Droplet entrainment correlation in vertical upward co-current annular two-phase flow

Upward annular two-phase flow in a vertical tube is characterized by the presence of liquid film on the tube wall and entrained droplet laden gas phase flowing through the tube core. Entrainment fraction in annular flow is defined as a fraction of the total liquid flow flowing in the form of droplets through the central gas core. Its prediction is important for the estimation of pressure drop and dryout in annular flow. In the following study, measurements of entrainment fraction have been obtained in vertical upward co-current air–water annular flow covering wide ranges of pressure and flow conditions. Comparison of the experimental data with the existing entrainment fraction prediction correlations revealed their inadequacies in simulating the trends observed under high flow and high pressure conditions. Furthermore, several correlations available in the literature are implicit and require iterative calculations.Analysis of the experimental data showed that the non-dimensional numbers, Weber number (We = ρ_gj_g²D/σ(Δρ/ρ_g)^1/4) and liquid phase Reynolds number (Re_f = ρ_fj_fD/μ_f), successfully collapse the data. In view of this, simple, explicit correlation was developed based on these non-dimensional numbers for the prediction of entrainment fraction. The new correlation successfully predicted the trends under the high flow and high pressure conditions observed in the current experimental data and the data available in open literature. However, in order to use the proposed correlation it is necessary to predict the maximum possible entrainment fraction (or limiting entrainment fraction). In the current analysis, an experimental data based correlation was used for this purpose. However, a better model or correlation is necessary for the maximum possible entrainment fraction. A theoretical discussion on the mechanism and modeling of the maximum possible entrainment fraction condition is presented.     

垂直加热通道内超临界水流动稳定性参数敏感性分析

给出了无量纲分析法与频域法相结合的稳定性分析方法的详细描述,并定义了影响稳定性的关键无量纲数。针对垂直加热通道内超临界水进行了密度波稳定性分析,并建立了稳定性边界。对系统入口阻力因数、出口阻力因数、摩擦因数、进出口压降和流动方向等进行了参数敏感性分析,结果表明高的入口阻力因数有利于系统的稳定,但高的出口阻力因数和高的摩擦因数不利于系统的稳定,系统进出口压差对系统的稳定性影响较小,向上流动比向下流动更有利于系统的稳定。计算结果对超临界水堆的堆芯和系统设计具有指导性作用。     

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.     

Numerical simulation of single bubble condensation in subcooled flow using OpenFOAM

The single condensing bubble behavior in subcooled flow has been numerical investigated using the open source code OpenFOAM. A coupled Level Set (LS) and Volume of Fluid (VOF) method (CLSVOF) model with a phase change model for condensation was developed and implemented in the code. The simulated results were firstly compared with the experimental results, they were in great agreements, and thus the simulation model was validated. The validated numerical model was then used to analyze the condensing bubble deformation, bubble lifetime, bubble size history, condensate Nusselt number and other interesting parameters with different variables in subcooled flow. The numerical results indicated that the initial bubble size, subcooling of liquid and system pressure play an important role to influence the condensing bubble behaviors significantly and bubble will be pierced when the subcooling and initial diameter reach a certain value at the later condensing stage. The bubble diameter history and condensate Nusselt number were found in good agreement with the empirical correlation. The drag force coefficient was predicted well by introducing a reduced drag coefficient.     

Prediction of critical heat flux in vertical pipe flow

A previously developed semi-empirical model for adiabatic two-phase annular flow is extended to predict the critical heat flux (CHF) in a vertical pipe. The model exhibits a sharply declining curve of CHF versus steam quality (X) at low X, and is relatively independent of the heat flux distribution. In this region, vaporization of the liquid film controls. At high X, net deposition upon the liquid film becomes important and CHF versus X flattens considerably. In this zone, CHF is dependent upon the heat flux distribution. Model predictions are compared to test data and an empirical correlation. The agreement is generally good if one employs previously reported mass transfer coefficients.     

