Pressure drop and friction factor of steady and oscillating flows in open-cell porous media

Open-cell metal foams are often used in heat exchangers and absorption equipment because they exhibit large specific surface area and present tortuous coolant flow paths. However, published research works on the characteristics of fluid flow in metal foams are relatively scarce, especially for the flow oscillation condition. The present experimental investigation attempts to uncover the behavior of steady and oscillating flows through metal foams with a tetrakaidecahedron structure. In the experiments, steady flow was supplied by an auto-balance compressor and flow oscillation was provided by an oscillating flow generator. The pressure drop and velocity were measured by the differential pressure transducer and hot-wire sensor, respectively. The friction factor of steady flow in metal foam channel was analyzed through the permeability and inertia coefficient of the porous medium. The results show that flow resistance in the metal foams increases with increasing form coefficient and decreasing permeability. The empirical equation obtained by the present study indicates that the maximum friction factor of oscillating flow through the tested aluminum foams with specific structure is governed by the hydraulic ligament diameter-based kinetic Reynolds number and the dimensionless flow amplitude.     

Effect of diameter on two-phase pressure drop in narrow tubes

The effect of tube diameter on two-phase frictional pressure drop was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6 and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01-50 m/s and 0.01-3 m/s, respectively. The gas and liquid flow rates were measured and the two-phase flow pattern images were recorded using high-speed CMOS camera. Unique flow patterns were observed for smaller tube diameters. Pressure drop was measured and compared with various existing models such as homogeneous model and Lockhart-Martinelli model. It appears that the dominant effect of surface tension shrinking the flow stratification in the annular regime is important. It was found that existing models are inadequate in predicting the pressure drop for all the flow regimes visualized. Based on the analysis of present experimental frictional pressure drop data a correlation is proposed for predicting Chisholm parameter “C” in slug annular flow pattern. For all other flow regimes Chisholm’s original correlation appears to be adequate except the bubbly flow regime where homogeneous model works well. The modification results in overall mean deviation of pressure drop within 25% for all tube diameters considered. This approach of flow regime based modification of liquid gas interaction parameter appears to be the key to pressure drop prediction in narrow tubes.     

Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels

Two-thousand and ninety-two data of two-phase flow pressure drop were collected from 18 published papers of which the working fluids include R123, R134a, R22, R236ea, R245fa, R404a, R407C, R410a, R507, CO₂, water and air. The hydraulic diameter ranges from 0.506 to 12 mm; Re_l from 10 to 37,000, and Re_g from 3 to 4 × 10⁵. Eleven correlations and models for calculating the two-phase frictional pressure drop were evaluated based upon these data. The results show that the accuracy of the Lockhart–Martinelli method, Mishima and Hibiki correlation, Zhang and Mishima correlation and Lee and Mudawar correlation in the laminar region is very close to each other, while the Muller-Steinhagen and Heck correlation is the best among the evaluated correlations in the turbulent region. A modified Chisholm correlation was proposed, which is better than all of the evaluated correlations in the turbulent region and its mean relative error is about 29%. For refrigerants only, the new correlation and Muller-Steinhagen and Heck correlation are very close to each other and give better agreement than the other evaluated correlations.     

Effect of inner gas pressure on the elastoplastic behavior of porous materials: A second-order moment micromechanics model

A new micromechanics model based on the second-order moment of stress is established to investigate the effect of gas pressure on the nonlinear macroscopic constitutive relationship of the porous materials. The analytical method agrees well with numerical simulation based on the finite element method. Through a systematic study, we find that the gas pressure has a prominent effect on the nonlinear deformation behavior of the porous materials. The gas pressure can cause tension–compression asymmetry on the uniaxial stress–strain curve and the nominal Poisson’s ratio. The pore pressure significantly reduces the initial yield strength and failure strength of the porous metals, especially when the relative density of the material is small. The gas phase also strongly compromises the composite strength when the temperature is increased. The model may be useful for the evaluation of mechanical integrity of porous materials under various working conditions and working temperatures.     

Peristaltic flow and heat transfer in a vertical porous annulus, with long wave approximation

In this paper, we study the interaction of peristalsis with heat transfer for the flow of a viscous fluid in a vertical porous annular region between two concentric tubes. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large in comparison with the radius of the tube) is used to linearise the governing equations. Using the perturbation method, the solutions are obtained for the velocity and the temperature fields. Also, the closed form expressions are derived for the pressure-flow relationship and the heat transfer at the wall. The effect of pressure drop on flux is observed to be almost negligible for peristaltic waves of large amplitude; however, the mean flux is found to increase by 10-12% as the free convection parameter increases from 1 to 2. Also, the heat transfer at the wall is affected significantly by the amplitude of the peristaltic wave. This warrants further study on the effects of peristalsis on the flow and heat transfer characteristics.     

