Prediction of two-phase pressure drop and void fraction in microchannels using probabilistic flow regime mapping

Probabilistic two-phase flow map pressure drop and void fraction models are developed for 6-port microchannels in order to provide a more accurate and common means of predicting void fraction and pressure drop. The models are developed for R134a, R410A, and air–water in 6-port microchannels at 10 °C saturation temperatures, qualities from 0 to 1, and mass fluxes varying from 50 to 300 kg/m² s. The probabilistic flow map models developed are found to accurately predict void fraction and pressure drop for the entire quality range and for all three fluids.     

Prediction of evaporation heat transfer coefficient based on gas–liquid two-phase annular flow regime in horizontal microfin tubes

A physical model of gas–liquid two-phase annular flow regime is presented for predicting the enhanced evaporation heat transfer characteristics in horizontal microfin tubes. The model is based on the equivalence of a periodical distortion of the disturbance wave in the substrate layer. Corresponding to the stratified flow model proposed previously by authors, the dimensionless quantity Fr₀ = G/[gd_eρ_v(ρ_l ? ρ_v)]^0.5 may be used as a measure for determining the applicability of the present theoretical model, which was used to restrict the transition boundary between the stratified-wavy flow and the annular/intermittent flows. Comparison of the prediction of the circumferential average heat transfer coefficient with available experimental data for four tubes and three refrigerants reveals that a good agreement is obtained or the trend is better than that of the previously developed stratified flow model for Fr₀ > 4.0 as long as the partial dry out of tube does not occur. Obviously, the developed annular model is applicable and reliable for evaporation in horizontal microfin tubes under the case of high heat flux and high mass flux.     

Flow regime transition criteria for upward two-phase flow in vertical tubes

Traditional two-phase flow-regime criteria based on the gas and liquid superficial velocities may not be suitable to the analyses of rapid transient or entrance flows by the two-fluid model. Under these conditions, it is postulated that direct geometrical parameters such as the void fraction are conceptually simpler and therefore more reliable parameters to be used in flow-regime criteria than the traditional parameters. From this point of view, new flow-regime criteria for upward gas-liquid flow in vertical tubes have been developed considering the mechanisms of flow-regime transitions. These new criteria can be compared to existing criteria and experimental data under steady-state and fully developed flow conditions by using relative velocity correlations. The criteria showed reasonable agreements with the existing data for atmospheric air-water flows. Further comparisons with data for steam—water in round tubes and a rectangular channel at relatively high system pressures have been made. The results confirmed that the present flow-regime transition criteria could be applied over wide ranges of parameters as well as to boiling flow.     

Condensation in horizontal tubes, part 1: two-phase flow pattern map

A new flow pattern map and flow pattern based heat transfer model for condensation inside horizontal plain tubes are proposed in this two-part paper. In Part I, a new version of a two-phase flow pattern map, originally developed by Kattan et al. [J. Heat Transfer 120 (1998) 140] for flow boiling, is presented for condensation inside horizontal tubes while a new heat transfer model is presented in Part II. The new flow pattern map incorporates a newly defined logarithmic mean void fraction (LMε) method for calculation of vapor void fractions spanning from low pressures up to pressures near the critical point. Several other modifications are also made that are appropriate for condensation as opposed to evaporation. In the absence of void fraction data at high reduced pressures for these conditions, the new LMε method has been indirectly validated using the convective condensation model for annular flow and corresponding heat transfer test data at reduced pressures up to 0.8. The new map has also been successfully compared to some recent flow pattern observations for condensation and other existing flow transition criteria and maps.     

Condensation heat transfer studies for stratified,cocurrent two-phase flow in horizontal tubes

Condensation heat transfer inside horizontal tubes is investigated for a stratified, cocurrent two-phase flow of vapor and liquid. The analysis takes into account the effects of interfacial shear, axial pressure gradient, saturation temperature level, driving temperature difference and the development of the stratified angle associated with the accumulated condensate layer at the bottom of the tube. The influence of these parameters is evaluated with respect to the peripheral condensate film heat transfer performance for the practically interesting laminar flow range of operating conditions of water-vapor flow. A theoretical predictive method is developed to obtain the overall heat transfer coefficient along the tube length. Results of the theoretical predictions are found to agree favorably with the reported experimental data which cover a variety of fluids with a relatively wide range of operating conditions. A simple, predictive heat transfer coefficient correlation is proposed from the numerical solution by means of regression analysis.     

