Bend Flow Research Articles

Computation of 2D Supercritical Free-Surface Flow in Rectangular Weak Channel Bends

Computation of 2D Supercritical Free-Surface Flow in Rectangular Weak Channel Bends

Investigating supercritical flow characteristics and movement of sediment particles in a narrow channel bend using PTV and video footage

This experimental study investigates the cause of nonuniform invert abrasion observed at sediment bypass tunnel (SBT) bends by examining the variations in velocity distributions, turbulence properties, bed shear stress, and bulk sediment movements under three supercritical bend flow conditions, detailed investigation of such flow is scarce. Using a laboratory-scaled model (1:22) of the downstream bend at Solis SBT, Switzerland, the research utilized particle tracking velocimetry and high-speed cameras with spherical sandstones and glass spheres representing sediments. The results indicate that as the secondary currents develop in the flow direction, the flow properties and sediments redistribute across the channel: the high-momentum fluids are directed toward the outer wall, the bed shear stress increases toward the outer wall, and the sediments are pushed toward the inner wall, which then follow this path downstream, even in straight sections, despite lower bed shear stress. This distribution of sediments, driven by secondary currents, leads to deeper invert abrasions toward the inner wall at SBT bends and downstream sections. Thus, these abrasions are primarily influenced by sediment movement rather than the bed shear stress alone. The study's findings are also valuable for validating future numerical simulations.

Application of Delaunay adaptive mesh refinement in flood risk assessment of multi-bridge system with short distance

To ensure bridge safety, the flood risk analysis is significant important. However, due to the small size and large number of piers in the short-distance multi-bridge system, the extremely long calculation time and low efficiency of the numerical model are induced by the small mesh size and large mesh number. In this paper, a flood risk assessment model of the multi-bridge system with short distance was established to improve the calculation efficiency based on the finite volume method combined with the Delaunay mesh adaptive refinement method. The calculated water level with refined and non-refined mesh was compared with the experimental data of a partial failure dam break test case and Shukry experiment of open channel bend flow. The calculated water level results are in good agreement with the experimental data. In addition, the mesh refinement model improved the calculation efficiency by more than 73% with ensuring the calculation accuracy. Finally, the flood risk of a real multi-bridge system with short distance was evaluated by using the numerical model. The calculated results shown that, different from the general flow law, the water level in the upstream and downstream channel of Bridge 2 rose with a maximum difference value of 0.326 m while the water level in the far downstream channel of Bridge 2 dropped result from the construction of Bridge 2 on the basis of the Bridges 1, 3 and 4. The construction of Bridge 2 also increased the flow velocity around Bridge 3 with maximum 0.013 m/s. This study provides a new tool and technical reference for flood risk analyses of similar multi-bridge system with short distance.

Hybrid aeroacoustic investigation of turbulent 90° pipe bend flow with source terms from Large-Eddy Simulation

The internal, low Mach number, turbulent flow-induced acoustic field of a cylindrical 90° pipe bend with a curvature radius Rm/D=1.02 is investigated using hybrid Computational Aero-Acoustics (CAA). Incompressible Large-Eddy Simulation (LES) is used to computationally describe the turbulent flow field at bulk Reynolds numbers ReB=5000,12000,26000 and 66000. The incompressible LES predicts all salient flow features, like the separation from the inner wall of the bend followed by a turbulent recirculation zone, in good agreement with literature. The internal flow-induced noise is predicted by Acoustic Propagation Simulations (APS) applying Lighthill’s Equation (LE), Ribner’s Dilatation Equation (RDE) and the Perturbed Convective Wave Equation (PCWE), provided with acoustic source terms obtained from the incompressible LES. The turbulent recirculation zone is the most active region for generating acoustic sources. Among the two constituent components of the PCWE source term, the local pressure time derivative term turned out as clearly dominant in this region, so that PCWE and RDE predicted similar acoustic fields. The sub-grid scale (SGS) model applied in LES notably contributes only at high frequencies to the total LE source term, starting from f=2000 Hz for the lower Reynolds numbers and beyond for the higher. The mapping of source terms from the boundary layer resolving LES grid onto the typically coarser preferably uniform APS grid leads to lower high-frequency signal amplitudes for coarser APS mesh size in regions with small turbulent structures. The impact of this amplitude reduction on the predicted acoustics sound power levels was still very small, exhibiting relative differences less than 0.7% for the different APS meshes. Despite the LES-specific limitations expected from the decrease of directly resolved content for higher Reynolds numbers, the use of increasingly underresolved source terms did not significantly lower the accuracy of finally predicted acoustics. The comparison of the acoustic results against data from dedicated measurements generally showed very good agreement for all Reynolds numbers.

