Contribution To Pressure Drop Research Articles

Entropy generation and sensitivity analysis of R134a flow condensation inside a helically coiled tube-in-tube heat exchanger

Entropy generation analysis is a key to evaluating heat transfer augmentation along with pressure drop in enhanced heat exchangers. In the present study, entropy generation during R134a flow condensation inside a helically coiled tube-in-tube heat exchanger is investigated. In that regard, heat transfer and pressure drop contributions to entropy generation are assessed and compared for such condensers. Also, the influence of variation in geometrical parameters and flow conditions on entropy generation is studied. The findings reveal that larger tube diameters and diameter ratios, higher mass and heat fluxes and inlet vapor qualities, and lower saturation temperatures result in higher entropy generation. Additionally, a sensitivity analysis is conducted to analyze such condensers’ sensitivity to changes in geometrical and flow conditions from an entropy generation perspective. The analysis results indicate that at high mass velocities (G≥300kg.m−2.s−1) and inlet vapor qualities (x≥0.5) and low saturation temperatures (Tsat≤46∘C), coils with larger tube diameters are of higher sensitivity to alterations in aforementioned flow conditions, while coils with different coil diameters are of nearly the same sensitivity at both high and low ranges of flow parameters. On the contrary, when heat flux changes, coils with larger coil diameters are seen to be more sensitive to entropy generation, while coils with different tube diameters show virtually the same level of sensitivity.

Multiscale Modeling and Analysis of Pressure Drop Contributions in Catalytic Filters

Catalytic monolith filters with a honeycomb structure represent a key component of modern automotive exhaust gas aftertreatment systems. In this paper, we present and validate a multiscale modeling methodology for the prediction of filter pressure loss depending on the monolith channel geometry as well as the microscopic structure of the wall including catalytic coating. The approach is based on the combination of a 3D pore-scale model of flow through the wall reconstructed from X-ray tomography and a 1D+1D model of the filter channels. Several cordierite and SiC filter samples with varying substrate pore sizes and catalyst distributions are examined. A series of experiments are performed at different gas flow rates and filter lengths in order to validate the model predictions and to distinguish individual pressure drop contributions (inlet and outlet, channel, and wall). The predicted pressure drop shows a strong impact of the coating location and agrees well with the experiments.

Bubble formation in viscous fluids by a microfluidic flow-focusing junction: a computational study

A three-dimensional (3D) numerical study of bubble formation process in viscous fluids in a microfluidic flow-focusing junction is carried out in the present study. The numerical approach is first validated by the experimental data and shows a very good agreement, and a reciprocal relationship can be derived between the normalized bubble length and liquid fraction. Afterwards, the numerical approach is further applied to study bubble formation in fluids with different viscosities ranging from 5.6 to 400 mPa s, and the viscosity ratio of liquid phase to gas phase (μl/μg) is up to 2.2 × 104. Two different interpolation treatments including the Geo-Reconstruction method and the CICSAM are implemented when dealing with the situation for high viscosity, and the results are compared with the experimental data, indicating a better performance of the Geo-Reconstruction method. The numerical results of the bubble shapes are also compared with the experimental visualization results, showing good agreements. The evolution of the gas tip is further investigated quantitatively, and the liquid film is found to play a very important role in affecting the velocity of the gas tip. Finally, the hydrodynamic behaviors of the Taylor bubble formed in the junction including velocity and pressure distributions are studied in detail, and the contribution of pressure drop within the channel is also discussed.

Entropy generation for flow boiling on a single semi-circular minichannel

The paper investigates the effects of parameters such as mass flux, heat flux, channel diameter and inlet pressure on the entropy generation in flow boiling inside a semi-circular minichannel. A general entropy generation equation is derived for a single minichannel for flow boiling with developing flow, while also relaxing some heat transfer assumptions such as ΔTTsat≪1. The Romberg integration technique is used to solve for the entropy generation. Our results show that an increase in the mass flux causes an abrupt change in the entropy generation when the flow changes from laminar to transitional flow at small diameters although the effect is less significant at larger diameters. The heat transfer contribution in the entropy generation is also higher than the pressure drop contribution for the larger diameters. The larger channel diameters produce higher entropy generation compared to the smaller diameters for every heat flux investigated due to the increase in heat transfer contribution. An increase in the inlet pressure also decreases the entropy generation for every mass flux and heat flux. The aims of this study are to enhance the knowledge of the effects of heat transfer, pressure drop and flow behavior on the entropy generation, and to encourage researchers and designers to explore more novel features that can take advantage on the minimization of entropy generation.