CFD and ERT investigations on two-phase flow regimes in vertical and horizontal tubes

In the present study, different two-phase flow regimes in horizontal and vertical tubes have been studied experimentally and theoretically. A 3-D Computational Fluid Dynamics (CFD) modeling was carried out in order to model gas–liquid two-phase flow using volume of fluid (VOF) model. An Electrical Resistance Tomography (ERT) system was used to visualize these flow regimes, which were produced by change in the gas to liquid flow rate ratio. The reconstructed images from the ERT measurement and corresponding captured photographs for different flow regimes have been compared with the CFD predictions and a good qualitative agreement was observed between them.     

Study of two-phase flow regime identification in horizontal tube bundles under vertical upward cross-flow condition using wavelet transform

A wavelet-transform based approach for flow regime identification in horizontal tube bundles under vertical upward cross-flow condition was presented. Tests on two-phase flow pattern of R134a were conducted under low mass velocity and flow boiling conditions over ranges of mass flux 4–25 kg/m²s, vapor quality 0.02–0.90. Time series of differential pressure fluctuations were measured and analyzed with discrete wavelet transform. Different time-scale characteristics in bubbly flow, churn flow and annular flow were analyzed. The wavelet energy distributions over scales were found to be appropriate for flow regime identification. Based on the wavelet energy distribution over characteristic scales, a criterion of flow regime identification was proposed. The comparison with experiment results show that it is feasible to use the discrete wavelet transform as the tool of flow regime identification in horizontal tube bundles under vertical upward cross-flow condition.     

Study of two-phase flow regime identification in horizontal tube bundles under vertical upward cross-flow condition using wavelet transform

A wavelet-transform based approach for flow regime identification in horizontal tube bundles under vertical upward cross-flow condition was presented. Tests on two-phase flow pattern of R134a were conducted under low mass velocity and flow boiling conditions over ranges of mass flux 4–25 kg/m²·s, vapor quality 0.02–0.90. Time series of differential pressure fluctuations were measured and analyzed with discrete wavelet transform. Different time-scale characteristics in bubbly flow, churn flow and annular flow were analyzed. The wavelet energy distributions over scales were found to be appropriate for flow regime identification. Based on the wavelet energy distribution over characteristic scales, a criterion of flow regime identification was proposed. The comparison with experiment results show that it is feasible to use the discrete wavelet transform as the tool of flow regime identification in horizontal tube bundles under vertical upward cross-flow condition. __________ Translated from Journal of Shanghai Jiaotong University, 2007, 41(3): 337–341, 346 [译自: 上海交通大学学报]     

Experimental study on condensation and evaporation flow inside horizontal three dimensional enhanced tubes

Experimental investigations of tube side condensation and evaporation in two 3-D enhanced heat transfer (2EHT) tubes were compared to the performance of a smooth surface copper tube. The equivalent outer diameter of all the tubes was 12.7 mm with an inner diameter of 11.5 mm. Both the inner and outer surfaces of the 2EHT tubes are enhanced by longitudinal grooves with a background pattern made up by an array of dimples/embossments. Experimental runs were performed using R410A as the working fluid, over the quality range of 0.2–0.9. For evaporation, the heat transfer coefficient ratio (compares the heat transfer coefficient of the enhanced tube to that of a smooth tube) of the 2EHT tubes is 1.11–1.43 (with an enhanced surface area ratio of 1.03) for mass flux rate that ranges from 80 to 200 kg/m² s. For condensation, the heat transfer coefficient ratio range is 1.1–1.16 (with an enhanced surface area ratio of 1.03) for mass flux that ranges from 80 to 260 kg/m² s. Frictional pressure drop values for the 2EHT tubes are very similar to each other. Heat transfer enhancement in the 2EHT tubes is mainly due to the dimples and grooves in the inner surface that create an increased surface area and interfacial turbulence; producing higher heat flux from wall to working fluid, flow separation, and secondary flows. A comparison was performed to evaluate the enhancement effect of the 2EHT tubes using a defined performance factor and this indicates that the 2EHT tubes provides a better heat transfer coefficient under evaporation conditions.     

