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.     

Flow boiling in horizontal flattened tubes: Part I – Two-phase frictional pressure drop results and model

Experiments of diabatic two-phase pressure drops in flow boiling were conducted in four horizontal flattened smooth copper tubes with two different heights of 2 and 3 mm. The equivalent diameters of the flat tubes are 8.6, 7.17, 6.25, and 5.3 mm. The working fluids are R22 and R410A, respectively. The test conditions are: mass velocities from 150 to 500 kg/m² s, heat fluxes from 6 to 40 kW/m² and saturation temperature of 5 °C (reduced pressures p_r are 0.12 for R22 and 0.19 for R410A). The experimental results of two-phase pressure drops are presented and analyzed. Furthermore, the predicted two-phase frictional pressure drops by the flow pattern based two-phase pressure drop model of Moreno Quibén and Thome [J. Moreno Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, Part I: Diabatic and adiabatic experimental study, Int. J. Heat Fluid Flow 28 (2007) 1049–1059; J. Moreno Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, Part II: New phenomenological model, Int. J. Heat Fluid Flow 28 (2007) 1060–1072] using the equivalent diameters were compared to the experimental data. The model, however, underpredicts the flattened tube two-phase frictional pressure drop data. Therefore, correction to the annular flow friction factor was proposed for the flattened tubes and now the method predicts 83.7% of the flattened tube pressure drop data within ±30%. The model is applicable to the flattened tubes in the test condition range in the present study. Extension of the model to other conditions should be verified with experimental data.     

Pressure drop studies on two-phase flow in a uniformly heated vertical tube at pressures up to the critical point

Measurements of two-phase flow pressure drop have been made during a phase-change heat transfer process with refrigerant (R-134a) as a working fluid for a wide range of pressures right up to the critical pressure. The experiments were conducted in a uniformly heated vertical tube of 12.7 mm internal diameter and 3 m length over a heat flux range of 35–80 kW/m², mass flux range of 1200–2000 kg/m² s, exit quality range of 0.19–0.81 and for reduced pressures ranging from 0.24 to 1 with a fixed inlet subcooling of 3 °C. The measurements were compared with the predictions from the homogeneous flow model, a separated flow model using correlations drawn from the literature for void fraction and frictional pressure drop, and finally, using a flow pattern-based predictive method accounting specifically for bubbly, slug and annular flow regimes. It was found that the best results were obtained with the flow pattern-based approach with a mean deviation of ±20% over the entire pressure range.     

Ammonia two-phase flow in a horizontal smooth tube: Flow pattern observations,diabatic and adiabatic frictional pressure drops and assessment of prediction methods

The present study illustrates new experimental two-phase flow pattern observations together with diabatic boiling and adiabatic two-phase frictional pressure drop results for ammonia (R717) flowing inside a 14-mm internal diameter, smooth horizontal stainless steel tube. The flow pattern observations were made for mass velocities of 50, 100 and 160 kg s^?1 m^?2 and saturation temperatures of ?14, ?2 and 12 °C for vapor qualities ranging from 0.05 to 0.6. The flow patterns observed during the study included: stratified-wavy, slug-stratified-wavy, slug, intermittent and annular. For all the experimental conditions, the flow structure observations were compared against the predictions of the flow pattern map model of Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes: part I – a new diabatic two-phase flow pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955–2969] and showed very good correspondence. The frictional pressure drop measurements were obtained for vapor qualities from 0.05 to 0.6, saturation temperatures from ?14 to 14 °C, mass velocities from 50 to 160 kg s^?1 m^?2 and heat fluxes from 12 to 25 kW m^?2. The experimental results show the traditional pressure drop trends: the frictional pressure drop increases with vapor quality and mass velocity. Moreover, the results also show that both diabatic and adiabatic frictional pressure drop values are similar, that is, the boiling process in itself does not affect the frictional pressure drop. The correlations of Friedel [L. Friedel, Improved friction drop correlations for horizontal and vertical two-phase pipe flow, in: European Two-Phase Flow Group Meeting, paper E2, Ispra, Italy, 1979], Lockhart and Martinelli [R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal two-phase two-component in pipes, Chem. Eng. Process 45 (1949) 39–48] and Müller-Steinhagen and Heck [H. Müller-Steinhagen, K. Heck, A simple friction pressure correlation for two-phase flow in pipes, Chem. Eng. Process 20 (1986) 297–308] predicted only 54%, 52% and 60% of the experimental data within ±30%, respectively. The correlation of Grönnerud [R. Grönnerud, Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type of evaporators, part iv: two-phase flow resistance in boiling refrigerans, in: Annexe 1972-1, Bull. de l’Inst. Froid, 1979] predicted 93% of the data and the flow pattern based method of Moreno Quibén and Thome [J. Moreno Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes. Part II: new phenomenological model, Int. J. Heat Fluid Flow 28 (2007) 1060–1072] predicted more than 97% of the experimental data within the same error band, while the latter method captures almost 89% of the data within ±20%.     