Pressure drop and flooding in rotating packed beds

Rotating packed beds (RPB) are an intensified alternative to conventional absorption columns. RPBs could substantially reduce costs associated with reactive-absorption processes, such as post-combustion CO2 capture. This study presents internal radial pressure profiles obtained experimentally from inside a rotating packed bed. This approach allows the individual contributions to the overall pressure drop to be investigated in greater detail than previous studies. Experiments examined the effect of rotation speed, gas flow and liquid flow on pressure drop in RPBs. The result illustrated the pressure drop can be described well using a simple 1D pressure drop contribution model. The casing pressure drop is due in part to a free vortex that forms in the RPB eye, along with entrance and exit losses. This result improves understanding of gas pressure drop, and how these factors affect the performance and design of full-scale RPBs.

A numerical study on the performance of a Savonius-type vertical-axis wind turbine in a confined long channel

High-rise buildings in urban environments provide tremendous opportunities for harvesting wind energy. For example, a through-building channel is beneficial for wind speed enhancement and thus wind power generation. In this study, we investigate the performance of a Savonius-type vertical-axis wind turbine (VAWT) placed in a confined long channel, based on computational fluid dynamics (CFD) simulations. Two-dimensional (2D) simulations are conducted using ANSYS Fluent, employing the shear-stress transport (SST) k-ω turbulence model. Incoming wind velocity at the channel inlet is Uo = 4.05 m/s, corresponding to a Reynolds number Re = 1.0 × 105, based on Uo and the diameter (D) of the wind turbine. The channel is 45D long. Three different widths, 2D, 3D and 4D, of the channel together with different wind turbine locations in the channel are considered. The performance of the Savonius-type VAWT in the long channel is discussed, taking into account the contribution of pressure drop towards power generation, and is compared with that in open space. Results show that the power output (Pout) of the Savonius-type VAWT placed in the channel can be significantly increased by 200% in the 2D-wide channel compared with that in open space. Furthermore, a higher optimum tip-speed ratio (TSR) is observed for the wind turbine located in the channel than in open space. A comprehensive comparison is made between the wind turbine in the channel and that in open space. Finally, the maximum power coefficient of a Savonius-type VAWT in the channel is predicted based on a correction to that of a propeller-type horizontal-axis wind turbine (HAWT) in a long channel.

Gas holdup and frictional pressure drop contributions in microstructured two-and three-phase bubbling bed with Newtonian and non-Newtonian liquids: Effect of coarse and fine particles with surface active agent

In the present work, experimental observations of the effect of coarse and fine particles, its concentration, and size on the gas holdup and frictional pressure drop with and without the presence of surfactants in a microstructured bubbling bed are reported. In-depth analysis of the effect of fine and coarse particles on gas holdup is performed. Frictional pressure drop and its component namely friction between fluid-wall, particle-wall, and fluid-particle are thoroughly investigated in two and three-phase systems. Five different particles (copper, zinc, alumina, silicon, and coal) of average particle size range (4.84−425 μm) and density range (1600 − 6310 kg/m3) are used for the present experimental study. An empirical correlation is developed to predict gas holdup and frictional pressure drop at the wide range of experimental conditions. The developed correlation is able to predict the experimental data of gas holdup and frictional pressure drop within the error range of ± 20%.

Experimental investigation of first and second laws in a direct absorption solar collector using hybrid Fe3O4/SiO2 nanofluid

In this study, energy and entropy analysis of a residential-type direct absorption solar collector using hybrid Fe3O4/SiO2 nanofluid is evaluated experimentally. The hybrid nanofluid samples are prepared in the different volume ratios of Fe3O4/SiO2 (25:75, 50:50 and 75:25) and different volume fractions (500 ppm, 1000 ppm and 2000 ppm). The appropriate nanofluid samples for using as the working fluid of the collector are chosen based on the results of stability and optical properties of nanofluid. Then, outdoor thermal performance of collector is investigated using the experimental setup based on EN12975-2. Measurement of nanofluid optical properties using the spectrophotometry method shows that the extinction coefficient of 2000 ppm hybrid Fe3O4/SiO2 nanofluid is on average 10 cm−1 higher than that of the base fluid. Results of energy analysis display that the collector efficiency is increased by mass flow rate and volume fraction of nanofluid asymptotically. The asymptotic value is about 83% for 2000 ppm hybrid Fe3O4/SiO2 nanofluid. The findings indicate that the variation of exergy efficiency of a direct absorption solar collector with the volume fraction and mass flow rate is similar to energy efficiency. The enhancement of exergy efficiency is 66.4% for mass flow rates of 0.0225 kg s−1 by increasing the volume fraction from 0 to 2000 ppm. It is also observed that dimensionless entropy generation number is decreased by nanofluid volume fraction and by mass flow rate. The lowest entropy generation number is obtained in the mass flow rate of 0.0225 kg s−1 and the volume fraction of 2000 ppm. The variation of Bejan number by volume fraction shows that the contribution of pressure drop in entropy generation is insignificant.

