Vortex Zone Research Articles

Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes

This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel’s central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas.

Experimental and numerical investigations on the microstructural features and mechanical properties of explosively welded aluminum/titanium/steel trimetallic plate

In this paper, 3A21Al/TA1/CCSB composite plate was fabricated successfully by explosive welding to improve the bond strength. The microstructure characteristics of aluminum/titanium and titanium/steel bonding interfaces were systematically investigated by two-step numerical simulation and SEM/EBSD characterizations. Firstly, the SPH (Smoothed Particle Hydrodynamics) and Lagrange methodology were used to simulate and calculate the collision velocity and collision angle, establishing an accurate impact condition. Secondly, the SPH model was used to simulate the high-speed oblique impact welding process. The simulation results reproduce the formation of wavy interface, vortex zone and jet, which are consistent with the experimental results. Combined with SEM, EBSD, and EDS analysis, continuous and uniform wavy structures were found at different interfaces of the composite plate, showing significantly different wave lengths and amplitudes. Dynamic recovery and recrystallization took place at the bonding interfaces which showed refined grain with different preferred orientations. The observed structural characteristics and the thermodynamic state predicted by SPH simulation inferred the evolutions of microstructures (including morphologies, micro defects, grain structures). The tensile strength and fracture elongation of the trimetallic plate reach 448.2 MPa and 14.15%, respectively. In addition, the shear strengths of each interface far exceed the corresponding acceptable standard values.

Моделирование трехмерного поля скорости в барабанной вращающейся печи

This paper deals with the problem of laminar axisymmetric incompressible flow in the working area of a rotary drum furnace. A system of second-order partial differential equations is derived and solved numerically using the finite difference method. The obtained solutions are tested for mesh convergence and compared with available analytical solutions for a laminar axisymmetric flow. The numerical results show that furnace rotation significantly affects the gas flow in the working section of the apparatus. Thus, the temperature distribution over the working area and furnace surface can be controlled through the furnace rotation velocity and gas flow rate. The input velocity profile also affects the flow pattern in the furnace. Vortex zones with counterflow occur near the walls, where the axial velocity profile is more elongated than the Poiseuille parabola. On the symmetry axis, the axial velocity is higher than that of the Poiseuille flow. The proposed mathematical model allows one to calculate more accurately the degree of thermal decomposition as a function of temperature and longitudinal coordinate along the furnace axis.

Field Measurement of Dust Concentration on Open-pit Coal Mine Truck Transportation Roads and Numerical Simulation of Dust Patterns

Dust generated by open-pit coal truck transportation is one of the main sources of pollution, adversely affecting road visibility and the surrounding air quality during transportation operations. To investigate the distribution patterns of transport dust on coal quality roads in open-pit coal mines, we conducted on-site measurements of transport dust pollution in a coal mine in Xinjiang, China. We also used numerical simulation software to simulate the distribution patterns of dust under different truck speeds. The results indicate that dust pollution on the coal quality road surfaces within the open-pit coal mine exceeds national standards. The concentration of dust behind the trucks at different speeds can be categorized into the following zones: vortex zone, rapid descent zone, and stable zone. The peak dust concentration occurs around 1.5 meters behind the rear of the trucks. Furthermore, the dust concentration behind the trucks follows an exponential decay pattern with increasing height and longitudinal distance.

Analysis of the hydrodynamic causes of thrombosis and hemolysis in the centrifugal pump of the artificial blood supply system

The article is devoted to the analysis of the hydrodynamic causes of complications of the use of centrifugal pumps in artificial circulation systems. In the treatment of cardiovascular diseases, rotary pumps began to be used: centrifugal, axial and disk. Of the three types of rotary pumps, centrifugal pumps have the highest power density due to the use of centrifugal force. Statistics show that the greatest blood damage in the form of thrombosis and hemolysis is observed in these pumps. The article concludes that the main hydrodynamic cause of thrombosis and hemolysis is the force field formed by the centrifugal force of inertia, which generates vortex and separation zones. When passing through these zones, red blood cells experience intense hydrodynamic effects in the form of local accelerations and impacts against the walls of the channels, which leads to their deformation, and then to the destruction of some red blood cells. On the one hand, thanks to this force, the intensity of energy conversion in a centrifugal pump becomes higher compared to other types of pumps. On the other hand, a large unevenness of speed and pressure occurs in the channels, which has a traumatic effect on red blood cells. Hydrodynamic solutions to weaken the force field that injures red blood cells will inevitably be accompanied by a decrease in the intensity of energy conversion and the benefits of using this type of pump.