Annular flow entrainment rate experiment in a small vertical pipe

Two-fluid model predictions of film dryout in annular flow, leading to nuclear reactor fuel failure, are limited by the uncertainties in the constitutive relations for the entrainment rate of droplets from the liquid film. The main cause of these uncertainties is the lack of separate-effects experimental data in the range of the operating conditions in nuclear power reactors. An air–water experiment has been performed to measure the entrainment rate in a small pipe. The current data extend the available database in the literature to higher gas and liquid flows and also to higher pressures. The measurements were made with the film extraction technique. A mechanistic model was obtained based on Kelvin–Helmholtz' instability theory. The dimensionless model includes the Weber number of the gas and the liquid film Reynolds number. Kataoka and Ishii's correlation (Kataoka, I., Ishii, M., 1982. NUREG/CR-2885, ANL-82-44) is modified based on this model and the new data. The new correlation collapses the present air–water data and Cousins and Hewitt's data (Cousins, L.B., Hewitt, G.F., 1968. UKAEA Report AERE-R5657) The effects of pressure and surface tension were considered in the derivation so it may be applied for boiling water reactor operating conditions.     

Two phase flow 1D turbulence model for poly-disperse upward flow in a vertical pipe

A 1D test-solver was developed in recent years for modeling of two phase bubbly flows in pipe geometry. The solver considers a number of bubble classes and calculates bubble-size resolved void fraction profiles in the radial direction. A successful implementation was achieved regarding bubble forces models (non-drag forces). Discrepancies appeared when coalescence and breakup rates were significant. These rates depend upon local turbulence quantities, which are possible reason for discrepancies. Originally the test-solver is equipped by Sato model (Sato, Y., Sadatomi, M., Sekoguchi, K., 1981. Momentum and heat transfer in two-phase bubble flow. I. International Journal Multiphase Flow 7, 167–177 .) which accounts for turbulence via shear- and bubble-induced viscosities calculated out of empirical correlations. One equation for the turbulent kinetic energy was solved, while the dissipation rate was calculated out of a correlation. In order to improve calculation of the local turbulence parameters, a two-phase k– turbulence model was adopted instead. The account for the bubble-induced turbulence was made via a source term taken out of literature. Comparisons between new and old turbulence modeling against experimental data showed better agreement for the new model. The experiments covered a wide range of water and air superficial velocities for upward bubbly flow in two pipe's diameters: 50 and 200 mm. The main feature of the new model is providing more reliable values of turbulence parameters for application in coalescence and breakup models. A comparison with CFX 5.7 calculations in a 50 mm pipe showed better calculation results when the source term was considered in the k– equations. An implementation into CFX is planned.     

Gas–liquid flow around an obstacle in a vertical pipe

This paper presents a novel technique to study the two-phase flow field around an asymmetric obstruction in a vertical pipe with a nominal diameter of DN200. Main feature of the experiments is the shifting of a half-moon shaped diaphragm causing the obstruction along the axis of the pipe. In this way, the 3D void field is scanned with a stationary wire-mesh sensor that supplies data with a spatial resolution of 3 mm over the cross-section and a measuring frequency of 2.5 kHz. Besides the measurement of time-averaged void fraction fields and bubble-size distributions, novel data evaluation methods were developed to extract estimated liquid velocity profiles as well as lateral components of bubble velocities from the wire-mesh sensor data. The combination of void fraction fields and velocity profiles offer the opportunity to analyse a two-phase flow in a geometry that owns a series of features characteristic for complex components of power and chemical plant equipment. Such characteristics are sharp edges with flow separation, recirculation areas, jet formation, stagnation points and curved stream-lines.

The tests were performed with an air–water flow at nearly ambient conditions and with a saturated steam–water mixture at 6.5 MPa. The superficial velocities of liquid and gas or, respectively, vapour were varied in a wide range.

The flow structure upstream and downstream of the obstacle is characterized in detail. Bubble size dependent effects of bubble accumulation and migration are discussed on basis of void-fraction profiles decomposed into bubble-size classes. A pronounced influence of the fluid parameters was found in the behaviour of bubbles at the boundary of the jet coming from the non-obstructed part of the cross-section. In case of an air–water flow, bubbles are restrained from entering the jet, a phenomenon which was not observed in high-pressure steam–water flow. A detailed uncertainty analyse of the velocity assessments finishes the presented paper. A blind pre-test calculation with CFX-10 based on the assumption of a mono-disperse bubbly flow has reproduced the overall void and velocity profiles. The results are used for the assessment of the influence of local accelerations on the liquid velocity measurement.     