Flow features of a horseshoe tunnel bend

Previous research on bend flow has mainly focused on rectangular channels or circular conduits with small bend radii. This study investigates the dynamics of bend flow in an unexplored geometry: the horseshoe cross-section with large bend radii, a typical configuration in hydraulic tunnels. We examine two critical flow features, energy losses and superelevation, employing theoretical equations and dimensional analysis based on experimental data collected on a physical model of a diversion tunnel. The findings reveal an exponential decrease in the bend loss coefficient with increasing Reynolds numbers and shockwaves within the bend for Froude numbers exceeding 1.945. These findings are relevant in a hydraulic tunnel design with similar features and offer insights to minimize energy losses and maintain stable flow conditions.

Numerical Investigation of the Impacts of Large Particles on the Turbulent Flow and Surface Wear in Series-Connected Bends

The deep sea harbors abundant mineral, oil, and gas resources, making it highly valuable for commercial development, including the extraction of minerals. Due to the relatively large particle size of these minerals, how they interact with fluids is significantly different from that of small particles. However, there has been limited simulation research on the impacts of large particles (the diameter of particles is at the level of centimeters) on the flow and wear characteristics in bends, because the simulation of the particles at such a size is difficult. Additionally, in the field of deep-sea mining, multiple bends are simultaneously connected in series, and the wear in such bends has garnered increasing attention. Based on an improved CFD-DEM model, this article solved the issue that traditional unresolved CFD-DEM methods cannot accurately simulate large particles in a hydraulic conveying pipe and bend. After validating the accuracy of this model against classical experiments, the paper comprehensively analyzes the modulation effect of large particles on turbulence, and the effects of different particle diameters, particle transport concentrations, and transport velocities on the wear of bends connected serially. Finally, the bends connected serially in various configurations are simulated to study the wear on the bent interior surfaces. Results indicate a pronounced modulation effect of large particles on turbulence at higher transport concentrations; the wear rate in the combined bends does not exhibit a linear correlation with the collision frequency of particles on the wall surface. Furthermore, different configurations of serially connected bends exhibit significant differences in the wear morphology of the second bend.

Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend

Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend

Novel design and numerical investigation of a windward bend flow field for proton exchange membrane fuel cell

3D flow field design usually improves the performance of proton exchange membrane fuel cell (PEMFC) with the penalty of a dramatically increasing pressure drop. To surmount this issue, a novel windward bend flow field that exhibits superior mass transfer performance under a constant pumping power is proposed in this study. The performance of PEMFC with windward bend flow field is numerically compared with two canonical 3D flow fields, namely 3D wave flow field and cutting cylindrical baffles flow field. Results demonstrated that compared with two canonical 3D flow fields, windward bend flow field gets a better water management capability. The optimal distance, tilt angle and direction for the windward bend structure embedded in channel are 2.0 mm, 15° (at the direction of the front section of the windward bend structure tilts towards membrane electrode assembly). Furthermore, the average enhancement rate of the maximum power density of PEMFC with optimal windward bend flow field is 7.6 % and 12.4 % compared with cutting cylindrical baffles flow field and 3D wave flow field owing to the larger Sherwood number of optimal windward bend flow field under the specified pumping power range.

