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EN
The paper presents results for S700MC high-strength steel and its weld at longitudinal and transverse orientations of specimens. The determination of anisotropy features is proposed for the parent material and welding joint due to the often usage of this steel for manufacturing of towing and coupling components in recovery vehicles. This means that the most important mechanical parameters of the regions questioned should be determined for numerical and analytical analysis with the target to get their type approval and to keep the road safety. The mini-specimens were used to reflect the joint behaviour subjected to monotonic tension. The weld behaviour was assessed using the longitudinal specimen that was manufactured from the joint. The results enabled to indicate differences in the section tested depending on the loading orientations considered.
EN
This article presents the technological problem related to the production of rotors with an internal permanent magnet. Most often, the magnetic circuits of such rotors used in alternating current synchronous motors (AC IPM) are made of isotropic magnetic sheets. At this point, it should be noted that it is often not taken into account that each isotropic magnetic sheet exhibits some anisotropy. This significantly affects the operational parameters of the brushless permanent magnet (PM) motor such as the cogging torque, electromagnetic torque ripples and an increase in induced voltage harmonics. To illustrate how important it is to properly design the rotor core, two rotors of the IPM motor were analyzed in this work. In the first rotor solution, minimization of the magnetic sheet anisotropy was not taken into account, and the skew of the magnets was not used. In the second case of the IPM motor, the problem of rotor magnetic circuit anisotropy was minimized and an additional skew of the PMs was used. The obtained measurements and calculations of selected useful parameters of both rotor designs were then compared with each other. Importantly, the conclusions drawn and the resulting comments will prove useful to designers, assemblers and manufacturers of electrical machine components.
EN
The roughness feature of a natural rock fracture surface is an important factor affecting the shear and poromechanical behavior of rock. The scale effect and spatial distribution characteristics of the fracture surface roughness are notable challenges at rock engineering sites. In this article, morphological data of a large-scale field rock fracture surface were collected using a 3D scanner. Then, the original surface was divided into several small fracture surfaces. With the use of a 2D roughness statistical index, the 2D roughness (JRC2D) of the fracture profile was evaluated. The 3D roughness (JRC3D) of the fracture surface along different directions was obtained via the weighted averaging method. Based on four oblique analysis schemes, the elevation statistical trend and roughness scale effect of fracture surfaces with different widths were examined. With increasing fracture size, the average elevation (^) and the standard deviation of elevation (a) showed different typical change patterns. The impact of size variation on the fracture surface roughness includes four types and exhibits significant anisotropy. Based on small fissure surfaces without mutual coverage, the spatial distribution characteristics of the fracture roughness were analyzed and were proven to exhibit high dispersion and anisotropy. With increasing width of the analyzed small fracture, the roughest position on the fracture surface basically remained the same, but there was a significant change in roughness anisotropy.
PL
W artykule przedstawiono analizę teoretyczną oraz pomiarową zależności kątowej prądu krytycznego w wysokotemperaturowych taśmach nadprzewodnikowych (HTS) pierwszej generacji. Badania skupiały się na analizie wpływiu wartości i kierunku pola magnetycznego na prądy krytyczne. W pracy opisano również budowę i działanie specjalnie zaprojektowanego stanowiska testowego, wykorzystującego magnesy neodymowe w konfiguracji Halbacha, które umożliwia dokładne pomiary i charakteryzację taśm HTS. Wyniki badań potwierdziły zgodność z modelem Kima i pozwoliły na rozwój modelu gęstości prądu krytycznego, który może być wykorzystany w dalszych symulacjach komputerowych.
EN
The article presents a theoretical and measurement analysis of the angular dependence of the critical current in high-temperature superconducting (HTS) tapes of the first generation. The research focused on the impact of the value and direction of the magnetic field on critical currents. The paper also describes the construction and operation of a specially designed test station using neodymium magnets in the Halbach configuration, which allows for precise measurements and characterization of HTS tapes. The results confirmed the consistency with the Kim model and contributed to the development of a critical current density model that can be used in further computer simulations.
