Pipe Friction Factor Research Articles

Forecasting particle Froude number in non-deposition scenarios within sewer pipes through hybrid machine learning approaches

Sediment deposition has a substantial effect on the hydraulic capacity of channels in urban drainage and sewer systems. In this sense, the self-cleaning concept has been extensively used in the construction of urban drainage and sewer systems. In this regard, the design of the sewer system heavily depends on the accurate forecasting of the particle Froude number (Fr). This study is conducted on experimental data sets collected from existing studies, including a wide range of dimensionless grain size of particles (Dgr), sediment median size (d), hydraulic radius (R), volumetric sediment concentration (Cv), and pipe friction factor (λ) for the condition of clear bed. We forecasted the particle Froude number using four different input combinations. We employed the Random Tree (RT) and Reduced Error Pruning Tree (REPT) methods as standalone methods, as well as Random Committee (RC) and Bagging (BA) methods as hybrid machine learning (ML) methods in particle Froude number forecasting. Hybrid machine learning methods demonstrate enhanced performance compared to both standalone machine learning methods and empirical equations. In the context of sewer system design under non-deposited bed conditions, there is a need to accurately forecast the particle Froude number, RC-RT (IA = 0.96, R = 0.928, MSE = 0.718, RRMSE = 0.197, NSE = 0.86, and PBias = −0.284) performed the best, followed by BA-RT, RC-REPT, BA-REPT, RT, and REPT. In our research, it was found that, in forecasting the particle Froude number under non-deposited bed conditions, Cv emerges as the most responsive input parameter among others.

Application of a hydrophobic coating to a pressurized pipe and its effect on energy losses and fluid flow profile

The use of additives, generally called DRAs (Drag Reducing Additives), has been proposed to re-duce the energy consumption in pressurized pipes. Although many research works have been conducted to analyze the effect of these additives, less attention have been devoted to the application of coatings to the pipe wall. This paper demonstrates that the application of a hydrophobic coating to the pipe can lead to a head loss reduction for a transition flow regime with moderate Reynolds number values (Re). For this purpose, an experiment was conducted to compare the performance of both coated and uncoated pipes by measuring the head losses and assessing the Drag Reduction Percentage (%DR) and the pipe friction factor (f). This was done for two Polyvinylchloride (PVC) pipes with different nominal diameters (PVC90 and PVC63). In addition, the flow velocity distribution was also measured in all these tests. The %DR decreased as the Re values increased, with the reduction being notably less pronounced for higher Re values. This could be explained by the fact that a partial slip condition is induced by the hydrophobic product. Its effect is significant for a transition regime where the effect of viscosity is important, but it becomes negligible for increasing levels of turbulence. No significant differences were observed in the flow distribution between coated and uncoated pipes, which seems to indicate that the velocity change could be limited to the near-wall viscous sublayer. The results of this work open an important research line aimed at reducing energy costs and the carbon footprint in pipe fluid distribution systems.

A unified friction factor formulation: Bridging laminar and turbulent friction factor with critical points analysis

The friction factor is widely recognized as a pivotal parameter in the analysis of fluid–boundary interactions; however, a comprehensive grasp of friction mechanics remains elusive. This investigation revisits measurements from the benchmark Nikuradse measurements, furnishing indirect evidence of two critical points in pipe turbulence. It underscores that friction factors within laminar and turbulent regimes are intimately interconnected, bearing significant relations to subcritical and critical phenomena. The two critical points directing the laminar–turbulent transition consist of a standard non-equilibrium phase transition and a fully matured turbulent regime, accompanied by an extensive crossover to its asymptotic scaling. Relying on a mathematical model, the scaled friction factor for rough pipes converges into a unified curve. New formula of friction factor of pipe flow is derived, and it was illustrated that it can be derived as a geometric weighted parameter, bridging the laminar and turbulent friction factors. Conclusively, the proffered model was juxtaposed with pipe experimental data from the antecedent study and more contemporaneous transitional pipe data to authenticate the aptness of the suggested model, and it united the friction factor in all three regimes.

