Pipe Flow Research Articles

Numerical Simulation of the Entrance Length in a Laminar Pipe Flow at Low Reynolds Numbers

According to Prandtl’s boundary layer theory, the entrance length refers to the axial distance required for a flow to transition from its initial entry condition to a fully developed flow where the velocity profile stabilizes downstream. However, this theory remains applicable only under the assumption of Re ≫ 1, while its validity diminishes under low-Reynolds-number conditions. This study utilizes OpenFOAM based on the finite volume method to numerically examine Newtonian and viscoelastic fluids in a laminar circular pipe flow. The objective is to determine the range of Reynolds numbers for which the differential equations from within the Prandtl boundary layer theory are strictly valid. Additionally, the study explores the effects of Reynolds numbers (Re) ranging from 50 to 100, s solvent viscosity ratio (β) fixed at 0.3 and 0.7, and Weissenberg numbers (Wi) ranging from 0.2 to 5 on the entrance length and friction factor for the Oldroyd-B model. The results indicate the presence of a lower Reynolds number that impedes the attainment of the outcomes predicted by the Prandtl boundary layer theory for the entrance length. The inertia effect, the increase in solvent viscosity contribution, and the elastic effect exhibit a linear relationship with the entrance length and friction factor.

Horizontal Shale Oil Production Wells Experience Hydraulic Fracture Choking Effect Under Closure Stress

The choke effect of hydraulic fractures on a horizontal shale oil well during production is shown using a coupled matrix–fracture–wellbore flow simulation model. The effect is the consequence of a significant loss in hydraulic fracture conductivity near the wellbore due to fracture closure stress. A consequence of the choke effect is that the fluid pressure in the fractures is maintained high enough to keep gas in the solution. The gas leaves the solution only after the choke region is passed when the oil with its solution gas begins the flow in the wellbore, and when it abruptly experiences a steep pressure gradient. This phenomenon has a long period of producing a constant gas–oil ratio (flat GOR) as its signature. The influence of the choke effect on the wellbore flow regimes is also investigated in the hydraulic-fractured horizontal section of the reservoir. During horizontal pipe flow, a distributed–intermittent flow sequence develops from the toe to the heel of the shale oil well over the production time. However, in the presence of the hydraulic fractures, a sequence of distributed–intermittent–transient–segregated flows develops. This indicates that the choke has the potential to affect the flow regimes in the horizontal section.

Non-linear Analysis of Two-Phase Flow Fluctuation by Means of SVD Entropy Surrogate Data Analysis

Two-phase flow in pipes displays a diverse range of patterns, influenced by factors such as pipe inclination, liquid superficial velocity and gas superficial velocity. Accurate classification of these flow patterns is essential for controlling fluid transport in various industries. This study investigates the non-linear dynamics of two-phase flow in inclined pipes using voltage fluctuations as a proxy signal. Singular value decomposition (SVD) entropy and surrogate data analysis were employed to quantify the non-linearity content in the voltage signals. The results, obtained from examining two-phase flow patterns under varying pipe inclination and gas superficial velocity, reveal that both entropy and non-linearity are dependent on flow conditions. The primary non-linear contribution was found to be linked to discontinuities in the proxy signal, reflecting the heterogeneity of the flow pattern. This analysis demonstrates the effectiveness of the entropy-non-linearity approach in classifying flow patterns based on pattern diversity and non-linearity contribution.

Measuring Variable Discharge Under Partially Full Pipe Flow

Accurately measuring the discharge in partially full pipe flow is both difficult and demanding. In this regard, a new meter sensor using microwave technology has been evaluated for determining partially full pipe discharge across a range of flow depths. A range of experiments with smooth PVC pipes of two different pipe diameters (101.6 and 152.4 mm) at two different pipe slopes (1° and 2°) were carried out under turbulent (Reynolds numbers = (0.27–3.25) × 105) and supercritical flows with Froude numbers Fr in the range of 1.5 ≤ Fr ≤ 3.6. Our results showed that when combining the microwave sensor readings with either the Chezy equation or Manning’s law, reliable discharge predictions were found compared to the measured discharge across all experiments. The range of R2 values obtained from the plots of predicted versus measured discharge were all greater than 97%, indicating an accuracy allowing the meter to be used in commercial applications.

