Flow structure of subcooled boiling flow in an internally heated annulus

Local measurements of flow parameters were performed for vertical upward subcooled boiling flows in an internally heated annulus. The annulus channel consisted of an inner heater rod with a diameter of 19.1 mm and an outer round pipe with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. The double-sensor conductivity probe method was used for measuring local void fraction, interfacial area concentration, and interfacial velocity. A total of 11 data were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s and two inlet liquid temperatures, 95.0 and 98.0 °C. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter, namely, interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment.     

Experimental study on interfacial area transport in vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, and interfacial velocity of vertical upward bubbly flows in an annulus with the hydraulic equivalent diameter of 19.1 mm were measured by the double-sensor conductivity probe. A total of 20 data were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The obtained data will be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flow systems.     

Local flow measurements of vertical upward bubbly flow in an annulus

Local measurements of flow parameters were performed for vertical upward bubbly flows in an annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Double-sensor conductivity probe was used for measuring void fraction, interfacial area concentration, and interfacial velocity, and laser Doppler anemometer was utilized for measuring liquid velocity and turbulence intensity. A total of 20 data sets for void fraction, interfacial area concentration, and interfacial velocity were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. A total of eight data sets for liquid velocity and turbulence intensity were acquired consisting of two void fractions, about 0.050, and 0.10, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter namely interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment using the annulus.     

Modeling of bubble-layer thickness for formulation of one-dimensional interfacial area transport equation in subcooled boiling two-phase flow

In relation to the formulation of one-dimensional interfacial area transport equation in a subcooled boiling flow, the bubble-layer thickness model was introduced to avoid many covariances in cross-sectional averaged interfacial area transport equation in the subcooled boiling flow. The one-dimensional interfacial area transport equation in the subcooled boiling flow was formulated by partitioning a flow region into two regions; boiling two-phase (bubble layer) region and liquid single-phase region. The bubble-layer thickness model assuming the square void peak in the bubble-layer region was developed to predict the bubble-layer thickness of the subcooled boiling flow. The obtained model was evaluated by void fraction profile measured in an internally heated annulus. It was shown that the bubble-layer thickness model could be applied to predict the bubble-layer thickness as well as the void fraction profile. In addition, the constitutive equation for the distribution parameter of the boiling flow in the internally heated annulus, which was used for formulating the bubble-layer thickness model, was developed based on the measured data. The model developed in this study will eventually be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flows.     

Interfacial area transport equation: model development and benchmark experiments

The interfacial area transport equation dynamically models two-phase flow regime transitions and predicts continuous changes of the interfacial area concentration along the flow field. It replaces the flow regime-dependent correlations for the interfacial area concentration in thermal-hydraulic system analysis. In the present study, detailed formulation of the interfacial area transport equation is presented along with its evaluation results based on the detailed benchmark experiments. In view of model evaluation, the equation is simplified into one-dimensional steady state one-group interfacial area transport equation. The prediction made by model agrees well with the experimental data obtained in round pipes of various diameters. The framework for the two-group transport equation and the necessary constitutive relations are also presented in view of bubble transport of various sizes and shapes.     

Modeling of the condensation sink term in an interfacial area transport equation

A model for the condensation sink term in an interfacial area transport equation (IATE) was developed. In the model, a bubble nucleation due to a wall surface boiling and a bubble collapse due to a condensation were assumed to be symmetric phenomena. Based on this consideration the condensing region for a subcooled condition can be divided into two regions: the heat transfer-controlled region and the inertia-controlled region. In the heat transfer-controlled region, the condensation Nusselt number approach is appropriate. On the other hand, in the inertia-controlled region, the resultant mechanical force may be balanced through an interface between a bubble and an ambient liquid. The modeled condensation sink term in an IATE in this study was evaluated against existing data which had been obtained from a bubble condensation in a subcooled water flow through a non-heated annulus. The evaluation result showed that the present model could predict the axial distribution of the interfacial area concentration accurately.     

PREDICTION AND MEASUREMENT OF LOCAL TWO-PHASE FLOW PARAMETERS IN A BOILING FLOW CHANNEL

A two-fluid model to predict subcooled boiling flow at low pressure is presented. Although considerable success has been achieved in good axial predictions, this study focuses on the capability of the model to predict local two-phase flow parameters within an annulus channel. Comparison of model predictions is made against local measurements carried out by our Korean collaborators. Although reasonable agreement of local profiles of the void fraction, interfacial area concentration, and bubble frequency were achieved, significant weakness of the model was evidenced in the prediction of the mean Sauter diameter, liquid, and vapor velocities. The formulation of a transport equation to account for the dynamically changing interfacial area concentration is proposed. Further modeling work is in progress to incorporate the bubble coalescence behaviour seen during experiments into the transport equation.     

