Pipe Flow Research Articles

Stabilizing Pipe Flow by Flattening the Velocity Profile

It is important to control turbulence in industrial processes. Past experimental and numerical researches have shown that a turbulent puff in pipe flow can be removed or delayed by flattening the profile of the upstream velocity because a flattened velocity profile causes the point of inflection on it to collapse. The energy gradient theory has been developed to study turbulent transition, and the relevant studies have shown that turbulence arises due to the generation of singularities in the flow field. In pressure-driven flows like the pipe flow, the point of inflection on the velocity profile leads to the appearance of a singular point in the unsteady Navier–Stokes equation. In this study, the energy gradient theory is used to demonstrate why the point of inflection on the profile of velocity of pipe flow is the critical point for generating turbulence. Then, it is shown how flattening the velocity profile leads to the elimination of the point of inflection on the velocity profile of pipe flows to delay turbulent transition. It is also clarified why this technique is not effective at higher Reynolds number because the flattened velocity profile violates the criterion for flow stability relating to transition to turbulence.

Biofilm growth Dynamics in a Micro-Irrigation with Reclaimed Wastewater in the Field scale.

The dripper clogging due to the development of biofilm can reduce the benefits of micro-irrigation technology implementation using reclaimed wastewater. The narrow cross-section and labyrinth geometry of the dripper channel enhance the fouling mechanisms. The aim of this study was to evaluate the water distribution and biofouling of drip irrigation systems at the field scale during irrigation with treated wastewater. Six 100 m lines of commercial pipes with two pressure-compensating dripper types (flow rate, Q, of 0.65 L.h-1 and 1.5 L.h-1, respectively) were monitored for four months. Different zones along the pipes were selected to evaluate the influence of hydrodynamical conditions (Reynolds number = 5400 to 0) on biofouling. Destructive methods involving the biofilm extraction by mechanical means, showed little biofilm development without significant differences in dry and organic matter content in function of the sampling location along the pipe or dripper flow rate (Q0.65 and Q1.5). These results were confirmed by non-destructive methods, such as optical coherence tomography, that nevertheless showed that biofouling concerned 15-20% of the total dripper labyrinth volume. Total organic carbon monitoring and its composition (by three-dimensional excitation and emission matrix fluorescence microscopy) showed that the biofilm did not significantly influence the organic matter nature. Our results indicated that the biological activity and biofilm development in irrigation systems were more affected by the environmental conditions, particularly water temperature, rather than flow conditions. This confirmed that treated wastewater with low organic content can be used in micro-irrigation systems without significant loss of efficiency, even in conditions requiring intensive irrigation, such as the Mediterranean climate.

Radial Mixing in Steady and Accelerating Pipe Flows

Radial Mixing in Steady and Accelerating Pipe Flows

Development of Machine Learning-Based Production Forecasting for Offshore Gas Fields Using a Dynamic Material Balance Equation

Offshore oil and gas fields pose significant challenges due to their lower accessibility compared to onshore fields. To enhance operational efficiency in these deep-sea environments, it is essential to design optimal fluid production conditions that ensure equipment durability and flow safety. This study aims to develop a smart operational solution that integrates data from three offshore gas fields with a dynamic material balance equation (DMBE) method. By combining the material balance equation and inflow performance relation (IPR), we establish a reservoir flow analysis model linked to an AI-trained production pipe and subsea pipeline flow analysis model. We simulate time-dependent changes in reservoir production capacity using DMBE and IPR. Additionally, we utilize SLB’s PIPESIM software to create a vertical flow performance (VFP) table under various conditions. Machine learning techniques train this VFP table to analyze pipeline flow characteristics and parameter correlations, ultimately developing a model to predict bottomhole pressure (BHP) for specific production conditions. Our research employs three methods to select the deep learning model, ultimately opting for a multilayer perceptron (MLP) combined with regression. The trained model’s predictions show an average error rate of within 1.5% when compared with existing commercial simulators, demonstrating high accuracy. This research is expected to enable efficient production management and risk forecasting for each well, thus increasing revenue, minimizing operational costs, and contributing to stable plant operations and predictive maintenance of equipment.