An experimental investigation on pressure drop of steam condensing in silicon microchannels

Experiments are carried out to study the two-phase pressure drop for water vapor condensation in four smooth trapezoidal silicon microchannels having hydraulic diameters of 109 μm, 142 μm, 151 μm, and 259 μm, respectively. It is found that two-phase frictional pressure drops in the microchannels are greatly influenced by the hydraulic diameter, mass flux and vapor quality. The two-phase pressure drop data in microchannels are compared with existing correlations for macro- and mini-channels based on the homogenous model and the separated flow model to determine their applicability to condensing flows in microchannels. A modified correlation for the Matinelli–Chisholm constant, taking into consideration of surface tension and diameter effects, is developed in the form of the Lockhart–Martinelli correlation for the pressure drop in steam condensation in microchannels. The resulting condensation pressure drop correlation equation is within ±15% of the experimental data.     

Two-phase flow in converging and diverging microchannels with CO2 bubbles produced by chemical reactions

The present study investigates experimentally the evolution of two-phase flow pattern and pressure drop in the converging and diverging, silicon-based microchannels with mean hydraulic diameter of 128 μm and CO₂ bubbles produced by chemical reactions of sulfuric acid (H₂SO₄) and sodium bicarbonate (NaHCO₃). Three different concentrations of 0.2, 0.5 and 0.8 mol/L of each reactant at the inlet before mixing and 10 different flow rates from 1.60 × 10⁻⁹ m³/s to 16.0 × 10⁻⁹ m³/s are studied. Flow visualization is made possible by using a high-speed digital camera. It is found that the present design of the microchannel, with the inlet chamber, results in much more intensive chemical reactions in the diverging microchannel than that in the converging one. The void fractions at the entrance and exit regions and pressure drop through the channel are also measured. The results reveals that the presence of small void fraction, <0.1, at the inlet may promote CO₂ generation in the microchannel, irrespective of the channel is converging or diverging, indicating the agitation effects of bubbly flow in the microchannel. The increase of inlet concentration of reactants does not increase the pressure drop in the converging microchannel significantly, while the inlet concentration presents significant but mild effects on the pressure drop in the diverging microchannel. The two-phase frictional multiplier may be positively correlated with the mean void fraction in the channel linearly, and the data agree well with predictions from the correlations in the literature.     

Adiabatic two-phase flow in rectangular microchannels with different aspect ratios: Part I – Flow pattern,pressure drop and void fraction