Computational Analysis of Rheological Secondary Flow in a Pipe-Manifold Containing In-Plane Double Bends

Non-Newtonian fluid flow in pipe bends is inevitable in industrial applications. Previous researchers have extensively explored Newtonian flow through curved ducts. However, the non-Newtonian counterpart gets little attention. We study the turbulent flow of shear-dependent fluids obeying the Power-Law model in a pipe manifold containing an in-plane double bend. Ostwald–de Waele's power law is used to model the fluid's rheology. We utilize computational fluid dynamics (CFD) to solve Reynolds-averaged Navier–Stokes (RANS) equations with the k-ε turbulence model. We validate our numerical results with previous experimental results. The in-plane double bend perturbs the flow in the pipe manifold to develop a Prandtl's secondary flow of the first kind. A fully developed flow at the bend upstream is disturbed due to the bend's curvature and regains its fully developed characteristics upon a certain downstream length after the exit of the bend. We study the rheological characteristics of the secondary flow within the bend and the evolution of fluid flow at the bend downstream. We demonstrate that the centrifugal force-dominated secondary flow increases with a decrease of the non-Newtonian power-law index. We capture the camel's-back-shaped velocity profiles within the bend due to accelerating-decelerating flow. The study reveals that the average flow velocity increases along the bend with a corresponding pressure head loss. We quantify this velocity rise by a newly introduced non-dimensional number, viz. enhancement ratio. The double bend's enhancement ratio decreases with an increase in n.

Study on the influencing parameters of rough-strip energy dissipators of curved spillways based on orthogonal tests and numerical simulation

Abstract Rough-strip energy dissipators (R-SEDs) can be arranged at the bend bottom of curved spillways to dissipate energy and divert flow for bend flow. Using the entropy weight and TOPSIS methods, a multi-criteria evaluation system was established for comprehensive energy dissipation and flow diversion effects of R-SEDs. Orthogonal tests and numerical simulation were conducted to analyze factors affecting these effects (average R-SED height, R-SED angle, R-SED spacing, bend width, bend centerline radius and discharge flow rate). It was found that bend width and bend centerline radius significantly affected R-SEDs' energy dissipation effects. Average R-SED height, R-SED spacing and bend centerline radius significantly affected R-SEDs' flow diversion effects. Bend width, average R-SED height and bend centerline radius significantly affected R-SEDs' combined effects of energy dissipation and flow diversion. Their energy dissipation effects were larger than the flow diversion effects. R-SEDs can effectively alleviate adverse hydraulic phenomena in curved spillways. With the recommended parameters, R-SEDs showed the best performance, with the energy dissipation rate increasing by 18.67% and the water surface superelevation coefficient decreasing by 26.14%. The accuracy of the multi-criteria evaluation system was verified. This study can provide a reference for the R-SED design of similar curved spillways.

