Damped Oscillation of Liquid Column in Vertical U-Tube for Newtonian and non-Newtonian Liquids

Damped oscillation of Newtonian liquid in a vertical U-tube is one of the well known phenomena and the solution of this liquid motion for the laminar flow regime in the circular pipe was solved, however, generally speaking, even if the period of the oscillational motion by this solution is nearly coincided with that of the experimental result, the estimation of the damped oscillational process with lapse of time by the solved equation is not in agreement with that of the experimental result. Therefore basing upon the experimental results of the velocity distributions of the oscillational motion in the circular U-tube for the Newtonian and non-Newtonian liquids, the velocity distribution of the Bingham plastic flow is assumed. The solutions of the damped oscillation and also of the vertical falling and rising velocities of the free surface in the vertical U-tube of the diameters D= 10mm, 20mm and 40mm are compared with water and water-glycerine solution for the Newtonian liquids and the acrylic co-polymer solutions for the non-Newtorlian liquid. The comparisons of these solved equations by the new flow model are shown in good agreement with the experimental results. The above stated results are described in detail.

SOLUTION FOR THE OSCILLATION OF A NEWTONIAN FLUID IN A CO-AXIAL VISCOMETER

When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effect was illustrated by a new exact solution of Navier-Stokes equation, which was derived herein by a scheme of reducing it to a two-point boundary value problem for ordinary differential equations. The numerical results indicate that, as the Womersley number or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed here can be easily extended to solve other linear periodic problems.

ANALYTICAL SOLUTIONS OF THE HELICAL FLOW OF NONNEWTONIAN FLUID IN ECCENTRIC ANNULAR SPACE

Many problems in petroleum and chemical industry can be reduced to the solution of the helical flow of non-Newtonian fluid in eccentric annular space. The laminar helical flows of the power law fluid and Bingham fluid in eccentric annular space were studied. An approximate analytical solution was obtained by the infinite subdivision method, namely, the eccentric flow was replaced by the infinite concentric flows. Then, the expressions for apparent viscosity distribution, velocity distribution and the flow rate were derived for the power law fluid and the Bingham fluid respectively. In addition, the expressions for pressure drop and stability parameter were also given. It is concluded that this method is much easier to use and more accurate than the method which solves the equations directly. The results are useful for the drilling technology of oil industry, etc.

RHEOLOGY FEATURE OF SIMPLE METAL MELT

The rheology feature of Sb, Bi melt and alloys was studied using coaxial cylinder high-temperature viscometer. The results showed that the curve of torsion-rotational speed for Sb melt presents a linear relation in all measured temperature ranges, whereas for the Bi melt, the curve presents obvious non-Newtonian feature within the low temperature range and at relative high shear stress. The rheology feature of Sb80Bi20 and Sb20Bi80 alloy melts was well correlated with that of Sb and Bi, respectively. It is considered that the rheology behavior of Sb melt plays a crucial role in Sb80Bi20 alloy and that of Bi melt plays a crucial role in Sb20Bi80 alloy.

ON THE FILTRATION OF NON-NEWTONIAN FLUID IN POROUS MEDIA WITH A MULTIPLE PARAMETER MODEL

A multiple parameter model to describe the Non-Newtonian properties of fluid filtration in porous media is presented with regard to the pressure gradient expression in terms of the velocity of filtration, where the multiple parameters should be determined by measurements. Based on such a model, an analysis was furnished to deduce the formula for the rate of production of an oil well, and the governing equations for single phase Non-Newtonian fluid filtration. In order to examine the effects of model parameters, the governing equations were numerically solved with the method of cross-diagonal decomposition ZG method. It is found that, for constant rate of production, the power index n of the model influences the pressure distribution considerably, particularly in the vicinity of a single well. The well-bore pressure of Leibenzonian fluid is lower than that of the power-law fluid in the case of the same parameter B and the power index n=0.5.

NUMERICAL INVESTIGATION ON MUD BED-GENERATION AND IMPACTING A WALL ALONG A SLOPE

In this paper mud was treated as the Bingham fluid. In staggered grids, two-dimensional incompressible Navier-Stokes equations for non-Newtonian fluid was solved by the MAC method. Numerical simulations were conducted on mud bed-generating phenomenon and mud impacting a wall along a slope. The distributions of free surface, pressure and velocity of mud and water were obtained. The results indicate that the computed layer thickness of mud bed almost equals the theoretically predicted value. Because of the differences in constitutive relationship, the distributions of free surface are different for water and mud. The distortion of water free surface is much more complicated.

UNSTEADY FLOW OF POLYMER FLUID BETWEEN COAXIAL CYLINDERS

In the present paper an unsteady flow of polymer fluid, i.e. non-Newtonian fluid is studied. The constitutive equation of upper-convected Maxwell fluid is used. The variational approach due to Kantorovich is used for the unsteady problem of the fluid. A special computer program `MACSYMA' is used to get the different approximation of the method of Kantorovich. The present method developed is called Computational Analytical Method which is available for the scientific research.