Flow Velocity Distribution Research Articles

A numerical model for calculating velocity distribution in cross-section of an open channel

Flow velocity in open channels is a fundamental hydraulic parameter with wide-ranging applications, including the development of rating curves and the study of sediment transport. While some river engineering projects may only require the calculation of average flow velocity, others, such as the design of hydraulic structures and stable channels, as well as the assessment of boundary shear stress, necessitate a more comprehensive understanding of flow dynamics, including the two-dimensional velocity distribution within open channels. To address this, various mathematical models have been proposed for estimating the two-dimensional distribution of flow velocity across transverse and depth directions. However, these models often come with complexities that hinder their practical application. In this research, we introduce a simplified numerical model that combines simplified Navier–Stokes equations with an eddy viscosity formula. This innovative approach aims to estimate velocity distribution in both rectangular and trapezoidal channels. The accuracy of our developed model hinges on the momentum transfer coefficient used in the eddy viscosity formula. Through the execution of the numerical model and the utilization of observational data, we determined the optimal value of the momentum transfer coefficient to be 0.241. To validate the effectiveness of our numerical model, we compared its predictions with laboratory data encompassing diverse hydraulic conditions. The results demonstrated a high level of accuracy, with the calculated velocity distribution and flow discharge differing by no more than 7.6% and 6.8%, respectively.

Modelling of gas-dynamic processes in the design of small-sized installation for the production of micro-powders by gas spraying melt quenching in a horizontal reactor.

A new scheme for obtaining metal powders by gas spraying is present. The atomization takes place in a horizontal reactor where the interacting flows of the melt and the atomizing gas are perpendicular. The theoretical calculations performed within the selected approximation, quantitative values of process parameters, describing the interaction of flows were obtained as a result. The penetration depth of the gas stream into the melt jet at different pressures and gas flow rates was appreciated. The liquid melt jet, in initial approximation, as a flow of non-reactive particles of a spherical shape with a diameter in the range 40-250 μm in order to evaluate the selected parameters of the design of the spray chamber (atomizer) was considered. A relationship between the distribution of gas flow velocities and the distribution of the velocities of condensed particles in the atomizer chamber was modelled. We have found the areas of the atomizer in which the “reverse” flow of light particles (with a diameter of less than 80 μm). The vortex motion of the gas in the chamber induces this effect. We have found and modeled the correlation between the distribution of gas flow velocities and the distribution of the velocities of condensed particles in the atomizer chamber. The simulation results show that the investigated range of gas-dynamic characteristics in the sprayer of the chosen design ensures the production of powder materials of a given dispersion.

Propeller–hull interaction simulation for self-propulsion with sinkage and trim

This paper presents numerical simulations of propeller–hull interaction of a ship model for the dynamic condition, demonstrating the ability of the developed self-propulsion module in OpenFOAM. A dynamic motion class has been developed based on the sliding mesh method to simulate a rotating propeller with ship motions. A body-force method is also implemented to simulate propeller–hull interaction to reduce the computational cost of propeller modeling. Validation studies were carried out for the Japan Bulk Carrier (JBC) ship model. The bare-hull resistance, sinkage, and trim are verified against the experimental data. The propeller open-water hydrodynamic characteristics are then computed and validated using sliding mesh and body-force methods. Finally, the self-propulsion simulations are carried out for the JBC model in calm water with sinkage and trim at the design speed. Numerical predictions of the self-propulsion parameters and axial flow velocity distributions at different transverse locations are presented.

