Pipe Geometry Research Articles

Analysis of Geometrical Relationships and Friction Losses in Small-Diameter Lay-Flat Polyethylene Pipes

The use of lay-flat polyethylene pipes to irrigate horticultural crops has been receiving widespread attention in the last decade, due to the significant improvements in their hydraulic performance, their potentially high application efficiency, and their limited installation costs. However, even if hydraulic design procedures for conventional microirrigation systems are fairly well established, there is still the need to know how different pipe-wall thicknesses of lay-flat pipes can affect the pipe geometry under different operating pressures as well as the related consequences on friction losses. This paper, after comparing two different procedures (caliper and photographic) to assess the geometry of lay-flat polyethylene pipes under different operating pressures, analyzes the friction losses per unit of pipe length, J, in order to identify and to assess a procedure for their evaluation. Hydrostatic tests, initially carried out on pipes with wall thicknesses of 6, 8, and 10 thousandth of an inch (mil), evidenced that the pipe dimensions measured with both methods are quite similar, despite the generally higher standard deviations characterizing caliper measurements when compared to photographic method. Tests allowed to verify that most of the changes in pipe dimensions occur within a range of pressure from 0 kPa to about 30 kPa, with pipe horizontal width and vertical height quite similar at higher pressures and pipes have a tendency to become circular. Additionally, due to the elasticity of the material, over a certain limit of water pressure, both the pipe dimensions tend to rise, with a trend depending on pipe thickness. According to the experimental data, the relationships between pipe effective diameter and water pressure were then determined for the three considered pipes. Moreover, based on measured friction losses and pipe effective diameters, it was confirmed that the relationship between the Darcy-Weisbach friction factor, f, and the Reynolds number, R, can be described by a power equation in which, by assuming a value of −0.25 for the exponent, it results a coefficient c=0.285, lower than the theoretical. For the three investigated pipes the errors associated to estimated J were finally evaluated by considering (1) the experimental relationships between friction factor and Reynolds number as well as between pipe diameter and operating pressure (Case A); (2) the same value of c, but pipe effective diameters of 16.20, 16.10, and 15.85 mm corresponding to p=plim (Case B); (3) the standard procedure, with a value of c=0.302 and the pipe diameter equal to 16.10 mm, as suggested by the manufacturer. The results evidenced that suitable estimations of J need to account for the variations of the pipe effective diameter with water pressure. On the other hand, incorrect values of pipe diameter combined with inexact values of the friction factor generate inaccurate estimations of friction losses, with unavoidable consequences in pipe design.

Nonlinear Control of Axisymmetric Swirling Flows in a Long Finite-Length Pipe

Feedback stabilization of inviscid and high Reynolds number, axisymmetric, swirling flows in a long finite-length circular pipe using active variations of pipe geometry as a function of the evolving inlet radial velocity is studied. The complicated dynamics of the natural flow requires that any theoretical model that attempts to control vortex stability must include the essential nonlinear dynamics of the perturbation modes. In addition, the control methodology must establish a stable desired state with a wide basin of attraction. The present approach is built on a weakly nonlinear model problem for the analysis of perturbation dynamics on near-critical swirling flows in a slightly area-varying, long, circular pipe with unsteady changes of wall geometry. In the natural case with no control, flows with incoming swirl ratio above a critical level are unstable and rapidly evolve to either vortex breakdown states or accelerated flow states. Following an integration of the model equation, a perturbation kinetic-energy identity is derived, and an active feedback control methodology to suppress perturbations from a desired columnar state is proposed. The stabilization of both inviscid and high-Re flows is demonstrated for a wide range of swirl ratios above the critical swirl for vortex breakdown and for large-amplitude initial perturbations. The control gain for the fastest decay of perturbations is found to be a function of the swirl level. Large gain values are required at near-critical swirl ratios while lower gains provide a successful control at swirl levels away from critical. This feedback control technique cuts the feed-forward mechanism between the inlet radial velocity and the growth of perturbation's kinetic energy in the bulk and thereby enforces the decay of perturbations and eliminates the natural explosive evolution of the vortex breakdown process. The application of this proposed robust active feedback control method establishes a branch of columnar states with a wide basin of attraction for swirl ratios up to at least 50% above the critical swirl. This study provides guidelines for future flow control simulations and experiments. However, the present methodology is limited to the control of high-Reynolds number (nearly inviscid), axisymmetric, weakly nonparallel flows in long pipes.

