Modeling of Mixing and Reaction in Turbulent Multi‐Phase Flows with Distribution Functions

Numerical simulation of turbulent reacting or multiphase flows is gaining popularity as a tool for the analysis and optimization of many complex applications in process engineering. To make possible the accurate modeling of relevant reaction and transport processes, the respective distribution functions of mixture fraction or particle size must be considered in an adequate manner. In the present paper, novel approaches to make possible a more detailed yet efficient representation of distribution functions in turbulent, reacting multiphase flows are introduced. The application of the methods to the example of a system with mixing and reaction among three species is discussed.     

Behavior of Pressure Gradient and Transient Pressure Signals during Liquid‐Liquid Two‐Phase Flow

Liquid‐liquid two‐phase flows are encountered in several process industries, multiphase reactors and oil industries. In each of these applications, identification of flow patterns poses a challenging problem and many efforts are directed towards developing suitable devices for this purpose. In the present work, attempts have been made to use pressure gradient and transient pressure signals to study flow patterns during the simultaneous flow of two liquids through a horizontal pipe. It is observed that the slope of the pressure gradient curves as a function of fluid superficial velocities is a weak function of the flow pattern. However, the variation of the slope with the pattern transition is much more significant when the pressure gradient is normalized with respect to only kerosene flow through the pipe (Δp_TP/Δp_KO). Further attempts have been made to identify flow patterns from transient pressure signals and the statistical analysis of these random signals has been undertaken. The PDF analysis and the wavelet multiresolution technique have been adapted to explain the signals in detail. The flow regimes identified are smooth stratified, wavy stratified, plug flow, ‘three‐layer' flow, ‘oil dispersed in water and water' and ‘oil and water in oil' flow patterns. The signal characteristics are depicted for each flow pattern.     

A Multi‐Block Approach to Obtain Angle‐Resolved PIV Measurements of the Mean Flow and Turbulence Fields in a Stirred Vessel

Two‐dimensional Particle Image Velocimetry (PIV) measurements have been used to characterize the complex turbulent flow generated by a T/3 45° pitched‐blade down‐flow turbine, operated at Re ≈ 5 · 10⁴, in a fully turbulent stirred vessel. To maintain high spatial resolution when viewing the whole vessel, a multi‐block approach has been developed, which combines data from different fields of view into a composite flow map. Using 500 measurements of instantaneous u and v velocity fields, angle‐resolved mean velocity maps and turbulence properties, such as the RMS velocities and the turbulence kinetic energy, have been estimated near to the blade, as well as in the bulk of the vessel, at a spatial resolution of between 1 and 2 mm. Vorticity maps have also been calculated to help visualize the trailing vortex structures close to the impeller blades and integral length scales have been estimated from the two‐dimensional spatial auto‐correlation function. It is shown than the common assumption that the integral length scale is about half the blade width is an overestimate close to the impeller and an underestimate far from the impeller.     

Comparison of Experimental Techniques for the Measurement of Mixing Time in Gas‐Liquid Systems

Measurements of the homogenisation characteristics during the agitation of a liquid and the mixing time by simple in situ conductivity probes are very well established. However, unless special precautions are taken, in the presence of the second phase such as gas, the conductivity trace becomes distorted to a greater or lesser extent, so that it is not possible to follow the transient change of concentration in the liquid phase or estimate the mixing time. In this paper it is confirmed that, without special precautions, simple in situprobes are unsatisfactory. However, by shielding the probe with a “cage”, the ingress of bubbles into the probe region is essentially prevented and satisfactory results can be obtained in situ with responses having as little noise as in the case without gas. A second technique involves elimination of the gas from a small sample stream and measurement of the stream's conductivity transient. By suitable and rather simple treatment of the response, results equivalent to that from the in situ shielded probes can be obtained. The latter technique is especially useful where the placement of in situ probes is difficult. It is also suggested that recent results, which disagree with much of the literature on liquid phase mixing times in gassed systems, arose due to the use of in situ unshielded conductivity probes.     

Effects of the Stirred Tank's Design on Power Consumption and Mixing Time in Liquid Phase

The influence of the stirrer type and of the geometrical parameters of both tank and agitator (clearance of an impeller from tank bottom, impeller diameter, draft tube and geometry of the tank bottom) on power consumption and mixing time in liquid phase under turbulent regime conditions (Re > 10⁴) have been studied. Different types of agitators have been used, namely Rushton turbine, 45° pitched‐blade turbine, MIXEL TT and TTP propellers and 1‐stage or 2‐stage EKATO‐INTERMIG propellers. All these stirrers were tested with the same power consumption per unit mass of liquid. On the basis of measured power consumption per unit mass, which is required to achieve the same degree of mixing, the results obtained in the present work show that the TTP propeller is the most efficient in liquid phase. Recommendations on the optimum geometric configuration have been made for each type of stirrer.     

