A general correlation for pressure drop in a Kenics static mixer

A new pressure drop correlation in a Kenics static mixer has been developed. Pressure drop data were generated from computational fluid dynamics (CFD) calculations, avoiding the experimental limitations in obtaining comprehensive data enough for developing a reliable pressure drop correlation. Dimensional analysis reveals that the pressure drop characteristic of the Kenics static mixer can be described by three dimensionless groups, i.e., the friction factor, Reynolds number (Re), and aspect ratio of a mixing element (AR). A systematic graphical analysis led to a single master curve governing the pressure drop behavior of the Kenics static mixer, which had never been achieved before. We derived a pressure drop correlation fitting well with the obtained master curve in a general form into which the AR effect on the pressure drop is directly incorporated. Unlike the already existing correlations available in the literature, the correlation proposed in this study can cover the whole range of Re from laminar to turbulence. The reliability of the proposed correlation was validated by the comparison with various pressure drop data reported in the literature.     

幂律流体在Kenics型静态混合器中流动特性分析

为了探究Kenics型静态混合器内扭旋叶片剪切作用对幂律流体流动的影响,利用旋转流变仪测量了浓度为0.5wt%, 0.7wt%, 0.9wt%的羧甲基纤维素(CMC)水溶液的流变参数,采用数值模拟与实验研究了扭旋叶片作用下幂律流体流动阻力和剪切稀化特性。对流场研究表明,扭旋叶片诱导产生了内流涡旋、绕流涡旋和近壁面涡旋,有效强化了静态混合器内流体流动的剪切作用。受多个纵向涡旋分布的影响,扭旋叶片局域流场中周向45°位置速度最高,周向30°位置涡量与剪切应力最高而黏度最低。径向0.4倍半径位置速度最高,0.7倍半径位置黏度最高。静态混合器有效提高了流体的二次流流动速度和剪切应力,降低了幂律流体的黏度和流动阻力系数。     

Liquid phase residence time distribution for gas–liquid flow in Kenics static mixer

The residence time distribution (RTD) of the liquid phase for co-current gas–liquid upflow in a Kenics static mixer (KSM) with air/water and air/non-Newtonian fluid systems was investigated. The effect of liquid and gas superficial velocities on liquid holdup and Peclet number was studied. Experiments were conducted in three KSMs of diameter 2.54 cm with 16 elements and 5.08 cm diameter with 8 and 16 elements, respectively, of constant L_e/D_e = 1.5 for different liquid and gas velocities. A correlation was developed for Peclet number, in terms of generalized liquid Reynolds number, gas Froude number and liquid Galileo number, where as for liquid holdup, a correlation was developed as a function of gas Reynolds number. The axial dispersion model was found to be in good agreement with the experimental data.     

Kenics型静态混合器内分散相液滴破碎和聚结过程的CFD-PBM数值模拟

采用CFD-PBM耦合方法对Kenics型静态混合器内分散相油滴破碎及聚并行为进行数值模拟研究,分析了雷诺数、混合元件数、元件长径比等参数对分散相液滴粒径的影响,揭示了分散相在Kenics静态混合器内流动过程中液滴粒径的演化规律.结果表明,随雷诺数增大,分散相液滴出口粒径不断减小,并出现临界趋势;静态混合器的前几个元件...     

带有Kenics静态混合器的水平液固两相流化床换热管的压降研究

以饱和硫酸钙为介质,在安装Kenics静态混合器的水平液固两相流化床换热管上进行实验研究,考察介质流速、Kenics静态混合器扭率、颗粒体积分数及颗粒尺寸对压降的影响,并与冷态实验条件下的压降变化规律进行比较。结果表明：同等操作条件,安装Kenics静态混合器后压降比安装前提高20%～140%;压降随雷诺数的增大而增大,随Kenics静态混合器扭率的增大而减小;颗粒体积分数对压降也有影响。根据实验数据,得出了稳定操作条件下压降与上述影响因素之间的经验关联式,为带有Kenics静态混合器的水平液固两相流化床换热器的设计提供计算依据。     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Development of positron emission particle tracking for studying laminar mixing in Kenics static mixer

