The formation of hydrodynamic slugs by the interaction of waves in gas–liquid two-phase pipe flow

This paper examines the effects of wave interaction on the formation of hydrodynamic slugs in two-phase pipe flow at relatively low gas and liquid superficial velocities. The experiments were conducted using a horizontal 31 m long, D = 10 cm internal diameter transparent pipe at atmospheric pressure. High resolution photography allowed the location of the gas–liquid interface to be measured with a high degree of accuracy at 5 Hz. Image analysis allowed individual waves to be tracked over a 14D section of the pipe. Regular waves having similar properties such as speed, amplitude and length were seen far from the region of slug formation. However, near the transition region, where hydrodynamic slugs were formed, significant differences between wave properties were observed which resulted in wave interaction leading to a type of sub-harmonic resonance and slug formation. The formation of hydrodynamic slugs due to wave interaction differs from predictions for slug formation using long wavelength stability theory. The properties of the waves were quantified which gave detailed information on the resonance mechanism found near the transition to slugging.     

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.     

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 1: Morphology of the air–water interface

In this work, the influence of surfactants on air–water flow was studied by performing experiments in a 12 metre long, 50 mm inner diameter, vertical pipe at ambient conditions. High-speed visualisation of the flow shows that the morphology of the air–water interface determines the formation of foam. The foam subsequently alters the flow morphology significantly. In annular flow, the foam suppresses the roll waves, and a foamy crest is formed on the ripple waves. In the churn flow regime, the flooding waves and the downwards motion of the liquid film are suppressed by the foam. The foam is transported in foam waves moving upwards superposed on an almost stagnant foam substrate at the pipe wall. Foam thus effectively reduces the superficial gas velocity at which the transition from annular to churn flow occurs. These experiments make more clear how surfactants can postpone liquid loading in vertical pipes, such as in gas wells.     

Upward and downward inclination oil–water flows

The effect of upward (+5°, +10°) and downward (−5°) pipe inclinations on the flow patterns, hold up and pressure gradient during two-liquid phase flows was investigated experimentally for mixture velocities between 0.7 and 2.5 m/s and phase fractions between 10% and 90%. The investigations were performed in a 38 mm ID stainless steel test pipe with water and oil as test fluids. High-speed video recording and local impedance and conductivity probes were used to precisely identify the different flow patterns. In both positive and negative inclinations the dispersed oil-in-water regime extended to lower mixture velocities and higher oil fractions compared to horizontal flow. A new flow pattern, oil plug flow, appeared at both +5° and +10° inclination while the stratified wavy pattern disappeared at −5° inclination. The oil to water velocity ratio was higher for the upward than for the downward flows but in the majority of cases and all inclinations oil was flowing faster than water. At low mixture velocities the velocity ratio increased with oil fraction while it decreased at high velocities. The increase became more significant as the degree of inclination increased. The frictional pressure gradient in both upward and downward flows was in general lower than in horizontal flows while a minimum occurred at all inclinations at high mixture velocities during the transition from dispersed water-in-oil to dual continuous flow.     

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re_G = 31,800 to 98,300 for the gas phase and Re_L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.     

Experimental study on oil–water flow in horizontal and slightly inclined pipes

Oil–water two-phase flow experiments were conducted in a 15 m long, 8.28 cm diameter, inclinable steel pipe using mineral oil (density of 830 kg/m³ and viscosity of 7.5 mPa s) and brine (density of 1060 kg/m³ and viscosity of 0.8 mPa s). Steady-state data on flow patterns, two-phase pressure gradient and holdup were obtained over the entire range of flow rates for pipe inclinations of −5°, −2°, −1.5°, 0°, 1°, 2° and 5°. The characterization of flow patterns and identification of their boundaries was achieved via observation of recorded movies and by analysis of the relative deviation from the homogeneous behavior. A stratified wavy flow pattern with no mixing at the interface was identified in downward and upward flow. Two gamma-ray densitometers allowed for accurate measurement of the absolute in situ volumetric fraction (holdup) of each phase for all flow patterns. Extensive results of holdup and two-phase pressure gradient as a function of the superficial velocities, flow pattern and inclinations are reported. The new experimental data are compared with results of a flow pattern dependent prediction model, which uses the area-averaged steady-state two-fluid model for stratified flow and the homogeneous model for dispersed flow. Prediction accuracies for oil/water holdups and pressure gradients are presented as function of pipe inclination for all flow patterns observed. There is scope for improvement for in particular dual-continuous flow patterns.     

Simulation of large amplitude waves in a slug tracking scheme compared to roll wave experiments at high pressure

Due to the similarities between large amplitude roll waves and slug flow in two-phase gas–liquid pipe flow, a slug tracking scheme is presented with the addition of a simplified model for roll waves. The waves are treated in a similar way to slugs, modelled as objects moving at the wave velocity and with a pressure variation across them. The two-fluid model is solved on a stationary staggered grid in stratified sections between moving waves and slugs. The model is dynamic meaning that the growth and decay of waves and slugs can be simulated. The wave model implementation within the tracking scheme is discussed and demonstrated in comparison to existing experimental data on wave velocities and averaged pressure drops. The results from the tracking scheme compared well to the experiments when waves were initiated with the experimental frequency. Wave initiation remains as a modelling challenge.     