Flow pattern based correlations of two-phase pressure drop in rectangular microchannels

Numerous pressure drop correlations for microchannels have been proposed; most of them can be classified as either a homogeneous flow model (HFM) or a separated flow model (SFM). However, the predictions of these correlations have not been compared directly because they were developed in experiments conducted under a range of conditions, including channel shape, the number of channels, channel material and the working fluid. In this study, single rectangular microchannels with different aspect ratios and hydraulic diameters were fabricated in a photosensitive glass. Adiabatic water-liquid and Nitrogen-gas two-phase flow experiments were conducted using liquid superficial velocities of 0.06–1.0 m/s, gas superficial velocities of 0.06–72 m/s and hydraulic diameters of 141, 143, 304, 322 and 490 μm. A pressure drop in microchannels was directly measured through embedded ports. The flow pattern was visualized using a high-speed camera and a long-distance microscope. A two-phase pressure drop in the microchannel was highly related to the flow pattern. Data were used to assess seven different HFM viscosity models and ten SFM correlations, and new correlations based on flow patterns were proposed for both HFMs and SFMs.     

Experimental and numerical investigations of pressure drop in a rectangular duct with modified power law fluids

Numerical solutions are presented for fully developed laminar flow for a modified power law fluid (MPL) in a rectangular duct. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian behavior at low shear rates, through a transition region, to power law behavior at higher shear rates. The analysis identified a dimensionless shear rate parameter which, for a given set of operating conditions, specifies where in the shear rate range a particular system is operating, i.e. in the Newtonian, transition, or power law regions. The numerical results of the friction factor times Reynolds number for the Newtonian and power law region are compared with previously published results showing agreement within 0.05% in the Newtonian region, and 0.9% and 5.1% in the power law region. Rheological flow curves were measured for three CMC-7H4 solutions and were found to be well represented by the MPL constitutive equation. The friction factor times Reynolds number values were measured in the transition region for which previous measurements were unavailable. Good agreement was found between experiment and calculation thus confirming the validity of the analysis.     

An approximate lower bound damage-based yield criterion for porous ductile sheet metals

An approximate lower bound damage-based yield criterion is developed for isotropic porous ductile sheet metals. The matrix of the sheet metals is assumed to be elastic-perfectly plastic and obey the von Mises yield criterion with periodically distributed voids. Gurson’s unit-cell model is simplified to characterize the sheet metals. To accommodate biaxial loading, an approach of stress superposition is adopted for the stress analysis. Numerical results were calculated and compared to Gurson’s extended yield criterion and experimental results.     

CFD modeling of pressure drop and drag coefficient in fixed beds: Wall effects

Simulations of fixed beds having column to particle diameter ratio (D/dp ) of 3, 5 and 10 were performed in the creeping, transition and turbulent flow regimes, where Reynolds number (dp VLL/L ) was varied from 0.1 to 10,000. The deviations from Ergun’s equation due to the wall effects, which are important in D/d p<15 beds were well explained by the CFD simulations. Thus, an increase in the pressure drop was observed due to the wall friction in the creeping flow, whereas, in turbulent regime a decrease in t...     

Pressure drop in two phase slug/bubble flows in mini scale capillaries

A segmented two phase slug/bubble flow occurs where a liquid and a gas are pumped into the same tube over a range of Reynolds numbers. This segmented two phase flow regime is accompanied by an increase in pressure drop relative to the single phase flow where only one fluid is flowing in a capillary. This work experimentally and theoretically examines the pressure drop encountered by the slug/bubble flow with varying slug lengths in mini channels. In the experimental work the dimensionless parameters of Reynolds number and Capillary number span over three orders of magnitude, and dimensionless slug length ranges over two orders of magnitude to represent flows typical of mini- and micro-scale systems. It is found, in agreement with previous work, that these dimensionless groups provide the correct scaling to represent the pressure drop in two phase slug/bubble flow, although the additional pressure drop caused by the interface regions was found to be ∼40% less than previously reported.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction,which limits their capability for increased predictive accuracy relative to experimental data.This is partly because of the nature of slug flow pneumatic conveying system,which,as a dynamic system,never becomes stable.By utilising conservation of mass (airflow),a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour.The rate of air permeation through slug,one of the important factors in the conservation model,is expressed as a function of a slug permeability factor.Other factors such as slug velocity,slug length and the fraction of stationary layer were also considered.Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model,showing good agreement between the model and experimental results.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

Assessment of pressure drop in conical spouted beds of biomass by artificial neural networks and comparison with empirical correlations

Pressure drop is an essential parameter in the operation of conical spouted beds (CSB) and depends on its geometric factors and materials used. Irregular materials, like biomass, are complex to treat and, unlike other gas–solid contact methods, CSB turn out to be a suitable technology for their treatment. Artificial neural networks were used in this study for the prediction of operating and peak pressure drops, and their performance has been compared with that of empirical correlations reported in the literature. Accordingly, a multi-layer perceptron network with backward propagation was used due to its ability to model non-linear multivariate systems. The fitting of the experimental data of both operating and peak pressure drop was significantly better than those reported in the literature, specifically in the case of the peak pressure drop, with R² being 0.92. Therefore, artificial neural networks have been proven suitable for the prediction of pressure drop in CSB.     