An aspect ratio is an important parameter for two-phase flow in a rectangular microchannel. To study the aspect ratio effect on the flow pattern, pressure drop and void fraction, experiments of adiabatic liquid water and nitrogen gas two-phase flow in rectangular microchannels were conducted. The widths and heights of rectangular microchannels are 510 μm × 470 μm, 608 μm × 410 μm, 501 μm × 237 μm and 503 μm × 85 μm. Therefore, the aspect ratios of the rectangular microchannels are 0.92, 0.67, 0.47 and 0.16; and the hydraulic diameters of the rectangular microchannels were 490, 490, 322 and 143 μm, respectively. Experimental ranges were liquid superficial velocities of 0.06–1.0 m/s and gas superficial velocities of 0.06–71 m/s. Visible rectangular microchannels were fabricated using a photosensitive glass. And pressure drop in microchannels was directly measured through embedded ports. The visualization of the flow pattern was carried out with a high-speed camera and a long distance microscope. Typical flow patterns in the rectangular microchannels observed in this study were bubble flow, transitional flow (multiple flow) and liquid ring flow. As the aspect ratio decreased, the bubble flow regime became dominant due to the confinement effect and the thickness of liquid film in corner was decreased. A void fraction in the rectangular microchannels has a linear relation with the volumetric quality. And the two-phase flow becomes homogeneous with decreasing aspect ratio owing to the reduction of the liquid film thickness. Like Zhang et al.’s [19] correlation, as the confinement number increased, the C-value in Lockhart and Martinelli correlation decreased. And a frictional pressure drop in the rectangular microchannels was highly related with the flow pattern.     

Thermo-hydraulic predictions for multi-pass evaporators by orthogonal collocation using a new flow pattern map

A recently published paper by this author [S. Thyageswaran, Analysis of multi-pass evaporators using orthogonal collocation, Int. J. Refrigeration doi:10.1016/j.ijrefrig.2007.06.011 (in press)], shows that orthogonal collocation is an effective alternative to traditional integration for the thermal analysis of multi-pass evaporators. The steady rate of heat exchanged (Q) and overall pressure drop (Δp), for an R-22 based chiller having one shell and eight tube passes, were predicted using the Kattan–Thome–Favrat and the Müller-Steinhagen and Heck models for the boiling R-22. While Q was over-predicted by 0.95%, Δp was over-predicted by 20.3%. In the present work, results have been obtained using state-of-the-art, unified heat transfer and pressure drop sub-models based upon an improved flow pattern map by Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes, part 1: a new diabatic two-phase flow pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955–2969; L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes, part 2: development of a new heat transfer model for stratified-wavy, dryout and mist flow regimes, Int. J. Heat Mass Transfer 48 (2005) 2970–2985], and Moreno Quibén and Thome [J.M. Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, part 1: diabatic and adiabatic experimental study, Int. J. Heat Fluid Flow 28 (5) (2007) 1049–1059; J.M. Quibén, J.R. Thome, Flow pattern based two-phase frictional pressure drop model for horizontal tubes, part 2: new phenomenological model, Int. J. Heat and Fluid Flow 28 (5) (2007) 1060–1072]. The new predictions for Q and Δp are 141.76 kW and 13.3 kPa, respectively, compared to their rated values of 140.67 kW and 13.789 kPa.     

Flow condensation in parallel micro-channels – Part 1: Experimental results and assessment of pressure drop correlations

In this first part of a two-part study, experiments were performed to investigate condensation of FC-72 along parallel, square micro-channels with a hydraulic diameter of 1 mm and a length of 29.9 cm, which were formed in the top surface of a solid copper plate. The condensation was achieved by rejecting heat to a counter flow of water through channels brazed to the underside of the copper plate. The FC-72 entered the micro-channels slightly superheated, and operating conditions included FC-72 mass velocities of 68–367 kg/m² s, FC-72 saturation temperatures of 57.2–62.3 °C, and water mass flow rates of 3–6 g/s. Using high-speed video imaging and photomicrographic techniques, five distinct flow regimes were identified: smooth-annular, wavy-annular, transition, slug, and bubbly, with the smooth-annular and wavy-annular regimes being most prevalent. A detailed pressure model is presented which includes all components of pressure drop across the micro-channel. Different sub-models for the frictional and accelerational pressure gradients are examined using the homogenous equilibrium model (with different two-phase friction factor relations) as well as previous macro-channel and mini/micro-channel separated flow correlations. Unexpectedly, the homogenous flow model provided far more accurate predictions of pressure drop than the separated flow models. Among the separated flow models, better predictions were achieved with those for adiabatic and mini/micro-channels than those for flow boiling and macro-channels.     