Laboratory Insights Into the Correlation Between Sediment Yield, Soil Electrical Conductivity and pH in Surface and Piping Erosion

ABSTRACTSoil erosion, driven by factors such as water, wind, tillage and so forth, has significant impacts on both humanity and the environment. Soil erosion, including surface and subsurface (piping) erosion, significantly affects the environment and infrastructure. This research examines the impact of soil properties, that is, electrical conductivity (EC) and pH, on sediment yield in both surface and piping erosion. Rigorous laboratory experiments were conducted on slopes of 5%, 10% and 15%, using a soil profile that consisted of a 5 cm water‐restrictive layer of clay loam and a 15 cm topsoil layer of loam. Three experimental configurations were devised: exclusive pipe flow at 27 L h−1 (M1), rainfall intensity at 30 mm h−1 (M2), and a composite scenario integrating both rainfall and pipe flow (M3), with each configuration executed three times. The pipe flow was simulated using a plastic tube with a 1 cm diameter, placed on top of the water‐restrictive layer, which helped create conditions for subsurface flow. Results showed that sediment yield predictions varied with slope. For surface erosion, the most favourable performance was observed at 5% slope with pipe flow (R2 = 0.76, NSE = 0.76), while combined scenarios performed adequately (R2 = 0.71). At 10% slope, performance was good (R2 = 0.66, NSE = 0.65), and at 15%, results ranged from acceptable to very good. In piping erosion, the combined scenario consistently performed best (R2 = 0.78–0.91, NSE = 0.67–0.82), particularly at 5% and 15% slopes. These findings offer valuable insights into erosion dynamics and can help improve soil management strategies.

Effect of turbulent dispersion force models on hydrodynamic behaviors of slurry flows in horizontal pipes

The Eulerian–Eulerian approach, coupled with the Reynolds-averaged Navier–Stokes (RANS) technique, is a practical combination for simulating industrial slurry flows. In such simulations, the turbulent dispersion force plays a critical role in driving particles from regions of high concentration to low concentration, thereby influencing particle distribution and overall hydrodynamic behaviors. The performance of the proposed numerous turbulent dispersion force models has not been evaluated systematically in simulating sand–water slurry flows in horizontal pipes. This study investigates turbulent slurry flows in horizontal pipes under various flow conditions using the Eulerian–Eulerian approach combined with RANS. Simulations without turbulent dispersion force and with three widely used turbulent dispersion force models—Lopez de Bertodano, Simonin, and Burns—are analyzed based on predictions of streamwise velocity, secondary flow, solid concentration distribution, and liquid turbulent kinetic energy. A comparison of the simulation results with experimental data from the literature on streamwise velocity and solid concentration distribution highlights the critical importance of incorporating the turbulent dispersion force for accurate predictions. The Lopez de Bertodano model significantly underestimates the turbulent dispersion effect and, therefore, is not recommended for such flows. The Simonin and Burns models exhibit better performance; however, further refinement is required to achieve higher predictive accuracy. A computational efficiency analysis is conducted. Considering both accuracy and efficiency, the Burns model is identified as the optimal choice for the flow cases examined in this study. These findings may serve as a useful reference for slurry simulations in horizontal pipelines and assist researchers in making more informed model selections.

