Investigation of two-phase flow pattern,liquid holdup and pressure drop in viscous oil–gas flow

An experimental investigation was carried out on viscous oil–gas flow characteristics in a 69 mm internal diameter pipe. Two-phase flow patterns were determined from holdup time-traces and videos of the flow field in a transparent section of the pipe, in which synthetic commercial oils (32 and 100 cP) and sulfur hexafluoride gas (SF₆) were fed at oil superficial velocities from 0.04 to 3 m/s and gas superficial velocities from 0.0075 to 3 m/s.     

Modeling of three-phase heavy oil–water–gas bubbly flow in upward vertical pipes

A bubbly gas–bubbly oil flow pattern may occur when water, heavy oil and gas flow simultaneously in vertical pipes in such a way that water is the continuous phase. In this work, a one-dimensional, thermal, transient two-fluid mathematical model, for such flow, is presented. The model consists of mass, momentum and energy conservation equations for every phase whose numerical solution is based on the finite difference technique in the implicit scheme. The model is able to predict pressure, temperature, volumetric fraction and velocity profiles. For accurate modeling of multiphase flows, the key issue is to specify the adequate closure relationships, thus drag and virtual mass forces for the gas and oil phases were taken into account and special attention was paid on the gas–oil drag force. When this force was included into the model it was found that: (1) such force had the same order of magnitude than the oil drag force and both forces were smaller than the gas drag force, (2) the pressure, gas and oil velocities and gas and oil volume fraction profiles were affected, (3) the numerical stability was increased. The model predictions are in agreement with experimental data reported in literature.     

The pressure drop characteristics of air–water bubbling flow for evaporative heat transfer

This paper presents a study on a novel water bubbling layer pressure drop and heat transfer experiment that was conducted to investigate the characteristics of pressure drop of air flow across the water bubbling layer. The attempt was to reduce the pressure drop while maintaining a higher value of the heat transfer coefficient. This type of heat transfer between water and merged tubes has potential application in evaporative cooling. To achieve the goal the pressure drop should be reduced by decreasing the bubble layer thickness through the water pump circulation. Pressure drops of air passing through the perforated plate and the water bubbling layer were measured for different heights of water bubbling layer, hole-plate area ratio of the perforated plate and the air velocity through the holes. Experimental data show that the increase of water bubbling layer height and air velocity both increase the pressure drop while the effect of the hole-plate area ratio of the perforated plate on the heat transfer coefficient is relatively complex. The measurements showed that even at a considerably lower height of water bubbling layer the heat transfer coefficient can exceed 5,000 W/m²-K. The heat transfer coefficients of 30 mm high water bubbling layer are higher than that of other higher water bubbling layers tested in the experiments     

Modelling of pressure–strain correlation in compressible turbulent flow

Previous studies carried out in the early 1990s conjectured that the main compressible effects could be associated with the dilatational effects of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence is generally achieved with the increased DNS and experimental research effort, there are still some discrepancies among these recent findings. Analysis of the DNS and experimental data suggests that some of the discrepancies are apparent if the compressible effect is related to the turbulent Mach number, Mt. From the comparison of two classes of compressible flow, homogenous shear flow and inhomogeneous shear flow （mixing layer）, we found that the effect of compressibility on both classes of shear flow can be characterized in three categories corresponding to three regions of turbulent Mach numbers： the low-Mr, the moderate-Mr and high-Mr regions. In these three regions the effect of compressibility on the growth rate of the turbulent mixing layer thickness is rather different. A simple approach to the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, and may even cause an increase in the growth rate. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of Mt to account for the compressibility effects on the flow. The model has been successfully applied to the compressible mixing layers.     

Frictional pressure drop during vapour–liquid flow in minichannels: Modelling and experimental evaluation

Condensation in minichannels is widely used in air-cooled condensers for the automotive and air-conditioning industry, in heat pipes and other applications for system thermal control. The knowledge of pressure drops in such small channels is important in order to optimize heat transfer surfaces. This paper presents a model for calculation of the frictional pressure gradient during condensation or adiabatic liquid–gas flow inside minichannels with different surface roughness. In order to account for the effects of surface roughness, new experimental frictional pressure gradient data associated to single-phase flow and adiabatic two-phase flow of R134a inside a single horizontal mini tube with rough wall has been used in the modelling. It is a Friedel (1979) [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In: Proceedings of the European Two-Phase Flow Group Meeting, Ispra, Paper E2] based model and it takes into account mass velocity, vapor quality, fluid properties, reduced pressure, tube diameter, entrainment ratio and surface roughness. With respect to the flow pattern prediction capability, it has been built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and mist flow are here predicted. However, the suggested procedure is extended to the intermittent flow in minichannels and it is also applied with success to horizontal macro tubes.     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

