Annular Flow Regime Research Articles

A mathematical approach to predict dryout in a rod bundle

In this paper, we present the development of a mathematical model to predict dry-out in a rod bundle using film thickness model and subchannel analysis. In two-phase annular flow regime, liquid phase is assumed to divide into liquid film attached to the rod surface and droplets entrained into the gas (vapor) phase existing in the subchannels. Conservation equations in two-phase annular flow regime for each subchannel consist of two mixture equations for the continuity and the momentum, gas phase continuity, liquid film continuity and liquid phase energy. Also, at the interface of adjacent subchannels, radial diversion cross flow equation is considered. It is assumed that dryout occurs when the local film thickness in the annular flow approaches zero. The transfer of mass, momentum and energy between adjacent subchannels are split into diversion cross-flow, turbulent mixing and void drift components. Rod-centered approach which is compatible with the annular flow regime is used for subchannel analysis. It was observed that turbulent mixing and void drift phenomena have significant effect on the prediction of dryout power. The model is verified against several available experimental data and proved viable for prediction of dryout heat flux in rod bundle geometry especially for mass flux greater than 400kg/m2s.

Churn and Wispy Annular Flow Regimes in Vertical Gas–Liquid Flows

Two-phase flows are extremely complex and, traditionally, attempts have been made to classify the myriad of possible flow configurations into “flow regimes” or “flow patterns”. Classically, vertical two-phase flows have been classified into the regimes of bubbly flow, slug flow, and annular flow. This paper makes an appeal for two other regimes, namely, “churn flow” and “wispy annular flow”, to be given more attention. As shown, these regimes are of considerable technological importance and possess unusual features that justify their separate designation and make them ripe for further study.

Experimental study of internal two-phase flow induced fluctuating force on a 90° elbow

Experiments were performed with a 52.5mm I.D., 90° elbow to study the internal two-phase flow induced fluctuating forces on pipe bends. The dynamic force signals were obtained directly from force sensors by separating the natural frequency of test section from the predominant frequency of excitation forces. A total of 36 tests were carried out to cover bubbly, slug, churn and annular flows. The results showed that for a fixed liquid flow rate, the predominant frequency of force peaked at slug flow regime. The root mean square value of force fluctuations continuously increased with gas flow rate and reached its maximum in annular flow regime. The excitation force presented a strong dependence on the momentum flux of two-phase flows. The integral of local pressure measurements could predict the time averaged momentum flux change reasonably well. However, the root mean square values of fluctuating forces were quite different due to the additional effect caused by the impact of liquid slugs on the elbow. The impact force, which has not been emphasized in the literature for the internal two-phase flow induced vibration analysis, is found to be significant in determining the force fluctuations in the slug flow regime. A two-phase flow induced excitation force model was developed based on the local instant formulation of two-fluid model. Analyses showed that the high frequency fluctuating components of centrifugal forces could be damped by the integral effect of the elbow.

Experimental study on condensation heat transfer and pressure drop of low GWP refrigerant HFO1234yf in a horizontal tube

Condensation heat transfer of low GWP refrigerant HFO1234yf was measured in a horizontal tube (inner diameter: 4mm) at a mass flux range of 100–400kgm−2s−1 and different saturation temperatures (40, 45, and 50°C), and the results were compared with that of R134a and R32. Effects of mass flux, vapor quality, saturation temperature, and thermophysical properties on the heat transfer coefficient were analyzed. Mass flux and vapor quality were presented to primarily affect the heat transfer coefficient in shear-force dominated flow regimes, whereas the thermal conductivity and density ratio are the primary parameters as thermophysical properties influencing the heat transfer coefficient. Observed annular flow regimes agreed with Tandon’s flow pattern map. The measured pressure drop compared with that predicted by the Lockhart–Matinelli correlation, Huang correlation and Haraguchi correlation. And, when comparing the experimental heat transfer coefficient with four heat transfer coefficient correlations, the Haraguchi correlation fairly agreed with the experimental data, with a 10.8% mean deviation.