EN
Hydrofracturing in sandstone is not an easy task. Sandstone is porous; fluid dissipation is common hence unable to obtain breakdown pressures in certain flow rates (0.0000005-0.0001 m3/s). The higher flow rate (0.00025 m3/s) is ascertained to determine the fracturing pressures. Due to this, fracture propagation and delineation are observed (Satya Subrahmanyam, 2022) [1]. To enhance, an experimental method is adopted by carrying out 6 Hydrofracturing tests in a borehole comprising sandstone. A high flow rate of 0.00025 m3/s and viscosity 0.001 Pa s is applied. Later, the fracture simulation was run on 12 core samples collected from the same depths in a lab. The fluid flow rates of 0.0000005-0.0000015 m3/s, viscosity 0.27 Pa- second, pore pressure of 4 MPa, confining pressures in vertical-12 MPa and horizontal 6, 18, 24, 30 MPa is applied. The fracture traces and the stress results exhibit a difference of 80°-300° observed in both cases. The major principle stress orientation obtained in the borehole is 20° and 40°. In lab tests with confining horizontal pressures at 6 and 18 MPa, it is 120° and 130°, and at 24 and 30 MPa is 20°. This indicated that there is fracture delineation occurred. It is observed in the higher flow rate and confining pressures.
EN
The aim of this work was to perform a mechanical and acoustic analysis of electric guitar bodies. Sam ples of ash, oak, walnut, lime tree, and fir were selected for mechanical tests - with constant moisture content, made of latewood, and free from defects. The tests were carried out on a Brinell device to determine the hardness of the wood, and on an MCT3 machine from Anton Paar to determine the microhardness and elastic moduli. The elastic properties of wood are determined by its anisotropy and have different values depending on the direction of force in relation to the fibers. The wood showed the greatest stiffness along the fibers; in the case of forces acting perpendicular to the fibers, the stiffness was much lower. Sound transmission tests of selected acoustic parameters were carried out. They involved measuring and analyzing the frequency and damping of vibrations of guitar bodies using a special vibration sensor. The acoustic parameters of a guitar body experimentally made from walnut were compared with those of a mass-produced Ibanez guitar made of ash wood. Each species of wood has its own characteristic blend of physical properties, such as grain structure, density, weight, and strength, which influence the final tonal power of the guitar. The test results of various wood species indicate significant differences in strength and acoustic-resonance properties, which determine the absorption of vibrations, sound amplification, and sound transmission. The use of a specific wood for a guitar body is dependent on the musician’s artistic vision and the purpose of the instrument.
EN
Although the elastic properties of porous materials depend mainly on the volume fraction of pores, the details of pore distribution within the material representative volume are also important and may be the subject of optimisation. To study their effect, experimental analyses were performed on samples made of a polymer material with a predefined distribution of spherical voids, but with various porosities due to different pore sizes. Three types of pore distribution with cubic symmetry were considered and the results of experimental analyses were confronted with mean-field estimates and numerical calculations. The mean-field ‘cluster’ model is used in which the mutual interactions between each of the two pores in the predefined volume are considered. As a result, the geometry of pore distribution is reflected in the anisotropic effective properties. The samples were produced using a 3D printing technique and tested in the regime of small strain to assess the elastic stiffness. The digital image correlation method was used to measure material response under compression. As a reference, the solid samples were also 3D printed and tested to evaluate the polymer matrix stiffness. The anisotropy of the elastic response of porous samples related to the arrangement of voids was assessed. Young’s moduli measured for the additively manufactured samples complied satisfactorily with modelling predictions for low and moderate pore sizes, while only qualitatively for larger porosities. Thus, the low-cost additive manufacturing techniques may be considered rather as preliminary tools to prototype porous materials and test mean-field approaches, while for the quantitative and detailed model validation, more accurate additive printing techniques should be considered. Research paves the way for using these computationally efficient models in optimising the microstructure of heterogeneous materials and composites.
8
Content available remote Behaviour of the aeolian sands under true-triaxial conditions
EN
To clarify the stress–strain behaviour, strength on the deviatoric plane, shear band formation, and dilatancy characteristics of aeolian sand under three-dimensional loading conditions, a series of true-triaxial tests with various intermediate principal stress coefficients b ∈ [0.0, 1.0] at constant effective mean principal stress p' were conducted under drained and undrained conditions. The results presented that the variations of the stress–strain, strength, and effective internal friction angle show its significant dependence on the relative magnitude of the intermediate principal stress expressed in terms of the b value. Because a clear penetrating shear band was produced in the prismatic specimen at b = 0.2 and b = 0.4, the stress–strain response exhibits softening, and its peak shear stress and effective internal friction angle are reduced. Besides, shear bands often appear in the hardening regime. Moreover, the dilatancy was the weakest at b = 0.0 and the strongest at b = 0.4, which depended on the stress path in terms of the b value. The peak shear stress on the deviatoric plane decreased in a transverse “S” shape with the b value varying from 0.0 to 1.0, correspondingly, the effective internal friction angle increased first and then decreased. But in the case of increasing p' value, aeolian sand has a unified critical state line and phase transformation line at constant b value.
