Two-phase Multiplier Research Articles

Effect of wide reactant relative humidity on PEMFC electrochemical and thermodynamic performance from both global and local perspectives

For realizing high-power and high-efficiency operation of proton exchange membrane fuel cell (PEMFC), influence mechanism of relative humidity (RH) on the fuel cell performance was explored in this study. Combining experimental and simulation methods, the effect of wide gas humidification on the fuel cell output power and irreversible losses were comprehensively studied. Rising RH negatively influenced PEMFC electrochemical and thermodynamic properties at I=1.6 A/cm2. Humidification of the gas can lead to a maximum increase of 36%, 43% and 14.5% in cell exergy efficiency at I=0.2-0.4 A/cm2, I=0.4-1.2 A/cm2 and I=1.2-1.4 A/cm2, respectively. The effect of RH on the pressure drop at a wide current densities was identified using a two-phase multiplier, and further can be categorized into three zones. Electrochemical impedance spectroscopy (EIS) results showed that mass transfer losses and activation losses are keys to influence the characteristics of the above regions. Cathode catalyst layer (CCL) and proton exchange membrane (PEM) contributed more than 90% to thermal irreversible loss, whose entropy generation rates change is consistent with activation loss. These study results can provide theoretical support for the development of PEMFC with high output power and high exergy efficiency at wide gas humidification conditions.

New Two-Phase Multiplier Model for Phase-Change Flows in Plate Heat Exchangers

A complete thermo-hydraulic understanding of condensing and evaporating flows in heat exchangers requires predictive modeling and analysis of not just heat transfer but also the hydraulics of the flow. While modeling the friction factor and pressure gradient yields a quantitative understanding of the pressure drop, only the two-phase multiplier and void fraction, in combination with the Martinelli parameter, help better understand the relative contributions of the liquid and vapor fractions to the overall pressure drop. This article reports the empirical modeling, analysis, and meta-analysis of the two-phase multiplier for condensing and evaporating flows in plate heat exchangers. Over three thousand data compiled from forty-two sources were modeled using various regression techniques to develop correlations for predicting the two-phase multiplier for condensing and evaporating flows in plate heat exchangers. The Weber number for most studies was less than one, indicating that drop condensation and pool boiling were impossible. Further, the Bond number for most studies was also much higher than one, indicating that the buoyancy effects were significant during condensation and evaporation. Meta-analysis for evaporators was statistically significant and positive, strongly recommending plate heat exchangers.

Study of developing a condensation heat transfer coefficient and pressure drop model for whole reduced pressure ranges

This study involves the collection of data from 10 different articles to develop experimental-based models for predicting the condensation heat transfer and the frictional pressure drop. The dataset comprises a total of 1168 condensation heat transfer coefficients and 792 frictional pressure drop data. The applied operating range considered is within the reduced pressure of 0.1–0.95, mass flux ranging from 75 to 700 kg/m2s, and an inner diameter between 3.4 and 12.5 mm. We developed the models for the condensation heat transfer coefficient based on Akers et al.’s model, whose parameters are the Prandtl number, density ratio, vapor quality, and mass flux. The total error for the condensation heat transfer coefficient is ± 22.6%. The data is further categorized into two groups of the reduced pressure: Pr < 0.5 with an error of ± 22.9% and Pr > 0.5 with an error of ± 18.9%. The frictional pressure drop models were developed based on the three different ranges of the reduced pressure. The utilized non-dimensionless parameters were the two-phase multiplier (Φlo2), the Bond number (Bo), the Weber number (We), and the Martinelli parameter (Xtt), along with the regression coefficients. Regarding the frictional pressure drop correlation, the total error is ± 32.7%, and the data is divided into three segments: Pr < 0.2 with an error of ± 24.6%, 0.2 < Pr < 0.3 with an error of ± 35.6%, and an error of ± 27.8% for the reduced pressure larger than 0.3. These correlations were developed using the MATLAB regression analysis to enhance their practicality and utility.

