Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder

PIV technique is applied for measurements of instant velocity distributions in a liquid film flowing down an inclined tube in the form of a wavy rivulet. An application of special optical calibration is applied to correct distortion effects caused by the curvature of the interface. A vortex flow of liquid is observed inside a wave hump in the reference system moving with wave phase velocity. Conditionally averaged profiles of longitudinal and transverse components of liquid velocity are obtained for different cross-sections of developed non-linear waves. It is shown that the increase in wave amplitude slightly changes the location of the vortex center. The analysis of modification of vortex motion character due to wavy flow conditions, such as tube inclination angle, film Reynolds number, wave excitation frequency, is fulfilled.     

Migrating sea ripples

Ripple formation under sea waves is investigated by means of a linear stability analysis of a flat sandy bottom subject to the viscous flow which is present in the boundary layer at the bottom of propagating sea waves. Nonlinear terms in the momentum equation are retained to account for the presence of a steady drift. Hence the work by Blondeaux is extended by considering steeper waves and/or less deep waters. Second order effects in the sea wave steepness are found to cause neither destabilizing nor stabilizing effects on the process of ripple formation. However, because of the presence of a steady velocity component in the direction of wave propagation, ripples are found to migrate at a constant rate which is predicted as function of sediment and wave characteristics. The analysis assumes the flow regime in the bottom boundary layer to be laminar and the results are significant for ripples at the initial stage of their formation or for mature ripples of small amplitude (rolling-grain ripples). A comparison of the theoretical findings with laboratory experiments supports the reliability of the approach and of the theoretical results.     

Measurements of gravity and gravity-capillary waves in horizontal gas-liquid pipe flow using PIV in both phases

An experimental study was performed in stratified wavy flow of air and water through a horizontal pipe. The velocity fields in both phases were measured simultaneously using PIV and the interfacial shape was resolved using a profile capturing technique. The objective of the study was to investigate the interfacial characteristics and the velocities of the liquid and gas phases in two wave patterns: ‘3D small amplitude’ and ‘2D large amplitude’ waves. The wave patterns were shown to consist of gravity and gravity-capillary waves, respectively, with substantial differences in the wave characteristics and liquid velocities. Contrary to this, the effect of the waves on the gas velocities was rather similar in both wave regimes, with both wave regimes causing an increase in the velocity fluctuations close to the interface. The current measurements also produced a valuable dataset that can be used to further improve the numerical modeling of the stratified flow pattern.     

Numerical analysis on flow dynamics and heat transfer of falling liquid films with interfacial waves

Flow dynamics and heat transfer of falling liquid films with interfacial waves flowing on a vertical plate have been studied with originally proposed numerical simulation method. To discretize basic equations a staggered grid fixed on a physical space is employed. A small amplitude disturbance generated at inflow boundary develops to a solitary wave which consists of a large amplitude roll wave and small amplitude capillary waves. Instantaneous streamwise velocity profiles at the wave crest and trough are very different from a laminar flow. A circulation flow occurs in the roll wave and it affects temperature distributions, especially the strong effect is observed for high Prandtl number liquids. The interfacial wave enhances the heat transfer by two kinds of effects which are a film thinning effect and a convection effect. The dominating effect depends on the Prandtl number. Received on 23 December 1998     

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.     

Behaviour of liquid films and flooding in counter-current two-phase flow. Part 2. Flow in annuli and rod bundles

Experiments are described on the gas velocity at the onset of flooding and the maximum height of the wavy liquid film flowing downwards on a rod surface. On the basis of a simple analysis for a large amplitude wave on the liquid film, a flooding condition relating the maximum wave height to the gas velocity at the onset of flooding is derived. The values predicted by this condition show a good agreement with the measured results.An equivalent diameter of the channel is defined for the flooding velocity. Applying this diameter, the present data for annuli and rod bundles are well correlated by the same empirical equation as that for flow in circular tubes presented previously.     

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.     

