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.     

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.     

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.     

Heat transfer coefficients in an agitated vessel using vertical tube baffles

Heat transfer coefficients for vertical tube baffles in an agitated vessel have been investigated in model vessels of three different dimensions. A modified Reynolds number has been introduced into the heat transfer equation which contains the product dn representating the fluid velocity at the tube baffle and the external tube diameter d_o. This Reynolds number is suitable for the correlation of experimental data for tube baffles of different geometrical proportions. Experiments have been carried out with Newtonian liquids.     

Power consumption for an agitated vessel equipped with pitched blade turbine and short baffles

Power characteristics for an agitated vessel equipped with planar short baffles of length L and pitched blade turbine of pitch β are presented in the paper. The studies were carried out in the vessel of inner diameter D = 0.6 m, where the baffles were located in the distance p from the vessel bottom (p + L = H). Torque was measured using strain gauge method within the turbulent regime of the flow of Newtonian liquid in the agitated vessel. The effects of the pitch β and geometrical parameter p/H on the power number Ne were determined mathematically. The results showed that, for the assumed value of the angle β, the function Ne = f (L/H) decreases with the decrease in the baffle length L (i.e. with the increase in the parameter p). Moreover, for the assumed value of the baffle length L, the function Ne = f (β) increases with the increase in the angle β of the inclination of the impeller blade.     

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.     

Tensile strength and fracture of glass fiber-reinforced plastic (GFRP) plate with an eccentrically located circular hole

In this paper, tensile strength and fracture of finite glass fiber-reinforced plastic GFRP (glass/polyester) composite materials with a through-the-thickness eccentrically located circular hole are experimentally studied. The strain response histories near the hole boundary for different eccentrically located holes during the whole damage and fracture process of the notched specimen are recorded. The effects of off-center distance and hole diameter on strength and fracture of the notched specimen are analyzed. The tensile fracture strength of the notched specimen with an eccentrically located hole is determined. Also, the initial stress concentrations in the composite laminate due to the presence of the eccentrically located hole are understood. These results play an important role for predicting strength and evaluating lifetime of laminate composite with complex geometrical cutouts.     

Transport phenomena in membranes

The realization that many elementary biological processes occur at membrane-like structures has led to renewed interest in the theory of molecular transport through membranes. Coupling phenomena in membranes, some of which are very complex, can now be rationally described with the aid of the thermodynamics of irreversible processes. The investigation of theoretical membrane models has proved a valuable complement to the thermodynamic method.     

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.     

Gas recirculation rate through impeller cavities and surface aeration in sparged agitated vessels

A novel method for determining gas recirculation rates through impeller cavities in sparged agitated vessels is described. It is based on the withdrawal, particularly from the cavities themselves, of gas samples forsubsequent analysis. Oxygen is used as the tracer gas and nitrogen for sparging. The method can also be used for determining surface aeration rates.The method gives values for the external distribution coefficient α (=Q_R/Q_S) of between 0 and 1. These values agree well with those calculated from power measurements at high impeller speeds N > N_R. However, the method also suggests that recirculation occurs at N < N_R but in this region the method is not entirely valid. The measurements of surface aeration clearly show that attempts to relate the effect of surface aeration without sparging to the sparged condition are unsatisfactory.     

Agitation of a gas-solid-liquid system in a vessel with high-speed impeller and vertical tubular coil

Experimental results of gas hold-up, power consumption and residence time of gas bubbles in a gas-solid-liquid system produced in an agitated vessel equipped with a high-speed impeller and a vertical tubular coil are presented in this paper. Critical agitator speed, needed for the dispersion of gas bubbles and solid particles in liquid were also identified. The studies were carried out in an agitated vessel of the inner diameter D = 0.634 m and the working liquid volume of about 0.2 m³. A tubular coil of the diameter of 0.7D, consisting of 24 vertical tubes of the diameter of 0.016D, was located inside the flat-bottomed vessel. The agitated vessel was equipped with a Rushton turbine with six blades or an A 315 impeller with four blades. Both impellers had diameter, d, equal to 0.33D. The vessel was filled with liquid up to the height H = D. In this study, air and particles of sea sand with the mean diameter of 335 μm and the concentration of up to 3.0 mass % were dispersed in distilled water as the liquid phase. The measurements were carried out within the turbulent regime of the fluid flow in the agitated vessel. Results of the measurements were processed graphically and mathematically. Lower values of the critical agitator speed, n _JSG, needed for simultaneous dispersion of gas bubbles and particles with the solids concentration from 0.5 mass % to 2 mass %, were obtained for the vessel equipped with the A 315 impeller. Higher values of the specific power consumption were reached for the vessel with the Rushton turbine. Higher values of the gas hold-up and residence time of the gas bubbles in the fluid were obtained for the system equipped with the Rushton turbine. Results of the gas hold-up as a function of the specific power consumption, superficial gas velocity and solids concentration were approximated with good accuracy using Eq. (5).     