The effect of liquid spreading due to micro-structures of flow boiling critical heat flux

The effect of a micro-structured Zirlo surface on the internal flow boiling critical heat flux (CHF) was examined under atmospheric pressure conditions for water. The Zirlo surface was modified by anodic oxidation, resulting in improved wettability with complete wetting and liquid spreading. The variation of the flow boiling CHF was investigated over a mass flux range from 300 to 1500kg/m2s, for inlet temperatures of 60°C, 80°C, and 95°C. The CHF values on a micro-structured Zirlo tube were enhanced compared to the values obtained on a bare surface, to a maximum increase of 60% at a mass flux of 1500kg/m2s. However, the inlet temperature had no significant effect on the results of CHF enhancement. The CHF enhancement ratio increased with the mass flux. According to previous nanofluid experiments, the reason for flow boiling CHF enhancement should be indicated as the flow regime. Surface wettability has been invoked as one possible reason for flow boiling CHF enhancement in the nucleate boiling regime, but not in the annular flow regime. In the present study, we suggest that the flow boiling CHF in the annular flow regime increases with mass flux because of the stability of the liquid film and the liquid replenishment, resulting from both improved surface wettability and liquid spreading.

Experimental constraints on the outgassing dynamics of basaltic magmas

The dynamics of separated two‐phase flow of basaltic magmas in cylindrical conduits has been explored combining large‐scale experiments and theoretical studies. Experiments consisted of the continuous injection of air into water or glucose syrup in a 0.24 m diameter, 6.5 m long bubble column. The model calculates vesicularity and pressure gradient for a range of gas superficial velocities (volume flow rates/pipe area, 10−2–102 m/s), conduit diameters (100–2 m), and magma viscosities (3–300 Pa s). The model is calibrated with the experimental results to extrapolate key flow parameters such as Co (distribution parameter) and Froude number, which control the maximum vesicularity of the magma in the column, and the gas rise speed of gas slugs. It predicts that magma vesicularity increases with increasing gas volume flow rate and decreases with increasing conduit diameter, until a threshold value (45 vol.%), which characterizes churn and annular flow regimes. Transition to annular flow regimes is expected to occur at minimum gas volume flow rates of 103–104 m3/s. The vertical pressure gradient decreases with increasing gas flow rates and is controlled by magma vesicularity (in bubbly flows) or the length and spacing of gas slugs. This study also shows that until conditions for separated flow are met, increases in magma viscosity favor stability of slug flow over bubbly flow but suggests coexistence between gas slugs and small bubbles, which contribute to a small fraction of the total gas outflux. Gas flow promotes effective convection of the liquid, favoring magma homogeneity and stable conditions.

Influence of surfactant on two-phase flow regime and pressure drop in upward inclined pipes

The influence of a surfactant on the two-phase flow regime and the pressure drop in upward inclined pipes is investigated for various gas/liquid flow rates. The air/water and air/100 ppm sodium dodecyl sulphate aqueous solution are used as the working fluids. The influence of the surfactant on the two-phase flow regime in upward inclined pipes is investigated using the electrical tomographic technique. For 0°, 2.5° and 5° pipe inclinations, the surfactant has obvious effect on the transition from the stratified wavy flow to the annular flow, and the range of the stratified smooth flow regime is also extended to higher gas velocities. For 10° pipe inclination, no stratified flow regime is observed in the air/water flow. In the air/surfactant solution system, however, the stratified flow regime can be found in the range of USH = 10m/s−28m/s and USL = 0.07m/s−0.2m/s. For all inclination angles, the changes of the pressure gradient characteristics are accompanied with the flow pattern transitions. Adding surfactant in a two-phase flow would reduce the pressure gradient significantly in the slug flow and annular flow regimes. In the annular flow regime, the pressure gradient gradually becomes free of the influence of the upward inclined angle, and is only dependent on the property of the two-phase flow.

