Pipe Flow Research Articles

Exploring the combined influence of primary and secondary vortex flows on heat transfer enhancement and friction factor in a dimpled configuration twisted tape with double pipe heat exchanger using SiO2 nano fluid

The double-pipe heat exchanger has a wider application in food industries, chemical industries, and a wide variety of fields where heat transmission is necessary. This investigation focuses on optimizing heat transfer rates through active, passive, and combined approaches. Within the realm of passive methods, this study specifically examines the use of twisted tape additions in pipe flow. In this study, different factors like swirl flow, primary and secondary vortex flows caused by tape twist, and the presence of a V-cut on the tape are studied. These factors include heat transfer rate, friction factor, and the standard for judging the performance of a V-cut on the tape insert. Experiments have been conducted on a double-pipe heat exchanger with nanofluid silicon dioxide as the working medium. This study encompasses a Reynolds number range of 6000–14,000. Notably, investigations reveal that the introduction of a v-cut on the tape engenders a secondary vortex flow. The enhancement in the Nusselt number at the higher Reynolds number for the primary vortex was observed ineffective as the depth of cut increases. The friction factor is increased by 6.37 times for the e/c ratio, which equals 0.17 (tooth to the depth of the v cut) in comparison to smooth pipe, while the increase in heat transfer rate for the same is 87.73% for Re = 6000.

Characterizing rheological behavior and fluidization of highly refined furnishes for process optimization

In this work, highly refined softwood bleached kraft pulp (SWBKP) furnishes, referred to here as XFC, were studied from the perspective of fiber suspension handling in processing. The rheology of the furnishes was studied with a rotational rheometer using a non-standard flow geometry to understand the viscosity development at different consistencies and the impact of temperature. For fluidization analysis during pipe flow, two optical methods were implemented; namely, optical coherence tomography (OCT) and high-speed video (HSV) imaging. The OCT was used to determine the small-scale floc structures near the pipe wall where the shear stress is highest, and the HSV imaging was applied for observing flow instabilities and XFC suspension uniformity at the pipe scale. All these issues can be significant in deciding the minimum flow rate required for a process pipe to get sufficient fluidization of XFC suspensions.

Modeling and simulation of xenon storage and supply system for electric propulsion system based on fundamental equation of state

The electric propulsion system (EPS) xenon storage and supply system (SSS) is a complex pipeline network system, which involves the multi-physics coupled fields of transcritical flow, heat transfer, rigid body motion, electromagnetics, and control. Based on the fundamental equation of state, a one-dimensional finite volume model system is proposed for compressible transcritical transient pipe flow. Six typical components of the SSS are modularization modeled by using an object-oriented programming method in Fortran 2018. To evaluate the performance of the algorithm, a simulation model consisting of 77 components is developed for a proportional controlled EPS xenon SSS, and a system-level simulation is performed. Compared with the standard case constructed on the Amesim platform, the model has a pressure rise time error lower than 6%, and the restrictors mass-flow-rate errors of the anode, cathode, and neutralizer are less than 2.8% of the rated flow rate after stabilization. Moreover, the proposed model yields more accurate results at certain operating points. The model system provides an efficient reference for the design and optimization of EPS SSSs, and offers a new approach to simulate complex cryogenic pipe flow systems.

Computational Fluid Dynamics Heat Transfer Analysis of Double Pipe Heat Exchanger and Flow Characteristics Using Nanofluid TiO2 with Water

A device called a heat exchanger is used to exchange heat transfer between two fluids with different temperatures. Because of its durability and ability to handle high-pressure application, the concentric double pipe heat exchangers are widely utilized for numerous industrial applications. To conserve pumping power energy, many researchers were involved in study of the nanoparticles to be embedded in the fluid, which will enrich the fluid thermal conductivity and surface area. This article demonstrates the flow characteristics and convective heat transfer of nanofluids containing 0.2, 0.4 and 0.6 of vol% TiO2 nanoparticles dispersed in water under turbulent conditions, which mainly can be used for cooling nuclear reactors applications. Reynolds numbers varying from 4000 to 18,000 are examined numerically. The convective heat transfer coefficient results of the nanofluid agree well against experimental data, which are slightly more than that of base water at 1.94%. The results of the numerical model showed that the convective heat transfer coefficient of nanofluids will increase when the Reynolds and volume fraction increases. By increasing the temperature of the annular hot water, the heat transfer rate will increase, showing no major impact to the convective heat transfer coefficient of nanofluids. A generalised solution predicting the convective heat transfer coefficient for extensive nanoparticle materials is proposed. The conclusion of the empirical equation is tested among published data and the results are highly congruent, confirming the strength of the gamma equation.

