Entrainment Rate Of Droplets Research Articles

Flow rate measurement of gas-liquid annular flow through a combined multimodal ultrasonic and differential pressure sensor

Natural gas is an important strategic reserve resource for the country, also plays an important role in energy transition. During mining and transportation, natural gas has high liquid content and high-pressure characteristics, typically exhibiting gas-liquid annular flow state. Accurate flow metering of each individual phase without separation is significant to academic research and industrial production. Therefore, a combined ultrasonic and differential pressure sensor is presented to acquire flowing information. Based on the limited flowing information (liquid film fraction and gas velocity) measured by dual mode ultrasonic sensor, a two-fluid model is established to solve liquid velocity and droplet entrainment rate for calculating phase flow rates by analyzing the momentum balance between gas and liquid phases. The pressure drop by differential pressure sensor is introduced to make this two-fluid model closed and solvable. Considering the effects of system pressure and pipe diameter on pressure drop, a closed correlation for friction factor at the gas-liquid interface is established. Furthermore, the phase flow rates are calculated by the experimental measurement values obtained by dual mode ultrasonic sensor and the two-fluid model. The relative error of total flow rate is within ±10 % and the mean absolute percentage error is 5.220 %.

Role of bubble dynamics in heat and mass transfer in annular flows

Though bubbles are abundantly formed during the nucleate boiling in annular flows and affect the industrial performance during nucleation, departure, and bursting, the contribution of bubble dynamics in the heat and mass transfer in annular flows still needs to be quantified. Here, we used the semi-analytical film flow model to simulate the annular flow boiling in a vertical tube. We found the liquid film significantly affects the bubble departure diameter at wide working conditions when its thickness is smaller than the bubble's free departure size. A model for the departure diameter of the bubble considering the confinement of the thin liquid film was proposed, based on which theoretical models for the bubble-induced heat flux due to bubble formation and the bubble-induced droplet entrainment rate due to bubble bursting ejection were proposed. The contributions of the bubble-induced heat flux to the total (wall-to-liquid) heat transfer and the bubble-induced droplet entrainment rate to the total (liquid film-to-vapor core) mass transfer of annular flows can be up to 61% and 38% in the studied parameter range, respectively. The contribution of the bubble-induced heat flux to the total heat transfer increases with decreasing inlet mass flux and increasing tube diameter, wall heat flux, and pressure. The contribution of the bubble-induced droplet entrainment rate to the total mass transfer increases with decreasing inlet mass flux and increasing tube diameter. The proposed models of bubble-induced heat and mass transfer in annular flows may offer the first step to precisely control industrial performance by governing the bubble dynamics.

Droplet entrainment and its role in the combustion of HTPB/paraffin fuels

Droplet entrainment offers high regression rate of HTPB/paraffin fuels, but also leads to more complicated mass and heat transfer mechanisms during combustion. The droplet entrainment of the fuels in a windowed two-dimensional (2D) slab burner were investigated by using a high-speed camera, and the convective heat transfer coefficient was modified. The results indicated that the entrained droplets could be easily generated below 1.29 MPa of combustion pressure (pc), which was dominant in the regression of fuels, whereas the regression rate decreased by approximately 0.9 mm when pc increased from 0.32 MPa to 1.29 MPa due to the negative correlation of droplet entrainment rate with pc. However, the regression at higher pc mainly depended on weak evaporation and thermal decomposition rather than droplet entrainment, which was insensitive to pc and decreased by only about 0.05 mm s−1 with the increase in pc from 1.85 MPa to 2.52 MPa. The carbonized layer could be easily formed on the burning surface at higher pc, which hindered the droplet entrainment. Additionally, the improvement of convective heat transfer coefficient with the presence of droplet entrainment was evaluated, and the blocking effect was weakened, especially under high oxidizer mass flux.

Relationships between Cloud Droplet Spectral Relative Dispersion and Entrainment Rate and Their Impacting Factors

Relationships between Cloud Droplet Spectral Relative Dispersion and Entrainment Rate and Their Impacting Factors

On the droplet entrainment from gas-sheared liquid film

We formulate the droplet entrainment detached from a thin liquid film sheared by a turbulent gas in a circular pipe. In a time-averaged sense, the film has a Couette flow with a mean velocity of um. Then, a roll wave of wavelength λ and phase velocity uc is formed destabilized through Kelvin–Helmholtz instability, followed by a ripple wave of wavelength λp due to Rayleigh–Taylor instability, wherein the vorticity thickness of the gas stream is consistently a characteristic length scale. Superposing the two types of waves in axial and transverse directions produces conical cusps as the root of ligaments, from which droplets are torn off. The droplet entrainment rate is derived as λpλucum, validated by recent experimental results.