Theoretical model for annular flow condensation in rectangular micro-channels

This study examines the pressure drop and heat transfer characteristics of annular condensation in rectangular micro-channels with three-sided cooling walls. A theoretical control-volume-based model is proposed based on the assumptions of smooth interface between the annular liquid film and vapor core, and uniform film thickness around the channel’s circumference. Mass and momentum conservation are applied to control volumes encompassing the liquid film and the vapor core separately. The model accounts for interfacial suppression of turbulent eddies due to surface tension with the aid of a new eddy diffusivity model specifically tailored to shear-driven turbulent films. The model predictions are compared with experimental pressure drop and heat transfer data for annular condensation of FC-72 along 1 × 1 mm² parallel channels. The condensation is achieved by rejecting heat to a counterflow of water. The data span FC-72 mass velocities of 248–367 kg/m² s, saturation temperatures of 57.8–62.3 °C, qualities of 0.23–1.0, and water mass flow rates of 3–6 g/s. The data are also compared to predictions of previous separated flow mini/micro-channel and macro-channel correlations. While some of the previous correlations do provide good predictions of the average heat transfer coefficient, they fail to capture axial variation of the local heat transfer coefficient along the channel. The new model accurately captures the pressure drop and heat transfer coefficient data in both magnitude and trend, evidenced by mean absolute error values of 3.6% and 9.3%, respectively.     

Influence of oil on R-410A two-phase frictional pressure drop in a small U-type wavy tube

This study presents single-phase and two-phase pressure drop data with oil concentration C = 0, 1, 3 and 5% in a copper wavy tube having an inner diameter of 3.25 mm and a curvature radius of 6.35 mm. The ratio of frictional factor between U-bend in wavy tube and straight tube (f_C/f_S) is about 1.5 to 2.5 for Re = 2500 ∼ 25000. The effect of secondary flow is very crucial in the U-bend that it increases the pressure drop considerably. However, the effect of oil concentration on friction factor is negligible provided the properties are based on mixture. The ratio between two-phase pressure gradients of U-bend and straight tube is about 3. This ratio is increased with oil concentration and vapor quality. The oil effect on two-phase pressure drop is especially pronounced at high vapor quality because the effective oil concentration in liquid mixture is increased with vapor quality. The frictional two-phase multiplier for straight tube can be fairly correlated by using the Chisholm correlation. A modified two-phase friction factor based on the Geary correlation is also utilized to predict the frictional two-phase pressure gradient in U-bend. The predictions give a good agreement to the present oil–refrigerant data with a mean deviation of 12.92%.     

Numerical study of microchannel heat sink performance using nanofluids

This study presents the numerical simulation of three-dimensional incompressible steady and laminar and turbulent fluid flow of a trapezoidal micro-channel heat sink (MCHS) using CuO/water nanofluid as a cooling fluid. Navier–Stokes equations with conjugate energy equation are discretized by the finite-volume method. CFD predictions of laminar and turbulent forced convection of CuO/water nanofluids by single-phase and two-phase models (mixture model) are compared. The parameters studied include the particle volume fraction (ϕ = 0.204 %, 0.256%, 0.294% and 0.4%), and the volumetric flow rate ($\dot{\mathit{V}}=10\mathrm{mL}/min$, 15 mL/min and 20 mL/min). Comparisons of the thermal resistance predicted by the single-phase and two-phase models with corresponding experimental results show that the two-phase model is more accurate than the single-phase model. In the laminar flow, the thermal resistance of nanofluids is smaller than that of the water, which decreases as the particle volume fraction and the volumetric flow rate increase. In addition, the pressure drop of both nanofluid-cooled MCHS and pure water-cooled MCHS is discussed. For the laminar flow case, the pressure drop increases slightly for nanofluid-cooled MCHS.     