Non-dimensional scaling of passive adaptive blades for a marine current turbine

For tidal energy to support access to off-shore electricity, further development is needed to decrease costs and increase reliability of current turbines at relevant scales. Blade pitch control strategies can significantly reduce structural loads in above-rated flow conditions by shedding power through decreased angles of attack. This can be accomplished through an active strategy using motorized blades or a passive adaptive strategy using flexible, self-twisting blades. We focus this study on the passive adaptive approach in which the composite fibers of the blade are oriented off-axis to produce a coupling between bend and twist deformations.
 Extending laboratory results to larger, open-water designs requires an understanding of hydrodynamic and hydroelastic scaling. While dimensionless scaling relations have been extensively studied for current turbines with rigid blades, relatively few studies discuss appropriate hydroelastic scaling for passive adaptive blades. In this study, we experimentally apply non-dimensional scaling laws to laboratory-scale passive adaptive turbine blades and demonstrate similarity in blade deformation and non-dimensional loads across scales.
 When Cauchy similarity is achieved between model and full-scale, the same steady-state blade loading and blade deformation are expected. We define Cauchy number as Ca = ρUo2/E, where ρ is the water density, Uo is the freestream velocity upstream of the turbine, and E is the transverse flexural modulus of the blade (i.e., elasticity corresponding to bending in the flapwise direction). We tested the effectiveness of Cauchy-scaling by designing an experiment in which blade bending stiffness and flow speed varied, but Cauchy number remained constant. The first blade used a 7-ply carbon fiber spar while the second blade used a 5-ply carbon fiber spar, both fabricated with unidirectional fibers oriented 10° off-axis and cast in a semi-rigid polyurethane using the same mold. All other non-dimensional parameters relevant to hydrodynamic scaling were held constant, where possible.
 As hypothesized, we observed agreement in thrust coefficient, deflection, and twist when Cauchy similarity was achieved, particularly when flow remained attached over the entire blade span. Small differences of 0-7% were observed in normalized thrust, deflection, and twist compared to 50-65% when Cauchy number was allowed to vary by 50%. We did not observe this similarity for normalized mechanical power between the 5-ply and 7-ply blades, but hypothesize that the source of the disagreement was a small surface defect in the urethane on the 5-ply blade. The experiment will be repeated to confirm this hypothesis and included in future presentations of this work.
 Our experimental result partially demonstrates the effectiveness of using Cauchy number to scale passive adaptive marine current turbine blades and model their steady-state hydrodynamic and hydroelastic behaviors in a consistent, non-dimensional manner. Accurate experimental models are critical to support the development of passive adaptive blades, which may obviate the need for an active pitch mechanism, thereby increasing reliability and decreasing maintenance costs. Finally, we present initial results from a field-scale turbine equipped with rigid and passive adaptive blades, demonstrating a path towards validating our conclusions from lab-scale testing.

Experimental Study of Secondary Flow in Narrow and Sharp Open-Channel Bends

Secondary flow is a prominent feature of channel bends; it alters the streamwise velocity and bed shear stress distributions. Experiments were conducted to investigate the complex pattern of secondary flow in a narrow and sharp open-channel bend and the underlying mechanism of generation of multiple circulation cells. Compared with the moderate bends, the sharp bends are characteristic of multiple circulation cells from the 90° section. In addition to the curvature-induced circulation cell (S1) and turbulence-induced counter-rotation circulation cell (C1) near the outer bank, another circulation cell (S2) was observed near the inner bank and was attributed to flow separation. A term-by-term analysis of the vorticity equations indicates that the centrifugal term favours S1 and C1 while opposing S2. The turbulence-related term accounts for the formation of C1 and S2. The advective transport term redistributes vorticity and maintains the existence of S2. The dependence of secondary flow structure on Reynolds number and aspect ratio was also explored. With an increase in the Reynolds number from 23000 to 37000, both the strength and size of C1 are reduced by 50%, whereas the size of S2 increases by 20%, and its strength slightly decreases. With a decrease in the aspect ratio from 3.3 to 2, the strengths of S1, S2, and C1 are doubled, and the sizes of C1 and S2 increase by 90% and 20%, respectively.

The effects of a spur dike location in a 90° sharp channel bend on flow field: Focus on anisotropy degree and anisotropy nature

In this research, the flow features around a spur dike located in a 90˚ sharp channel bend have been studied experimentally in detail. Results showed that the effects of the spur dike on upstream sections increased by increasing α (spur dike location from the beginning of the bend). In addition, by increasing α, the horseshoe vortex (C3) and secondary flow in the channel bend (C1) strengthened. The energy and the Reynolds shear stress in the C3 region decreased by increasing α. It is recommended to use a Barycenteric Map (BM) instead of the normal Reynolds stresses to find the anisotropy nature accurately. A strong anisotropic condition was detected at the border of the recirculation flow region and the main flow. However, in the C3 and the interaction regions, the isotropy condition improved. In the main flow region, by increasing α, the isotropy degree improved. However, by increasing α, an increase in the development of the region with a high anisotropy degree towards the recirculation region was observed. The anisotropy degree in the near-bed layer region and the shear layer region is comparable. However, the anisotropy nature is different. The maximum error of the numerical simulation based on isotropic turbulence occurred at the shear layer region where the severe cigar-shaped turbulence occurred.