EN
The purpose of the article is to analyze the influence of print orientation, using the DLMS method, on the strength of the tested material before and after heat treatment. The heat treatment involved heating the material to 490˚C and subsequently cooling it within the furnace for four hours. Experimental research involves X3NiCoMoTi 18-9-5 tool steel. Analysis of the test results indicates a strength increase following heat treatment. Additionally, a numerical study was conducted to investigate the mechanical characteristics of X3NiCoMoTi 18-9-5 tool steel fabricated via 3D printing. Fractographic analysis of specimen failure was performed, and the results were subsequently compared.
EN
Non-oriented electrical steels constitute the most important segment of the market of soft magnetic materials. In the paper the usefulness of the model based on hyperbolic tangent nonlinear transformation for the description of quasi-static hysteresis loops for this type of material is verified.
PL
Blachy elektrotechniczne o ziarnach niezorientowanych stanowią najważniejszy segment rynku materiałów magnetycznie miękkich. W pracy zweryfikowano użyteczność modelu opartego na nieliniowej transformacji tangens hiperboliczny do opisu quasi-statycznych pętli histerezy dla tego typu materiału.
EN
In the past ten years, InAs/InAsSb type-II superlattice has emerged as a promising technology for high-temperature mid-wave infrared photodetector. Nevertheless, transport properties are still poorly understood in this type of material. In this paper, optical and electro-optical measurements have been realised on InAs/InAsSb type-II superlattice midwave infrared photodetectors. Quantum efficiency of 50% is measured at 150 K, on the front side illumination and simple pass configuration. Absorption measurement, as well as lifetime measurement are used to theoretically calculate the quantum efficiency thanks to Hovel’s equation. Diffusion length values have been extracted from this model ranging from 1.55 μm at 90 K to 7.44 μm at 200 K. Hole mobility values, deduced from both diffusion length and lifetime measurements, varied from 3.64 cm²/Vs at 90 K to 37.7 cm²/Vs at 200 K. The authors then discuss the hole diffusion length and mobility variations within temperature and try to identify the intrinsic transport mechanisms involved in the superlattice structure.
EN
Hydrogen induced cracking is a form of wet H2S cracking. Blistering or crack propagation is a result of the mechanical tearing of material by high-pressure hydrogen gas forming on internal material discontinuities, like non-metallic inclusions. This failure mechanism is typically associated with low and medium-strength pipeline steels, however, it does also occur in high-strength rolled wire. This evaluation aims to elucidate the mechanism of this susceptibility. The characteristic failure pattern where cracking occurs near the wire centreline and propagates perpendicular to the rolling direction leads to believe that the wire anisotropy, developed during cold rolling, plays a critical role. A mechanical property – flow resistance in principal directions – was measured using the Wheeler and Ireland technique. It was found that the “weak” direction is perpendicular to the crack propagation direction. The failure rate does not correspond to the flow resistance, but rather to the flow resistance ratios. It is proposed that those ratios are not only a measure of anisotropy but also a measure of microstructural damage inflicted by the cold rolling process. This microstructural damage is partially reversible by heat treatment processes.
PL
Pękanie wodorowe jest mechanizmem degradacji często zachodzącym w środowiskach korozyjnych, w których występuje siarkowodór. Propagacja pęknięć postępuje na skutek fizycznego rozrywania materiału przez cząsteczkowy wodór pod wysokim ciśnieniem, tworzący się na nieciągłościach wewnętrznych, takich jak na przykład wtrącenia niemetaliczne. Praca badawcza dotyczy mechanizmu pękania wysoko wytrzymałego kształtowego drutu stalowego. Drut pęka w charakterystyczny sposób: pęknięcie tworzy się w pobliżu środka drutu i propaguje równolegle do płaskich powierzchni. Obserwacja ta każe przypuszczać, że propagacja związana jest z anizotropią właściwości mechanicznych drutu. Anizotropię zbadano jako opór płynięcia plastycznego materiału pod wgłębnikiem twardościomierza metodą Wheelera i Irelanda. Zaobserwowano, że pęknięcia propagują prostopadle do kierunku, w którym występuje najmniejszy opór płynięcia. Pękanie podczas testów w środowisku korozyjnym z siarkowodorem nie jest skorelowane bezpośrednio z oporem płynięcia, a ze stosunkiem oporów płynięcia w dwu kierunkach, a więc miarą anizotropii. Z badań wynika, że proces walcowania na zimno powoduje uszkodzenia mikrostruktury, które można szacować miarą anizotropii właściwości mechanicznych drutu i które są częściowo odwracalne w procesie obróbki cieplnej.