Application of maximum statistical entropy in formulating a non-gaussian probability density function in flow uncertainty analysis with prior measurement knowledge

In mechanical, civil and chemical engineering systems the accuracies of flow measurement instruments is conventionally specified by certified measurement capabilities (CMCs) that are symmetric, however it is physically possible for some flow instruments and equipment to exhibit asymmetric non-Gaussian behaviour. In this paper the influence of non-Gaussian uncertainties is investigated using direct Monte Carlo simulations to construct a probability density function (PDF) using representative non-Gaussian surface roughness data for a commercial steel pipe friction factor. Actual PDF results are compared and contrasted with a symmetric Gaussian PDF, and reveal inconsistencies in the statistical distributions that cannot be neglected in high accuracy flow measurements. The non-Gaussian PDF is visualized with a kernel density estimate (KDE) scheme to infer an initial qualitative shape of the actual PDF using the approximate locations of the normalized peaks as a initial metrologist estimate of the measurement density. This is then utilized as inputs in a maximum statistical entropy functional to optimize the actual non-Gaussian PDF using a nonlinear optimization of Lagrange multipliers for a mathematically unique PDE. Novelties in the present study is that a new methodology has been developed for statistical sampling from non-monotonic non-Gaussian distributions with accompanying Python and Matlab/GNU Octave computer codes, and a new methodology for utilizing metrologist's expert prior knowledge of PDF peaks and locations for constructing an a priori estimate of the shape of unknown density have been incorporated into the maximum statistical entropy nonlinear optimization problem for a faster and more efficient approach for generating statistical information and insights in constructing high accuracy non-Gaussian PDFs of real world messy engineering measurements.

Explicit pipe friction factor equations: evaluation, classification, and proposal

The Colebrook equation has been used to estimate the friction factor (f) in turbulent fluids. In this regard, many equations have been proposed to eliminate the iterative process of the Colebrook equation. The goal of this article was to perform an evaluation, classification, and proposal of the friction factor for better development of hydraulic projects. In this study, Gene Expression Programming (GEP), Newton-Raphson, and Python algorithms were applied. The accuracy and model selection were performed with the Maximum Relative Error (∆f/f), Percentage Standard Deviation (PSD), Model Selection Criterion (MSC), and Akaike Information Criterion (AIC). Of the 30 equations evaluated, the Vatankhah equation was the most accurate and simplest to obtain the friction factor with a classification of very high, reaching a value of ∆f/f<0.5% and 1.5<PSD<1.6. A new equation was formulated to obtain the explicit f with fast convergence and accuracy. It was concluded that the combination of GEP, error theory, and selection criteria provides a more reliable and strengthened model.

GIS-Based Identification of Locations in Water Distribution Networks Vulnerable to Leakage

The detection of leakages in Water Distribution Networks (WDNs) is usually challenging and identifying their locations may take a long time. Current water leak detection methods such as model-based and measurement-based approaches face significant limitations that impact response times, resource requirements, accuracy, and location identification. This paper presents a method for determining locations in the WDNs that are vulnerable to leakage by combining six leakage-conditioning factors using logistic regression and vulnerability analysis. The proposed model considered three fixed physical factors (pipe length per junction, number of fittings per length, and pipe friction factor) and three varying operational aspects (drop in pressure, decrease in flow, and variations in chlorine levels). The model performance was validated using 13 district metered areas (DMAs) of the Sharjah Electricity and Water Authority (SEWA) WDN using ArcGIS. Each of the six conditioning factors was assigned a weight that reflects its contribution to leakage in the WDNs based on the Analytic Hierarchy Process (AHP) method. The highest weight was set to 0.25 for both pressure and flow, while 0.2 and 0.14 were set for the chlorine and number of fittings per length, respectively. The minimum weight was set to 0.08 for both length per junction and friction factor. When the model runs, it produces vulnerability to leakage maps, which indicate the DMAs’ vulnerability classes ranging from very high to very low. Real-world data and different scenarios were used to validate the method, and the areas vulnerable to leakage were successfully identified based on fixed physical and varying operational factors. This vulnerability map will provide a comprehensive understanding of the risks facing a system and help stakeholders develop and implement strategies to mitigate the leakage. Therefore, water utility companies can employ this method for corrective maintenance activities and daily operations. The proposed approach can offer a valuable tool for reducing water production costs and increasing the efficiency of WDN.

