CFD modelling of pump-around jet mixing tanks: a reliable model for overall mixing time prediction

Over the past two decades or so, computational fluid dynamics (CFD) has been employed to predict overall mixing times inside jet mixing tanks instead of non-universal mixing time correlations obtained by experiments. However, the numerical methods for jet mixing tank simulations were not clearly tested and the discretization errors of the previous CFD models were not assessed. So, in this paper, the suitable turbulence model and numerical methods for pump-around jet mixing tank simulations were investigated. Further, the discretization errors of the present CFD models were estimated with the help of grid convergence index (GCI). The results revealed that the realizable k-epsilon model, SIMPLE, second order upwind, and first order implicit were proper turbulence model and numerical methods for pump-around jet mixing tank simulations. From GCI analyses, the maximum discretization uncertainty in overall mixing time of the present CFD models was about ±0.08 s.     

CFD modelling of pump-around jet mixing tanks: a discrepancy in concentration profiles

ABSTRACT

Jet mixing tanks are important in chemical processes. Over the past two decades or so, computational fluid dynamics (CFD) has been employed to study jet mixers. The shortfalls of the previous CFD models were the discrepancy in concentration profiles between simulation and experiment and the absence of exact inlet turbulence conditions. So, in our present work, the CFD model was developed to investigate the proper conditions for jet mixing tank simulation and improve the accuracy of concentration profile prediction by using an appropriate grid arrangement, a realizable k-epsilon model, and a second-order upwind discretization scheme. The results revealed that the CFD model with proper inlet conditions predicted the overall mixing time well and somewhat improved the predicted concentration profiles. Further, the reasons for discrepancies in concentration profiles were inappropriate inlet turbulence conditions and overprediction in total momentum available for mixing due to the flat top liquid surface assumption. In addition, this discrepancy may be caused by the dynamic response of concentration measuring device.     

Numerical simulation of solid-liquid mixing characteristics in a stirred tank with fractal impellers

The hydrodynamics of solid-liquid mixing process in a stirred tank with four pitched-blade impellers, fractal 1 impellers, and fractal 2 impellers were investigated using computational fluid dynamics (CFD) simulation. An Eulerian-Eulerian approach, standard k-ε turbulence model, and multiple reference frames (MRF) technique were employed to simulate the solid-liquid two-phase flow, turbulent flow, and impeller rotation, respectively. The effects of impeller speed, impeller type, impeller spacing, impeller blade tilt angle, impeller blade shape, solid particle size and initial solid particle loading on the solid particle suspension quality were investigated. Results showed that the homogenous degree of solid-liquid system increased with the increase of impeller speed. The impeller spacing of T5/6 and T and impeller blade tilt angle of 60° and 45° were appropriate for the solid-liquid suspension process. Fractal shape impeller was more efficient than jagged shape impeller in solid-liquid mixing process. Larger particle diameter and higher initial solid particle loading resulted in less homogenous distribution of solid particles. It was found that fractal impeller could improve the solid particle suspension quality compared with four pitched-blade impeller under the same power consumption, increasingly so with the fractal iteration number of fractal impeller. Moreover, fractal impeller reduced the size of impeller trailing vortex and consumed less power consumption compared with four pitched-blade impeller at the same impeller speed, and the more the number of fractal iteration, the higher the impeller energy utilization rate of fractal impeller.     

气动发动机缸内流场特性研究

以全新研制的电控气动发动机气缸流场域为研究对象,建立其几何模型,运用CFD前处理软件ICEM对流场域几何模型进行网格划分,再运用Fluent动网格技术进行动态模拟计算,分析其气缸内部流场特性,进而得出气体在工作过程中各个阶段的压力场和速度场分布.同时,将模拟计算数值与气动发动机台架实验所得值进行比较.结果表明:动网格数值模拟结果与实验结果较为接近,气动发动机气缸内流场动态仿真过程准确可靠,仿真结果可为气动发动机设计提供参考.当转速稳定于450r/min时,由仿真模拟所得数据计算得此气动发动机指示功率为0.62kW,实验时测算得同条件下实验指示功率为0.55kW,求得仿真和实验指示功率的最大误差为11.2%.利用自制的测功装置测得实验时有效功率为0.45kW,进而求得机械效率为81.8%.研究结果为下一步改善气动发动机性能提供了依据.     