On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm

In cities, flood waves may propagate over street surfaces below which lie complicated pipe networks used for storm drainage and sewage. The flood and pipe flows can interact at connections between the underground pipes and the street surface. The present paper examines this interaction, using the shallow water equations to model the flood wave hydrodynamics. Sources and sinks in the mass conservation equation are used to model the pipe inflow and outflow conditions at bed connections. We consider the problem reduced to one dimension. The shallow water equations are solved using a Godunov‐type wave propagation scheme. Wave speeds are modified in the wave propagation algorithm to enable flows to be simulated over nearly dry beds and dry states. First, the model is used to simulate vertical flows through finite gaps in the bed. Next, the interaction of the vertical flows with a dam break flow is considered for both dry and wet beds. An efflux number, En, is defined based on the vertical efflux velocity and the gap length. Comparisons are made with numerical predictions from STAR‐CD, a commercial Navier–Stokes solver that models the free‐surface motions, and a parameter study is undertaken to investigate the effect of the one‐dimensional approximation of the present model, for a range of non‐dimensional efflux numbers. It is found that the shallow flow model gives sensible predictions at all time provided En<0.5, and for long durations for En>0.5. Dam break flow over an underground connecting pipe is also considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental study on interfacial waves in stratified horizontal oil–water flow

Interfacial wave characteristics were studied experimentally in horizontal oil–water pipe flows during stratified flow and at the transition to dual continuous flow, where drops of one phase appear into the other (onset of entrainment). The experimental investigations were carried out in a stainless steel test section with 38 mm ID with water and oil (density 828 kg/m³and viscosity 5.5 mPas) as test fluids. Wave characteristics were obtained with a high speed video camera and a parallel wires conductivity probe that measured the instantaneous fluctuations of the interface. Experiments were conducted at 2 m and at 6 m from the inlet. Visual observations revealed that no drops are formed when interfacial waves are absent. It was also found that waves have to reach a certain amplitude before drops can detach from their crests. Wave amplitudes are increased as the superficial velocities of both phases increase. In the stratified region, the mean wave amplitude decreases by increasing the oil–water input ratio while mean wavelength increases as the slip velocity between the two-phase decreases. At the onset of entrainment, the mean amplitude and length are found to be a function of the relative velocity between the oil and water layers and of the turbulence in each layer.     

The role of buoyancy–frequency oscillations in the generation of mountain gravity waves

There is evidence from balloon measurements that atmospheric buoyancy–frequency profiles, apart from a sharp increase (roughly by a factor of two) at the tropopause, often feature appreciable oscillations (typical wavelength 1–2 km) with altitude. It is argued here that such short-scale oscillatory variations of the background buoyancy frequency, which usually are ignored in theoretical models, can have a profound effect on the generation of mountain waves owing to a resonance mechanism that comes into play at certain wind speeds depending on the dominant oscillation wavelength. A simple linear model assuming small sinusoidal buoyancy–frequency oscillations suggests, and numerical solutions of the Euler equations for more realistic flow conditions confirm, that under resonant conditions the induced gravity-wave activity is significantly increased above and upstream of the mountain, similarly to resonant flow of finite depth over topography.      

Prediction of the transition from stratified to slug flow or roll-waves in gas–liquid horizontal pipes

In stratified gas–liquid horizontal pipe flow, growing long wavelength waves may reach the top of the pipe and form a slug flow, or evolve into roll-waves. At certain flow conditions, slugs may grow to become extremely long, e.g. 500 pipe diameter. The existence of long slugs may cause operational upsets and a reduction in the flow efficiency. Therefore, predicting the flow conditions at which the long slugs appear contributes to a better design and management of the flow to maximize the flow efficiency.     

Void fraction and pressure waves in a transient horizontal slug flow

The void fraction and the pressure waves in an air–water mixture flowing in the slug regime are experimentally investigated in a horizontal line. The test section is made of a transparent Plexiglas pipe with 26 mm ID and 26.24 m long, operating at ambient temperature and pressure. The flow induced transients are made by quickly changing the air or the water inlet velocity. The test grid has four operational points. This choice allows one to create expansion and compression waves due to the changes to the gas or to the liquid. Each experimental run is repeated 100 times to extract an ensemble average capable of filtering out the intrinsic flow intermittence and disclosing the void fraction and pressure waves’ features. The slug flow properties such as the bubble nose translational velocity, the lengths of liquid film underneath the bubble and the liquid slug are also measured. The objective of the work is two-fold: access the main characteristics of the void fraction and pressure waves and disclose the mechanics of the transient slug flow as described through the changes of the slug flow properties.     

Fluid–structure interaction in water-filled thin pipes of anisotropic composite materials

The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small.     