Prediction of frictional pressure drop of R134a during condensation inside smooth and corrugated tubes

In the present paper, in order to understand the accuracy of 38 different correlations derived by various researchers in this field, the correlations were executed for condensation frictional pressure drop. To accomplish this goal, experimental data provided from authors' previous publications encompassing 412 points for two smooth tubes, and 334 points for five corrugated tubes, have been utilized so as to compare the determined results. The experimental setup is composed of a 2.5 m double tube for horizontal configuration and smooth and corrugated tubes at the inner diameters of 0.0081 m, while the applied mass flux range spans between 709 and 1974 kg m^− 2 s^− 1. The average quality of vapor and saturation pressure ranges lie within 0.09 to 0.97, and 10 to 13 bar, respectively. Determining the frictional pressure drop in two-phase flows does not involve corrugated tube geometry in the calculation of friction factor, to make this available, a slight alteration that requires the replacement of a correlation with another one in the literature was suggested with regard to friction factor approach. As a result of this, it was noticed that performances of some correlations were optimized to predict the frictional pressure drop in corrugated tubes. Additionally, the most effective correlations have been selected for the horizontal double pipe heat exchanger having smooth and corrugated tubes. Finally, alteration of the condensation pressure drop with Reynolds number are presented using both experimental data and best predictive correlations.     

Numerical prediction of airfoil characteristics in a transonic droplet-laden air flow

A transonic airfoil moving in an air–water droplet two-phase flow is investigated numerically to study the effect of droplet size and volume fraction. The droplets we consider are in the size 1–100 μm and the volume fraction is in 0.01%–10%. A compressible two-fluid model is solved by the WAF-HLL scheme developed earlier by the authors which includes drag force, heat transfer, phase change, and droplet fragmentation of the droplets. The numerical results show that the droplet breakup layer can be extended to a later distance as large as about 60% of a chord length at the trailing edge. Also the droplets have made the shock wave dissolved in compression waves and the airfoil performance seriously deteriorated.     

Investigation on the void fraction of gas–liquid two-phase flows in vertically-downward pipes

A special experimental loop is designed and constructed to study the characteristics of the void fraction of gas–liquid two-phase flow in vertically-downward pipes. The test section is made of transparent pipe with a length of 6 m and an internal diameter of 25 mm. The void fraction ranging from 0.1 to 0.98 widely is measured using quick-closing valve method. It is found that the range of the void fraction could be divided into three regions with different flow patterns and different relationships between the void fraction and the gas–liquid volumetric flow rate ratio. Moreover, 39 correlations for calculating the void fraction collected from present literature, are classified, and evaluated using the experimental data obtained in this study. The prediction of correlations in the literature needs to be improved when the void fraction is small.     

Detection of two-phase flow patterns using the recurrence network analysis of pressure drop fluctuations

The two-phase flow (water–air) occurring in the square minichannel (3 × 3 mm) has been analysed. In the minichannel it has been observed: flow of grouped isolated bubbles, flow of confined bubbles, flow of elongated bubbles, slugs flow and semi-annular flow. The time series of pressure drop fluctuations was analysed using the analyses of traditional recurrence quantification and recurrence network. The two coefficients: recurrence period density entropy and transitivity have been used for identification of differences between the dynamics of two-phase flow patterns. The algorithm which has been used normalizes the analysed time series before calculating the recurrence plots. Despite the neglect of quantitative signal characteristics the analysis of its dynamics allows us to identify the two-phase flow patterns. This confirms that this type of analysis can be used to identify the two-phase flow patterns in minichannels.     