Structural stability for double-diffusion Brinkman fluid with Soret effect

This paper considers the double diffusive Brinkman flow in a semi-infinite pipe. By establishing a priori estimates of the solutions and setting an appropriate “energy” function, we not only obtain the continuous dependence and convergence of the solution on the Soret coefficient but also prove that the solutions decay exponentially with the distance from the finite end of the cylinder.

Investigation of Churn and Annular Flow Transition Boundaries in Vertical Upward Gas-Water Two-Phase Flow

ABSTRACT Flow patterns in two-phase flow in vertical upward pipes are crucial for predicting phase distribution, flow transitions, and stability. Existing studies on churn to annular flow transitions primarily focus on flow rates, physical parameters, pressure, and temperature, often overlooking pipe diameter. This study addresses this gap using a multiphase pipe flow experimental setup to examine transitions under varying pipe diameters, gas flow rates, and liquid flow rates. Results show that with a constant liquid flow rate, increasing pipe diameter requires a higher gas flow rate to form annular flow, leading to greater pressure gradients and smoother fluctuations. Conversely, with a constant gas flow rate, larger pipe diameters decrease the liquid flow rate needed for annular flow, resulting in smaller pressure gradients and smoother fluctuations. Smaller pipe diameters make annular flow formation easier, with smaller pressure gradients but larger fluctuations. A novel churn-annular flow transition boundary model was developed, considering factors like gas shear force, surface tension, gravity, viscous force, and pressure gradient. Evaluated with 804 experimental data sets, the new model’s prediction accuracy exceeds 98.19%, outperforming traditional models with 53.92%-86.27% accuracy, enhancing applicability across varying diameters.

Acceleration is the key to drag reduction in turbulent flow

A turbulent pipe flow experiment was conducted where the surface of the pipe was oscillated azimuthally over a wide range of frequencies, amplitudes, and Reynolds numbers. The drag was reduced by as much as 35%. Past work has suggested that the drag reduction scales with the velocity amplitude of the motion, its period, and/or the Reynolds number. Here, we find that the key parameter is the acceleration, which greatly simplifies the complexity of the phenomenon. This result is shown to apply to channel flows with spanwise surface oscillation as well. This insight opens potential avenues for reducing fuel consumption by large vehicles and for reducing energy costs in large piping systems.

The minimal seed for transition to convective turbulence in heated pipe flow

It is well known that buoyancy suppresses, and can even laminarise, turbulence in upward heated pipe flow. Heat transfer seriously deteriorates in this case. A new direct numerical simulation model is established to simulate flow-dependent heat transfer in an upward heated pipe. The model shows good agreement with experimental results. Three flow states are simulated for different values of the buoyancy parameter $C$ : shear turbulence, laminarisation and convective turbulence. The latter two regimes correspond to the heat transfer deterioration regime and the heat transfer recovery regime, respectively (Jackson & Li 2002; Bae et al., Phys. Fluids, vol. 17, issue 10, 2005; Zhang et al., Appl. Energy, vol. 269, 2020, 114962). We confirm that convective turbulence is driven by a linear instability (Su & Chung, J. Fluid Mech., vol. 422, 2000, pp. 141–166) and that the deteriorated heat transfer within convective turbulence is related to a lack of rolls near the wall, which leads to weak mixing between the flow near the wall and the centre of the pipe. Having surveyed the fundamental properties of the system, we perform a nonlinear non-modal stability analysis, which seeks the minimal perturbation that triggers a transition from the laminar state. Given the differences between shear and convective turbulence, we aim to determine how the nonlinear optimal (NLOP) changes as the buoyancy parameter $C$ increases. We find that at first, the NLOP becomes thinner and closer to the wall. Most importantly, the critical initial energy $E_0$ required to trigger turbulence keeps increasing, implying that attempts to trigger it artificially may not be an efficient means to improve heat transfer at larger $C$ . At $C=6$ , a new type of NLOP is discovered, capable of triggering convective turbulence from lower energy, but over a longer time. It is active only in the centre of the pipe. We next compare the transition processes, from linear instability and by the nonlinear non-modal excitation. At $C=4$ , linear instability leads to a state that approaches a travelling wave solution or periodic solutions, while the minimal seed triggers shear turbulence before decaying to convective turbulence. Deeper into the parameter space for convective turbulence, at $C=6$ , the new nonlinear optimal triggers convective turbulence directly. Detailed analysis of the periodic solution at $C=4$ reveals three stages: growth of the unstable eigenfunction, the formation of streaks, and the decay of the streaks. The stages of the cycle correspond to changes in the linear instability of the turbulent mean velocity profile. Unlike the self-sustaining process for classical shear flows, where the streak is disrupted via instability, here, decay of the streak is more closely linked to suppression of the linear instability of the mean flow, and hence suppression of the rolls. Flow visualisations at $C$ up to $10$ also show similar processes, suggesting that the convective turbulence in the heat transfer recovery regime is sustained by these three typical processes.

