Interfacial area transport and evaluation of source and sink terms for confined air–water bubbly flow

The interfacial area transport equation applicable to the bubbly flow is presented. The model is evaluated against data acquired by a state-of-the-art miniaturized double-sensor conductivity probe in an adiabatic air–water co-current vertical test loop under atmospheric pressure condition. In general, a good agreement, within the measurement error of ±10%, is observed for a wide range in the bubbly flow regime. The evaluation of the individual particle interaction mechanisms demonstrates the active interactions between the bubbles and highlights the mechanisms playing the dominant role in interfacial area transport. The analysis employing the drift flux model is also performed for the data acquired. Under the given flow conditions, the distribution parameter of 1.076 yields the best fit to the data.     

Liquid mean velocity and turbulence in a horizontal air-water bubbly flow

The liquid phase turbulent structure of an air-water bubbly horizontal flow in a circular pipe has been investigated experimentally. Three-dimensional measurements were implemented with two X type probes oriented in different planes, and local liquid-phase velocities and turbulent stresses were simultaneously obtained. Systematic measurements were conducted covering a range of local void fraction from 0 to 11.7%. The important experiment results and parametric trends are summarized and discussed.     

Structure of air–water two-phase flow in helically coiled tubes

Air–water two-phase flow in helically coiled tubes is investigated experimentally to elucidate the effects of centrifugal acceleration on the flow regime map and the spatial and the temporal flow structure distribution. Three kinds of test tubes with 20 mm inner diameters including a straight tube are used to compare the turbulent flow structure. Superficial velocities up to 6 m/s are tested so that the centrifugal Froude number covers a range from 0 to 3. The interfacial structure is photographed from two directions by a high-speed video system with synchronized measurement of local pressure fluctuations. The results reveal that the flow transition line alters due to centrifugal force acting on the liquid phase in the tube. In particular, the bubbly flow regime is narrowed significantly. The pressure fluctuation amplitude gets large relatively to the average pressure loss as void fraction increases. The frequency spectra of the pressure fluctuation have plural peaks in the case of strong curvature, implying that the periodicity of slugging two-phase flow is collapsed by an internal secondary flow activated inside the liquid phase. Moreover, under large Froude number conditions, the substantial velocity of the gas phase that biases to the inner side of the helical coil is slower than the total superficial velocity because the liquid flow is allowed to pass through the outer side and so resembles a radial stratified flow.     

Phase idstribution in horizontal gas-liquid two-phase bubbly flow

An investigation on phase distribution in air-water two-phase flow in horizontal circular channel was conducted by using the double-sensor resistivity probe.The variations of phase distribution with variations of gas and liquid volumetric fluxes were analyzed and the present data were com0pared with some of other researcher‘s data and existing models,It was fund there exists more complicated phase distribution pattern in horizontal flow system than invertical flow.The radial local void fraction profiles are similar at the same measurement angle with various gas and liquid flow rates.However,an asymmetric profile can be observed at a given slice of the pipe cross-section.     

Evolution of interfacial area concentration in a vertical air–water flow measured by wire–mesh sensors

An application of wire–mesh sensors to obtain the interfacial area concentration in vertical pipes is presented as an alternative to the widely used multiple-tip electrical or optical fibre probes. The measuring data of a mesh sensor consists of a three-dimensional matrix of local instantaneous gas fractions measured at each crossing point of the wires and recorded as a time sequence. Bubbles are clearly distinguishable in this data matrix, since they represent regions of interconnected elements containing the gaseous phase. The method to deduce the interfacial area concentration from this data is based on a full reconstruction of the gas–liquid interface, where the interfacial area of each bubble is recovered as the sum of the surface area of all surface elements belonging to the given bubble. The new method can be applied to large bubbles with an arbitrary shape. To study the change of the interfacial area concentration along the pipe the distance between sensor and gas injection was varied. The axial development of the interfacial area density measured in the test pipe of 195.3 mm inner diameter was compared to the measurements carried out by Sun et al. [Sun, X., Smith, T., Kim, S., Ishii, M., Uhle, J., 2002. Interfacial area of bubbly flow in a relatively large diameter pipe. Exp. Thermal Fluid Sci. 27, 97–109] in a pipe of 101.6 mm diameter, which is the largest pipe for which interfacial area densities are presented in literature. An acceptable agreement was found, whereas deviations are consistent with the differences in the boundary conditions of both experiments.     