EN
In this paper, the problem of deformation induced by an open pit excavation in anisotropic stiff soils is analysed by FE modelling. The presented research is focused on the influence of material model with anisotropic stiffness on the accuracy of deformation predictions as compared with the field measurements. A new hyperelastic-plastic model is applied to simulate anisotropic mechanical behaviour of stiff soils. It is capable to reproduce mixed variable stress-induced anisotropy and constant inherent cross-anisotropy of the small strain stiffness. The degradation of stiffness depending on strain is modelled with the Brick-type model. The model formulation and parameters are briefly presented. General deformation pattern obtained in the exemplary 2D boundary value problem of an open pit excavation is investigated considering different values of inherent cross-anisotropy coefficient of small strain stiffness. The numerical simulations are performed as a coupled deformation-flow analysis which allows to properly model the drainage conditions. The excavation phases are simulated by removal of soil layers according to the realistic time schedule. Finally, the monitored case of the trial open pit excavation in heavily overconsolidated Oxford Clay at Elstow, UK is simulated with proposed material model both in 2D and 3D conditions. The obtained calculation results are compared with displacement measurements and discussed.
PL
Modelowanie numeryczne zagadnień geotechnicznych związanych z odciążeniem podłoża (np. tunelowanie, wykopy) wymaga odpowiedniego opisu materiałowego gruntu, który pozwala na prawidłową symulację charakterystyki mechanicznej w zakresie małych odkształceń. Najważniejszymi elementami są tutaj nieliniowość sztywności związana z barotropią oraz degradacją stycznego modułu ścinania z odkształceniem oraz inherentna anizotropia sztywności. Modele konstytutywne dostępne w popularnych systemach obliczeniowych rzadko pozwalają na uwzględnienie anizotropii sztywności w zakresie małych odkształceń. Najczęściej przyczyną jest bardziej skomplikowana procedura implementacji niż w przypadku modeli z izotropową sztywnością, jak również ograniczona dostępność parametrów materiałowych związanych z anizotropią. Rozwój technik pomiarowych w eksperymentalnej mechanice gruntów, obserwowany w ostatnich latach na całym świecie, pozwala jednak na zaprojektowanie i przeprowadzenie badań anizotropii sztywności w warunkach ważnych inwestycji lub projektów badawczych. Najczęściej jest to pomiar współczynnika anizotropii αG w aparacie trójosiowym wyposażonym w elementy sejsmiczne bender zorientowane zarówno w pionie jak i w poziomie. System taki pozwala na bezpośrednie wyznaczenie modułów ścinania w płaszczyźnie pionowej Gvh oraz poziomej Ghh (αG= Ghh/Gvh). W artykule przedstawiono własny hipersprężysto-plastyczny model konstytutywny uwzględniający zarówno nieliniowość jak i anizotropię sztywności w zakresie małych odkształceń. W modelu tym wykorzystano anizotropową hipersprężystość do opisu sztywności początkowej, system zagnieżdżonych powierzchni plastyczności w przestrzeni odkształcenia do opisu degradacji sztywności (tzw. model Brick) oraz konwencjonalne kryterium wytrzymałości na ścinanie do ograniczenia dewiatorowych stanów naprężenia. Model został zaimplementowany w programie metody elementów skończonych Plaxis w ramach opcji User Defined Soil Model (UDSM). Analizowanym zagadnieniem brzegowo początkowym jest próbny otwarty wykop wykonany w ile oxfordzkim w Elstow, Wielka Brytania. Szeroka baza danych dotyczących niestandardowych badań laboratoryjnych iłu oksfordzkiego zorientowanych, oprócz wyznaczenia parametrów standardowych, na charakterystykę anizotropii sztywności dostępna jest w literaturze. Dokładny opis realizacji wykonanego próbnego wykopu z danymi pozwalającymi na przeprowadzenie własnych analiz wraz z wynikami monitoringu przemieszczeń dostępne są w publikacji Hird&Pierpoint (Geotechnique 47(3), 1997). Umożliwiło to, kalibrację parametrów anizotropowego modelu hipersprężysto-plastycznego i przeprowadzenie analizy wstecz będącej cenną weryfikacją przydatności opracowanego modelu konstytutywnego. Przed wykonaniem symulacji numerycznych próbnego wykopu w Elstow przeprowadzono również serię obliczeń na uproszczonym przykładowym modelu wykopu otwartego w płaskim stanie odkształcenia w celu rozpoznania wpływu czystej anizotropii inherentnej na deformację powstającą podczas odciążenia podłoża gruntowego takim wykopem. Symulację numeryczną wykopu próbnego w Elstow przeprowadzono zarówno w płaskim stanie odkształcenia jak i na modelu przestrzennym. Metoda symulacji odpowiadała podejściu sprzężonemu konsolidacji z równoczesnym uwzględnieniem przepływu wody w gruncie (coupled deformation flow analysis). Warunki czasowe wykonania wykopu próbnego, jak również parametry filtracyjne oraz mechaniczne zalegających gruntów powodują jednak, że przedmiotowe zagadnienie brzegowo-początkowe zachodzi ostatecznie w warunkach bliskich warunkom braku drenażu. Wyniki przeprowadzonych symulacji numerycznych porównano z wynikami monitoringu przemieszczenia. Uzyskano zadowalającą zgodność obliczonego i pomierzonego pola przemieszczenia. Dokładność wyników obliczeń jest jednak zmienna w zależności od obszaru analizowanego zagadnienia. Odpowiednie porównania przedstawiono na rysunkach w artykule.
