CFD simulation. The impeller rotation was solved using a moving reference frame method. Flow pattern, power number and solid holdup distribution were obtained and compared with the results in literature. The effects of operating condition on floating particles suspension characteristics were studied. It indicated that the influences of impeller speed and solid loading on particle suspension varied with particle sizes. For small particles, the impeller speed and solid loading have no obvious effects on solid holdup distribution and suspension quality. For large particles, particle suspension quality becomes better first, and then keeps almost unchanged with enhancing of the impeller speed. Suspension quality is better for higher solid loading of large particles. Within the scope of the present study, solid loading has no great effect on suspension quality. Suspension quality becomes worse with increasing of the particle size. Large particles are easy to accumulate in the centres of the liquid free surface and the upper circular loop, and the vicinity of the shaft.     

Transport phenomena in an agitated vessel with an eccentrically located impeller

The paper presents results of an experimental analysis of the transport phenomena at the vicinity of the wall of an unbaffled agitated vessel with an eccentrically located impeller. Distributions of the transport coefficients were experimentally studied using an electrochemical method within the turbulent regime of the Newtonian liquid flow. Measurements were carried out in an agitated vessel with the inner diameter T = 0.3 m. Liquid height in the vessel was equal to the inner diameter, H = T. The agitated vessel was equipped with a Rushton or a Smith turbine or an A 315 impeller. Eccentricity of the impeller shaft was varied from 0 to 0.53. Local values of the dimensionless shear rate, shear stress, dynamic velocity and friction coefficient were integrated numerically for the whole surface area of the cylindrical wall of the vessel. Averaged values of these quantities were correlated with the impeller eccentricity and modified Reynolds number. The proposed Eqs. (5)–(8), with the coefficients given in Table 2, have no equivalent in open literature concerning this subject. Distributions of the shear rate, γ/n, and friction coefficient, f, at the vicinity of the cylindrical wall of the unbaffled vessel equipped with eccentric Rushton or Smith turbine or A 315 impeller are very uneven and they depend significantly on the impeller eccentricity, e/R. Maximum local values of these variables are located on the wall section closest to the impeller blades. From among the tested impellers, the greatest effects of the impeller eccentricity, e/R, and the liquid turbulence (described by the modified Reynolds number Re _P,M) on the averaged dimensionless shear rate (γ/n)_m and friction coefficient, f _m, are found for the radial-flow Rushton turbine located eccentrically in an unbaffled agitated vessel.     

Modelling the flow of liquid in continuous dialyzer

The paper deals with the modelling of the flow of liquid in a compartment of continuous dialyzer. Two simple models, the dispersion model and tanks-in-series model, were used. Their parameters Peclet number, the mean residence time of liquid in dialyzer compartment, the number of tanks and the mean residence time of liquid in each tank were determined from a nonideal step input of a tracer and its response. It has been found that in the range of the Reynolds number from 0.44 to 3.64, the Peclet number and the number of tanks are in the range from about 200 to 320 and from 100 to 310, respectively. Both these parameters and the mean residence time of liquid in the compartment of dialyzer and in each tank decrease with the increasing Reynolds number. Furthermore, it has been proved that the values of the mean residence time of liquid in the compartment of dialyzer calculated from the dispersion model agree well with those calculated from the tanks-in-series model. The obtained values of the Peclet number and the number of tanks indicate that the flow in the dialyzer does not significantly differ from the plug flow.     

A new model of cavern diameter based on a validated CFD study on stirring of a highly shear-thinning fluid

Results of numerical simulations of momentum transfer for a highly shear-thinning fluid (0.2% Carbopol) in a stirred tank equipped with a Prochem Maxflo T type impeller are presented. The simulation results were validated using LDA data and both tangential and axial force measurements in the laminar and early transitional flow range. A good agreement between the predicted and experimental results of the local fluid velocity components was found. From the predicted and experimental values of both tangential and axial forces, the power number, Po, and thrust number, Th, were also calculated. Values of the absolute relative deviations were below 4.0 and 10.5%, respectively, for Po and Th, which confirms a satisfactory agreement with experiments. An intensive mixing zone, known as cavern, was observed near the impeller. In this zone, the local values of fluid velocity, strain rate, Metzner–Otto coefficient, shear stress and intensity of energy dissipation were all characterized by strong variability. Based on the results of experimental study a new model using non-dimensional impeller force number was proposed to predict the cavern diameter. Comparative numerical simulations were also carried out for a Newtonian fluid (water) and their results were similarly well verified using LDA measurements, as well as experimental power number values.     