Reeling of pipe with Lüders bands

Bending of tubes with a material that exhibits Lüders banding results in banded, localized deformation organized in diamond-shaped pockets on the tensioned and compressed sides of the tube. Furthermore, the Lüders-deformed section exhibits higher ovalization and curvature than the rest of the structure. Under deformation controlled bending, the higher deformation and curvature tend to propagate until the whole length of the structure is so deformed. The present study examines the behavior of a pipe as it is gradually wound on a large diameter reel. The material is modeled as a finitely deforming, elastic–plastic solid undergoing isotropic hardening/softening calibrated to a stress–strain response with a negative slope over the extent of the Lüders deformation. The reeling process is modeled with finite elements with a mesh that is fine enough to capture the evolution of Lüders banding that develops.During reeling with some back tension, Lüders banding again produces inclined bands of localized deformation, but the bands are organized in clusters with distinctly different spatial distribution than that of pure bending. The clusters are now separated by sections of pipe free of Lüders bands. For realistic pipe and reel geometries, the average bending strain imposed by the curvature of the reel is lower than the strain induced by Lüders banding. Accordingly, the clusters are separated by relatively undeformed sections so that the bending strain averages out to the value imposed by the reel. Because of the applied tension the bands on the compressed side are somewhat more diffuse and exhibit a more regular distribution along the length. Reeling induces ovalization of the pipe cross section, which is intensified by the application of back tension. It is demonstrated that as a consequence of the clustering of Lüders bands, the ovalization develops axial undulations. Such undulations can act as imperfections in subsequent, particularly compressive, loadings of the structure. Problem variables like the Lüders strain, the applied tension, the ratio of the reel diameter to that of the pipe, and the pipe diameter-to-thickness ratio all influence the amplitude and spatial distribution of localized deformation patterns that develop. The influence of each of these was examined in a detailed parametric study.

A Pipe Bend Subject to a Uniformly Distributed Radial Force

The effects of a distributed radial load on an elbow or bend within a piping system, caused by changes in momentum due to fluid flow, can be represented by one or more point loads. Simplified methods result in inaccurate results in some cases. Modeling the bend with multiple nodes and forces increases accuracy. The method presented here will provide accurate results, comparable to breaking up the bend into many nodes and forces. A number of example analyses are presented for comparison with simplified modeling methods and the potential importance of considering momentum change forces in some power piping geometries are discussed.

Finite element simulation of guided waves in pipelines for long range monitoring against third party attacks

Guided waves (GW) are finding more applications for structural health monitoring (SHM) of pipelines and other long, slender structures, particularly in the areas of corrosion and crack detection. Third party impact, both accidental and intentional, is also a major cause of pipeline failure. The use of low frequency (below 10 kHz) GW to detect damage caused by a third-party is investigated. Field test data on a 1 km long pipeline are compared with finite element (FE) predictions to illustrate the potential of low frequency GW to travel long distances along a pipeline. An FE study indicates the type and frequency of GW that can propagate long distances (low attenuation) without significant change in shape (low dispersion). The FE analysis is conducted on a typical 10 in (255 mm) diameter steel pipe with 7.8 mm wall thickness. The effects of pipe diameter and thickness on the GW propagation characteristics are illustrated. It is shown that certain frequencies for certain pipe geometries produce a very dispersive signal and should be avoided for GW SHM and the reasons for this are discussed.

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.

