Entrance laminar flows of viscoplastic fluids in concentric annuli

Developing flows of generalized Bingham (Herschel-Bulkley) fluids in concentric annuli were studied numerically. A control volume approach based upon an upwinding finite difference technique was used to solve the equation of motion. The results in terms of velocity and pressure drop profiles are shown graphically. Radius ratios of 0.02, 0.2, 0.4 and 0.6; power-law indices (n) of 0.7, 1.0 and 1.2; generalized Bingham numbers of 5, 10 and 15 were investigated. At present, there are no experimental results with which to make comparisons. However, there are results for fully developed flows and comparison has been made with these. In all cases the agreement was good.     

Flow simulation of herschel-bulkley fluids through extrusion dies

The flow of viscoplastic materials through extrusion dies has been studied numerically using the finite element method. Rheological data for viscoplastic doughs have been fitted by the Herschel-Bulkley model, which incorporates a yield stress into the power-law model. Non-isothermal simulations show the extent and shape of yielded/unyielded regions and the development of temperature field assuming different modes of heat transfer at the boundaries. The results reveal that viscous dissipation causes appreciable temperature rises in the extrudate in agreement with measured values at the extruded material surface. The extrudate swell results show a maximum for a certain range of apparent shear rates also observed experimentally. However, the inelastic simulations based on the Herschel-Bulkley model always under-predict the experimental swelling values. A heuristic approach is also used to determine the level of elasticity required to produce the experimental values.     

Viscoplastic fluid flow in irregular eccentric annuli due to axial motion of the inner pipe

Fully developed axial laminar flow of viscoplastic Herschel-Bulkley fluids in eccentric annuli between two pipes has been investigated numerically. The pipes are closed at one end and flow is due to the axial motion of the inner pipe. The annuli may be filly open or partially blocked. General non-orthogonal, boundary-fitted curvilinear coordinates have been used to accurately model the irregular annular geometry due to the presence of a flow blockage. A computer code has been developed using a second-order finite-difference scheme. An exponential model for the shear stress, valid for both yielded and unyielded regions of the flow, is used in the computation. The effects of generalized Bingham number, flow behavior index, eccentricity, and blockage height on the pressure gradient or the surge pressure have been studied and the results are presented in dimensionless form. The pressure gradient is found to decrease with increasing eccentricity. For a partially blocked eccentric annulus the pressure gradient is found to decrease with an increase in the blockage height.     

A simplified couette flow solution of non-newtonian power-law fluids in eccentric annuli

Flow of non-Newtonian fluids in both the concentric and eccentric annuli is of great importance in extruders for molten plastics and wellbore fluid circulation for the removal of drilling cuttings. The steady laminar couette flow of non-Newtonian power-law fluids in eccentric annulus is employed in this study to analyze the problems of surge or swab pressures encountered when running or pulling tubular goods (pipes) in a liquid filled borehole. This is similar to the annular space created by two long co-axial cylinders with the inner cylinder in motion at a steady velocity, and a stationary outer cylinder. The solutions of the equations of motion are presented in both dimensionless form and as a family of curves for different pipe/borehole eccentricity ratios and power-law fluid index values for a more general application. The expected error in surge computation for concentric annulus as a result of eccentricity is evaluated.     

Inertia Effects on the Flow of Bingham Plastics Through Sudden Contractions in a Pipe

The present numerical study concentrates on the effects of moderate and high Reynolds numbers on the laminar flow of a non-Newtonian rigid viscoplastic (Bingham) fluid through a sudden contraction in a pipe. The flow is assumed to be steady, incompressible, and isothermal. Results are presented for a wide range of the governing Reynolds and yield numbers and the significant effects of these two parameters both on the integral and local kinematic properties of the flow field are established. Low yield numbers result in the disappearance of the recirculating flow region at the corner replacing it with a region of very low rates of deformation. The evolution of the centerline velocity in the vicinity of the contraction plane is shown to be independent of the yield number and dependent on the Reynolds number, while the concavities in the streamwise velocity profiles appearing at high Reynolds numbers are independent of the yield number. The pressure losses through the contraction increase with yield number with the effect being more pronounced at lower Reynolds numbers.     