Comparisons of laser-saturated, laser-induced, and planar laser-induced fluorescence measurements of nitric oxide in a lean direct-injection spray flame

We report quantitative, spatially resolved laser-saturated fluorescence (LSF), linear laser-induced fluorescence (LIF), and planar laser-induced fluorescence (PLIF) measurements of nitric oxide (NO) concentration in a preheated, lean direct-injection spray flame at atmospheric pressure. The spray is produced by a hollow-cone, pressure-atomized nozzle supplied with liquid heptane, and the overall equivalence ratio is unity. NO is excited by means of the Q(2)(26.5) transition of the gamma(0, 0) band. LSF and LIF detection are performed in a 2-nm region centered on the gamma(0, 1) band. PLIF detection is performed in a broad ~70-nm region with a peak transmission at 270 nm. Quantitative radial NO profiles obtained by LSF are presented and analyzed so as to correct similar LIF and PLIF profiles. Excellent agreement is achieved among the three fluorescence methodologies.     

Numerical modelling and flow visualization of mixing of stratified layers and rollover in LNG

A numerical model has been developed to study the mixing of two initially stratified layers which are subjected to a uniform lateral heat flux. An important distinction is made between the free surface and the liquid/liquid interface with regard to the different flow characteristics of the two layers. In the upper layer where warm liquid is cooled at the evaporating surface, the convective circulation is featured by a strong downward core flow; in contrast, the fluid flow in the lower layer is mainly confined to the wall boundary and is much weaker. Flow visualization experiments show that mixing of two stratified layers generally involves two stages in sequence: migration of the interface and rapid mixing between the remaining liquids. The interface movement is due to entrainment mixing at the interface. When the two layers approach density equalization, the interface becomes increasingly unstable and the core flow in the upper layer is able to break into the lower layer. The base to side heat flux ratio appears to be a major factor in determining the mode and intensity of the subsequent mixing at a rollover incident.     

Non-uniform mixing of hepatic venous flow and inferior vena cava flow in the Fontan conduit

Fontan patients require a balanced hepatic blood flow distribution (HFD) to prevent pulmonary arteriovenous malformations. Currently, HFD is quantified by tracking Fontan conduit flow, assuming hepatic venous (HV) flow to be uniformly distributed within the Fontan conduit. However, this assumption may be unvalid leading to inaccuracies in HFD quantification with potential clinical impact. The aim of this study was to (i) assess the mixing of HV flow and inferior vena caval (IVC) flow within the Fontan conduit and (ii) quantify HFD by directly tracking HV flow and quantitatively comparing results with the conventional approach. Patient-specific, time-resolved computational fluid dynamic models of 15 total cavopulmonary connections were generated, including the HV and subhepatic IVC. Mixing of HV and IVC flow, on a scale between 0 (no mixing) and 1 (perfect mixing), was assessed at the caudal and cranial Fontan conduit. HFD was quantified by tracking particles from the caudal (HFD_{caudal conduit}) and cranial (HFD_{cranial conduit}) conduit and from the hepatic veins (HFD_HV). HV flow was non-uniformly distributed at both the caudal (mean mixing 0.66 ± 0.13) and cranial (mean 0.79 ± 0.11) level within the Fontan conduit. On a cohort level, differences in HFD between methods were significant but small; HFD_HV (51.0 ± 20.6%) versus HFD_{caudal conduit} (48.2 ± 21.9%, p = 0.033) or HFD_{cranial conduit} (48.0 ± 21.9%, p = 0.044). However, individual absolute differences of 8.2–14.9% in HFD were observed in 4/15 patients. HV flow is non-uniformly distributed within the Fontan conduit. Substantial individual inaccuracies in HFD quantification were observed in a subset of patients with potential clinical impact.     

The Effect of Gas Properties on Bubble Formation,Growth, and Detachment

Bubble formation and growth play an important role in various processes and industries, where the dispersion of gas bubbles in a liquid medium occurs frequently. In this paper, the formation, growth, and detachment of gas bubbles produced from a submerged needle in water are numerically and experimentally investigated. The effect of injected gas properties on bubble characteristics, including bubble diameter, contact angle, and the frequency of bubble formation, is evaluated. In particular, the changes in bubble characteristics during the injection process are investigated for three different gases to evaluate the effect of density and surface tension on the bubble detachment criteria. The present numerical results show an acceptable agreement with experiments under different operating conditions. The results show that the increase in surface tension, and the decrease in gas density result in larger bubble sizes before detachment occurs. Moreover, the bubble generation frequency is found to strongly depend on the contact angle and the surface tension.     