Performance evaluation of modified hydrokinetic turbines in pipe flow with velocity correction technique

Performance evaluation of modified hydrokinetic turbines in pipe flow with velocity correction technique

Heat transfer characteristics of downward saturated boiling flow in vertical round pipes

Heat transfer characteristics of downward saturated boiling flow in vertical round pipes

Experimental and numerical study of primary instability of a two-phase stratified flow in a circular pipe

Experimental and numerical study of primary instability of a two-phase stratified flow in a circular pipe

Numerical simulation of coarse particle-liquid two-phase flow in deep-sea mining vertical pipes

Numerical simulation of coarse particle-liquid two-phase flow in deep-sea mining vertical pipes

A new mechanistic perspective on the prediction of deposition velocity in turbulent liquid-solids pipe flow

A new mechanistic perspective on the prediction of deposition velocity in turbulent liquid-solids pipe flow

Particle size segregation in granular pipe flow.

The flow of granular material through pipes is characterized by significant variations in solid fraction (density waves) along the pipe. Previously, it has been shown that this intermittent flow behavior can be mitigated by adding a texture to the pipe's inner wall. This work shows that adding surface roughness can lead to particle size segregation as a side effect in bidisperse systems. Using particle simulations, we characterize the parameter ranges in which segregation occurs.

A general double layer-averaged model for water–air two-phase pipe flows

A general double layer-averaged model for water–air two-phase pipe flows

Scale Inhibition by Ultrasonic Reactor Operating in Pipelines

Calcium carbonate scaling can lead to several problems in the oil and gas industry, reducing pipe flow and deteriorating thermal processes. This work investigates the mechanism of scale inhibition using ultrasonic technology. An ultrasonic device designed to minimize the adhesion of calcium carbonate crystals in pipelines is detailed. The device equipped with three high-power ultrasonic transducers (60 W x 40 kHz) was used to stimulate calcium carbonate precipitation in a hydraulic system specifically assembled to study the calcium carbonate scaling by simultaneous injection of CaCl2·2H2O and NaHCO3. A transparent plastic hosepipe 5 m long was used as a proof-pipe enabling visual observation. Pressure drop and crystal morphology were evaluated. Ultrasonic field evaluation tests inside the developed device showed strong cavitation activity and significant erosion on aluminium foils. After 140 minutes of continuous flow through the pipe under US irradiation, volumetric flow rate remained stable. A reduction in hydraulic resistance of 42% was found, if compared to the test condition without any scaling protection. The morphology of the crystals evaluated by scanning electron microscopy showed that crystals became smaller and more rounded.

Commingling of 2-D Darcian seepage with pipe flow: the Polubarinova-Kochina –Chanson problem revisited

ABSTRACT Toe drains in earth dams intercept seepage and convey water through a perpendicular pipe. This study investigates commingled flow at contrasting Reynolds numbers using sand tank (ST) experiments and HYDRUS2D modeling. In ST, the flow rate, Q, through a bottom outlet (orifice) connected to a valved-pipe is discharged into a measuring burette. In coupled flow, Darcian heads and flow rates depend on soil compartment size, hydraulic conductivity, and pipe characteristics. The ST experiment found Q from ST orifice (STO) higher than from connected pipe by 63%. Q increases with shorter pipe length. STO is analytically modeled as a Zhukovsky “slot drain.” HYDRUS2D simulations show similar flow rates for an impermeable-lateral-boundary ST rather than equipotential. An analytical 2D solution for an infinitely long ST gives nearly the same flow rate as the HYDRUS2D model. These findings enhance the understanding of commingled Darcian-pipe flows and aid efficient drainage design in earth dams.

Numerical Investigation of Geothermal Steam-Water Two-Phase Flow in Horizontal Pipes