竖直矩形窄流道内过冷沸腾汽泡生长特性及对换热的影响

在一个大气压下以水为工质研究了竖直矩形窄流道内过冷沸腾的汽泡生长特性。采用Laplace数(La)和时间因子(ξ)无量纲化汽泡半径和汽泡生长时间,得到了不同工况下的无量纲汽泡生长曲线。通过分析质量流速和热流密度变化对无量纲汽泡生长的影响,发现增加质量流速会抑制汽泡生长;增加热流密度则会促进汽泡生长。汽泡的生长行为会严重影响核态沸腾换热系数hNB,从而影响总沸腾两相流动换热系数htp。采用与雷诺数(Re)相关的无量纲时间(t*)的1/3次方模型来预测无量纲汽泡生长,发现此模型能较好地预测本研究中所得到的无量纲汽泡生长数据。     

Numerical simulation of bubble condensation using CF-VOF

In present study, subcooled boiling is simulated using color function volume of fluid (CF-VOF) method. For this purpose, energy equation and Tanasawa mass transfer model accompanied with some suitable source terms are implemented in OpenFOAM solver (interFoam). The surface tension between vapor–liquid phases is considered using continuous surface force (CSF) method. In order to reduce spurious current near interface, a smoothing filter is applied to improve curvature calculation. The variation of saturation temperature in vapor bubble with local pressure is considered with Clausius–Clapeyron relation. The numerical model is validated with one-dimensional Stefan problem.The shape and life time history of single vapor bubble condensation are verified with existing experimental data. Computational study shows bubble life time is nearly proportional with bubble size and it is prolonged at bubble swarm motion. The present study reveals some fundamental characteristics of single and multiple vapor bubble condensation and is expected to be instructive for further applications.     

Free convective condensation in a vertical enclosure

Free convective condensation in a vertical enclosure was studied numerically and the results were compared with experiments. In both the numerical and experimental investigations, mist formation was observed to occur near the cooling wall, with significant droplet concentrations in the bulk. Large recirculation cells near the end of the condensing section were generated as the heavy noncondensing gas collecting near the cooling wall was accelerated downward. Near the top of the enclosure the recirculation cells became weaker and smaller than those below, ultimately disappearing near the top of the condenser. In the experiment the mist density was seen to be highest near the wall and at the bottom of the condensing section, whereas the numerical model predicted a much more uniform distribution. The model used to describe the formation of mist was based on a modified critical saturation model (MCSM), which allows mist to be generated once the vapor pressure exceeds a critical value. Equilibrium, nonequilibrium, and MCSM calculations were performed, showing the experimental results to lie somewhere in between the equilibrium and nonequilibrium predictions of the numerical model. A single adjustable constant (indicating the degree to which equilibrium is achieved) is used in the model in order to match the experimental results.     

Extension of the inhomogeneous MUSIG model for bubble condensation

Bubble condensation plays an important role, e.g. in sub-cooled boiling or steam injection into pools. Since the condensation rate is proportional to the interfacial area density, bubble size distributions have to be considered in an adequate modeling of the condensation process. The effect of bubble sizes was clearly shown in experimental investigations done previously at the TOPFLOW facility of FZD. Steam bubbles were injected into a sub-cooled upward pipe flow via orifices in the pipe wall located at different distances from measuring plane. 1 mm and 4 mm injection orifices were used to vary the initial bubble size distribution. Measurements were done using a wire-mesh sensor. Condensation is clearly faster in case of the injection via the smaller orifices, i.e. in case of smaller bubble sizes. Recently the Inhomogeneous MUSIG model was implemented into the CFD code CFX from ANSYS enabling the simulation of poly-dispersed flows including the effects of separation of small and large bubbles due to bubble size dependent lift force inversion. It allows to divide the dispersed phase into size classes regarding the mass as well as regarding the momentum balance. Up to now transfers between the classes in the mass balance can be considered only by bubble coalescence and breakup (population balance). Here an extension of the model is proposed to include the effects due to phase transfer. The paper focuses on the derivation of equations for the extension of the Inhomogeneous MUSIG model and presents some first results for verification and validation.     

Transition flow boiling heat transfer to water in a vertical annulus

Transition boiling heat transfer coefficients for water at 25–30 psia flowing upward at low velocities have been obtained Hot mercury, flowing on the inside of a tube with a 0.54 in. o.d. served as the heat source. Water flowed in the annular space between the heat source and an outer glass tube having a 1 in. dia. Thermocouples placed at several elevations within the mercury stream allowed the rate of heat transfer to be determined. The heat transfer coefficients appear consistent with other transition boiling data providing an appropriate allowance is made for the reduction in critical heat flux at high void fractions.     