Experimental and numerical investigation of pressure drop coefficient and static pressure difference in a tangential inlet cyclone separator

The aim of this study was to investigate the pressure drop coefficient and the static pressure difference related to the natural vortex length and to evaluate the results for gas-particle applications. CFD simulations were carried out using a numerical technique which had been verified previously. Results obtained from the numerical simulations were compared with the experimental data. Analysis of the results showed that the pressure drop coefficient decreases with the increasing inlet velocity, becoming almost constant above a certain value of the inlet velocity. The reason is that the effect of viscous forces decreases at high Reynolds numbers. The pressure drop coefficient also decreases with the increasing exit pipe diameter and decreasing exit pipe length.     

Scale-adaptive simulation of liquid mixing in an agitated vessel equipped with eccentric HE 3 impeller

The current study presents the results of a numerical simulation of hydrodynamics in an agitated vessel equipped with an eccentric HE 3 impeller. CFD (computational fluid dynamics) simulations were carried out using ANSYS 14.0 software. Time-dependent simulations of turbulent flow were carried out using the SAS-SST (scale adaptive simulation-shear stress transport) method coupled with the SM (sliding mesh) method. The results of the calculations are presented as contours of velocity in different cross-sections of the agitated vessel, as well as profiles of components of velocity vector and turbulence kinetic energy and its dissipation rate. The iso-surface of vorticity, which shows the region of possible vortex existence, is also presented. A numerically obtained data set of impeller power number was used to calculate the averaged impeller power number. This value was compared with the experimental data with good results. The relationship between impeller position and fluctuation of the impeller power number was also analysed.     

LES and URANS modelling of turbulent liquid-liquid flow in a static mixer: Turbulent kinetic energy and turbulence dissipation rate

The present study deals with numerical simulations of turbulent flow of a liquid-liquid system in a Kenics static mixer with ten inserts. CFD approach was used in two modes: large eddy simulation (LES) and unsteady Reynolds averaged Navier-Stokes (URANS). Large eddy simulation in the static mixer was carried out using the dynamic kinetic energy subgrid-scale model with standard wall functions whereas in URANS approach the standard k-ɛ turbulent model and standard wall functions were applied. Two-phase flow was modelled employing the “mixture model” of the Eulerian type. The simulations were performed mainly for the Reynolds number of 10000 with the volumetric ratio of 99 % of water to 1 % of oil. The investigations revealed that due to distinct distributions of the turbulence measures, the drop breakup process occurs with varying intensity in different locations within the mixer inserts. Significantly higher local values of the dissipation rate, ɛ, were predicted in URANS than in LES. However, both modelling methods indicated high values of ɛ at the beginning and the end of the mixer inserts, which implies the maximum shearing action exerted on the drops. Consequently, the inflow and outflow zone of each insert are the regions of the highest breakup intensity.     

Mixing time of a non-Newtonian liquid in an unbaffled agitated vessel with an eccentric propeller

Experimental study of mixing time of non-Newtonian shear-thinning fluids within the transitional regime (3 × 10² < Re < 3 × 10³) of liquid flow is presented. The purpose of this study was to analyze the effect of eccentricity and pumping mode of the impeller as well as of position of the tracer dosage point into the agitated liquid on mixing time. The measurements were conducted in an unbaffled agitated vessel with inner diameter D = 0.7 m equipped with an up-or down-pumping propeller located centrically (e/R = 0) or eccentrically (e/R ≠ 0) in the vessel. Experiments were carried out by means of computer-aided unsteady-state thermal method for three positions of the tracer dosage point. The experimental data show that eccentric position of the propeller in an unbaffled vessel causes a decrease of the mixing time compared to that obtained in a vessel with a centrically located propeller. Mixing time depends also on the pumping mode of the propeller as well as on the position of the tracer dosage point. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Multiscale Modeling of Mixing Behavior in a 3D Atom Transfer Radical Copolymerization Stirred‐Tank Reactor

Multiscale mixing phenomena in stirred‐tank polymerization reactors are mainly caused by stir agitation, which performs a key function in macroscopic and microscopic flow fields. Both macroscopic and microscopic flow fields interact with each other and significantly affect the microstructure and product distribution of the resultant polymers. In this work, a computational fluid dynamics model combining the moment method used in the polymerization engineering field is implemented and validated using open data. Multiscale properties are characterized in terms of macroscopic mixing fields and the polymer microscopic structure of the atom transfer radical copolymerization system of methyl methacrylate and 2‐(trimethylsilyl) ethyl methacrylate. Agitation in a 3D stirred tank is also thoroughly studied by using the multiple reference frame approach, and the effects of several important para­meters, such as impeller speed, impeller types, and feeding position, on the macroscopic and microscopic flow fields are investigated on the basis of the validated model. Interdependent relationships among agitation, multiscale flow fields, and polymerization are described clearly. The results highlight the function of stirring and provide useful guidelines for the scale‐up of stirred‐tank polymerization reactors.

