Mixing of miscible shear-thinning fluids in a lid-driven cavity

The concentration and velocity fields of two refractive index matched miscible shear-thinning fluids in a lid-driven cavity were investigated by using planar laser-induced fluorescence and particle image velocimetry,as well by computational fluid dynamics.Quantitative analyses show that the results obtained by flow simulations with the species transport model are in good agreement with the experimental results.The effects of different parameters were studied by using the intensity of segregation.For two fluids with the same rheological parameters,the relative amounts of liquids H_(1)/H and the power-law index n dominate the mixing process while the Reynolds number Re plays a marginal role.As for two fluids with density difference,buoyancy has significant influence on the mixing process.The dimensionless group Ar/Re(redefined such as to include shear thinning behavior)is proposed for assessing the effect of buoyancy and rheological properties on the mixing of miscible shear-thinning fluids.

Quadrature-based moment methods for the population balance equation: An algorithm review

The dispersed phase in multiphase flows can be modeled by the population balance model(PBM). A typical population balance equation(PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods(QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function(NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments(QMOM), direct quadrature method of moments(DQMOM),extended quadrature method of moments(EQMOM), conditional quadrature method of moments(CQMOM),extended conditional quadrature method of moments(ECQMOM) and hyperbolic quadrature method of moments(Hy QMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics(CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.

Effects of rotational speed and fill level on particle mixing in a stirred tank with different impellers

The particle mixing was studied in a cylindrical stirred tank with elliptical dished bottom by experiments and simulations.The impeller types used were double helical ribbon(HR) + bottom HR,pitched blade ribbon + bottom HR,inner and outer HR + bottom HR,and pitched blade ribbon + Pfaudler + bottom HR labeled as impellers Ⅰ to Ⅳ,respectively.The quantitative correlations among the rotational speed,fill level and power consumption for impeller Ⅰ and impeller Ⅱ were obtained by experiments to validate the discrete element method(DEM) simulations.The particle mixing at different operating conditions was simulated via DEM simulations to calculate the mixing index using the Lacey method,which is a statistical method to provide a mathematical understanding of the mixing state in a binary mixture.The simulation results reveal that as the rotational speed increases,the final mixing index increases,and as the fill level increases,the final mixing index decreases.At the same operating conditions,impeller Ⅲ is the optimal combination,which provides the highest mixing index at the same revolutions.

Mass transfer in gas–liquid stirred reactor with various triple-impeller combinations

The gassed power demand and volumetric mass transfer coefficient(kLa) were investigated in a fully baffled,dished-base stirred vessel with a diameter of 0.30 m agitated by five triple-impeller combinations. Six types of impellers(six-half-elliptical-blade disk turbine(HEDT), four-wide-blade hydrofoil impeller(WH) pumping down(D) and pumping up(U), parabolic-blade disk turbine(PDT), and CBY narrow blade(N) and wide blade(W)) were used to form five combinations identified by PDT + 2CBYN, PDT + 2CBYW, PDT + 2WHD,HEDT + 2WHDand HEDT + 2WHU, respectively. The results show that the relative power demand of HEDT + 2WHUis higher than that of other four impeller combinations under all operating conditions. At low superficial gas velocity(uG), kLa differences among impeller combinations are not obvious. However,when uG is high, PDT + 2WHDshows the best mass transfer performance and HEDT + 2WHUshows the worst mass transfer performance under all operating conditions. At high uGand a given power input, the impeller combinations with high agitation speed and big projection cross-sectional area lead to relatively high values of kLa. Based on the experimental data, the regressed correlations of gassed power number with Froude number and gas flow number, and kLa with power consumption and superficial gas velocity are obtained for five different impeller combinations, which could be used as guidance for industrial design.

