Studies on low viscous oil-water flow through return bends

In the present work, investigations have been carried out on the hydrodynamics of kerosene-water flow through return bends connecting two horizontal conduits. Extensive experiments are performed on two bend geometry (U and rectangular) and three flow directions through the bend (up, down and horizontal flow). It is observed that bend geometry has a strong influence on the downstream phase distribution while the direction of flow through the bend does not significantly affect the same. The pressure drop has been observed to be higher in the rectangular as compared to the U bend. The loss coefficients have been estimated for each of the cases. They have been found to be independent of flow patterns for all cases. Two different pressure drop correlations have also been proposed for each bend geometry to estimate liquid-liquid pressure drop across bend.     

Effect of glycerol addition on phase inversion in horizontal dispersed oil-water pipe flows

The effect of interfacial tension on the phase inversion process during horizontal pipe flow of an oil-aqueous solution was investigated. Interfacial tension was varied by adding small amounts of glycerol in the water phase. At these glycerol concentrations the density and viscosity of the aqueous phase changed by 1% or less. Exxsol™ D140 (5.5 mPa s, 828 kg m⁻³) was used as the oil phase. The experiments were carried out in a 38 mm ID acrylic test pipe. The phase continuity and appearance of phase inversion were investigated using conductivity (wire and ring) probes and an Electrical Resistance Tomographic (ERT) system. The ERT also provided diagrams of the phase distribution in a pipe cross section. Drop size distribution was monitored using a dual impedance probe. It was found that starting from a water continuous flow with increasing oil fraction at constant mixture velocity the mixture inverted initially in the middle of the pipe (measured at 19 mm from the top pipe wall) while a higher oil fraction was required for inversion at the top (measured at 4 mm from the top pipe wall) and finally the rest of the pipe. The addition of glycerol did not affect the phase fraction where the initial inversion occurred but caused an increase in the oil fraction needed to complete the inversion. The drop size measurements were used to explain this behaviour. Pressure drop was found to decrease with increasing oil fraction but this trend reversed when inversion spread to the pipe wall and the oil continuous phase came in contact with it.     

Measurements of cross-sectional instantaneous phase distribution in gas–liquid pipe flow

Two novel complementing methods that enable experimental study of gas and liquid phases distribution in two-phase pipe flow are considered. The first measuring technique uses a wire-mesh sensor that, in addition to providing data on instantaneous phase distribution in the pipe cross-section, also allows measuring instantaneous propagation velocities of the phase interface. A novel algorithm for processing the wire-mesh sensor data is suggested to determine the instantaneous boundaries of gas–liquid interface. The second method applied here takes advantage of the existence of sharp visible boundaries between the two phases. This optical instrument is based on a borescope that is connected to a digital video camera. Laser light sheet illumination makes it possible to obtain images in the illuminated pipe cross-section only. It is demonstrated that the wire-mesh-derived results based on application of the new algorithm improve the effective spatial resolution of the instrument and are in agreement with those obtained using the borescope. Advantages and limitations of both measuring techniques for the investigations of cross-sectional instantaneous phase distribution in two-phase pipe flows are discussed.     

Slip between the phases in two-phase water–oil flow in a horizontal pipe

This paper is devoted to slip phenomenon between the phases that occurs in unstable two-phase water–oil flow systems in a horizontal pipe. The emphasis is placed on the relation between the slip and the real (in situ) water fraction in a flowing mixture, as well as the substitute physical properties of the whole two-phase system. The experimental data collected throughout research served for the evaluation of the accuracy of the methods of real phase fraction in a water–oil flow system in horizontal pipes as they were referred to in the bibliography. Subsequently we have suggested the author indicate a method of determination of the fraction for two-phase liquid systems like O/W, W/O and W + O. In order to establish the specific equations, the drift-flux model has been used here.     

Slip flow due to a stretching cylinder

The slip flow due to a stretching cylinder is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations. Asymptotic solutions for large Reynolds number and small slip show the problem can be related to the existing two-dimensional stretching cases. Due to algebraic decay, the equations are further transformed through a compressed variable, and then integrated numerically. It is found that slip greatly reduces the magnitudes of the velocities and the shear stress.     