Two-group interfacial area transport in vertical air–water flow: I. Mechanistic model

In a companion paper, mechanistic models of major fluid particle interaction phenomena involving two bubble groups have been proposed. The prediction of interfacial area concentration evolution using the one-dimensional two-group transport equation and evaluation with experimental results are performed in the paper. These evaluations are based on solid databases for a 2-inch air–water loop with sufficient information on the axial development and the radial distribution of the local parameters. Model evaluation strategies are systematically analyzed. The predictions for the interfacial area concentration evolution demonstrate satisfactory accuracy. The proposed model predicts a smooth transition across the bubbly-to-slug flow regime boundary and demonstrates mechanisms for the generation and development of the cap/slug bubble group. The two-group interfacial area transport equation covers a wide range from bubbly, slug, to churn turbulent flow regimes for adiabatic air–water upward flow in moderate diameter pipes. The generality of the interfacial transport model is also discussed.     

Two-phase minor loss in horizontal bubbly flow with elbows: 45° and 90° elbows

The present study investigates the geometric effects of a 45° elbow on the pressure drop due to the minor loss in horizontal bubbly flow. A round glass tube with inner diameter of 50.3 mm is employed as a test section, along which a 45° elbow is installed at L/D = 353.5 from the two-phase mixture inlet. In total, 15 different flow conditions are examined. The local static pressures are measured at four axial locations at L/D = 197, 342, 363 and 419 from the two-phase mixture inlet. The effect of the elbow is clearly demonstrated in the pressure data along the axial direction. In the data analysis, the pressure data previously acquired with a 90° elbow is also utilized as well. The conventional Lockhart-Martinelli correlation with parameter C = 30 predicts the overall two-phase frictional pressure loss between the inlet and exit of the test section relatively well for both the 90° and 45° elbow experiments. However, it fails to predict the pressure loss across the elbows, because the existing model does not account for the additional loss due to the flow restrictions. In view of this, a new correlation analogous to Lockhart and Martinelli’s is developed for the two-phase frictional pressure loss across the elbows. The new correlation with the parameter C = 65 and the minor loss factors of k = 0.58 and k = 0.35 for the 90° and 45° elbows, respectively, yields the best fit to the data. The average percent differences between the predictions made by the new correlation and the data are ±2.1% and ±1.3% for 90° and 45° cases, respectively.     

Local studies in horizontal gas–liquid slug flow

The axial liquid-phase velocity profile development in a horizontal air–water plug/slug flow-pattern was experimentally investigated by simultaneously using two hot-film anemometers. One of the probes which was kept in a fixed location was exclusively used as a phase identifier while the other probe was traversed vertically for local velocity measurements. The experimental observations were focused on the intermittent and transient characteristics of the slug flow-pattern. It was shown that the velocity rapidly develops into an asymmetric but nearly fully-developed profile within liquid slug with the maximum value occurring below the pipe center line. On the other hand it was documented that the velocity never develops into a quasi-fully-developed profiles within the liquid layer below a passing slug. At a given location the velocity gradually decelerates toward the gas slug tail, but rapidly accelerates towards the wake of the gas slug.     

