Adiabatic two-phase flow in rectangular microchannels with different aspect ratios: Part II – bubble behaviors and pressure drop in single bubble

One of the major flow patterns in a microchannel is an elongated bubble flow, which is similar to a long slug bubble. Behaviors and pressure drop for a single bubble in a rectangular microchannel were studied. Based on the experiments in Part I of this paper, data for liquid superficial velocities of 0.06–0.8 m/s, gas superficial velocities of 0.06–0.66 m/s and AR of 0.92, 0.67, 0.47 and 0.16 were analyzed. The velocity, length, number, and frequency of the single bubble in the rectangular microchannel were obtained from image processing based on a unit cell model. The bubble velocities were proportional to total superficial velocity. As the aspect ratio decreased, the portion of the bubble area increased due to the corner effect. New correlation of the bubble velocity for different aspect ratio was proposed. Also, bubble and liquid slug length, the number of the unit cell and bubble frequency were analyzed with different aspect ratios. The pressure drop for the single bubble in the rectangular microchannels was evaluated using the information of the bubble behavior. The pressure drop in the single elongated bubble was proportional to the bubble velocity. The pressure drop in the single elongated bubble in the rectangular microchannel increased as the aspect ratio decreased.     

Effect of Channel Length on the Gas–Liquid Two-Phase Flow Phenomena in a Microchannel

An optical measurement system was used to investigate the effect of microchannel length and inlet geometery on adiabatic gas–liquid two-phase flow. Experiments were conducted with 146-mm- and 1571-mm-long, circular microchannels of 100 μm diameter. Void fraction and gas and liquid plug/slug lengths and their velocities were measured for two inlet configurations for gas–liquid mixing: (a) reducer and (b) T-junction. The superficial gas velocity was varied from 0.03 to 14 m/s, and superficial liquid velocity from 0.04 to 0.7 m/s. The test section length was found to have a significant effect on the two-phase flow characteristics measured at the same axial location (37 mm from the inlet) in both microchannels. The mean void fraction data for the short (146 mm) microchannel with the reducer inlet agreed well with the equation previously proposed by Kawahara et al. (2002). On the other hand, the mean void fraction data for the long (1571 mm) microchannel obeyed the homogeneous flow model and Armand's equation for both the reducer and T-junction inlet configurations. Many long and rapidly moving gas plugs/slugs and long, slowly moving liquid plugs/slugs were observed in the short microchannel compared to the long microchannel, leading to the differences in the time-averaged void fraction data. The mean velocity of liquid plugs/slugs generally agreed well with Hughmark's equation and the homogeneous flow model predictions, regardless of the inlet configurations and microchannel lengths. Thus, both the microchannel length and inlet geometry were found to significantly affect the two-phase flow characteristics in a microchannel.     

Gas–Liquid Two-Phase Flow Evolution in a Long Microchannel

A pair of optical void sensors and a high-speed video camera were used to investigate the evolution of adiabatic gas–liquid two-phase flow in a long microchannel. Experiments were conducted with a 1676-mm-long, circular microchannel with an inner diameter of 100 μm. Two-phase flow patterns, void fraction, and velocities of gas plug/slug and liquid slugs were measured at different axial locations between the gas–liquid mixer and microchannel exit. The pressure decreased linearly in the first half of the microchannel, and more rapidly and nonlinearly in the second half of the test section. As a result, the flow accelerated significantly in the second half of the microchannel such that the void fraction and liquid slug velocity increased nonlinearly. The measured mean void fraction and mean velocity of liquid slugs also agreed well with the homogeneous flow model predictions when the liquid flow rate was constant and the mass velocity of the gas was low.     

ADIABATIC GAS–LIQUID FLOW IN MICROCHANNELS

This article presents a review of adiabatic two-phase flow in minichannels and microchannels. Differences between them are identified and explained based on this review and our own research. Several channels of decreasing diameter were used in our experiments to determine the effect of the channel size on the two-phase flow of nitrogen gas and water. The effect of channel geometry was examined by characterizing the two-phase flow in a circular and square microchannel of similar size. Only slug flow was observed in the microchannels. Four new sub-classes of slug flow were subsequently defined. A new correlation was developed for the time-averaged void fraction data in the microchannels. The two-phase pressure drop in microchannels was predicted by treating the two phases as being separate with a large velocity difference. Regarding the effect of microchannel geometry, the transition boundaries on the two-phase flow regime maps were shifted for the slug flow subcategories.     