Numerical study of the MHD flow around a bounded heating cylinder: Heat transfer and pressure drops

This work studies numerically the flow around an electrically insulated heating cylinder, bounded by walls of non-uniform electrical conductivity and subjected to a transversal magnetic field, with non-null components in the toroidal and poloidal directions. The configuration is representative of a typical breeding blanket segment in tokamak fusion reactors: to minimize magnetohydrodynamic (MHD) pressure drops, the liquid metal can be employed just as tritium breeder, whereas a non-conductive secondary fluid is used as coolant. The coolant is carried in the breeding zone by pipes that, being transversal to the stream-wise direction, affect the flow features and heat transfer. The flow is investigated by simulations performed in a 3D domain for Reynolds number 20 and 40, 0≤M≤50 for the Hartmann number and 0°≤α≤32° for the magnetic field inclination on the toroidal axis. The transition to the MHD regime causes the suppression of the cylinder wake and the disappearance of the steady vortex structures. Electromagnetic coupling balances the flow rates between the top and bottom sub-channels, individuated by the cylinder. The flow pattern modifications affect the heat transfer, which is found to increase with both M and α in the considered range, albeit for the latter in a non-monotonic trend. The pressure drop in the channel exhibits a similar behaviour. Moreover, it is dominated by the fully developed component due to the 2D currents, whereas the cylinder pressure drop contribution decreases steadily with the intensity of the applied magnetic field. The simulations were performed with ANSYS CFX-15.

Investigations on thermal hydraulic consequences of planar blockage in a prototype sodium cooled fast reactor fuel subassembly

A Computational Fluid Dynamics (CFD) based investigation has been carried out to understand the thermal hydraulic consequences of planar blockage within a 217 pin wire wrapped prototype fuel bundle. The computational domain comprising of 7 helical pitch lengths is meshed with structured hexahedral mesh. To reduce the computational time it is decomposed into 84 sub domains and each sub domain is handled by a separate processor. Detailed validation of the models used in the present analysis has been carried out with the data from an appropriate experiment, reported in open literature. Consequences of various radial extents of planar blockage located in the central pin and corner pin of the fuel subassembly are studied and compared. The contribution of pressure drop by the blockages and the associated flow reduction in the affected fuel subassembly has been quantified. Based on this, the increase in the bulk sodium outlet temperature of the subassembly and the efficiency of blockage detection by core temperature monitoring thermocouple has been assessed. Based on the parametric studies, it is found that inception of sodium boiling is likely if 3 or more rows are obstructed by a blockage located either in the center or in the corner pin of the subassembly. Even when the blockage is symmetric about the subassembly axis, large asymmetry in temperature field is observed within the blockage. This asymmetry is observed to be strongly dependent on the wire orientation in the upstream of blockage. As expected, a large reverse flow zone is observed in the downstream of the blockage. But, for similar number of blocked rows, corner blockage is found to have a larger reverse flow zone than that of central blockage. This is attributed to the fact that the presence of hexcan walls inhibits flow redistribution. Further, in accordance with size of reverse flow zone, higher sodium temperature is found in the downstream of corner blockage than a central blockage, even though the blocked cross section is less in the former case. This suggests that, sodium boiling is more likely in the case of corner blockage. Large circumferential temperature variation up to 650 °C is possible in the case of 4-row blockage and the peak variation is observed in the periphery of the blockage. Further it is found that monitoring of online bulk sodium temperature of subassembly exit cannot ensure blockage detection before inception of local sodium boiling within the subassembly. But, in the cases of both central and corner blockages, the disturbance generated in the temperature field prevails up to the outlet. This could act as a means for blockage detection.