A study of gas and solid mixing behaviors in a three partitioned fluidized bed

A previously unknown partitioned fluidized bed gasifier (PtFBG) has been developed for improving coal gasification performance. The basic concept of the PtFBG is a fluidized bed divided into two parts, a gasifier and a combustor, by a partitioned wall. Char is burnt in the combustor and the generated heat is supplied to the gasifier along with the bed materials. During that time, highly concentrated CO₂ is inevitably generated in the combustor. Therefore, vigorous solid mixing is an essential precondition as well as minimizing horizontal gas mixing. In this study, gas and solid mixing behaviors were verified in a cold model three partitioned fluidized bed (3-PtFB). Glass beads with an average diameter of 150 μm and a particle density of 2500 kg/m³ were used as bed materials. For the gas mixing experiments, CO₂ and N₂ were introduced into the beds through each distributor. Then, outlet gas flow rates and concentrations were measured by gas flow meters and an IR gas analyzer respectively. The calculated gas exchange ratios ranged from 3% to 10% with varying gas flow rates. For the solid mixing experiments, 1000 μm polypropylene particles with a density of 883 kg/m³ were continuously fed into the reactor. Then, the polypropylene particles were distributed to the entire beds evenly. Solid mixing behaviors were very analogous to liquid mixing behaviors in a continuous stirred tank reactor (CSTR).     

Numerical modelling of fluids mixing,heat transfer and non‐equilibrium redox chemical reactions in fluid‐saturated porous rocks

Non‐equilibrium redox chemical reactions of high orders are ubiquitous in fluid‐saturated porous rocks within the crust of the Earth. The numerical modelling of such high‐order chemical reactions becomes a challenging problem because these chemical reactions are not only produced strong non‐linear source/sink terms for reactive transport equations, but also often coupled with the fluids mixing, heat transfer and reactive mass transport processes. In order to solve this problem effectively and efficiently, it is desirable to reduce the total number of reactive transport equations with strong non‐linear source/sink terms to a minimum in a computational model. For this purpose, the concept of the chemical reaction rate invariant is used to develop a numerical procedure for dealing with fluids mixing, heat transfer and non‐equilibrium redox chemical reactions in fluid‐saturated porous rocks. Using the proposed concept and numerical procedure, only one reactive transport equation, which is used to describe the distribution of the chemical product and has a strong non‐linear source/sink term, needs to be solved for each of the non‐equilibrium redox chemical reactions. The original reactive transport equations of the chemical reactants with strong non‐linear source/sink terms are turned into the conventional mass transport equations of the chemical reaction rate invariants without any non‐linear source/sink terms. A testing example, for some aspects of which the analytical solutions are available, is used to validate the proposed numerical procedure. The related numerical solutions have demonstrated that (1) the proposed numerical procedure is useful and applicable for dealing with the coupled problem between fluids mixing, heat transfer and non‐equilibrium redox chemical reactions of high orders in fluid‐saturated porous rocks; (2) the interaction between the solute diffusion, solute advection and chemical kinetics is an important mechanism to control distribution patterns of chemical products in an ore‐forming process; and (3) if the pore‐fluid pressure gradient is lithostatic, it is difficult for the chemical equilibrium to be attained within permeable cracks and geological faults within the crust of the Earth. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental investigation and CFD simulation of multiphase flow behavior in air reverse circulation drilling

In reverse circulation (RC) down-the-hole hammer (DTH) drilling, hole cleaning has a great impact on reducing accidents and improving efficiency. There is a technical difficulty in RC drilling to select the minimum air influx while keeping cuttings discharged smoothly according to different water invasion conditions. A novel experimental device was used to study the physics of multiphase flow associated with the cleaning process. Air influx required for cuttings transport was measured under different conditions in Rate of Penetration (ROP), cuttings diameter, and water yield, and influence among three factors were revealed. Furthermore, the computational fluid dynamic (CFD) method simulated and analyzed multiphase flow behavior. The results show that factors of ROP, cuttings diameter, and water yield obviously impact minimum air influx during the cuttings transport process. The accuracy and credibility of CFD method have been confirmed on account of reasonable agreement with experimental data (a relative error of less than 14% is achieved). The CFD simulation of multiphase transport reveals that cuttings velocity and pressure drop could be influenced by ROP, cuttings diameter, and water yield. Therefore, these factors should be carefully characterized during air RC drilling and hole cleaning to maximize the efficiency of cuttings transport.     