Transport phenomena in flow injection analysis without chemical reaction

Dispersion phenomena play a very important role in flow injection analysis. In this paper, physical transport phenomena in flow injection methods are discussed. Three different types of reactor — a straight tube, a helically coiled tube and a new single bead string reactor — are compared. Under similar flow conditions, the dispersion in the single bead string reactor is the lowest. The specific advantages of single bead string reactors are their very simple preparation and maintenance and the good reproducibility of the peaks. It is shown that in open capillary tubes (coiled or not) the Taylor dispersion equation is of very limited use, because the residence times are too short, and because secondary flow occurs in the case of coiled tubes.     

Transport phenomena in bubble column reactors I: Flow pattern

A new model has been developed for the liquid phase flow pattern in bubble columns. This model satisfies the mass, momentum and energy balances for the gas and liquid phases. Further, it takes into account the variations in the flow pattern due to changes in the physical properties of the liquid phase. The model can be used for batch as well as continuous (co-current and counter-current) modes of operation. A satisfactory agreement is shown between model predictions and experimental observations. A simplified procedure is suggested for quick estimation of the liquid phase velocity profile. The proposed model is expected to be useful for the rational prediction of transfer coefficients for momentum, mass and heat. The prediction and measurement of the pressure drop is discussed in the companion paper.     

Transport phenomena in bubble colunm reactor II: Pressure drop

The two-phase frictional pressure drop was measured in a 0.15 m internal diameter bubble column operated in a continuous co-current manner. The fractional gas hold-up was measured using the gamma-ray absorption technique and the pressure drop using modified differential manometry. The superficial gas and liquid velocities were varied in the ranges 0.127–0.451 m s⁻¹ and 0.047–0.236 m s⁻¹ respectively. The effects of liquid viscosity, non-Newtonian behaviour, and the presence of electrolyte were investigated.A coherent model was developed to predict the pressure drop in homogeneous (bubbly flow) and heterogeneous (churn-turbulent) regimes. For this purpose, knowledge of the liquid phase flow pattern was used. A comparison between model predictions and experimental observations is presented.On the basis of the pressure drop, a criterion was developed to predict the transition from the homogeneous to the heterogeneous regime. A favourable comparison is shown between model predictions and experimental observations.     

Electron transport across liquid membranes with an asymmetrically located electron mediator

The addition of a surface active dipyridinium or nicotinamide chloride into a liquid membrane containing vitamin K₃ (VK₃), brought about a large enhancement in the rate of the electron transport from S₂O₄^2? to Fe(CN)₆^3?. The asymmetric location of this salt at one interface of the membrane was achieved by the used of a small porre-sized millipore filter.     

Computation of multiphase equilibrium phenomena with an equation of state

This paper presents a general approach to multiphase equilibrium computations using an equation of state. Various types of calculations are described: flash calculations, saturation-pressure and saturation-temperature calculations, and calculations of the feed composition corresponding to a given saturation pressure and temperature.A stagewise procedure for flash calculations using the QNSS method allows efficient computation of phase equilibria for systems with any number of phases. The initial guess of the composition of an extra phase which is required to start the iteration is obtained from an analysis of the Gibbs-energy surface.Newton's method is used to construct multiphase boundaries on various types of diagrams (pressure-temperature, pressure-composition and temperature-composition). Multiphase critical points on these boundaries are also estimated by interpolation.The algorithms developed are tested for a typical reservoir-oil-CO₂ mixture which exhibits three-phase liquid 1-liquid 2-vapor (L₁L₂V) separation. The predictions obtained using the Peng-Robinson of state are satisfactory.     

Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank

The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of N = 4.1 or 8.2 s^?1 inducing transitional (Re = 499 or 1307) or turbulent (Re = 2.43 × 10⁴) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid (0.2 wt% aqueous solution of carboxymethyl cellulose, CMC) exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.