Analysis of main influencing factors of energy dissipation and flow diversion effects of rough-strip energy dissipators in curved spillways based on Plackett–Burman design

Abstract Rough-strip energy dissipators (R-SEDs) at the bottom of spillway bends have energy dissipation and flow diversion effects on bend flow. In this paper, twelve Plackett-Burman tests were conducted. Energy dissipation rate and coefficient of variation of superelevation were used as evaluation indices. Influencing factors (i.e., relative height, height ratio, spacing, angle and thickness of R-SEDs as well as centerline radius, width, angle and bottom slope of the bend) of R-SEDs' energy dissipation and flow diversion effects were analyzed using Minitab 21.1 in combination with the entropy weight method and the TOPSIS method. Relative height of R-SED and bend angle were significant factors affecting energy dissipation effects; height ratio of R-SED and centerline radius of the bend were significant factors affecting flow diversion effects; the coefficient of variation of superelevation had a larger weight (0.549) than the energy dissipation rate (0.451), indicating that R-SEDs' flow diversion effects were larger than their energy dissipation effects; height ratio of R-SED, centerline radius of the bend and bend angle were significant factors affecting overall energy dissipation and flow diversion effects and selected as key factors for further steepest climbing tests and response surface design.

Analysis of Effects of Rough Strip Energy Dissipator on Hydraulic Property of Bend Flow

Installing rough strip energy dissipators (R-SEDs) at the bottom of curved spillways can facilitate energy dissipation and flow stabilization. In this study, the effects of R-SEDs set at the bottom of a 60° bend in a spillway were examined. This spillway had a large width-to-depth ratio ( B / H > 5 ). Based on physical model tests, the distribution of hydraulic properties of the spillway under different runs was studied and analyzed. The results show that the R-SEDs effectively improved the flow pattern in the bend. The R-SEDs reduced the average dimensionless flow velocity by about 37.9% by increasing the roughness at the bottom of the bend. The energy dissipation rate of the R-SED decreased with an increase in discharge flow rate and ranged between 30% and 50%. These indicate that it is feasible to apply the R-SEDs to 60° bends of spillways with a large width-to-depth ratio at low-flow runs ( the tested discharge flow rate = 15 L / s ). These results will provide a theoretical basis for the R-SED design of similar curved spillways.

Reynolds number dependence of particle transport in a 90° bend with electrostatic effects

In this work, particle transport in a fully developed turbulent 90° bend flow at the “electrostatic equilibrium” state is simulated using large eddy simulation coupled with Lagrangian particle tracking technique. The flow Reynolds numbers (based on bulk velocity) considered is from 34000 to 58000. Three particle size 5, 10 and 50 μm are considered and their corresponding St number are from 2.2 to 547. Simulation results of the bend flow agree well with experimental data. The electrostatic field formed in the bend is symmetric in the spanwise direction but asymmetric in the vertical direction and radial direction, which is independent of Reynolds number. The minimum electrostatic field strength occurs at r/ra = 0.25 near the inner wall of the bend. Particles transported in a bend gradually accumulate near the wall due to turbophoresis, such trend is improved by electrostatics. In addition, under the effect of electrostatics, the plume pattern of particle distribution disappeared. Particle concentration at the inner wall of the bend is higher than that at the outer wall, which depends on the combined effect of electrostatics and Dean vortices in the bend.

On the Impacts of Ice Cover on Flow Profiles in a Bend

AbstractWe investigate the impact of ice coverage on flow and bed shear stress profiles in a river bend. We perform field measurements using Acoustic Doppler Current Profiler in a bend of the Red River, North Dakota, the United States. Field campaigns were carried out under both open‐surface and ice‐covered conditions in 2020 and 2021. Our results show that the time‐averaged velocity profile follows closely the quartic solution (Guo et al., 2017, under full ice coverage. While the flow profile under open‐surface condition follows closely the logarithmic law near the bed, it is challenging to identify the logarithmic layers in our measured data under ice‐covered condition. Our results also show that the impact of ice coverage is most significant near both banks where the vertical velocity profile is modified significantly due to the interaction of turbulent flows with the ice cover. Our results suggest that the bend curvature and ice coverage both have significant impacts on the velocity profile as well as the distribution of the bed shear stresses. Our findings provide new insights on sediment transport processes of ice‐covered rivers, especially during the break‐up period when the surface coverage changes rapidly.