Experimental Study of the Mixing Time in a Jet‐Mixed Gas‐Liquid System

In the present work, the impeller in the conventional gas‐liquid mixed vessels was replaced by a fluid jet as the mixer. Using an experimental setup, the effect of several parameters on the mixing time as a measure of the liquid‐phase mixing intensity, which is one of the required transport characteristics for designing gas‐liquid mixed systems, was studied. The results show that gas injection decreases the mixing time in comparison with the ungassed condition, but the mixing time is not necessarily decreased by increasing the gassing rate. On the basis of the amount of the jet Reynolds number and gassing rate, and thus the created circulation pattern, the mixing time may be decreased or increased. Also, the location of the probe for cases in which there are more dead zones in the vessel have a considerable effect on the measured mixing time. With increasing uniformity of the velocity domain, the influence of the probe location was reduced. Also, by increasing the jet flow rate and decreasing the nozzle diameter, the length of the jet, the amount of entrained bulk fluid, and the intensity of recirculation flow increased, and thus the mixing time decreased.     

Two‐Phase Bubbly Flow Structure in Large‐Diameter Vertical Pipes

The two‐phase flow structure of an air‐water, bubbly, upward flow in a 20 cm diameter pipe is presented with particular emphasis on the local interfacial area concentration. The radial distribution of void fraction, bubble velocity, bubble size, bubble frequency, and interfacial area concentration were measured using a local dual‐optical probe. The experimental results showed that the saddle‐type distribution of void fraction and interfacial area concentration, which are common for bubbly flow in small diameter pipes, only appeared in the present experiments under conditions of very low area‐averaged void fraction (<?> < 0.04). The values for the interfacial area concentration were higher in large diameter pipes when compared with data obtained under the same flow conditions in small pipes. The area‐averaged void fraction data were correlated using the drift‐flux model.     

Mixing in Sub‐micron Ducts

This paper considers a class of fluidic devices, anticipated to become important in the near future, where characteristic channel dimensions are in the range 0.1 to 1.0 microns. Typical current applications of microfluidics have device sizes of 10 to 100 micron, this is sufficiently small to force laminar flow but not so small that molecular diffusion is a dominant factor. In the smaller devices contemplated here, diffusion is important and existing mixing strategies and correlations are no longer applicable. Novel results and interesting complexities are discussed for reactive, single and two phase flows in sub‐micron channels.     

MD Simulations of Diffusivities in Methanol‐n‐hexane Mixtures Near the Liquid‐liquid Phase Splitting Region

Molecular Dynamics (MD) simulations have been carried out to determine the self‐diffusivities in binary mixtures of methanol and n‐hexane with varying compositions at four different temperatures of 303.15 K, 307.7 K, 310.7 K, and 313.15 K. The Darken relation was used to determine both the Fick diffusivity and the Maxwell‐Stefan diffusivity. The values of the Fick diffusivity obtained from the simulations are in very good agreement with published experimental data of Clark and Rowley [17]. These diffusivities approach zero near composition regions where liquid‐liquid phase splitting occurs. On the other hand, the Maxwell‐Stefan diffusivity is well‐behaved and appears to be practically insensitive to the complex thermodynamics.     

Simulation of Turbulent Flow in a Packed Bed

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data.     

Explicit Critical Pressure Ratio for Choked Two‐Phase Homogeneous Nozzle Flow

The throat‐to‐stagnation critical pressure ratio for a frictionless and adiabatic nozzle flow of a homogeneous, nonflashing two‐phase mixture can only be expressed as the numerical solution of a transcendental equation. A simple, physically plausible approximation is herein proposed, which fits well over the whole range of mass flow qualities.     

一种圆管紊流混合长度理论的修正

对普朗特混合长度理论在圆管紊流流动中的应用进行了修正。基于尼古拉兹的圆管紊流速度分布实验结果:在除管中心及其附近位置外的紊流核心区内精确符合对数分布,结合力平衡方程,得出混合长度表达式;考虑圆管紊流实际情况,对混合长度表达式进行合理假设并引入阻尼函数进行改进,形成适用于圆管不同半径位置处的混合长度计算公式,修正后的混合长度表达式在整个圆管半径范围内光滑连续。基于修正后的混合长度表达式,推导出圆管剪切速率分布函数,并得出速度分布沿半径是一条存在二阶导数的光滑曲线;对剪切速率分布函数进行数值积分,计算某一流动状态下的管道速度分布,与实验结果精确吻合,且在圆管中心位置和层流子层区边界不再存在速度突变,更符合流体实际流动情况。     

