Vertical Annular Two-phase Flow Research Articles

Interfacial Friction Prediction in a Vertical Annular Two-Phase Flow Based on Support Vector Regression Machine

Accurate prediction of interfacial friction factor is critical for calculation of pressure drop and investigation of flow mechanism of vertical annular two-phase flows. Theoretical models of interfacial friction factor based on physical insight have been developed; however, these are inconvenient in engineering practice as too many parameters need to be measured. Although many researchers have proposed various empirical correlations to improve computation efficiency, there is no generally accepted simple formula. In this study, an efficient prediction model based on support vector regression machine (SVR) is proposed. Through sensitivity analysis, five factors are determined as the input parameters to train the SVR model, relative liquid film thickness, liquid Reynolds number, gas Reynolds number, liquid Froude number and gas Froude number. The interfacial friction factor is chosen as the output parameter to check the overall performance of the model. With the help of particle swarm algorithm, the optimization process is accelerated considerably, and the optimal model is obtained through iterations. Compared with other correlations, the optimal model shows the lowest average absolute error (AAE of 0.0004), lowest maximum absolute error (MAE of 0.006), lowest root mean square error (RMSE of 0.00076) and highest correlation factor (r of 0.995). The analysis using various data in the literature demonstrates its accuracy and stability in interfacial friction prediction. In summary, the proposed machine learning model is effective and can be applied to a wider range of conditions for vertical annular two-phase flows.

Electrical Capacitance Probe Characterization in Vertical Annular Two-Phase Flow

The paper presents the experimental analysis and the characterization of an electrical capacitance probe (ECP) that has been developed at the SIET Italian Company, for the measurement of two-phase flow parameters during the experimental simulation of nuclear accidents, as LOCA. The ECP is used to investigate a vertical air/water flow, characterized by void fraction higher than 95%, with mass flow rates ranging from 0.094 to 0.15 kg/s for air and from 0.002 to 0.021 kg/s for water, corresponding to an annular flow pattern. From the ECP signals, the electrode shape functions (i.e., the signals as a function of electrode distances) in single- and two-phase flows are obtained. The dependence of the signal on the void fraction is derived and the liquid film thickness and the phase’s velocity are evaluated by means of rather simple models. The experimental analysis allows one to characterize the ECP, showing the advantages and the drawbacks of this technique for the two-phase flow characterization at high void fraction.

ICONE19-43772 DROPLET DEPOSITION RATE IN VERTICAL ANNULAR TWO-PHASE FLOW

Droplet entrainment and deposition phenomena plays important role in dynamics of annular two-phase flow. Modeling of these phenomena is essential for the estimation of dryout margins in light water reactors and boilers. In this study, the droplet entrainment and deposition rates are measured in adiabatic vertical annular two-phase flow. Two types of experiments are performed: air-water and organic fluid (Freon-113) experiments. Liquid film extraction technique is used for the measurement of entrainment fraction (i.e., amount of entrained droplets), droplet entrainment rate, and deposition rate. Additionally, in air-water experiments, liquid film thickness is measured using ring type conductance probes. This paper presents analysis of the deposition rate data. Several mechanistic and empirical correlations are available for prediction of droplet deposition rate; however, due to lack of complete understanding of the deposition phenomenon, the mechanistic correlations are still not as accurate as the empirical correlation. Assessment of the most recently published empirical deposition rate correlation (Okawa, et al., 2005) using the experimental data obtained in this study and the data available in literature shows that the correlation could not predict the data correspond to high gas velocity conditions and in a transition region between the low and high droplet concentrations. The experimental data indicates that the deposition rate approaches a maximum limiting value at high gas velocity; however, the correlation predicted continuously increasing or decreasing deposition rates. Detailed understanding of the deposition mechanism under high gas velocity is developed based on the study of droplet dynamics.

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible. Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.

Properties of disturbance waves in vertical annular two-phase flow

Disturbance waves play an important role in interfacial transfer of mass, momentum and energy in annular two-phase flow. In spite of their importance, majority of the experimental data available in literature on disturbance wave properties such as velocity, frequency, wavelength and amplitude are limited to near atmospheric conditions (Azzopardi, B.J., 1997. Drops in annular two-phase flow. International Journal of Multiphase Flow, 23, 1–53). In view of this, air–water annular flow experiments have been conducted at three pressure conditions (1.2, 4.0 and 5.8 bar) in a tubular test section having an inside diameter 9.4 mm. At each pressure condition liquid and gas phase flow rates are varied over a large range so that the effects of density ratio, liquid flow rate and gas flow rate on disturbance wave properties can be studied systematically. A liquid film thickness is measured by two flush mounted ring shaped conductance probes located 38.1 mm apart. Disturbance wave velocity, frequency, amplitude and wavelength are estimated from the liquid film thickness measurements by following the statistical analysis methods. Parametric trends in variations of disturbance wave properties are analyzed using the non-dimensional numbers; liquid phase Reynolds number ( Re f), gas phase Reynolds number ( Re g), Weber number ( We) and Strouhal number ( Sr). Finally, the existing correlations available for the prediction of disturbance wave velocity and frequency are analyzed and a new, improved correlation is proposed for the prediction of disturbance wave frequency. The new correlation satisfactorily predicted the current data and the data available in literature.

