Horizontal Bubbly Flow Research Articles

Improvement of the two-fluid momentum equation for turbulent bubbly flows

A two-fluid model is widely employed to predict gas–liquid two-phase flows. Conventional two-fluid equations, derived by assuming that all phases are interpenetrating continua, occasionally yield impractical results. For example, the bubble velocity is predicted to be higher than the water velocity for a horizontal fully developed bubbly flow. One solution for this irrational result is two-fluid momentum equations based on the motion of fluid particles. This study revisits the particle-motion-based two-fluid equations. Previously, it was validated only with respect to the difference between the bubble and liquid velocities. Recently, we observed an erroneous prediction of the void fraction distribution by the existing particle-motion-based momentum equations. This study, through rigorous analysis, discovered that this error could be resolved by neglecting the turbulent kinetic energy term in the particle-motion-based equation for the gas phase. Subsequently, the revised momentum equations were applied to the vertical and horizontal air–water bubbly flows. The conventional and revised momentum equations produced similar results for upward bubbly flows because the relative velocity between the bubble and water phases was mainly governed by buoyancy. For horizontal bubbly flows, the revised momentum equations led to a downward shift in the liquid velocity distributions, which was attributed to the modified momentum diffusion term. At a higher modification factor of turbulent dispersion, the velocity distributions exhibited an upward shift. We conclude that the optimization of physical models should be based on the revised two-fluid momentum equations.

Effects of Swirl on Bubble Flow and Its Development in a Horizontal Pipe

Effective length of swirl flow is important for its application in the industry, however, the length of the swirl flow in a horizontal pipe is largely unexplored. In this article, effects of swirl on a horizontal bubbly flow and its development in a 25 mm horizontal pipe with a length of 4 m were studied by an experimental and theoretical method. In the experiments, the superficial gas velocities ranged from 0.068 to 0.566 m/s and the liquid velocities ranged from 0.283 to 1.132 m/s. The results show that: instead of dispersed bubbles in the non-swirl bubbly flow, a gas column flow is transformed downstream of the swirler; then, it breaks up into separated gas slugs, and finally, transforms to a non-swirl bubble flow. The pressure drop in the swirl flow gradually decreases and approximates to that in the non-swirl flow along the streamwise direction. The transition mechanism for the gas column flow was proposed here, and the transition criteria of the gas column flow were developed based on Kelvin–Helmholtz instability, then, the effective length of swirl on the gas column flow can be predicted.

RANS Simulation of Flow Structure and Heat Transfer in Horizontal Bubbly Flow in Sudden Duct Expansion

RANS Simulation of Flow Structure and Heat Transfer in Horizontal Bubbly Flow in Sudden Duct Expansion

Partition method of wall friction and interfacial drag force model for horizontal two-phase flows

The improvement of thermal-hydraulic analysis techniques is essential to ensure the safety and reliability of nuclear power plants. The one-dimensional two-fluid model has been adopted in state-of-the-art thermal-hydraulic system codes. Current constitutive equations used in the system codes reach a mature level. Some exceptions are the partition method of wall friction in the momentum equation of the two-fluid model and the interfacial drag force model for a horizontal two-phase flow. This study is focused on deriving the partition method of wall friction in the momentum equation of the two-fluid model and modeling the interfacial drag force model for a horizontal bubbly flow. The one-dimensional momentum equation in the two-fluid model is derived from the local momentum equation. The derived one-dimensional momentum equation demonstrates that total wall friction should be apportioned to gas and liquid phases based on the phasic volume fraction, which is the same as that used in the SPACE code. The constitutive equations for the interfacial drag force are also identified. Based on the assessments, the Rassame-Hibiki correlation, Hibiki-Ishii correlation, Ishii-Zuber correlation, and Rassame-Hibiki correlation are recommended for computing the distribution parameter, interfacial area concentration, drag coefficient, and relative velocity covariance of a horizontal bubbly flow, respectively.