Evaluation of the performance of the empirical correlations used to predict R134a's boiling frictional pressure drop inside smooth and corrugated tubes

Owing to the generalization problem, there aren't sufficient empirical correlations for two-phase flows. So as to investigate the thermal features of the two-phase flow in smooth and enhanced tubes, a suitable procedure of the models and correlations related with the heat transfer coefficients, friction factors and two-phase multipliers are needed because a significant variation in thermal properties happens during phase-change. Comparison of frictional pressure drop of R134a during flow boiling phenomena occurred in a smooth and 5 enhanced tubes with well-known empirical correlations were performed in this study. The apparatus has 0.85 m long double tube for vertical configuration as a test section that includes smooth and corrugated copper tubing having inner diameters of 0.0087 m, and the range of mass fluxes are between 200 and 400 kg m^− 2 s^− 1. The average vapor qualities vary from 0.14 to 0.86, and saturation pressure interval is between 4.5 and 5.7 bar. The mean boiling heat transfer coefficient of R134a is determined via energy balance in the test section. The estimation performance of 36 empirical correlations in literature proposed for convective boiling flows in smooth and corrugated tubes are evaluated by means of authors' database (350 data points for vertical tubes). Boiling trend lines have been plotted for the change of vapor quality, liquid phase Reynolds numbers with gas phase ones. In addition, the most successful correlations are confirmed their predictabilities for the vertical adjusted evaporator having smooth and corrugated tubes using the database of authors' earlier publications in open sources.     

Correlation of critical heat flux and two-phase friction factor for subcooled convective boiling in structured surface microchannels

Critical heat flux (CHF) and pressure drop of subcooled flow boiling are measured for a microchannel heat sink containing 75 parallel 100 μm × 200 μm structured surface channels. The heated surface is made of a Cu metal sheet with/without 2 μm thickness diamond film. Tests and measurements are conducted with de-ionized water, de-ionized water +1 vol.% MCNT additive solution, and FC-72 fluids over a mass velocity range of 820–1600 kg/m² s, with inlet temperatures of 15(8.6)°C, 25(13.6)°C, 44(24.6)°C, and 64(36.6)°C for DI water (FC-72), and heat fluxes up to 600 W/cm². The CHF of subcooled flow boiling of the test fluids in the microchannels is measured parametrically. The two-phase pressure drop is also measured. Both CHF and the two-phase friction factor correlation for one-side heating with two other side-structured surface microchannels are proposed and developed in terms of the relevant parameters.     

The pressure drop in microtubes and the correlation development

This study investigated the pressure drop characteristics in microtubes using R-134a as a test fluid. The test tubes were the circular stainless steel tubes with inner diameters of 0.244, 0.430, and 0.792 mm. Although some of the existing studies reported the early flow transition at the Reynolds number of less than 1000, it was not found in the single-phase flow pressure drop tests. The conventional theory predicted the friction factors well within an absolute average deviation of 8.9%. The two-phase flow pressure drop increased with increasing quality, increasing mass flux, and decreasing tube diameter. The existing correlations failed to predict the two-phase friction multipliers in the microtubes of this study. A new correlation to predict the two-phase flow pressure drop in microtubes was developed in the form of the Lockhart–Martinelli correlation. It includes the effect of the tube diameter, surface tension effect, and the effect of the Reynolds number on the two-phase flow pressure drop in microtubes. The new correlation developed in this study predicted the experimental data within an absolute average deviation of 8.1%.     

Measurement and modeling of liquid film thickness evolution in stratified two-phase microchannel flows

Polymer electrolyte membrane (PEM) fuel cells incorporating microchannels (D < 500 μm) can benefit from improved fuel delivery and convective cooling. However, this requires a better understanding of two-phase microchannel transport phenomena, particularly liquid–gas interactions and liquid clogging in cathode air-delivery channels. This paper develops optical fluorescence imaging of water films in hydrophilic channels with varying air velocity and water injection rate. Micromachined silicon test structures with optical access and distributed water injection simulate the cathode channels of a PEM fuel cell. Film thickness data vary strongly with air velocity and are consistent with stratified flow modeling. This work facilitates the study of regime transitions in two-phase microchannel flows and the effects of flow regimes on heat and mass transfer and axial pressure gradients.