Analytical solutions of the helical flow of non newtonian fluid in eccentric annular space

ＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＳＯＦＴＨＥＨＥＬＩＣＡＬＦＬＯＷＯＦＮＯＮＮＥＷＴＯＮＩＡＮＦＬＵＩＤＩＮＥＣＣＥＮＴＲＩＣＡＮＮＵＬＡＲＳＰＡＣＥＺｈａｎｇＨａｉ－ｑｉａｏ（张海桥）ＷｕＪｉ－ｚｈｏｕ（吴继周）（ＴｈｅＤｅｐａｒｔｍｅｎｔｏｆ...     

Measurements of pulsating and oscillating flows of non-Newtonian fluids through concentric and eccentric cylinders

The unsteady flow of non-Newtonian fluids through concentric and eccentric cylinders was investigated experimentally. Two experiments were carried out; one was pulsating flow and the other was flow under a constant pressure gradient with the inner cylinder oscillating longitudinally. The flow enhancement was examined and its dependence on the frequency of the oscillations and the eccentricity of the apparatus was determined.     

Flow of a viscoelastic fluid between eccentric cylinders

The velocity field in the annular region between two eccentric cylinders for a second-order fluid is determined. Second-order velocity terms appear only as a result of the interaction between imposed axial and planar motions. When only one of the two motions is imposed by the boundary conditions, the velocity field coincides with that of a Navier-Stokes fluid.The results of the present study are to be used in a future investigation of the stresses, forces, and torques acting on the walls of the cylinders to enable a rheometer based on the present boundary value problem to be suggested.     

Pertubation solution of non-newtonian fluid axial laminar flow through eccentric annuli

Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity ε is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.     

Study on steady surge pressure for Yield-Pseudoplastic fluid in a concentric annulus

Surge pressure caused by pipe moving through the wellbore full of drilling fluid is the main factor affecting wellbore stability, on which the additional mud density is designed. Thus it is desired to predict the surge pressure with high accuracy. While this is closely related with the selection of mud rheological models. Yield-Pseudoplastic model which has three parameters and is famous for its higher accuracy has been used to describe the mud rheological properties in recent years. Based on this model the paper presents a new theoretical model for calculating surge pressure caused by mud viscosity during tripping or casing in a concentric annulus of directional wells under steady laminar situation. For convenience, the paper plots the distribution of the coefficients of surge pressure for different conditions. An example is given. These results provide the basis for controlling pressure surges and tripping velocity.     

最大偏心圆环空间自然对流传热的数值分析

采用正切圆坐标变换 ,对不同直径比以及上、下、侧面三种偏心位置 ,偏心率达到最大值± 1的变壁温水平圆柱环形封闭空间内空气的自然对流传热进行了数学模拟 ,求出的二维空间温度分布与实验拍摄相应的温度干涉条纹图片吻合良好。计算结果同时给出流线分布及内、外壁面的局部传热系数、热流量。并与现有的偏心率小于 1的有关资料作对比分析。数值计算的范围是 :2 .0× 1 0 2 ≤ Ra≤ 3 .0× 1 0 5,1 .3≤ Do/Di≤ 3 .8,Pr=0 .70 6,|ε|=1 .     

Axial Couette flow of an Oldroyd-B fluid in an annulus

This paper establishes the velocity field and the adequate shear stress corresponding to the motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders by means of finite Hankel transforms. The flow of the fluid is produced by the inner cylinder which applies a time-dependent longitudinal shear stress to the fluid. The exact analytical solutions, presented in series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. The general solutions can be easily specialized to give similar solutions for Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid motion are graphically illustrated.     

Flow of viscoelastic fluids through an abrupt contraction

Summary Developing and fully developed velocity profiles were measured for viscoelastic fluids flowing through an abrupt 2 to 1 glass-contraction. An R 16Weissenberg-Rheogoniometer was used to measure the rheological properties of the viscoelastic fluids in the shear rates range of interest in the contraction. The measured entry lengths for the viscoelastic fluids were significantly less than predictions and experimental values for inelastic fluids with the same power-law parameters. Deviations from inelastic entry behaviour ranged from 11.6–100%, were independent ofReynolds number, but were strongly dependent on the ratio of the friction velocity to the shear wave velocity. Increasing the friction velocity relative to the shear wave velocity resulted in an increased deviation from inelastic behaviour. When the friction velocity was of the same order as the shear wave velocity a zero entry length and a fully developed entry velocity profile were observed. Further increase in the friction velocity relative to the shear wave velocity resulted in anomalous entry behaviour accompanied by unusual flow patterns upstream of the contraction.