The numerical calculation of heat transfer performance for annular flow of liquid nitrogen in a vertical annular channel

According to a separated phase flow model for vertical annular two-phase flow in an annular channel, the liquid film thickness, distributions of velocities and temperatures in the liquid layer are predicted in the range of heat fluxes: 6000–12000 W/m 2, mass flux: 500–1100 kg/m 2 s . The pressure drop along the flow channel and heat transfer coefficient are also calculated. The liquid film thickness is in the order of micrometers and heat transfer coefficient is 2800–7800 W/m 2 K of liquid nitrogen boiling in narrow annular channels. The measured heat transfer coefficient is 29% higher than the calculated values. With the mass flux increasing and the gap of the annular channel decreasing, pressure drop and heat transfer coefficient increase.

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

Abstract A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.

Characteristics of vertical annular two-phase flow with local liquid fall-back

Characteristics of vertical annular two-phase flow with local liquid fall-back

Characteristics of Vertical Annular Two-Phase Flow with Local Liquid Fall-Back.

A new analytical method for two-phase flow is proposed, in which the most easily occurring and, thus, most stable two-phase flow situation is assumed to be realized. Flow structure is considered to be self-controlled so as to realize the most stable two-phase flow situation. In the present study, the flow situation with smaller pressure energy consumption rate for unit mass of penetrating two-phase fluid through each channel cross section is assumed to be more stable. In addition, two-dimensional turbulent flow analysis is applied to the annular flow regime in which partical or total downflow of the liquid film is allowed. Experimental analysis based on the data from an air-water two-phase flow experiment, which was performed at atmospheric pressure and room temperature, indicated the applicability of the proposed analytical method.

Detailed Measurements of Vertical Annular Two-Phase Flow—Part I: Drop Velocities and Sizes

Phase anemometry and laser diffraction techniques have been employed to measure drop sizes in annular two-phase flow. The former technique also provides drop velocities. When converted to the same basis, the drop size distributions from the two techniques are in agreement. Drop velocities were 20 percent below the corresponding local velocities for the gas. Standard deviations of the drop velocities were 10 to 65 percent higher than those for the gas.

Detailed Measurements of Vertical Annular Two-Phase Flow—Part II: Gas Core Turbulence

Laser anemometry techniques have been employed to measure gas velocities in annular two-phase flow. Mean velocities and Reynold’s stresses in the gas appear to be similar to those in corresponding rough pipes. However, turbulence intensities are higher than the values corresponding to flow over a wall with a roughness equivalent to the film interface.

Disturbance wave frequencies, velocities and spacing in vertical annular two-phase flow

A systematic study of disturbance wave properties in annular flow is reported. Frequencies and velocities were deduced from correlational analysis of film thickness records. The data is shown to agree with the more reliable earlier studies, though these were not so extensive. The spacing between waves has also been deduced. The effects of flow rates on this parameter are explained and its relationship to wave height is examined.

Wave coalescence and entrainment in vertical annular two-phase flow

A rigorous model for wave coalescence has been derived. The wave coalescence process has also been modelled by a Monte-Carlo technique. The results of the theories are in general in good agreement with the available experimental data. It had been noted that coalescence of two waves was accompanied by a large burst of entrainment. The above coalescence theory has been used to calculate that component of entrainment that is due to coalescence. Comparison of this and experimental data shows that the entrainment due to coalescence can be a significant portion of the total entrainment.

Discussion: “The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow” (Wallis, G. B., and Makkenchery, S., 1974, ASME J. Fluids Eng., 96, pp. 297–298)

Discussion: “The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow” (Wallis, G. B., and Makkenchery, S., 1974, ASME J. Fluids Eng., 96, pp. 297–298)

Closure to “Discussion of ‘The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow’” (1975, ASME J. Fluids Eng., 97, pp. 130–131)

Closure to “Discussion of ‘The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow’” (1975, ASME J. Fluids Eng., 97, pp. 130–131)

The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow

The Hanging Film Phenomenon in Vertical Annular Two-Phase Flow

Transient flow redistribution in annular two-phase flow

A model is described for the prediction of transient flow redistribution in vertical annular two-phase flow. The model is based on an analysis of the local parameters controlling the flow and takes account of the diffusive motion of entrained droplets and the delay time for change in the wave structure on the film. Comparisons are made with experimental results on inlet effects and it is shown that the wall injection experimental results can be described by the model. The jet injection results are not fitted by the model and it is shown that some additional deposition mechanism must be present.