Optical Measurement of Void Fraction and Bubble Size Distributions in a Microchannel

An optical measurement system was developed to investigate gas-liquid two-phase flow characteristics in a circular microchannel of 100 μ m diameter. By using multiple optical fibers and infrared photodiodes, void fraction, gas and liquid plug lengths, and their velocities were measured successfully. The probes responded to the passage of gas and liquid phases through the microchannel adequately so that the time-average void fraction could be obtained from the time fraction for each phase. Also, by cross-correlating the signals from two neighboring probes, the interface velocity representing gas plug velocity or ring-film propagation velocity depending on the flow pattern could be computed. Within the ranges of superficial gas and liquid velocities covered in the experiments (j _L = 0.2～0.4 m/s and j _G = 0～5 m/s), the gas plug length was found to increase with the increasing superficial gas velocity, but the liquid plug length was found to decrease sharply as the superficial gas velocity was increased; thus, the total length of the gas-liquid plug unit decreased with the superficial gas velocity.     

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.     

Experimental and numerical investigation of two-phase pressure drop in vertical cross-flow over a horizontal tube bundle

Experimental pressure drop data for vertical two-phase air–water flow across horizontal tubes is presented for gas mass fractions in the range 0.0005–0.6 and mass fluxes in the range 25–700 kg/m² s. The square in-line tube bundle had one column containing ten tubes and two columns of half tubes attached to the walls. The tubes had a diameter of 38 mm and a pitch to diameter ratio of 1.32. This data and air–water and R113 vapour–liquid data available in the literature are compared with the predictions from two kettle reboiler models, the one-dimensional model and a one-dimensional formulation of the two-fluid model. The one-dimensional model was implemented with three separate void fraction correlations and one two-phase friction multiplier correlation. The results show that the two-fluid model predicts air–water void fraction data well but R113 data poorly with pressure drop predictions for both being unsatisfactory. The one-dimensional model is shown to predict pressure drop and void fraction data reasonably well, provided a careful choice is made for the void fraction correlation.     

Numerical study on the formation of Taylor bubbles in capillary tubes

Numerical simulations have been carried out for the transient formation of Taylor bubbles in a nozzle/tube co-flow arrangement by solving the unsteady, incompressible Navier–Stokes equations. A level set method was used to track the two-phase interface. The calculated bubble size, shape, liquid film thickness, bubble length, drift velocity, pressure drop and flow fields of Taylor flow agree well with the literature data. For a given nozzle/tube configuration, the formation of Taylor bubbles is found to be mainly dependent on the relative magnitude of gas and liquid superficial velocity. However, even under the same liquid and gas superficial velocities, the change of nozzle geometry alone can drastically change the size of Taylor bubbles and the pressure drop behavior inside a given capillary. This indicates that the widely used flow pattern map presented in terms of liquid and gas superficial velocities is not unique.     

An investigation of two-phase flow pressure drop in helical rectangular channel

Numerical simulations have been carried out to evaluate the two-phase frictional pressure drop for air-water two-phase flow in horizontal helical rectangular channels by varying configurations, inlet velocity and inlet sectional liquid holdup. The investigations performed using eight coils, five different inlet velocity and four different inlet sectional liquid holdups. The effects of curvature, torsion, fluid velocity and inlet sectional liquid holdup on two-phase frictional pressure drop have been illustrated. It is found that the two-phase frictional pressure drop relates strongly to the superficial velocities of air or water, and that the curvature and torsion have some effect on the pressure drop for higher Reynolds number flows in large-scale helical rectangular channel; the inlet sectional liquid holdup only increases the magnitude of pressure drop in helical channel and has no effect on the development of pressure drop. The correlation developed predicts the two-phase frictional pressure drop in helical rectangular channel with acceptable statistical accuracy.     

Two-phase hydrodynamics in a miniature direct methanol fuel cell

We present controlled experiments on a miniature direct methanol fuel cell (DMFC) to study the effects of methanol flow rate, current density, and void fraction on pressure drop across the DMFC anode. We also present an experimental technique to measure void fraction, liquid slug length, and velocity of the two-phase slug flow exiting the DMFC. For our channel geometry in which the diameter of the largest inscribed sphere (a) is 500 μm, pressure drop scales with the number of gas slugs in the channel, surface tension, and a. This scaling demonstrates the importance of capillary forces in determining the hydrodynamic characteristics of the DMFC anode. This work is aimed at aiding the design of fuel pumps and anode flow channels for miniature DMFC systems.     

Effect of Void Fraction and Two-Phase Dynamic Viscosity Models on Prediction of Hydrostatic and Frictional Pressure Drop in Vertical Upward Gas–Liquid Two-Phase Flow

In gas–liquid two-phase flow, the prediction of two-phase density and hence the hydrostatic pressure drop relies on the void fraction and is sensitive to the error in prediction of void fraction. The objectives of this study are to analyze dependence of two-phase density on void fraction and to examine slip ratio and drift flux model-based correlations for their performance in prediction of void fraction and two-phase densities for the two extremes of two-phase flow conditions, that is, bubbly and annular flow or, alternatively, the low and high region of the void fraction. It is shown that the drift flux model-based correlations perform better than the slip ratio model-based correlations in prediction of void fraction and hence the two-phase mixture density. Another objective of this study is to verify performance of different two-phase dynamic viscosity models in prediction of two-phase frictional pressure drop. Fourteen two-phase dynamic viscosity models are assessed for their performance against 616 data points consisting of 10 different pipe diameters in annular flow regime. It is found that none of these two-phase dynamic viscosity models are able to predict the frictional pressure drop in annular flow regime for a range of pipe diameters. The correlations that are successful for small pipe diameters fail for large pipe diameters and vice versa.     

