Steam-water Two-phase Flow Research Articles

Frictional pressure drop correlation of steam-water two-phase flow in helically coiled tubes

Helically coiled tubes are utilized as the heat transfer tubes for High-Temperature Gas-cooled Reactor (HTGR) steam generators due to their compactness, thermal expansion accommodation and high heat transfer coefficient. A clear understanding of the pressure drop characteristics is important for the design and operation of steam generators. In this study, experiments were conducted to investigate the frictional pressure drop characteristics in helically coiled tube with a very large curvature ratio of 0.109. The experiments were carried out in a steam quality range of 0.1–0.9, system pressure range of 3.5–7 MPa, mass flux range of 320–1100 kg/m2s. The results indicate that the frictional pressure drop increased with the increase of mass flux, decreased with the increase of system pressure. It first increased with the increase of steam quality, and reached a maximum value at a steam quality of approximately 0.8, then decreased until steam quality reached unity. Based on the present work and existing experimental database, 25 existing correlations are evaluated and none of them could satisfactorily fit all the data. Therefore, a new correlation based on the Martinelli and Nelson correlation was proposed. Compared with existing correlations, it has a broader range of applicability (operating pressure from 0.75 to 8 MPa, mass flux from 200 to 1100 kg/(m2·s), steam quality from 0.03 to 0.99, and curvature ratio from 0 to 0.109.), and higher accuracy (weighted mean MAPE of 8.92 % and arithmetic mean MAPE of 8.81 %). It also has better compatibility with straight tubes.

Interfacial area concentration correlation for boiling steam-water two-phase flows in annulus flow channels

The investigation of boiling two-phase flows in annulus flow channels has garnered increasing significance given its extensive utilization in various heating devices and its crucial contribution as a fundamental basis for comprehending boiling two-phase flow behavior in intricate flow channels, such as rod bundle flow channels. Accurate modeling of Interfacial Area Concentration (IAC) in boiling steam-water two-phase flows is essential for enhancing the predictive performance of the two-fluid model in simulating complex two-phase behaviors in a diverse range of practical boiling systems. The present study evaluates the predictive performance of seven representative IAC correlations using available typical experimental IAC data from boiling steam-water two-phase flows in annulus flow channels. Although some representative IAC correlations exhibit favorable predictive performance for specific experimental databases, none of the reviewed existing correlations consistently maintain acceptable predictive performance across all collected experimental data. In order to enhance the accuracy and reliability of IAC predictions under boiling flow conditions, a novel IAC correlation has been proposed grounded in physical-based considerations to effectively model the IAC contributions of small (group-1) and large (group-2) bubbles in boiling steam-water two-phase flows in annulus flow channels. The newly proposed two-group bubble IAC correlation has been validated through the examination of 303 boiling steam-water data obtained from annulus flow channels, demonstrating satisfactory predictive performance with the mean relative error of 0.216. Moreover, the applicability of the newly proposed IAC correlation to rod bundle flow channels has been evaluated using 53 boiling steam-water data taken from a 3 × 3 rod bundle flow channel, yielding a favorable prediction result with a mean relative error of 0.173. The anticipated improvement in the accuracy of predicting IAC for steam-water two-phase flows through the newly proposed correlation is expected to provide a scientific foundation for enhancing the performance and safety of thermal systems.

Experimental investigation on steam-water flow patterns in a vertical narrow rectangular channel utilizing conductance scanning measurement

In order to tackle the challenges in two-phase flow measurement in narrow rectangular channels, especially under pressurized conditions, a novel conductance scanning sensor, consisting of two ceramic-substrate printed circuit (CSPC) boards, has been developed based on the concept of wire mesh sensor. A leak-tight structure was also fabricated to avoid leakage at the penetrations of lead wires through the sensor housing. Measurements have been carried out in a narrow rectangular channel, with inner the cross-sectional dimension 70 mm × 2 mm, under pressure between 0.20 and 0.90 MPa. In the experiment, bubbly, churn and annular flows have been observed, except for slug flow. Flow pattern maps have been proposed for the steam-water two-phase flow. Comparing with those in the literature, it can be found that as the channel width/gap increases, the flow pattern transition boundaries shift towards the higher vapor superficial velocity direction. Additionally, the transition criteria for narrow rectangular channels were investigated by separately evaluating the critical void fraction and the superficial velocity calculation correlations. Results show that the critical void fraction of bubbly to churn flow and churn to annular flow can be approximately estimated as 0.2 and 0.75, respectively. However, the existing correlations for superficial velocity calculation are not suitable for the steam-water flows with a void fraction less than 0.5.

