THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

1　ＴｈｅＦｌｏｗＭｏｄｅｌｏｆＰｏｗｅｒ＿ＬａｗＦｌｕｉｄｉｎＲａｄｉｃａｌＦｒａｃｔａｌＲｅｓｅｒｖｏｉｒＴｈｅｔｒａｎｓｉｅｎｔｆｌｏｗｏｆｐｏｗｅｒ＿ｌａｗｆｌｕｉｄｉｎｒａｄｉｃａｌｆｒａｃｔａｌｒｅｓｅｒｖｏｉｒｉｓｓｔｕｄｉｅｄｉｎＲｅｆ.[1 ] ,ａｎｄａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｏｆＬａｐｌａｃｅｓｐａｃｅｉｓｄｅｒｉｖｅｄ .ＩｎＲｅｆ.[2 ] ,ｔｈｅｔｒａｎｓｉｅｎｔｅｌｌｉｐｔｉｃａｌｆｌｏｗｉｓｒｅｓｅａｒｃｈｅｄｏｎｍｏｄｅｌｏｆｅｘｐａｎｄｉｎｇｒｅｃｔａｎｇｌｅ .Ｔ…     

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

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

分形油藏不稳定渗流问题的精确解

研究了分形油藏无限大地层和有界地层渗流模型，引入了一类有限广义Ｈａｎｋｅｌ变换，利用这种变换和Ｗｅｂｅｒ变换，在井底定流量和定压生产时，对无限大地层及有界地层（包括封闭和定压地层）六种情况，求得了实空间解析解用双参数（ｄｆ，ｄｓ）来刻画分形油藏的分形特性，分析了分形油藏压力动态特征以及分形参数和边界对压力动态的影响     

Exact solutions for nonlinear transient flow model including a quadratic gradient term

The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform.Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.     

Finite element analysis of non-Newtonian fluid flow in 2-d branching channel

This paper presents finite element analysis of non-Newtonian fluid flow in 2-d branching channel. The Galerkin method and mixed finite element method are used. Here the fluid is considered as incompressible, non-Newtonian fluid with Oldyord differential-type constitutive equation. The non-linear algebraic equation system which is formulated with finite element method is solved by means of continuous differential method. The results show that finite element method is suitable for the analysis of non-Newtonian fluid flow with complex geometry.     

An investigation on internal thermal flow of non-Newtonian fluid

In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the fiow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied, For the flow into mould cavity the constitutive equation of power-law fluid is used as a rheological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid fiow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting differen     

基于分形理论的煤层气非达西流动分析

在考虑了煤层的分形特征和启动压力梯度影响的基础上,建立了无限大煤层中气体低速非达西流动的数学模型,并求得了量纲为一的井底压力的Laplace空间解析解,并根据数值求解结果绘制了典型的井底压力动态曲线。研究结果表明:在定产量生产的情况下,分形维数和量纲为一的启动压力梯度对早期井底压力动态无显著影响;在生产的中后期,由于受二者的影响,压力导数曲线上的径向流水平直线段消失;量纲为一的井储系数的影响主要表现在续流阶段,而吸附系数则主要影响煤基质向裂隙扩散的过渡阶段。     

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied.The existence and uniqueness of the solutions are examined,which are found to depend on the curvature of the solutions for different values of the power law index n.It is established with the aid of the Picard-Lindel¨of theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions.This is done after a suitable transformation of the dependent and independent variables.For 0 n 1,the solution has a positive curvature,while for n 1,the solution has a negative or zero curvature on some part of the global domain.Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.     

Magnetohydrodynamic transient flows of a non-Newtonian fluid

Some exact solutions of the time-dependent partial differential equations are discussed for flows of an Oldroyd-B fluid. The fluid is electrically conducting and incompressible. The flows are generated by the impulsive motion of a boundary or by application of a constant pressure gradient. The method of Laplace transform is applied to obtain exact solutions. It is observed from the analysis that the governing differential equation for steady flow in an Oldroyd-B fluid is identical to that of the viscous fluid. Several results of interest are obtained as special cases of the presented analysis.     