Determination of the void fraction and drift velocity in a two-phase flow with a boiling solar collector

This paper presents an approach to determine the void fraction and the drift velocity in a two-phase flow with a boiling solar collector using easily obtained experimental data. The solar collector operates in a thermal siphon circuit, where the working fluid absorbs solar radiation mostly while boiling. The vapor bubbles release their latent heat in a condenser, while heating up a flow of water–glycol. Two numerical procedures are developed to calculate the void fraction because its experimental values cannot be easily measured. The use of a flow meter causes an additional pressure drop in the thermal siphon circuit and, consequently, changes the circulated mass flow rate. The first numerical procedure is based on a force balance in the thermal siphon loop and is used to estimate the total mass flow rate and the void fraction in the circuit. The second uses a drift flux correlation to estimate the void fraction and the drift velocity. Both procedures use the experimental values for the vapor mass flow rate, which is determined by an energy balance in the condenser. The volumetric flow rate of the water–glycol mixture and its temperature difference across the condenser are experimentally measured. The pipe length of the two-phase flow in the solar collector is experimentally determined using 44 thermocouples attached to the back of flow channels in the absorber plate. The results show that the two numerical models compare well and that either one can be used to estimate the void fraction in the two-phase flow solar circuit.     

Void Fraction Variations in a Fractal-Like Branching Microchannel Network

Based on predictions of lower pressure drop penalties in fractal-like branching channels compared to parallel channels, an experimental investigation of two-phase void fraction variations was performed. The flow network, mimicking flow networks found in nature, was designed with a self-similar bifurcating channel configuration and etched 150 μ m into a 38.1 mm diameter silicon disk. A Pyrex® cover was anodically bonded to the silicon disk to allow for flow visualization. The length and width scale ratios between channels on either side of a bifurcation are fixed. The channel widths range in size from 100 μ m to 400 μm over a total channel length of approximately 17 mm. Experimental results of flow boiling are presented for a heater energy input power of 66 W and an inlet water flow rate of 45 g/min at a fixed inlet fluid temperature of 88°C. High-speed, high-resolution imaging was used to visualize the flow and quantify void fraction values in several channels within a branching structure. Both time-averaged and instantaneous two-dimensional void fraction data are presented, showing a correlation between channels at the same bifurcation level and between channels at different bifurcation levels.     

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.     

Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks – Part 2. Subcooled boiling pressure drop and heat transfer

This second part of a two-part study explores the performance of a new cooling scheme in which the primary working fluid flowing through a micro-channel heat sink is indirectly cooled by a refrigeration cooling system. The objective of this part of study is to explore the pressure drop and heat transfer characteristics of the heat sink. During single-phase cooling, pressure drop decreased with increasing heat flux because of decreased liquid viscosity. However, pressure drop began increasing with increasing heat flux following bubble departure. These opposite trends produced a minimum in the variation of pressure drop with heat flux. Increasing liquid subcooling decreased two-phase pressure drop because of decreased void fraction caused by strong condensation at bubble interfaces as well as decreased likelihood of bubble coalescence. It is shown macro-channel subcooled boiling pressure drop and heat transfer correlations are unsuitable for micro-channel flows. However, two new modified correlations produced good predictions of the present heat transfer data.     

Unsteady-state fluctuations analysis during bubble growth in a “rectangular” microchannel

Boiling in microchannels shows great potential for cooling systems and compact heat removal applications. However for confidence in this cooling technique, it is essential that any excursions from typical flow boiling are understood and predicted. Confined bubble growth can cause pressure fluctuations which interfere with bubble nucleation and growth and can also lead to flow reversal and instances of temperature excursions. Boiling experiments are performed in a single rectangular microchannel of hydraulic diameter 771 μm, using n-Pentane as the working fluid. A heating technique was incorporated on the exterior walls of the microchannel; a transparent, metallic, conductive deposit, which allows simultaneous uniform heating and visualisation to be achieved. In conjunction with obtaining high-speed imaging, an infrared camera is used to record the temperature profile at the microchannel wall, and sensitive pressure sensors are used to record the pressure drop across the microchannel over time. During flow boiling in the microchannel periodic and non-periodic fluctuations in both the channel pressure drop and channel temperature profile over time are apparent. In this paper we provide a full analysis of the temperature measurements and pressure data obtained during the growth of a vapour bubble in the microchannel. An augmentation of the heat transfer coefficient of over 216% has been achieved during periodic two-phase flow boiling in the microchannel. However overpressure (over 410% increase) in the microchannel occurs at corresponding instances to the heat transfer enhancement. The two time steps during the periodic bubble dynamics, namely the bubble expansion time period and the waiting time period in-between the bubble expansion fluctuations, are also investigated and modelled. It was determined that both the bubble dynamics and the channel wall heating time period are responsible for the pressure and temperature fluctuation time periods observed.     