     

Diminishing vortex intensity and improving heat transfer by applying magnetic field on an injectable slip microchannel containing FMWNT/water nanofluid

In this study, heat transfer and entropy generation were investigated in a microchannel containing FMWNT/water nanofluids given the slip condition. The main focus was on utilizing injection technique in the presence of the magnetic field. The injection from the upper high-temperature wall was incorporated into the flow field. Injection at high Reynolds number causes vortex formation, which ultimately reduces local heat transfer in the adjacent injection zone. By applying the magnetic field, the vortex intensity as well as boundary layer thickness was diminished which in turn improved the heat transfer. Based on numerical results, at higher nanoparticle volume fraction, the effect of the magnetic field on heat transfer enhancement was amplified. Moreover, at higher Reynolds numbers, the magnetic field efficacy is more obvious. The highest heat transfer occurred at the highest values of the Hartmann and Reynolds numbers and eventually the nanoparticle volume fraction. Owing to applying the magnetic field on the injectable microchannel containing nanofluid, heat transfer improvement can reach up to 79%. From the second law prospective, the entropy generation intensified by 82.8%.

     

检索CAS化学物质数据库的必要性和方法

以ＤＩＡＬＯＧ系统为例,讨论了检索ＣＡＳ化学物质数据库的必要性和方法。     

Distribution of local heat transfer coefficient values in the wall region of an agitated vessel

Experimentally found local heat transfer coefficients are analyzed as a function of the measuring point on the heat transfer surface area of the agitated vessel wall and of the impeller eccentricity. Eccentric Rushton turbine and A 315 impeller are considered. Local heat transfer coefficients were measured by means of the computer-aided electrochemical method. The measurements were performed in an agitated vessel with inner diameter 0.3 m, filled with liquid up to the height equal to the vessel diameter. The experiments were carried out within the turbulent regime of the Newtonian liquid flow in the agitated vessel. The results were compared with the data obtained for the agitated vessel equipped with an eccentrically located axial flow propeller or an HE 3 impeller. Experimental studies show that the distributions of the heat transfer coefficient values depend on the impeller eccentricity, impeller type and the direction of the liquid circulation in the agitated vessel. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Dynamic Response Studies on Aggregation and Breakage Dynamics of Colloidal Dispersions in Stirred Tanks

Aggregation and breakage of aggregates of fully destabilized polystyrene latex particles in turbulent flow was studied experimentally in both batch and continuous stirred tanks using small‐angle static light scattering. It was found that the steady‐state values of the root‐mean‐square radius of gyration are fully reversible upon changes of stirring speed as well as solid volume fraction. Steady‐state values of the root‐mean‐square radius of gyration were decreasing with decreasing solid volume fraction as well as with increasing stirring speed. Moreover, it was found that the steady‐state structure and shape of the aggregates is not influenced by the applied stirring speed.     

Numerical study of two-dimensional multi-layer spacer designs for minimum drag and maximum mass transfer

Based on the insights gained from previous published works, a series of multi-layer spacer designs for use in spiral wound membrane modules are proposed and evaluated via computational fluid dynamics simulations. The filament diameter to channel height ratio of traditional cylindrical filaments is reduced from 0.6 to 0.4 and 0.3, and one or two layers of elliptical filaments with various attack angles are introduced in the middle region of the channel. The mass transport equations are solved in conjunction with the momentum and continuity equations for a solute with Schmidt number of 600, and the hydraulic Reynolds number is varied from 50 up to 800. Spacer performance is evaluated via a basic permeate processing cost analysis. The proposed designs did not lower processing costs when operating at hydraulic Reynolds numbers above 200, but showed potential for reducing costs in the steady laminar flow regime, at hydraulic Reynolds numbers equal to or less than 200. Implications for design improvements of spacer meshes, such as extra layers of spacer filaments to direct the bulk flow towards the membrane walls, and changes to the filament profiles to reduce form drag are discussed.     

Orientation of a dispersion of kaolinite flowing in a jet

Orientational alignment in a dilute dispersion of kaolinite particles has been investigated in a flow pattern that combines both shear and elongational stress, namely flow at a jet created by a 2 mm diameter nozzle inserted in a 6 mm diameter pipe. Spatially-resolved X-ray diffraction with synchrotron radiation permits detailed maps of the alignment to be deduced and compared with fluid mechanics calculations of the flow. The angular distribution of diffracted intensity from a given position in the pipe provides information about the orientation distribution of the particles. This is quantified and presented in terms of order parameters. The cone-shaped nozzle provides a jet of liquid giving a high degree of alignment of the particles that is uniform along lines across the conical section and constant in the small straight-sided region at the exit of the nozzle. The vortex motion that arises from the flow with a modest Reynolds number could be determined as well as the tendency for some particles to align with their large faces perpendicular to the overall flow direction at the flat surface of the nozzle outlet.     