Role of wall roughness on interaction of leakage flow and main flow in a mixed flow pump with tip clearance

Due to machining precision, spraying coating, cavitation, and erosion, walls of pump flow passage components have different roughness, which will affect the flow state near the wall and even the main flow. In the present work, four types of roughness Ra = 0, 0.1, 1, and 10 μm are set to investigate the influence of wall roughness on the interaction of leakage flow and main flow in a mixed flow pump with tip clearance. Results show that the interaction area of leakage flow and main flow can be divided into three regions: (a) tip clearance zone, (b) shear flow zone, and (c) primary vortex zone. In the tip clearance zone, as roughness increases, the velocity magnitude and its derivative at the same wall distance gradually decrease, and the velocity angle at blade tip continuously increases in the inner circular boundary layer. As the roughness increases, the leakage flow gradually decreases, especially in the center chord region. In the shear flow zone, the velocity gradient rapidly decreases along the direction of pressure side to suction side, and finally, it becomes stable. As roughness increases, the velocity gradient intensity decreases, and the main reason is that the differences of velocity magnitude and velocity direction between the inner circular boundary layer and potential region decrease. In the primary vortex zone, the tip leakage vortex core indicated by the Liutex vortex method coincides with the low-pressure core location. As the roughness increases, the tip leakage vortex core becomes closer to the next blade. The pressure coefficient and vorticity of the tip leakage vortex core decrease with increasing of roughness, and the slopes remain constant on different cross sections with value of 5.9 × 103 and 2.4 × 103 m−1, respectively.

Pollutant diffusion in multiple-face tunnel construction: theoretical analysis and numerical validation

As the length of the tunnel continues to increase, it will be common for a single fan to undertake the ventilation of two or more tunnel faces. However, the construction of multiple faces in a single tunnel will lead to a complex construction environment in the tunnel, the mutual interference of ventilation, and difficulty in discharging pollutants. Based on the simultaneous construction of multiple tunnel faces in a single tunnel, this study analyzed the transport law of pollutants. The diffusion laws of carbon monoxide and dust in multiple-face tunnels under different working conditions were obtained by numerical simulation. It was found that when both sides of the tunnel are ventilated at the same time, the airflow in the tunnel is spiral, the vortex zone will appear near both sides of the face, and the vortex and unstable airflow will appear at the intersection with the inclined shaft. The airflow in the non-equal-length tunnel at both sides is more disordered than that in the equal-length tunnel, and there will be a wider range of eddy currents at the intersection. The change of dust diffusion in the non-equal-length tunnel at both sides is not obvious, and the length of the multiple-face tunnel has little effect on dust settlement and diffusion. The research results are of great significance for improving the construction environment of tunnel faces and improving the working conditions of personnel.

Experimental analysis of smoke dispersion in belt fires by using a real-size model of the underground space

It is essential to investigate the dispersion of a large amount of toxic and harmful smoke in coal mine network during belt fires. A real-size model of an underground space was used to study the additional thermal resistance of single roadway and the dispersion characteristics of CO in bending structure, as well as the effect of air velocity on CO dispersion. The results show that the resistance of high temperature air flow is related to the ventilation resistance of the roadway under normal airflow, and is proportional to airflow temperature. The additional thermal resistance increases first and then decreases with time, and curve trend is similar to multiple “humps” with the increase of distance, which indicates that temperature is dominant factor. The distribution of CO is V-shaped at 90° corner, and the distribution pattern is unaffected by corner number. The increase of the air velocity destroys the CO distribution at the initial corner, and the air vortex zone appears at the bottom of the roadway. Meanwhile, the smoke flow diffused to the working face shifts from the outer wall to the inner wall of the working face. The results are helpful for selecting emergency evacuation areas and implementing safe measures.

Effect of electrode configuration on minichannel heat sink with EHD vortex generators