Experimental study on the transition between stratified and non-stratified horizontal oil-water flow

The effect of oil and water velocities, pipe diameter and oil viscosity on the transition from stratified to non-stratified patterns was studied experimentally in horizontal oil-water flow. The investigations were carried out in a horizontal acrylic test section with 25.4 and 19 mm ID with water and two oil viscosities (6.4 and 12 cP) as test fluids. A high-speed video camera was used to study the flow structures and the transition. At certain oil velocity, stratified flow was found to transform into bubbly and dual continuous flows as superficial water velocity increased for both pipe diameters using the 12 cP oil viscosity. The transition to bubbly flow was found to disappear when the 6.4 cP oil viscosity was used in the 25.4 mm pipe. This was due to the low E?tv?s number. Transition to dual continuous flow occurred at lower water velocity for oil velocity up 0.21 m/s when 6.4 cP oil was used in the 25.4 mm ID pipe, while for U_so > 0.21 m/s, the transition appeared at lower water velocity with the 12 cP oil.The effect of pipe diameter was also found to influence the transition between stratified and non-stratified flows. At certain superficial oil velocity, the water velocity required to form bubbly flow increased as the pipe diameter increased while the water velocity required for drop formation decreased as the pipe diameter increased. The maximum wave amplitude was found to grow exponentially with respect to the mixture velocity. The experimental maximum amplitudes at the transition to non-stratified flow agreed reasonably well with the critical amplitude model. Finally, it was found that none of the available models were able to predict the present experimental data at the transition from stratified to non-stratified flow.     

Periodic viscous flow: A bench-mark problem

A double-transform technique provides a semi-analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi-infinite rigid cylindrical tube. This in turn offers an appropriate bench-mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench-mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench-mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.     

Slip flow of non-plasticized PVC compounds

Measurements on seven rigid PVC compounds were carried out with a slit rheometer working in combination with an injection moulding machine. Plastication of the compounds occurred in the screw of the plastication unit, which also forced the melt through the die with a controlled forward velocity. The rectangular slit had a length of 90 mm and a widthB of 20 mm. The heightH could be varied between 0.8 and 3.3 mm. Pressures and temperatures were recorded at several positions in and before the die. Measurements were carried out at shear rates from 10 to 2000 s^–1.When the reduced volume output was plotted against the wall shear stress _W , only four compounds showed master curves independent ofH, which is indicative of wall adhesion. In the other cases this plot did not produce such a master curve, but the plot of the mean velocity against _W was independent ofH (slip curve). This indicated that slip flow prevailed with a slip velocityv _G When, in the case of wall slip, the smooth inner surfaces of the die were replaced by surfaces with grooves perpendicular to the direction of flow, slip flow was prevented and the flow curves were shifted to much higher values of _Wc Above a critical value of the wall shear stress ( _Wc ) at which slip flow began, the output became nearly independent of _W . From the measurements made below _Wc a vs. relation for the shear flow could be derived, which was used to calculate the superimposed shear flow . Exact values of the slip velocity were then given by . Wall slip only occurred for compounds with a high shear viscosity, which corresponds to a high molecular weight (K-value).Dedicated to Professor H. Janeschitz-Kriegl on the occasion of his 60th birthday.     

Slip and no-slip squeezing flow of liquid food in a wedge

Squeezing flow in a wedge simulates a number of practical processes, e.g. lubrication, coating and the sensory evaluation of liquid foods. This paper reports analytical approximate solutions for both slip (or lubricated) and no-slip squeezing flow of liquid food in a wedge, in which the power law fluid model was used. The solutions do not seem to be more complex than that for squeezing flow between two parallel disks and may be used as a variation of the psycho-physical models of in-mouth viscosity and food spreadability. Alternatively, a rheometer for testing liquid foods may be developed according to the equations described in this paper.     