A novel model for calculating critical droplet entrainment rate of gas well considering droplet deformation and multiple parameters

AbstractWhen a spherical droplet moves parallel to the direction of motion of its surrounding gas medium, it will deform into an ellipsoidal droplet. In this paper, an exposition of a novel model for predicting the minimum flow rate for the continuous removal of liquids from gas wells based on two theories is presented. First, droplet breakup principle is utilized to microscopically obtain the maximum size parameters of ellipsoidal droplets, and second, droplet force equilibrium is adopted to macroscopically calculate the critical droplet entrainment rate. Moreover, effect of variations in the windward area (attributed to droplet deformation) on the drag coefficient is determined. Impacts of variations in pressure, temperature, and pipe diameter on the gas‐liquid two‐phase friction resistance and gas‐liquid surface tension are also considered. For model verification and comparison with other droplet entrainment models, field data from 3436 gas wells are utilized. The field data well validates the results with a 92% accuracy, indicating that the new model has a better comprehensive performance in determining whether or not a gas well is loaded. Besides, parameter sensitivity analyses including the effects of drag coefficient, surface tension, and friction coefficient on the minimum flow rate of gas are performed. Finally, the relationship curve of critical droplet entrainment rates corresponding to different pressures and pipe diameters is established.

Force balance droplet entrainment model for the horizontal stratified flow condition

Under the horizontal stratified flow condition, a droplet with a large interfacial area influences the mass, momentum, and heat transfer between the gas and liquid phases. In this study, we developed a force balance droplet entrainment rate model applicable to the horizontal stratified flow condition. This model is based on the balance of forces that act on the interfacial wave, which consists of an interfacial shear force, a surface tension force, and the force of gravity. In addition, the force balance droplet entrainment rate model includes constitutive relations for the parameters that are related to the geometry and the characteristics of the interfacial wave. This includes the wave frequency, wave height, wave slope, the wave velocity along the flow direction, and the lateral length of the interfacial wave along the circumferential direction of the flow pipe. The prediction of the onset of entrainment by the proposed force balance droplet entrainment rate model was compared to that with the existing models. Subsequently, the model was evaluated with the latest droplet deposition rate correlation from the literature against the experimental data obtained under the horizontal stratified flow condition. It showed a good prediction capability with a MAPE of 15.34%. Finally, the applicability of the force balance droplet entrainment rate model to a large-sized pipe was investigated. The force balance model showed a reasonable prediction performance. The applicable ranges of the gas and liquid Reynolds numbers (Reg and Rel, respectively) proposed by droplet entrainment rate model are 65,500–571,400 and 170–11,000, respectively.

Modeling of the droplet entrainment rate in the post-dryout regime for the analysis of a reflood phase

Many droplets are generated during the reflood phase of a large-break loss-of-coolant accident (LOCA) in a pressurized water reactor (PWR). The droplets greatly contribute to the cooling of the reactor core and, thus, have a great influence on the temperature behavior of the fuel rods. This requires an accurate model for droplet entrainment rate, especially for the reflood phase. However, the existing droplet entrainment models in thermal-hydraulic system codes cannot properly capture the entrainment phenomena in the post-dryout regime during the reflood process. In this study the observation results of visualization experiments for the post-dryout regime were utilized for modeling the droplet entrainment rate. Through the experiments, it was confirmed that droplets are mainly detached from the core liquid jet and the liquid sheet. We suggest a new droplet entrainment rate model based on the observation results and instability analysis. The new model is implemented in the CUPID code and evaluated using a set of the FEBA and the FLECHT SEASET reflood experiments. The results are compared with those of the existing droplet entrainment models. It was shown that the new model predicts the peak clad temperature (PCT) and the quenching time(QT) very well.