An anisotropic elastic–viscoplastic model for soft clays

Experimental evidences have shown deficiencies of the existing overstress and creep models for viscous behaviour of natural soft clay. The purpose of this paper is to develop a modelling method for viscous behaviour of soft clays without these deficiencies. A new anisotropic elastic–viscoplastic model is extended from overstress theory of Perzyna. A scaling function based on the experimental results of constant strain-rate oedometer tests is adopted, which allows viscoplastic strain-rate occurring whether the stress state is inside or outside of the yielding surface. The inherent and induced anisotropy is modelled using the formulations of yield surface with kinematic hardening and rotation (S-CLAY1). The parameter determination is straightforward and no additional experimental test is needed, compared to the Modified Cam Clay model. Parameters determined from two types of tests (i.e., the constant strain-rate oedometer test and the 24 h standard oedometer test) are examined. Experimental verifications are carried out using the constant strain-rate and creep tests on St. Herblain clay. All comparisons between predicted and measured results demonstrate that the proposed model can successfully reproduce the anisotropic and viscous behaviours of natural soft clays under different loading conditions.     

Investigations of phase inversion and frictional pressure gradients in upward and downward oil–water flow in vertical pipes

The present study has attempted to investigate phase inversion and frictional pressure gradients during simultaneous vertical flow of oil and water two-phase through upward and downward pipes. The liquids selected were white oil (44 mPa s viscosity and 860 kg/m³ density) and water. The measurements were made for phase velocities varying from 0 to 1.24 m/s for water and from 0 to 1.87 m/s for oil, respectively. Experiments were carried either by keeping the mixture velocity constant and increasing the dispersed phase fraction or by keeping the continuous phase superficial velocity constant and increasing the dispersed phase superficial velocity. From the experimental results, it is shown that the frictional pressure gradient reaches to its lower value at the phase inversion point in this work. The points of phase inversion are always close to an input oil fraction of 0.8 for upward flow and of 0.75 for downward flow, respectively. A few models published in the literature are used to predict the phase inversion point and to compare the results with available experimental data. Suitable methods are suggested to predict the critical oil holdup at phase inversion based on the different viscosity ratio ranges. Furthermore, the frictional pressure gradient is analyzed with several suitable theoretical models according to the existing flow patterns. The analysis reveals that both the theoretical curves and the experimental data exhibit the same trend and the overall agreement of predicted values with experimental data is good, especially for a high oil fraction.     

The effects of channel diameter on flow pattern,void fraction and pressure drop of two-phase air–water flow in circular micro-channels

Two-phase air–water flow characteristics are experimentally investigated in horizontal circular micro-channels. Test sections are made of fused silica. The experiments are conducted based on three different inner diameters of 0.53, 0.22 and 0.15 mm with the corresponding lengths of 320, 120 and 104 mm, respectively. The test runs are done at superficial velocities of gas and liquid ranging between 0.37–42.36 and 0.005–3.04 m/s, respectively. The flow visualisation is facilitated by systems mainly including stereozoom microscope and high-speed camera. The flow regime maps developed from the observed flow patterns are presented. The void fractions are determined based on image analysis. New correlation for two-phase frictional multiplier is also proposed for practical applications.     

Two-phase flow patterns across triangular tube bundles for air–water upward flow

This paper presents flow pattern experimental results obtained during two-phase upward flow across a horizontal tube bundle. Experiments were performed for flows across a normal triangular tube bundle with 19 mm OD tubes and transversal pitch of 24 mm. Results were obtained for gas and liquid superficial velocities ranging from 0.13 to 10.00 m/s and 0.02 to 1.50 m/s, respectively. Flow patterns were identified subjectively based on visual observations through side windows, and objectively using the k-means clustering method based on signals of a differential pressure transducer and a capacitive sensor. Bubbles, large bubbles, dispersed bubbles, churn, intermittent and annular flow patterns were identified subjectively. The clustering method satisfactorily identified groups of data corresponding to the distinct flow patterns, which were compared with predictive methods available in the open literature. New predictive methods for transitions between flow patterns are proposed based on the flow patterns identified objectively. The proposed methods predicted accurately the data obtained in the present study as well as experimental results and flow pattern maps available in the open literature for distinct geometries.     