Experimental study for the stratified to slug flow regime transition mechanism of gas-oil two-phase flow in horizontal pipe

Theoretical relations that predict the transition from a stratified pattern to a slug pattern, including a one-dimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model, and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented. Superficial velocities of each phase, as the onset of slugging occurs, were predicted, and theoretical analysis was conducted on the stratified to slug flow regime transition. The friction, existing between the fluid and pipe wall, and on the interface of two phases, was especially taken into account. A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe. The effect of pipe diameter on the transition was also studied. The results show that this approach gives a reasonable prediction over the whole range of flow rates, and better agreement has been achieved between predicted and measured critical parameters.     

Experimental study for the stratified to slug flow regime transition mechanism of gas-oil two-phase flow in horizontal pipe

Theoretical relations that predict the transition from a stratified pattern to a slug pattern, including a onedimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model, and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented. Superficial velocities of each phase, as the onset of slugging occurs, were predicted, and theoretical analysis was conducted on the stratified to slug flow regime transition. The friction, existing between the fluid and pipe wall, and on the interface of two phases, was especially taken into account. A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe. The effect of pipe diameter on the transition was also studied. The results show that this approach gives a reasonable prediction over the whole range of flow rates, and better agreement has been achieved between predicted and measured critical parameters. __________ Translated from Journal of Shanghai Jiaotong University, 2006, 40(10): 1782–1785, 1789 [译自: 上海交通大学学报]     

Investigation of flow boiling in horizontal tubes: Part I—A new diabatic two-phase flow pattern map

Several important modifications to the flow pattern map of Kattan-Thome-Favrat [J. Heat Transfer 120(1) (1998) 140-147] made, resulting in a significantly new version of the map. Based on the dynamic void fraction measurements described in [Int. J. Multiphase Flow 30 (2004) 125-137], the stratified-wavy region has been subdivided into three subzones: slug, slug/stratified-wavy and stratified-wavy. Furthermore, annular-to-dryout and dryout-to-mist flow transition curves have been added and integrated into the new flow pattern map, identified by distinct trends of the heat transfer coefficient as a function of vapor quality and by flow pattern observations to determine (and then predict) the inception and completion of dryout in horizontal tubes.     

Modified theoretical models of film condensation in horizontal microfin tubes

The previously proposed theoretical models of film condensation in horizontal microfin tubes have been modified to describe the characteristics of condensing two-phase flow more accurately. The stratified flow regime and the annular flow regime were considered. For the stratified flow regime, the previously proposed theoretical model was modified to take account of the curvature of stratified condensate due to the surface tension force. For the annular flow regime, a more accurate expression for the interfacial shear stress was incorporated. Generally, the modified theoretical models predicted a lower circumferential average heat transfer coefficient than the previously proposed ones. Comparison of the theoretical predictions with available experimental data for six tubes and five refrigerants revealed that a good agreement (r.m.s error of less than 21.1%) was obtained for all cases when the higher of the two theoretical predictions were adopted as the calculated value.     

Traveling void wave in horizontal two-phase flow

In the framework of pattern dynamics approach, the discrete bubble model was developed for simulating inherent fluctuation of void fraction in a horizontal two-phase flow. Then flow patterns were identified based on the statistical properties of void fraction fluctuation, and the flow pattern map agreed with the experimental observation of high-pressure two-phase flow of CO₂ in horizontal tubes. The time-averaged pressure drop and the void fraction obtained in the simulation agreed reasonably with the existing correlations. Thus the horizontal flow version of the discrete bubble model demonstrates its relevance in simulating inherent fluctuation of two-phase flow.     