The study of entropy generation during flow boiling in a micro-fin tube

Increasing in the heat transfer rate in flow boiling is a common and key issue for engineers. Generally, the heat transfer coefficient augmentation methods are divided into two main categories (active and passive methods). In passive methods the increase in heat transfer rate causes the increase in pressure drop. In order to evaluate the contribution of heat transfer and pressure drop mechanisms, the entropy generation analysis is used. In this paper, the entropy generation in micro-fin tube is investigated under flow boiling condition. The effect of different geometrical parameters and flow conditions is discussed on pressure drop contribution and heat transfer one in entropy generation, irreversibility distribution ratio (IDR) and Bejan number (Be). The frictional pressure drop and heat transfer coefficient in the micro-fin tube and the helically coiled one are compared as two enhancements passive heat transfer methods with the smooth straight tube in the literatures. Therefore, by introducing entropy generation number (Ns), the favorable geometry between the micro-fin tube and the helically coiled one with respect to the smooth straight tube is recognizable at equivalent boundary conditions.

Hydrodynamics of Layered Wire Gauze Packing

The hydrodynamics of layered wire gauze packing is studied. An experimental setup is established to measure the pressure drop of the packing. By some rational simplification, a 3D model is built to investigate the liquid film flow behavior in the packing, with which the influences of gas load and liquid spray density on liquid holdup and wetting area are analyzed in detail. Simulated results show that the liquid tends to accumulate at the intersection where the film is thicker. Based on the simulated results of liquid holdup and part of experimental data, a pressure drop correlation is proposed which can well predict experimental pressure drop of other operation conditions. The average relative errors are less than 10% in the study range. To study the pressure drop contribution of each term, a 3D single phase model is built. The results show that the concentrated losses caused by changes in the flow directions are the main factor to the pressure drop.

Entropy generation analysis and dimensional optimization of an evaporator for use in a microscale refrigeration cycle

Entropy generation in the evaporator of a microscale vapor compression refrigeration cycle is investigated under the effects of vapor quality, mass and heat flux, saturation temperature, and channel dimensions. For a variety of channel heights and mass flow rates, the optimum vapor quality, and the channel and fin widths yielding minimum entropy generation are obtained. The variation of heat transfer coefficient with vapor quality, and pressure drop with heat flux compare very well with literature. The vapor quality yielding the minimum entropy generation is found as 0.846. The optimum channel and fin widths are 66 and 50 μm, respectively, for 700 μm channel height. Heat transfer is the major source of the total entropy production for 200–400 μm wide channels, while the contribution of pressure drop becomes comparable for narrower channels. The study is unique in the literature in pursuing an entropy generation minimization study for microscale two-phase flow.

Statistical modelling of ammonia absorption in an acid spray scrubber

The use of acid spray wet scrubbers for recovering ammonia (NH3) emissions is promising due to its high NH3 removal efficiency, simplicity in design, and minimal pressure drop contribution on fans. An experimental study was conducted to evaluate the performance of a lab-optimised acid spray scrubber using simple modelling tools. Important parameters that significantly affect scrubber efficiency were identified as inlet NH3 concentration, air retention time, Sauter mean diameter of spray droplets, and liquid flow rate. Two statistical models (additive and multiplicative models) were developed from the experimental data using regression analysis of scrubber efficiency as a function of the significant operating parameters. The additive model had better performance accuracy with an R2 value of 0.93, MSE of 0, RMSE of 0.06, and MAPE of 8.89%. Both models have good predictive ability based on residual analysis, power analysis, and cross-evaluation. This study was able to develop simplified models to aid in predicting NH3 removal efficiency of an acid spray scrubber, which can be installed at animal facilities for NH3 abatement.

Development and evaluation of a full-scale spray scrubber for ammonia recovery and production of nitrogen fertilizer at poultry facilities

Significant ammonia emissions from animal facilities need to be controlled due to its negative impacts on human health and the environment. The use of acid spray scrubber is promising, as it simultaneously mitigates and recovers ammonia emission for fertilizer. Its low pressure drop contribution on axial fans makes it applicable on US farms. This study develops a full-scale acid spray scrubber to recover ammonia emissions from commercial poultry facilities and produce nitrogen fertilizer. The scrubber performance and economic feasibility were evaluated at a commercial poultry manure composting facility that released ammonia from exhaust fans with concentrations of 66–278 ppmv and total emission rate of 96,143 kg yr−1. The scrubber consisted of 15 spray scrubber modules, each equipped with three full-cone nozzles that used dilute sulphuric acid as the medium. Each nozzle was operated at 0.59 MPa with a droplet size of 113 μm and liquid flow rate of 1.8 L min−1. The scrubber was installed with a 1.3-m exhaust fan and field tested in four seasons. Results showed that the scrubber achieved high NH3 removal efficiencies (71–81%) and low pressure drop (<25 Pa). Estimated water and acid losses are 0.9 and 0.04 ml m−3 air treated, respectively. Power consumption rate was between 89.48 and 107.48 kWh d−1. The scrubber effluents containing 22–36% (m/v) ammonium sulphate are comparable to the commercial-grade nitrogen fertilizer. Preliminary economic analysis indicated that the break-even time is one year. This study demonstrates that acid spray scrubbers can economically and effectively recover NH3 from animal facilities for fertilizer.