Modeling of void fraction and relative velocity covariance for dispersed bubbly and intermittent flows in horizontal channels

The interfacial drag force governs the momentum exchange between gas and liquid phases and is a key parameter in predicting void fraction using a one-dimensional thermal-analysis code. The interfacial drag force is formulated by the product of the overall drag coefficient and the area-averaged relative velocity between two phases. The area-averaged relative velocity for gas-dispersed two-phase flows has been formulated with the aid of the distribution parameter, which expresses the covariance due to the distributions of void fraction and mixture volumetric flux. It has been pointed out that the term due to void fraction covariance is missing in the formulation of the area-averaged relative velocity adopted in one-dimensional thermal-analysis codes. This study has been conducted to develop void fraction and relative velocity covariance models for gas-dispersed two-phase flows in horizontal pipes. The database of local void fraction distributions for horizontal bubbly flows was established, and an artificial database for intermittent horizontal flows was modeled with assumed distributions of local void fractions. The developed void fraction covariance model for gas-dispersed horizontal two-phase flows could reproduce the data with the mean relative deviation (i.e., bias) of 8.33% and the mean absolute relative deviation (i.e., random uncertainty) of 21.4%. The developed relative velocity covariance model for gas-dispersed horizontal two-phase flows could reproduce the data with the mean relative deviation (i.e., bias) of -0.265% and the mean absolute relative deviation (i.e., random uncertainty) of 7.11%.

Bubble characteristics and turbulent dissipation rate in horizontal bubbly pipe flow

The energy dissipation rate is a crucial parameter for system control and turbulence modeling but is difficult to quantify in gas–liquid two-phase flows. Little relevant information is available, especially in horizontal pipe flows. Based on the consideration that the bubble characteristics in a stable bubbly flow are a reflection of flow turbulence, the bubble shape and bubble size spectrum are investigated in a 10-m-long horizontal rectangular pipe by means of high-speed imaging and graphic processing techniques. The bubble size spectra indicate a critical length scale, deemed to be the Hinze scale, and the spectral shape is related to turbulent fragmentation and, thus, enables calculation of the turbulence dissipation rate. After careful validation of the approach for estimating the turbulence dissipation rate, an empirical prediction equation is proposed based on the present tested flow conditions, reflecting the effects of both the pipe flow velocity and the gas flow rate. Such information is useful for the modeling of turbulent two-phase flows.

Experimental Study on Methane Hydrate Formation in Drilling Fluid under a Horizontal Bubbly Flow Condition

In deepwater environments, where the water depth is greater than 800 m, hydrate formation in the drilling wellbore becomes a crucial problem for flow assurance and wellbore pressure management. In ...

Experimental and numerical study of air-water flow characteristics in a horizontal duct

The horizontal bubbly two-phase flow is preferably used in various industrial applications because it provides high interfacial areas which enhance the heat and mass transfer. In the present research, the phase distribution of controlled air-water flow in a horizontal acrylic round pipe with 60 mm inside diameter (D) has been investigated experimentally and modeled numerically. The modeled differential pressure and the mixture velocity profile at a distance of 33D from the mixing section (fully developed region) are computed numerically and compared with those obtained experimentally from the two-phase flow system established and maintained at the National Institute of Standards (NIS-Egypt). Furthermore, the numerical and the experimental data have been compared with previous correlations and models. Reasonable quantitative agreement between all data is found. An electronic device based on Arduino Uno board was designed and used with careful data manipulation for measuring the slug bubble velocity. The results point out that the air volume fraction has a maximum value at the upper pipe wall as the gas bubbles tend to migrate to the upper wall. A new correlation was obtained for bubble migration length to the upper pipe wall which is very important in chemical industrial processes and other engineering application.

Methodology for pressure drop of bubbly flow based on energy dissipation

Abstract Pressure drop of bubbly flow is a widely used parameter in petroleum industry. The energy dissipation rate is induced by three factors, including wall resistance, bubble breakup and coalescence, which is studied here from the perspective of the macroscopic flow and microscopic bubbles. This work details a model using the principle of energy conservation to clarify the mechanism of the pressure drop for turbulent bubbly flow in horizontal pipes. The model was validated via a comparison with experimental data of horizontal bubbly flow collected from nine previous studies with 200 points. Most of the errors are within ±20%. The proportions of pressure drop induced by wall resistance, bubble breakup and coalescence were calculated by the model. The results indicate that the largest proportion is from wall resistance, followed by bubble coalescence, with bubble breakup having the smallest proportion. In addition, the trends of proportion induced by the three factors above are analyzed by increasing gas volume fraction and mixture viscosity. The results show that the proportion induced by wall resistance decreases with the increasing volume fraction of the gas, and increases with the increasing mixture viscosity. The proportions induced by the bubble breakup and coalescence in the opposite case.