Experimental investigation of droplet entrainment and deposition in horizontal stratified wavy flow

An experimental study of the local droplet parameters for an atmospheric horizontal stratified wavy flow was conducted in a horizontal circular pipe with an inner diameter of 40 mm and a length of 5.5 m. The local distributions of the droplet fraction, droplet velocity, droplet diameter, and droplet mass flux in the cross section of the pipe were measured using single optical fiber probes at four locations with length-to-diameter ratios of 17.5, 55.0, 80.0, and 105.0 from the inlet of the test section. The average droplet mass flow rate along the axial direction of the flow channel was also obtained from the droplet parameters. The combination of the droplet entrainment and deposition rate models of Schimpf et al. was evaluated for droplet mass flow rates obtained from five different experiments including the present experiment in the horizontal stratified flow. However, its prediction accuracy was not good for the present and REGARD data. Finally, new droplet entrainment and deposition rate models for the horizontal stratified flow were proposed based on those five experiments. The applicable ranges of the proposed models are 65,500–571,400 and 170–11,000 for the gas (Reg) and liquid (Rel) Reynolds numbers, respectively.

Analysis of the effect of liquid droplet models on the reflood heat transfer using the CUPID code

The effects of liquid droplet models on the reflood heat transfer are analyzed using the CUPID code. Because the code adopts the two-fluid three-field, the droplet models for entrainment rate, deposition rate, and diameter are involved in the governing equations and constitutive models. It is, however, assumed that the droplet deposition on the heated rod during the reflood period is negligibly small. Thus, only the droplet entrainment rate and diameter models are investigated. Using the CUPID code with three well-known entrainment rate models and three diameter models, i.e., nine model combinations, six FLECHT SEASET reflood tests were calculated. The tests were also simulated using the MARS code that uses a two-fluid model. The CUPID codes with three combinations of the droplet entrainment rate and diameter models provided more accurate peak clad temperature (PCT) and quenching time (QT) than MARS, and all the nine combinations yielded better PCT prediction than MARS. Thereafter, the reflood heat transfer tests are quantitatively analyzed by using sensitivity calculations with respect to the models for film boiling heat transfer, interfacial drag, and interfacial heat transfer as well as the droplet models. The results showed the film boiling heat transfer plays the most dominant role in the PCT and the droplet entrainment at the quench front has the second largest impact on the PCT and the greatest effect on the QT.

수직 2상 유동에 대한 액적 이탈율 모델 개발

수직 2상 유동에 대한 액적 이탈율 모델 개발

Development of a droplet entrainment rate model for a vertical adiabatic two-phase flow

The authors have assessed some well-known droplet entrainment and deposition rate models against a wide range of vertical annular-mist flow experiments. The results of assessment showed that the Hewitt model predicts quite well for low-pressure air-water experiments and the Hewitt and the Okawa models are reasonably good for high-pressure steam-water experiments. However, the models still have large errors and significant deviations. Especially, it is known that their entrainment rate models are inappropriate to the developing region of an annular-mist flow because they were developed using experimental data estimated with the equilibrium assumption that the entrainment rate is equal to the deposition rate. To solve these problems, a new entrainment rate model is proposed here.Key variables for droplet entrainment are deduced from the analysis of experimental data and then the basic form of the new model is suggested as an empirical correlation. For the least-square fitting of the new correlation, the experimental data set of entrainment rate versus flow condition were needed. However, the entrainment rate cannot be measured in experiments but should be estimated. In this study, the droplet entrainment rates of 349 experiments were realistically estimated by using the continuity equation of the liquid film in an annular-mist flow, where the measured axial change of the liquid film mass flux can be taken into account, that is, the equilibrium assumption is not always needed. The new model was fitted using the data set and, then, assessed against 470 annular-mist flow experiments. The results showed that the new entrainment rate model in combination with the Okawa’s deposition rate model is definitely better than the existing models in terms of both accuracy and precision.

Generalization of droplet entrainment rate correlation for annular flow considering disturbance wave properties

A full knowledge of the interfacial disturbance wave effects on droplet entrainment is crucial for accurately predicting entrainment rate in annular flow. However, most entrainment models in literatures do not account for interfacial properties but only consider global flow parameters than precise wave characteristics. In view of this, based on the shearing-off mechanism of disturbance wave crest, a comprehensive model of droplet entrainment rate for annular flow has been established considering the characteristics of disturbance wave. Effects of hydraulic parameters on the instability of disturbance wave and their relationship with the droplet entrainment rate are presented. Results reveal that the gas and liquid flow rate, hydraulic diameter, surface tension and pressure have a great influence on the wave properties, i.e., critical wavelength, wave amplitude and wave velocity, and hence the droplet entrainment rate. Taking these influencing factors into account, a more accurate and reasonable formula for entrainment rate in annular flow is proposed. Comparison of the present correlation with the existing empirical correlations reveals that the new developed correlation can be correlated reasonably well with the experimental data within ±25% deviation for both air-water and steam-water annular flow.