Flow boiling pressure drop correlation in small to micro passages

An accurate and acceptable correlation for the prediction of two-phase pressure drop is considered a crucial step in heat exchanger design. Although many existing models and correlations were developed and proposed in the past, their ability to predict within acceptable error bands when applied in general to flow boiling flows is limited, even within their originally recorded ranges. The discrepancies are worse when predicting two-phase pressure drop in small to micro-scale passages. Therefore, the aim of the work described in this paper is to assess the most well-known models and correlations using a large experimental data-bank. The data-bank includes four refrigerants, namely R134a, R245fa, HFE-7100 and HFE-7200, small to micro heat exchangers made of different metals and different channel configurations. In addition, the data cover a large range of operating conditions, which can allow generally applicability of new correlations developed. This range covers channel hydraulic diameter of 0.46−4.26 mm, heated length of 20−500 mm, system pressure of 1 − 14 bar, mass flux of 50−700 kg/m2 s, wall heat flux ranging from 2 to 234 kW/m2 and exit vapour quality up to one. Twenty six existing models and correlations that were developed and proposed for vertical/horizontal flow, single/multi-channels and circular/non-circular channels were evaluated. Moreover, the effect of using different equations for calculating the two-phase mixture viscosity, void fraction, Fanning friction factor and Lockhart–Martinelli parameter was assessed and discussed. The mean absolute error of the existing correlations when compared with our data-bank was more than 30 %. Therefore, a new correlation for calculating the two-phase multiplier, which was strongly dependent on the Boiling number and the Lockhart–Martinelli parameter, was developed and then the frictional component and total two-phase pressure drop relationships were completed.

Experimental investigation of two-phase flow in Chevron-type compact plate heat exchangers: A Study on pressure drops and flow regimes visualization

Compact plate heat exchangers are a very promising technology and lately they are being considered for potential use as steam generators in Small Modular Reactors. However, there is a lack of scientific literature on their operation with two-phase flows, especially with non-refrigerant fluids. In this study, we conducted experiments to visualize and measure the pressure drop of a two-phase flow in a Chevron-type Plate Heat Exchanger. An air–water mixture was used in adiabatic conditions as the operating fluid in upward-flow configuration. Visualization was achieved through high-framerate videos. This study covers a wide range of operating conditions, surpassing those documented in existing literature by specifically analyzing also the region of very low mass flux for both phases. The tested conditions ranged from 6 to 365 kg/m2s of water and from 0.02 to 5 kg/m2s of air. Single-phase pressure drops were measured to establish a correlation for the Darcy friction factor. Instead, measurements of the pressure drop in two-phase conditions were processed and presented using a non-dimensional form referred to as the two-phase multiplier. The adoption of a void-fraction model played a crucial role in accurately extrapolating the frictional component of the pressure drop from the measurements, resulting in less scattered data on the Lockhart–Martinelli plot. In addition, the observed flow structures were categorized into distinct regimes (fine-coarse bubbly, Taylor-like bubbly, heterogeneous, partial film, and film flow) based on visual observation and were represented on a flow map. Finally, these data were used to develop new criteria for predicting flow pattern transitions.

PARAMETRIC STUDY AND DEVELOPMENT OF A CORRELATION FOR NUSSELT NUMBER IN NANOFLUID JET IMPINGEMENT

Numerical simulations for nanofluid ( water with Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; nanoparticles) jet impinging perpendicularly on a flat circular heated p late have been performed. A heated p late is subjected to constant heat flux boundary condition. A two-phase modified mixture mo del was used for the prediction of heat transfer coefficient, and comparisons are made with standard mixture model. Present results for average Nusselt number are validated with experimental data available in the literature. Though a standard mixture model predicted heat transfer with accepted accuracy, it was found that accuracy of modified mixture model is better (around 5&amp;#37; improvement) compared to standard mixture model. Thereafter, parametric study was performed considering nozzle exit Reynolds number (Re), spacing ratio (&lt;i&gt;H/D&lt;/i&gt;), nanoparticle volume fraction (&amp;phi;), and nanoparticle diameter (dp) on heat transfer prediction. The results reveal that particle diameter in the range 10-100 nm has no effect on the Nusselt number, Furthermore, heat transfer increased with increasing Reynolds number and volume fraction. However, spacing ratio shows first increasing and then, decreasing trend (similar to a log-normal distribution curve) in the prediction of heat transfer. Finally, a new correlation was developed for Nusselt number using nonlinear regression analysis. In the correlation, a two-phase multiplier was used, which is the ratio between two-phase Nusselt number (Nu&lt;sub&gt;nf&lt;/sub&gt; ) and single-phase Nusselt number (Nu&lt;sub&gt;sp&lt;/sub&gt;). The simplified correlation is found to predict data with maximum error of 8.9&amp;#37;, average error of 2.74&amp;#37; and &lt;i&gt;R&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; &amp;#61; 0.955.