DIY-PIV system for Poiseuille flow investigation in undergraduate fluid mechanics course

Fluid flow visualization techniques are becoming more widespread every year due to the availability of lasers, high-speed cameras, and the development of a large amount of image processing software. Nowadays, one of the most popular methods of flow optical visualization is particle image velocimetry (PIV). PIV is an innovative way to measure and analyze fluid characteristics, giving students a more in-depth understanding of how fluids move. This paper is focused on using low-cost components and free software to implement PIV for Poiseuille flow investigation in an undergraduate fluid mechanics course. The introduction discusses how PIV is being used as a complementary method in educational institutions, highlights the high cost of equipment to implement PIV, and gives examples of low-cost do-it-yourself (DIY)-PIV systems. The following sections present the theoretical background, descriptions of the DIY-PIV experimental setup, and plan of the investigation for the Poiseuille flow analysis. A brief overview of free image processing software for the PIV implementation is also provided. The last section presents the results of the Poiseuille flow study and analyzes the measurement quality using the created DIY-PIV system. The present experimental investigation covers topics and reinforces skills related to concepts: laminar flow, Poiseuille flow (velocity distribution, maximum and average velocity), Reynolds number, and measurement error.

Modeling of the Flow Field and Clad Geometry of a Molten Pool during Laser Cladding of CoCrCuFeNi High-Entropy Alloys

A flow field analysis was performed in this research using the ANSYS Fluent module, and a dynamic heat source employing UDF was constructed using the DEFINE_PROFILE macro. A VOF model was developed to track the volume fraction of each fluid throughout the computational domain as well as the steady-state or transient condition of the liquid–gas interface in the free liquid surface area. To determine the distribution state and regularity of the molten pool flow field, the flow field velocity was calculated iteratively by linking the Simple algorithm with the horizontal set method. The molten pool was concave, indicating that the key hole was distributed narrowly. Inserting cross-sections at different depths yielded the vector distribution of the molten pool flow velocity along the depth direction. We set up monitoring sites along the molten pool’s depth direction and watched the flow change over time. We investigated the effects of the process parameters on the flow field’s vector distribution.

Analysis of Influencing Factors on Silicon Epitaxial Growth in Horizontal Single‐Wafer Reactor through Orthogonal Test

AbstractSilicon epitaxy is a crucial process used in semiconductor manufacturing to deposit high‐quality films of silicon. This technique is widely used in the production of integrated circuits, as it enables the fabrication of intricate electronic structures with enhanced performance characteristics. This study conducts numerical simulations on a chemical vapor deposition (CVD) reactor to explore the impact of process parameters on the growth rate and non‐uniformity of silicon. The investigation encompasses both the gas and surface reactions of the trichlorosilane‐hydrogen (TCS‐H2) system. The distributions of gas flow velocity, temperature, and main components are systematically studied by varying the process parameters, including susceptor temperature, inlet gas velocity, susceptor rotating speed, inlet gas temperature, upper wall temperature, and TCS mole fraction. Furthermore, the orthogonal test method is introduced to assess the effect of all parameters on the growth non‐uniformity. The results reveal that the inlet gas velocity and susceptor temperature have a significant influence on the growth rate and non‐uniformity. The silicon growth rate is primarily influenced by the TCS mole fraction, whereas the rotation speed of the substrate primarily influences the growth non‐uniformity of growth. Finally, the optimal scheme is proposed as valuable guidance for enhancing silicon chemical vapor deposition processes in industrial applications.

Оценка стадии перемещения наносов при действии волнового потока на элементы русла водного объекта АПК

The purpose of the work is to determine, in laboratory conditions, the magnitude and laws of distribution of bottom wave flow velocities, at which various stages of particle movement and riffle formation occur in the area of beach slopes of water bodies of the agro-industrial complex. The results of studies of velocities characterizing the regimes of sediment movement in a wave flow acting on loose slopes and bottom areas of the shallow zone of reservoirs and streams are presented. The influence of artificial flow turbulization on characteristic flow speeds, including wave speed on the parameters of bottom riffles, is considered. An analysis of the influence of artificial turbulization on the speed of sediment movement is given and recommendations are given for determining the non-erosive speed of the wave flow in its absence. A dependence is presented for determining the height of the riffles. It has been established that the velocities on the riffle crest increase by no more than 1.7 times compared to the speed on the flat bottom of the near-shore zone of a large water body.