Two-phase flow is commonly encountered in various industrial and technological processes, including geothermal systems. The flow pattern, pressure drop, and water holdup of two-phase flow formation are critical parameters that affect the efficiency and safety of geothermal systems. This study employed CFD simulations with both 2D and 3D approaches. The inner diameter of the pipe was set to 26 mm, and the length was set to 1000 mm. The superficial velocities of steam (JS) ranged from 6 to 30 m/s, and for water (JW) from 0.02 to 0.2 m/s. The operating conditions were at temperature of 443.15 K and pressure of 791 kPa. Validation was performed by comparing the simulation results with experimental data. The findings indicated that the flow pattern, pressure drop, and water holdup were significantly influenced by the superficial velocities of steam and water. The flow patterns observed in this study include stratified wavy, annular, and mist flow. Stratified wavy flow is considered a safe flow pattern, especially in the context of steam-water flow in geothermal systems. Moreover, the results show that both pressure drops and water holdup (at a fixed JW) increased as JS increased. A 3D approach provides more realistic results, while the 2D approach is recommended for faster simulations of simpler models. This research contributes to improving the design quality and optimizing the operation of geothermal systems.

Three-dimensional coherent structures in a curved pipe flow

Dean’s approximation for curved pipe flow, valid under loose coiling and high Reynolds numbers, is extended to study three-dimensional travelling waves. Two distinct types of solutions bifurcate from the Dean’s classic two-vortex solution. The first type arises through a supercritical bifurcation from inviscid linear instability, and the corresponding self-consistent asymptotic structure aligns with the vortex–wave interaction theory. The second type emerges from a subcritical bifurcation by curvature-induced instabilities and satisfies the boundary region equations. A connection to the zero-curvature limit was not found. However, by continuing from known self-sustained exact coherent structures in the straight pipe flow problem, another family of three-dimensional travelling waves can be shown to exist across all Dean numbers. The self-sustained solutions also possess the two high-Reynolds-number limits. While the vortex–wave interaction type of solutions can be computed at large Dean numbers, their branch remains unconnected to the Dean vortex solution branch.

Numerical Simulation of Non-Isothermal Laminar Oil Flow in an Axisymmetric Pipe

Numerical Simulation of Non-Isothermal Laminar Oil Flow in an Axisymmetric Pipe

What Is the Turbulence Problem, and When May We Regard It as Solved?

Turbulent motion of fluids is often thought of as a grand problem, but what exactly is this “turbulence problem”? Because it has often been proclaimed as very difficult and unsolved, when can we claim that it is solved? How does this situation in turbulence compare with other complex problems in physical sciences? Addressing these questions is not trivial because everyone has their favorite idea of what is required of the “solution.” The answers range from being able to calculate the pressure drop in turbulent pipe flow to being able to calculate anomalous scaling exponents to answering the regularity problem of the Navier–Stokes equations. Taking an absolute position on the basis of any of these, or other similar examples, is incomplete at best and potentially erroneous at worst. We believe that it is beneficial to have an open discussion of this topic for the advancement of the research agenda in turbulence. This article is an attempt to address the question of what constitutes the turbulence problem, its place in the scientific enterprise as a whole, and how and when one may declare it as solved.

Advancing Pressure-Based Flow Rate Soft Sensors: Signal Filtering Effects and Non-Laminar Flow Rate Determination

Precise flow measurement is crucial in fluid power systems. Especially in combination with pressure, hydraulic power can be particularly beneficial for predictive maintenance and control applications. However, conventional flow sensors in fluid power systems are often invasive, thus disrupting the flow and yielding unreliable measurements, especially under transient conditions. A common alternative is to estimate the flow rate using pressure differentials along a pipe and the Hagen–Poiseuille law, which is limited to steady, laminar, and incompressible flows. This study advances a previously introduced analytical soft sensor, demonstrating its ability to accurately determine the transient pipe flow beyond laminar conditions, without requiring a dedicated flow rate sensor. This method provides a robust and computationally efficient solution for real-world hydraulic systems by applying two pressure transducers. A key contribution of this work is the investigation of signal filtering, revealing that even a simple first-order low-pass filter with a 100 Hz cutoff frequency significantly improves accuracy, which is demonstrated for pulsation frequencies of 5, 10, and 15 Hz, where the filtered results closely match experimental data from a test rig. These findings underscore the soft sensor’s potential as a reliable alternative to traditional flow sensors, offering high accuracy with minimal computational overhead for a wide range of flow conditions.