Investigation of droplet breakup in liquid–liquid dispersions by CFD–PBM simulations：The influence of the surfactant type

The accurate prediction of the droplet size distribution(DSD)in liquid–liquid turbulent dispersions is of fundamental importance in many industrial applications and it requires suitable kernels in the population balance model.When a surfactant is included in liquid–liquid dispersions,the droplet breakup behavior will change as an effect of the reduction of the interfacial tension.Moreover,also the dynamic interfacial tension may be different with respect to the static,due to the fact that the surfactant may be easily desorbed from the droplet surface,generating additional disruptive stresses.In this work,the performance of five breakup kernels from the literature is assessed,to investigate their ability to predict the time evolution of the DSD and of the mean Sauter diameter,when different surfactants are employed.Simulations are performed with the Quadrature Method of Moments for the solution of the population balance model coupled with the two-fluid model implemented in the compressible Two Phase Euler Foam solver of the open-source computational fluid dynamics(CFD)code Open FOAM v.2.2.x.The time evolution of the mean Sauter diameter predicted by these kernels is validated against experimental data for six test cases referring to a stirred tank with different types of surfactants(Tween 20 and PVA 88%)at different concentrations operating under different stirrer rates.Our results show that for the dispersion containing Tween 20 additional stress is generated,the multifractal breakup kernel properly predicts the DSD evolution,whereas two other kernels predict too fast breakup of droplets covered by adsorbed PVA.Kernels derived originally for bubbles completely fail.

Investigation of extraction fraction in confined impinging jet reactors for tri-butyl-phosphate extracting butyric acid process

The extraction fraction E and overall volumetric mass transfer coefficient kLa of TBP extracting butyric acid process in confined impinging jet reactors(CIJR) with two jets were investigated.The main variables tested were the concentration of tri-butyl-phosphate(TBP) and butyric acid,the impinging velocity V,the impinging velocity ratio of two phases Vorg/Vaq,the nozzle inner diameter diand the distance L between the jet axes and the top wall of the impinging chamber.The results showed that E and kLa increase with an increase of the impinging velocity V,the concentration of TBP Corg,and the impinging velocity ratio Vorg/Vaq.However,E and kLa decrease with an increase of the inner diameter difrom 1 to 2 mm,the concentration of butyric acid Caqfrom 0.5%(v/v) to2%(v/v).The factor L ranging from 3 to 11 mm has a negligible effect on E and kLa.A correlation on these variables and kLa was proposed based on the experimental data.These results indicated good mass transfer performance of CIJR in the extraction operation.

Mass transfer area in a multi-stage high-speed disperser with split packing

In this study, the mean droplet diameter in the cavity zone and the total mass transfer area of a multi-stage highspeed disperser(HSD) reactor with different packing combinations were measured and evaluated. The effects of rotational speed and packing radius, as well as the packing ring radius and numbers, on the mean droplet diameter and the total mass transfer area were evaluated. A model was established to calculate the mass transfer area in the cavity zone in the HSD reactor, and it was found that the packings contribute 61%–82% of the total mass transfer area. A correlation for predicting the mass transfer area in the packing zone was regressed by the dimensionless analysis method. An enhancement factor based on the mass transfer area in the packing zone was proposed to evaluate the effect of packing combination on mass transfer area. Two optimum packing combinations were proposed in consideration of the mean droplet diameter and the enhancement factor.

Torque and bending moment acting on a flexible shaft agitated by disk turbines in a gas–liquid stirred vessel

The torque and bending moment acting on a flexible overhung shaft in a gas–liquid stirred vessel agitated by a Rushton turbine and three different curved-blade disk turbines(half circular blades disk turbine, half elliptical blades disk turbine, and parabolic blades disk turbine) were experimentally measured by a customized moment sensor. The results show that the amplitude distribution of torque can be fitted by a symmetric bimodal distribution for disk turbines, and generally the distribution is more dispersive as the blade curvature or the gas flow rate increases. The amplitude distribution of shaft bending moment can be fitted by an asymmetric Weibull distribution for disk turbines. The relative shaft bending moment manifests a "rising-falling-rising" trend over the gas flow number, which is a corporate contribution of the unstable gas–liquid flow around the impeller, the gas cavities behind the blades, and the direct impact of gas on the impeller. And the "falling" stage is greater and lasts wider over the gas flow number for Rushton turbine than for the curved-blade disk turbines.