Positron emission particle tracking (PEPT) is a flow visualisation technique that has found application in a wide range of processes. In this work, PEPT has been used to study laminar flow of a high viscosity Newtonian and non-Newtonian fluid in a Kenics static mixer (KM). Through analysis of the trajectories of many hundreds of passes of the tracer particle through the mixer, it is possible to compute the overall flow field and to visualise how the fluid twists and folds as it passes along the mixer. Eulerian velocity maps plotted for the Newtonian and non-Newtonian fluids showed that the length required for the flow to develop is shorter for the non-Newtonian fluid than the Newtonian. The stretching and folding mechanism of mixing was observed by grouping the trajectories into clusters according to whether the trajectory passes to the left or right of the blade at the transition between elements. Those trajectories making the same L–R–L decision tended to remain in the same striation through two or three elements until that striation became stretched and folded back on itself, sandwiching other layers. It is clear that the PEPT data is rich and powerful. We are hopeful that the techniques we develop for the flow and mixing in the Kenics mixer will be applicable to studying more complex laminar flows.     

Pressure drop and heat transfer study in tube-in-tube helical heat exchanger

In the present work attempts were made to investigate the hydrodynamics and heat transfer characteristics of tube-in-tube helical heat exchanger at the pilot plant scale. The experiments were carried out in counter current mode operation with hot fluid in the tube side and cold fluid in the annulus area. The outer tube was fitted with semicircular plates to support the inner tube and also to provide high turbulence in the annulus region. Overall heat transfer coefficients were calculated and heat transfer coefficients in the inner and outer tube were determined using Wilson plots. A commercial Computational Fluid Dynamics package [FLUENT User's Guide, release 6.0, Fluent Inc., Lebnon, NH, 1994] was used to predict the flow and thermal development in tube-in-tube helical heat exchanger. The Nusselt number and friction factor values in the inner and outer tubes were compared with the experimental data collected in the present study as well as reported in the literature. The CFD simulations were in agreement with the present experimental data. In case of literature data a reasonable comparison was found even though the boundary conditions in the present work were different.     

Mathematical modelling of hydrothermal performance for Kenics type static mixer using power law obeying fluids

In this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non-Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in-house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.     

Single and two-phase flows in a horizontal pipe with a Kenics static mixer: Effect of pressure drop on mixing

Single and two-phase flows pressure drops through a Kenics static mixer were investigated, for liquid and gas Reynolds numbers ranging from 8110 < Re_L < 18 940 to 1730 < Re_G < 8680, respectively. New friction factor correlations were established for single and two-phase flows, showing better agreement than those available in the literature. Dissipated energy and characteristic time constants were estimated from experimental data. For instance, a dissipated energy with a maximum value of 510 W/kg was calculated in two-phase flow with the drift-flux model. The dispersed phase reduced the characteristic mixing times and its influence was more important than the continuous phase for all the characteristic mixing time investigated. Furthermore, the macroscopic characteristic mixing time was shown to be the governing mixing process for almost all gas and liquid flow rates explored.     

SK型静态混合器壁压脉动信号的多尺度多分形特性

为了探讨静态混合器内非线性、非均匀性和混沌特性机理,利用高速数据采集系统对SK型静态混合器管壁处脉动压力进行测量。结合小波变换模极大值理论,对采集的不同进口流量下壁压波动时间序列用Daubechies二阶小波提取1～7尺度下的特征信号,并分别对提取的信号进行R/S分析。通过对压力波动信号不同尺度下的细节信号与概貌信号研究,发现在不同尺度下其表现出不同的分形结构,且随着进口流量的增大,分形结构的变化趋势基本一致。此外,该系统不仅存在确定性非周期成分,而且不同尺度的旋涡之间的能量交换导致混沌的产生。各尺度信号的能量分布表明,压力波动信号主要体现了宏观尺度的旋涡级串的相互作用。     

CFD modeling of immiscible liquids turbulent dispersion in Kenics static mixers: Focusing on droplet behavior

