Hyperbolicity and one-dimensional waves in compressible two-phase flow models

Hyperbolic models for compressible two-phase flows including a conservative symmetric hyperbolic model are reviewed. The basis for a theory of shock waves is developed within the framework of the latter. The analysis of small amplitude discontinuities allows us to conclude that in general there are two types of shocks corresponding to two sound waves. The problem of transition between a pure phase and a mixture (the phase vacuum problem) is analysed. It is proved that for some models the smooth centred wave solution can not provide such a transition. Within the framework of our conservative model there is the possibility of constructing discontinuous solutions which can resolve the phase vacuum problem.PACS: 47.55Kf, 47.40.-xE. Romenski: On leave from Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia     

On the hyperbolicity of one-dimensional models for transient two-phase flow in a pipeline

Characteristic properties of one-dimensionalmodels of transient gas-liquid two-phase flows in long pipelines are investigated. The methods for studying the hyperbolicity of the systems of equations of multi-fluid and drift-fluxmodels are developed. On the basis of analytical and numerical studies, the limits of the hyperbolicity domains in the space of governing dimensionless parameters are found, and the impact of the closure relations on the characteristic properties of the models is analyzed. The methods of ensuring the global unconditional hyperbolicity are proposed. Explicit formulas for the eigenvelocities of the system of the drift-flux model equations are obtained and the conclusions about their sign-definiteness are drawn.     

Effect of pipe length on the transition boundaries for high-viscosity liquids

This paper analyzes the hydrodynamics near the discharge of a pipe carrying gas and liquid in horizontal stratified flow. It is shown that for high-viscosity liquids, pipe length may have a considerable effect on the transition from the stratified to nonstratified (annular or intermittent) flow pattern. This leads to a flow-pattern map which contains the pipe length as a parameter for this transition boundary.     

Flow pattern and pressure fluctuation in air-solid two-phase flow in a pipe at low air velocities

An experiment was made on an air-solid two-phase flow in a horizontal pipe. The main concern was the relation between flow patterns and pressure fluctuation at low air velocities. First, the flow patterns were classified into five different types depending on the air and particle flow rates. Next, it was shown how the properties of pressure fluctuation change as the air velocity decreases. Further, fluctuation signals were analyzed in detail and differences due to the flow patterns and particle size were discussed.     

Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media

An extended formulation of Darcy's two-phase law is developed on the basis of Stokes' equations. It leads, through results borrowed from the thermodynamics of irreversible processes, to a matrix of relative permeabilities. Nondiagonal coefficients of this matrix are due to the viscous coupling exerted between fluid phases, while diagonal coefficients represent the contribution of both fluid phases to the total flow, as if they were alone. The coefficients of this matrix, contrary to standard relative permeabilities, do not depend on the boundary conditions imposed on two-phase flow in porous media, such as the flow rate. This formalism is validated by comparison with experimental results from tests of two-phase flow in a square cross-section capillary tube and in porous media. Coupling terms of the matrix are found to be nonnegligible compared to diagonal terms. Relationships between standard relative permeabilities and matrix coefficients are studied and lead to an experimental way to determine the new terms for two-phase flow in porous media.     

The nonlinear analysis of horizontal oil-water two-phase flow in a small diameter pipe

Horizontal oil-water two-phase flows are frequently encountered in many industrial processes but the understanding of the dynamic behavior underlying the different flow patterns is still a challenge. In this study, we first conduct experiments of horizontal oil-water flows in a small diameter pipe, and collect the fluctuation signals from conductance probes. The multi-scale power-law correlations of the oil-water flow structures are investigated using detrended fluctuation analysis (DFA) based on the magnitude and sign decomposition of the raw signals. The analysis reveals the scaling behavior of different flow structures; five conductive flow patterns are indentified based on the magnitude and sign scaling exponents at different time scales. In addition, the transfer entropy (TE) in a state space is used to study the information transferring characteristics of the oil-water mixture flowing past a conductance cross-correlation velocity probe. The results of TE indicate that the transferring information depends on the flow conditions and can be used to show changes in the flow patterns.     

Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models

The differences between two differential Reynolds stress models (DRSM) and their corresponding explicit algebraic Reynolds stress models (EARSM) are investigated by studying fully developed axially rotating turbulent pipe flow. The mean flow and the turbulence quantities are strongly influenced by the imposed rotation, and is well captured by the differential models as well as their algebraic truncations. All the tested models give mean velocity profiles that are in good qualitative agreement with the experimental data. It is demonstrated that the predicted turbulence kinetic energy levels vary dramatically depending on the diffusion model used, and that this is closely related to the model for the evolution of the length-scale determining quantity. Furthermore, the effect of the weak equilibrium assumption, underlying the EARSMs, and the approximation imposed for 3D mean flows on the turbulence levels are investigated. In general the predictions obtained with the EARSMs rather closely follow those of the corresponding DRSMs.     