Distribution parameter and drift velocity of drift-flux model in bubbly flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for bubbly flow regime. The constitutive equation that specifies the distribution parameter in the bubbly flow has been derived by taking into account the effect of the bubble size on the phase distribution, since the bubble size would govern the distribution of the void fraction. A comparison of the newly developed model with various fully developed bubbly flow data over a wide range of flow parameters shows a satisfactory agreement. The constitutive equation for the drift velocity developed by Ishii has been reevaluated by the drift velocity calculated by local flow parameters such as void fraction, gas velocity and liquid velocity measured under steady fully developed bubbly flow conditions. It has been confirmed that the newly developed model of the distribution parameter and the drift velocity correlation developed by Ishii can also be applicable to developing bubbly flows.     

Application of a two-phase flow model for natural convection in an electrochemical cell

A two-phase mathematical model is applied to natural convection in an electrochemical cell. The model solves transport equations for both phases with an allowance of interphase mass and momentum exchange. The effect of current density and bubble size on the gas release rate, velocity field and void fraction distribution are investigated in a range of parameter. The flow in the system was generated due to the density difference between gas and liquid phases. It is found that both current density and bubble size significantly affect the gas release rate and velocity field. At an intermediate current density two circulation patterns form at the vicinity of the free surface. The circulations rotating opposite directions enhance lateral diffusion of gas phase. The gas evolution is enhanced with higher current density and lower bubble diameters.     

Experimental Investigation and RELAP5 Modeling of Two-Phase Flow in Horizontal Rectangular Channel

The investigation of steam, water, and air flow characteristics in horizontal channel is a part of major investigations program at the Lithuanian Energy Institute. The objective of this program is to identify condensation effects on two-phase flow stability and to predict conditions when rapid condensation could be induced in two-phase condensable flow. This article presents investigation of steam–water and air multiphase flow in nearly horizontal rectangular channel. The experimental data for pressure drop and interfacial and wall shear stresses in the channel with uniform distribution of void fraction are presented in this paper. Overall channel dimensions are length = 1.2 m, width = 0.02 m, height = 0.1 m; however, the test section was about 0.84 m in length. Three different flow types were analyzed at atmospheric pressure: (1) single-phase air flow (height of the channel was reduced to 0.075 m); (2) non-condensable air–water two-phase flow at void fraction of 0.75; (3) two-phase steam–water flow at almost saturation conditions, and void fraction of 0.75. RELAP5 Mod3.3 code was selected to model test cases. Modeling results and experimental measurements show good agreement with each other. The developed model will be used for calculating different cases of the process.     

Condensation pressure drop characteristics of various refrigerants in a horizontal smooth tube

The two-phase pressure drop characteristics of the pure refrigerants R410a, R502, and R507a during condensation inside a horizontal tube-in-tube heat exchanger were investigated to determine the two-phase friction factor, the frictional pressure drop, and the total pressure drop. The two-phase friction factor and frictional pressure drop are predicted by means of an equivalent Reynolds number model. Eckels and Pate's experimental data, presented in Choi et al.'s study provided by NIST, were used in the analysis. In their experimental setup, the horizontal test section was a 3.81 m long countercurrent flow double tube heat exchanger with refrigerant flowing in the inner smooth copper tube (8.01 mm i.d.) and cooling water flowing in the annulus (13.7 mm i.d.). Their test runs were performed at saturated condensing temperatures from 38.33 °C to 51.78 °C while the mass fluxes were between 119 and 617 kg m⁻² s⁻¹ for the horizontal test section. The separated flow model was modified by ten different void fraction models and correlations, as well as six different correlations of friction factors, in order to determine the best combination for the validation of the experimental pressure drop values. Carey's friction factor was found to be the most predictive. The refrigerant side total and frictional pressure drops were determined within ± 30% using the above friction factor and the void fraction combinations of Carey, Baroczy, and Armand for R410a; and those of Carey, Spedding and Spence, and Rigot for R502 and R507a. The equivalent Reynolds number model was modified using the void fraction correlation of Rigot in order to determine the frictional condensation pressure drop and the two-phase friction factor. The effects of vapor quality and mass flux on the pressure drop are discussed in this paper. The importance of using the alternative void fraction and friction factor models and correlations for the separated flow model is also addressed.