A net inflow method for incompressible viscous flow with moving free surface

A new finite element procedure called the net inflow method has been developed to simulate time-dependent incompressible viscous flow including moving free surfaces and inertial effects. As a fixed mesh approach with triangular element, the net inflow method can be used to analyse the free surface flow in both regular and irregular domains. Most of the empty elements are excluded from the computational domain, which is adjusted successively to cover the entire region occupied by the liquid. The volume of liquid in a control volume is updated by integrating the net inflow of liquid during each iteration. No additional kinetic equation or material marker needs to be considered. The pressure on the free surface and in the liquid region can be solved explicitly with the continuity equation or implicitly by using the penalty function method. The radial planar free surface flow near a 2D point source and the dam-breaking problem on either a dry bed or a still liquid have been analysed and presented in this paper. The predictions agree very well with available analytical solutions, experimental measurements and/or other numerical results.     

Potential flow of viscous fluids: Historical notes

In this essay I will attempt to identify the main events in the history of thought about irrotational flow of viscous fluids. I am of the opinion that when considering irrotational solutions of the Navier–Stokes equations it is never necessary and typically not useful to put the viscosity to zero. This observation runs counter to the idea frequently expressed that potential flow is a topic which is useful only for inviscid fluids; many people think that the notion of a viscous potential flow is an oxymoron. Incorrect statements like “… irrotational flow implies inviscid flow but not the other way around” can be found in popular textbooks.     

Multidomain collocation techniques for a viscous compressible flow

This paper presents a viscous compressible flow problem to which an equilibrium solution, in terms of density and velocity, can be given implicitly by elementary functions. The corresponding initial boundary value problem is solved by time discretization by the Crank-Nicolson method, Newton linearization and space discretization using multidomain Chebyshev collocation techniques. The physical interval is covered by subintervals of equal length. Each subinterval utilizes the same number of collocation points and each interface consists of one or two points. Six ways of patching are tested. All of them yield solutions with spectral accuracy for a few time steps, but only three are stable in the long run. Details of the density evolution are illustrated.     

Internal three-dimensional viscous flow solutions using the vorticity-potential method

A numerical solution procedure for internal three-dimensional viscous flow is proposed in this paper. The formulation is based on the non-primitive variables, the vorticity and potentials, on a curvilinear grid. A new upwind difference scheme is introduced to overcome the convective instabilities arising in the central difference scheme for the vorticity transport equations, while keeping false diffusion to a minimum level. Developing flows in both straight and curved square ducts are simulated to validate the procedure. The results are compared with both experimental measurements and analytical solutions.     

MHD rotating flow of a viscous fluid over a shrinking surface

This study is concerned with the magnetohydrodynamic (MHD) rotating boundary layer flow of a viscous fluid caused by the shrinking surface. Homotopy analysis method (HAM) is employed for the analytic solution. The similarity transformations have been used for reducing the partial differential equations into a system of two coupled ordinary differential equations. The series solution of the obtained system is developed and convergence of the results are explicitly given. The effects of the parameters M, s and λ on the velocity fields are presented graphically and discussed. It is worth mentioning here that for the shrinking surface the stable and convergent solutions are possible only for MHD flows.     

Effect of viscous plane stagnation flow on the freezing of fluid

This article investigates the phase-change problem from liquid to solid in the viscous plane stagnation flow. The solution at the initial stage of freezing is obtained by expanding it in powers of time, and the final equilibrium state is determined from the steady-state governing equations. The effect of the stagnation flow on the pure conduction problem can be clearly seen from the explicit analytic solutions, and the characteristics of the growth of solid and the transient heat transfer for all the dimensionless parameters are elucidated.     

An orthogonal mapping technique for the computation of a viscous free-surface flow

In this paper we describe finite element computations of the free-surface flow of a viscous fluid down an undulating inclined plane. The technique developed here employs an orthogonal mapping that is computed along with the velocity and pressure. This is allied to a technique to compute symbolically the Jacobian and other derivatives required for numerical continuation methods. The solutions obtained are compared with laboratory experiments and finite element computations reported by Pritchard and co-workers. The finite element computational method used by these authors employs spines to represent the free surface. An excellent agreement is shown to exist between the new computations and the laboratory experiments, and with the numerical solutions of Pritchard and co-workers.     