Void fraction prediction and one-dimensional drift-flux analysis for horizontal two-phase flow in different pipe sizes

The current work seeks to perform the one-dimensional drift-flux analysis for horizontal gas-dispersed flow, to provide closure models for void fraction and to investigate the relative motion between gas and liquid phases. A reliable experimental database for void fraction and bubble velocity is first established over a wide range of flow conditions for bubbly, plug and slug flows in different pipe sizes, due to the limitations of existing database. It is found that the effects of flow regime and pipe size on the drift-flux analysis are insignificant. The drift velocity is found to be negative in horizontal bubbly flow. This is consistent with the conclusion by the 〈α〉–〈β〉 analysis, where the slope is found to be greater than one. This indicates that the gas phase moves slower than the liquid phase in horizontal bubbly flow. The analysis also indicates that the horizontal plug and slug flows are relatively more homogeneous than horizontal bubbly flow. As such, the homogeneous flow model can predict the void fraction better for plug and slug flows. The current drift-flux analysis provides closure relations for C0 and 〈〈Vgj〉〉 that can be employed in TRACE, while existing closure relations are developed for vertical flow and cannot be used for horizontal flow prediction. In addition, various void fraction models in literature are evaluated. It is found that the correlations modified from vertical flow generally cannot predict the void fraction well for horizontal flow. The correlations for plug and slug flows by Franca and Lahey, and Lamari underestimate the void fraction, which may be because these correlations are developed for relatively low jf conditions, while the current work focuses on conditions at jf greater than 2.0 m/s.

Interfacial area transport models for horizontal air-water bubbly flow in different pipe sizes

The current work seeks to develop the interfacial area transport models for horizontal bubbly flow applicable to various pipe sizes. A steady-state one-dimensional, one-group interfacial area transport equation (IATE) for horizontal adiabatic air-water bubbly flow is presented. The models discussed include: (a) frictional pressure drop prediction based on Lockhart–Martinelli approach; (b) drift-flux based closure relations for void-weighted bubble velocity and void fraction; (c) bubble interaction mechanisms; and (d) local void fraction reconstruction to calculate covariance parameters associated with asymmetric bubble distribution in horizontal bubbly flow. To develop these models, experiments are performed to establish local databases in bubbly flow using the four-sensor conductivity probe in horizontal test facilities with three different inner diameters (38.1 mm, 50.8 mm, and 101.6 mm). In total, 23 test conditions with superficial liquid and gas velocities in the ranges of 3.00–6.00 m/s and 0.08–1.00 m/s, respectively, are employed in the current work. The range of void fraction for the established database is 0.017–0.193. It is demonstrated that, the void weighted bubbly velocity (<<vg>>), void fraction (<α>), and frictional pressure loss can be predicted very well with an averaged percent difference of ±4.8%, ±4.7%, and ±2.1%, respectively. The covariance parameters can be predicted generally within ±30% using the current approach for void fraction reconstruction. As a result, the IATE can predict the measured interfacial area concentration with an averaged percent difference of ±5.9%, except for the test conditions with large bubbles generated as flow develops. Meanwhile, it is found that decreasing liquid velocity decreases the contributions to the total change of interfacial area concentration by random collision induced bubble coalescence, and turbulent impact induced bubble breakup.

Effects of pipe size on horizontal two-phase flow: Flow regimes, pressure drop, two-phase flow parameters, and drift-flux analysis

This paper performs experimental studies to investigate the effects of pipe size on horizontal air–water two-phase flow in a wide range of flow configurations. Some of the major characteristic two-phase flow phenomena of interest include flow regime transitions, two-phase frictional pressure drop, local interfacial structures, and drift-flux analysis. Based on the experimental results obtained in two pipe sizes, the flow regime maps and the correlations for two-phase frictional pressure drop employed in conventional nuclear reactor system analysis codes (TRACE and RELAP) are evaluated. It is found that the flow regime maps in the codes incorrectly predict plug and slug flows as bubbly flow. Effects of pipe size on flow regime transitions are observed, while these effects are not reflected on the maps employed in the codes. The frictional pressure drop analysis suggests that the closure relations used in both TRACE and RELAP can be improved for horizontal two-phase flow. The local time-averaged two-phase flow parameters acquired by a four-sensor conductivity probe including void fraction, interfacial area concentration, bubble velocity, and bubble Sauter-mean diameter provide quantitative descriptions for the interfacial structures in different pipe sizes. It is found that increasing the pipe size tends to cause bubbles to be more concentrated near the top wall in bubbly flow. As a result, the bubble layer occupies a smaller portion of the flow area as pipe diameter increases. Based on the experimental database, drift-flux analysis using both the 〈〈vg〉〉 vs. 〈 j〉 and 〈α〉 vs. 〈β〉 methods is performed. The effect of pipe size on drift-flux analysis is found to be negligible. The global slip is found to be less than one, indicating that the gas phase moves slower than the liquid phase in horizontal bubbly flow. This analysis also provides a predictive method to estimate the void-weighted bubble velocity and void fraction, which can be predicted with an average percent difference of ±3.3% and ±3.1%, respectively.

