Longitudinal Velocity Distribution Research Articles

Full-scale experimental, numerical, and theoretical research on the spatio-temporal evolution of the flow structure in longitudinal and semi-transversal ventilated tunnels

This paper presents full-scale experimental, numerical, and theoretical research on the spatial and temporal structure of airflow for different modes of ventilation system operation in a road tunnel. The tunnel under investigation is equipped with a semi-transverse ventilation system. There are 19 pairs of axial jet fans in each tunnel tube and 164 air supply vents on both sides of a tube located just above the road surface. A set of seven stand poles with mounted vane anemometers were arranged along the tunnel tube axis. Different configurations of axial jet fans and air supply vents were employed, and changes in airflow velocity were recorded. Since the main objective of the study is to achieve a deeper understanding of the examined phenomena, a numerical model of the flows in the tunnel was built, and the acquired data was used to validate it. Some theoretical considerations are provided and also validated. All of this together reveals a very uneven distribution of longitudinal air velocity along the tunnel axis. Then, time constants when switching the fans on and off are determined. It is shown that the time needed to achieve a stable flow after the fans are turned on is in the order of five minutes, and the decay time after the fans are turned off is much longer; it takes about 15 min to calm down the flow. Next, it is determined that the transverse air supply significantly changes the airflow structure: the average longitudinal air velocity at the inlet portal was up to 25% lower than without it, while values at the outlet portal were similar. Finally, it is indicated that axial fans that operate in the suction mode are similarly efficient to those in the pumping mode.

On the effect of flow regime and slope of the channel bed on the hydraulic performance of the sharp-crested rectangular side weir: a numerical simulation

The aim of this study is to numerically investigate the effect of bed slope on the hydraulic performance of side weirs in supercritical and subcritical flow regimes. Increasing the bed slope decreases the weir efficiency and discharge coefficient in the subcritical flow regime up to 14.54% and in the supercritical flow regime up to 9.26%. By examining the longitudinal velocity distribution, it was observed that in the subcritical flow regime, the maximum longitudinal velocity occurs at the beginning of the upstream of the side weir, and by moving towards the downstream of the weir, the flow velocity decreases and increases again after leaving the length of the weir. In the supercritical flow regime, it has an increasing trend when the flow enters from the upstream of the side weir. The increase in discharge coefficient with the increase of the weir height varied between 4.6% and 7.8%. With increase of the slope of the channel bed, the velocity along the length of the weir increases by 10.88% and 6.17%, respectively, in the subcritical and supercritical regimes, and the transverse velocity along the transverse direction for the subcritical and supercritical flow regimes decreased by 22.23% and 4.80%, respectively.

ОСОБЕННОСТИ ГЛУБИННОГО СЕЙСМИЧЕСКОГО СТРОЕНИЯ ТИХООКЕАНСКОГО ТЕКТОНИЧЕСКОГО ПОЯСА В СТВОРЕ ОПОРНОГО ПРОФИЛЯ 8-ДВ

The article presents the results of deep seismic studies over the Sikhote-Alin fragment of the 8-DV reference geophysical profile running across the large fold structures of the Pacific tectonic belt, that is, the Sikhote-Alin orogenic belt with the superimposed Middle Amur sedimentary basin and the East Sikhote-Alin volcanoplutonic belt. A deep seismic section of the Earth's crust and upper mantle with the distribution of longitudinal wave velocities is constructed. In the upper part of the section, P-wave velocities vary from 4.0–5.0 km/s within the Middle Amur sedimentary basin and the eastern part of the Eastern Sikhote-Alin volcanoplutonic belt to 5.5–5.6 km/s in the central part of the Sikhote-Alin orogenic belt. It is found that the thick Paleozoic assemblage of sediments within the Middle Amur sedimentary basin is complexly faulted and folded. Crystalline rocks with compressional wave velocities of 6.0–6.2 km/s occur at depths of 8 to13 km in different parts of the Middle Amur sedimentary basin and at depths of 4 to 6 km within the Sikhote-Alin orogenic complex. Compressional wave velocities of the crust in the Sikhote-Alin fragment of the 8-DV profile are between 6.3 and 6.35 km/s. The crust varies in thickness from 32–34 km in the northern part of the fragment to 36–37 km in its central and eastern parts. Along the Moho, P-wave velocities are 8.1 to 8.3 km/s; a number of areas of reduced Vp from 7.8 to 8.0 km/s were identified in the junction zones of large crustal blocks. P-wave data were used to identify anomalies which were correlated with structural-tectonic zones, deep fault zones, and seismicity. Thus, along the deep Central Sikhote-Alin fault, the Middle Amur basin is identified, which is infilled by low-velocity sediments of considerable thickness, with Paleozoic sediments shifted to between 4 and 5 km at its junction with the Sikhote-Alin orogenic. Zones of increased heterogeneity in the upper crust projected onto the area within the contours of the Middle Amur sedimentary basin are characterized by increased seismicity.