Further validation to the variational method to obtain flow relations for generalized Newtonian fluids

We continue our investigation to the use of the variational method to derive flow relations for generalized Newtonian fluids in confined geometries. While in the previous investigations we used the straight circular tube geometry with eight fluid rheological models to demonstrate and establish the variational method, the focus here is on the plane long thin slit geometry using those eight rheological models, namely: Newtonian, power law, Ree-Eyring, Carreau, Cross, Casson, Bingham and Herschel-Bulkley. We demonstrate how the variational principle based on minimizing the total stress in the flow conduit can be used to derive analytical expressions, which are previously derived by other methods, or used in conjunction with numerical procedures to obtain numerical solutions which are virtually identical to the solutions obtained previously from well established methods of fluid dynamics. In this regard, we use the method of Weissenberg-Rabinowitsch- Mooney-Schofield (WRMS), with our adaptation from the circular pipe geometry to the long thin slit geometry, to derive analytical formulae for the eight types of fluid where these derived formulae are used for comparison and validation of the variational formulae and numerical solutions. Although some examples may be of little value, the optimization principle which the variational method is based upon has a significant theoretical value as it reveals the tendency of the flow system to assume a configuration that minimizes the total stress. Our proposal also offers a new methodology to tackle common problems in fluid dynamics and rheology.

Numerical investigation of hydrodynamics and thermal performance of a specially configured heat pipe for high-temperature thermal energy storage systems

In the present study, a complex geometry, high temperature heat pipe was investigated numerically. The heat pipe was designed specifically to improve the performance of the thermal energy storage system incorporated in a concentrated solar power system. Due to the complexity of the heat pipe geometry, a new numerical approach was developed. The heat conduction in the wall and wick regions was included in the two-dimensional axisymmetric model. The compressibility of the working fluid and viscous dissipation were taken into account. Due to the high expansion ratio from adiabatic section to condenser, high speed vapor flow impinges on the condenser wall. The combined vapor jet impingement and condensation on the condenser wall was modeled by attaching a porous layer. This porous layer forces the impinging vapor jet to split out radially while it allows the wall suction. The heat rejection via the vapor condensation was estimated from the mass flux by energy balance at vapor–liquid interface. The heat transfer limits due to heat pipe geometry, working fluid, wick structure, and operational temperature were calculated. The vapor–wick interface temperature predicted by the current simulation agrees very well with the available experimental data. The performance of the heat pipe was evaluated by calculating the corresponding thermal resistance. The results showed that the thermal resistance decreases with the increase of the operating temperature and vapor radius while increases with the increase of the heat input. It was also shown that, for the cases studied, adiabatic section radius of 15 mm is sufficient. Further increase of the radius does not reduce the thermal resistance of the heat pipe.

Compute Critical and Normal Depths of Arch and Elliptical Pipes

AbstractArch and elliptical pipes are commonly used as roadway culverts. The pipe section is composed of three radii, which result in complex equations to compute cross-sectional geometry and hydraulic parameters, such as normal and critical depths. Basic sizing charts do not allow direct calculation of hydraulic properties of these pipe sections. Therefore, general formulas were developed to compute hydraulic properties for any given arch pipe cross section. An Excel workbook capable of calculating normal and critical depths for given flow rates was created using the developed formulas and the solver function. Worksheets to compute geometric properties and water surface profiles using the direct-step method were also developed. These user-friendly worksheets are useful for hydraulic design and analysis of arch and elliptical culverts. A case study was conducted on several standard pipe geometries to demonstrate the comparative results from the developed workbook and existing sizing charts.

Numerical and experimental verification of new method for connecting pipe to flange by cold forming

In this paper a new method of connecting pipe to flange without welding is presented. This method is a cold forming process that is based on plastic expansion/deformation of the pipe into a modified standard flange by use of a cold forming tool. The method is patented by Quickflange Technology AS and represents a highly feasible alternative to welding. The successful use of the method requires the ability to predict dimensional and stress/strain characteristics of the pipe and flange after the connection process in order to evaluate the connectivity to the adjacent flange as well as the leak tightness. In addition the ability to predict the process force during the connection process is needed in order to control the process and design the hydraulically actuated cold forming tool. It is shown that it is possible to simulate this process using the finite element (FE) method and achieve a good accordance with experimental results. For this purpose a non-linear FE model of the flange, pipe and forming tool is developed and analyzed using Abaqus.Experimental work, including tensile material testing and Quickflange joining tests were carried out for material model calibration and Quickflange process model validation, respectively. The FE model results are in good accordance with experimental observations in terms of actuation force for the process, deformations and strains of pipe and flange during and after the process. It is concluded that the developed FE model is a useful tool for simulating the presented process within reasonable computational time as long as careful considerations are given to model complexity, material parameters, friction, and pipe geometry tolerances.