Numerical and physical modeling of the aerodynamic process in a direct-flow coil-type boiler using a laboratory stand

The article examines the modes of gas passage through the chimney of a direct-acting steam generator set using a laboratory stand made of a cylindrical coil. The criterion for determining the gas flow regime is a dimensionless quantity called the Reynolds number. The air flow velocities and temperatures were determined experimentally. Based on these results, the Reynolds number was calculated and the flow regimes at each measurement point were determined, and the dependence of the Reynolds number on temperature and velocity was obtained, and the experiment was analyzed. With the help of the ANSYS program, a model of air movement on the stand was built. When deciphering the geometric model, the ANSYS SpaceClaim program was used. The model made it possible to estimate the distribution of the air flow velocity in the boiler model based on experimental values. Further, after constructing a geometric model using the ANSYS Icem CFD program, a dispersion model was cre-ated that showed the temperature distribution of flue gases in the external gas flow of the basic model of a direct-flow steam boiler. The processing of experimental data showed a further prospect of intensification of the heat exchange process in a direct-flow steam boiler of the coil type.

Turbulence characteristics in partially vegetated open channels with alternating sparse and dense patches

A large amount of vegetation in nature exists in the form of heterogeneous vegetation patches, and variations in vegetation characteristics significantly affect water flow structures. The objective of this study is to investigate the effect of alternating sparse and dense patches on turbulence characteristics. Multiple sets of heterogeneous vegetation scenarios were designed for numerical simulation analysis, and a comparison was made with homogeneous vegetation. Results indicate that compared with that of homogeneous vegetation, the arrangement of heterogeneous vegetation alters the distribution of flow velocities in the vegetation zone and the main channel, promoting material exchange between these regions. The vegetation density difference between sparse and dense vegetation patches in heterogeneous vegetation effect on the main channel increases with larger vegetation density differences, but the magnitude of the effect is limited and generally remains within 10% of the vegetation width. In the balance equation of turbulent kinetic energy, the terms are influenced differently by changes in vegetation density. As vegetation density difference increases, the convective term gradually increases, while the production and diffusion terms exhibit a “lower in the middle, higher at both ends” pattern. The dissipation term demonstrates a reduction effect at low-density differences, gradually increases with larger differences, and ultimately exhibits an amplification effect. Furthermore, this study determines that using data from mid-height to represent the entire cross section for heterogeneous vegetation may result in a maximum error of up to 11%.

Research on the Protective Effect of Twin-groyne Arrangement on Riverbank

A curved channel with intersecting streams can be easily scoured by incoming flow, and the concave bank is badly damaged. This research showed that the twin-groyne could effectively adjust and optimize the flow velocity distribution, change the shape of the free water surface of the bend, prevent erosion, and promote silting on the concave bank, and it could provide a scouring and silting effect on the convex bank. When the spacing of twin-groyne was increased to more than four times the body length of the single-groyne (spur dike), the protective effect on the concave bank was weakened, and the scouring and silting effect of the convex bank was reduced. Excessive spacing of the twin-groyne could cause local erosion damage to the concave bank. When the distance exceeded the theoretical optimum, it was equivalent to the effect of single-groyne. With the increase in the submergence degree, the velocity of the concave bank decreased first and then increased, while the velocity of convex bank decreased continuously. The protective effect of a non-submerged twin-groyne with a dam spacing of four times the body length of the single-groyne was better than that of other conditions, and it is recommended to be used in practice.

Numerical simulation of hydrothermal flow in the North China Plain: A case study of Henan Province

The distribution and flow of geothermal energy in the North China region are influenced by geological structures and rock thermal properties. However, the interactions between geothermal energy, groundwater movement, and hydrogeochemical processes are not well understood. In this study, a numerical model was developed to simulate these interactions under different geological conditions. The results showed that the stress field of geological structures affects the flow path and velocity distribution of geothermal fluid, leading to distortion and uneven temperature distribution. The distribution of high-mineralized zones of geothermal water indicated the main recharge area in the northern part of the North China Basin (Henan). Hydrochemistry analysis revealed a dynamic balance between centrifugal and centripetal flows in sandstone geothermal water. The study provides important insights for the exploration and development of underground geothermal water, as well as the assessment and optimization of geothermal resources in large basins.