Oscillatory flow of rheological complex fluid in a flat channel

The article examines the oscillatory flow of rheological complex fluids in a flat channel, in which the rheological complex fluid was obtained based on the Maxwell model, and its mixture is described based on the Newtonian fluid model. Both mixtures of fluids are represented as a homogeneous model of a two-component liquid. In this case, differential equations of motion of homogeneous liquid mixtures are given. Based on this equation, the problem of oscillatory flows of rheological complex fluids in a flat channel is solved analytically. When solving, formulas are given for determining the longitudinal velocity. Using the obtained formulas, graphs of the longitudinal velocity distribution over the cross section of the channel are determined depending on the change in the oscillation frequency parameter, and with their help, appropriate conclusions are drawn.

The Impact of Geometrical Parameters on Two-Layer Flow Patterns with Evaporation in an Inclined Channel

The paper focuses on studying two-layer stationary convective flows of liquid and the accompanying flows of gas and vapor in inclined layers, taking into consideration the effects of heat and mass transfer. The thermocapillary boundary condition is assumed to be non-deformable. Mathematical modeling of two-layer flows in an infinite channel with solid impermeable walls is based on the exact solutions of a special form of differential convective equations. The effects of thermal diffusion and diffusive thermal conductivity are considered in the upper layer of the system. The vapor in the gas is assumed to be an admixture that does not affect the properties of the gas. The flow is studied when the vapor concentration function meets the condition of zero flux on the upper wall of the channel. The influence of the layer thicknesses on the flow topology is studied using the exemplary “benzine — air” system. The author’s programming code helps produce the data set for plotting the profiles of longitudinal velocity and concentration distributions of temperature and vapor for layers with different thicknesses. At the same time, all the other parameters of the system remain fixed. The results presented in the paper are obtained for the case when the closure condition for liquid flow is fulfilled, and at a given value of the gas flow rate. It is shown that a change in the thickness of the layer leads to both quantitative and qualitative changes in the characteristics of the flow process.

Numerical Simulation of the Influence of Ski-jump Deck on the Take-Off Zone Flow Field Based on CFD

Ski-jump take-off is a standard procedure for carrier-based aircrafts, and it is one of the key technologies for the generation of the combat effectiveness of the system. A 3D model carrier with a ski-jump deck is conceptually designed. The airflow field over the carrier is numerically simulated based on CFD. The longitudinal airstream line and velocity distribution, the velocity distributions in normal-wash area, tangential-wash area are derived and the influence of the ski-jump deck on the take-off zone is analyzed. The numerical simulation shows that the body-shedding vortex on both sides of the bow affects the engine intake at Take-off Point 1 and 2 and 3.

Natural convection in vertical solar heat collector nanotextured with reduced graphene oxide and silver nanowires

In this study, a vertical shaft is coated using silver nanowires (AgNWs) together with reduced graphene oxide (rGO) via the supersonic spray-coating technique to enhance the absorption of solar radiative heat for use in solar air heaters. The rGO/AgNW-coated surface induces multiple light reflections, similar to that in a perfect black body inside a Helmholtz jar, thus enhancing the collection of solar radiation. Air fed into the vertical heated shaft ascends owing to buoyancy. The air temperature difference, ΔT, between the outlet and inlet is measured for various mass flow rates to quantify the heat transferred to the air from the solar-heated vertical shaft. The longitudinal air velocity and temperature distributions inside the shaft are numerically simulated using the fire dynamics simulator. Both two- and three-dimensional simulations are performed, and the results are compared with experimental data for various mass flow rates. The results confirm that the trends observed in both the experiments and simulations agree well for all cases. Multiple metal meshes are installed inside the vertical shaft to induce turbulence, which enhances the heat transfer intensity. This turbulence enhancement is confirmed via smoke visualization and infrared images.