Droplet characteristics in the multi-staged high speed disperser with single inlet

Droplet characteristics in the cavity zone of a multi-staged high speed disperser with single inlet were studied in this paper. The influences of both the operating and structural parameters on the mean droplet diameter, size distribution and liquid flux distribution were quantitatively analyzed. The result showed that the mean droplet diameter decreased with the increase of rotational speed and the number of rotors;whilst there is little influence on the inlet flow rate. In the experimental range, the minimum value of mean droplet diameter is 0.57 mm, 0.48 mm, 0.41 mm in the two-staged, three-staged and four-staged rotors, respectively. The Rosin–Rammler(R–R) distribution could describe the droplet size distribution appropriately, and it became uniform with the increase of rotational speed and the number of rotor, while the inlet flow rate had little effect on the droplet size distribution. The liquid flux distribution curves were always unimodal. With the increase of rotational speed, the location of maximum liquid flux ratio moved from zone 3 to zone 4 and this value decreased from 22.1% to 18.1%. Using Coefficient of Variation(CV) to indicate the uniformity of liquid flux distribution, it was found that the CV decreases from 47.5% to 22.7%when the number of rotor increased from 2 to 4.

PIV experiment and large eddy simulation of turbulence characteristics in a confined impinging jet reactor

Confined impinging jet reactor(CIJR) is a typical process intensification device used in the chemical industry.In this study, two dimensional Particle Image Velocimetry(PIV) and Large Eddy Simulation(LES) method were used to investigate the flow field in a CIJR with jets of diameter 3 mm under highly turbulent condition.The results showed LES can predict the velocity and Turbulence Kinetic Energy(TKE) distributions in the reactor well by comparing with the PIV results.In the CIJR, the stagnation point fluctuates with the turbulence, and its instantaneous position accords with the normal distribution.Three methods, including s–t representation, Lumley–Newman triangle and A–G representation, were used to compare the turbulence anisotropy in the mixing chamber.It was found that the anisotropy in the impinging area and at the edge of impinging jet was strong and the maximum deviation was up to 40%.The results from 2 DPIV would lead to an overestimation of the turbulent kinetic energy as much as 20% to 30% than the results from the three dimensional numerical simulation.

Coupling simulation of fluid structure interaction in the stirred vessel with a pitched blade turbine

The interaction between fluid and a down-pumping pitched blade turbine fixed with a flexible shaft in the stirred vessel, as a typical fluid structure interaction phenomenon, was simulated by coupling the Computational Fluid Dynamics and Computational Structural Dynamics. Based on the verification of the simulated impeller torque and dimensionless shaft bending moment with experimental result, the dimensionless shaft bending moment and various loads acting on impeller(including lateral force, axial force and bending moment) were discussed in detail. By separating and extracting the fluid and structural components from those loads, the results show that the shaft bending moment mainly results from the lateral force on impeller although the axial force on impeller is much larger. The impeller mass imbalance increases the shaft bending moment and the lateral force on impeller, but has little influence on the axial force and bending moment acting on impeller. The dominant frequencies of impeller forces are macro-frequency, speed frequency and blade passing frequency, and are associated with the impeller mass imbalance.

Compressibility induced bubble size variation in bubble column reactors:Simulations by the CFD–PBE

Bubble column reactors can be simulated by the two fluid model(TFM) coupled with the population balance equation(PBE). For the large industrial bubble columns, the compressibility due to the pressure difference may introduce notable bubble size variation. In order to address the compressibility effect, the PBE should be reformulated and coupled with the compressible TFM. In this work, the PBE with a compressibility term was formulated from single bubble dynamics, the mean Sauter diameters predicted by the compressible TFM coupled with the PBE were compared with the analytical solutions obtained by the ideal gas law. It was proven that the mesoscale formulations presented in this work were physically consistent with the macroscale modeling. It can be used to simulate large industrial plants when the compressibility induced bubble size variation is important.