A steady state pressure drop model for screen channel liquid acquisition devices

This paper presents the derivation of a simplified one dimensional (1D) steady state pressure drop model for flow through a porous liquid acquisition device (LAD) inside a cryogenic propellant tank. Experimental data is also presented from cryogenic LAD tests in liquid hydrogen (LH2) and liquid oxygen (LOX) to compare against the simplified model and to validate the model at cryogenic temperatures. The purpose of the experiments was to identify the various pressure drop contributions in the analytical model which govern LAD channel behavior during dynamic, steady state outflow. LH2 pipe flow of LAD screen samples measured the second order flow-through-screen (FTS) pressure drop, horizontal LOX LAD outflow tests determined the relative magnitude of the third order frictional and dynamic losses within the channel, while LH2 inverted vertical outflow tests determined the magnitude of the first order hydrostatic pressure loss and validity of the full 1D model. When compared to room temperature predictions, the FTS pressure drop is shown to be temperature dependent, with a significant increase in flow resistance at LH2 temperatures. Model predictions of frictional and dynamic losses down the channel compare qualitatively with LOX LADs data. Meanwhile, the 1D model predicted breakdown points track the trends in the LH2 inverted outflow experimental results, with discrepancies being due to a non-uniform injection velocity across the LAD screen not accounted for in the model.

Hydrodynamics of liquid–liquid Taylor flow in microchannels

An understanding of the hydrodynamics of the flow of long liquid droplets in another liquid phase is necessary for droplet-based microfluidics and other Lab-on-a-Chip devices. In this work, we use high speed photography/brightfield microscopy and CFD simulations to study the hydrodynamics of vertically upward flow of Taylor droplets of water dispersed in a continuous hexadecane phase in a channel of diameter 1.06mm. The volume-of-fluid (VOF) method is used to model two-phase flow and the shapes and velocities of the droplets measured experimentally are in excellent agreement with those obtained from CFD simulations. It is observed that the film thicknesses and the dynamic pressure drop caused by the presence of the droplets for these low viscosity droplets (viscosity ratio=0.3) can be predicted by the Bretherton's expressions for an inviscid bubble. For a sufficiently long droplet, the flow field in the uniform thickness film region can be predicted by an ideal annular flow solution. A model to predict the overall pressure drop in a unit cell, consisting of a Taylor droplet surrounded by the two halves of continuous phase slugs is also presented by summing up the pressure drop contributions from the continuous phase liquid slugs, uniform thickness film region and interfacial pressure drops at the droplet front and rear. The model was accurate for long droplets and slugs but was not reliable for shorter droplets and slugs, for which the slug and film flows may not be fully-developed and the shapes of the front and rear of the droplets interact.

Inlet and Outlet Pressure-Drop Effects on the Determination of Permeability and Form Coefficient of a Porous Medium

The determination of permeability K and form coefficient C, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the total pressure drop caused by the porous medium (i.e., inlet, core, and outlet) per unit of porous medium length. The inlet and outlet pressure-drop contributions, however, are not related to the porous medium length. Hence, for situations in which these pressure drops are not negligible, e.g., for short or very permeable porous media core, the definition of K and C via the HDD equation becomes ambiguous. This aspect is investigated analytically and numerically using the flow through a restriction in circular pipe and parallel plates channels. Results show that inlet and outlet pressure-drop effects become increasingly important when the inlet and outlet fluid surface-fraction φ decreases and the Reynolds number Re increases for both laminar and turbulent flow regimes. A conservative estimate of the minimum porous medium length beyond which the core pressure drop predominates over the inlet and outlet pressure drop is obtained by considering a least restrictive porous medium core. Finally, modified K and C are proposed and predictive equations, accurate to within 2.5%, are obtained for both channel configurations with Re ranging from 10−2 to 102 and φ from 6% to 95%.