Simulation study on factors influencing the entrainment behavior of liquid steel as bubbles pass through the steel/slag interface

In this study, a water/silicone oil interface was used to simulate the steel/slag interface in a converter. A high-speed camera was used to record the entrainment process of droplets when air bubbles were passed through the water/silicone oil interface. Motion parameters of the bubbles and droplets were obtained using particle kinematic analysis software, and the entrainment rate of the droplets was calculated. It was found that the entrainment rate decreased from 29.5% to 0 when the viscosity of the silicone oil was increased from 60 mPa·s to 820 mPa·s in the case of bubbles with a 5 mm equivalent diameter passing through the water/silicone oil interface. The results indicate that increasing the viscosity of the silicone oil is conducive to reducing the entrainment rate. The entrainment rate increased from 0 to 136.3% in the case of silicone oil with a viscosity of 60 mPa·s when the equivalent diameter of the bubbles was increased from 3 mm to 7 mm. We therefore conclude that small bubbles are also conductive to reducing the entrainment rate. The force analysis results for the water column indicate that the entrainment rate of droplets is affected by the velocity of the bubble passing through the water/silicone oil interface and that the entrainment rate decreases with the bubble velocity.

On Theoretical Models for Oil Droplets Size Distribution under the Influence of Surface Wave Breaking

Marine oil spill often forms oil droplets in stormy conditions. Based on the dimensional analysis Rayleigh method, the relationship is established between entrainment rate of oil droplets and statistical physical quantities such as the energy dissipation rate, intrusion depth et al. An expression of size spectrum of oil droplets is derived based on theorem and relationship between the capillary number, the dimensionless intrusion time and viscosity ratio. Preliminary results show that the slope of the derived spectrum is-2.29, which agrees well with the measured slope-2.3 in laboratory. Shear rate, surface tension, droplet radius, oil and water viscosity is the main factors controlling the total number of the oil droplets.

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.

Update on Condensation Heat Transfer and Pressure Drop inside Minichannels

The present paper reviews published experimental work focusing on condensation flow regimes, heat transfer, and pressure drop in minichannels. New experimental data are available with high (R410A), medium (R134a), and low (R236ea) pressure refrigerants in minichannels of different cross-section geometries and with hydraulic diameters ranging from 0.4 to 3 mm. Because of the influence of flow regimes on heat transfer and pressure drop, a literature review is presented to discuss flow regimes transitions. The available experimental frictional pressure gradients and heat transfer coefficients are compared with semi-empirical and theoretical models developed for conventional channels and models specifically created for minichannels. Starting from the results of the comparison between experimental data and models, the paper will discuss and evaluate the opportunity for a new heat transfer model for condensation in minichannels; the new model attempts to take into account the effect of the entrainment rate of droplets from the liquid film.

Correlations for the mass transfer rate of droplets in vertical upward annular flow

New correlations for the deposition rate and entrainment rate of droplets in vertical upward annular flow were developed from simple models and available experimental data. In the correlation for the deposition rate, the superficial gas velocity was used as the parameter of primary importance at low droplet concentration while the droplet concentration itself at high droplet concentration. In correlating the rate of droplet entrainment, the ratio of interfacial shear force to the surface tension force acting on the surface of liquid film was the appropriate scaling parameter to correlate the experimental data measured in varied conditions. The experimental data for air–water annular flow were used in the development of the present correlations since extensive databases were available. It was however confirmed that the present model provides satisfactory agreements with the experimental data for high-pressure steam–water annular flow.

Experiments for liquid phase mass transfer rate in annular regime for a small vertical tube

The double film extraction technique was used to measure the deposition rate and the entrainment rate of droplets for vertical upward annular two-phase flow in a small diameter tube. The test section was a round tube of 5 mm in inside diameter, air and water were used as test fluids and the system pressure was varied within 0.14–0.76 MPa. It was shown in the present experimental conditions that the deposition rate was primarily influenced by the droplet concentration in the gas core and that the entrainment rate was correlated well with the dimensionless number denoting the ratio of interfacial shear force to surface tension force acting on the surface of liquid film. These results were consistent with available empirical correlations that were developed using the experimental data for larger diameter tubes.