A full-field residual stress estimation scheme for fitness-for-service assessment of pipe girth welds: Part II – A shell theory based implementation

With the two key controlling parameters identified and their effectiveness demonstrated in Part I of this study series for constructing a continuous residual stress profile at weld region, a classical shell theory based model is proposed in this paper (Part II) for describing through-thickness residual stress distributions of both axial and hoop components at any axial location beyond weld region. The shell theory based model is analytically constructed through an assembly of two parts: One represents weld region and the other represents the remaining component section away from weld. The final assembly of the two parts leads to a closed form solution to both axial and hoop residual stress components as a function of axial distance from weld toe position. The effectiveness of the full-field residual stress estimation scheme is demonstrated by comparing with a series of finite element modeling results over a broad range of pipe weld geometries and welding conditions. The present development should provide a consistent and effective means for estimating through-thickness residual stress profile as a continuous function of pipe geometry, welding heat input, as well as material characteristics.

Solid oxide fuel cell numerical study: modified MOLB-type and simple planar geometries with internal reforming

In this paper two different types of solid oxide fuel cell (SOFC) geometries are studied via CFD numerical simulations: a) a mono-block-layer build type (MOLB-type) with a porous embedding pipe in the air side of the geometry and a simple planar geometry were modeled feeding biogas obtained from local sludge. The numerical simulations integrated the internal reforming of methane in the anode side and different several phenomena that occur inside of the SOFC such as: mass transfer, heat transfer, species transport, chemical and electrochemical reactions. A detailed comparison of the results such as: current density, species concentration and temperature distributions along the fuel cells is reported. The results showed that the CH4, H2O, CO, CO2 concentration and current density distributions had similar trends for both MOLB-type with embedding porous pipe geometry and simple planar geometry. However, higher H2 concentration and lower average temperature value are obtained from the MOLB-type with embedding porous pipe geometry, which help to handle higher current densities and reduces thermal stress, increasing the performance of the fuel cell.

STUDY OF THE CONFIGURATION AND PERFORMANCE OF AIR-AIR EJECTORS BASED ON CFD SIMULATION

This paper describes a numerical study of gas-gas ejector performance for different operating conditions and geometrical configurations. The performance of ejector obtained based on a simulation procedure of linearized and axisymmetric subsonic and supersonic flow using Fluent Package. A conventional finite-volume scheme utilized to solve two-dimensional transport equations with the standard k-ω SST turbulence model. The model is solved in three regions namely, the primary flow nozzle, the secondary flow channel, and the region of interaction between the supersonic nozzle jet and the secondary flow. The effect of gas motive pressure the mixing part and tail section (pipe or diffuser) geometry on the ejector performance are studied. The computational results are validated using published experimental data with acceptable agreements. The numerical results indicate that the ejector geometry has a pronounced effect on the flow parameters (i.e., pressure and gas velocity) and the ejector performance. In addition, predicted numerical results indicate that when the motive-stream velocity exceeds the speed of sound, shock waves are unavoidable inside ejectors and that shock wave pattern in mixing part has a dominant effect on ejector performance. In addition, the results indicate that the shock location inside the nozzle and the separation point are affected by the motive pressure. The results show also that configuration with convergent-divergent mixing section is much better for mixing process than the other tested configurations.

