Drag on non-spherical particles in non-newtonian fluids

Extensive experimental results on the free fall of a range of non-spherical particles such as square bars, cylinders, spheres and crushed rock chips in Newtonian, inelastic, viscoelastic and Boger fluids are presented. It is demonstrated that the use of a volume equivalent sphere diameter in addition to a shape factor provides an adequate approximation for the non-sphericity of particles used in this study. The applicability of two rheological models, namely, the power-law and the Carreau viscosity model has been examined in representing the drag coefficient results. Appropriate predictive expressions of the drag coefficient as a function of the particle Reynolds number and the Deborah number, encompassing wide ranges of rheological and kinematic conditions, are presented.     

Drag coefficients of irregularly shaped particles

The steady-state free-fall conditions of isolated groups of ordered packed spheres moving through Newtonian fluids have been studied experimentally. Measurements of the drag coefficients are reported in this paper for six different geometrical shapes, including isometric, axisymmetric, orthotropic, plane and elongated conglomerates of spheres. From these measurements, a new and accurate empirical correlation for the drag coefficient, C_D, of variously shaped particles has been developed. This correlation has been formulated in terms of the Reynolds number based on the particle nominal diameter, Re, the ratio of the surface-equivalent-sphere to the nominal diameters, d_A/d_n, and the particle circularity, c. The predictions have been tested against both the experimental data for C_D collected in this study and the ones reported in previous works for cubes, rectangular parallelepipeds, tetrahedrons, cylinders and other shapes. A good agreement has been observed for the variously shaped agglomerates of spheres as well as for the regularly shape particles, over the ranges 0.15<Re<1500, 0.80<d_A/d_n<1.50 and 0.4<c<1.0.     

Drag coefficient and settling velocity for particles of cylindrical shape

Solid particles of cylindrical shape play a significant role in many separations processes. Explicit equations for the drag coefficient and the terminal velocity of free-falling cylindrical particles have been developed in this work. The developed equations are based on available experimental data for falling cylindrical particles in all flow regimes. The aspect ratio (i.e., length-over-diameter ratio) has been used to account for the particle shape. Comparisons with correlations proposed by other researchers using different parameters to account for the geometry are presented. Good agreement is found for small aspect ratios, and increasing differences appear when the aspect ratio increases. The aspect ratio of cylindrical particles satisfactorily accounts for the geometrical influence on fluid flow of settling particles.     

New simple correlation formula for the drag coefficient of non-spherical particles

A simple correlation formula for the standard drag coefficient (i.e. a single stationary particle in a uniform flow) of arbitrary shaped particles is established using a large number of experimental data from the literature and a comprehensive numerical study [A. Hölzer, M. Sommerfeld, IUTAM Symposium on Computational Approaches to Multiphase Flow, Springer, 2006]. This new correlation formula accounts for the particle orientation over the entire range of Reynolds numbers up to the critical Reynolds number. Such a correlation may be easily used in the frame of Lagrangian computations where also the particle orientation along the trajectory is computed.     

An experimental study of non-newtonian fluid flow through fixed and fluidized beds of non-spherical particles

Extensive measurements of pressure drop in fixed beds, minimum fluidization velocity and expansion characteristics for beds of non-spherical particles are reported in the following ranges of conditions: 10^-3 ≤ Re ≤ 20; 0.66 ≤ n ≤ 1 and 0.41 ≤ ? ≤ 0.75. Based on an analysis of these results, it is illustrated that the existing frameworks originally developed for Newtonian fluid flow through beds of spherical particles are also satisfactory for power law fluid flow through beds of non-spherical particles, provided a volume equivalent diameter modified by a sphericity factor and a modified Reynolds number are used instead of their usual definitions.     

Comparison of formulas for drag coefficient and settling velocity of spherical particles

Two formulas are proposed for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region. Comparisons with fourteen previously-developed formulas show that the present study gives the best representation of a complete set of historical data reported in the literature for Reynolds numbers up to 2 × 10⁵.     

Fractions design of irregular particles in suspensions for the fabrication of multiscale ceramic components by gelcasting

A new approach for the preparation of suspensions with a high solid loading and low viscosity by using irregular particles was proposed. These suspensions were prepared for the fabrication of multiscale ceramic components by gelcasting. Based on the Funk-Dinger function and fractal theory, the closest packing theory was applied to optimize the volume fractions of different particles. The maximum solid loading of slurries prepared for gelcasting was 62 vol%, and the viscosity at a shear rate of 100 s^?1 was only 0.29 Pa s. By as-prepared suspensions, a decimeter-scale ceramic part with submillimeter features was fabricated successfully by gelcasting, which verify the feasibility of the proposed method.     