Heat transfer model for downward two-component two-phase flows in inclined pipes

Downward two-component two-phase flows are commonly encountered in many chemical engineering applications. Accurate prediction of the heat transfer coefficient is of great importance to the design and operation of heat transfer systems. The mechanism of two-phase heat transfer is complicated because of the complex interactions between gas and liquid phases. Therefore, this study was aimed at developing a robust and theoretically supported heat transfer coefficient correlation for downward two-component two-phase flow in inclined pipes with the extended Chilton-Colburn analogy. First, an extensive literature review was performed to collect more than 1700 experimental data for downward two-phase heat transfer coefficients in inclined pipes and 10 heat transfer coefficient correlations. Poor predictive performance of the existing correlations was identified using the whole collected database. Then, the dependence of the heat transfer coefficient on void fraction and two-phase multiplier was analyzed using the extended Chilton-Colburn analogy. The dependence of the heat transfer coefficient on the pipe inclination angle was discussed in depth. The exponents in the newly-developed heat transfer coefficient correlation were correlated in terms of the pipe inclination angle. A robust and semi-theoretically supported correlation was developed for predicting the heat transfer coefficient of downward two-component two-phase flows in inclined pipes. The mean relative deviation (bias), mrel, and the mean absolute relative deviation (random uncertainty), mrel, ab, were −4.54 % and 13.8 %, respectively. The new heat transfer coefficient correlation will be of practical importance in understanding the two-component two-phase heat transfer characteristics.

Development of a one-dimensional system code for the analysis of downward air-water two-phase flow in large vertical pipes

In nuclear thermal-hydraulic system codes, most correlations used for vertical pipes, under downward two-phase flow, have been developed considering small pipes or pool systems. This suggests that there could be uncertainties in applying the correlations to accident scenarios involving large vertical pipes owing to the difference in the characteristics of two-phase flows, or flow conditions, between large and small pipes. In this study, we modified the Multi-dimensional Analysis of Reactor Safety KINS Standard (MARS-KS) code using correlations, such as the drift-flux model and two-phase multiplier, developed in a plant-scale air-inflow experiment conducted for a pipe of diameter 600 mm under downward two-phase flow. The results were then analyzed and compared with those based on previous correlations developed for small pipes and pool conditions. The modified code indicated a good estimation performance in two plant-scale experiments with large pipes. For the siphon-breaking experiment, the maximum errors in water flow for modified and original codes were 2.2% and 30.3%, respectively. For the air-inflow accident experiment, the original code could not predict the trend of frictional pressure gradient in two-phase flow as ⟨jg⟩/⟨j⟩ increased, while the modified MARS-KS code showed a good estimation performance of the gradient with maximum error of 3.5%.

A New Two-Phase Multiplier for Flow Pressure Drop in Multiport Minichannel Condensers and Evaporators

Due to flow maldistribution, the condensation and evaporation flow patterns in multiport minichannels are considerably different from single minichannels or macrochannels. This article compiled the friction pressure drop data from experimental phase-change investigations in multiport minichannel condensers and evaporators over the past two decades. The data was reduced to friction pressure gradients, and a new two-phase multiplier was proposed for estimating the phase-change pressure drop in multiport condensers and evaporators. Thirteen hundred and forty-four condensation pressure drop and six hundred and twenty-three evaporation pressure drop data from twenty-nine studies were correlated to yield four predictive two-phase multiplier equations in the laminar and turbulent flow regimes. The predictive correlations fit 67% of the laminar condensation and 80% of the turbulent pressure drop data within ±50%. Further, 57% of the laminar evaporation and 100% of the turbulent evaporation pressure drop data were fit within ±50%. The correlations were compared with widely published correlations and were a significant improvement. Meta-analysis revealed that multiport minichannels are most effective for reducing turbulent flow condensation pressure drop and laminar flow evaporation pressure drop. The compiled data and presented correlations and analysis should be helpful to the process, electronics packaging, aviation, and aerospace industries designing compact, lightweight, and high-efficiency condensers, and evaporators.

New flow boiling frictional pressure drop multipliers for smooth and microfin tubes

Abstract The accurate calculation of pressure drop of evaporators/condensers are crucial and related with the pumping power, performance coefficient and energy consumption in a refrigeration equipment. This work aligns frictional pressure drop models/correlations with the experimental outcomes of boiling pressure drop of R134a in horizontal smooth and microfin copper tubes with equivalent outer diameter of 9.52 mm. The pressure drop through the test tube is obtained with a differential pressure transducer directly. Effective parameters are specified for smooth and microfin tubes and the most compatible models/correlations, 12 for smooth tubes and 9 for microfin ones, are determined accurately in relation to the consequences of investigation during intermittent and annular flow regime. Moreover, new two-phase multipliers have been developed by using regression analyses of 182 data points based on Lockhart-Martinelli parameter for each test tubes separately, and their predictability are found to be better than others in the literature as novel ones. Average errors of the developed empirical correlations are 11% for smooth and for 7% for microfin tubes. Finally, the measured data is given for the validation issues of researchers who can benefit from most of the investigated pressure drop models with tolerable accuracy regarding with their HEX design analyses.