Numerical study of steady pipe flows and head loss coefficients

The study concerns steady pipe flows within 90o-bend and T-junctions, the head loss coefficients and the physical mechanisms responsible for the energy loss. Numerical viscous flow modelling based on SimpleFOAM solver were implemented in the study. Although secondary flow acts as the mechanism of energy loss in both the bend and in the branch flow of T-junction, the head loss coefficient in the former more critically depends on Reynolds (Re) number. This is supported by the comparison of the streamline fields and the radially varying profiles of the pressures from both cases. The location of flow separation prior to the secondary flow in the bend changes with Re number unlike the fixed location at the junction in the branch flow. The study confirms a practical implication related to the dependence of the head loss coefficients for pipe with 90o-bend and T-junction on flow velocity in an analysis of pipe network.

Effect of internal flow of Venturi-type power generation device on piston movement

ABSTRACT In the development and utilisation of hydraulic resources, high head and low flow hydraulic resources have not been fully utilised. To develop hydronic resources with low flow at high heads, this work designs a Venturi-type power generation device and studies the internal flow of the device by combining experiments and numerical simulations. The results indicate that the diameter ratio of the leading and branch pipes in the device significantly impacts pressure loss, and the diameter ratio at the throat is close, resulting in a significant pressure loss and an impact on the internal flow of the primary pipe. When the flow rate ratio of the leading and branch pipes is more than 4.03%, the piston can complete the reciprocating stroke, and the completion time decreases with the flow rate increase. When the flow rate ratio of the primary and branch pipes reaches 5.27%, the completion time approaches its limit. When the flow rate of the Venturi primary pipe is greater than 30 m3/h, the device begins to experience local cavitation, and noticeable noise appears at the diffusion tube.

A dynamic one-dimensional model for simulating unsteady air-water stratified flow in sewer pipes.

Ventilation is paramount in sanitary and stormwater sewer systems to mitigate odor problems and avert pressure surges. Existing numerical models have constraints in practical applications in actual sewer systems due to insufficient airflow modeling or suitability only for steady-state conditions. This research endeavors to formulate a mathematical model capable of accurately simulating various operational conditions of sewer systems under the natural ventilation condition. The dynamic water flow is modeled using a shock-capturing MacCormack scheme. The dynamic airflow model amalgamates energy and momentum equations, circumventing laborious pressure iteration computations. This model utilizes friction coefficients at interfaces to enhance the description of the momentum exchange in the airflow and provide a logical explanation for air pressure. A systematic analysis indicates that this model can be easily adapted to include complex boundary conditions, facilitating its use for modeling airflow in real sewer networks. Furthermore, this research uncovers a direct correlation between the air-to-water flow rate ratio and the filling ratio under natural ventilation conditions, and an empirical formula encapsulating this relationship is derived. This finding offers insights for practical engineering applications.

Modelling the piping-assisted erosion of clay barriers

Recent laboratory and field experiments have provided evidence of the erosion and piping of clay-based barriers. Predicting these phenomena is essential for the performance assessment of bentonite barriers and containments. This paper presents a non-local multi-physics model for bentonite erosion induced by piping flow that includes swelling, detachment of particles and co-transport of detached particles with piping flow. The erosion is controlled by the balance between the cohesive strength, which depends on the swelling, and the shear force, which depends on the water velocity and chemistry. The accuracy of the model is tested by comparison of simulation results with experimental data from pinhole tests and material erosion in boreholes. It is demonstrated that the model predicts accurately the total mass eroded by the piping flow. For example, the results show that the mass loss induced by piping-assisted erosion during the installation of a bentonite plug can reach 10·3% of the original mass, which may significantly reduce the sealing capacity of bentonite plugs in boreholes. The results of simulations show that the eroded mass depends on the borehole diameter and flow rate. The minimum flow rates required to erode 10% of the original mass are 0·8 l/s and 0·045 l/s for borehole diameter, db = 56 mm and 160 mm, respectively. These results demonstrate how the proposed formulations can be used to quantify the piping-assisted erosion of clay barriers, such as buffers, backfills and plugs considered for geological disposal of higher activity waste, and the sealing of investigation boreholes and abandoned geo-energy wells.