Hydrodynamics of Swirling Steam–Water Two-Phase Flows under External Shear

The hydrodynamics of steam–water two-phase flows under the effects of shearing, swirling, and large-scale discrete boundary conditions were investigated on an experimental basis. The steam was injected in a swirling configuration into concurrently flowing water. Both the steam and water were injected at gauge pressures of 1.0 and 2.0 bars, whereas the swirling was caused by a propeller moving at rotational speeds of 60 and 300 rpm. The ensembled normalized amplitudes of the velocity fluctuations across a layer defined by spatial positions along the radial and axial directions inhibited the swirling steam–water two-phase flows. This ensembled nature and the normalized amplitudes of the velocity fluctuations were investigated under the action of the above-stated operating conditions, and it was found that the swirling steam–water two-phase body of the flow showed proportionally varying percentages of ensembled-normalized amplitudes of the velocity fluctuations.

Study on Performance and Operation Mechanism of a Separation Equipment for a PWR Steam Generator

Computational fluid dynamics (CFD) is adopted to calculate and analyze the performance and separation mechanism of a steam-water separation equipment for a pressurized water reactor (PWR) steam generator. The steam-water two-phase flow is simulated by the Euler two-fluid model, and several representative water droplet diameters are selected among 50 to 400 μm. The influence mechanism of water droplet diameter on the performance is investigated by analyzing the flow parameters such as phase volume fraction, velocity, and turbulent kinetic energy. The results show that the integrated calculation and analysis of the separation equipment can more truly reflect the flow state between the separators, improving the reliability of the performance prediction and mechanism analysis. With the increase in water droplet diameter, the separation efficiency of the separation equipment and each separator gradually increases, the outlet wetness gradually decreases, and the pressure loss first decreases and then stabilizes. When 400 μm is taken as the characteristic value of the actual droplet diameter distribution at the inlet of the separation equipment, the performance prediction is more accurate, the pressure loss of each separator is relatively close, and the pressure loss of the primary separator is less affected by the droplet diameter and smaller than that of the swirl-vane primary separator, which is conducive to achieving a higher circulation ratio (CR). Re-entrainment occurs at the perforations of the primary separator and the outlet of the secondary separator, and the corresponding structure is suggested to be optimized to further improve separation efficiency of the separation equipment.

Experimental study on flow patterns in narrow rectangular channels

Plate fuel elements are commonly used in compact nuclear reactors due to the advantages of high fuel consumption. In this paper, the two-phase flow pattern in the coolant channel of plate fuel elements, i.e. the rectangular narrow channel was studied. Visualization flow pattern experiments of upward steam-water two-phase flow in narrow rectangular channels, 745 mm long and 67 mm wide with gap widths of 1.3 mm and 1.9 mm, were investigated. The experiments were performed in the conditions of pressure ranging from 1 to 2 MPa, mass flow rate ranging from 200 to 1500kg/(m2⋅s), inlet subcooling ranging from 20–100 °C and tilt angle ranging from 0 to 45°. Three flow patterns, consisting of bubble flow, churn flow and annular flow, were obtained in a wide range of thermal parameters. Flow patterns maps were plotted and the influences of pressure, mass flow rate, inlet subcooling, channel gap and tilt angle on the flow pattern transformation of narrow rectangular channel were studied. This study is of great significance for investigating the subsequent heat transfer process of two-phase flow in compact nuclear reactors.