Experiments on Slug Flow Dynamics in Helically Coiled Tubes

Slug flow characteristics in helically coiled tubes were investigated in experiments. Pressure loss, slug velocity, and slug passing frequency were measured using pressure transducers and backlight imaging of dyed water under illumination. For a 20-mm-diameter tube, parametric dependencies on gas and liquid volume flow rates for total superficial velocities of up to 6 m/s with three different radii of curvature (R = 0.270 m, R = 0.375 m, and R = infinity/straight tube) were explored. The main experimental results obtained are (1) the bubbly flow regime shrinks because of centrifugal acceleration from the coiled geometry, (2) the liquid slug length remains unchanged regardless of changes in gas and liquid flow rates, and (3) the pipe friction factor decreases with slug passing frequency.

CFD-based Estimation of Friction Factor in Rough Pipes with Herschel-Bulkley Fluids

The appropriate estimation of frictional losses in a pipeline system is essential. So far, little attention has been paid to determining the friction factors with non-Newtonian fluids, especially in rough pipes. This study aims at calculating the friction factor using validated three-dimensional Computational Fluid Dynamics models in Ansys CFX. Steady-state computations are performed with three different incompressible Herschel-Bulkley fluids in rough pipes with relative roughness of the inner pipe surface ε = 0.0005 – 0.01. A power-law type bath gel as a test fluid is used for experiments to validate our numerical model. The numerical results are compared with the measured values and also with numerous existing friction factor estimation models with the help of generalization of the Reynolds number in the relevant engineering range of Regen = 100 – 40,000. This paper shows that the existing approximations can not accurately describe the friction factor with pseudoplastic fluids in rough pipes. On the contrary, in the case of Bingham plastic fluid, a new, explicit calculation relation is found in a unified form accepted by the literature.

Thermal Performance of Four-Lobe Swirl Generator and its Transition Parts Under a Different Type of Nanofluids

Due to the importance of promoting the thermal performance of heat exchangers, innovating a new technique is the main goal of many researchers. In swirl flow techniques, keeping the pressure drop at the practical level still requires more and more attention. In the current paper, a numerical study is conducted to explore the impact of a novel lobe swirl generator and its transition parts on forced convective heat transfer and friction factor in a circular pipe subjected to constant heat flux.The swirl mechanism is investigated at the pitch to a diameter of P/D = 8 as the optimum design. The transition part under several parameters of variable beta (β), transition multiplier (n= 0.5) and variable helix (t = 1) have been adopted. The effect of SiO2, Al2O3, and CuO volume concentrations (1 to 5%) in water under various Reynolds numbers (Re) from 15,000 to 35,000 have been carried out. The turbulent swirling flow was modelled using the applicable shear-stress transport (SST) k-ω. The outcome demonstrated an enhancement in heat transfer value ranging from 1.35 to 1.87 with an increased pressure drop value from 1.23 to 1.67. It was also found that using SiO2/water at 5% volume concentration and Re 15000 created the highest thermal performance, with a significant factor of 1.67.

Estimate Friction Factor for Polypropylene Pipes

The major losses of fluid flow in plastic pipes due to friction are usually few or negligible in some cases, and this is due to the assumption that the value of the friction factor is small (small roughness). This work aimed to estimate the friction factor vs Reynolds number and to compared against previous data, the friction factor was estimated using an experimental model consisting of a polypropylene pipe with a nominal outside diameter 16mm and length of 8.5 meter and eighteen elbows connect to it, the results showed that the practical coefficient of friction factor is less than the value using the Basilius equation for smooth pipes which indicates that polypropylene pipes are smoother and that the numerical formula similar to the Basilius equation was . Finally, the amount of energy lost due to the friction factor in PPR pipes is small compared to other types of pipes and this is due to the extrusion process that makes the inner wall smooth, but it cannot be neglected in fluid flow.