A numerical study has been performed to understand the effects of electrode spacing on thermo-hydraulic performance in a minichannel assisted with electrohydrodynamics (EHD) based active vortex generation. A minichannel design with alternate high voltage and grounded electrodes flushed to the walls of the channel is considered. Multiple cases with different combinations of electrode length and spacing (pitch) at Reynolds number varying from 200 to 1000 are investigated. The numerical framework consisting of the two-way coupled governing equations for flow, thermal, charge, and electric potential fields is developed in the open-source finite-volume framework of OpenFOAM®. Applying an electric field induces the Onsager–Wien effect, producing flow vortices from electrode pairs. The EHD vortices disrupt the inherent laminar flow structure in the minichannel. The flow morphology is characterized by alternate vortex and shear dominant zones near the top and bottom walls. The EHD vortex dominant zones near the channel wall disrupt the laminar boundary layers. Thus, fluid mixing and heat transfer in the minichannel are enhanced. Electrode size and spacing influence the electric field distribution in the flow domain. As a result, electrode length and the inter-electrode spacing notably influenced the flow structure and the resulting heat transfer in the minichannel. The electrode spacing or the pitch decides the number of electrode pairs in the minichannel. An increase in pitch leads to fewer electrode pairs; thus, the electric field intensity is weak. Hence, EHD vortices in configurations with wider electrode spacing are weaker in strength. Longer electrodes produced stronger electric fields due to increased charge accumulation. Therefore, EHD vortices generated by longer electrodes are prominent and influential. The influence of EHD vortices on flow disruption and heat transfer is significant at lower Reynolds numbers. Cases with smaller electrodes perform well at higher Reynolds numbers, whereas usage of bigger electrodes exhibits higher performance at lower Reynolds numbers. Within the parameter space of this study, a minimum of 38.1% and a maximum of 60.6% enhancement in heat transfer is observed. A maximum performance factor of 1.46 is obtained in the present study using an electric current of 30μA with an electric power consumption of 30.1mW, which are notably low. Thus, the results of the present study exhibit that EHD vortex generation using the Onsager–Wien effect is a viable and economical option for thermo-hydraulic performance enhancement in a minichannel. Insights provided in the present study will be helpful to engineers and researchers in designing minichannel heat sinks with EHD-based performance improvement.

Determination of the influence of the incoming flow on the vortex zones at the entrance to the suction sockets. Part 1. The Axisymmetric problem

The features of the construction of a computational algorithm for calculating circular suction sockets in the conditions of an incoming flow by the method of discrete vortex rings are considered. Flow patterns are given at different ratios of the incoming and intake air flow velocities. The dependences of the characteristic sizes of vortex zones arising at the inlet to the suction-sockets on the velocity of the incoming flow, the length and angle of inclination of the socket are determined. Expressions are obtained for the critical velocity of the incoming flow, at which the flow separation mode for the first vortex zone changes from separation inside the bell to separation outside it. The obtained results can be useful for the construction of local suction systems, profiled according to the found outlines of vortex zones.

Numerical study on atmospheric explosive welding based on the 2D structured arbitrary Lagrangian-Eulerian method

Smooth particle hydrodynamics (SPH) is often adopted to simulate the waveform interface, which has a crucial effect on the bonding quality in explosive welding (EXW). However, owing to the nature of the SPH method, it is difficult to evaluate the influence of the air medium and calculate detailed waveform structure. In this study, a Cu-Q235 steel EXW model containing air medium was established using a structured arbitrary Lagrangian-Eulerian (S-ALE) method. A full-size 2D model was first performed to acquire welding parameters, which were set to the initial conditions for the next oblique collision method. Subsequently, the experiment was conducted to verify the accuracy of the simulations. The results show that the S-ALE method can effectively predict the waveform and acquire the detailed process of the EXW. With the addition of an air medium, the calculated velocity and pressure of the shock wavefront were approximately 3300 m·s−1 and 15 MPa, respectively. Despite the limited effect of the gas shockwave on the overall waveform, the influence on the large-scale or thin plates cannot be ignored. Furthermore, the simulation indicates that the participation of the air during the wave formation led to the generation of the pore in the vortex zone. The proposed method could predict the waveform structure and optimize the manufacturing process of composite plates in the atmospheric EXW.

Influence of triangular spoilers on the performance of serpentine solar air heaters

In order to improve the efficiency of the conventional serpentine solar air heaters, this article proposed a serpentine solar air heater containing a triangular spoiler. A 3-D verified mathematical model of serpentine solar air heaters with triangular spoilers was established. The results showed that the arranging triangular spoiler had a positive effect on enhancing the thermal performance of solar air heaters. It could be seen from the velocity and temperature contours that the triangular spoiler could reduce the intensity and area of the vortex zones, and hence decrease the temperature dead zone in the flow channel. The collection efficiency reached its peak value when the angle of triangular spoiler was 64°. Compared with the nontriangular spoiler, the collection efficiency was increased by 4.4% ∼6.2%. In general, the optimal angle of triangular spoiler was determined to be 40° by comprehensive analysis of effective efficiency.