Synchronization Optimization of Pipeline Layout and Pipe Diameter Selection in a Drip Irrigation Network System Based on the Jaya Algorithm

To address the complexity and high computational burden in the design of drip irrigation networks, the Jaya algorithm is utilized to study factors affecting project costs, including equipment and pipeline depreciation and the operation and management costs of the irrigation area. A mathematical model of synchronization optimal design of pipe layout and pipe diameter selection in a drip irrigation network system with constraints on pipe diameter, flow velocity, and pipe pressure is established. Using an irrigation district in Xinjiang, China, as an example, the Jaya algorithm optimization design program was run independently 50 times, and the relative deviation of each optimization result from the optimal solution was calculated. The results show that the annual cost per unit area o is reduced to 635.99 RMB/hm2, a 25.34% reduction compared to the original engineering program, and the investment-saving effect is obvious. The relative deviation is controlled within 3%, which shows that the algorithm has stable convergence performance and can meet the requirements of actual engineering design. The Jaya algorithm eliminates the need for parameter tuning, and it excels in cost savings, algorithm stability, and computational accuracy, making it an effective method for the single-objective optimization design of drip irrigation networks.

A revisit of the development of viscoplastic flow in pipes and channels

This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves onto a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.

Entropy generation analysis of unsteady MHD nanofluid flow in a porous pipe

This article presents a numerical investigation into the entropy production of nanofluids flowing through a porous medium in a permeable conduit, focusing on water-based solutions containing Titanium Carbide (TiC) and Silicon Carbide (SiC) nanoparticles. These nanoparticles are selected for their heat transfer properties. The flow system's governing equations are developed and solved using the Runge-Kutta-Fehlberg method. The study examines the influence of key nondimensional parameters, including the solid volume fraction of nanoparticles, radiation parameters, and Reynolds number, on temperature, velocity profiles, and entropy generation. The results show that Silicon Carbide-water nanofluids perform efficiently in terms of heat transfer and entropy minimization. Additionally, Silicon Carbide exhibits low skin friction at the pipe wall, with this effect increasing as the solid volume percentage of nanoparticles rises. The study also indicates that irreversibility due to heat transfer becomes more significant near the pipe wall as the solid volume fraction decreases and increases with higher radiation parameters and Reynolds number. These findings are presented graphically and in tabular form to illustrate the physical significance of the problem.

Energy-based characterisation of large-scale coherent structures in turbulent pipe flows

Large-scale coherent structures in incompressible turbulent pipe flow are studied for a wide range of Reynolds numbers ( $Re_\tau =180, 550, 1000, 2000$ and $5200$ ). Employing the Karhunen–Loève decomposition and a novel approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions and $Re_{\tau }$ . With increasing $Re_{\tau }$ , two distinct classes of structures become more energetic, namely wall-attached and detached eddies. The Voronoi methodology is shown to delineate these two classes without the need for specific criteria or thresholds. At the highest $Re_{\tau }$ , the attached eddies scale linearly with the wall-normal distance with a slope of approximately $l_y\sim 1.2y/R$ , while the detached eddies remain constant at the size of $l_y \approx 0.26R$ , with a progressive shift towards the pipe centre. We extract these two classes of structures and describe their spatial characteristics, including radial size, helix angle and azimuthal self-similarity. The spatial distribution could help explain the differences in mean velocity between pipe and channel flows, as well as in modelling large and very-large-scale motions (LSM and VLSM). In addition, a comprehensive description is provided for both wall-attached and detached structures in terms of LSM and VLSM.