Gas–liquid two-phase flow in narrow horizontal annuli

Experimental data associated with the two-phase flow regimes, void fraction and pressure drop in horizontal, narrow, concentric annuli are presented. Two transparent test sections, one with inner and outer diameters of 6.6 and 8.6 mm, and an overall length of 46.0 cm; the other with 33.2 and 35.2 mm diameters and 43.0 cm length, respectively, were used. Near-atmospheric air and water constituted the gas and liquid phases, respectively. The gas and liquid superficial velocities were varied in the 0.02–57 and 0.1–6.1 m s⁻¹ ranges, respectively. The major two-phase flow patterns observed included bubbly, slug/plug, churn, stratified, and annular. Transitional regimes, where the characteristics of two distinct flow regimes could be observed in the test sections, included bubbly-plug, stratified-slug and annular-slug. The obtained flow regime maps were different than flow regime maps typical of large horizontal channels and microchannels with circular cross-sections. They were also different from the flow regimes in rectangular thin channels. The measured average void fractions for the two test sections were compared with predictions of several empirical correlations. Overall, a correlation proposed by Butterworth [Butterworth, D., 1975. A comparison of some void fraction relationships for co-current gas–liquid flow. Int. J. Multiphase Flow 1, 845–850] based on the results of Lockhart and Martinelli (1949) provided the most accurate prediction of the measured void fractions. The measured pressure drops were compared with predictions of several empirical correlations. The correlation of Friedel [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. 3R Int. 18, 485–492] was found to provide the best overall agreement with the data.     

Interfacial measurements in horizontal stratified flow patterns

The interfacial characteristic parameters of horizontal stratified wavy flow patterns were experimentally investigated for a mixture of air and water two-phase flow by using the double-sensor, parallel wire conductance probe method. The experiments were conducted in a horizontal flow loop 15.4 m long consisting of Pyrex glass tubing of 50.3 mm i.d. The range of gas superficial velocities was from 0.85 to 31.67 ms⁻¹ and the liquid superficial velocities ranged from 0.014 to 0.127 ms⁻¹. Several interfacial wave patterns as described by Andritsos and Hanratty (Int. J. Multiphase Flow 13 (1987a) 583–603) were identified and their characteristic parameters such as wave height, most dominant frequency, mean propagation velocity and mean wavelength were investigated in terms of liquid and gas flow rates. The interfacial shear stress calculated from the experimental measurements was used to evaluate the most widely used interfacial shear models.     

Numerical study of the influence of the internal structure of a horizontal bubbly flow on the average void fraction

This paper presents the results of a numerical experiment aimed to study the influence of the void fraction profile on integral flow characteristics of horizontal bubbly flows. To perform this analysis, a particular model which reflects better both the effect of non-uniform flow and concentration profiles as well as the effect of the local relative velocity between the phases than the well known drift flux model, was used. The relative phase velocity has been estimated by considering the movement of a single bubble in a liquid flow having a non-uniform velocity distribution. The analysis has shown that, in the case of strongly gravity-skewed local void fraction profiles, the volumetric flow quality β can be smaller than the average void fraction 〈α〉. This 〈α〉-β relationship is conditioned by the fact that the corresponding distribution parameter is less than 1, while the void fraction weighted average relative velocity of the gas phase is negative.     

Investigation of liquid film behavior at the onset of flooding during adiabatic counter-current air–water two-phase flow in an inclined pipe

The liquid film characteristics at the onset of flooding in an inclined pipe (16 mm i.d. and 2.2 m in length) have been investigated experimentally. A constant electric current method and visual observation were utilized to elucidate the flow mechanisms at the onset of flooding. Two mechanisms are clarified to control the flooding in lower flooding and upper flooding, respectively. The lower flooding occurred at lower liquid flow rate and high pipe inclination angle. In this mechanism, the liquid film does not block the pipe cross-section. On the other hand, the upper flooding occurred at higher liquid flow rate and low pipe inclination angle. In this case, blocking of the pipe cross-section by large wave and entrainment plays an important role. The experimental data indicated that there was no reversal motion of liquid film at the onset of flooding during the operation of both lower flooding and upper flooding. The effects of pipe inclination angle on the onset of flooding are also discussed.     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.     