Justification of the drift-flux model for two-phase flow in a circular pipe

A flow of a gas-liquid dispersed mixture in a circular pipe with a variable inclination to the horizon, as applied to oil and gas flows in wells, is considered. Within the framework of a multi- fluid approach, the equations of an asymptotic drift-flux model, which contains an algebraic relation between the phase velocities and one momentum equation for the volume-averaged velocity of the mixture, are derived. It is shown that the drift-flux model in this formulation strictly follows from the balance laws under assumption of inertialess velocity slip of the phases in case of validity of one of the following conditions: (i) the dispersed-phase volume fraction is small; (ii) the phase velocity slip may be neglected; or (iii) the flow regime is inertialess and the acceleration of the mixture can be neglected. A numerical algorithm based on the SIMPLE method is implemented for solving the obtained equations of the drift-flux model. The possibility of modeling the gravitational segregation and the pressure buildup in a shut-in well and transient slug flows is demonstrated.     

长药室装药中多点点传火一维两相流数值模拟

针对药室长度超过3m的长药室装药设计问题,设计了以电点火具为点火源的多点点火系统,在点传火模拟实验装置上进行了多点点火的实验研究.同时,建立了点传火模拟实验装置中多点点传火过程的数学物理模型,采用MacCormack差分格式进行了数值求解,得到了点传火模拟装置中传火管的压力分布、固相和气相速度以及空隙率等数值解,分析了...     

Existence and properties of flow structure waves in two-phase bubbly flows

Structure waves occur in two-phase flows because one phase drifts with respect to the other, the drift flux being primarily a function of the flow structure. The wave properties provide information on the closure laws required in engineering models. Experiments made with an air-water bubbly mixture flowing in a vertical annular test section are reported. Void fluctuations involving structure disturbances were detected by capacitance measurements, the effect of individual bubbles being always negligible. Only low frequency disturbances were present, high frequency disturbances being strongly damped. Within the low frequency range, the wave velocity is independent of the frequency, and the damping is small. The wave velocity is always comprised between the average liquid velocity and the average gas velocity.

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Résumé Des ondes de structure apparaissent dans les écoulements diphasiques parce que les phases n'ont pas la même vitesse moyenne, le flux de glissement correspondant étant essentiellement fonction de la structure de l'écoulement. Les propriétés des ondes apportent des informations sur les lois de fermetures requises par les modèles pratiques. On présente les résultats d'expériences effectuées avec un écoulement eau-air à bulles dans une section annulaire verticale. Les fluctuations de taux de vide dues aux perturbations de structure sont détectées par mesure de capacité (l'effect d'une bulle unique est toujours négligeable). Seules les perturbations de basse fréquence peuvent subsister, les perturbations de haute fréquence étant fortement amorties. Dans la gamme basse fréquence, la vitesse des ondes est indépendante de la fréquence et l'amortissement est faible. La vitesse des ondes est toujours comprise entre la vitesse moyenne du liquide et la vitesse moyenne du gaz.

     

Surface wettability effect on flow pattern and pressure drop in adiabatic two-phase flows in rectangular microchannels with T-junction mixer

Wettability is an important parameter in micro-scale flow patterns. Previous research has usually been conducted in conventional microtubes due to limitations of visualizing flow patterns and fabricating microchannels. However, most microchannels in practical applications have rectangular shape. Furthermore, pressure drop is closely related with flow pattern. Hence, we studied water liquid and nitrogen gas flows in rectangular microchannels with different wettabilities. The rectangular glass microchannels were fabricated from photosensitive glass, whose surface is hydrophilic. The surface of one was silanized using octadecyl-trichloro-silane (OTS) to prepare a hydrophobic microchannel. The two-phase flow pattern was visualized with a high-speed camera and a long distance microscope. The frictional pressure drop in the microchannel was measured directly with embedded pressure ports. The flow pattern and pressure drop in the hydrophobic microchannel were totally different from those in the hydrophilic microchannel. Finally, the two-phase frictional pressure drop was analyzed based on the flow patterns of different wettabilities.     

On the suitability of first-order differential models for two-phase flow prediction

The stability features of a general elass of one-dimensional two-phase flow models are examined. This class of models is characterized by the presence of first-order derivatives and algebraic functions of the flow variables, higher-order differential terms being absent, and can accommodate a variety of physical effects such as added mass and unequal phase pressures in some formulations. By taking a general standpoint, a number of results are obtained applicable to the entire class of models considered. In particular, it is found that, despite the presence of algebraic terms in the equations (describing, e.g. drag effects) the stability criteria are independent of the wavenumber of the perturbation. As a consequence, reality of characteristics is necessary, although not sufficient, for stability. To illustrate the theory, three specific models are considered in detail.     

Flow pattern,void fraction and pressure drop of refrigerant two-phase flow in a horizontal pipe—I. Experimental data

Experiments with refrigerant two-phase flow in a horizontal pipe have been performed and data on flow pattern, void fraction and pressure drop have been obtained. Refrigerants used were R12 and R22, and the range of saturation pressure was from 5.7 to 19.6 bar.In this paper, the experimental equipment and procedure are described in detail, and the data are both tabulated and presented graphically.     

The use of drift-flux techniques for the analysis of horizontal two-phase flows

New data is presented for horizontal air/water two-phase flow having various flow regimes. It is shown that drift-flux models are able to correlate these data and that the drift velocity, V_gj, is normally finite.