AN EXPERIMENTAL STUDY ON EFFERVESCENT ATOMIZATION OF BIO-OIL FUELS

This paper presents the work on detailed characterization of effervescent spray of Jatropha and Pongamia pure plant oils. The spray characteristics of these biofuels are compared with those of diesel. Both macroscopic and microscopic spray characteristics at different injection pressures and gas-to-liquid ratio (GLR) have been studied. The particle/droplet imaging analysis (PDIA) technique along with direct imaging methods are used for the purpose of spray characterization. Due to their higher viscosity, pure plant oils showed poor atomization compared to diesel and a blend of diesel and pure plant oil at a given GLR. Pure plant oil sprays showed a lower spray cone angle when compared to diesel and blends at lower GLRs. However, the difference is not significant at higher GLRs. Droplet size measurements at 100 mm downstream of the exit orifice showed reduction in Sauter mean diameter (SMD) diameter with increase in GLR. A radial variation in the SMD is observed for the blend and pure plant oils. Pure oils showed a larger variation when compared to the blend. Spray unsteadiness has been characterized based on the image-to-image variation in the mean droplet diameter and fluctuations in the spray cone angle. Results showed that pure plant oil sprays are more unsteady at lower GLRs when compared to diesel and blend. A critical GLR is identified at which the spray becomes steady. The three regimes of spray operation, namely "steady spray," "pulsating spray," and "spray and unbroken liquid jet" are identified in the injection pressure-GLR parameter space for these pure plant oils. Two-phase flow imaging inside the exit orifice shows that for the pure plant oils, the flow is highly transient at low GLRs and the bubbly, slug, and annular two-phase flow regimes are all observed. However, at higher GLRs where the spray is steady, only the annular flow regime is observed.

Modeling of hydrodynamics in microchannel reactor for Fischer–Tropsch synthesis

Hydrodynamics of liquid and gaseous products in microchannel reactor for Fischer–Tropsch synthesis is considered. It is supposed, that liquid and gaseous products of the synthesis move downward in annular flow regime. A microchannel with irregular internal walls is investigated in cylindrical symmetry. In proposed numerical technique the peculiarities of coating the microchannel walls by cobalt-based catalytic particles are taken into account. System of equations of two-phase hydrodynamics is based on the generalized equations for mass flowrate and momentum of liquid film and gaseous phase. Stable numerical algorithm for calculation the thermodynamic equilibrium in gas–liquid mixtures of synthesis products is proposed. Calculation results illustrate thermophysical properties of liquid and gaseous products. In the hydrodynamics model variations along a microchannel mass fractions and thermophysical properties of liquid and gaseous products were taking into account. Principal hydrodynamical difference between a smooth microchannel and a microchannel with random roughness is explained. Hydrodynamical parameters and gradient of pressure are investigated as functions of pressure, temperature, averaged diameter of a microchannel and chain growth probability.

Characteristics of the Interfacial Wave Velocity on the Liquid Film of Annular Flow for Gas-Oil-Water Three-Phase Flow in a Horizontal Pipe

The experiments were conducted in a horizontal multiphase flow test loop (50mm inner diameter, 40m long) and the cross-correlation technology was used for the study of the characteristics of the interfacial wave velocity about two types of annular flow regimes (AN║DO/W and AN║DW/O) for gas-oil-water three-phase flow. The results show that the interfacial wave velocity on the liquid film of AN║DO/W flow pattern and AN║DW/O flow pattern all increases with the increase of gas superficial velocity and liquid superficial velocity on the condition of fixed ratio of oil and water flow rates, but the difference is that the increase is a linear monotonic increase for AN║DO/W flow pattern and a non-linear increase for AN║DW/O flow pattern, and the liquid superficial velocity makes a larger contribution than the gas superficial velocity. The interfacial wave velocity also increases with the increase of input water cut in liquid at different gas superficial velocities under the conditions of liquid superficial velocity fixed.

Heterogeneous catalysis in a microchannel using a layer of carbon nanofibers on the channel wall

This paper presents the increase of the overall reaction rate of a heterogeneously catalyzed multi-phase reaction using a carbon nanofiber (CNF) based catalyst with a factor of 3.5–4 compared with an unsupported flat plate catalyst in a microreactor. This was done by quantifying the hydrogen reaction rates for three different CNF layers with different layer and fiber thicknesses and permeability attached to a microchannel wall at different flow regimes and comparing them with the reaction rate of an unsupported flat plate catalyst. The CNF layer with the most open structure and the largest CNF layer thickness shows an increase of the overall reaction rate with a factor of approximately 3.5–4 in comparison with the unsupported flat plate catalyst, whilst keeping the selectivity towards the intermediate product over 95%. Furthermore, the influence of the CNF layers on the gas hold-up and the flow regimes were investigated. The gas hold-up is linearly dependent on the relative gas velocity according to the Armand correlation for all the tested CNF layers. The CNF layers do not influence the flow patterns, and the Taylor/slug, slug/ring, ring and annular flow regimes are observed for all CNF layers.