Characteristics of slurry transport regimes: Insights from experiments and interface-resolved Direct Numerical Simulations

A common way to transport solids in large quantities is by using a carrier fluid to transport the solids as a concentrated solid/liquid mixture or slurry through a pipeline. Typical examples are found in dredging, mining and drilling applications. Dependent on the slurry properties and flow conditions, horizontal slurry pipe flow is either in the fixed-bed, sliding-bed or fully-suspended regime. In terms of non-dimensional numbers, the flow is fully characterized by the bulk liquid Reynolds number (Re), the Galileo number (Ga, a measure for the tendency of particles to settle under gravity), the solid bulk concentration (ϕb), the particle/fluid density ratio (ρp/ρf), the particle/pipe diameter ratio (Dp/Dpipe), and parameters related to direct particle interactions such as the Coulomb coefficient of sliding friction (μc). To further our fundamental understanding of the flow dynamics, we performed experiments and interface-resolved Direct Numerical Simulations (DNS) of slurry flow in a horizontal pipe. The experiments were performed in a transparent flow loop with Dpipe=4 cm. We measured the pressure drop along the pipeline, the spatial solid concentration distribution in the cross-flow plane through Electrical Resistance Tomography (ERT), and used a high-speed camera for flow visualization. The slurry consisted of polystyrene beads in water with Dp=2mm, ρp/ρf=1.02, Ga between 40–45 and ϕb between 0.26–0.33. The different flow regimes were studied by varying the flow rate, with Re varying from 3272 till 13830. The simulations were performed for the same flow parameters as in the experiments. Taking the experimental uncertainty into account, the results from the DNS and the experiments are in reasonably good agreement. The results for the pressure drop agree also fairly well with popular empirical models from literature. In addition, we performed a parametric DNS study in which we solely varied Re and Ga. In all flow regimes, a secondary flow of Prandtl’s second kind is present, ascribed to the presence of internal flow corners and a ridge of densely packed particles at the pipe bottom during transition towards the fully-suspended regime. In the bulk of the turbulent flow above the bed, secondary flow transport of streamwise momentum dominates over turbulent diffusion in regions where the secondary flow is strong and vice versa where it is weak. The transition between flow regimes appears to be governed by the competition between the net gravity force on the particles and shear-induced particle migration from particle–particle interactions. This competition can be expressed by the Shields number, θ. For θ≲0.75, gravity is dominant and the flow is in the fixed-bed regime. For θ≳0.75, shear-induced migration becomes progressively more important for increasing θ. Low-concentration zones flanking the sliding bed start to form at the top corners of the bed, and gradually expand downwards along the pipe wall till the pipe bottom is reached. For θ≳1.5, shear-induced migration is responsible for lifting the particle bed away from the wall, associated with the onset of the suspended regime. For θ≫1, gravity is of minor importance and the mean flow eventually reaches axi-symmetry with a high-concentration particle core at the pipe center and negligible secondary flow.

Resolvent analysis of turbulent flow laden with low-inertia particles

We extend the resolvent framework to two-phase flows with low-inertia particles. The particle velocities are modelled using the equilibrium Eulerian model. We analyse the turbulent flow in a vertical pipe with Reynolds number of $5300$ (based on diameter and bulk velocity), for Stokes numbers $St^+=0-1$ , Froude numbers $Fr_z=-4,-0.4,0.4,4$ and $1/Fr_z = 0$ (gravity omitted). The governing equations are written in input–output form and a singular value decomposition is performed on the resolvent operator. As for single-phase flows, the operator is low rank around the critical layer, and the true response can be approximated using one singular vector. Even with a crude forcing model, the formulation can predict physical phenomena observed in Lagrangian simulations, such as particle clustering and gravitational effects. Increasing the Stokes number shifts the predicted concentration spectra to lower wavelengths; this shift also appears in the direct numerical simulation spectra and is due to particle clustering. When gravity is present, there are two critical layers, one for the concentration field, and one for the velocity field. For upward flow, the peak of concentration fluctuations shifts closer to the wall, in agreement with the literature. We explain this with the aid of the different locations of the two critical layers. Finally, the model correctly predicts the interaction of near-wall vortices with particle clusters. Overall, the resolvent operator provides a useful framework to explain and interpret many features observed in Lagrangian simulations. The application of the resolvent framework to higher $St^+$ flows in combination with Lagrangian simulations is also discussed.