Master curves for unidirectional flows of FENE-P fluids in rectilinear and curvilinear geometries

We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio Wi/L , for a fixed solvent to solution viscosity parameter β. Here, Wi is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while L is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of Wi/L≫1, that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the Wi/L≫1 regime, for all the flows considered, the limit of zero solvent (β=0) is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for β=0 and β→0.

Calcium Carbonate Deposition Model Supporting Multiple Operating Conditions Based on the Phase-Field Method for Free-Surface Flows

The drainage systems of tunnels situated in limestone regions frequently encounter crystallization blockages. Numerous studies have addressed this issue, and their findings identified factors such as the flow velocity and temperature as influencing the crystallization process. However, these studies could not predict the occurrence of crystallization. Regarding theoretical approaches, most studies have focused on full-pipe operations or have solely considered flow-field dynamics without including simulations of the chemical reactions and mass transfers. This study introduces a mass-transfer model for drainage pipes based on a two-phase flow (water and air) with a free surface and non-full pipe flow that simulates the crystallization deposition process in drainage pipes. This model can predict the deposition conditions at varying flow velocities and intuitively visualize the crystallization process under the influence of various factors. The impact of flow velocity on the overall crystallization deposition process can be directly analyzed through simulations developed using this model. The results show that under conditions of incomplete pipe flow with no pressure at the outlet, the weight of the deposition first increases and then decreases within a certain velocity. This model can depict the variations within a 30 d period.

Predicting the urban stormwater drainage system state using the Graph-WaveNet

Graph Neural Networks (GNNs) have been applied to network data such as traffic flow and water distribution systems, yet their use in predicting the state of urban stormwater drainage systems remains rare. This study investigates the application of Graph-WaveNet (GWN), a type of GNN, in forecasting the states of stormwater systems in Kowloon, Hong Kong. Data was sourced from the Storm Water Management Model (SWMM) spanning 43 rainfall events from 2020 to 2023. Based on the preceding 30 to 60 min of network states and rainfall data, GWN predicted junction inflows, pipe flow rates, and relative water depths (fraction of full area filled by flow) for lead times up to 20, 20, and 30 min, with an R2 greater than 0.6, respectively. Prediction accuracy declines with longer forecast horizons. GWN predicts more time steps ahead for pipes’ flow rates and junctions’ inflows, but fewer for relative water depths during peak versus non-peak periods. It is also more effective at predicting states of large pipes and connected junctions downstream, compared to smaller upstream components. GWN's accuracy improves significantly with precise rainfall nowcasting inputs. This study establishes a significant baseline for GWN's performance in predicting urban stormwater systems during rainfall events.

Research on digital vibration model of typical components in pipe system

The spatial distribution of pipe system is complex, long span and multi-point elastic support, so vibration analysis of pipe system is required in the pipeline design. This paper takes the pipe system as a typical component, based on the Timoshenko beam model, establishes a dynamic procedure for straight pipe elements that considers the axial flow rate of fluid, the pressure on the pipe wall, the Poisson coupling effect of fluid and pipeline structure, and the axial, transverse and torsional vibration. Through Laplace transform, the frequency simplified dynamic model is established. And the frequency transfer matrix model of straight pipe elements and the boundary constraint matrix of common boundary (such as fixed support) is established. Finally, the frequency domain transfer matrix model of different pipeline elements are set to the overall transfer matrix of the flow pipe system, providing a convenient means for rapid optimization of pipe system vibration.

Quantifying the tangential oscillation of thermal stratification by using principal component analysis

Tangential oscillation of thermal stratification is a new finding in previous investigations on thermal-mixing process at pipeline T-junctions. This phenomenon can create regular temperature changes on the pipeline inner surface and lead to material damage caused by the degradation mechanism of thermal fatigue, which has been frequently reported as a reason for incidents in piping systems of nuclear power plants. Previous investigations cannot provide a quantitative description of this phenomenon, making it difficult to understand or evaluate the fatigue potential due to this phenomenon. In this study, a new method namely principal component analysis has been employed for quantitatively estimating the angular shift of the thermal stratification in pipe tangential direction. Time-dependent angular shift is extracted from the temperature data of the transient simulations of the pipe flow and confirms the initiation of the tangential oscillation of thermal stratification. Moreover, a characteristic frequency of approximately 2.3 Hz has been identified from the frequency spectrum of the time-dependent angular shift. It indicates a potential risk in the piping material due to thermal fatigue. Furthermore, results of this study show a high efficiency and accuracy of the principal component analysis method in quantifying tangential oscillation. It can be applied in further investigations of similar phenomena of thermal stratification.