Drag coefficients of variously shaped solid particles,drops, and bubbles

This article, which is largely a review, deals with the drag force and drag coefficient for rigid spherical and deformable particles in ordinary and non-Newtonian fluids. The most important theoretical formulas for small Reynolds numbers of Re ≪ 1 and semiempirical formulas for the drag coefficient in a wide Re range up to 10⁶ are presented. The deformation of drops and bubbles and its effect on the drag coefficient are considered.     

溶剂对聚合物减阻剂流变行为和减阻性能的影响

采用博力飞旋转粘度计测定了减阻剂在不同溶剂中溶液的流变性能,通过减阻剂室内模拟环道评价装置测定了不同溶剂合成的聚合物的减阻率。结果表明,减阻剂属于典型的剪切增稠型非牛顿流体;减阻剂在不同溶剂中溶液的粘度随着温度升高而降低;当环己烷与减阻剂的溶度参数相等时,减阻剂在环己烷中的溶解性能最好。并探讨了剪切增稠流体的减阻机理,分析了不同溶剂合成的减阻剂对减阻性能的影响。     

溶液聚合合成减阻剂及其特征对减阻的影响

油相减阻剂的合成方法主要分为本体聚合法和溶液聚合法.对溶液聚合法合成的α-烯烃聚合物进行室内模拟环道评价装置、凝胶渗透色谱、核磁共振及红外光谱测试,分析结果表明,溶液聚合转化率高达97.92%,产物为超高分子质量聚合物,减阻率达到56.45%接近于美国固体产品的减阻率.     

The Use of Drag Reduction Agent and a Detergent for Drag Reduction in Circulatory Vertical Pipe Flow

This paper describes the results of an experimental study of drag reduction in a circulatory vertical pipe system for both upward and downward flows using a drag reduction agent, corrosion inhibitor, and a cheap detergent (washing-up liquid) with various concentrations for different flow rates.

It was found that the corrosion inhibitor did not produce any drag reduction effect for both upward and downward flows while the drag reduction agent was effective for both flows; whereas, the detergent was effective only for upward flow. A comparison of the effectiveness of the drag reduction agent against the detergent showed that the effectiveness of the drag reduction agent is much higher than that of the detergent. The effect of liquid detergent is only noticeable if a large concentration is used. A 1000-ppm of detergent produces the same results as 25 ppm of drag reduction agent, which undermined the lower cost of the detergent. Over the range of Reynolds numbers tested the maximum drag reduction for upward flow is 35% while for the downward flow is 42%.     

Effect of Blockage on Heat Transfer Phenomena of Spheroid Particles at Moderate Reynolds and Prandtl Numbers

Effects of the confining wall or blockage on the heat transfer phenomena of spheroid particles were numerically investigated. The heated spheroid particles were maintained at constant temperature and allowed to sediment in cylindrical tubes filled with Newtonian liquids. In this flow configuration, the heat transfer took place from the heated spheroid particles to the surrounding Newtonian liquid. The governing conservation equations of the mass, momentum, and energy together with appropriate boundary conditions were numerically solved using commercial software based on computational fluid dynamics. A simple correlation for the average Nusselt number of the confined spheroid particles was developed which can be applied in new applications.     

抽油机及其拖动系统节能综述

目前,油田在用的游梁式抽油机效率低、耗能高,在一定程度上加重了企业生产成本,节能降耗问题越来越受到关注。通过分析抽油机系统效率的影响因素、抽油机负荷以及电机的工作原理,得出抽油机低效率、高耗能的原因（也是抽油机拖动系统的高耗能原因）,并总结了节能型抽油机、节能驱动设备和节能减速器三类节能方法,介绍了现有抽油机拖动系统的节能措施。     

Drag Reduction by Wormlike Micelles of a Biodegradable and Non-Biodegradable Surfactants