The effect of permeability on the flow structure of porous square cylinders

This study experimentally investigates the wake structure of a porous square cylinder in terms of permeability over two decades of $Da$ (i.e. $2.4 \times 10^{-5} < Da < 2.9 \times 10^{-3}$ ). The porous cylinder, featuring a simple cubic lattice structure, was fabricated using an additive manufacturing technique. This unique method, combined with a periodic and scalable lattice structure, effectively isolates permeability from porosity, making it suitable for an in-depth parametric study. The key parameter, permeability, was directly estimated by measuring the pressure drop and superficial velocity for each porous case in an open-loop pipe flow system. The downstream flow fields were obtained using standard planar particle image velocimetry measurements in an open-loop wind tunnel. Based on the experimental data, structural modifications in the near wake were examined in relation to permeability, leading to the identification of four distinct flow regimes depending on $Da$ . Additionally, the downstream flow adjustment length ( $L_i$ ) was assessed by introducing a permeability-based source term into the momentum equation, facilitating the development of an analytical model for $L_i$ . The present experimental data support this analytical model, and our results further confirmed that $L_i$ plays a crucial role as a characteristic length scale in the near wake.

A Note on the Moody Diagram

In this work, we underscore the significance of selecting an appropriate scaling to derive dimensionless quantities that accurately reflect their dimensional counterparts, thereby enhancing the comprehension of the underlying physics. For the loss of head in a pipe flow, we argue that employing inertial force (or kinetic energy) to non-dimensionalized pressure force (or mechanical energy loss) lacks physical justification. As a result, an anomalous trend emerges for the classical friction factor: it decreases as the dimensionless flow rate (Reynolds number) increases, contrary to the behavior observed in the corresponding dimensional quantities. Conversely, by non-dimensionalizing the pressure force with the viscous force, a novel friction factor arises. In laminar flow, it is constant, while in turbulent flow, it is a monotonically increasing function of the Reynolds number, mirroring the behavior observed in the dimensional problem.

PARAMETRIC EVALUATION OF HEAT RECOVERY IN A RECUPERATIVE HEAT EXCHANGER

As urban centers grow and environmental regulations become more stringent, the complexity of integral systems within vehicles, aircraft, and other urban essentials escalates. A pivotal response to this challenge involves achieving enhanced energy efficiency and environmental appeal while maintaining cost-effectiveness. In this context, mathematical modeling, coupled with simulation and optimization techniques, emerges as a pivotal tool. This approach yields favorable outcomes with modest initial investments, contrasting with the resource-intensive nature of purely experimental design. Amongst the fundamental components, heat exchangers find widespread use, facilitating thermal exchange between fluids across diverse applications. Consequently, meticulous design and parametric optimization of these devices to attain peak performance and optimal energy efficiency are imperative, aligning with evolving environmental and energy trends. The simulation of such systems operates within an expansive range of operational and geometric parameters. These encompass mass flow rates, line pressures, pipe diameters, and pipe placements. However, excessive parameter combinations can render optimization computationally infeasible, necessitating judicious simplifications. Striking a balance between precision and computational efficiency, reduced-order models present a valuable intermediary solution. These models, situated between low- and high-order methods, offer robust mathematical representations without significant precision compromises. Thus, reduced-order models, which constitute an intermediate approach when compared to low- and high-order methods, can be used as a mathematical modeling tool without a significant loss of precision in the results. The present work presents an optimization and parametric analysis of a recuperative heat exchanger using a reduced-order approach employing the volume element model (VEM) as a discretization method, which is capable of providing accurate results at low costs. computational. The Laws of Conservation of Mass and Energy are applied to volume elements in combination with empirical correlations in order to quantify the quantities of interest, such as the convection heat transfer coefficient and temperature distribution. A parametric analysis was performed in order to observe the behavior of entropy generation in order to find its minimum points. The mass flow of water varied from 0.001 kg/s to 0.0085 kg/s with the mass flow of hot gases and the mass flow rate of gas was held constant in three stages, namely: 0.14 kg/s; 0.2 kg/s; and 0.3 kg/s. The local minimum was obtained for each of the three gas mass flow rate considerations, 8.53 W/K, 8.78 W/K, and 9.20 W/K respectively.