14
Content available remote Anisotropy on the ductile-to-brittle transition for rock in process of drilling
EN
Anisotropy is an inherent property of rocks. It refers to the different response of the rock properties in each direction. Understanding the anisotropy characteristics of rock failure by drilling has practical applications in improving drilling efficiency, especially for engineering applications. In this paper, a criterion is established to clarify the ductile-to-brittle transition in the drilling process of rock. Moreover, a new anisotropy index has been proposed to evaluate the effect of anisotropy on the critical state of the ductile-to-brittle transition. The digital drilling tests are conducted on six types of rock to study the drilling mechanical performance in the X, Y, and Z directions. The anisotropy characteristics of drilling parameters and mechanical specific energy (MSE) are analysed at the critical state of ductile–brittle failure. The results show that the critical state of ductile–brittle failure is manifested as an inflection point of the depth of cut. The evolution of MSE is fitted as two linear functions, which corresponds to the two stages. The order of anisotropy in MSE is obtained as: gneiss > slate > red sandstone > granite > argillaceous sandstone > sandstone. The anisotropy in the uniaxial compressive strength and MSE for different rock types has the same sequences. The advantages of the proposed method in determining rock anisotropy are illustrated.
EN
Interfacial interactions have an important influence on the properties of energetic materials. The anisotropy of interfacial adhesive strength between various 1,3,5-trinitro-1,3,5-triazinane (RDX) single crystal faces and a typical binder was studied in this work by experimental and theoretical investigations. An RDX single crystal was prepared and processed into three kinds of orientated crystal faces, including (002), (020) and (210). These crystal slices were used as substrates, and fluorinated polymer F2314 was used as a binder. The surfaces of the RDX slices were analyzed by X-ray photoelectron spectroscopy (XPS) and an atomic force microscope (AFM). The work of adhesion was obtained from direct tensile tests, using designed samples of the sandwich structure of RDX-F2314-RDX, with various RDX single crystal surfaces. The polarity component of the surface energy and the work of adhesion was obtained by Young’s equation and the Fowkes theory, based on surface contact angle tests. The results in this work indicated the anisotropy of the interfacial adhesion of F2314 on various RDX crystal faces.
EN
The methods of severe plastic deformation (SPD) of metals and metal alloys are very attractive due to the possibility of refinement of the grains to nanometric sizes, which facilitates obtaining high mechanical properties. This study investigated the influence of SPD in the process of hydrostatic extrusion (HE) on the anisotropy of the mechanical properties of the CuCrZr copper alloy. The method of HE leads to the formation of a characteristic microstructure in deformed materials, which can determine their potential applications. On the longitudinal sections of the extruded bars, a strong morphological texture is observed, manifested by elongated grains in the direction of extrusion. In the transverse direction, these grains are visible as equiaxed. The anisotropy of properties was mainly determined based on the analysis of the static mini-sample static tensile test and the dynamic impact test. The obtained results were correlated with microstructural observations. In the study, three different degrees of deformation were applied at the level necessary to refine the grain size to the ultrafine-grained level. Regardless of the applied degree of deformation, the effect of the formation of a strong morphological texture was demonstrated, as a result of which there is a clear difference between the mechanical properties depending on the test direction, both by the static and dynamic method. The obtained results allow for the identification of the characteristic structure formed during the HE process and the more effective use of the CuCrZr copper alloy in applications.