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Zusammenfassung Es wurden sich bildende sowie voll ausgebildete Geschwindigkeitsprofile viskoelastischer Flüssigkeiten in einer scharfkantigen Rohrverengung von 2 zu 1 gemessen. Ein Weissenbergsches Rheogoniometer R 16 diente zur Charakterisierung der viskoelastischen Flüssigkeiten im betreffenden Deformationsgeschwindigkeitsbereich.Meßergebnisse für die Einlauflänge viskoelastischer Flüssigkeiten weichen bedeutend von den Voraussagen sowie von Meßergebnissen für unelastische Flüssigkeiten ab, die, nach demOstwald- de Waeleschen Modell berechnet, die gleichen Kenngrößen aufzeigen.Die Abweichung vom viskosen Einlaufverhalten beträgt 11,6 bis 100%. Sie ist unabhängig von der Reynoldschen Zahl, hängt aber sehr stark ab von dem Verhältnis zwischen zwei Geschwindigkeiten u^*=Schubspannungsgeschwindigkeit undu=Scherwellengeschwindigkeit.Eine Erhöhung vonu ^* gegenüberu verursacht eine erhöhte Abweichung vom unelastischen Verhalten. Wenn die zwei Geschwindigkeitenu ^* undu von der gleichen Größenordnung sind, verschwindet die Einlaufsentwicklung und ein vollausgebildetes Geschwindigkeitsprofil tritt schon am Eingang auf. Ein weiteres Erhöhen vonu ^* überu verursacht anomales Einlaufverhalten mit ungewöhnlichem Strömungsbild oberhalb der Verengung.

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On Sabbatical Leave: Dept. of Chemical Engineering, University of Toronto, Toronto 181, Ontario, Canada.     

大间隙环流中偏心转子动特性系数的数值分析方法

基于作者用整体流动理论和Moody壁面摩擦系数方程建立的大间隙环流中转子动特性系数数值计算模型,应用摄动方法推导了大间隙环流流场非线性控制方程组的一阶摄动方程,提出了求解大间隙环流中偏心转子动力学特性系数的数值分析方法。用该方法得到的数值结果与已有的解析解和实验结果具有较好的一致性。     

Entry flow behaviour of viscoelastic fluids in an annulus

Developing and fully developed velocity profiles in the entrance region of an abrupt 2-to-1 annular contraction were measured for a number of visco-elastic polymer solutions. Experimental results were obtained for Reynolds number and flow behaviour index in the range 9.8 ? Re ? 355 and 0.372 ? n ? 0.55 respectively. A momentum-energy integral technique was employed in the boundary layer analysis. The deviation from inelastic behaviour was indicated by the ratio of elastic to inertial forces, Ws/Re. Within the limits of confidence of the experimental results, good agreement with theoretical predictions was obtained and very little deviation from inelastic behaviour was observed for Ws/Re < 0.08. For the test fluids investigated, the entrance length was found to be longer than that predicted for the corresponding inelastic fluids of the same n.     

Numerical study of flows of complex fluids between eccentric cylinders using transformation functions

In this paper, we investigate fluid flows between eccentric cylinders by means of two stream‐tube analyses. The first method considers a one‐to‐one global transformation function that allows the physical domain to be transformed into a mapped domain, used as computational domain, that involves concentric streamlines. The second approach uses local transformations and domain decomposition techniques to deal with mixed flow regimes. Both formulations are particularly adapted for handling time‐dependent constitutive equations, since particle‐tracking problems are avoided. Mass conservation is verified in both formulations and the relevant numerical procedure can be carried out using simple meshes built on the mapped streamlines. Fluids obeying anelastic and viscoelastic constitutive equations are considered in the calculations. The numerical results are consistent with those in the literature for the flow rates tested. Application of the method to the K‐BKZ memory‐integral constitutive equation highlights significant differences between the model predictions and those provided by more simple rheological models. Copyright © 2002 John Wiley & Sons, Ltd.     

On exact solutions of the flow equations for Bingham visco-plastic fluids through an eccentric annular cross-section

We discuss properties of solutions of the Bingham flow equations for visco-plastic fluids through an eccentric annular cross-section. Particularly, we perform arguments which are not in favor of the well-known Szabo–Hassager’s conjecture that the rigid zone is confined by circles provided the eccentricity is small (J Non-Newtonian Fluid Mech 45:149-169, 1992).     

Self-similar solutions for displacement of non-Newtonian fluids through porous media

This paper presents a class of self-similar solutions describing piston-like displacement (single-phase flow is included as a special case) of one slightly compressible non-Newtonian, power-law, dilatant fluid by another through a homogeneous, isotropic porous medium. These solutions can be used to evaluate the validity and accuracy of existing approximate solutions, such as the assumption of constant flow rate at each radial distance that Ikoku and Ramey use to linearize the partial differential equation for the flow of non-Newtonian, power-law fluid through a porous medium.Nomenclature a parameter, defined by (A8) - A cross-section area of linear reservoir - B constant - c fluid compressibility - c _f formation compressibility - c _t system compressibility - c t dimensionless system compressibility, defined by (24) - C constant of integration - D _I dimensionless coefficient, directly proportional to injection rate, for linear displacement case, defined by (22). - D ₂ dimensionless coefficient, directly proportional to injection rate, for radial displacement case, defined by (55) - erf(x) error function - ercf(x) complementary error function - Ei(x) exponential integral - f dimensionless pressure, defined by (10) - h formation thickness - k permeability - l linear location of moving boundary between the displacing and displaced fluids - n flow behavior parameter - p pressure - p _i injection pressure - p ₀ initial pressure; reference pressure - p ₀ dimensionless initial pressure, defined by (19) - q injection rate - r radial distance - R radial location of moving boundary between the displacing and displaced fluids - t time - u superficial velocity - U substitution of variable - x linear distance - _e effective viscosity - _e dimensionless effective viscosity, defined by (24) - dimensionless variable, defined by (9) or (45) - _i0 value of corresponding to the location of the moving boundary between the displacing and displaced fluids - density - ₀ value of density at reference pressure - porosity - ₀ value of porosity at reference pressure - 1 displacing fluid - 2 displaced fluid     