Numerical simulation of R410A condensation in horizontal microfin tubes

The heat transfer characteristics of condensation for R410A inside horizontal microfin tubes with 0° and 18° helical angles were investigated numerically. The numerical data fit well with the experimental results and with the empirical correlations. The results indicate that local heat transfer coefficients increase with increasing mass flux, vapor quality, and helical angle. The heat transfer enhancement in the helical microfin tubes is more pronounced at higher mass flux and vapor quality. The centrifugal force induced by the microfin with a 18° helical angle tends to spread the liquid from the bottom to the top, leading to a nearly symmetrical liquid–vapor interface during condensation. Swirling flows in the liquid phase are observed in the tube with the 18° helical angle, but the liquid phase tends to flow to the bottom due to gravity in the tube with the 0° helical angle.     

Numerical study of condensation flow regime transition in wavy microchannels

A numerical research on flow regime transition in wavy microchannels was conducted. The model was based on the volume of fluid approach and user-defined routines including interfacial mass transfer and latent heat. The observed droplet flow, annular–wavy flow, injection flow, and slug–bubbly flow were qualitatively compared against experimental data and transition lines were established. The effects of inlet vapor velocity, wall heat flux, and microchannel geometry characteristics on the annular length, occurrence frequency of injection flow, initial slug volume, and bubble detachment frequency were investigated.     

Numerical modeling of two-phase refrigerant flow through adiabatic capillary tubes

Literature shows that the homogeneous flow assumption has been commonly used in most of the adiabatic capillary tube modeling studies due to its simplicity. The slip effect between the two phases was often not considered in this small diameter capillary tube. This paper attempts to exploit the possibility of applying the equilibrium two-phase drift flux model to simulate the flow of refrigerant in the capillary tube expansion devices. Attempts have been made to compare predictions with experimental results. The details flow characteristics of R134a in a capillary tube, such as distribution of pressure, void fraction, dryness fraction, phase’s velocities and their drift velocity relative to the center of the mass of the mixture are presented.     

Development of a diabatic two-phase flow pattern map for horizontal flow boiling

An improved two-phase flow pattern map is proposed for evaporation in horizontal tubes. Based on new flow pattern data for three different refrigerants covering a wide range of mass velocities, vapor qualities and heat fluxes. The new flow pattern map includes the prediction of the onset of dryout at the top of the tube during evaporation inside horizontal tubes as a function of heat flux and flow parameters and is an extension to the flow pattern map model of Kattan et al. [J. Heat Transfer 120 (1998) 140]. The proposed modifications allow an accurate prediction of the flow pattern for very different fluids which are the substitute refrigerants (HFC-134a and HFC-407C) and the natural refrigerant R-717 (ammonia).     

Pressure drop increase of forced convective condensation inside horizontal coiled wire inserted tubes

An experimental study was performed to investigate the increment of the pressure drop during condensation of R-134 a vapor inside a horizontal tube with different coiled wire inserts. A double-pipe counter-flow heat exchanger of 1040-mm length was used as the test condenser while, the refrigerant flowed inside the inner tube and the coolant flowed in the annulus. Four coiled wires of 10.0-mm pitch and different diameters of 0.5, 0.7, 1.0 and 1.5-mm and also four springs of 1.0-mm diameter and different pitches of 5, 8, 10 and 13-mm were inserted on the refrigerant side of the test condenser. Data were recorded for different mass flow rates in plain tube and each coiled wire inserted tube. Investigating the results for the coiled wire inserted tubes revealed that inserting the springs increased the pressure drop in a range of 260 to 1600% in comparison with that for a plain tube. Also, influence of coiled wire geometry on the pressure drop was investigated. Based on the collected data, an empirical correlation was developed to predict the pressure drop during the condensation inside a horizontal tube in the presence of a spring insert. Finally, the performance evaluation of the coiled wire inserted condensers was done.