Mixing and Crystallization Kinetics in Gas‐liquid Reactive Crystallization

A study of gas‐liquid reactive crystallization for CO₂‐BaCl₂‐H₂O system was performed in a continuous flow crystallizer. The influences of mixing on the crystallization kinetics of barium carbonate crystals were investigated. The mixing parameters are stirrer speed, feed concentration, gas‐flow rate, pH of solution, addition rate of NaOH solution, and mean residence time. Under pH‐stat operation, the crystallization mechanism can be assessed by the addition rate of NaOH solution, which acts as an indicator for the absorption rate of carbon dioxide. Assuming a size‐independent agglomeration mechanism, the nucleation rate, growth rate and agglomeration kernel can be obtained, simultaneously, at steady state, by the method of moments. Evidence shows that feed concentration, feed rate, gas‐flow rate, and stirrer speed have a significant influence on the nucleation rates and mean particle sizes. This shows the effect of micromixing. The crystallization mechanism tends to be reaction limited when the feed concentration of barium chloride solution is higher than 5 mM, while at lower stirrer speeds and feed concentrations, the mechanism tends to be both mixing and reaction controlled. The growth rate depends on the mean supersaturation value and the pH of the solution and the mass‐transfer resistance cannot be completely eliminated in this work. For a monodispersal collision model, in the viscous sub‐range of turbulence, the agglomeration kernel can be expressed as β ∝ d^{3 –1/4}, showing a low efficiency of collision. The result is also demonstrated by the agglomeration kernel expression. Comparison with a liquid‐liquid‐mixing reactive crystallization system is also discussed.     

Accuracy of Safety Valve Two‐Phase Mass Flow Capacity Sizing

The method specified in ISO/CD 4126–10 exhibits the highest accuracy compared to other models used in industry and academia. At the same time it allows for an oversizing of the necessary relief area under all test conditions. The average or statistical reproductive accuracy is characterized by an unacceptable logarithmic scatter of about 80 %.     

Generation of Two‐Phase Air‐Water Flow with Fine Microbubbles

Aiming at the development of a low‐cost technology for multipurpose water and surface treatment in the chemical industry and beyond, using microbubbles, a novel scheme of liquid‐gas interaction within a specially designed bubble generator was tested. Its efficiency for the production of microbubbles with a size distribution in the micron range is confirmed. The basic element of the device is a vortex chamber with water supply through tangential ducts, while the gas (air) is introduced in a highly turbulent swirling flow of water in radial direction through the orifice in the gas supply duct, located on the chamber axis. Bubble diameters, bubble velocities in the pipe flow and effect of the output pressure on the bubble size distribution were studied.     

Void Fraction Measurement for Two‐Phase Flow Using Electrical Resistance Tomography

Measurement of void fraction of two‐phase flows remains a challenging area. In this paper the application of an electrical resistance tomography (ERT) system for this purpose has been studied. A new approach through the direct use of the voltage data measured by the ERT system is presented. The measured voltage data are first compressed through a feature extraction, and a polynomial regression procedure is followed to obtain the relationship between the void fraction and the feature extracted. Both simulation and experiment are carried out to verify the approach. The methodology of the new approach, simulation and experimental results are presented in the paper.     

Phase Distribution Measurements during Transient Bubbly Two‐Phase Flow in a Vertical Pipe

An experimental procedure for investigating transient bubble flow for an adiabatic air/water system with vertical upward flow in a pipe is presented. The results of the measured local transient two‐phase flow parameters are shown along a pipe length of approx. four meters. From the measured radial phase distributions under steady and under transient conditions one can draw conclusions about the interfacial forces. Here, the effects indicate the action of forces such as a transverse lift force and a time dependent force like the virtual mass force during the transient. For modelling the transverse lift force which seems to play a dominant role for that flow regime the formulation of Zun was chosen and it was implemented into the commercial CFD‐Code Fluent Release 4.4.4 via user‐defined subroutines. Finally, results from the simulation of the steady states of start and end conditions of an experimental measured transient are shown.     

Study of Turbulent Flow in a Long Permeable Channel

Stationary liquid flow in a long (to L/d = 1440) permeable channel was studied for input Reynolds numbers from 28700 to 83000. The distributions of water pressure along the channel were obtained. Experimental data were compared with the numerical solution of equations derived from the energy equation.     

Simulation and Experimental Validation of Two‐Phase Flow in an Aerosol Counter‐Flow Reactor using Computational Fluid Dynamics

A simulation of the hydrodynamic behavior of an aerosol‐counter flow reactor was conducted using an Euler‐Lagrange method. The simulation results were then verified with experiments. The process simulated was a separation process required during the production of biodiesel (fatty acid methyl ester). In this process, the liquid ester/glycerol phases are continuously injected through a hollow cone nozzle with an overpressure of 10⁶ Pa into the reactor, operated at 15000 Pa. The liquid is atomized because of the pressure drop and a liquid particle spray is generated with an inlet velocity of 44.72 m/s. Water vapor of temperature 333 K is injected tangentially through two side, gas inlets with an inlet velocity of 1.2 m/s. Excess methanol is subjected to a mass transfer from the liquid phase into the gas phase, which is withdrawn through the head of the reactor and condensed in an external condenser unit. The stripping of the methanol off the liquid leads to a sharp interface between the glycerol and the ester phase, which can then be easily separated by gravity or pumping. The gas velocity field, pressure field and the liquid particle trajectories were calculated successfully. Simulated dwell time distribution curves were derived and analyzed with the open‐open vessel dispersion model. Experimental dwell time distribution curves were measured, analyzed with the open‐open vessel dispersion model, and compared with the simulated curves. A good consistency between simulated and measured Bodenstein numbers was achieved, but 25 % of the simulated particles exited at the reactor's head, contrary to experimental observations. The difference between simulated and measured dwell times was within one order of magnitude.