Method of calculation of the flow motion model in water intake facilities

One of the urgent problems of our time is the uneven distribution of the flow velocity in the forebay of the intake structure, which leads to the destruction of the flow structure due to the water level, the amount of turbidity in the water, the size of the fraction and the change in speed. As a result, turbidity can be observed in the forebay and water intake units, an increase in hydraulic resistance in the suction network, a decrease in pump fluid loss, the formation of cavitation and the destruction of internal parts. In the article, the forebay of an irrigation pumping station and in the intake section, a mathematical model of the dynamics of water distribution over the velocity field, longitudinal and transverse distribution based on the shape of the forebay was created and numerous results were obtained. Taking into account the above, according to the identified Lax scheme, the Eyler differential equation of flow motion was numerically solved, and the calculation of the longitudinal and transverse velocity distributions in the forebay and water intake was carried out by setting the boundary conditions for the state of the flow.

Numerical Investigation of the Influence of Boulder Concentration on Longitudinal Velocity and Shear Stress Distribution in Rough Bed Stream

Numerical Investigation of the Influence of Boulder Concentration on Longitudinal Velocity and Shear Stress Distribution in Rough Bed Stream

Spatial Transformations for Reacting Gas Shock Tube Experiments

Shock tube flows can be used to investigate nonequilibrium thermochemistry and radiative processes found in hypersonic flows. The flow in a shock tube contains many flow nonuniformities, in particular boundary-layer effects. For the purpose of studying the properties of the test slug, the flow behind the shock is usually considered analogous to the stagnation line flow over a blunt body. In reality, radial and longitudinal velocity distributions in the two flows are different, and so a coordinate transformation is needed to match time-of-flight profiles. This work develops a method to approximately transform the postshock distance for normal and blunt body shocks to a shock tube flow using a Mirels analysis. The effects of shock tube diameter and shock speed variation are highlighted along with the importance of postshock temperature and density rises. This is then applied to blunt body simulations of NASA EAST data for air and Titan tests. This showed that minimal difference is encountered for fast reacting flows. However, large differences can be seen in the slower reacting Titan tests, which to date have been misinterpreted when compared to blunt body simulations.

Modeling of Non-Isothermal Polymer Melt Flow in a Conical Annular Channel of a Disk Extruder

Purpose. The homogenization zone consists of various channels with different configurations, for each of which it is necessary to determine the passage of the melt flow process, and on its basis - the velocity fields, which determine the quality of mixing and distribution of components in the melt. To ensure a flexible and controllable homogenization process with the possibility of improving the quality of the melt, it is necessary to study the flow processes in the channels of a disk extruder. Therefore, the main objective of this work is to perform hydrodynamic modeling of processes during melt flow in a conical channel. Methodology. To achieve this goal, we propose a methodology for determining the flow processes in a conical channel, and find out which zones are convenient to consider in a special conical orthogonal coordinate system. For this purpose, the change in the radial coordinate , which has the same meaning in both the straight and the conical gap, was described - it is a coordinate along the width of the gap. This makes it possible to further apply this coordinate for the width of the disk gap - between the moving and stationary disks. Findings. A method has been proposed that describes the flow processes in the conical channel of the homogenization zone of a disk extruder. The calculation procedure is presented in an analytical form, and graphical dependences of the distribution of tangential and longitudinal velocities and shear velocities of the melt flow along the width of the annular channel at the nominal and maximum disk speeds and at the nominal and maximum disk gap are also given. Originality. For the first time, a methodology for calculating the conical channel of the homogenization zone of a disk extruder is presented, which describes the flow processes in a conical orthogonal coordinate system, which allows taking into account the common coordinate for the entire homogenization zone. The general procedure for calculating the channels of the homogenization zone has been supplemented. Practical value. The procedure for calculating the channels of the homogenization zone, which was started earlier, was extended and applied to the flow in a conical annular channel. This coordinate allows us to describe the flow processes along the width of the channel for all channels of the homogenization zone of a disk extruder, which greatly simplifies the calculations. Important results of hydrodynamic and thermal processes were obtained for the annular channel, which makes it possible to design disk extruders with greater accuracy and calculate their optimal operating modes.