Stability of roll waves in open channel flowsStabilité de trains d'ondes dans un canal découvert

The stability of finite amplitude roll waves that may develop at a liquid free surface in inclined open channels of arbitrary cross-section is studied. In the framework of shallow water theory with turbulent friction the modulation equations for wave series are derived and a nonlinear stability criterion is obtained. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 330 (2002) 291–295.     

Multi-shock structure of roll wavesStructure multi-chocs d'ondes à rouleaux

The special class of periodic travelling waves which is known as roll waves is investigated for nonhomogeneous hyperbolic equations of gas dynamics type. In this Note these equations are applied to shallow water flows in inclined open channels, but the results obtained are more general and far-reaching. The necessary conditions for the existence of a roll wave are derived. It is shown that for a nonconvex pressure term, multi-shock configurations of roll waves of finite amplitude exist. A new type of periodic travelling wave, which corresponds to the slug flow regime in two-layer flows, is found. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 332 (2004).     

Breaking of gravity waves in the motion of a vertical plate in a two-layer liquid

Results of experimental studies of surface and internal waves generated by translational motion of a vertical plate covering the entire cross section of the channel are discussed. It is found that the waves do not break at the critical propagation speeds predicted by the linear theory or the first approximation of shallow water theory. Breaking begins only at higher propagation speeds, at which the stabilizing effect of wave dispersion ceases. Quantitative information is given that can be used to test mathematical models and numerical methods. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 11–18, September–October, 1998.     

Counter-current gas–liquid flow in a vertical narrow channel—Liquid film characteristics and flooding phenomena

Results are reported of an experimental investigation of gas–liquid counter-current flow in a vertical rectangular channel with 10 mm gap, at rather short distances from liquid entry. Flooding experiments are carried out using air and various liquids (i.e., water, 1.5% and 2.5% aqueous butanol solutions) at liquid Reynolds numbers Re_L < 350. Visual observations and fast recordings suggest that the onset of flooding at low Re_L (<250) is associated with liquid entrainment from isolated waves, whereas “local bridging” is dominant at the higher Re_L examined in this study. Significant reduction of flooding velocities is observed with decreasing interfacial tension, as expected. Instantaneous film thickness measurements show that under conditions approaching flooding, a sharp increase of the mean film thickness, of mean wave amplitude and of the corresponding RMS values takes place. Film thickness power spectra provide evidence that by increasing gas flow the wave structure is significantly affected; e.g., the dominant wave frequency is drastically reduced. These data are complemented by similar statistical information from instantaneous wall shear stress measurements made with an electrochemical technique. Power spectra of film thickness and of shear stress display similarities indicative of the strong effect of waves on wall stress; additional evidence of the drastic changes in the liquid flow field near the wall due to the imposed gas flow, even at conditions below flooding, is provided by the RMS values of the wall stress. A simple model is presented for predicting the mean film thickness and mean wall shear stress under counter-current gas–liquid flow, below critical flooding velocities.     

Application of a borescope to studies of gas–liquid flow in downward inclined pipes

The aim of the present study is to investigate stratified downward gas–liquid pipe flow with a non-intrusive measurement technique that is based on a borescope connected to a digital video camera. The borescope-based technique enables to determine the instantaneous cross-sectional distribution of both phases within the pipe. Water and air were used as working fluids. Quantitative data was extracted from sequences of recorded video images by applying a developed data processing technique for instantaneous gas–liquid interface boundaries determination. Experiments were performed for a wide range of downward pipe inclinations and gas and liquid flow rates. The instantaneous and time-average cross-sectional holdup for each set of flow parameters was calculated. Particular attention was given to the study of the interface shape that in many occasions was not flat and was characterized by the penetration of the liquid along the pipe periphery. Temporal variation of the surface elevation was also studied and various regimes characterizing interfacial waves were defined using both the recorded time series of the instantaneous depth of the water layer and the Fourier analysis of those records.     

滚波演化中聚合过程的数值模拟研究

滚波是一种重力作用下自由液面失稳诱发的水面波动现象, 通常可分为具有相对稳定波形和波速的周期性滚波与波形和波速不断变化的不规则滚波(自然滚波). 不规则滚波的相互作用和发展演化过程十分复杂, 至今对其认识尚不成熟. 本文采用基于雷诺平均Navier-Stokes方程的立面二维数值模型, 对不规则滚波发展过程中的吸收聚合和追赶聚合现象进行了数值模拟研究. 分析了两种聚合模式的演化过程, 给出了滚波聚合过程中完整的波形、波速、速度剖面以及湍流黏性等重要信息. 结果表明滚波的聚合过程是不规则滚波演化和增长的重要机制, 在特定条件下滚波增长由自然增长模式转变为以吸收聚合和追赶聚合为主的增长模式. 滚波聚合过程中, 依次经历后波追赶、爬升、与前波合并、内部流场调制等多个步骤, 最终形成一个具有更大波长和波高的滚波. 本文发现了在3个滚波间距较近的情况下, 会发生二重聚合现象, 即后两个滚波首先聚合, 然后与前波进一步聚合形成一个新的滚波.