Numerical investigation of heat exchanger pipe equipped with chamfered circular ring separated from wall to intensify thermo-hydraulic performance

Chamfered circular ring (CCR) innovated from conventional circular ring by introducing chamfered surface on its periphery at 30o attack angle is numerically investigated to study its effect on fluid flow characteristics, heat transfer enhancement, and friction factor in a heat exchanger pipe. In order to study flow blockage effect on overall performance of device, three diameter ratios (DR = Di/Do = 0.6, 0.7 and 0.8) with three spacing ratios (SR = s/D = 1, 2 and 3) are used. Turbulent model k – ε, RNG with enhanced wall treatment is used to solve governing equations. Results showed that CCR chamfered surface produced nozzle jet effect on pipe wall surface through clearance of 1 mm, which further induced turbulent and recirculating flow effect near pipe wall area. This resulted into higher heat transfer rate. All the diameter ratios with SR = 1 showed thermal performance factor value more than unity at most of the lower Reynolds number. The range of TPF shown by DR = 0.6, 0.7 and 0.8 with SR =1 is 1.21–0.93, 1.23–0.97, and 1.19–0.99, respectively. Compromised results of TPF are shown by DR = 0.7 and DR = 0.8 at SR = 1. Chamfered circular ring has shown better results over circular ring, perforated conical ring, short length twisted tape, twin co-twisted tape, wire rod bundles, and perforated twisted tape. Numerical results showed better agreement with predicted results within the range of 10%. Highest TPF of 1.23 is shown by DR = 0.7 and SR = 1 at Re 6000.

Augmentation of laminar flow heat transfer in annular flat tubes by means of helical screw-tape inserts in the inner tube.(Dept.M)

The heat transfer characteristics and friction factor in horizontal double pipes of flat tubes with full length helical screw element of different twist ratio and helical screw inserts with different spacer length are investigated. Cold and hot water are used as working fluid in tube side and shell side respectively. The experiments covered a range of Reynolds numbers 5.7*102 ≤ Re ≤ 1.31*103. The effect of spacer length and twist ratio on the heat transfer augmentation and friction factor on heat transfer have been presented separately. The study shows that, Nusslet number (Nu) and friction factor (f) decrease with the increase of spacer length (S) and twist ratio (Y) for flat tube. The comparison between the data of present plain circular tube with that of previous plain circular tubes showed good agreement but the data of present plain flat tube showed a higher in heat transfer and pressure drop than that of plain circular tube. The correlations of average Nusselt number and friction factor with Re, S and Y are presented.

A new universal model for friction factor in smooth pipes

Friction factor models for turbulent flow in smooth pipes express friction factor λ as a function of the bulk Reynolds number ReD and may be broadly grouped into two categories: power-law models and log-law models. While the former stem from the spectral scaling arguments applied to eddy momentum transfer close to the wall, the latter are derived from the mean velocity log law and are known to be consistent with the attached eddy model of wall turbulence structure. Interestingly, none of these models individually describes the entire range of Reynolds numbers (Re) accessed to date, without requiring adjustment of coefficients and/or exponents, i.e., these models are not universal. In this work, we present a new semi-empirical universal model that combines, without introducing any additional empirical coefficients, the essence of both power-law and log-law models. Due to this, our model successfully describes the variation of friction factor over the entire range of Reynolds numbers (more than four decades in ReD) at once. The physical basis for our model is the observation that at finite Reynolds numbers, the flow appears to be a small perturbation of the so-called ultimate regime of smooth-pipe turbulence, as far as friction is concerned; in the ultimate regime, λ→0 asymptotically as ReD→∞. The new model has significant potential toward accurate estimation of friction factor or flow rate in smooth pipe flows.