The present study is concerned with the computational fluid dynamics(CFD) simulation of turbulent dispersion of immiscible liquids, namely, water–silicone oil and water–benzene through Kenics static mixers using the Eulerian–Eulerian and Eulerian–Lagrangian approaches of the ANSYS Fluent 16.0 software. To study the droplet size distribution(DSD), the Eulerian formulation incorporating a population balance model(PBM) was employed. For the Eulerian–Lagrangian approach, a discrete phase model(DPM) in conjunction with the Eulerian approach for continuous phase simulation was used to predict the residence time distribution(RTD) of droplets.In both approaches, a shear stress transport(SST) k-ω turbulence model was used. For validation purposes, the simulated results were compared with the experimental data and theoretical values for the Fanning friction factor, Sauter mean diameter and the mean residence time. The reliability of the computational model was further assessed by comparing the results with the available empirical correlations for Fanning friction factor and Sauter mean diameter. In addition, the influence of important geometrical and operational parameters, including the number of mixing elements and Weber number, was studied. It was found that the proposed models are capable of predicting the performance of the Kenics static mixer reasonably well.     

Mass transfer enhancement in supercritical fluid extraction by acoustic waves

A computational fluid dynamics model of extraction of a solute (caffeine) from a porous solid matrix (coffee beans) using a supercritical solvent (carbon dioxide) is developed. Supercritical fluid extraction of a solute from a solid matrix is a slow process even when solute free solvent is circulated. The use of acoustic waves represents a potential efficient way of enhancing mass transfer processes. The effect of acoustically excited flows on supercritical fluid extraction from a porous solid matrix is investigated. The mathematical model considers diffusion-controlled regime in the porous solid matrix and convective-diffusive transport in the bulk fluid. Henry's law is used to describe the equilibrium states of the solid and the fluid phases. Accurate representation of the thermo-physical properties of supercritical solvent is considered by using the NIST Standard Reference Database 12. The conservation equations for mass, momentum, energy and species are numerically solved using implicit finite volume method. The effect of process parameters, such as initial state (pressure and temperature) of solvent and acoustic waves on the yield of solute extraction is also investigated numerically.     

SK型静态混合器切割区内速度混沌特性

为揭示SK型静态混合器内非稳态流动特性,利用激光多普勒粒子分析仪对直径为0.04m、长径比为1.25的SK型静态混合器的切割区瞬时流场进行测量。采用功率谱和最大Lyapunov指数识别混合器内瞬时速度时间序列的混沌特性,利用湍流高阶矩参数分析混沌运动的统计特征。实验结果表明:SK型静态混合器切割区速度波动时间序列具有混沌特性;功率谱函数随频率的增加呈幂函数衰减,瞬时速度脉动主要能量集中在31.25Hz以下;湍流高阶矩分布揭示了切割区内的速度脉动存在非线性拟序结构,混沌运动的概率密度函数偏离高斯分布。     

An experimental study of flow and heat transfer of supercritical carbon dioxide in multi-port mini channels under cooling conditions

This paper presents the fluid flow and heat transfer characteristics of supercritical CO₂ in a horizontal multi-port extruded aluminum test section consisting of 10 circular channels with an inner diameter of 1.31 mm. Both local and average pressure drop and heat transfer coefficients were measured as CO₂ was cooled in the multi-port circular channels with pressures ranging from 7.4 to 8.5 MPa, inlet fluid temperatures ranging from 22 to , and mass velocity ranging from 113.7 to 418.6 kg/m² s. The results indicate that the operating pressure, the mass velocity and the temperature of CO₂ had significant effects on fluid flow and heat transfer characteristics. The pressure drop and the average heat transfer coefficient increased greatly with increasing the average temperatures of CO₂ in the near-critical region; the average heat transfer coefficient attained a peak value near the corresponding pseudocritical temperature; and the maximum heat transfer coefficient decreased as the pressure increased. Both the pressure drop and the heat transfer coefficient increased with the mass velocity, but decreased with the operating pressure. The measured average heat transfer coefficients were compared with the experimental data reported in the literatures and a large discrepancy was observed. Based on the experimental data collected in the present work, a new correlation was developed for forced convection of supercritical CO₂ in horizontal multi-port mini channels under cooling conditions.     