Modeling and analysis of steam-water two-phase flow distribution and wall temperature distribution in parallel heated pipes with different manifold types

In solar tower receiver, boiler water-wall and various heat exchangers, the uneven distribution of two-phase flow often occurs among parallel heated pipes, which seriously reduces the operating efficiency and may further induce heat transfer deterioration and soaring wall temperature. In this paper, a coupling model for the flow distribution and heat transfer process of steam-water two-phase flow in parallel heated pipes was established based on the discrete methods. In the present model, two main improvements were proposed as below. On one hand, the calculated equations for the pressure drop and the phase distribution of two phase fluid in both the combining T-junction and dividing T-junction were established to consider the coupling effects of the inlet manifold and outlet manifold on the flow distribution characteristics. On the other hand, the calculation module for the heat transfer and wall temperature along the branch pipes was also coupled in the present model with considering of different heat transfer regions (saturated nucleate boiling region, liquid deficient region, and superheated steam region) along the pipe. The present model was then verified and used to investigate the effects of system pressure, inlet fluid flow, inlet steam quality and manifold type on the flow distribution characteristics of high temperature and high pressure steam-water in parallel vertical upward pipes, and the effect of the uneven distribution of the gas-liquid two phases on the system safety was analyzed and evaluated. It was found that gas phase preferentially enters the first branch pipe near the inlet of the dividing manifold affected by buoyancy, and this results that the inlet steam quality of the corresponding branch pipe is always obviously higher than that of the subsequent pipes. As the system pressure decreases, the outlet fluid enthalpy distribution and outlet wall temperature distribution among branch pipes become more uneven. Moreover, the outlet fluid enthalpy and outlet wall temperature of the branch pipes closer to the inlet of the dividing manifold increase sharply with the decrease of system pressure. In the U-type parallel pipe system, the branch pipes away from the inlet of the dividing manifold are more prone to wall overheating at the outlet, while the opposite is true for the Z-type parallel pipe system.

Influence of Vertical Downward Annulus Eccentricity on Steam-Water Two-Phase Flow Pressure Drop

Concentric dual-tubing steam injection technique is one of the main methods to improve heavy oil recovery efficiency. From field data, it was discovered that hot fluid at high temperature and pressure caused steam injection casing to have elongation strain and “necking” eccentric buckling, and the eccentricity change affected the accurate prediction of steam-water two-phase flow pressure drop in the steam injection casing. This paper established a coupling model for the steam-water two-phase flow pressure drop in vertical downward eccentric annulus and the wellbore heat transfer and developed a mathematical model calculation program, to validate the accuracy of calculating the liquid holdup and pressure gradient of fully eccentric annulus. This revealed the influential law of eccentricity on the annulus steam-water two-phase pressure, dryness, and enthalpy value. The results indicated that when the eccentricity e increased from 0 to 1, the saturation pressure of steam at annulus wellbore bottom increased by 0.265 MPa, and the dryness and enthalpy value decreased by 8.54 × 10−3 and 11.22 kJ kg−1, respectively. Compared to the concentric layout, the eccentrically arranged steam injection inner tube cannot promote the wet steam dryness at annulus wellbore bottom.

Hydrodynamics of the swirling steam-water two-phase flows over a surface with protrusions: Shape optimization and effect of rise in temperature on drag reduction

The current study studies the drag reduction offered by the plate with protrusions to the swirling steam-water two-phase flows. Protrusions of different types, having triangular, sinusoidal, and trapezoidal shapes, are investigated. The variations and modifications were made in the dimensions and orientations (facing along or across, flush-mounted or protruded into the swirling flows), to test the effectivity of these protrusions. At 5 bars of inlet gauge pressure and rpm varying from 360 to 1440, the trapezoidal shape provides the most effective drag reduction. It is also found from the PIV images of the fluid region near the protrusions that the drag reduction in the trapezoidal-shaped protrusions occurs mainly due to the secondary flow structures formation over those protrusions.On the one hand, the lateral spacing between the adjacent protrusions created the region of strengthening and expansion against the higher opposite inertial forces from the main swirling core fluids. While on the other hand, these spacings justify the impact of the axial elongation of the vortices above the protrusion tips. Further trends in drag reduction have also been investigated by observing the effect of the rise in the temperature of the fluid medium. Reduction in drag from 1.3 to 1.6% is noted using the trapezoidal protrusions for a temperature rise of 25–60 °C. It is also observed that the drag reduction profiles show a rising trend under the influence of the rising Nusselt Number. This trend is attributed to the decrease in viscosity. Whereas under the influence of a rising Prandtl number, the drag reduction shows a decreasing trend, mainly attributed to the rise in the pressure drop at the boundary layers and the pressure drop due to the friction.