Pipe sizing of district cooling distribution network including in energy transfer station

A district cooling system (DCS) distributes chilled water to different buildings connected to the main plant. The benefits of a DCS include greatly increasing energy efficiency and decreasing life cycle operation costs. The installation, maintenance, and design of a DCS can be expensive, however. Therefore, means of decreasing costs without cutting quality is necessary. Given this, a hypothetical DCS is presented with a constant temperature difference set-point of 9°C. The DCS was set to have a system diversity of about 80%. Hydraulic calculation will be used in the study in order to determine the smallest possible pipe sizes that would permit normal operation below allowable limits. The network is divided into 3 parts; namely the main line (ML), the plot take-off (PTO), and the plate-type heat exchangers (PHEs). The DCS will have a piping network connected to 12 energy transfer stations, each with 3 sets of PHEs. Initial guess values of pipe dimensions and friction factors will first be calculated using continuity and the Von Karman equation. A single-variable Newton-Raphson method is then used on the implicit Colebrook-White equation to estimate the actual friction factor for each pipe. Then, the calibrated pipe sizes will be determined by cross-referencing theoretical values with industry-standard sizes as specified in ASHRAE. In calculating the friction factor, it was found that the values increase as the given tonnage decreases, thus implying a decrease in pipe size as the chilled water flows toward the last building. The entire study was conducted on MATLAB. It must be noted that the study is only limited to the selection and design of a simple DCS.

IMPROVEMENT OF APPROACHES AND METHODS OF TURBULENT FLOW THEORY IN THE PIPES

Abstract. The article consideres the analysis of the literature about the development of the water turbulent flow theory in the pipes. According to the results of analysis and theoretical studies, we obtained mathematical models. These models described the kinematic structure of the water turbulent flow in the pipes for different regions of turbulence. For the first time, the hypothesis was accepted that the dependence obtained from the Navier-Stokes differential equation for constructing the velocity profile in the laminar regime is suitable for calculating the average velocities in the turbulent regime of flow, but for this, it is necessary to replace the molecular kinematic viscosity with the total turbulent kinematic viscosity, which includes kinematic viscosity on the inner surface of the pipe and turbulent kinematic viscosity , which occurs due to the movement of masses from one layer into another, as recommended in J.V. Boussinesq. Based on experimental data I. Nikuradze and F.O. Shevelev, we obtained a distribution of the total kinematic viscosity in the pipes, including the kinematic viscosity on the pipe inner surface and the kinematic turbulent viscosity. For the first time, we used the kinematic viscosity distribution equation in the pipes and obtained the averaged velocity profile equation. This equation corresponds to the boundary conditions on the pipe inner surface and on the axis of the pipe. The equation of maximum averaged velocity, the equation of distance from the axis of the pipe to the points having average velocity, the equation of the ratio of maximum velocity to average velocity was obtained. For the first time, the equation of the tangent stresses components ( , ) and the tangent stresses equation in radial coordinates ( ) were obtained. The equation of the maximum value of the tangent stresses located on the inner surface of the pipe was obtained. The tangent stresses assume a zero value on the pipe axis. The equation of the vortex components ( , ) was obtained. We have shown that vortex lines are concentric circles whose centers are located on the pipe axis. The equation of angular velocity of flow particles rotation relative to the vortex lines was obtained. The maximum value of the particle rotation angular velocity on the pipe inner surface is determined. It decreases monotonically to zero on the axis of the pipeline. It is zero on the pipe axis. In this article, all equations reveal the kinematic structure of the water flow. We described these equations by the Reynolds number and the pipe friction factor. Such equations are adopted to show the dependencies between the regimes and the flow kinematic structure. These equations make it possible to calculate the distribution profile of the total kinematic viscosity, averaged velocity, tangential stresses and angular velocity of flow particle rotation.