Experimental investigation of nanosecond laser-induced shock waves in water using multiple excitation beams.

Revealing the expansion and interaction dynamics of multiple shock waves induced by a nanosecond laser is important for controlling laser surgery. However, the dynamic evolution of shock waves is a complex and ultrafast process, making it difficult to determine the specific laws. In this study, we conducted an experimental investigation into the formation, propagation, and interaction of underwater shock waves that are induced by nanosecond laser pulses. The effective energy carried by the shock wave is quantified by the Sedov-Taylor model fitting with experimental results. Numerical simulations with an analytic model using the distance between adjacent breakdown locations as input and effective energy as fit parameters provide insights into experimentally not accessible shock wave emission and parameters. A semi-empirical model is used to describe the pressure and temperature behind the shock wave taking into account the effective energy. The results of our analysis demonstrate that shock waves exhibit asymmetry in both their transverse and longitudinal velocity and pressure distributions. In addition, we compared the effect of the distance between adjacent excitation positions on the shock wave emission process. Furthermore, utilizing multi-point excitation offers a flexible approach to delve deeper into the physical mechanisms that cause optical tissue damage in nanosecond laser surgery, leading to a better comprehension of the subject.

COMPUTATION OF THREE-DIMENSIONAL BLOOD FLOW DEVELOPMENT IN A 180∘ CURVED TUBE GEOMETRY

Computational blood flow studies are providing an increasingly important complement to clinical experiments in 21st century biomedical engineering. Motivated by probing deeper into this topic, a theoretical and numerical study is presented of the flow induced by an impulsive acceleration to steady state hemodynamics in a curved tube which is investigated as a boundary layer developing with time from the curved entrance to a straight tube (blood vessel). The transient processes are simulated with a finite volume method solution of the Navier–Stokes equations. The rapid growth of the boundary layer with the core flow is captured in the curved entrance, along the tube to an axisymmetric flow in the downstream. Secondary flow patterns, centrifugal pressures and total head contours are correlated with longitudinal velocity distributions across various sections. It is observed that the entrance zone is controlled by uniform inlet velocity and centrifugal forces. The high pressure drop in the onset flow is associated with strong acceleration which is comparable to generating systolic pressures. The simulations further indicate that a sustained increment in volumetric flow rate is necessary to maintain the pressure wave in the aorta. Furthermore, the velocity distributions are shown to approach Hagen–Poiseuille flow in the downstream zone. The complex hemodynamic characteristics are visualized effectively with computational simulations and the study demonstrates the excellent ability of this approach in elaborating critical flow details in aortic hemodynamics.

A multiple-fluids-mechanics-based model of velocity profiles in currents with submerged vegetation

Submerged aquatic vegetation can provide a habitat and food for marine and river organisms, and it has the ecological effect of purifying water by absorbing harmful substances. Therefore, it plays an important role in the maintenance, restoration, and improvement of marine and river ecosystems. Hydrodynamic problems caused by submerged vegetation have been a matter of wide concern. According to the distribution of submerged vegetation, the flow can be divided into three layers in the vertical direction: uniform, mixing, and logarithmic layers. This paper proposes an analytical model for the vertical distribution of longitudinal velocity in open-channel flows with submerged vegetation. A concept of velocity superimposition is applied in mixing and logarithmic layers. The velocity inside the vegetated layer can be solved by the balance between the drag force and bed gradient. The velocity difference between the vegetated layer and the free surface layer results in the formation of a mixing layer near the top of the vegetation. Flow at the junction between the vegetation and free surface layers is mainly controlled by the vortices in the mixing layer. The velocity in the mixing layer is commonly described by a hyperbolic tangent formula. The logarithmic distribution formula is applied to the free surface layer, where the velocity without effect arising from vortices is similar to the open-channel flow. The concept of the wake function is introduced to modify the distribution of velocity in the free surface layer. The longitudinal velocities from the theoretical model are compared to the measured velocities in the literature. The theoretical velocities agree well with the measured values in the flows with submerged vegetation, proving that the theoretical model proposed here can successfully predict the vertical distribution of velocity and has extensive adaptability.