The analysis of silica suspensions atomization

The paper contains the results of experimental investigation of air–water and air–silica suspension atomization process in effervescent nozzles with internal mixing obtained by the use of the digital microphotography method. In experiments the different aqueous solutions of silica Aerosil 300 of different concentration have been used. The suspensions containing up to 0.04 (kg solid particles/kg solution) have Newtonian rheological properties. The observations were carried out at liquid flow rates changed from 0.0014 to 0.011 (kg/s) and gas flow rates from 0.00015 to 0.0065 (kg/s). It corresponded to gas to liquid mass ratios ( GLR) values from 0.014 to 0.46. The analysis of photos shows that the droplets which have been formed during the liquid atomization have very different sizes. The differences between characteristics of effervescent atomization for water and suspensions used have not been observed. The present study confirmed the previous reports which suggested that the small particles added to solution do not change spray characteristics. The experimental results show that C D and SMD are non-linear functions of GLR. Their values are decreasing rapidly as GLR is increased from zero to around 0.07 and thereafter decreasing at a slower rate with further increase in GLR. In the same point ( GLR = 0.07) the value of α is maximal. The first regime is characteristic for bubbly flow. The second is typical of annular flow regime. Boundary between bubbly and annular flow regime is observed at GLR = 0.07 for investigated systems. The correlations for C D and Sauter mean diameter were proposed. The results may be used for example to verify numerical models or comparisons with respect to similar atomization processes.

Model for Predicting the Mean Drop Size in Effervescent Sprays

This paper is focused on the development of a model for predicting the mean drop size in effervescent sprays. A combinatorial approach is followed in this modeling scheme, which is based on energy and entropy principles. The model is implemented in cascade in order to take primary breakup (due to exploding gas bubbles) and secondary breakup (due to shearing action of surrounding medium) into account. The approach in this methodology is to obtain the most probable drop size distribution by maximizing the entropy while satisfying the constraints of mass and energy balance. The comparison of the model predictions with the past experimental data is presented for validation. A careful experimental study is conducted over a wide range of gas-to-liquid ratios, which shows a good agreement with the model predictions: It is observed that the model gives accurate results in bubbly and annular flow regimes. However, discrepancies are observed in the transitional slug flow regime of the atomizer.

Ozonolysis in Flow Using Capillary Reactors

Reactions of n-decene with ozone and subsequent quenching of the formed ozonides were carried out under flow conditions using the standard Vapourtec flow system equipped with a cooled flow cell. The reactions were performed continuously and in the annular flow regime within the circular cross-section channels. Typical flow rates were 0.25–1 mL min–1 for liquid and 25–100 mL min–1 for gas, reactor volumes were 0.07–10 mL formed of 1 mm ID PFA tubing. The reaction temperature was −10 °C. The flow was not always smooth, while waves in the liquid film and droplets in the gas core were observed. Liquid residence times were found to be independent of gas flow rates and increasing with decreasing liquid flow rates. Substrate residence times in the ozonolysis reactor ranged between 1 and 80 s, and complete conversion could be achieved at ∼1 s residence time. Two common reductants, triethylphosphite and triphenylphosphine, were examined as to their suitability under flow conditions. Triphenylphosphine achieved fas...

Numerical simulation of flow boiling for organic fluid with high saturation temperature in vertical porous coated tube

A semi-analytical model is developed for the prediction of flow boiling heat transfer inside vertical porous coated tubes. The model assumes that the forced convection and nucleate boiling coexist together in the annular flow regime. Conservations of mass, momentum, and energy are used to solve for the liquid film thickness and temperature. The heat flux due to nucleate boiling consists of those inside and outside micro-tunnels. To close the equations, a detailed analysis of various forces acting on the bubble is presented to predict its mean departure diameter. The active nucleation site density of porous layer is determined from the pool boiling correlation by introducing suppression factor. The flow boiling heat transfer coefficients of organic fluid (cumene) with high saturation temperature in a vertical flame-spraying porous coated tube are studied numerically. It is shown that the present model can predict most of the experimental values within ±20%. The numerical results also indicate that the nucleate boiling contribution to the overall heat transfer coefficient decreases from 50% to 15% with vapor quality increasing from 0.1 to 0.5.