Comparative numerical study on pressure drop in helically coiled and longitudinally C-shaped pipes

In the present work, the shear stress transport (SST) $$k - \omega$$ model is used to simulate internal turbulent flows in curved tubular heat exchangers and the resulting friction factors $$C_{f}$$ are calculated. A helically coiled configuration was used in the validation process of the model that showed a good agreement between numerical results of the friction factors $$C_{f}$$ and the standard experimental correlations of the literature, with a maximum relative error of 4.24%. A comparative study was performed to investigate the possibility of applying friction factor correlations, established mainly for helical coils, to longitudinally C-shaped pipes. Preliminary results confirm the inability of coil-specific correlations to predict the friction factor $$C_{f}$$ inside C-shaped pipes. It was also noted that, unlike helical coils, the C-shaped pipe friction factor appears to be affected by ratios other than the curvature ratio as highlighted in this study by introducing the effect of the amplitude ratio $$\beta$$ defined as the ratio of the amplitude to the curvature radius.

Experimental and Numerical Investigation of the Loss Coefficient of a 90° Pipe Bend for Power-Law Fluid

This study presents an investigation on the flow of two non-Newtonian fluids. These materials can be found in industrial environment, such as pharmaceutical and food industries, and also in wastewater treatment. In industrial environment, these fluids are usually driven by pumps between two workstations in the system, which represents a significant proportion of the costs. In order to operate the system cost-efficiency and environment friendly accurate sizing is necessary, which requires data on the hydraulic resistance of the elements. In the case of Newtonian fluids, these parameters are well-known. However, the non-Newtonian fluids have a considerably narrower literature, so laboratory and numerical tests are desirable. In our work, the hydraulic losses of two real non-Newtonian fluids were studied which can be described with the power law rheological model. These studies included laboratory measurements and numerical simulations (Computational Fluid Dynamics, CFD), respectively. We investigated the friction factor of a straight pipe and loss coefficient of an elbow (R/D=2). The calculations were validated with our laboratory measurements and compared with the literature. Furthermore, the flow pattern in the pipe bend was also examined. The study presents the applicability and importance of the modification of the Reynolds number. Furthermore, the velocity profiles and the secondary flow structure in the elbow are also presented.

Approximations of the Darcy–Weisbach friction factor in a vertical pipe with full flow regime

Abstract The discharge in a full flow regime represents the discharge capacity of a vertical pipe, and the Darcy–Weisbach friction factor () is an important variable to calculate discharge. Since all existing equations for contain the Reynolds number (Re), it is problematic if the velocity is unknown. In this study, the performance of existing equations collected from studies on vertical pipes is assessed, and an approximation for the of vertical pipes in the full flow regime, without Re, is proposed. The performance of the Brkić and Praks equation is the best, with a maximum relative error (MRE) of 0.003% (extremely accurate). The MRE of the new approximation is 0.43%, and its assessment level is very accurate. This work is expected to provide a reference for the design and investigation of the drainage of vertical pipes.

Interfacial Friction Factors in Vertical Circular Pipes under Flooding Conditions at the Bottom End

Interfacial Friction Factors in Vertical Circular Pipes under Flooding Conditions at the Bottom End

Improving basic relationships of pipe hydraulics

This communication presents the approaches set up for processing spinner flowmeter well logs in vertical wells with a single fluid phase, which is the most widely used in assessing wells productivity. These focus on improving the pipe hydraulics relationships so that the different fluid inputs throughout the well can be quantified. Since vertical flow inside wells varies with depth between laminar flows (very low Reynolds number, i.e. Re < 103) and turbulent (Re > 4·103) the aim has been to reduce the uncertainty in the transition interval. Starting from bibliographical data and/or well-known formulas for laminar and for turbulent flow, several continuous relationships have been developed for any regime: 1) an expression for the radial distribution of velocity inside the pipeline (velocity profile) was developed. 2) A relationship between the average velocity and the velocity at the axis (velocity factor) was created. 3) A third equation was generated to obtain the friction factor in smooth pipes (and starting from this, a new explicit equation for rough pipes). The purpose has been to have a set of empirical expressions of easy and continuous application for any regime, as an alternative to the use of computer simulations.