Modeling Of Polymer Melt Flow In The Annular Channel Of A Disk Extruder

Purpose. Polymer products are used in industry due to their performance properties. The homogeneity of the melt is essential for the quality of the final product. Uniform distribution of components and properties ensures homogeneity of the product's physical and mechanical characteristics. Insufficient homogeneity can lead to defects in the product. The homogenization zone plays an important role in ensuring a homogeneous melt. In a disc extruder, the homogenization zone consists of four consecutive channels. In order to describe the flow for the entire homogenization zone, it is necessary to model the first channel first. Therefore, the main purpose of this work is to model hydrodynamic and thermal processes during the flow of a non-Newtonian fluid in a straight annular channel in a non-isothermal regime, as well as to create a general procedure for further calculations for other channels. Methodology. The analysis of publications was carried out. The procedure for calculating the velocity and shear rate of the longitudinal and tangential melt flow, the effective melt viscosity, and the calculation of the melt temperature change along the length of the annular gap in an analytical form was developed. Findings. In accordance with the developed procedure, the values of tangential and longitudinal velocities and shear rates were calculated. The graphical dependences of the distribution of tangential and longitudinal velocities and shear velocities of the melt flow along the width of the annular channel, the distribution of pressure and the temperature of the polymer melt averaged over the width of the gap along the length of the annular channel are presented. Originality. In this work, a stationary flow in a straight annular channel was modeled for LDPE of the 15803-020 grade in a non-isothermal regime. A general procedure for further calculations for other channels of the homogenization zone has been developed. Practical value. The given calculation procedure can be applied to the following channels of the homogenization zone, which allows describing the melt flow for the entire homogenization zone.

Laminar Flow in a PEM Fuel Cell Cathode Channel

A Berman’s model for the laminar flow of incompressible fluid in a channel with permeable walls is extended for variable along the channel velocity of injection. The system of two–dimensional continuity and Navier–Stokes equations is reduced to a single ODE for the transversal velocity with coefficients depending on position along the channel. Numerical solution for the flow in the cathode channel of a PEM fuel cell is presented. The flow velocity profile across the channel is almost indistinguishable from the Poiseuille’s parabolic shape; however, the distribution of pressure gradient and longitudinal velocity differ quite significantly from the Berman’s result.

Comprehensive use of the Gutenberg–Richter law and geotomography for improving seismic hazard evaluation in hard coal mines

Mining-induced seismicity occurs in numerous underground mines worldwide where extraction is conducted at great depths or in areas characterised by complex tectonic structure. It is accompanied by rock bursts, which result in the loss of working functionality and the possibility of accidents among personnel. The issue of a constant and reliable seismic hazard evaluation is of key significance for both the safety of miners and the stability of production. Research on its improvement is directed at developing new interpretive solutions and methods. The nature of the presented solution is the complex interpretation of seismological data that characterise rock mass seismicity and of underground measurement results in the form of a map presenting the longitudinal wave propagation velocity distribution in the rock surrounding the mined coal seam. The solution was tested in hard coal mines located in the Upper Silesian Coal Basin. The mines are equipped with a modern seismological system enabling the constant monitoring of seismicity together with hazard level evaluation as well as with seismic apparatus for conducting periodic measurements of the seismic wave propagation velocity before the mining face. Comprehensive seismic hazard evaluation criteria were determined based on the obtained results, involving the anomaly of the Gutenberg–Richter law “b” value and the maximum longitudinal seismic wave propagation velocity in the roof rock. The obtained experience and the result validation of this new comprehensive hazard evaluation method confirm its practical usefulness and indicate the directions of improvement for the solution in question.