SV型静态混合器湍流阻力的初步研究

为了获得流体在SV型静态混合器中湍流流动时的流动阻力规律,提出一种新的含有SV型静态混合器重要几何结构参数的流体阻力计算模型。对于不可压缩流体,将其在SV型静态混合器中的运动分解成沿管壁与轴线方向平行和沿混合元件凹槽方向的直线运动。运用流体力学理论,分别求解出流体作2种运动时所产生的湍流流体阻力的计算式,并计入相邻混合元件交接部分的局部阻力,然后进行叠加得到流体阻力理论计算式。以水为实验介质,对SV型静态混合器流体湍流阻力进行了实验测量,与理论结论进行比较分析,得出摩擦因子λ与Re-0.2呈线性关系的结论。     

混合元件数对SK型静态混合器流场特性的影响

以SK型静态混合器为对象,运用激光多普勒测速仪对混合器内流场进行测量分析,研究混合元件数对混合器内速度分布和湍动性能影响。结果表明：在扭旋叶片作用下,流体在混合器内的速度会重新分布,湍动会被强化,这一过程主要在前3个混合元件中实现,且湍动逐渐增加,但增加速度逐渐减弱,第1个混合元件强化作用最为显著,进入第4个混合元件后基本达到稳定;当混合叶片数量超过3个以后,对流体湍动的强化基本达到混合器强化能力的极限,继续增加元件数量不能提高流体的湍动程度,但可以维持这种湍动。     

Ross LPD型静态混合器内湍流传热与混合强化特性

在湍流状态Re=2640~17600下,采用恒热通量传热实验与数值模拟相结合的方法,系统研究Reynolds数Re和交错角对Ross LPD型静态混合器内湍流流动与传热性能影响,采用Nusselt数、Darcy摩擦系数、综合传热系数、速度场与温度梯度和压力梯度协同角等参数评价混合器内传热强化性能;基于CFD与LPT相耦合分析混合器内流体微元拉伸率。研究结果表明：SST k-ω模型预测Ross型静态混合器湍流阻力及传热结果与实验结果具有很好一致性;Ross混合器流场内形成与流场尺度较为接近的纵向涡,其涡心在圆形截面与半圆形截面中心间周期性迁移,横截面内湍流分散混合效率是Kenics的3.36~1.72倍;当Re>7040时,Ross LPD综合传热性能明显优于KSM;当叶片夹角为30°时,综合传热性能系数具有最大值;Ross LPD内插件具有高效低阻的技术优势和结构改进潜力。     

CFD study on particle-to-fluid heat transfer in fixed bed reactors: Convective heat transfer at low and high pressure

Computational fluid dynamics (CFD) has proven to be a reliable tool for fixed bed reactor design, through the resolution of 3D transport equations for mass, momentum and energy balances. Solution of these equations allow to obtain velocity and temperature profiles within the reactor. The numerical results obtained allow estimating useful parameters applicable to equipment design. Particle-to-fluid heat transfer coefficient is of primal importance when analyzing the performance of a fixed bed reactor. To gain insight in this subject, numerical results using a modified commercial CFD solver are presented and particle-to-fluid heat transfer in fixed beds is analyzed. Two different configurations are studied: forced convection at low pressure (with air as circulating fluid) and mixed (i.e., free+forced) convection at high pressure (with supercritical CO₂ as circulating fluid). In order to impose supercritical fluid properties to the model, modifications into the CFD code were introduced by means of user defined functions (UDF) and user defined equations (UDE). The obtained numerical data is compared to previously published data and a novel CFD-based correlation (for free, forced and mixed convection at high pressure) is presented.     

Ross LPD型静态混合器内湍流传热与混合强化特性

在湍流状态Re=2640~17600下,采用恒热通量传热实验与数值模拟相结合的方法,系统研究Reynolds数Re和交错角对Ross LPD型静态混合器内湍流流动与传热性能影响,采用Nusselt数、Darcy摩擦系数、综合传热系数、速度场与温度梯度和压力梯度协同角等参数评价混合器内传热强化性能;基于CFD与LPT相耦合分析混合器内流体微元拉伸率。研究结果表明：SST k-ω模型预测Ross型静态混合器湍流阻力及传热结果与实验结果具有很好一致性;Ross混合器流场内形成与流场尺度较为接近的纵向涡,其涡心在圆形截面与半圆形截面中心间周期性迁移,横截面内湍流分散混合效率是Kenics的3.36~1.72倍;当Re>7040时,Ross LPD综合传热性能明显优于KSM;当叶片夹角为30°时,综合传热性能系数具有最大值;Ross LPD内插件具有高效低阻的技术优势和结构改进潜力。