Flow Boiling of R134a in Circular Microtubes—Part II: Study of Critical Heat Flux Condition

A detailed experimental study was carried out on the critical heat flux (CHF) condition for flow boiling of R134a in single circular microtubes. The test sections had inner diameters (ID) of 0.50 mm, 0.96 mm, and 1.60 mm. Experiments were conducted over a large range of mass flux, inlet subcooling, saturation pressure, and vapor quality. CHF occurred under saturated conditions at high qualities and increased with increasing mass fluxes, tube diameters, and inlet subcoolings. CHF generally, but not always, decreases with increasing saturation pressures and vapor qualities. The experimental data were mapped to the flow pattern maps developed by Hasan [2005, “Two-Phase Flow Regime Transitions in Microchannels: A Comparative Experimental Study,” Nanoscale Microscale Thermophys. Eng., 9, pp. 165–182] and Revellin and Thome [2007, “A New Type of Diabatic Flow Pattern Map for Boiling Heat Transfer in Microchannels,” J. Micromech. Microeng., 17, pp. 788–796]. Based on these maps, CHF mainly occurred in the annular flow regime in the larger tubes. The flow pattern for the 0.50 mm ID tube was not conclusively identified. Four correlations—the Bowring correlation, the Katto-Ohno correlation, the Thome correlation, and the Zhang correlation—were used to predict the experimental data. The correlations predicted the correct experimental trend, but the mean absolute error (MAE) was high (>15%) A new correlation was developed to fit the experimental data with a MAE of 10%.

A Review of Cuttings Transport in Directional-Well Drilling

A Review of Cuttings Transport in Directional-Well Drilling This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 132372, “Review of Cuttings Transport in Directional-Well Drilling: Systematic Approach,” by T. Nazari, SPE, and G. Hareland, SPE, University of Calgary, and J.J. Azar, SPE, University of Tulsa, originally prepared for the 2010 SPE Western Regional Meeting, Anaheim, California, 27–29 May. The paper has not been peer reviewed. Hole cleaning during directional-well drilling is a major concern in the oil field and must be monitored and properly controlled during the entire drilling operation. Inadequate drilled-cuttings removal can cause many costly problems. Low annular-fluid velocity, lack of drillpipe rotation, and the wrong mud properties are primary factors in ineffective hole cleaning. The full-length paper presents a review of previous hole-cleaning studies and discusses an approach that is better suited for monitoring and controlling hole-cleaning problems. Introduction The rotary-drilling process consists of a rock-cutting tool (drill bit) upon which a downward force is applied [weight on bit (WOB)] and rotation (rev/min) is imposed. The drilled cuttings generated by the drill bit are removed by circulating a drilling fluid from surface to bottomhole and back to surface (cuttings transport) (Fig. 1). During directional-well drilling, cuttings removal becomes more difficult and if not controlled properly can result in serious problems such as mechanical pipe sticking (fishing or hole loss), excessive frictional torque (increase in rotary-power requirement) and frictional drag (inability to reach target), difficulty in landing casing, channeling problems during cementing, and difficulty in logging. The factors that are known to affect hole cleaning include annular eccentricity, inclination angle, drillpipe rotation, fluid flow rate (annular velocity and flow regime), rate of penetration (ROP), mud rheology and density, and cuttings (i.e., size, shape, and density). It is well documented that flow rate and drillpipe rotation have the most positive effect on hole cleaning. However, an increase in flow rate causes an increase in frictional pressure losses, which in turn causes an increase in equivalent circulating density (ECD), pump-pressure requirement, and potential hole erosion. An increase in pipe rotation can result in premature pipe fatigue failures caused by the induced cyclic stresses. Cuttings-Transport Problem In contrast to other industrial processes, the cuttings-transport problem in the drilling industry is more complex because of the many parameters that are interconnected nonlinearly. In simpler processes, some of the steps could be neglected. Comparing this scheme to a drilling process results in the following correlations: Process—drilling procedure Reference—ECD limitation, pump hydraulic-horsepower limitation, hole erosion, ROP limitation, geological-target limitation, rotary-power limitation Process inputs—flow rate, rev/min, hookload Process outputs—pressures, ROP, torque Internal states—WOB, eccentricity, hole cleaning Monitoring/control—lost circulation, drag, torque, cuttings returns, ROP, circulating standpipe pressure For a complete and reliable automated design process, the following steps must be taken: Signal measurements Monitoring of critical parameters Modeling Control

Experimental Study on the Modeling of Condensation Heat Transfer Coefficients in High Mass Flux Region of Refrigerant HFC-134a Inside the Vertical Smooth Tube in Annular Flow Regime