Interactions and Collisions of Bubbles in Thermocapillary Motion: A 3D Study

Two- and three-dimensional simulations (created using volume of fluid-fluent) concerning the rise and interactions of two/multiple thermocapillary bubbles arranged horizontally and perpendicular to a hot surface are investigated and presented in this paper. The results indicate that thermocapillary bubble agglomeration can occur in zero gravity. Furthermore, the temperature gradient and bubble diameter were found to have a major impact on the collision between bubbles. The results of Nas and Tryggvason (1993 Nas, S., and G. Tryggvason. 1993. Computational investigation of the thermal migration of bubbles and drops. 175 Fluid Mechanics Phenomena In Microgravity 71–83. [Google Scholar]) in their three-dimensional numerical study reported that no such collisions could occur in zero gravity and that bubbles repel each other due to the cold liquid carried between particles during migration. Their results contrast with both the present results and those recorded onboard the Chinese 22nd recoverable satellite experiment by Kang et al. (2008 Kang, Q., H. L. Cui, L. Hu, and L. Duan. 2008. On-board experimental study of bubble thermocapillary migration in a recoverable satellite. Microgravity Science And Technology 20:67–71.[Crossref], [Web of Science ®] , [Google Scholar]), who observed a total of 19 coalescences between the air bubbles injected in the direction of the temperature gradient of the stagnant heated liquid.     

Numerical study of particle mixing in a tilted three-dimensional tumbler and a new particle-size mixing index

A new mixing index is proposed, which is an improved Lacey index based on coordination number fraction. The differences and similarities among many mixing indices are compared, including the new mixing index, the information entropy based on coordination number fraction, the Lacey index based on local concentration, and the information entropy based on local concentration. The first two indices are microscopic since the coordination number fraction is on particle-scale, whereas the latter two are mesoscopic as the local concentration is mesoscopic scale. The newly proposed mixing evaluation indices does not include inauthentic temporal oscillations. Moreover, using mixing index, the mixing characteristics of particles in a tilted tumbler are studied by discrete element method (DEM). The tumbler’s angle of tilt α = 0°, 10°, 20°, 30°, 40°, 50°, 60° and 70°, at five rotating velocities ω = 0.175, 0.35, 0.5, 0.6, 0.7 and 1.4 rad/s corresponding to Froude number F_r = 0.0025, 0.001, 0.002, 0.003, 0.004, 0.016 respectively are simulated. It is found that both increasing the tilt angle and the rotating speed have negative effects on the particle mixing within the scope of this study.     

Intensity dependence suppression and enhancement of four-wave mixing in a micrometric thin vapour

We theoretically investigate dressed-four-wave mixing (dressed-FWM) spectroscopy of rubidium atoms in a micrometric thin vapour. It is found that Dike-narrowing type Autler–Townes (AT) spectroscopy with high resolution can be achieved in a reverse Y-type four-level atomic system due to the phase-conjugated configuration of laser beams and the transient effects of atom–wall collision in the thin vapour. We also show that controllable suppression and enhancement of the dressed-FWM signal due to the evolution of atomic coherence can be obtained by selecting different coupling field intensities at the proper detuning of the probe and the coupling fields. This control of FWM processes can be interpreted by dressed state analysis and probably used in the design of optical switch and the enhancement of FWM processes for frequency conversion.     

Experimental and modeling studies on mixing behavior of binary mixtures in a spout-fluid bed

Experimental and modeling studies have been performed to determine mixing characteristics of binary mixtures in a spout-fluid bed. Spherical glass beads of diameters (3.075, 1.7, 1.2, and 0.75?mm) and air as fluidizing medium have been used in the study. Effect of various system parameters, namely, initial static bed height, gas velocity, diameter ratio, mixture composition, and sampling time on mixing of binary particles has been experimentally investigated. A dimensionless correlation has been developed for mixing index. Mixing behavior has been modeled using artificial neural networks (ANNs). Training of ANN was performed using the Levenberg–Marquardt (LM) backpropagation algorithm to predict the mixing index. The predictions of the ANN were found to be in good agreement with the experimental results and predictions from developed correlations.     