This study describes the effects of wormlike micelles formed by the commercial surfactants tallowalkylamidopropyl dimethylamine oxide (Aromox APA-TW) and oleyl methyl bis(2-hydroxyethyl) ammonium chloride (Ethoquad O/12) as drag reducers. Ethoquad O/12 is immune to degradation by heat and microorganisms. Conversely, Aromox APA-TW is biodegradable in the environment, and its susceptibility to heat-induced degradation was previously assessed. This work considers the effects of temperature, salt, and time on the drag-reduction capacity (in different Reynolds number) of wormlike micelles of these two surfactants. Wormlike micelles formed by Aromox APA-TW are able to reduce drag at higher temperatures compared to wormlike micelles formed by Ethoquad O/12. However, Aromox APA-TW can degrade after being heated to 80 °C and also after storage of the wormlike micelle solutions. Ethoquad O/12 does not undergo degradation after being heated or stored. These surfactants have the potential to be used as additives in industrial operations, as the wormlike micelles formed are able to reduce drag in systems with long pumping distances or recirculation, even in solutions with high salt concentrations (brine) and high temperatures.     

容器焊缝错边残余应力与载荷应力的测定研究

本文对焊接容器错边和不错边的焊接接头进行了电测法的残余应力测试，确定了焊接残余应力的大小及方向，并在加载的条件下，对各焊接接头测点进行了综合应力测试，并给出了受载条件下的应力分布。     

聚1-十二烯减阻剂粘均分子量与减阻率关系的研究

用室内模拟环道评价装置测定了聚1-十二烯减阻剂的减阻率,乌氏粘度计测定了聚1-十二烯减阻剂的特性粘数,并通过25℃下聚辛烯的Mark-Houwink方程估算了样品的粘均分子量,最后比较发现,减阻率随粘均分子量增大而增加,但粘均分子量过大时,减阻率反而减小。     

On the drag coefficient of flat and non-flat solid particles of irregular shapes: An experimental validation study

The very wide varieties of geometries of irregular particles makes it difficult to study their motion also propose a simple and general equation to estimate their drag coefficient (C_D). The goal of this research is to (1) experimentally validate the general C_D correlation previously proposed by the authors of this article as a simple tool to estimate the C_D of spherical to highly irregular particles over a wide ranges of Re from 0.001 to 300,000, and (2) examine and expand the reference model particles proposed by the authors to represent a wide range of irregular shapes (60 non-flat and 36 flat). A comparison between the C_D experimentally measured using reference model particles over a range of Re from 9 to 2481 and the C_D estimated using general C_D correlation, also comparing with C_D correlations by others, demonstrated the accuracy and simplicity of the proposed general C_D correlation.     

含高比例疏水单体的降阻剂的合成及性能评价

使用3-溴丙烯和N,N-二甲基十八烷基叔胺合成水溶性阳离子疏水单体N,N-二甲基十八烷基烯丙基溴化铵(DOAB),仅使用水作为溶剂,合成了含有高摩尔分数疏水单体的部分水解聚丙烯酰胺型降阻剂,以核磁氢谱和元素分析得到降阻剂的结构为P(AM0.877-AA0.113-DOAB0.01);激光光散射法测得降阻剂摩尔质量为1.22×10~7 g/mol;黏度法测得临界缔合浓度(CAC)为2.8 g/L。测试了不同质量浓度下降阻剂稀溶液(即滑溜水)在不同流速下的摩阻,以清水为空白组计算降阻率,当降阻剂质量浓度为1.3 g/L时,降阻率最高可达72%;在盐水中,滑溜水降阻率下降,通过提高降阻剂质量浓度的方式可以提升降阻率,盐水中的降阻剂质量浓度为2 g/L时,降阻率最高达70.06%。由SEM得知,降阻剂在水中形成的网状结构是聚合物具有降阻性的直接原因。     

低粘附功管壁的内流减阻研究

以乙烯基三乙氧基硅烷 无水乙醚溶液处理玻璃管道内壁 ,降低流体水与管壁间的粘附功 ,研究了低粘附功内壁管道的内流减阻性能。结果表明 ,在管壁与液体间的粘附功小于液体的内聚功条件下 ,当雷诺数大于临界雷诺数时 ,低粘附功内壁管道呈现明显的内流减阻效果 ,临界雷诺数的值与一定的临界壁面剪力值或层流底层临界厚度值相对应 ;在减阻区内 ,减阻率随雷诺数的增加及管道内径的减小而增大 ,阻力系数的无因次关联式可表示为λ=f (Re ,X) ,其中X为无因次数群 [W / (du2 ρ) ]。