水力旋流器内非牛顿流体多相流场的数值模拟

利用一种非牛顿流体黏度修正模型描述水力旋流器内高浓度矿浆的非牛顿流动特性,并结合雷诺应力模型(RSM)、混合多相流模型(Mixture)以及拉格朗日颗粒追踪模型(LPT)建立了一种适用于模拟水力旋流器内非牛顿流体多相流场的数学模型。模拟结果与报道的实验值的相对误差均在10%以内,表明了该模型的可靠性。结果表明,非牛顿流体黏度的空间分布与矿浆密度的空间分布类似。沿零轴速包络面(LZVV)的轮廓存在一个高密度环,其原因为某粒径范围内的颗粒受到的径向合力为零,颗粒群沿LZVV做高速旋转运动。分散相的空间分布取决于不同粒径的颗粒受力。对于不同粒径的单位质量颗粒,向外离心力的数值大约为向内压力梯度力的两倍左右,使得大颗粒进入下行流并在底流口收集。随着颗粒粒径的减小,总体向内且具有波动性的流体曳力呈指数增长。向内的流体曳力将部分颗粒推向轴心,经上行流逃逸,同时也增强了颗粒运动的随机性。当颗粒粒径小于一定值后,流体曳力远远大于离心力和压力梯度力,颗粒运动的随机性非常强,宏观表现为均匀分布。     

在同心和偏心圆环中有屈服应力的黏塑性流体流动的模型和数值模拟(英文)

Numerical solution of yield viscoplastic fluid flow is hindered by the singularity inherent to the Herschel-Bulkley model.A finite difference method over the boundary-fitted orthogonal coordinate system is util-ized to investigate numerically the fully developed steady flow of non-Newtonian yield viscoplastic fluid through concentric and eccentric annuli.The fluid rheology is described with the Herschel-Bulkley model.The numerical simulation based on a continuous viscoplastic approach to the Herschel-Bulkley model is found in poor accordance with the experimental data on volumetric flow rate of a bentonite suspension.A strict mathematical model for Herschel-Bulkley fluid flow is established and the corresponding numerical procedures are proposed.However,only the case of flow of a Herschel-Bulkley fluid in a concentric annulus is resolved based on the presumed flow structure by using the common optimization technique.Possible flow structures in an eccentric annulus are pre-sumed,and further challenges in numerical simulation of the Herschel-Bulkley fluid flow are suggested.     

微通道内屈服应力型流体的流变特性及多相流研究进展

屈服应力型流体（YSFs）是一种典型的非牛顿流体,因其丰富的流变特性被广泛关注。屈服应力是高浓度的粒子分散系统和凝胶状物质（多相乳液、微胶囊、3D打印复杂结构、药物输送凝胶等）的基本特征。本文对微通道内简单屈服应力型流体的流动特征和流变行为,及其流变性对多相流系统的影响进行了综述,剖析了受限空间内流体流动与流体流变性,及多相流动力学和界面现象的耦合机制,并对亟需推进的研究方向进行了展望。为微通道内屈服应力型流体的数值模拟、实验研究和应用提供参考。     

偏心组合桨搅拌槽内层流混合过程的数值模拟

目前,处理高黏流体和对剪切敏感介质的层流搅拌槽的报道并不多见。本文建立了描述双层组合桨搅拌槽内高黏非牛顿流体层流流动、混合过程的数学模型,利用Laminar模型、多重参考系法（MRF）和示踪剂浓度法对其流场特性、示踪剂扩散过程进行数值模拟,分析搅拌槽内轴向速度曲线、示踪剂浓度响应曲线和混合时间。结果表明：中心搅拌中间面将介质阻隔在各自的半层内运动,偏心搅拌介质作全局运动,轴向混合能力突出;转轴中心搅拌依靠上下半层浓度差的增大向下扩散,转轴偏心搅拌通过不对称结构扩散示踪剂,叶轮相对转轴偏心搅拌则利用叶片的不对称分布;距离加料点较近和较远的监测点浓度响应曲线因振荡和调整,混合时间较长,处于中间面的监测点拥有最短的混合时间。     