Numerical simulation of clogging of two types of emitters with similar properties

AbstractThe benefits of drip irrigation are numerous and include water savings, control of fertilizer applications, and improved water and energy use efficiency of irrigation. In these systems, the emitter is the most vulnerable component to clogging, which in critical states can cause a reduction in performance and shorten the life of the distribution system. It can also have several impacts on water, its economy, and its wastage. In the absence of adequate filtration and when the flow is through the narrow labyrinth channel of the emitter, clogging can be created by continuous deposition of solid particles, organic matter, dissolved salts, chemical precipitates, bacteria, and other impurities. It is obvious that it is impossible to physically visualize the hydraulic behavior of the flowing water in the labyrinths. However, due to the increasing performance of computational tools and simulation software, it is possible to simulate this flow through Computational Fluid Dynamics (CFD), which has become one of the main techniques for describing the flow and deposition of the solid phase inside the emitter. This study aims to numerically simulate the behavior and the flow of the fluid inside two emitters, widely used in the industry, with different types but approximately identical flow rates. The fluid takes in its flow an inert solid suspension of fixed concentration. One of the emitters is compensating‐pressure, and the other is non‐compensating‐pressure; the numerical simulation model used is the RNG κ‐ε two‐phase model. The results showed that the regions affected by clogging are mainly the corners of the labyrinth channel and the recirculation vortex zones. The trajectory field plot reveals that as the clogging increases, the serpentine fluid threads become thinner.

Obtaining Vortex Formation in Blood Flow by Particle Tracking: Echo-PV Methods and Computer Simulation

Micrometer-sized particles are widely introduced as fluid flow markers in experimental studies of convective flows. The tracks of such particles demonstrate a high contrast in the optical range and well illustrate the direction of fluid flow at local vortices. This study addresses the theoretical justification on the use of large particles for obtaining vortex phenomena and its characterization in stenotic arteries by the Echo Particle Velocimetry method. Calcite particles with an average diameter of 0.15 mm were chosen as a marker of streamlines using a medical ultrasound device. The Euler–Euler model of particle motion was applied to simulate the mechanical behavior of calcite particles and 20 µm aluminum particles. The accuracy of flow measurement at vortex regions was evaluated by computational fluid dynamics methods. The simulation results of vortex zone formation obtained by Azuma and Fukushima (1976) for aluminum particles with the use of the optical velocimetry method and calcite particles were compared. An error in determining the size of the vortex zone behind of stenosis does not exceed 5%. We concluded that the application of large-size particles for the needs of in vitro studies of local hemodynamics is possible.

Analysis of hydrodynamic characteristics and loss mechanism of hydrofoil under high Reynolds number

Hydrofoil is widely used in hydraulic machinery, the complex shear flow and wake vortex with it can cause energy dissipation of system, affecting the stable operation of the unit. This paper takes the guide vane of a Francis turbine as the research object, and adopts the SST k−ω turbulence model to simulate the complex unsteady flow in a three-dimensional hydrofoil-channel. Entropy production theory is introduced to evaluate the energy dissipation. The effects of attack angle, gap ratio and Reynolds number on the flow loss are studied. The results show that: (1) In the hydrofoil-channel, the dissipation caused by the velocity gradient always dominates the irregular flow of fluid field. So the loss caused by the turbulent dissipation term is the main source of the loss in mainstream zone, accounting for more than 95%, while the loss caused by the viscous dissipation term accounts for only about 2% of the total loss, which can be almost ignored; (2) Changing the attack angle have a significant effect on the flow separation of the suction surface and the shear effect in the wake vortex zone, causing the energy loss to fluctuate accordingly. And 2.5° is the optimal attack angle. On this working condition, the loss decreases to the minimum value of 2.2714W/K and 0.1432 m, a decrease of 57% compared to the initial value; (3) The bottom boundary of channel suppress the development of wing tip vortex, reducing gap ratio will reduce the loss caused by wake vortex to some extent. Among them, S = 0.3 is the optimal gap ratio. Under this operating condition, the loss is 2.2941W/K and 0.1447m, a decrease of 56% compared to the initial value; (4) Affected by flow separation and wake vortexes, more than 80% of energy loss occurs in the middle and downstream zones. The effects of attack angle, gap ratio and Reynolds number on the fluid field are different. Increasing attack angle and flow velocity significantly exacerbate the flow separation and shear flow, while reducing gap ratio would inhibit the adverse flow in downstream wing tip vortex zone.