МЕТОДИКА И РЕЗУЛЬТАТЫ МОДЕЛИРОВАНИЯ В «Flow Simulation» «SOLIDWORKS 2018» ПРОЦЕССА ОБТЕКАНИЯ ЛОПАТКИ СМЕСИТЕЛЯ КОРМОВ

It is impossible to obtain high-quality combined feeds without effective mixers. To improve them, you can use programs that simulate the behavior of bulk materials, but most of them are inaccessible and difficult to master. The use of more accessible software that simulates the process of fluid flow - “Flow Simulation” “SOLIDWORKS 2018” is proposed for assessing the movement of bulk materials. A previously developed design scheme was used, in which the working bodies of the mixer are combined and contain several sections of blades with reasonable geometric parameters for different purposes (transportation and mixing). A model of the scapula has been made. The parameter under study was the installation angle of the mixer blades relative to the shaft of the working element. The criterion for selecting blade installation angles was the presence of a maximum number of flow areas with velocities different from those specified for the overall material flow. As a result of the simulation, flow velocity distributions were obtained at given blade installation angles with a gradation step of flow velocity fields of 0.393 m/s. The limit values for the installation angles of the mixer blade are set from 0° to 60°. This criterion is met by blade installation angles from 45° to 0°. It is shown that the results of modeling the flow around a flat blade with given dimensions generally do not contradict the results of existing studies. Further research will be aimed at assessing the simulation results based on full-scale experiments with subsequent adjustments.

An improved method combined modified drag model and modified erosion model based on LES for solid-liquid multiphase flow and erosion with application in a 90° elbow

In various industrial processes, solid-liquid multiphase flows involving continuous carrier and discrete particle phases have erosion challenges. In this work, a modified drag model that considers the influence of turbulence intensity and a modified erosion model that considers the effect of low-angle impact are developed. An improved method combined modified drag model and modified erosion model based on LES is proposed for numerical simulation of solid-liquid multiphase flow and erosion. The commercial software ICEM for grid generation and ANSYS FLUENT for LES are used in the present work. In validation test of velocity distribution of solid-liquid multiphase flow in a vertical pipe, the mean relative error of the liquid phase pulsation velocity is 10.01 % for modified drag model, whereas the mean relative error is 16.11 % for original drag model. In validation test of the maximum erosion depth from a submerged impact test at a tilt angle of 45°, the relative error is 0.23 % for modified erosion model, while the relative error is 13.39 % for original erosion model. Then, the improved method is employed to compute the characteristics of solid-liquid flow and erosion in a 90° elbow. Particles have a significant influence on liquid flow in the shear layer area where the inner arch separation zone interacts with the main flow, and this influence is most pronounced at the position of r* = 0.3 at yd = 0.4D. At this position, particles result in 15.27 % reduction in liquid velocity and 8.75 % increase in turbulence intensity. The mean relative error of the elbow erosion rate by using the improved method is 16.95 %, whereas it is 31.34 % of the reference work. The erosion is affected by impact velocity, angle, and particle number, and the most significant parameter is the particle number in the severe erosion area.

Heat transfer in β-Ga2O3 crystal grown through a skull melting method

Heat and mass transfer in β-gallium oxide crystals grown via a skull melting method were numerically studied. Specifically, we calculated the temperature and velocity distributions in a furnace for the skull melting method. The distributions covered the entire system: the growing crystal, melt, raw material, basket, and coils generating heat through the radio frequency electromagnetic field. We determined the dependences of temperature and melt flow velocity distributions on the coil position.The results indicate that the melt flow direction is opposite to that in the Czochralski method and that a descending flow exists near the periphery of the melt. The results also show that the maximum temperature of the melt, which affects the overheating conditions of the melt, depends on the position of the coil.