Transition from creeping via viscous-inertial to turbulent flow in fixed beds

This review is concerned with the analysis of flow regimes in porous media, in particular, in fixed beds of spherical particles used as reactors in engineering applications, or as separation units in liquid chromatography. A transition from creeping via viscous-inertial to turbulent flow is discussed based on macro-scale transport behaviour with respect to the pressure drop-flow rate dependence, in particular, the deviation from Darcy's law, as well as direct microscopic data which reflect concomitant changes in the pore-level hydrodynamics. In contrast to the flow behaviour in straight pipes, the transition from laminar to turbulent flow in fixed particulate beds is not sharp, but proceeds gradually through a viscous-inertial flow regime. The onset of this steady, nonlinear regime and increasing role of inertial forces is macroscopically manifested in the failure of Darcy's law to describe flow through fixed beds at higher Reynolds numbers. While the physical reasons for this failure still are not completely understood, it is not caused by turbulence which occurs at Reynolds numbers about two orders of magnitude above those for which a deviation from Darcy's law is observed. Microscopic analysis shows that this steady, nonlinear flow regime is characterized by the development of an inertial core in the pore-level profile, i.e., at increasing Reynolds number velocity profiles in individual pores become flatter towards the center of the pores, while the velocity gradient increases close to the solid-liquid interface. Further, regions with local backflow and stationary eddies are demonstrated for the laminar flow regime in fixed beds. The onset of local fluctuations (end of laminar regime) is observed at superficial Reynolds numbers on the order of 100. Complementary analysis of hydrodynamic dispersion suggests that this unsteady flow accelerates lateral equilibration between different velocities in fixed beds which, in turn, reduces spreading in the longitudial (macroscopic flow) direction.     

Heat transfer in a jacketed agitated vessel equipped with multistage impellers

In this work, heat transfer via the cylindrical part of the jacket in an agitated vessel has been investigated. Heat transfer coefficients were determined using the transient method based on measuring the temperature dependency of the liquid batch on time. A multistage impeller made of two impellers was used in a cylindrical vessel with dished bottom. The lower impeller was a curved blade turbine with the diameter of d = 100 mm and the upper impeller was either a pitched three-blade or pitched four-blade impeller with the diameter of d₁ = 67 mm. Three different impeller clearances in a multistage configuration, H₃/d₁ = 1, 1.5, and 2, were used in our measurements. The vessel was equipped with two baffles. Experimental results were evaluated using the Euler’s method and nonlinear regression procedure in the Matlab® software and they are summarized in form of Nusselt number correlations describing their dependency on the Reynolds number.     

Comparative study between continuum and atomistic approaches of liquid flow through a finite length cylindrical nanopore

Steady state pressure driven flow of liquid argon through a finite length cylindrical nanopore was investigated numerically by classical Navier-Stokes (NS) hydrodynamic models and nonequilibrium molecular dynamics (MD) simulations. In both approaches, the nanopore was nominally 2.2 nm in diameter and 6 nm long. For the MD simulations, the intermolecular properties of the walls were specified independently from the liquid. Comparisons between the approaches were made in terms of the gross feature of total flow rate through the nanopore, as well as the more refined considerations of the spatial distributions of pressure, density, and velocity. The results showed that for the NS equations to predict the same trends in total flow rate with increasing pressure difference as the MD simulation, submodels for variations in density and viscosity with pressure are needed to be included. The classical NS boundary conditions quantitatively agreed with the flow rate predictions from MD simulations only under the condition of having a neutral-like solid-liquid interaction. Under these conditions, the NS and MD models also agreed well in streamwise distributions of pressure, density, and velocity, but not in the radial direction.     

Scale-up of the necessary power input in stirred vessels with suspensions

One of the most essential problems in dealing with solid-liquid suspensions in stirred vessels is the determination of a reliable scale-up rule from small stirred tanks to large vessels on an industrial production scale. According to a new approach based on physical modelling of the complex fluid dynamics, the necessary power input in stirred suspensions can be calculated as a sum of the circulation power and the sinking power of a particle swarm. The following results, which are compared with a great variety of experimental data in the literature, reveal that there is no simple and constant scale-up rule applicable to describe the power input for a large range of suspension properties, tank size, geometrical conditions or comparable suspension criteria.