Flow regime identification of steam-water two-phase flow using optical probes, based on local parameters in vertical tube bundles

Flow regime identification based on local parameters of axial upward two-phase flow in vertical tube bundles, at high-temperature and high-pressure, was performed using optical probes. A staggered arrangement of the tube bundles was simulated inside a non-circular test channel, the tube size and pitch are same as that in a real steam generator of a PWR under design. Optical probes were utilized to acquire the void fraction, interface frequency, and fluctuation characteristics of the local void fraction at two typical locations (centroid of the three tubes, named op-1, and centre of the minimum gap between two tubes, named op-2). The system pressure ranged from 5 to 9 MPa, mass flux from 100 to 350 kg m−2 s−1, thermodynamic steam quality from 0 to 1, and inlet fluid temperature from 263.9 to 303.3 °C, depending on the saturation pressure. This study investigated local parameters and flow pattern characteristics of high-pressure steam-water two-phase flow in vertical tube bundles using optical probes, with the measurement error of less than 2%. Results showed that local void fraction at op-1 was much larger than that at op-2, and the local void fraction difference between op-1 and op-2 increased first and then gradually decreased, which was primarily affected by the transition in flow regimes. The flow pattern characteristics of steam-water two-phase flow were described based on three aspects, namely, variation in interface frequency with local void fraction, fluctuation characteristics of local void fraction, and statistical analysis of local void fraction deviating from the average. Additionally, the flow regime identification criteria, applicable to the steam-water two-phase flow in vertical tube bundles, were proposed based on local parameters.

In-Plane Fluidelastic Instability Evaluation of Triangular Array Tube Bundle Using Fluid Force Measured Under Steam–Water Two-Phase Flow Condition

Abstract Recently, tube-to-tube wear indications of triangular tube bundle steam generators (SGs) caused by fluidelastic instability (FEI) in the in-plane direction of U-bend region (in-plane FEI) have been reported. Several experiments were conducted to investigate the characteristics of in-plane FEI by our research groups. In a series of experiments, particular characteristics of in-plane FEI were found. For example, there are the critical velocity difference between the in-plane and the out-of-plane directions, the difference between straight tube bundle tests and U-bend tube bundle tests, etc. To explain these characteristics, unsteady fluid force acting on tubes were measured. The experimental investigation was conducted under high temperature and high-pressure steam–water flow conditions close to the SGs. Stability analyses were conducted using the measured unsteady fluid forces as inputs. First, stability analyses were done to simulate straight tube bundle tests. Analysis results agreed well with experiments and it could explain the effect on critical velocity trend by number of flexible tubes and directions of vibration. Second, U-tube stability analyses were performed by applying unsteady fluid force coefficients for each location of U-bend tube finite element method (FEM) model. From the results, mechanisms of in-plane FEI were understood.