Particle image velocimetry investigation of a finite amplitude pressure wave

Particle image velocimetry is used to study the motion of gas within a duct subject to the passage of a finite amplitude pressure wave. The wave is representative of the pressure waves found in the exhaust systems of internal combustion engines. Gas particles are accelerated from stationary to 150 m/s and then back to stationary in 8 ms. It is demonstrated that gas particles at the head of the wave travel at the same velocity across the duct cross section at a given point in time. Towards the tail of the wave viscous effects are plainly evident causing the flow profile to tend towards parabolic. However, the instantaneous mean particle velocity across the section is shown to match well with the velocity calculated from a corresponding measured pressure history using 1D gas dynamic theory. The measured pressure history at a point in the duct was acquired using a high speed pressure transducer of the type typically used for engine research in intake and exhaust systems. It is demonstrated that these are unable to follow the rapid changes in pressure accurately and that they are prone to resonate under certain circumstances.     

Air–water counter-current slug flow data in vertical-to-horizontal pipes containing orifice type obstructions

This paper presents experimental counter-current air–water flow data on the onset of flooding and slugging, the slug propagation velocity, the predominant slug frequency and the average void fraction collected by using different size orifices installed at two locations in a horizontal pipe. For the flow conditions covered during these experiments, it was observed that there is no significant difference between the onset of flooding and the onset of slugging when an orifice is installed in the horizontal run. However, a difference was observed for the experiments carried out without orifices. Furthermore, the position of the orifice with respect to the elbow does not affect the onset of flooding and slugging. When an orifice is installed in the horizontal run, it was observed that slugs occur due to the mutual interaction (constructive interference) of two waves traveling in opposite directions. This means that a completely different mechanism seems to govern the formation of slugs in counter-current two-phase flows in horizontal partially blocked pipes. This is in contrast to that described for the slugging phenomena in co-current flow, where wave instability seems to be the principal mechanisms responsible of bridging the pipe. The mutual interaction of waves traveling in opposite directions seems to control the behaviour of the slug propagation velocity, the slug frequency and average void fraction with increasing the gas superficial velocity.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Capillary wave gas exchange in the presence of surfactants

 The effect of surfactants on gas exchange across an air/water interface populated with capillary waves, is considered. Experiments were conducted on capillary waves having a wavelength of 2.87 mm in the presence of oleyl alcohol and stearic acid, as well as on surfaces which were surfactant-free. The presence of these surfactants decreased the gas exchange rate by at most a factor of two when the energy delivered to the tank was held constant. Thus, even in the presence of surfactants, pure capillary waves still caused significant gas exchange, indicating that partially damped capillary waves may play an important role in air/sea gas exchange. When the gas exchange coefficient was plotted as a function of mean square slope, the presence of surfactants was found to negligibly affect the gas exchange rate, with the possible exception of the high wave slope regime for stearic acid. This result suggests that it is principally the kinematics of wave motion which accounts for the enhancement of transport due to the capillary waves investigated here. Moreover, these results agree with those obtained from polychromatic, wind-generated waves, suggesting that, for non-breaking waves, knowledge of the statistics of the wave field may be all that is required to parameterize the gas exchange coefficient. Received: 10 June 1998/Accepted: 3 November 1998     

Wave development on a thinning liquid film

Experimental results are presented for the growth of surface waves on a liquid film that thins as it flows under gravity over the surface of an upright circular cone. The characteristics of the mean film are calculated on the assumption of quasi-parallel flow, and the actual mean thickness found to relate very closely to that found on this basis. The development of the film was found to fall into three phases: the entry zone in which the velocity profile of the film becomes established where no waves are visible, a region of wave growth in which amplitude, wave speed, and wave length all grow, and a final region in which amplitude and wave speed decline as the film thins further although wave length continues to grow. An empirical relationship is presented which expresses the wave number at any point on the cone in terms of the flow rate and a parameter based on the local Reynolds and Weber numbers and cone angle. It was found that for a given flow rate the maximum wave amplitude was reached at a value of wave number of 0·048.     