Volumetric interfacial area prediction in upward bubbly two-phase flow

In two-phase flow studies, a volumetric interfacial area balance equation is often used in addition to the multidimensional two-fluid model to describe the geometrical structure of the two-phase flow. In the particular case of bubbly flows, numerous works have been done by different authors on the subject. Our work concerns two main modifications of this balance equation: (1) new time scales are proposed for turbulence induced coalescence and breakup, (2) modeling of the nucleation of new bubbles on the volumetric interfacial area. The 3D module of the CATHARE code is used to evaluate our new model, in comparison to three other models for interfacial area found in the literature, on two different experiments. First, we use the DEBORA experimental data base for the comparison in the case of boiling bubbly flow. The comparison of the different volumetric interfacial area models to the DEBORA experimental data shows that even though the theoretical values of the coefficients are adopted in our modified model, this model has a quite good capability to predict the local two-phase geometrical parameters in the boiling flow conditions. Secondly, we compare the predictions obtained with the same models to the DEDALE experimental data base, for the case of adiabatic bubbly flow. In comparison to the other models tested, our model also gives quite good predictions of the bubble diameter in the case of adiabatic conditions.     

An experimental study on local interfacial area concentration using a double-sensor probe

Interfacial area concentration is an important parameter in modeling the interfacial transfer terms in the two-fluid model. In this paper, the interfacial area concentration, void fraction, and bubble Sauter mean diameter for air-water bubbly flow through a vertical transparent pipe with 40 mm internal diameter was investigated experimentally using both digital high-speed camera system and a double-sensor conductivity probe. Based on the experimental data of digital high-speed camera system, the statistical models derived by different researchers for local interfacial area concentration measurement using double-sensor conductivity probe were evaluated. The results show that there are obvious differences among the values of local interfacial area concentration calculated by different statistical models even from the same probe signals. The section-averaged values of the local interfacial area concentration calculated using the statistical model by Kataoka et al. agree best with experimental data of digital high-speed camera system. Therefore, the statistical model developed by Kataoka et al. is recommended for the local measurement of interfacial area concentration using a double-sensor conductivity probe in bubbly two-phase flow. Using the verified double-sensor probe method, we carry out experiment to study the local distribution characteristic of the interfacial area concentration and void fraction in air-water bubbly flow through a vertical pipe.     

Axial developments of interfacial area and void concentration profiles in subcooled boiling flow of water

Axial developments of the local void fraction, interfacial area concentration and bubble Sauter mean diameter were measured in subcooled boiling flow of water in a vertical internally heated annulus using the double-sensor conductivity probe technique. Measurements were performed under varying conditions of heat flux, inlet liquid velocity and inlet liquid temperature. A total of 10 data sets were acquired. Based on these measurements with the previous data obtained in the present test loop, the influence of flow condition on the profiles of local two-phase flow parameters was discussed. The measured average void fraction and interfacial area concentration were compared with the predictions by existing correlations for drift-flux parameters and interfacial area concentration. Also, the recently proposed bubble layer thickness model in subcooled boiling was evaluated for the measurement data.     

静止液体中浸没垂直导管口气泡形成实验

利用高速摄像技术研究气流通过浸没垂直导管口在液体中形成气泡的机理及其行为规律,分析导管内径、气体流量、导管口浸没深度和导管外径对气泡脱离直径的影响。结果表明:在导管内径分别为7、10和14 mm,气体流量在0~450 mL/s的条件下,气泡脱离直径随导管内径和气体流量的增加而增大;在浸没深度为0.05~1 m的条件下,导管口浸没深度对气泡脱离直径的影响很小可以忽略;当气体流量在100 mL/s以上,导管内径为10 mm、导管外径为14~26 mm时,随着导管外径的增加,气泡脱离直径减小。     

Mechanistic study for the interfacial area transport phenomena in an air/water flow condition by using fine-size bubble group model

A set of number density transport equations based on the bubble size are used to predict the void fraction and the interfacial area concentration in an air/water flow conditions. As the closure relations for the number density transport equations, a coalescence due to random collisions and a breakup due to an impact of the turbulent eddies are modified based on previous studies. The bubble expansion term due to a pressure reduction and a coalescence due to a wake entrainment are modeled for the number density transport equation. In order to predict the local experimental data, a computational fluid dynamic (CFD) code coupling the two-fluid model and number density transport equations are developed in this study. As for the results of the numerical analysis, the developed model predicts well the void fraction and interfacial area concentration although some deviations between the prediction and the experiment are shown for the high void fraction conditions.     

Development of a Multi-Dimensional Fluid Dynamics Code and Its Benchmarking for the Subcooled Boiling Flow

In a two-phase flow analysis, the interfacial area concentration (IAC) is a dominant factor governing the interfacial transfer of the momentum or energy. For a dynamic analysis with the implementation of IAC transport equation, a multi-dimensional computational fluid dynamics code was developed. The code is based on the two-fluid model and the simplified marker and cell algorithm by using the finite volume method, where the conventional approach for a single-phase flow has been modified in order to consider the term for a phase change. As benchmark problems of a single-phase flow and two-phase flow, a natural convection in a rectangular cavity and a subcooled boiling in an annulus channel were selected, respectively. In the calculation for the single-phase flow, the developed code predicted a reasonable behavior for a buoyancy-driven flow depending on the Rayleigh number. In the analysis of the subcooled boiling, the calculation results showed the robustness of code for the analysis of the boiling phenomena and void propagation, where they represented limitations of the one-dimensional IAC model. To conduct a multi-dimensional analysis for the two-phase flow, it is confirmed that the implementation of an IAC transport equation into the code is essential.     