Numerical simulation of flow and mixing behavior of impinging streams of shear-thinning fluids

Due to their high efficiency, impinging streams, which involve the use of two inlet streams that enter the system through two closely spaced inlets along the same axis in opposite directions, have recently found many applications in the chemical and food industry as alternatives to conventional mixing operations. However, there is no prior work that focuses on the flow and mixing behavior of non-Newtonian impinging streams. Numerical simulation was therefore performed to investigate the flow and mixing behavior of steady-state, two-dimensional laminar confined impinging streams of shear-thinning fluids. The coupled heat, mass and momentum balance equations were solved with the finite element method using commercial software FEMLAB™ 3.0. The effects of various parameters, i.e., inlet jet Reynolds number based on the inlet slot width (Re_j) in the range of 10-200 and the flow behavior index of the fluids in the range of 0.6161-1, on the flow and mixing behavior of impinging streams were then investigated. Temperature of the mixing fluid was used as a passive tracer to monitor mixing in this study. The results were also compared and discussed with those of Newtonian impinging streams.     

最大叶片式桨在假塑性流体中的搅拌流场模拟

为研究最大叶片式桨在高黏假塑性流体中的搅拌流动行为,以黄原胶溶液为研究体系,采用计算流体力学方法重点研究了釜内流体的功耗特性、速率分布、剪切速率、表观黏度分布和总体流动状况。结果表明:最大叶片式桨具有与大多数径流桨相似的"双循环"流型结构,且预测的功耗特性与实验数据一致性良好。最大叶片式桨适用于高黏假塑性流体的混合,而对于高黏牛顿流体的混合则效果不佳。釜内的剪切速率分布较宽泛,且受转速影响较大。转速可作为该桨改善黄原胶体系混合效率的重要参数之一。     

Effect of agitation and aeration on gas dispersion efficiency in coaxial mixers containing yield-pseudoplastic fluids: Experimental and numerical analysis

Aerated stirred vessels are commonly employed to enhance gas dispersion. However, the associated high energy consumption is a challenging feature, particularly when dealing with complex non-Newtonian fluids. Coaxial mixers comprising a central impeller and a close-clearance impeller have emerged as an energy-efficient alternative that effectively intensifies gas dispersion. Hence, the objective of this study is to investigate the effect of aeration and agitation on the gas dispersion effectiveness of a coaxial mixer containing a yield-pseudoplastic fluid. An anchor-pitched blade turbine was employed to disperse air into a 1 wt.% xanthan gum solution, and the analysis primarily focused on characterizing the gas holdup and fluid flow behaviour. Gas holdup data were obtained experimentally using electrical resistance tomography (ERT), while computational fluid dynamics (CFD) simulations provided a detailed analysis of fluid flow patterns within the coaxial mixer. The rotational speed of the impeller exhibited a non-monotonic effect on the gas holdup, and a significant influence of the interaction between variables was identified. For instance, the experimental data showed that the aeration effect varied with the anchor speed. Nevertheless, the variables' interaction effect was explained by the change in flow pattern observed numerically. Furthermore, the CFD results demonstrated that high gas holdup does not necessarily indicate intensified mixing. Therefore, combining experimental data and numerical simulations enables a more accurate characterization of mixing performance. These findings contribute to the understanding and improvement of mixing performance in such a complex system, which is crucial for designing efficient operations.     