Geometric effects of 90-degree Elbow in the development of interfacial structures in horizontal bubbly flow

Present study investigates the geometric effects of flow obstruction on the distribution of local two-phase flow parameters and their transport characteristics in horizontal bubbly flow. The round glass tubes of 50.3 mm in inner diameter are employed as test sections, along which a 90-degree Elbow is located at L/D = 206.6 from the two-phase mixture inlet. In total, 15 different flow conditions are examined within the air–water bubbly flow regime. The detailed local two-phase flow parameters are acquired by the double-sensor conductivity probe at four different axial locations. The effect of elbow is found to be evident in both the distribution of local parameters and their development. The elbow clearly promotes bubble interactions resulting in significant changes in interfacial area concentration. It is also found that the elbow-effect propagates to be more significant further downstream (L/D = 250) than immediate downstream (L/D = 225) of the elbow. Furthermore, it is shown that the elbow induces significant oscillations in the flow in both vertical and horizontal directions of the tube cross-section. Characteristic geometric effects due to the existence of elbow are also shown clearly in the transport of one-dimensional interfacial area concentration and void fraction along the flow.     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

Interfacial area density, mean radius and number density measurements in bubbly two-phase flow

This paper presents a new experimental method for measuring the local interfacial area density, average bubble radius and number density for bubbly two-phase flow. Experiments were performed using a KfK dual-sensor resistivity probe. The results obtained for interfacial area density using this method agreed with other methods previously proposed, except for high void fractions, close to the transition to slug flow, where prior methods are known to no longer be valid.     

Influence of the void fraction profile on the distribution parameter C0 for a bubbly gas–liquid flow in a horizontal round pipe

This paper presents the results of a numerical experiment on the influence of the void fraction profile on the distribution parameter C₀ in a horizontal bubbly two-phase flow. It was shown that for non-symmetric void fraction profiles, which occur normally in horizontal flows, the distribution parameter may be less than 1. In this case, the ratio of the volumetric flow quality β to the average void fraction α can also be less than 1.     

Boiling heat transfer behavior of lead–bismuth–steam–water direct contact two-phase flow

The boiling heat transfer behavior of lead–bismuth (Pb–Bi)–steam–water direct contact two-phase flow was experimentally investigated. Experimental study was performed using Pb–Bi–steam–water direct contact boiling two-phase flow loop. The heat transfer rate was estimated from data of one-dimensional flow direct contact boiling of water in Pb–Bi. It is assumed in the analysis that film boiling occurs at the surfaces of a small water droplet after water is injected into hot Pb–Bi flow, because of the large temperature difference between water and Pb–Bi (i.e. 493 K and 733 K for injection water and Pb–Bi temperature, respectively). The heat transfer occurs between Pb–Bi and steam without phase change after all water completely evaporates. The overall heat transfer coefficient decreased with the superheat at low injection flow rate and was nearly constant for high injection flow rate. The local heat transfer coefficient was higher than average one in the whole tube, which means that the direct contact boiling heat transfer coefficient was high and it decreased in the downstream direction. Almost all the water vaporized in the test tube at high pressure according to the local and total heat transfer rate.     

Numerical simulation of secondary flow in bubbly turbulent flow in sub-channel

Secondary flow in bubbly turbulent flow in sub-channel was simulated by using an algebraic turbulence stress model. The mass, momentum, turbulence energy and bubble diffusion equations were used as fundamental equation. The basis for these equations was the two-fluid model: the equation of liquid phase was picked up from the equation system theoretically derived for the gas-liquid two-fluid turbulent flow. The fundamental equation was transformed onto a generalized coordinate system fitted to the computational domain in sub-channel. It was discretized for the SIMPLE algorithm using the finite-volume method. The shape of sub-channel causes a distortion of the computational mesh, and orthogonal nature of the mesh is sometimes broken. An iterative method to satisfy a requirement for the contra-variant velocity was introduced to represent accurate symmetric boundary condition. Two-phase flow at a steady state was simulated for different magnitudes of secondary flow and void fraction. The secondary flow enhanced the momentum transport in sub-channel and accelerated the liquid phase in the rod gap. This effect was slightly mitigated when the void fraction increased. The acceleration can contribute to effective cooling in the rod gap. The numerical result implied a phenomenon of industrial interest. This suggested that experimental approach is necessary to validate the numerical model and to identify the phenomenon.