Improvement of the two-fluid momentum equation using a modified Reynolds stress model for horizontal turbulent bubbly flows

Two-fluid equations are widely used for practical applications involving multi-phase flows in chemical reactor, nuclear reactor, desalination systems, boilers, and internal combustion engines. The popular two-fluid equation for a gas-liquid two-phase flow is based on the assumption of interpenetrating continua. According to the experimental data of fully-developed turbulent bubbly flows in a horizontal pipe, the bubble phase velocity is close to or slightly smaller than the liquid phase velocity. The velocity profile is nearly symmetric along the vertical centerline of the horizontal pipe, or tends to be slightly skewed toward the bottom region of the pipe. However, numerical simulations using the momentum equation based on interpenetrating continua showed that, in contrast, the bubble phase was faster than the liquid phase. In addition, the velocity profile was predicted to be skewed toward the upper region of the pipe. These simulation results are not consistent with experimental observations. In the meantime, there are particle averaged momentum equations in which the continuous and disperse phase equations are developed from the equations of motions of fluid and particle, respectively. We considered two different particle averaged momentum equations. The form of one particle averaged momentum equation is similar to that of the momentum equation based on interpenetrating continua, except for the laminar viscosity term. Thus, for a turbulent bubbly flow, this particle averaged equation showed similar results as observed in the momentum equation based on interpenetrating continua. The other particle averaged equation differs from the momentum equation based on interpenetrating continua in both laminar and turbulent viscosity terms. This particle averaged equation showed good agreement with experimental observations.

Investigation on Effect of Gravity Level on Bubble Distribution and Liquid Turbulence Modification for Horizontal Channel Bubbly Flow

Bubbly flows in the horizontal channel or pipe are often seen in industrial engineering fields, so it is very necessary to fully understand hydrodynamics of horizontal bubbly flows so as to improve industrial efficiency and to design an efficient bubbly system. In this paper, in order to fully understand mechanisms of phase distribution and liquid–phase turbulence modulation in the horizontal channel bubbly flow, the influence of gravity level on both of them were investigated in detail with the developed Euler–Lagrange two–way coupling method. For the present investigation, the buoyance on bubbles in both sides of the channel always points to the corresponding wall in order to study the liquid–phase turbulence modulation by bubbles under the symmetric physical condition. The present investigation shows that the gravity level has the important influence on the wall–normal distribution of bubbles and the liquid–phase turbulence modulation; the higher the gravity level is, the more bubbles can overcome the wall–normal resistance to accumulate near the wall, and the more obvious the liquid–phase turbulence modulation is. It is also discovered that interphase forces on the bubbles are various along the wall–normal direction, which leads to the fact that the bubble located in different wall–normal places has a different wall–normal velocity.

構造物加振による水平管内気泡流の速度変動挙動

構造物加振による水平管内気泡流の速度変動挙動

Characterization of horizontal air–water two-phase flow

This paper presents experimental studies performed to characterize horizontal air–water two-phase flow in a round pipe with an inner diameter of 3.81cm. A detailed flow visualization study is performed using a high-speed video camera in a wide range of two-phase flow conditions to verify previous flow regime maps. Two-phase flows are classified into bubbly, plug, slug, stratified, stratified-wavy, and annular flow regimes. While the transition boundaries identified in the present study compare well with the existing ones (Mandhane et al., 1974) in general, some discrepancies are observed for bubbly-to-plug/slug, and plug-to-slug transition boundaries. Based on the new transition boundaries, three additional test conditions are determined in horizontal bubbly flow to extend the database by Talley et al. (2015a). Various local two-phase flow parameters including void fraction, interfacial area concentration, bubble velocity, and bubble Sauter mean diameter are obtained. The effects of increasing gas flow rate on void fraction, bubble Sauter mean diameter, and bubble velocity are discussed. Bubbles begin to coalesce near the gas–liquid layer instead of in the highly packed region when gas flow rate increases. Using all the current experimental data, two-phase frictional pressure loss analysis is performed using the Lockhart–Martinelli method. It is found that the coefficient C=24 yields the best agreement with the data with the minimum average difference. Moreover, drift flux analysis is performed to predict void-weighted area-averaged bubble velocity and area-averaged void fraction. Based on the current database, functional relations for ≪vg≫ vs. <j> and <α> vs. <jg>/<j> have been studied. It is found that ≪vg≫ – <j> method predicts the void-weighted area-averaged bubble velocity and area-averaged void fraction better compared to <α> – <jg>/<j> method.