Determination of the Influence of Oncoming Flow on the Vortex Zones at the Inlet of the Suction Sockets. Part 2. Axisymmetric Problem

Determination of the Influence of Oncoming Flow on the Vortex Zones at the Inlet of the Suction Sockets. Part 2. Axisymmetric Problem

Characteristic Features of the Hydrodynamics and Combustion of Fine Fuel Particles in the Vortex Zone of a Cyclone-Grate-Fired Chamber

Characteristic Features of the Hydrodynamics and Combustion of Fine Fuel Particles in the Vortex Zone of a Cyclone-Grate-Fired Chamber

Simulation of gas dynamics of oxygen flow and hydrodynamics of cooling water flow in tuyere tips with tangential optimized nozzles and results of their pilot tests.

The blowing mode largely determines the technical and economic indicators of BOF smelting, which was confirmed during the technological audit of the BOF shop of Azovstal Iron and Steel Works, carried out in 2021. It was found that the blowing mode of the process using an oxygen lance of the basic design was noticeably shifted from the optimal one in the direction of “hard” blowing. In a significant number of melts this led to an increase in the specific consumption of metal sheets, deterioration of lime assimilation by slag, dephosphorization and desulphurization of the metal. Taking into account that adjustment of the blowing mode by changing the working height of blowing and oxygen consumption did not provide a stable positive result, changes were made in the design of the tuyere tip. The design of the head with tangential arrangement of nozzles is proposed to “soften” the blowing of melts. The advantages and dis-advantages of oxygen lances of this type are considered. Numerical modeling of the gas dynamics of the oxygen flow and the hydrodynamics of the flow of cooling water in a tip with a tangential arrangement of nozzles has been per-formed. On the basis of simulation results, two variants of an improved design of the tips of 350-t LD converters with five (variant 1) and four (variant 2) main peripheral tangentially oriented nozzles and a central nozzle of lower throughput were developed to use them mainly in the second and first periods of the campaign according to the lining of the converters, respectively. It is shown that the design parameters of the nozzle blocks provide an oxygen jet outflow regime close to the design one in the main range of oxygen operating flow rates and a “non-separated” outflow regime with a decrease in the off-design ratio down to 0.8. The design parameters of the cooling system provide both an acceptable loss of water pressure in the head (0.9 MPa), the absence of local low-speed vortex zones of water, and a fairly high average coolant flow rate along the most heat-stressed (the lower) surface of the tip (about 4.5 m/s). As a result of industrial testing of a pilot batch of experimental heads with five main peripheral tangentially oriented nozzles, manufactured at the plant’s own repair and mechanical base, an increase in the resistance of copper tips was found to be 1.2 times, the resistance of lances to removal for cleaning from accretion was found to be 6.8 times, reduction in the specific consumption of metal charge by 0.9–5.6 kg/t, an increase in the dephosphorization and desulfurization coefficients of metal in the converter by 0.7–1.5 and 1.3–3.2%, respectively.

Study on the dynamics and wake characteristics of a floating tidal stream turbine with pitch motion under free surface

To improve knowledge of the unsteady hydrodynamic characteristics of a floating horizontal-axis tidal turbine (HATT) in complex marine environments, a computational fluid dynamics (CFD) numerical method is established to analyze the functioning of a HATT under free surface and pitch conditions: an amplitude of 2.5°–12.5° and a period of 3–15 s. The appropriateness of the CFD method is validated against piled turbine tests in a circulating flume, which turned out to be only 1.43% off at the rated tip speed ratio. The power and thrust coefficients exhibit periodic variation with a frequency twice the pitch's motion. From the ecological perspective, the wake velocity field presents radial warps accompanied by several ellipsoidal low-velocity core regions, which corresponds to the fused vortex rings in the vortex zone. Notably, the wake is more influenced with large rather than small amplitudes and periods; meanwhile, the wake is more sensitive to frequency changes than to amplitude changes. The results could lay a foundation for future research into more complex motion response of floating tidal turbines.

Real-time economic and safe operation diagnosis of hydropower units

In order to ensure the safety and economy of the operation of hydropower units under the big data technology application platform and the automatic generation control system, and to tap the maximum power generation potential of the units, an effective method of economic operation evaluation of hydropower units combined with state diagnosis is proposed. Taking Unit 1 of Longtan Hydropower Station as an example, the economic evaluation and status diagnosis of the daily operating conditions are carried out, the real-time efficiency of the turbine is queried through the unit operating conditions data, and the economic operation of the unit is comprehensively evaluated using the standard water consumption index. In addition, the real-time operation condition of the unit shall be diagnosed according to the working condition zoning diagram, and the economic operation condition shall be combined with the unit state operation condition for joint assessment. It is strictly forbidden to operate the unit in the vibration zone and the vortex zone and it is determined that the unit can maximize the power generation efficiency after operating in the safe operation zone.