A review on single bubble gas–liquid mass transfer

It is common to empirically correlate volumetric mass transfer coefficient kLa for predicting gas–liquid mass transfer in industrial applications,and the investigation of single bubble mass transfer is crucial for a detailed understanding of mass transfer mechanism.In this work,experiments,models and simulations based on the experimental results were highlighted to elucidate the mass transfer between single bubbles and ambient liquid.The experimental setups,measurement methods,the mass transfer of single bubbles in the Newtonian and the nonNewtonian liquid,models derived from the concept of eddy diffusion,the extension of Whitman’s,Higbie’s and Danckwerts’models,or dimensionless numbers,and simulation methods on turbulence,gas–liquid partition methods and mass transfer source term determination are introduced and commented on.Although people have a great knowledge on mass transfer between single bubbles and ambient liquid in single conditions,it is still insufficient when facing complex liquid conditions or some phenomena such as turbulence,contamination or non-Newtonian behavior.Additional studies on single bubbles are required for experiments and models in various liquid conditions in future.

Transfer characteristics of dynamic biochemical signals in non-reversing pulsatile flows in a shallow Y-shaped microfluidic channel: signal filtering and nonlinear amplitude-frequency modulation

The transports of the dynamic biochemical signals in the non-reversing pulsatile flows in the mixing microchannel of a Y-shaped microfluidic device are ana- lyzed. The results show that the mixing micro-channel acts as a low-pass filter, and the biochemical signals are nonlinearly modulated by the pulsatile flows, which depend on the biochemical signal frequency, the flow signal frequency, and the biochemical signal transporting distance. It is concluded that, the transfer characteristics of the dynamic biochemical signals, which are transported in the time-varying flows, should be carefully considered for better loading biochemical signals on the cells cultured on the bottom of the microfluidic channel.

Impingement and mixing dynamics of micro-droplets on a solid surface

The hydrodynamics and mixing during the nonaxisymmetry impingement of a micro-droplet and a sessile droplet of the same fluid are investigated by many-body dissipative particle dynamics(MDPD) simulation.In this work,the range of the impingement angle(θ_(i)) between the impinging droplet and the sessile droplet is 0°-60° and the contact angle is set as 45° or 124°.The droplets impingement and mixing behavior is analyzed based on the droplet internal flow field,the concentration distribution and the time scale of the decay of the kinetic energy of the impinging droplet.The dimensionless total mixing time(τ_(m)) is calculated by a modified mixing function.With the Weber number(We) ranging from 5.65 to22.7 and the Ohnesorge number(Oh) ranging from 0.136 to 0.214,we find rm hardly changes with We and Oh.Whereas,θ_(i)and surface wettability are found to have a significant effect on τ_(m).We find that θ_(i)has no clear effect on τ_(m)on a hydrophobic surface,while on the hydrophilic surface,τ_(m)increase with the θ_(i).Thus,reducing the impinging angle is a valid method to shorten the τ_(m).

Transformation of single drop breakup from binary to ternary and multiple in turbulent jet flows

By releasing liquid drops in turbulent jet flows,we investigated the transformation of single drop breakup from binary to ternary and multiple.Silicone oil and deionized water were the dispersed phase and continuous phase,respectively.The probability of binary,ternary,and multiple breakup of oil drops in jet flows is a function of the jet Reynolds number.To address the underlying mechanisms of this transformation of drop breakup,we performed two-dimensional particle image velocimetry(PIV)experiments of single-phase jet flows.With the combination of drop breakup phenomenon and two-dimensional PIV results in a single-phase flow field,these transformation conditions can be estimated:the capillary number ranges from 0.17 to 0.27,and the Weber number ranges from 55 to 111.