Ultrasonic pulse echography for bubbles traveling in the proximity of a wall

The behavior of a bubbly two-phase flow in the vicinity of a wall affects heat, mass, and momentum transfer; therefore, there is great interest in developing a quantitative technique to monitor this behavior. Herein we propose a new method based on ultrasound echo signal processing that it feasible for industrial applications where the boundary layer is modified by traveling bubbles. By introducing time-resolved direct waveform analysis at 100 MHz, we have succeeded in the spatio-temporal detection of bubble surfaces at echographic profiling frequencies in the range of 15–20 kHz. Unlike conventional approaches, which use short pulses, a relatively long pulse length is applied to allow ultrasound Doppler velocimetry in the liquid phase. Examination of the horizontal bubbly two-phase turbulent channel flows demonstrated the feasibility of this method; spatio-temporal echography of moving bubble surfaces is successfully achieved as the bubbles travel on length scales smaller than the spatial ultrasonic pulse length near the wall. The applicable range of parameters (e.g. bubble size and shape, and flow speed) was determined by 3D numerical analysis of the wave equation and its application to bubbles flowing beneath a flat-bottom model ship.

Characterization of horizontal air–water two-phase flow in a round pipe part II: Measurement of local two-phase parameters in bubbly flow

The current work seeks to develop an additional database in air–water horizontal bubbly flow through a 3.81cm inner diameter test section with a total development length of approximately 250 diameters. The experimental conditions are chosen to cover a wide range of the bubbly flow regime based upon flow visualization using a high-speed video camera. A database of local time-averaged void fraction, bubble velocity, interfacial area concentration, and bubble Sauter mean diameter are acquired throughout the entire pipe cross-section using a four-sensor conductivity probe for nine flow conditions. To investigate the evolution of the flow, measurements are made at axial locations of 44, 116, and 244 diameters downstream of the inlet. Using this database, the effects of gas flow rate, liquid flow rate, and development length on the local and area-averaged two-phase flow parameters are presented. From the local profiles, it is found that highly turbulent liquid flow conditions cause the void fraction profile to become more uniform with increasing development length through a turbulent mixing process which counters the effect of buoyancy. Bubble interactions are also observed to play a significant role in the evolution of the flow such that the area-averaged void fraction and interfacial area concentration can have different axial trends.

Experimental study on behavior of horizontal bubbly flow under structure vibration

Experimental study on behavior of horizontal bubbly flow under structure vibration

Bubble dissolution in horizontal turbulent bubbly flow in domestic central heating system

In a domestic central heating system, the phenomenon of microbubble nucleation and detachment on the surface of a boiler heat exchanger finds its origins in the high surface temperature of the wall and consequential localised super saturation conditions. If the surrounding bulk fluid is at under-saturated conditions, then after exiting the boiler, the occurrence is followed by bubbly flow and bubble dissolution. A comprehensive understanding of the fundamentals of bubble dissolution in such a domestic wet central heating system is essential for an enhanced deaeration technique that would consequently improve system performance. In this paper, the bubble dissolution rate along a horizontal pipe was investigated experimentally at different operating conditions in a purpose built test rig of a standard domestic central heating system. A high speed camera was used to measure the bubble size at different depths of focal plane using two square sectioned sight glasses at two stations, spaced 2.2m apart. A dynamic model for bubble dissolution in horizontal bubbly flow has been developed and compared with experimental data. The effects of several important operating and structural parameters such as saturation ratio, velocity, temperature, pressure of the bulk liquid flow, initial bubble size and pipe inside diameter on the bubble dissolution were thus examined using the model. This model provides a useful tool for understanding bubble behaviours in central heating systems and optimising the system efficiency.