Pool boiling heat transfer on the tube surface in an inclined annulus

An experimental study was carried out to investigate the pool boiling heat transfer in an inclined annular tube submerged in a pool of saturated water at atmospheric pressure. The outer diameter and the length of the heated inner tube were 25.4 mm and 500 mm, respectively. The gap size of the annulus was 15 mm. For the tests, annuli with both open and closed bottoms were considered. The inclination angle was varied from the horizontal position to the vertical position. At a given heat flux, the heat transfer coefficient was increased with the inclination angle increase. Effects of the inclination angle on heat transfer were more clearly observed in the annulus with open bottoms. The main cause for the tendencies was considered as the difference in the intensity of liquid agitation and bubble coalescence due to the enclosure by the outer tube. One of the important factors in the annulus with open bottom was the convective fluid flow.     

Effects of pool subcooling on boiling heat transfer in a vertical annulus with closed bottom

Effects of inlet subcooling on pool boiling heat transfer in a vertical annulus with closed bottom have been studied experimentally. For the test, a tube of 19.1 mm diameter and the water at atmospheric pressure have been used. Up to 50 K of pool subcooling has been tested and results of the annulus are compared with the data of a single unrestricted tube. The increase in pool subcooling results in much change in heat transfer coefficients. As the heat flux increases and the subcooling decreases, a deterioration of heat transfer coefficients is observed. The governing mechanisms are suggested as single-phase heat transfer and liquid agitation for the single tube while liquid agitation and bubble coalescence are the major factors at the bottom closed annulus.     

Effects of outer tube length on saturated pool boiling heat transfer in a vertical annulus with closed bottoms

To improve pool boiling heat transfer in an annulus with closed bottoms, the length of an outer tube has been changed between 0.2 m and 0.6 m. For the test, a heated tube of 19.1 mm diameter and water at atmospheric pressure has been used. To elucidate effects of the outer tube length on heat transfer results of the annulus are compared with the data of a single unrestricted tube. The change in the outer tube length results in much variation in heat transfer coefficients. As the outer tube length is 0.2 m the deterioration point of heat transfer coefficients gets moved up to the higher heat fluxes because of the decrease in the intensity of bubble coalescence.     

The flow characteristics of an upward gas‐liquid two‐phase flow in a vertical tube with a wire coil: Part 1. Experimental results of flow pattern,void fraction,and pressure drop

Experiments were carried out to investigate the flow pattern, average void fraction, and pressure drop of an upward air‐water two‐phase flow in vertical tubes of 25‐mm inside diameter with wire coils of varying wire diameter, pitch, and number of coils in cross section. Five kinds of flow patterns—bubble, slug, churn, semiannular, and annular flow—were defined based on the observation of flow behavior in the experiments. At higher water flowrates, the bubble‐to‐slug transition occurred at lower air flowrates in tubes with wire coils than in smooth tubes. The average void fraction was found by using the drift flux model. Further, the experimental results of the friction pressure drop were compared with the Lockhart‐Martinelli correlation. As a result, a correlation with the constant C in Chisholm's equation was obtained as a function of the wire coil pitch‐to‐diameter ratio. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(8): 639–651, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10066     

Size effect on two‐phase regime for condensation in micro/mini tubes

Analysis was conducted to predict the influence of tube size on two‐phase flow regimes for flow condensing in mini/micro tubes. According to the importance of the interfacial tension compared to the interfacial stress, the regimes were classified into three kinds: axial symmetrical, semisymmetrical, and asymmetrical. The results indicated that the surface tension of the fluid media obviously affects the flow regimes; for tubes with an inner diameter less than 100 to 600 mm, the flow regimes would be axially symmetrical depending on the media. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 65–71, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10076     

Drift-flux model for downward two-phase flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for downward two-phase flows. The constitutive equation that specifies the distribution parameter in the downward flow has been derived by taking into account the effect of the downward mixture volumetric flux on the phase distribution. It was assumed that the constitutive equation for the drift velocity developed by Ishii for a vertical upward churn-turbulent flow determined the drift velocity for the downward flow over all of flow regimes. To evaluate the drift-flux model with newly developed constitutive equations, area-averaged void fraction measurement has been extensively performed by employing an impedance void meter for an adiabatic vertical co-current downward air-water two-phase flow in 25.4-mm and 50.8-mm inner diameter round tubes. The newly developed drift-flux model has been validated by 462 data sets obtained in the present study and literatures under various experimental conditions. These data sets cover extensive experimental conditions such as flow system (air-water and steam-water), channel diameter (16-102.3 mm), pressure (0.1-1.5 MPa), and mixture volumetric flux (−0.45 to −24.6 m/s). An excellent agreement has been obtained between the newly developed drift-flux model and the data within an average relative deviation of ±15.4%.