Evolution of the structure of a gas–liquid two-phase flow in a large vertical pipe

The evolution of the structure of a gas–liquid flow in a large vertical pipe of 195 mm inner diameter was investigated at the TOPFLOW test facility in Rossendorf. Wire-mesh sensors were used to measure sequences of two-dimensional distributions of local instantaneous gas fraction within the complete pipe cross-section. The sensors own a resolution of 3 mm at a frequency of 2500 Hz. Superficial velocities were varied in a range covering flow regimes from bubbly to churn-turbulent flow. The distance between the gas injection and the sensor position was changed using a so-called variable gas injection system. It consists of six gas injection units, each equipped with three rings of injection orifices in the pipe wall (orifice diameter: 1 and 4 mm), which are fed from ring chambers. The gas flow towards these distributor chambers is individually controlled by valves. Measured bubble-size resolved radial gas fraction profiles reveal differences in the lateral migration of bubbles of different size starting from the injection at the wall. The evolution of bubble-size distributions allows to study bubble coalescence and break-up. The influence of the physical properties of the fluid was studied by comparing cold air–water experiments with steam–water tests at 65 bar.     

A 2D numerical simulation of sub-cooled flow boiling at low-pressure and low-flow rates

The main purpose of this study is to apply a two-fluid mathematical model to numerical simulation of two-phase flow at low-pressure condition. Although models of sub-cooled boiling flow at one-dimension and high-pressure have been studied extensively, there are few equivalent studies for numerical simulation at two-dimension and low-pressure (1-2 bar) conditions. Recent literature studies on sub-cooled boiling flow at low-pressure have shown that empirical models developed for high-pressure situations are not valid at low-pressures. Since the mathematical model used in this study is accomplished at low-pressure, the transport equations for the variables of each phase are substituted in low-pressure. The governing equations of two-phase flow with an allowance to inter-phase transfer of mass, momentum and heat, are solved using a two-fluid; non-equilibrium model. The finite volume discretization scheme is used to create a linearized system of equations that are solved by SIMPLE staggered grid solution technique for a rectangular channel. Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow boiling conditions was achieved. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection. Good agreement is achieved with the predicted results against the experimental data’s available in the literatures for a number of test cases.     

Numerical analysis of thermal-hydraulic behavior of supercritical water in vertical upward/downward flow channels

Investigations on the thermal-hydraulic behavior in the SCWR fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding of the heat transfer behavior of supercritical fluids. In this paper, the numerical analysis is carried out to study the thermal-hydraulic behaviour in vertical sub-channels cooled by supercritical water. Remarkable differences in characteristics of secondary flow are found, especially in square lattice, between the upward flow and downward flow. The turbulence mixing across sub-channel gap for downward flow is much stronger than that for upward flow in wide lattice when the bulk temperature is lower than pseudo-critical point temperature. For downward flow, heat transfer deterioration phenomenon is suppressed with respect to the case of upward flow at the same conditions.     

Probability of pipe breakage regarding transient flow in a small pipe network

A reliability model was developed for the calculations of the probability of pipe breakage associated with transient effect. The statistical distribution for the maximum pressure wave heights was determined from the results of 168 transient analyses. It was found that the statistical distribution for internal pressure among the random variables of reliability function is well matched with the Gumbel distribution. The probability of pipe breakage in a small pipe network was calculated according to pipe diameter, thickness, allowable stress, and internal pressure. From the results, it was found that transient effect significantly increases the probability of pipe breakage. Using the present reliability model, it could be possible to find a pipe that contains the high probability of pipe breakage in a water distribution system. If the reliability model developed in the present study is applied for the design, a safe design will be accomplished. Furthermore, it can be effectively used for the management and maintenance of a water distribution system.     

Diffusion layer modeling for condensation in vertical tubes with noncondensable gases

Noncondensable gases significantly modify the mechanism of condensation for cocurrent downward flow in vertical tubes. Two-dimensional experimental measurements presented here show similarity between gas concentration distributions and the temperature distributions encountered in laminar and turbulent heat transfer. Thus the analogy between heat and mass transfer, coupled with a reasonable condensate film model, can provide predictions of the local condensation rate. This work presents a simple 9-step iterative calculation procedure for calculating the local heat flux. The empirical model, based on a modified Dittus-Boelter formulation and utilizing an effective condensation thermal conductivity, converges with 2 to 10 iterations at each axial location. Experimental results from several investigators are compared with the predictions of the model, with good agreement.