This article presents an experimental investigation on the co-current downward condensation of R134a in a vertical smooth copper tube having inner diameter of 8.1 mm and a length of 500 mm. Condensation experiments are done at mass fluxes varying between 260 and 515 kg/m2-s. The condensing temperatures are 40°C and 50°C; heat fluxes are between 10.16 and 66.61 kW/m2. The quality of the refrigerant in the test section is calculated considering the temperature and pressure obtained from the experiment. The pressure drop across the test section is directly measured by a differential pressure transducer. The average experimental heat transfer coefficient of the refrigerant is calculated by applying an energy balance based on the energy transferred from the test section. The average predicted heat transfer coefficient of the refrigerant is determined by means of the model of Kosky and Staub, and Von Karman universal velocity distribution correlations using different interfacial shear stress equations valid for annular flow in horizontal and vertical tubes to investigate the Chen et al. annular flow theory. The effects of heat flux, mass flux, and condensation temperature on the pressure drop are also discussed. A new correlation using a large number of data points for the turbulent condensation heat transfer coefficient is proposed.

ICONE19-43536 Development of CFD Analysis Method Based on Droplet Tracking Model for BWR Fuel Assemblies

It is well known that the minimum critical power ratio (MCPR) of the boiling water reactor (BWR) fuel assembly depends on the spacer grid type. Recently, improvement of the critical power is being studied by using a spacer grid with mixing devices attaching various types of flow deflectors. In order to predict the critical power of the improved BWR fuel assembly, we have developed an analysis method based on the consideration of detailed thermal-hydraulic mechanism of annular mist flow regime in the subchannels for an arbitrary spacer type. The proposed method is based on a computational fluid dynamics (CFD) model with a droplet tracking model for analyzing the vapor-phase turbulent flow in which droplets are transported in the subchannels of the BWR fuel assembly. We adopted the general-purpose CFD software Advance/FrontFlow/red (AFFr) as the base code, which is a commercial software package created as a part of Japanese national project. AFFr employs a three-dimensional (3D) unstructured grid system for application to complex geometries. First, AFFr was applied to single-phase flows of gas in the present paper. The calculated results were compared with experiments using a round cellular spacer in one subchannel to investigate the influence of the choice of turbulence model. The analyses using the large eddy simulation (LES) and re-normalisation group (RNG) k-ε models were carried out. The results of both the LES and RNG k-ε models show that calculations of velocity distribution and velocity fluctuation distribution in the spacer downstream reproduce the experimental results qualitatively. However, the velocity distribution analyzed by the LES model is better than that by the RNG k-ε model. The velocity fluctuation near the fuel rod, which is important for droplet deposition to the rod, is also simulated well by the LES model. Then, to examine the effect of the spacer shape on the analytical result, the gas flow analyses with the RNG k-ε model were performed for three kinds of spacers of actual fuel assemblies: a lattice type spacer, a round cell type spacer, and a grid spacer with mixing vanes, respectively. The results indicate that the swirling flow is generated by the mixing vane, and the turbulence energy increases near the surface of fuel rod. The Lagrangian method was applied to droplet behavior in turbulent gas flow around the round cell type spacer and that around a mixing vane spacer as trial analyses. It was confirmed that liquid droplet deposition is promoted in downstream from the mixing vane spacer because of swirling flow.

Studying the influence of refrigerant type on thermal efficiency of annular two-phase flows; mass transfer viewpoint

Many parameters influence the thermal efficiency of two-phase systems; among them, the type of refrigerant employed in two-phase systems is of great importance. Carbon dioxide has been reintroduced as a possible R22 replacement, because of having more heat transfer rate and lower pressure drops, along with better environmental treatment compared with widely-used refrigerants. In the present article carbon dioxide is studied and compared with some thermophysically-different refrigerants from the viewpoint of probability of dry-out occurrence. Dry-out phenomenon in two-phase systems should be avoided as far as possible to prevent sudden drops in heat transfer. Dry-out occurrence is strongly influenced by entrainment mass transfer. In the present study a semi-empirical model is proposed for simulation of entrainment mass transfer in annular flow regime of liquid-vapor in a vertical tube. The significance of entrainment phenomenon in carbon dioxide is compared with that of some other refrigerants to figure out the probability of dryout occurrence in different refrigerants. It will be demonstrated that CO2 relative to other refrigerants has much lower amounts of entrainment. This issue along with other mentioned advantages shows the prominent effectiveness of carbon dioxide among other conventional refrigerants.