Orifice plate modeling with two-phase multiplier including the effect of the area contraction ratio

The flow of a gas-liquid across the orifice plate occurs a pressure drop. It employs a two-phase multiplier to estimate the average pressure drop. In the present times, the two-phase multiplier does not account for the orifice size, becoming incomplete models. The introduction of the area contraction ratio is the novelty of this paper. The proposed model employs a two-phase multiplier depending on the quality, densities ratio, area contraction ratio, and two constants extracted from experimental databases. The proposed model has a low bias, applicable for densities ratio, (ρL/ρG), of 3.05 to 800 and an area contraction ratio of 0.072 to 1.000.

Robust and General Model to Forecast the Heat Transfer Coefficient for Flow Condensation in Multi Port Mini/Micro-Channels

A general correlation for predicting the two-phase heat transfer coefficient (HTC) during condensation inside multi-port mini/micro-channels was presented. The model was obtained by correlating the two-phase multiplier, φtp with affecting parameters using the genetic programming (GP) method. An extensive database containing 3503 experimental data samples was gathered from 21 different sources, including a broad range of operating parameters. The newly obtained correlation fits the broad range of measured data analyzed with an average absolute relative deviation (AARD) of 16.87% and estimates 84.73% of analyzed data points with a relative error of less than 30%. Evaluation of previous correlations was also conducted using the same database. They showed the AARD values ranging from 36.94% to 191.19%. However, the GP model provides more accurate results, AARD lower than 17%, by considering the surface tension effects. Finally, the effect of various operating parameters on the HTC was studied using the proposed correlation.

Single-Phase and Two-Phase Flow Pressure Drop in a Long Double Helicoidally Coiled Tube

Abstract Single-phase and two-phase frictional pressure drop in horizontally oriented double helically coiled tubes confined in a cylindrical shell are experimentally studied using an instrumented test loop that represents a prototypical liquified natural gas (LNG) fuel delivery system for internal combustion (IC) engines. Adiabatic experimental data addressing liquid (water) and gas (nitrogen) single-phase flows, as well as two-phase flows (air–water) in the helicoidally coiled tubes are presented. The range of Reynold numbers for single-phase flow experiments is 2600–4800. In two-phase flow experiments, the only liquid and only gas Reynolds numbers varied in 1030–6600 and 1700–17700 ranges, respectively. In a laminar single-phase flow regime, the measured friction factors are in relatively good agreement with well-established correlations. In the turbulent flow regime, the measured friction factors are moderately higher than the prediction of well-established published correlations. Two-phase flow frictional pressure drops are compared with some relevant correlations, with the poor agreement. The generated experimental data are empirically correlated based on the two-phase flow multiplier concept.

Saturated flow boiling inside conventional and mini/micro channels: A new general model for frictional pressure drop using genetic programming

• A new general model for FPD during saturated boiling was proposed using GP. • 6021 experimental data samples from 42 published sources were analyzed. • Present model showed favor outcomes for different flow regimes and channel sizes. • The accuracy of previous models was considerably lower than the present one. • The new model presented favor physical trends at different operating conditions. This study presents a general explicit model for estimating the saturated flow boiling frictional pressure drop (FPD) in conventional (macro) and mini/micro channels heat exchangers. An extensive database including 6021 experimental data samples has been gathered from 42 published sources, covering a broad range of fluids, channel diameters and operating parameters. The new model is based on the separated model suggested by Lockhart and Martinelli (1949) for two-phase flow. Thus, the two-phase multiplier, ϕ l o 2 has been estimated using the intelligent approach of genetic programming (GP). The presented model predicts the mentioned database with a reasonable value of average absolute relative deviation (AARD) of 21.34%. Moreover, 74.85% of predicted data have an error of lower than 30% of the experimental values. The entire database is compared with ten well-known two-phase pressure drop correlations for the evaluation of previous models. But all of them showed a total AARD of more than 27%. The GP model shows good accuracy for both conventional and mini/micro channels and different flow regimes, including low and high Reynolds numbers. In addition, it is applicable for estimating the boiling FPD in different operating conditions. Based on 752 additional data from 4 independent sources, the new model provides the best predictions for estimating the FPD in conventional and mini/micro channels.