Experimental analysis of flow regimes and pressure drop reduction in oil–water mixtures

The physical understanding of two-phase flow characteristics in horizontal pipes is of importance in the petroleum industry since significant savings in pumping power can be derived from the water-lubricated transportation of crude oil.     

Surface wettability effect on flow pattern and pressure drop in adiabatic two-phase flows in rectangular microchannels with T-junction mixer

Wettability is an important parameter in micro-scale flow patterns. Previous research has usually been conducted in conventional microtubes due to limitations of visualizing flow patterns and fabricating microchannels. However, most microchannels in practical applications have rectangular shape. Furthermore, pressure drop is closely related with flow pattern. Hence, we studied water liquid and nitrogen gas flows in rectangular microchannels with different wettabilities. The rectangular glass microchannels were fabricated from photosensitive glass, whose surface is hydrophilic. The surface of one was silanized using octadecyl-trichloro-silane (OTS) to prepare a hydrophobic microchannel. The two-phase flow pattern was visualized with a high-speed camera and a long distance microscope. The frictional pressure drop in the microchannel was measured directly with embedded pressure ports. The flow pattern and pressure drop in the hydrophobic microchannel were totally different from those in the hydrophilic microchannel. Finally, the two-phase frictional pressure drop was analyzed based on the flow patterns of different wettabilities.     

Two-phase pressure drop in multiple thick- and thin-orifice plates

Two-phase flow pressure changes through singularities such as sudden expansion and sudden contraction of thick- and thin-orifice plates were modeled. The modeling was based on the reversible and irreversible losses through contractions and expansions. The volume-averaged momentum equation and the reversible mechanical energy equation were used to evaluate the irreversibilities. Local slip ratios, which were necessary for the prediction of pressure drop through these singularities, were correlated from a large number of experimental data. To check the validity of the analytical predictions, an experimental test section was designed, and experiments were performed to produce benchmark pressure-drop data for thin- and thick-plate orifices. The working fluid used for these experiments was R-113. The predictive methods developed agree well with the experiments by the authors and with a wide range of two-phase flow test results obtained by others for steam-water systems. A parametric study shows the relative importance of geometry and of the flow variables such as quality, liquid-to-vapor density, and viscosity ratios on the pressure drop multipliers conventionally used in two-phase flows.     

Experimental evaluation of pressure drop in round tubes provided with physically separated, multiple, short-length twisted tapes

Isothermal pressure drop tests were performed on horizontal round tubes each containing identical, physically separated, equally spaced, short-length twisted tapes (TTs). The tests investigated the dependence of the Darcy friction factor, f, on the empty tube Reynolds number Re, TT twist ratio y, and TT spacing s. The variation of f across TTs belonging to the same test section was also examined. Ranges of the experimental variables examined were: 10,000 ? Re ? 90,000, 1.5 ? y ? 6, and s = 30, 40 and 50. The number of 360° revolutions was held constant for all the tapes and equal to 1.5. Tap water at room temperature and nearly atmospheric pressure was used as the working fluid. A correlation for the Darcy friction factor, in the form f = f (Re, y, s), was developed from the collected experimental data, with excellent accuracy.     

Flow of linear molecules through a 4:1:4 contraction–expansion using non-equilibrium molecular dynamics: Extensional rheology and pressure drop

In this work, non-equilibrium molecular dynamics simulations are used to generate the flow of linear polymer chains (monomer-springs with FENE potential) and a Lennard–Jones fluid (Newtonian fluid) through a contraction–expansion (4:1:4) geometry. An external force field simulating a constant pressure gradient upstream the contraction region induces the flow, where the confining action of the walls is represented by a Lennard–Jones potential. The equations of motion are solved through a multiple-step integration algorithm coupled to a Nosé-Hoover dynamics [S. Nose, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81 (1984) 511–519], i.e., to simulate a thermostat, which maintains a constant temperature. In this investigation, we assume that the energy removed by the thermostat is related to the viscous dissipation along the contraction–expansion geometry. A non-linear increasing function between the pressure drop and the mean velocity along the contraction for the linear molecules is found, being an order of magnitude larger than that predicted for the Lennard–Jones fluid. The pressure drop of both systems (the linear molecules and Lennard–Jones fluid) is related to the dissipated energy at the contraction entry. The large deformation that the linear molecules experience and the evolution of the normal stress at the contraction entry follow a different trajectory in the relaxation process past the contraction, generating large hysteresis loops. The area enclosed by these cycles is related to the dissipated energy. Large shear stresses developed near the re-entrant corners as well as the vortex formation, dependent on the Deborah number, are also predicted at the exit of the contraction. To our knowledge, for the first time, the excessive pressure losses found in experimental contraction flows can be explained theoretically.