Interactions between two in-line drops rising in pure glycerin

The behaviors of time-dependent interaction between two buoyancy-driven in-line deformable drops rising in pure glycerin at Re b 1 were studied,where the diameter for the leading drops ranged from 9.51 mm to12.6 mm and for trailing drops from 12.7 mm to 15.8 mm.The situation while a larger drop chasing a smaller one was specifically considered which typically led to the smaller drop "coating" the larger one.Two approaches,the geometric feature approach and the energy change one,were used to judge the starting and ending times of the interaction between two drops.Based on a conical wake model,the drag coefficient of two approaching drops was calculated.Due to the approaching effect of the trailing drop,the leading drop was accelerated and the average drag coefficient was smaller than that for a free rising single drop.The frequency spectrums of the lateral oscillation of two drops during the interaction were obtained by using Fourier analysis.The oscillation frequency of the interactional drops was also different from that for a free rising single drop because of the wake effect produced by the leading drop.Due to a superposition of the drop shape oscillation and the drop internal circulation,the transverse oscillation frequencies of two drops have the same trend during the approaching process.

Gas dispersion and solid suspension in a three-phase stirred tank with triple impellers

The hydrodynamics is still not fully understood in the three-phase stirred tank equipped with multi-impeller due to the intensive interaction between phases.In this work,the solid critical suspension speed(NJSG),relative power demand(RPD)and overall gas holdup(ε_G)were measured in an air–water–glass beads stirred tank equipped with multi-impeller,which consists of a parabolic blade disk turbine below two down-pumping hydrofoils.Results show that either the NJSGor the specific power consumption increases when increasing the volumetric solid concentration or superficial gas velocity.RPD changes less than 10%when solid volumetric concentration ranges from 0 to 15%.ε_G decreases with the increase of solid concentration,and increases with the increase of both superficial gas velocity and the total specific power consumption.The quantitative correlations of NJSG,RPD andεGwere regressed as the function of superficial gas velocity,specific power consumption,Froude number and gas flow number,in order to provide the reference in the design of such three-phase stirred tank with similar multi-impellers.

过渡流搅拌槽内固-液悬浮的直接数值模拟

采用格子玻尔兹曼方法(lattice Boltzmann method),研究了过渡流搅拌槽内颗粒悬浮过程的流体力学特征.模拟中搅拌槽为平底方槽,搅拌桨采用下压式45°四斜叶桨,搅拌雷诺数Re=1334,属于过渡流;颗粒体积分率最高达到8%.本模拟解析了包括颗粒周围和颗粒间流动的搅拌槽内整个流场,从而实现了在颗粒尺度上对颗粒-流体相互作用的研究.同时,本文也研究了体积分率、相位角对液相平均速度、液相湍流动能等流体力学特征值的影响规律.结果表明,随着搅拌槽内颗粒体积固含率的增加,液相平均速度和液相湍流动能均衰减.

Discrete element method study of effects of the impeller configuration and operating conditions on particle mixing in a cylindrical mixer

We employed the discrete element method to study the effects of the impeller configuration(i.e.,blade diameter,inclination angle,and blade number),rotational speed,and fill level on the flow and mixing of particles in a cylindrical mixer equipped with flat and inclined blades.The coefficient of rolling friction,coefficient of static friction,and coefficient of restitution were experimentally determined before the simulation,and simulation results of the torque and surface particle distribution were validated in experiments,particularly when using a true Young's modulus in the discrete element method.The performance of the mixer was assessed using the Lacey mixing index.The input work per unit volume was used to represent the mixing efficiency.The circumferential velocity and axial diffusion coefficient of the particles were quantitatively analyzed to reveal the effect of particle flow on the mixing.It was found that the mixing performance and efficiency of a three-blade mixer are better than those of two-and four-blade mixers.For pitched blades,a three-fiat-blade mixer has better mixing performance than a three-45°-blade own-pumping or a three-45°-blade up-pumping mixer,but the mixing efficiency of the three-45°-blade up-pumping mixer is the best among these three mixers.As the rotational speed increases,the mixing performance improves but the mixing efficiency hardly changes.When the fill level is 0.4 times the cylinder diameter,the 160D two-flat-blade mixer has good mixing performance with high mixing efficiency.The circumferential velocity has the greatest effect on mixing performance for side-by-side initial loading.