On the non-destructive measurement of local mass transfer using X-ray computed tomography

Abstract A novel methodology is developed here to measure wall mass transfer rates non-destructively using X-ray computed tomography (CT). The mass transfer was measured using a gypsum lined 203 mm diameter straight pipe section using a dissolving wall method to water. The measurements were performed at a Reynolds number of 86,000 and Schmidt number of 1200. The local wear of the internal surface is obtained from the CT scans by aligning and analyzing the cross-sectional scanned images of the test section before and after the experiment. The full surface wear contours and the corresponding mass transfer rates are obtained by a three-dimensional reconstruction of the entire test section. The measurements from the CT scans are compared to results obtained from ultrasonic (UT) measurements of the wall thickness and internal surface measurements using a Coordinate Measuring Machine (CMM) and digital laser scans. The results from the CT scan methodology are in good agreement with the other methods, indicating that the method is robust and can be used to obtain the local mass transfer and roughness over the entire surface. Thus, it can be used as a principal method to investigate mass transfer non-intrusively in complex piping geometries.

A model of kimberlite pipe formation after the collision of a comet with the Earth at an angle to the horizon

A model of kimberlite pipe formation after the collision of a comet with the Earth at an angle to the horizon is proposed and studied. The proposed shock-wave model allows one to determine the pipe geometry according to initial conditions.

Experimental investigation of countercurrent flow limitation (CCFL) in a large-diameter hot-leg geometry: A detailed description of CCFL mechanisms, flow patterns and high-quality HSC imaging of the interfacial structure in a 1/3.9 scale of PWR geometry

Countercurrent flow limitation (CCFL) is experimentally investigated in large-diameter hot-leg geometry. COLLIDER test facility consists of reactor vessel simulator (RVs), hot-leg pipe, and a steam generator simulator (SGs) and was constructed to be a 1/3.9 scale model of a real PWR geometry. The facility is completely transparent providing excellent conditions for optical observation of the gas/liquid interface. Experiments were performed at atmospheric pressure using air/distilled water as flow mediums. High-quality high speed recording (HSC) was implemented to acquire the air/water interface which provided a unique and detailed look into the interface structure within the entire hot-leg geometry. This allowed a precise and a high-qualitative identification and description of the flow patterns and mechanisms by which the onset of CCFL occurs. A systematic experimental investigation of the onset of CCFL and deflooding was carried out for water inlet velocities in the range Jw,in*0.5=0.085−0.305, ΔJw,in*0.5=0.01. Air velocity was increased and decreased stepwise to identify the onset of CCFL and deflooding limits precisely. Two onset of CCFL mechanisms were identified and labeled as: bend-CCFL and ADE-CCFL. The results were arranged into four regions according to the inlet water velocity Jw,in*0.5. The four regions differentiate by sub-mechanisms that appear during bend-CCFL and ADE-CCFL. A detailed description of the successive events and mechanisms by which the onset of CCFL during the increase of air velocity, and deflooding occur is provided. The description is supported by high-quality images of the interface structure. The resulting experimental onset of CCFL curve and deflooding curve are provided and discussed. The experimental investigation clarifies the onset of CCFL phenomenon in a large-diameter hot-leg pipe geometry and provides valuable images of the air/water interface for future CFD validation. The current study shows that from a safety point of view, the onset of ADE-CCFL precedes the onset of bend-CCFL as Jw,in*0.5>0.185; its intensity and the amount of backflow water cannot be ignored for Jw,in*0.5>0.27.

Point Load Effect Determination for Different Pressure Pipe SDR Series

In the paper the polymer pipes loaded by internal pressure with additional point load on the external surface are studied using numerical methods. It is shown that the additional external loading can significantly influence residual lifetime of the pressured pipe. In this study the effect of the pipe geometry is considered. The shape of the propagating crack is estimated based on a special algorithm and the stress intensity factor is evaluated by direct method. The relation between crack size and a geometric function YasYas for specific material and geometrical properties is found. The results of this paper should contribute to better understanding of the real pipe behavior and to prevent unexpected failure of the pressured pipe system due to non-homogenous distribution of the soil load.