Numerical study of turbulent heat transfer and particle deposition in enhanced pipes with helical roughness

Large-eddy simulations of turbulent heat transfer and solid particle deposition in helically rib-roughened pipe flows have been performed for different Reynolds numbers Re and various particle diameters Dp. An Euler–Lagrange approach, using cyclic boundary conditions for the continuous and the dispersed phase, have been applied to achieve a fully developed turbulent flow. An adhesion and removal model have been added to the multiphase large-eddy simulations to take into account the physical effect of particle re-entrainment. The complex interactions between particle-laden turbulent flow and the structured pipe wall in multiple-started helically ribbed pipes are numerically investigated with regard to heat transfer, pressure loss, and particulate deposition. The results of the Nusselt numbers Nu, friction factors fd, and particle deposition rates Ṅd are presented for each geometry variant. For same Reynolds numbers Re, significant differences of those values have been observed for the differently structured pipes.

Enhanced high-frequency piezoelectric ultrasonic transducer based on integrated AlN honeycomb structure

Ultrasonic transducers are vital components for transmitting and receiving sound waves, which are customized to specific applications based on their operating frequencies.Small-sized high-frequency ultrasonic transducers have gained considerable attention and adoption in medical ultrasound imaging and small pipe flow testing. However, the significant impact of attenuation on high-frequency ultrasound restricts detection distance and degrades the signal-to-noise ratio. Additionally, thin-film high-frequency ultrasound transducers exhibit low output sound pressure, due to their low resonance displacement. In this study, we present an innovative approach to address these challenges through the design of an integrated small-size honeycomb-type top, two-electrode aluminum nitride (AIN)-based high-frequency ultrasonic transducer. A comprehensive investigation of the relationship between transducer size, sensitivity, and transmitted sound pressure levels is conducted. Leveraging microelectromechanical systems (MEMS) micro-nano-machining technology, we fabricate a 14 × 13 array with a unit diameter of 50 µm, and a matching circuit is employed to enhance the transducer's amplitude. Experimental results demonstrate remarkable transmit sound pressure levels (SPL) exceeding 210 dB (re:1 µPa/V) at a distance of 2 cm, with a maximum transmit SPL of 233 dB, and the receive sensitivity surpasses − 175 dB (re:1 V/µPa) and, at the 5 MHz resonance, the sensitivity reaches − 143 dB (re:1 V/µPa). Moreover, the transmit and receive linearity values demonstrate 99% and 98%, respectively. Our findings highlight the significant potential of the proposed high-frequency ultrasonic transducer for a diverse range of applications.

Series Solution of Unsteady Tank Drainage for Third Order Fluid using Adomian Decomposition Method

In this research study the tank model of isothermal and unsteady drainage is considered. Geometry of the tank is in cylindrical and at the bottom a pipe for flow of the fluid is attached. Sub class of viscoelatic non-newtonian fluid is considered. It is planed to obtain the series solution of the model with Adomian Decompositon in the light of no slip conditon. It is also decided to compare the velocity profile of adomain decompositon with the perturbation method for this fluid. On the basis of the results and comparison efficiency of both methods will be disscussed.

Experimental investigation on flow patterns and pressure gradients of shale oil–water flow in a horizontal pipe

With the growing demand for hydrocarbon resources and the depletion of conventional oil and gas reservoirs, the development of shale oil will become popular. As the shale oil fields gradually enter the middle and late stages of exploitation, the water content reaches as high as 60–80 %. Analyzing the flow characteristics of shale oi–water flow during high water content can help optimize the range of flow parameters and improve pipeline transportation efficiency. However, research on shale oil–water flow patterns and pressure drop prediction models is still lacking. Therefore, this work conducted shale oil–water flow experiments in the multi-test section pipe flow loop, considering the temperatures (40–70 °C), mixture velocity (0.2–1.2 m/s), and water contents (60–80 %). The flow patterns of shale oil–water flow are studied, and the flow pattern maps are created. Moreover, the influence factors on pressure gradient are analyzed, including pipe diameter, water content, mixture velocity, and temperature. Eventually, the pressure drop prediction models are modified based on the pressure gradient and holdup experimental data. The results show that a thin oil film and an oil-sticking layer are adhered to the pipe wall at 40 °C and 50 °C, respectively. The mixture velocity increased from 0.4 m/s to 1.2 m/s, and the pressure gradient increased by 69.89 % when the temperature and water content are constant. The lubrication coefficient is introduced in stratified flow (ST) and three-phase stratified flow (TPS) models, and the pipe flow friction coefficient is modified in dispersed flow (DF) and intermittent flow (IF) models. Moreover, the average relative deviations between experimental data and calculated values of ST, TPS, DF, and IF modified models are 4.49 %, 4.23 %, 4.40 % and 5.17 %, respectively. Therefore, surface wettability reduces the friction between the oil phase and the pipe wall, and the oil film and oil-sticking layer increase the pipe flow resistance.