Low-order models for a circular hydraulic jump on a spherical cap

In this work, we analyze the flow of a thin layer of viscous liquid over the outer surface of a sphere due to inertia and gravity. We use the classical problem of a circular hydraulic jump as a starting point and observe the changes in the flow structure as the gravity component along the surface becomes significant. We assume that the flow is stationary and axisymmetric, the curvature of the spherical surface is small, and the capillary forces are negligible. The depth-averaged thin-layer equations describe the flow. We perform a qualitative analysis using a one-parametric representation of the longitudinal velocity distribution and find the necessary conditions for the hydraulic jump existence. The intensity of the jump monotonically decreases, and its radius grows to a certain finite value. The jump vanishes at a finite distance from the axis of symmetry. Using a two-parametric representation, we locate zones of recirculating flow and find the condition of their existence. We find the optimal strategy of averaging by comparing the results of our calculations with the data obtained experimentally and by using simulations in the framework of the full Navier–Stokes equations.

Reynolds stress modeling of supercritical narrow channel flows using OpenFOAM: Secondary currents and turbulent flow characteristics

In this study, the full Launder, Reece and Rodi pressure-strain model, and nonlinear boundary damping functions were incorporated in OpenFOAM® to simulate the turbulence-driven secondary currents in supercritical narrow channel flows, such as in sediment bypass tunnels. Five simulations were performed under uniform flow conditions covering Froude numbers from 1.69 to 2.56 and aspect ratios (channel width to flow depth) ar from 0.9 to 1.91 to investigate the formation of secondary currents and their impacts on longitudinal velocity, turbulence characteristics, and bed shear stress distribution. The numerical results of the maximum longitudinal velocity and the average shear velocity show marginal deviations, of less than 2.6%, from two-dimensional experimental results acquired under decelerating flow conditions. However, some differences are observed for the secondary currents and for the vertical turbulence intensity and Reynolds shear stress in the outer flow region, especially for cases with higher flow nonuniformity (that can influence the surface perturbation) whose influence is missing in the numerical model. No intermediate vortex is observed for ar = 1.91. However, it develops for lower ar and detaches from the free surface vortex when ar ≤ 1.05. Such vortex bulges the longitudinal velocity contour lines inward and the zone of higher longitudinal velocity narrows and deepens with a decrease in ar. The decrement reduces the magnitude of the normalized maximum secondary velocity. It also affects the bottom vortex which alters the bed shear stress distribution.

An Analytical Solution to Predict the Distribution of Streamwise Flow Velocity in an Ecological River with Submerged Vegetation

Aquatic submerged vegetation is widespread in rivers. The transverse distribution of flow velocity in rivers is altered because of the vegetation. Based on the vegetation coverage, the cross-section of the ecological channels can be divided into the non-vegetated area and the vegetated area. In the vegetated area, we defined two depth-averaged velocities, which included the water depth-averaged velocity, and the vegetation height-averaged velocity. In this study, we optimized the ratio of these two depth-averaged velocities, and used this velocity ratio in the Navier–Stokes equation to predict the lateral distribution of longitudinal velocity in the open channel that was partially covered by submerged vegetation. Based on the Navier–Stokes equations, the term “vegetation resistance” was introduced in the vegetated area. The equations for the transverse eddy viscosity coefficient ξ, friction coefficient f, drag force coefficient Cd, and porosity α were used for both the non-vegetated area and the vegetated area, and the range of the depth-averaged secondary flow coefficient was investigated. An analytical solution for predicting the transverse distribution of the water depth-averaged streamwise velocity was obtained in channels that were partially covered by submerged vegetation, which was experimentally verified in previous studies. Additionally, the improved ratio proposed here was compared to previous ratios from other studies. Our findings showed that the ratio in this study could perform velocity prediction more effectively in the partially covered vegetated channel, with a maximum average relative error of 4.77%. The improved ratio model reduced the number of parameters, which introduced the diameter of the vegetation, the amount of vegetation per unit area, and the flow depth. This theoretical ratio lays the foundation for analyzing the flow structure of submerged vegetation.