Pressure drop modelling for liquid feed direct methanol fuel cells Part II. Model based parametric analysis

A pressure drop model for the direct methanol fuel cell (DFMC), described in Part 1 of this contribution, based on the homogeneous two-phase flow theory and mass conservation equation, which describes the hydraulic behaviour of a large (272 cm 2) cell, is used in a parametric analysis. The model allows assessment of the effect of operating parameters (temperature gradient, current density, flow bed design, fuel and oxidant flow rates and pressure) on the pressure losses at the anode and cathode side of the cell. The model is applied to an existing flow bed design, based on a plate heat exchanger, used in current fuel cell scale up studies. The role of the flow bed design is examined by presenting the pressure drop contributions for each of the three sections that comprise the flow bed.

Liquid Holdup Correlations for Inclined Two-Phase Flow

Summary Liquid holdup behavior in two-phase inclined flow was studied in an inclined pipe-flow simulator. Two sets of empirical equations, one each for uphill and downhill flow, are presented. For downhill stratified flow, a third equation is presented. The liquid holdup equations are functions of dimensionless liquid and gas velocity numbers in addition to liquid viscosity number and angle of inclination. These four parameters uniquely define the flow-pattern transitions in inclined two-phase flow. Consequently, the holdup equations are also implicitly flow-pattern dependent. Introduction An accurate prediction of liquid holdup is required to compute the hydrostatic head loss in two-phase inclined flow. In this case, hydrostatic head may be the most important of the pressure gradient components. There are many liquid holdup correlations in the literature, but almost all are for horizontal or vertical uphill flow. Eaton et al. proposed a holdup correlation based on data for natural gas, water, crude oil, and distillate oil mixtures in 2-and 4-in. (5- and 10-cm) diameter horizontal pipes. This correlation is based on five dimensionless groups reflecting various physical properties, flow rates, system pressures, and pipe diameters. A study by Vohra et al. showed that this correlation performed best on a collection of horizontal data taken by Eaton et al. and Beggs and Brill. Cunliffe found that using the Eaton et al correlation to predict the total liquid volume in a wet gas pipeline was quite successful for determining the incremental volume of liquid removed from rate increases. Using dynamic similarity analysis, Dukler et al developed a holdup correlation for horizontal two-phase flow. This holdup correlation is implicit in liquid holdup, requiring an iterative calculation. Experience has shown that most wet gas-transmission applications will result in a no-slip liquid holdup calculation when the Dukler et al. correlation is used. The Beggs and Brill correlation was developed from data obtained in an air/water flow system with 1- and 1 1/2-in. (2.5-and 3.8-cm) diameter pipes. They considered a range of inclination angles from 0 to 1900. Use pipes. They considered a range of inclination angles from 0 to 1900. Use of the correlation requires first determining the holdup for horizontal flow according to predicted horizontal flow patterns. The horizontal holdup is then corrected for angle of inclination. Palmer found that the Beggs and Brill liquid holdup was overpredicted for both uphill and downhill flow and suggested proper correction factors. For uphill flow from 0 to 9, Guzhov et al. proposed a holdup correlation that is independent of inclination angle. Hughmark and Pressburg developed a general holdup correlation for gas/liquid flow covering a wide range of physical properties and diameters. This correlation is based on data taken physical properties and diameters. This correlation is based on data taken in 1-in. (2.54-cm) diameter pipe for vertical uphill flow of air, water, oils of different viscosities, and carefully selected data of other investigators. In addition to these empirical liquid holdup correlations, at least two analytical holdup correlations deserve mention. Bonnecaze et al. developed a slug flow model for inclined pipe based on a mass and force balance around a simplified slug unit. The pressure drop contributions caused by the liquid film and the gas bubble were neglected. Using this holdup correlation, they correlated pressure drop data obtained in 1 1/2-in. (3.8-cm) diameter pipe inclined at various angles around 1100 to find an expression for friction factor. The holdup equation and friction factor correlation were compared with field data taken in a 6-in. (15.24-cm) diameter, 10,000-ft (3048-m) long pipe with a maximum deviation of 5%. With a very similar mechanistic approach, Singh and Griffith proposed a simple model for two-phase slug flow in inclined pipes. Most of their model parameters were experimentally determined using five different diameters of copper pipe at 5, 10, and 150 inclinations with an air/water system. For stratified flow, the authors developed a holdup model based on Chezy's open-channel flow equation. JPT p. 1003