水平管道内固液两相流流动特性的CFD模拟

引言固液两相流管道水力输送技术始于20世纪初,现已广泛应用于能源、化工、石油、矿业、水利、冶金及环保等各工业领域,量化管道内固液两相流流动特性对于指导输送系统的安全运行及优化设计尤为关键。长期以来,两相流复杂的力学特性给     

压缩空气A类泡沫水平管路压降实验及数值模拟

压缩空气A类泡沫是具有非平衡自组织结构的两相可压缩非牛顿流体,针对不同发泡倍数的泡沫特性进行水平管路压降实验及数值模拟研究。泡沫具有良好的压缩性能,其内部压力随着压缩体积的增加呈指数型增长,并在1 MPa的实验压力下可保持结构稳定而不发生泡沫破碎。泡沫属于非牛顿流体,具有剪切变稀的性质,其黏度流变行为符合Herschel-Bulkley模型。综合考虑其压缩性能及黏度变化,运用Fluent数值模拟软件针对不同发泡倍数的泡沫在水平管路中的层流流动进行模拟,并通过实验检验其压降模拟结果的可靠性,结果表明其误差可控制在10%以内,模拟方法具有一定的准确性。     

矩形截面螺旋管内气液两相流型转换数值模拟

采用CLSVOF(coupled level set and volume of fluid method)方法,以空气和水为介质对矩形截面螺旋管内气液两相流动进行数值模拟,气相折算速度U_G为0.1～2.5 m·s^-1,液相折算速度U_L为0.09～4.5 m·s^-1.研究螺旋直径、螺旋升角对流型转换边界的影响,并绘制了不同螺旋直径、不同螺旋升角下的流型图.数值结果表明,与传统VOF方法相比,CLSVOF可以得到更精确的相界面;随着螺旋升角的增加,塞状流向泡状流的转换边界向U_L减小的方向进行,但是幅度很小,塞状流向弹状流的转换边界向U_L减小的方向进行;随着螺旋直径的增加,塞状流向泡状流的转换边界向U_L减小的方向进行,塞状流向弹状流的转换边界向U_L减小、U_G增大的方向进行;与Murai流型图相比,流型转换边界有所差异.     

流动聚焦微通道内牛顿微液滴在幂律剪切致稀流体中的生成研究

采用开源CFD软件OpenFOAM中的interFoam求解器对流动聚焦微通道内微液滴的形成过程进行了数值模拟。通过与文献中的实验数据进行对比,验证了VOF模型和幂律非牛顿流体模型的准确性。并以此为基础模拟了幂律剪切致稀流体中牛顿微液滴的形成过程,研究了幂律流体的幂律指数n和稠度系数K对微液滴生成的影响。研究表明,在滴状和挤压状流型中,离散线颈部宽度与周期内剩余时间呈幂律关系;离散线长度在坍塌阶段呈现线性缓慢增长,在夹断阶段呈现近似指数迅速增长的趋势。随着n和K的增大,液滴的尺寸逐渐减小,而生成频率则逐渐增大,且n的变化比K的变化对其产生的影响更明显。     

Modeling of cavern formation in yield stress fluids in stirred tanks

Prediction of cavern formation in yield stress fluids in stirred tanks is of great importance for optimization. A new torus model is developed and then validated by experimental data and computational fluid dynamics simulation. Unlike existing mathematical models, the new torus model assumes that the circular center of the torus should not be outside the impeller swept region as the Reynolds number (Re) increases. Hence the cavern boundary is shaped like an apple torus rather than a horn torus. The new model also considers the cavern‐vessel interactions. At relatively high Re, the new model predicts cavern shape and size better than other models. It correctly captures the cavern outline at various Re, which verified the assumption about torus center. The new model is then used to identify the influence of rheological parameters on cavern formation, and further extended to the cavern prediction of the dual‐impeller system. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3057–3070, 2014     

微通道内非牛顿流体中液滴生成机理研究进展

微流体技术良好的可控性为制备均一可控的微液滴提供了新的途径,而非牛顿流体因广泛的应用而受到关注。综述了近年来剪切变稀和黏弹性两类典型非牛顿流体中液滴生成机理的研究进展。围绕流动聚焦型和T型微通道两种典型微通道构型,介绍了非牛顿流体分别作为分散相和连续相时液滴生成过程的界面演化动力学,并与牛顿流体液滴生成过程进行了对比,分析了剪切变稀特性和弹性对主液滴和卫星液滴生成的影响。展望了非牛顿流体液滴生成过程待解决的关键科学问题,为进一步的模拟和实验研究提供了借鉴和参考。