The hidden structure of hydrodynamic transport in random fracture networks

We study the large-scale dynamics and prediction of hydrodynamic transport in random fracture networks. The flow and transport behaviour is characterized by first passage times and displacement statistics, which show heavy tails and anomalous dispersion with a strong dependence on the injection condition. The origin of these behaviours is investigated in terms of Lagrangian velocities sampled equidistantly along particle trajectories, unlike classical sampling strategies at a constant rate. The velocity series are analysed by their copula density, the joint distribution of the velocity unit scores, which reveals a simple, albeit hidden, correlation structure that can be described by a Gaussian copula. Based on this insight, we derive a Langevin equation for the evolution of equidistant particle speeds. In this framework, particle motion is quantified by a stochastic time-domain random walk, the joint density of particle position, and speed satisfies a Klein–Kramers equation. The upscaled theory quantifies particle motion in terms of the characteristic fracture length scale and the distribution of Eulerian flow velocities. That is, it is predictive in the sense that it does not require the a priori knowledge of transport attributes. The upscaled model captures non-Fickian transport features, and their dependence on the injection conditions in terms of the velocity point statistics and average fracture length. It shows that the first passage times and displacement moments are dominated by extremes occurring at the first step. The presented approach integrates the interaction of flow and structure into a predictive model for large-scale transport in random fracture networks.

Effect of Plasma Actuator Layout on the Passage Vortex Reduction in a Linear Turbine Cascade for a Wide Range of Reynolds Numbers

This study examined how various plasma actuator (PA) configurations affect the passage vortex (PV) reduction in a linear turbine cascade (LTC) utilizing dielectric barrier discharge PAs. The experiments were carried out under three specific layout conditions: axial placement of the PA, slanted placement at the blade inlet, and slanted placement inside the blade. Particle image velocimetry was employed to measure the velocity distribution of the secondary flow at the LTC exit, followed by an analysis of the streamline patterns, turbulence intensity distribution, and vorticity distribution. At a Reynolds number of 3.7 × 104, the PA with an oblique orientation at the blade inlet provided the most effective PV suppression. The average value of the secondary flow velocity and the peak vorticity value at the LTC exit decreased by 59.0% and 68.8%, respectively, compared to the no-control case. Furthermore, the wind tunnel blower’s rotation speed was modified, adjustments were made to the LTC’s mainstream velocity, and the Reynolds number transitioned from 1.0 × 104 to 9.9 × 104, approximately 10 times. When the slanted PA was used at the blade inlet, the PV suppression effect was the highest. The peak vorticity value owing to the PV at the LTC exit decreased by 62.9% at the lowest Reynolds number of 1.0 × 104. The Reynolds number increased with a higher mainstream velocity and decreased flow induced by the PA, consequently reducing the PV suppression effect. However, the drive of the PA was effective even under the most severe conditions (9.9 × 104), and the peak vorticity value was reduced by 20.2%.

Experimental and Numerical Simulations of Pore Structures and Seepage Characteristics of Deep Sandstones

Previously conducted studies have established that deep underground rock masses have complex pore structures and face complex geological conditions. Therefore, the seepage problem of such rock masses seriously affects engineering safety. To better explore the seepage law of deep rock masses and ensure engineering safety, indoor experimental methods such as casting thin sections, scanning electron microscopy, and mercury intrusion testing were utilized in this study. The microscopic pore shape, size, distribution, and other structural characteristics of sandstone in coal bearing strata were analyzed. The tortuosity calculation formula was obtained by the theoretical derivation method. And a numerical model was established for seepage numerical simulation research through microscopic digital image methods. The seepage law of surrounding rocks in the Tangkou Coal Mine roadway under different conditions is discussed. The research results indicate that the complexity of the pore structure in porous media leads to an uneven distribution of flow velocity and pressure within the medium. Meanwhile, with the change of physical properties, the fluid flow characteristics also undergo significant changes. The research results can effectively guide micropore water blocking, reduce the impact of groundwater on the environment, ensure the environment and safety of the project, and provide guidance for other geological projects.