Assessment of subcooled boiling wall boundary correlations for two-fluid model CFD

Abstract An assessment of the heat and mass transfer wall boundary conditions used for subcooled boiling simulations with a CFD two-fluid model has been performed. This assessment was focused on the wall heat flux partitioning model using the state-of-the-art multidimensional Freon experimental data available in the literature. Various constitutive relations used to close the vapor generation rate at the heated wall were studied in order to obtain the best suited combination(s). The current study was restricted to vertical flows through pipe and annulus geometries. Two Freon data sets from the literature were considered: the first with R12 at about 2.6 MPa pressure and the second with R113 at 269 kPa pressure. In these data sets, the bubble diameter distribution measurements across the ducts were available. Bubble diameter estimation is the largest uncertainty in the boiling two-fluid model predictions and hence using the data with known bubble sizes allowed to focus on the assessment of other parameters to model vapor generation rate at the wall, in particular bubble nucleation site density and bubble departure frequency. From the parametric simulations with different combinations of the nucleation site density and frequency models, the discrepancy in obtaining a consistent frequency model for Freon became evident. The state-of-the-art frequency model under consideration is a function of the wall temperature which is estimated using a well-known empirical nucleate boiling heat transfer coefficient correlation. The frequency model provided inaccurate predictions in cases where the nucleate boiling heat transfer coefficient was inadequate to predict the wall superheat. The frequency model is now improved by using a more recent nucleate boiling heat transfer coefficient correlation with wider applicability, i.e., Freon. The simulations were carried out using the CFD code CFX (version 12). The Freon data used here corresponds to fluid-vapor density ratios ranging from 6 to 76. This assessment validated a consistent site density-departure frequency correlation combination for subcooled boiling simulations which has not been used so far for CFD simulations and an extension of the applicability of the correlation combination to high pressure steam–water conditions due to the favorable scaling of Freon physical properties.

Steady and Pulsating Turbulent Flows in Complex Pipe Geometries

In this paper, measurements of velocity and stress fields in rigid pipes are performed by means of planar particle image velocimetry (PIV). The attention is focused onto the effect of Reynolds number and of continuous or pulsating flows by investigating pipe geometries ranging from the straight pipe to the reduced section and bifurcated ones. The obtained results show that, in the tested range, the effect of Reynolds number is limited for straight and reduced section pipes, while significant for the bifurcated one. Independently of Reynolds number, different geometries and forcing (continuous or pulsed) produce strong variations in intensity and spatial distribution of velocity and stress fields. Considering the latter, the contribution of viscous and turbulent stresses are measured separately and compared. Indeed turbulent stresses are always larger than the viscous ones, but the relative intensity is highly variable as also the spatial distribution of maxima and minima. Specifically, in the pulsating flows, this distribution is phase-dependent reflecting the oscillations of regions of flow separation which form especially in reduced section and bifurcated pipes. These results are useful for all engineering applications in which turbulent pipe flows are involved.

Investigation of Diametral Acoustic Modes in a Model of a Steam Control Gate Valve

The objective of the present study is to provide an insight into mechanism of coupling between turbulent pipe flow and partially trapped diametral acoustic modes associated with a shallow cavity formed by the seat of a steam control gate valve. First, the effects of the internal pipe geometry immediately upstream and downstream of the shallow cavity on the characteristics of partially trapped diametral acoustic modes were investigated. The mode shapes were calculated numerically by solving a Helmholtz equation in a three-dimensional domain corresponding to the internal geometry of the pipe and the cavity. Second, the set of experiments were performed using a scaled model of a gate valve mounted in a pipeline that contained converging–diverging sections in the vicinity of the valve. Acoustic pressure measurements at three azimuthal locations at the floor of the cavity were performed for a range of geometries of the converging–diverging section and inflow velocities. The experimentally obtained pressure data were then used to scale the amplitude of the pressure in the numerical simulations. The present results are in good agreement with the results reported in earlier studies for an axisymmetric cavity mounted in a pipe with a uniform cross-section. The resonant response of the system corresponded to the second diametral mode of the cavity. Excitation of the dominant acoustic mode was accompanied by pressure oscillations corresponding to other acoustic modes. As the angle of the converging–diverging section of the main pipeline in the vicinity of the cavity increased, the trapped behavior of the acoustic diametral modes diminished, and additional antinodes of the acoustic pressure wave were observed in the main pipeline.