Experimental investigation on flow regimes and transitions of steam-water two-phase flow in narrow rectangular horizontal channels

Experimental investigations on atmospheric steam-water two-phase flow regimes and transitions in two transparent narrow rectangular channels with cross-section areas of 1 mm × 20 mm and 2 mm × 20 mm were carried out under conditions of 0.007 ≤ Jf ≤ 0.27 m s−1, 0.05 ≤ Jg ≤ 65.2 m s−1, 0 < q ≤ 18 kW m−2. Four flow patterns were observed in narrow rectangular horizontal channels under heated condition, i.e., bubbly flow, slug flow, churn flow and annular flow. New dryout phenomenon of annular flow was observed under high wall heat flux conditions. The liquid phase occupies half of the middle of narrow channel above the bottom rectangular plate. Below the top plate, liquid phase is concentrated to a slender streamline in the middle of upper half narrow channel by high speed steam flow. For the flow regime transitions, the critical values of void fraction for transitions from bubbly flow to slug flow, slug flow to churn flow, and churn flow to annular flow in narrow rectangular horizontal channels under heated condition are 0.7, 0.8 and 0.9, respectively. The heat flux decays flow regime transitions because the generated bubbles from heated wall surfaces promote the separation of bubbles in the upstream and downstream. Flow regime transitions under larger surface tension condition need greater vapor phase velocities to disturb the mainflow. In a general, new flow regime transition criteria were developed and can present excellent predictions for the present data of flow regimes and transitions in narrow rectangular horizontal channels under heated condition.

Hydrodynamics of the steam-water two-phase flows behind a pair of bluff cylinderical bodies inside and around the wake region

A significant number of natural and industrial phenomena exist, where steam-water, two-phase flows face resistance due to the cylindrical shaped bodies. It is useful to explore such flows for their direct relevance to the steam driven industrial processes having Direct Contact Condensation (DCC) as the core phenomena for heat, mass, and momentum transfer. An experimental setup has been fabricated to study the influence of twin, different sized cylinders with a gap between them on the formation of wake region as the steam-water flow past the cylinders. Hot and cold wire sensors were used to measure the fluctuations in the velocity and temperature respectively of the flow within the wake and the region surrounding wake. The diameter of the smaller cylinder was fixed as 0.5 cm and the dimensions of the larger cylinder was varied from 1, 1.5 and 2.0 cm. Values for the fluctuating velocity were measure for all the cases and based on these measurements, the turbulent normal stresses and Reynolds shear stresses were determined. The asymmetry of the wake region increases by raising the gap between the two cylinders as the wake region aligned to the smaller cylinder has been deflected larger than the wake aligned to the larger cylinder. The wake asymmetry signified the possible effect of buoyancy on the thermal and momentum diffusivities, which was emphasized here through the measured values of turbulent normal and Reynolds stresses.

Drift-flux correlation for upward gas-liquid two-phase flow in vertical rod bundle flow channel

This paper has reviewed 17 available drift-flux correlations and collected 959 existing void fraction experimental data for air-water and steam-water two-phase flows in the vertical rod bundle flow channels. The performances of these drift-flux correlations have been evaluated with the collected experimental data. The evaluations conclude that the recently-developed drift-flux correlation of Schlegel and Hibiki gives the best predictions, and the drift-flux correlations of Clark et al. and Ye et al. can provide reasonable predictions for the collected experimental data. However, these drift-flux correlation series of Clark et al., Ye et al. and Schlegel and Hibiki are found to have the following three shortcomings. (1) Their distribution parameter correlation has ignored the flow regime and bubble behavior effects due to the different combinations of the non-dimensional superficial gas and liquid velocities at the same non-dimensional mixture volumetric flux under the high non-dimensional mixture volumetric flux conditions. (2) Their distribution parameter correlation has used the non-dimensional superficial gas and liquid velocities which cannot effectively reflect the pressure effect on the distribution parameter. (3) Their drift velocity correlation has ignored the drift velocity difference due to the flow regime transitions and has used the bubbly flow drift velocity correlation for all flow regimes, including the cap-bubbly, churn and annular flows. In view of these shortcomings, the present drift-flux correlation development adopts the segmented drift velocity correlations considering the features of bubbly, cap-bubbly, churn and annular flows in vertical rod bundle flow channel. The analysis for the experimental data of the asymptotic distribution parameter has shown that the asymptotic distribution parameter depends on the gas-phase Reynolds number with a feature that it linearly increases with gas-phase Reynolds number in the low gas-phase Reynolds number region, peaks at a critical gas-phase Reynolds number and exponentially decreases in the high gas-phase Reynolds number region under a certain liquid-phase Reynolds number flow conditions. This phenomenon is found to be caused by the formation and breakup processes of large-cap bubbles and their resultant intensive secondary flows corresponding to the flow regime transitions in the vertical rod bundle flow channel. So, a new distribution parameter correlation has been developed based on the gas- and liquid-phase Reynolds numbers reflecting the ratio of each phase inertial force to viscous force for the two-phase flows in vertical rod bundle flow channel. The newly-developed drift-flux correlation has been checked against various experimental data of air-water and steam-water two-phase flows in the rod bundle flow channel and a good agreement has been reached.