Machine learning based pressure drop estimation of evaporating R134a flow in micro-fin tubes: Investigation of the optimal dimensionless feature set

The present study is focused on proposing, implementing, and optimizing machine learning based pipelines for estimating the pressure drop in evaporating R134a flow passing through micro-fin horizontal tubes. Accordingly, an experimental activity is first conducted, in which the pressure drop of the flow at various operating conditions is measured. Physical models that are available in the literature are then implemented and the corresponding accuracy, while being applied to the obtained dataset, is determined. Machine learning based pipelines, with dimensionless parameters provided as features and two-phase flow multipliers as targets, are then developed. In the next step, a feature selection procedure is performed and an optimization process is then conducted to find the algorithms and the corresponding hyper-parameters, using which results in the highest possible accuracy. The optimal pipeline is demonstrated to be the one in which the liquid only two-phase multiplier is chosen as the target and is provided with only 5 dimensionless parameters as selected input features. Employing the latter pipeline leads to a mean absolute relative deviation (MARD) of 6.27 % on the validation set and 6.41 % on the test set, which is notably lower than the one achieved using the most promising physical model (MARD of 18.74 % on the validation set and 18.08 % on the test set). Furthermore, as the dataset and the obtained optimal pipeline will be made publicly accessible, the proposed methodology also offers higher ease of use and reproducibility.

An Experimental Analysis of Water–Air Two-Phase Flow Pattern and Air Entrainment Rate in Self-Entrainment Venturi Nozzles

For self-entrainment venturi nozzles, the effects of nozzle shapes and operating conditions on the water–air two-phase flow pattern, and the characteristics of the air entrainment rate have been investigated. A rectangular venturi nozzle with width and height dimensions of 3 mm and 0.5 mm was used with a vertically downward flow direction. The pressure ratio, which is the ratio of the inlet and outlet pressures, water flow rate, and diverging angle were set as experimental parameters. From the flow visualization, annular and bubbly flows were observed. In the case of bubbly flow, the more bubbles that are generated with a higher water flow rate, the smaller the pressure ratio. In the case of annular flow, the increased pressure ratio and water flow rate induce the breakup of air core in the diverging area and make the interfacial oscillation stronger, which finally causes the flow transition from annular to bubbly flow, by accompanying a sharp increase in the air entrainment rate. During this flow transition, the frictional pressure drop of the two-phase flow is reduced, showing that a two-phase multiplier gets smaller.

Two-phase pressure drop and void fraction in a cross-corrugated plate heat exchanger channel: Impact of flow direction and gas-liquid distribution

Two-phase pressure drop is studied in a transparent cross-corrugated channel for uniform and non-uniform gas–liquid distribution. Both uniform and non-uniform distribution are created by injecting air and water through different numbers of nozzles directly into the channel. The frictional pressure drop clearly indicates the impact of maldistribution.The single channel is pivot-mounted to allow horizontal, vertical upward and downward flow. Two-phase frictional pressure drop can be directly measured only for horizontal flow, neglecting acceleration pressure drop. In vertical flow, a void fraction model is necessary to deduct gravitational pressure drop from the measured pressure difference.The two-phase friction factors of all flow directions are compared to the correlation of single-phase flow. In this manner, homogeneous flow is distinguished from slip. Homogenous flow is confirmed for homogeneous void fractions up to 0.7 at uniform and up to 0.25 at non-uniform gas injection. The single-phase correlation is valid for homogeneous flow when inserting two-phase variables. The experimental two-phase multiplier is compared to correlations from literature.The pressure measurement data are used to determine the actual void fraction. The results are compared to published void fraction models. The homogeneous model fits best for uniform two-phase distribution. For maldistribution, the correlations of Margat et al. (1997) and of Rouhani and Axelsson (1970) predict the experimental void fractions reasonably well, except for very small flow rates.Analysis of experimental results is facilitated by previously published research on flow pattern visualization and modelling in the same test channel. The cross-corrugated geometry generates a swirling motion inducing centrifugal forces often much larger than buoyancy, which thus loses impact on flow pattern, pressure drop and void fraction. The ratio of buoyancy to centrifugal force is expressed by the corrugation Froude number. Slip independent of buoyancy is identified by introducing the hydrostatic correction factor to evaluate friction factors deviating with flow direction.