Flow characterization of various singularities in a real-scale ventilation network with rectangular ducts

Flow characterization in ventilation ducts is important for adequate modeling of contamination transfer. Turbulent flow through straight tubes with circular cross-section has been widely studied, but HVAC networks are quite unlike such ideal cases. Industrial ducts are of large scale, their sections can be rectangular, and they include many singularities (bends, T-junctions, reducers). The objective of this paper is to study the effect of such singularities on the flow in an industrial-scale rectangular ventilation network including over ten vertical and horizontal bends, one T-junction, a ventilation damper, and one section reducer, by performing experimental measurements and numerical simulations.Regarding bend flow, simulations of mean velocity profiles downstream of horizontal and vertical bends are validated on the experimental data. The analysis of the T-junction flow shows that this flow is a mix of bend and straight duct flows and probably depends on the flow distribution in the two inlet branches, as well as on the curvature radius of the T-junction. It is also observed experimentally that a deflector inserted inside a bend strongly impacts the velocity profiles up to 8Dh downstream. Experiments conducted on the impact of leakage in a closed ventilation damper show that this leakage flow cannot be ignored in the simulations. Measurements of the flow downstream of an open ventilation damper show significant variations in concentration homogeneity.These tests form an extensive database for flow measurements at industrial scale, useful for CFD validation, a necessary step before simulating gaseous and particulate flow in ventilation ducts.

Numerical Simulation of Turbulent Flow in Bends and Confluences Considering Free Surface Changes Using the Volume of Fluid Method

The impact of secondary flows on the flow velocity in open channel bends and confluences was simulated using three-dimensional (3D) numerical models. The Reynolds-averaged Navier–Stokes equation system was utilized as the governing equations and two different turbulence models were employed in this study: the standard k-ε model and the realizable k–ε model. In a recent study by the authors, the rigid lid approach was used, which does not allow for vertical displacement of the water surface. In this study, the simulation of free surface displacements was simulated using the volume of fluid free-surface tracking method. The numerical models were evaluated and validated by using the experimental data of a sharply curved channel and a confluent channel. The accuracies of the two turbulence models were evaluated and discussed. This study found that both models can satisfactorily reproduce the experimental data. However, the standard k–ε model performed better for the curved channel case while the Realizable k–ε model performed better for the confluent channel case.

Transient separation and fluctuation of turbulent flow in an axisymmetric U-turn channel perturbed by periodically passing gust inflow

The flow in the vane-less diffuser bend and return the channel of radial turbo-machines which is perturbed by the time-periodic and circumferentially passing jet-wake structure exited from the upstream impeller, and the transient characteristics of separation and fluctuation occurring in these stationary components determine the operational stability and performances of the turbo-machines especially for the next stage. In this work, we present a numerical investigation on the transient separation and fluctuation behaviors of turbulent flow in a sector of a 180° bended axisymmetric U-turn channel subjected to time-periodic gust inflow which passes in the circumferential direction. The objective is to explore the effect of period of gust inflow, in simulating the non-dimensional blade passing frequency (BPF*) in turbo-machines, on the characteristics of flow in the whole U-turn channel. Numerical results reveal that flow separation occurs in the curved section for about half the cycle at BPF* = 1 and 2, and earlier separation is observed for BPF* = 2, while there is no separation for BPF* = 5 and 10. There is a phase lag between the local skin friction coefficient in the channel and gust inflow, and the magnitude of the phase lag is related to BPF*. As BPF* increases, the thickness of the boundary layer on both walls decreases.