A Two-Phase Flow Model for Thermal Design of the Riser-Downcomer System Pertaining to a 600 MW Subcritical Boiler

Abstract In the present work, a numerical model is developed to analyze the riser-downcomer system of a natural circulation steam generator. The design and operation of the riser-downcomer system involve many complex issues such as multiphase flow inside the riser tubes, numerous possibilities of different flow regimes, and undesirable tube overheating due to the occurrence of critical heat flux (CHF). A separated flow model is developed to analyze steam-water two-phase flow inside the heated riser tubes. Further, the model is coupled with the implementation of the complex flow regime map and evaluation of wall temperature rise of the riser tubes. The present model is adequately validated with the existing experimental and numerical data as a direct problem. The model accuracy in predicting the tube dry-out and practical design is tested with the experimental data and real plant data, respectively. A typical 600 MW thermal power plant boiler is then investigated along with techno-economic efforts to find the possible design solutions of the boiler riser-downcomer circuit. The safe and unsafe zones of operations have been identified in the present study and, consequently, a range of feasible design solutions is provided in great detail. The diameters and thicknesses of the tubes used in the present analysis are in compliance with the ASME boiler code.

Experimental study on vertically upward steam-water two-phase flow patterns in narrow rectangular channel

Experiments of vertically upward steam-water two-phase flow have been carried out in single-side heated narrow rectangular channel with a gap of 3 mm. Flow patterns were identified and classified through visualization directly. Slug flow was only observed at 0.2 MPa but replaced by block-bubble flow at 1.0 MPa. Flow pattern maps at the pressure of 0.2 MPa and 1.0 MPa were plotted and the difference was analyzed. The experimental data has been compared with other flow pattern maps and transition criteria. The results show reasonable agreement with Hosler's, while a wide discrepancy is observed when compared with air-water two-phase experimental data. Current criteria developed based on air-water experiments poorly predict bubble-slug flow transition due to the different formation and growth of bubbles. This work is significant for researches on heat transfer, bubble dynamics and flow instability.

Periodic compression and cavitation induced shear between steam-water two-phase flows for bio-materials degradation

Steam–water-induced shear has multiple applications. Steam–water layers-induced periodic shear as a consequence of compression and cavitation has been investigated here. On an experimental basis, CCD-based shadowgraphy along with pressure sensor and laser Doppler anemometry has been applied to measure the spatial extent of compression–cavitation and shear. The superior impact has been found to be imparted due to rotational speed on transverse pressure and velocity as compared to the influence due to the inlet pressure of steam. A constructive coupling has been found between the operating parameters, which has shown the significance of the order of application of the operating parameters. Vertical velocity and pressure trends within the region of interest have been computed numerically. The extent of positive buoyancy, as well as the swirl intensification strength, has been measured using analytical approaches. It has been found that rotational speed has more potential to induce shear among steam–water two-phase flows, followed by the inlet pressure of steam/water and compressibility. It has also been found that the effectiveness of the manufactured experimental facility in terms of material degradation ranges from 22 to 45% under the influence of the operating parameters.