Моделирование эрозионного износа титанового сплава высокоскоростным потоком частиц

Introduction. Predicting solid particle erosion (SPE) in gaseous flow and managing its intensity is still a relevant problem in mechanical engineering. It requires the development of a general modeling methodology, which also depends upon many special cases studying various physical processes. Such studies should also include verification analysis, process parameters and model sensitivity studies. Mainly computational fluid dynamics and finite element analysis (and mesh-free methods such as smooth particle hydrodynamics or similar) are used to simulate the erosion process. Papers focused on CFD simulation of solid particle erosion of metal alloys are widely presented, but most of it is associated with relatively low or medium particle velocities (< 100–150 m/s) and is close to uniform diameter distribution. This paper presents a CFD study of Ti6Al4V titanium alloy SPE at relatively high particle velocities and sufficiently non-uniform unimodal particle diameter distribution. The paper also studies the turbulence model influence and particle shape effect which appears as a “shape factor” coefficient in the particle drag model. Methods. The heterogenous flow simulation was based on the Reynolds-averaged Navier-Stokes formulation, where the particles, according to Euler-Lagrange formulation, were simulated as mathematical points with corresponding properties. The influence of turbulence models, such as k-epsilon standard, RNG k-epsilon, and a relatively new Generalized equation k-omega (GEKO) model and its coefficients were also studied. Oka and DNV erosion models were also compared based on the general sample mass loss and more specific erosion intensity profile criterions. The simulation results were compared to the lab-scale experimental results. Results and discussion. It is shown that neither erosion intensity profile or sample mass loss do not depend upon the turbulence model choice or GEKO parameters variation. As expected, erosion is dependent on the erosion model and its coefficients. A notable influence of the shape factor is shown. As the drag coefficient increased due to the particle shape, the erosion intensity decreased and the erosive profile on the surface also changed due to the changing velocity and diameter distribution of the heterogenous flow. It is expected that such results would be useful not only for erosion prediction in all areas of mechanical engineering, but also for wear management in mechanical assemblies and shot peening / shot peen forming management and simulation.

A novel continues multi-shear extrusion process on the microstructure and mechanical property evolution of AZ31 magnesium alloys

This study presents a novel technology in the fabrication of AZ31 Mg alloy sheets using continuous shear extrusion (CSE) with multiple shear platforms at 340 °C. Compared with the conventional extrusion (CE), an asymmetric shear deformation was introduced so that the basal texture deflects towards to extrusion direction. Through finite element simulation, it was found that the differences in flow velocity and strain distributions along the thickness direction can be achieved by introducing the shear strain through CSE technology. Finer grains and more uniform microstructure were obtained in CSEed Mg samples compared to conventional extrusion. The average grain size decreased from 6.33 μm in CE samples to 3.94 μm in CSE samples, and 3.39 μm in CSE-II samples. The continuous asymmetric shear force also led to the basal plane inclining approximately 15° towards the extrusion direction, leading to a weakening of basal texture intensity. In terms of mechanical properties, the CSE Mg plates exhibited higher yield strength (YS), ultimate tensile strength (UTS), and fracture elongation (FE) along the extrusion direction. These improvements in mechanical performance can be attributed to enhanced work hardening ability, texture weakening, finer grains generation, and the dislocation strengthening induced by shear strain.

A Method for Determining the Density and Velocity of Pulse Gas Flows of Millisecond Duration

An experimental setup for studying pulse gas flows within short periods (up to 1 ms) was developed and an experimental data processing method is presented. Based on high-speed frame interferometry data and the results of dynamic pressure measurements, the spatial and temporal distributions of the helium flow density and velocity are determined. The optimal method for reconstructing the spatial density distributions with consideration for the experimental errors is described. The presented method allows characterization of the gas flows with a density of more than 0.0001 kg/m3 and a velocity of more than 400 m/s.