Pattern analysis of viscous oscillation in a shear flow induced by an exothermic reaction

An investigation is made of oscillatory phenomenon induced by an exothermic reaction. This oscillatory phenomenon occurs in a very thin mixing layer between two miscible and reacting fluids. A qualitative model based on the interaction among reaction, molecular momentum transfer, molecular heat transfer, molecular mass transfer and forced convective transfer was proposed by Kuroda and Ogawa [1994. Nonlinear waves in a shear flow with a diffusive exothermic reaction and its qualitative reasoning. Chem. Eng. Sci. 49(16), 2699-2708]. It is experimentally shown in the present study that the oscillatory patterns change in the flow direction. In the upstream area where oscillatory patterns are nearly straight stripes, effects of viscosity on those stripes are investigated. In the downstream area where stripes are wavy and disordered, fractal analysis is introduced to investigate the relationship between the transition of oscillatory flow patterns and process factors, i.e. the viscosity ratio, the entire viscosity, flow rate and the flow rate ratio. Fractal analysis is also applied to temperature oscillation, and it is confirmed that the characteristic patterns of oscillation become obscure as the entire viscosity increases. The entire viscosity is an important factor for controlling both oscillatory patterns of flow and temperature in this reactive flow system.     

A total linearization method for solving viscous free boundary flow problems by the finite element method

In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of boundary integrals. This means that the implementation of the method is simple. Numerical experiments show that the iterative method gives accurate results and converges very fast.     

Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles

In this work, we present a numerical study to investigate the hydrodynamic characteristics of slug flow and the mechanism of slug flow induced CO₂ corrosion with and without dispersed small bubbles. The simulations are performed using the coupled model put forward by the authors in previous paper, which can deal with the multiphase flow with the gas–liquid interfaces of different length scales. A quasi slug flow, where two hypotheses are imposed, is built to approximate real slug flow. In the region ahead of the Taylor bubble and the liquid film region, the presence of dispersed small bubbles has less impacts on velocity field, because there are no non-regular intensive disturbance forces or centrifugal forces breaking the balance of the liquid and the dispersed small bubbles. In the liquid slug region, the strong centrifugal forces generated by the recirculation below the Taylor bubble lead to the effect of heterogeneity, which makes the profile of the radial liquid velocity component sharper with higher volume fraction of dispersed small bubbles. The volume fraction has a maximum value in the range of r/R = 0.5–0.6. Meanwhile, it is usually higher than 0.35, which means that larger dispersed bubbles can be formed by coalescences in this region. These calculated results are in good agreement with experimental results. The wall shear stress and the mass transfer coefficient with dispersed small bubbles are higher than those without dispersed small bubbles due to enhanced fluctuations. For short Taylor bubble length, the average mass transfer coefficient is increased when the gas or liquid superficial velocity is increased. However, there may be an inflection point at low mixture superficial velocities. For the slug with dispersed small bubbles, the product scales still cannot be damaged directly despite higher wall shear stress. In fact, the alternate wall shear stress and the pressure fluctuations perpendicular to the pipe wall with high frequency are the main cause for breaking the product scales.     

An inverse dispersed multiphase flow model for liquid production rate determination

The aim of this study is to develop a model for the determination of the superficial velocities in horizontal and slightly inclined oil–water pipe flow conditions by using pressure gradient and mixture density information. In this article an inverse model is suggested for a dispersion of oil in water and of water in oil. This approach permits to select dispersed flow conditions from a set of experimental data, and uses a new hybrid model for the effective viscosity. A set of 310 oil–water experimental data points collected on an experimental set-up of length L = 15 m and diameter D = 8.28 cm at various (slight) orientations is used to validate the inverse method. The comparison between model reconstructions and measured flow velocities show a reasonable agreement.