Void fraction measurements of steam–water two-phase flow in vertical rod bundle: Comparison among different techniques

Void fraction is a fundamental parameter to characterize two-phase flows and is very important for the proper design and safety operation of steam generator in a nuclear power plant. In the present work, void fraction measurements of steam–water two-phase upward flow in a triangular-configured vertical rod bundle were conducted at pressures from 5 to 9 MPa and mass velocities from 100 to 350 kg·m−2·s−1. Local, chordal and average void fractions were measured by the optical probe (OP), gamma-ray densitometry (GD), and differential pressure (DP) methods respectively. The effects of pressure and mass velocity on void fractions were investigated in detail. The results showed that a non-uniform distribution of local void fractions could be clearly revealed. The average void fractions obtained by GD and DP were found to approach the volumetric quality under higher pressure and higher mass velocity conditions owing to the homogeneous flow trends. This also occurred under a high volumetric quality condition for the homogeneous vapor flow and low volumetric quality condition for the homogeneous bubble flow. The results obtained from the different techniques were compared for the same experimental conditions. It was found that the void fractions measured by both OP and DP agreed well with that of GD, with relative deviations less than 10% and 15% respectively. Besides, an assessment of four void fraction correlations was carried out to predict the present area-average void fraction data from GD. The results showed that both the Bestion correlation and the Chexal and Lellouche correlation predict the present data well when measured void fraction greater than 0.3.

Analytical model for predicting oil fraction in horizontal oil–water two-phase flow

The oil fraction is one of the key parameters in the design of horizontal pipes and relevant equipment in the oil production and transportation process of the petrochemical industry. Several existing models and correlations were applied as the predictive method, but due to the empirical nature of the models and correlations and limited data used for the benchmarking process, the applicability of the existing models and correlations to all flow regimes and full oil fraction range has not been well-examined. In view of these issues, this study is aiming at developing a predictive model of oil fraction in horizontal oil–water two-phase flow applicable to all flow regimes as well as full oil fraction range. In the modeling process, the oil–water two-phase flow is geometrically modeled as the stratified flow with dispersed water-continuous oil flow in the upper part of the circular channel and dispersed oil-continuous water flow in the lower part of the circular channel. An analytical model for predicting oil fraction in horizontal oil–water two-phase flows has been derived based on the assumption of velocity heads of two phases being equal. The analytical model includes two entrainment factors, e1 and e2, and the values of e1 and e2 are determined to be 0.2 considering bi-lateral droplet entrainments to oil and water phases. The analytical model has been validated with existing experimental data taken in a variety of test conditions. The comparison results demonstrate that the predictive capability of the analytical model is reasonably good for most of the existing test database including all six distinct oil–water two-phase flow regimes with the mean absolute error (or bias), standard deviation (random error), mean relative deviation, and mean absolute relative deviation of 0.0116, 0.0422, 1.61%, and 8.50%, respectively. Additionally, it is confirmed that the applicability of the analytical model can be ex tended to the steam–water two-phase flow in horizontal channels.

Experimental investigations on single-phase convection and two-phase flow boiling heat transfer in an inclined rod bundle

Single-phase convection and steam-water two-phase flow boiling heat transfer experiments in an electrically heated 4 × 25 staggered inclined rod bundle were carried out for the following range: 15 kg m−2 s−1 ≤ G ≤ 50 kg m−2 s−1, 20.0 kW m−2 ≤ q ≤ 55.0 kW m−2, 0.05 ≤ xout ≤ 0.79 and 117 kPa ≤ Pin ≤ 260 kPa. Single-phase convective results show that the independence principle can be applied to the case that all tubes were heated in inclined rod bundles. With respect to two-phase results, the local flow boiling heat transfer coefficient increases from the bottom row to the eleventh row and then can be considered as a constant value from the eleventh row to the top row. An increasing heat flux results in a decrease of the flow boiling heat transfer coefficient. However, no significant effects of mass velocity and quality were observed. The inclination angle has a small effect on the flow boiling heat transfer coefficient at low heat fluxes. However, when heat flux is high, the flow boiling heat transfer coefficient in the inclined rod bundle is the minimum while that in the vertical rod bundle is the maximum compared with that in the horizontal rod bundle. In a general, a Chen-type correlation was developed to predict 98.5 percent of local flow boiling heat transfer coefficient data in the inclined rod bundle with a maximum deviation of ±20%.