A frictional soliton controls the resistance law of shear-thickening suspensions in pipes

Pipe flows are commonly found in nature and industry as an effective mean of transporting fluids. They are primarily characterized by their resistance law, which relates the mean flow rate to the driving pressure gradient. Since Poiseuille and Hagen, various flow regimes and fluid rheologies have been investigated, but the behavior of shear-thickening suspensions, which jam above a critical shear stress, remains poorly understood despite important applications (e.g., concrete or food processing). In this study, we build on recent advances in the physics of shear-thickening suspensions to address their flow through pipes and establish their resistance law. We find that for discontinuously shear-thickening suspensions (large particule volume fractions), the flow rate saturates at high driving stress. Local pressure and velocity measurements reveal that this saturation stems from the emergence of a frictional soliton: a unique, localized, superdissipative, and backpropagating flow structure coexisting with the laminar frictionless flow phase observed at low driving stress. We characterize the remarkably steep effective rheology of the frictional soliton and show that it sets the resistance law at the whole pipe scale. These findings offer an unusual perspective on low-Reynolds suspension flows through pipes, intriguingly reminiscent of the transition to turbulence for simple fluids. They also provide a predictive law for the transport of such suspensions in pipe systems, with implications for a wide range of applications.

Mass transfer of CO2 gas pocket in horizontal pipe flow

ABSTRACT The mass transfer from a stagnant CO2 gas pocket to the flowing water in a horizontal pipe was investigated experimentally, considering the application of pH adjustment by injecting gaseous CO2 for raw water in water treatment industries. In the experiments, the variation of the CO2 gas pocket volume and the corresponding pH values of the pipe flow with time under different conditions were recorded. The mass transfer coefficient of the CO2 gas pocket in the pipe flow was then calculated. The results showed that the injection of gaseous CO2 into the pipe flow could effectively adjust the pH. The volume of the CO2 gas pocket decreased exponentially. Different from most studies on bubble mass transfer, it was found that the ambient CO2 concentration could not be neglected in this study due to the large volume of the gas pocket and the restricted space in the pipe. The mass transfer coefficient increased with the increasing ratio of the CO2 injection rate to the water flow rate and exhibited a sharp reduction as the volume of the CO2 gas pocket decreased by about 80%. The outcomes of this paper can contribute to a better understanding of gas bubble mass transfer in pipe flows.

Development of a friction factor correlation applicable to both wet and dry foam flow in circular vertical pipes

BackgroundFoam flow, distinguished by its low density and extensive specific surface area, is employed for the cleaning of plant systems. However, its dual nature as a gas-liquid mixture and a non-Newtonian fluid complicates the prediction of the frictional pressure drop. MethodsThis study constructed a laboratory-scale experimental setup to illustrate the upward flow behavior of aqueous foam in a vertical circular pipe, capturing the foam flow using a high-speed camera. Utilizing the collected data and images, a model was developed for the friction factor to predict the frictional pressure drop of the foam flow, under the assumption that the foam flow is a non-Newtonian, quasi-homogeneous, steady, and fully developed laminar flow. Significant findingsWet foam, characterized by small, uniformly distributed spherical bubbles, is observed at lower foam quality levels. In contrast, dry foam, marked by a larger mean bubble diameter, non-uniform bubble distributions, and slugs, is observed at higher foam quality levels. A notable inflection point in the frictional pressure drop is observed during the transition from wet to dry foam within a vertical pipe. The foam regime and frictional pressure drop characteristics of the foam flow show limited sensitivity to surfactant concentration within the experimental range. A correlation for friction factors, applicable to both wet and dry foam flows in vertical circular pipes, was developed based on the Reynolds number, exhibiting a prediction error of 23.6 %.