Unsteady rotative flow of non-Newtonian fluid in an annular pipe

ＵＮＳＴＥＡＤＹＲＯＴＡＴＩＶＥＦＬＯＷＯＦＮＯＮ－ＮＥＷＴＯＮＩＡＮＦＬＵＩＤＩＮＡＮＡＮＮＵＬＡＲＰＩＰＥＨｕａｎｇＪｕｎ－ｑｉ（黄军旗）（Ｄｅｐｔｏｆ＇Ｒｅｓｏｕｒ＆Ｅｎｖｉ．Ｓｃｉ．Ｂｅｉｊｉｎｇ．ＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙＢｅｉｊｉｎ...     

Flow of Maxwell fluids in porous media

In this paper we analyze the flow of a Maxwell fluid in a rigid porous medium using the method of volume averaging. We first present the local volume averaged momentum equation which contains Darcy-scale elastic effects and undetermined integrals of the spatial deviations of the pressure and velocity. A closure problem is developed in order to determine the spatial deviations and thus obtain a closed form of the momentum equation that contains a time-dependent permeability tensor. To gain some insight into the effects of elasticity on the dynamics of flow in porous media, the entire problem is transformed to the frequency domain through a temporal Fourier transform. This leads to a dynamic generalization of Darcy's law. Analytical results are provided for the case in which the porous medium is modeled as a bundle of capillary tubes, and a scheme is presented to solve the transformed closure problem for a general microstructure.     

Analytical solution of flow of second-order non-Newtonian fluids through annular pipes

This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method.Based on the numerical results,the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed.It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity,average velocity have a(?)aller value for a given Hc.Else,when radii ratio keeps unchanged,the shear stress of inner wall of annular flow will change with the inner radius compared with the general pipe flow and is always smaller than that of the outer wall.     

环空流道液流失速水击特性及其成因的研究

环空流道与圆管的结构差异,使得其失速水击特性及其成因亦有不同。为了对其进行分析研究,利用PIV对套管环空和圆管流水击流场进行拍摄,并通过Tecplot显示流场,提取轴向速度和径向速度、等速度线等参数加以分析;同时采用高精度智能动态压力传感器采集了套管环空内、外壁及内管内壁压力,对环空中水击特性进行了进一步研究。结论是:水击发生时环空断面外壁面水击压力大于内壁面水击压力;同初速情况下环空液流水击压力大于圆管流水击压力;环空中水击压力衰减速度快于圆管中;涡流是水击压力衰减以及速度变化的主要因素;水击压力振荡变化主要是压力涡流引起的断面能量的相互转化形成的。     

偏心圆柱塞状管流的数值模拟

在全面调研了国内外关于两相在管道中的偏心圆柱塞状管流的研究文献之后，发现几乎都利用经验公式或近似估计式进行水力计算，这与石油工业中两相流的广泛应用极不相适应。根据流体力学中N-S方程对层流的描述，再结合经典的力学理论分析，对两相偏心圆柱塞状管流的相界面提出严密而科学的力学耦合条件，得到了完整描述偏心环状管流的适定的偏微分方程组，然后利用双极坐标变换化不规则的区域为规则的矩形域及计算机仿真技术，得到了两相流中偏心圆柱塞状管流的流动规律，对石油工业具有重要的工程应用价值。     

Studies on the law of laminar helical flow of power-law fluid in eccentric annuli

According to the principle of fluid mechanics,the law of laminar,helical flow of power-law fluid in eccentric annuli is studied extensively in this paper.The apparent viscosity,velocities distribution of laminar helical flow of power-law fluid are discussed and calculating methods of flow rate and pressure loss are presented.The factors influencing flow are also analysed.On the basis of theoretical studies some new results of the present paper are compared with the theories of the helical flow of the power-law fluid in concentric annuli.The test verified that theoretical formulas in this article are proper and general.They can be used for calculating hydraulic parameters in drilling engineering.     

Elastic–plastic near field solution of an eccentric crack under shear in a finite width plate

The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite width plate, and the analytical solution is obtained in this paper. The solution includes: the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line, variations of the length of the plastic zone along the crack line with an external loads, and the bearing capacity of a finite plate with a centric crack loaded by shear stress in the far field. The results obtained in this paper are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions have been taken. Subsequently, the present results are compared with the traditional line elastic fracture mechanical solutions and elastoplastic near field solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.