Robust and General Model to Forecast the Heat Transfer Coefficient for Flow Condensation in Multi Port Mini/Micro-Channels

A general correlation for predicting the two-phase heat transfer coefficient (HTC) during condensation inside multi-port mini/micro-channels was presented. The model was obtained by correlating the two-phase multiplier, [[EQUATION]] with affecting parameters using the genetic programming (GP) method. An extensive database containing 3503 experimental data samples was gathered from 21 different sources, including a broad range of operating parameters. The newly obtained correlation fits the broad range of measured data analyzed with an average absolute relative deviation (AARD) of 16.87% and estimates 84.73% of analyzed data points with a relative error of less than 30%. Evaluation of previous correlations was also done using the same database. They showed the AARD values ranging from 36.94% to 191.19%. However, the GP model provides more accurate results, AARD lower than 17%, by considering the surface tension effects. Finally, the effect of various operating parameters on the HTC was studied using the proposed correlation.

Experimental investigation and correlation development for two-phase pressure drop characteristics of flow boiling in offset strip fin channels

The plate-fin heat exchangers with pressure-resistant offset strip fins are widely used in the C3MR and other liquid natural gas (LNG) systems, and the two-phase pressure drop characteristics of flow boiling in pressure-resistant offset strip fin channels is a crucial factor for designing and optimizing the compact heat exchangers. A cryogenic experimental rig was established to obtain two-phase pressure drop data in the present study and the fin thickness of 0.4 mm is selected based on an actual compact heat exchanger in the C3MR LNG liquefaction system. The tested fluid is R22, and the experimental conditions include mass fluxes of 64–128 kg/(m2·s), vapor qualities of 0.1–1.0, saturation pressures of 0.22–0.26 MPa, and heat fluxes of 0.7–5.5 kW/m2. The comparison between the obtained data for fin thickness of 0.4 mm and those for fin thickness of 0.1–0.4 mm in literatures show that, the friction factor f of gas flow in channels increases with the increasing fin thickness, and the increment is 306%–451% as the fin thickness increases from 0.1 mm to 0.4 mm. The research results of two-phase flow show that, as the vapor quality increases, the frictional pressure drops initially increase and then decrease, representing a maximum at vapor quality of 0.90. With the increment of heat fluxes, the average vapor quality increases, resulting in the increasing frictional pressure drops. The two-phase multiplier of two-phase pressure drop varies from 3 to 35 and increases with the decreasing fin thickness and hydraulic diameter. A new correlation of two-phase pressure drops in offset strip fins with different fin thicknesses was developed within a deviation of ±25%.

Liquid blockage and flow maldistribution of two-phase flow in two parallel thin micro-channels

In this study, flow maldistribution in a system of two parallel thin micro-channels with shared inlet and outlet manifolds is experimentally investigated with one channel subject to single-phase flow and the other to two-phase one. The flow pattern, pressure drop, gas flow rate in the single-phase flow channel Q1 and two-phase flow channel Q2 are studied. Film flow patterns are observed for all the cases of the study, consistent with literature work. The Q2Q1 ratio is defined as a direct measure to flow maldistribution. Theoretical derivation shows that Q2Q1 is inverse of the two-phase multiplier ϕ or Q2Q1=1ϕ. Three levels of liquid flow rate are examined and presented to show three representative trends: (1) For the highest water flow rate, i.e. 10−2 m/s, Q2Q1 is found to monotonically increase with the air flow rate, with its value Q2Q1 as low as about 0.2 at 0.86 m/s gas velocity and approaching 0.65 at 3.44 m/s. (2) For the lowest water velocity, i.e. 10-4 m/s, Q2Q1 shows decrease at first, followed by an increase, as the superficial gas velocity increases from 0.86 m/s to 3.44 m/s. It reaches about 0.76 at 0.86 m/s gas velocity and drops to about 0.55 at 1.72 m/s. (3) For the intermediate water velocity, i.e. 10-3 m/s, two “steady” states are identified at 0.86 m/s gas velocity with one having Q2Q1 as high as about 0.69 and the other about 0.52. The rest follows a similar trend as 10-4 m/s liquid velocity. The observed two “steady” states and changing trend at the two low liquid velocities may be due to the altered liquid blockage near the channel exit. It is also indicated that the two-phase multiplier ϕ obtained in single channel testing may not be used to measure flow maldistribution in multiple-channel systems. The work is important to study of two-phase flow, multi-channel design, flow maldistribution, and flow control in micro-channels for PEM fuel cells, electrolyzers, and thermal devices.