Simulation and numerical investigations of the kinetics of atmospheric aerosol droplets in the wake behind a flat plate

Within the framework of the physicomathematical model of evolution of a polydisperse condensate, numerical investigations of the kinetics of atmospheric aerosol droplets in a supersonic two-phase flow past a flat plate were carried out. The gas flow was described by the Reynolds equations with the use of the two-parameter turbulence model. In view of the smallness of the condensate mass fraction in the incoming flow, the inverse effect of the dispersed phase on the gas was not considered. For various regimes of exposure to a flow, the characteristic features of the spatial distribution of the main parameters of the condensate fractions have been studied: the number densities, radii, temperatures, and averaged velocities of microdrops. The dependence of the dispersed phase dynamics on the Mach number and the incoming flow angle of attack has been investigated and the influence of the allowance for the processes of coagulation/fragmentation on the mass spectrum of droplets is shown. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 331–341, March–April, 2009.     

Numerical-based non-dimensional analysis of critical flow of R-12, R-22, and R-134a through horizontal capillary tubes

Development of correlations predicting critical mass flow rate and critical pressure distribution through capillary tubes is presented. In order to accomplish such a work, the critical mass flow rate and pressure distribution for nearly 500 operational conditions for R-12, R-22, and R-134a are evaluated. Operational conditions include inlet pressure varying from 800 to 1500 kPa, inlet subcold temperature between 0 and 10 °C, length varying from 1 to 2 m, and inner diameter between 0.5 and 1.5 mm. By performing non-dimensional analysis on numerical data, general correlations are presented to predict the critical mass flow rate through capillary tubes. In addition, by utilizing numerical data for down-stream pressure, non-dimensional analysis is performed to present correlations to predict critical down-stream pressure and pressure distribution through capillary tubes.     

具有热阻、热漏和内不可逆性的联合卡诺热机生态学优化

用有限时间热力学的方法分析具有热阻、热漏、内不可逆性的定常流联合卡诺型热机循环．导出了在傅立叶导热定律下联合循环功率、效率和生态学指标的性能，并进行优化；得到功率、效率和生态学指标之间的优化关系，并由数值计算分析了功率、效率和循环熵产率之间的关系．所得的结果表明，最大生态学指标下的效率十分接近于联合循环可以达到的最大效率；相应的熵产率也要低于以输出功率为优化目标时的熵产率．     

Surface force spectroscopic point load measurements and viscoelastic modelling of the micromechanical properties of air flow sensitive hairs of a spider (Cupiennius salei)

The micromechanical properties of spider air flow hair sensilla (trichobothria) were characterized with nanometre resolution using surface force spectroscopy (SFS) under conditions of different constant deflection angular velocities (rad s⁻¹) for hairs 900–950 μm long prior to shortening for measurement purposes. In the range of angular velocities examined (4×10⁻⁴−2.6×10⁻¹ rad s⁻¹), the torque T (Nm) resisting hair motion and its time rate of change (Nm s⁻¹) were found to vary with deflection velocity according to power functions. In this range of angular velocities, the motion of the hair is most accurately captured by a three-parameter solid model, which numerically describes the properties of the hair suspension. A fit of the three-parameter model (3p) to the experimental data yielded the two torsional restoring parameters, S _3p=2.91×10⁻¹¹ Nm rad⁻¹ and =2.77×10⁻¹¹ Nm rad⁻¹ and the damping parameter R _3p=1.46×10⁻¹² Nm s rad⁻¹. For angular velocities larger than 0.05 rad s⁻¹, which are common under natural conditions, a more accurate angular momentum equation was found to be given by a two-parameter Kelvin solid model. For this case, the multiple regression fit yielded S _2p=4.89×10⁻¹¹ Nm rad⁻¹ and R _2p=2.83×10⁻¹⁴ Nm s rad⁻¹ for the model parameters. While the two-parameter model has been used extensively in earlier work primarily at high hair angular velocities, to correctly capture the motion of the hair at both low and high angular velocities it is necessary to employ the three-parameter model. It is suggested that the viscoelastic mechanical properties of the hair suspension work to promote the phasic response behaviour of the sensilla.