Experimental characterization of coherent states in turbulent magnetohydrodynamic pipe flow

Investigating magnetohydrodynamic (MHD) flows, whether through experimental or numerical study, presents significant challenges. A minimum requirement for experimentally studying MHD flows using optical measurement methods is the use of highly conductive, transparent fluids and strong magnetic fields in close proximity to the flow confinement. In response to these complexities, this work introduces a large-scale pipe rig setup, integrating a magnetic frame structure with a Stereoscopic Particle Image Velocimetry system for MHD flow field characterizations. This allows for the detailed analysis of coherent flow patterns under conditions of fully developed MHD turbulence. In alignment with earlier numerical studies on turbulent MHD pipe flow, our research confirms that low Hartmann number turbulence statistics are minimally affected by the applied magnetic field. Nevertheless, we show that the magnetic field significantly extends the streamwise extent of detected coherent organizational states, while their wave number distribution and morphology largely remain unchanged.

Two-group interfacial area concentration model for dispersed gas-liquid flows in large-diameter pipes

Interfacial area concentration (IAC) plays a critical role in heat and mass transfers between gas and liquid phases through the interfaces. As interfacial area increases, mass and heat transfers between phases increase. Hence, a reliable IAC estimation is important for two-phase flow numerical simulations to conduct engineering designs and safety analyses. Gas bubbles show different behavior according to their shapes and sizes. Based on the size, gas bubbles can be classified into two groups that show different characteristics, such as IAC. Hence, two-group modeling helps to achieve a general approach for estimating the IAC in bubbly to beyond-bubbly flow regimes. Available models in the literature use empirical correlations to obtain group one and group two void fractions. These empirical approaches are not reliable for different flow conditions. In addition, these models are usually complex with several empirical constants. This study aims to develop a two-group area-averaged IAC model for upward vertical dispersed flows through large-diameter pipes. In addition, this study proposes using a general approach based on the two-group drift-flux model to calculate two-group void fractions rather than applying empirical correlations. The models are evaluated using 156 two-group measured data points in dispersed flow conditions through large-diameter pipes. The resulting prediction errors for group one and group two IAC models are 24.1 % and 34.2 %, and the errors for group one and group two void fraction predictions are 22.8 % and 25.6 %, respectively.

Investigation on intermittent flow characteristics in horizontal pipe by visualization measurement method

Accurate measurement and prediction of the intermittent flow characteristics in horizontal pipes is important for constructing multiphase flow models and ensuring pipe flow safety. In this paper, a quantitative image post-processing technique for intermittent flow characteristics based on gray histogram image similarity is proposed, which can realize the measurement of slug frequency. In addition, the technique also has the ability to classify a large number of images, and can quickly find the elongated bubble head, liquid film area and liquid slug area of intermittent flow. On the basis of this technique, combined with image post-processing methods such as gas–liquid interface feature analysis, a set of intermittent flow image processing technique with perfect route is formed. Based on this post-processing technique, the similarity image oscillation trajectories of plug flow and slug flow are obtained. There are differences in the similarity image oscillation trajectories of the two intermittent sub-flow patterns, and the similarity image of the plug flow has an obvious platform period and trailing rising line, which can be used as a basis for the classification of the two intermittent sub-flow patterns. A correlation for predicting the slug frequency of intermittent sub-flow patterns is developed. The accuracy of this slug frequency prediction correlation can be improved by about 10 % compared to not dividing the sub-flow patterns. When the mixture Froude number Frm is less than 5.0, the radial position of the elongated bubble head decreases linearly as the Frm increases. When the Frm is greater than 5.0, the elongated bubble head oscillates near the middle of the pipe. Prediction correlations for the radial position of the elongated bubble head and the slug velocity are established separately, and the maximum error is ± 10 %. The modified mixed Froude number is proposed, and based on this, a new prediction model for the transition from plug flow to slug flow is established.