An exact solution for the three-phase thermo-electro-magneto-elastic cylinder model and its application to piezoelectric–magnetic fiber composites

A three-phase cylindrical model for analyzing fiber composite subject to in-plane mechanical load under the coupling effects of multiple physical fields (thermo, electric, magnetic and elastic) is presented. By introducing an eigenstrain corresponding to the thermo-electro-magnetic-elastic effect, the complex multi-field coupling problem can be reduced to a formal in-plane elasticity problem for which an exact closed form solution is available. The present three-phase model can be applied to fiber/interphase/matrix composites, such that a lot of interesting thermo-electro-magnetism and stress coupling phenomena induced by the interphase layer are revealed. The present model can also be applied to fiber/matrix composites, in terms of which a generalized self-consistent method (GSCM) is developed for predicting the effective properties of piezoelectric–magnetic fiber reinforced composites. The effective piezoelectric, piezomagnetic, thermoelectric and magnetoelectric moduli can be expressed in compact explicit formulae for direct references and applications. A comparison of the predictions by the GSCM with available experimental data is presented, and interesting magnification effects and peculiar product properties are discussed. As a theoretical basis for the GSCM, the equivalence of the three sets of different average field equations in predicting the effective properties are proved, and this fact provides a strong evidence of mathematical rigor and physical realism in the formulation.     

Rankine pseudo-static earth pressure for c–ϕ soils

This study provides an analytical solution for calculation of seismic active earth pressure on the back of a rigid wall retaining cohesional–frictional (c–φ) soil. The proposed formulation is based on the conjugate stress concept, without employing any additional assumptions, similar to Rankine's original earth pressure formulation. The effects of sloping backfill and wall inclination are considered. In addition, a closed form solution has been derived for the soil–wall friction angle as a function of inertial forces and problem geometry for any given pseudo-static acceleration, as opposed to the constant value commonly employed in practice. The net seismic active force calculated based on the proposed formulations is found to be comparable with those obtained from previously published methods.     

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure–saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850–1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491–511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29–39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362–372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52–62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343–2348, 1992; Attou et al., Chem. Eng. Sci., 54:785–802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039–5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459–2474, 2002), but they still lack proper terms causing liquid dispersion.     

Kutta–Joukowsky theorem in viscous and unsteady flow

Nominally two-dimensional air flow over a thin flat plate at low Reynolds number is investigated. The primary objective is to experimentally determine with good accuracy the small magnitude lift force, generated by the plate at various angles of attack, by means of application of the Kutta–Joukowsky theorem where circulation is obtained from the line integral of velocity around the flat plate using non-invasive laser doppler velocimeter. Specific focus is on assessing applicability of the Kutta–Joukowsky theorem, originally theorized for inviscid and steady flow, in the post-stall region. At high angles of attack, due to severe flow separation from both the edges of the flat plate and occurrence of periodic vortex shedding, wake flow is found to be highly viscous, turbulent and unsteady. Nevertheless, the results show a remarkably good agreement with previous investigations in both the linear range and the non-linear range of the lift curve without any correction applied to the data. The line integral of velocity along the rectangular loop enclosing the flat plate shows that the vertical components, albeit smaller in magnitude, possess the same sign and hence are additive in contribution to the circulation, whereas the horizontal components possess opposite signs and hence are subtractive in their contribution to the circulation. The paper presents some interesting and hitherto undisclosed features of flow field around the flat plate.     

Bubble capture and migration in Couette–Taylor flow

 Bubble capture and migration under the effect of organized structures in weak turbulent Couette–Taylor flow between two concentric cylinders, the inner one rotating, has been investigated. Bubbles generated at the free surface for large enough angular velocities are sucked into the flow by the upper organized structures. Then they migrate progressively from top to bottom by jumping from cell to cell. With an upper solid stationary wall instead of the free surface, injected bubbles are trapped by the coherent vortices beyond a critical Taylor number. However, in this situation there is no migration mechanism carrying the bubbles from top to bottom. This particular migration and capture process, able to act against the forces of buoyancy, has been investigated by perturbing the flow by adding a vertical plate protruding from the inner surface of the solid stationary wall. The perturbation so introduced causes the deformation of the upper coherent structures and reinstalls the migration of the bubbles. Received: 27 October 1997/Accepted: 21 May 1998