Nitrogen/non-Newtonian fluid two-phase upward flow in non-circular microchannels

This paper presents experimental investigations on nitrogen/non-Newtonian fluid two-phase flow in vertical noncircular microchannels, which have square or triangular cross-section with the hydraulic diameters being D_h = 2.5, 2.886 and 0.866 mm, respectively, by visualization method. Three non-Newtonian aqueous solutions with typical rheological properties, i.e., 0.4% carboxymethyl cellulose (CMC), 0.2% polyacrylamide (PAM) and 0.2% xanthan gum (XG) are chosen as the working fluids. The common flow patterns are identified as slug flow, churn flow and annular flow. The dispersed bubble flow is only found in the case with nitrogen/CMC solution two-phase flow in the largest channel. A new flow pattern of nitrogen/PAM solution two-phase flow, named chained bubble/slug flow, is observed in all the test channels. The flow regime maps are also developed and the results show that the rheological properties of the non-Newtonian fluid have remarkable influence on the flow pattern transitions. The geometrical factors of the microchannel such as the cross-section shape and hydraulic diameter of the channel can also affect the flow regime map. Finally, the results obtained in this work are compared with the available flow pattern transitions.     

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.     

Unsteady unidirectional micropolar fluid flow

This paper considers the unsteady unidirectional flow of a micropolar fluid, produced by the sudden application of an arbitrary time dependent pressure gradient, between two parallel plates. The no-slip and the no-spin boundary conditions are used. Exact solutions for the velocity and microrotation distributions are obtained based on the use of the complex inversion formula of Laplace transform. The solution of the problem is also considered if the upper boundary of the flow is a free surface. The particular cases of a constant and a harmonically oscillating pressure gradient are then examined and some numerical results are illustrated graphically.     

A perturbation solution for non-Newtonian fluid two-phase flow through Porous media

In this paper, the mathematical problem of weak non-Newtonian fluid two-phase flow through porous media, including the effect of capillary pressure, is solved by singular perturbation method in combination with regular perturbation method. The asymptotic analytical solutions of the fractional flow function and the wetting phase saturation are obtained. The results are verified by numerical calculations and by classical solutions for corresponding Newtonian case. The influences of the non-Newtonian exponent and capillary pressure are discussed.     

Computational intellectual analytical theory of computational analytical approach to rotating flow of non-Newtonian fluid

Ａｎｅｗｆｉｅｌｄｏｆｍｏｄｅｒｎｃｏｍｐｕｔｅｒｓｃｉｅｎｃｅ—ａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅｉｓｄｅｖｅｌｏｐｅｄｒａｐｉｄｌｙ．Ｔｈｅｓｙｍｂｏｌｉｃｍａｎｉｐｕｌａｔｉｏｎｉｓｔｈｅｆｒｏｎｔｄｉｒｅｃｔｉｏｎｉｎｔｈｅａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅ．Ａｓｅｒｉｅｓｏｆｔｈｅｃｏｍｐｕｔｅｒｓｏｆｔｗａｒｅｉｓｄｅｖｅｌｏｐｅｄｆｏｒｔｈｅｃｏｍｐｕｔａｔｉｏｎａｌｍａｎｉｐｕｌａｔｉｏｎ,ｓｕｃｈａｓＭａｃｓｙｍａ,Ｍａｐｌｅ,Ｍａｔｈｅｍａｔｉｃａ,ｔｏｃ…     

On the dispersion of soluble matter in a channel flow of non-Newtonian fluid

Summary An analysis of the dispersion of a solute in Rivlin-Ericksen third-order fluid in a parallel plate channel is carried out. It is seen that the solute which is dispersed relative to a plane moving with the mean speed of the flow has its effective Taylor diffusion coefficient which decreases with increasing the non-Newtonian parameter With 1 table     

基于WDQ法的粘弹性输流管道稳定性分析

在微分求积法（DQ法）基础上,根据多分辨分析理论,以尺度函数为基础构造插值基函数,形成小波微分求积法（WDQ法）,用该方法研究了简支Kelvin型粘弹性输流管道的稳定性问题,给出了不同参数下管道复频率随内部流速的变化关系,分析了外部流速对Kelvin型粘弹性输流管道在不同延滞时间下的振动特性及稳定性的影响。     

Generalized integral transform solution for boundary layer flow over a sphere

The generalized integral transform technique is applied to the boundary layer equations for flow over a sphere in their primitive variables. Even though a diffusion-based eigenvalue problem is used, the velocity profile, shear stress and separation point have been calculated with high accuracy. Low-order approximations are shown to be accurate near the surface and the predictions of the separation point is very good. Comparison with finite difference results shows the better convergence behaviour of the integral transform method.     

Extended thermodynamics of a non-Newtonian fluid

Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.     

Heat transfer and entropy generation analysis of non-Newtonian fluid flow through vertical microchannel with convective boundary condition

The entropy generation and heat transfer characteristics of magnetohydrodynamic(MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogel's model. The equations describing flow and heat transport along with boundary conditions are first made dimensionless using proper non-dimensional transformations and then solved numerically via the finite element method(FEM). An appropriate comparison is made with the previously published results in the literature as a limiting case of the considered problem.The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space-and thermal-dependent heat source(ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.