EN
In this study, the effect of the coiling temperature on the tensile properties of API X70 linepipe steel plates is investigated in terms of the microstructure and related anisotropy. Two coiling temperatures are selected to control the microstructure and tensile properties. The API X70 linepipe steels consist mostly of ferritic microstructures such as polygonal ferrite, acicular ferrite, granular bainite, and pearlite irrespective of the coiling temperature. In order to evaluate the anisotropy in the tensile properties, tensile tests in various directions, in this case 0° (rolling direction), 30°, 45° (diagonal direction), 60°, and 90° (transverse direction) are conducted. As the higher coiling temperature, the larger amount of pearlite is formed, resulting in higher strength and better deformability. The steel has higher ductility and lower strength in the rolling direction than in the transverse direction due to the development of γ-fiber, particularly the {111}<112> texture.
EN
The article presents experimental results on orientation of polymer macromolecules in compression moulded high density polyethylene sheets. Properties anisotropy of thermoplastic films or sheets, that are usually formed in the extrusion process, causes deformation of thermoformed products and is a serious technological problem. One of the possible solutions of this problem is application of compression moulded sheets. The paper presents the results of tests of selected strength characteristics of compression moulded PE-HD sheets. A static tensile test was performed and Charpy impact strength was determined. Additionally Chrystler’s orientation test was executed. For comparison the same experiments were performed on extruded sheets. Samples were cut in directions perpendicular and parallel to the direction of polymer flow in pressing and extrusion processes. The obtained results indicate that the compression moulding technique allows the production of sheets that do not exhibit statistically significant anisotropy of the tested strength properties.
EN
Numerical simulations of tension and shear tests for a polycrystalline, anisotropic material were performed using crystal plasticity theory. The slip was considered here as the main mechanism of plastic deformation. Constitutive equations to describe the elastic-plastic deformation caused by the slip are presented. The generation and meshing of various shapes geometries (cubic and paddy shapes) with randomly-orientated grains by means of open source program NEPER program was shown. The Voronoi tessellation was used in order to include morphological properties of a crystalline material. The selected results of elastic-plastic analyses (stress, strain distributions and the macroscopic stress-strain resulting from homogenization) are presented here. The results obtained show the non-uniform distribution of stress and strain for different grains associated with their crystal orientation. The crystal plasticity finite element modelling of materials subjected to plastic deformation is important for microstructure-based mechanical predictions, as well as for the engineering design and to perform simulations involving not only the change of a material’s shape at a macro level but also the phenomena occurring in material in a micro-scale.
20
Content available remote Hydrodynamics and turbulence anisotropy for complex flow in a sinuous channel
EN
Sinuous channel flows are the most natural form of alluvial streams. The complex flow in the channel bends has been the main focus of the study. This paper examines the flow velocity and the three-dimensional velocity fluctuations in a pure sinuous channel. The main focus of the study is on the characterization of turbulence anisotropy along the sinuous bend. Experiments were conducted in a sinuous channel of a rectangular cross-section to identify the turbulence present in the flow. Secondary flow, Reynolds shear stress, turbulent kinetic energy, and anisotropy turbulence were evaluated in the sinuous bend. The bend apex is composed of a large circulation cell at the center of the bend section. The maximum Reynolds shear stress (RSS) is located at the bend apex with the streamwise-transverse and transverse-vertical components of RSS showing high peaks of positive and negative values. This fact is in support of the secondary flow observed in this study. Anisotropic stress tensors were estimated at different bend sections and are shown to have greater contribution toward streamwise and transverse direction. Anisotropic invariant map (AIM) identified the turbulence at bend sections and varying flow depth. Two dimensional, cigar-shaped, and pancake-shaped turbulence was observed at the bend upstream and downstream. Isotropic turbulence was observed at the bend apex. Near the bed (z∕h ≤ 0.2) and away from the bed (z∕h ≥ 0.4), pancake-shaped and cigar-shaped turbulence was observed.
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