Behaviour of liquid films and flooding in counter-current two-phase flow—Part 1. Flow in circular tubes

Experimental results are presented on the flooding gas velocity in tubes over a wide range of parameters—tube diameter, tube length, liquid flow rate, liquid viscosity and surface tension. The flooding phenomenon is caused by interaction between the waves on the liquid film and the upward gas stream. By measuring variation of the maximum height of the wavy liquid films with an increase of the gas flow rate, the complicated effects of tube length and surface tension on flooding are revealed. The data of the flooding velocity are empirically correlated in termes of nondimensional groups for each tube length.     

Analysis of the characteristic lengths in the bubble and slug flow regimes generated in a capillary T-junction

We present an analysis of the geometry of the continuous and disperse phases in the bubble and slug flow regimes in air–water mixtures generated in a capillary T-junction of 1  mm internal diameter. Bubble size dispersion is very low in the considered flow patterns. The concept of unit cell is used to identify two characteristic lengths of the two-phase flow, namely, the unit cell length and the bubble length. The relationship between these lengths and the gas and liquid superficial velocities, gas mean velocity, bubble generation frequency and volume average void fraction is analysed. We conclude that in the considered configuration the unit cell and bubble lengths can be predicted either by the ratio of the gas–liquid superficial velocities or the volume average void fraction.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

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.     

Study of gas-sheared liquid film in horizontal rectangular duct using high-speed LIF technique: Three-dimensional wavy structure and its relation to liquid entrainment

The flow of a liquid film sheared by high velocity gas stream in a horizontal rectangular duct was investigated using a high-speed laser-induced fluorescence technique. Measurements of local film thickness were resolved in both longitudinal and transverse coordinates with high spatial and temporal resolution. It was found that the generation of fast and slow ripples by the disturbance waves was qualitatively the same as it was observed earlier in completely different conditions. The transverse size and curvature of the disturbance waves and ripples were measured. A relationship between the three-dimensional structure of ripples on top of disturbance waves and the two mechanisms of liquid entrainment, known as ‘bag break-up’ and ‘ligament break-up’, is proposed.     

Propagation of shock waves in a porous medium saturated by a liquid with bubbles of a soluble gas

The process of evolution and reflection of shock waves of moderate amplitude from a rigid boundary in a porous medium saturated by a liquid with bubbles of a soluble gas is studied experimentally. Experimental values of the amplitude and velocity of the reflected wave are compared with the calculated results obtained using mathematical models. The process of dissolution of gas bubbles in the liquid behind the shock wave is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 91–102, September–October, 2000.     

An experimental investigation on the effects of surface gravity waves on the water evaporation rate in different air flow regimes

Estimating rate of evaporation from undisturbed water surfaces to moving and quiet air has been the topic a vast number of research activities. The obvious presence of various shapes of gravity waves on the water body surfaces was the motivation of this experimental investigation. In this investigation experimental measurements have been done to quantify evaporation rate from wavy water surfaces in free, mixed and forced convection regimes. The effects of a wide range of surface gravity waves from low steepness, round shaped crest with slow celerity, to steep and very slight spilling crest waves, on the water evaporation rate have been investigated. A wide range of ${\text{Gr}}/{\text{Re}}^{2} (0.01 \le {\text{Gr}}/{\text{Re}}^{2} \le 100)$ was achieved by applying different air flow velocities on a large heated wave flume equipped with a wind tunnel. Results reveal that wave motion on the water surface increase the rate of evaporation for all air flow regimes. For free convection, due to the effect of wave motion for pumping rotational airflows at the wave troughs and the dominant effect of natural convection for the air flow advection, the maximum evaporation increment percentage from wavy water surface is about 70 %. For mixed and forced convection, water evaporation rate increment is more sensitive to the air flow velocity for the appearance of very slight spilling on the steep wave crests and the leeward air flow structures.