Search results for: velocity gradient tensor
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2326

Search results for: velocity gradient tensor

1636 A Nonlinear Dynamical System with Application

Authors: Abdullah Eqal Al Mazrooei

Abstract:

In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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1635 Discharge Estimation in a Two Flow Braided Channel Based on Energy Concept

Authors: Amiya Kumar Pati, Spandan Sahu, Kishanjit Kumar Khatua

Abstract:

River is our main source of water which is a form of open channel flow and the flow in the open channel provides with many complex phenomena of sciences that needs to be tackled such as the critical flow conditions, boundary shear stress, and depth-averaged velocity. The development of society, more or less solely depends upon the flow of rivers. The rivers are major sources of many sediments and specific ingredients which are much essential for human beings. A river flow consisting of small and shallow channels sometimes divide and recombine numerous times because of the slow water flow or the built up sediments. The pattern formed during this process resembles the strands of a braid. Braided streams form where the sediment load is so heavy that some of the sediments are deposited as shifting islands. Braided rivers often exist near the mountainous regions and typically carry coarse-grained and heterogeneous sediments down a fairly steep gradient. In this paper, the apparent shear stress formulae were suitably modified, and the Energy Concept Method (ECM) was applied for the prediction of discharges at the junction of a two-flow braided compound channel. The Energy Concept Method has not been applied for estimating the discharges in the braided channels. The energy loss in the channels is analyzed based on mechanical analysis. The cross-section of channel is divided into two sub-areas, namely the main-channel below the bank-full level and region above the bank-full level for estimating the total discharge. The experimental data are compared with a wide range of theoretical data available in the published literature to verify this model. The accuracy of this approach is also compared with Divided Channel Method (DCM). From error analysis of this method, it is observed that the relative error is less for the data-sets having smooth floodplains when compared to rough floodplains. Comparisons with other models indicate that the present method has reasonable accuracy for engineering purposes.

Keywords: critical flow, energy concept, open channel flow, sediment, two-flow braided compound channel

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1634 Structural Health Monitoring of Buildings–Recorded Data and Wave Method

Authors: Tzong-Ying Hao, Mohammad T. Rahmani

Abstract:

This article presents the structural health monitoring (SHM) method based on changes in wave traveling times (wave method) within a layered 1-D shear beam model of structure. The wave method measures the velocity of shear wave propagating in a building from the impulse response functions (IRF) obtained from recorded data at different locations inside the building. If structural damage occurs in a structure, the velocity of wave propagation through it changes. The wave method analysis is performed on the responses of Torre Central building, a 9-story shear wall structure located in Santiago, Chile. Because events of different intensity (ambient vibrations, weak and strong earthquake motions) have been recorded at this building, therefore it can serve as a full-scale benchmark to validate the structural health monitoring method utilized. The analysis of inter-story drifts and the Fourier spectra for the EW and NS motions during 2010 Chile earthquake are presented. The results for the NS motions suggest the coupling of translation and torsion responses. The system frequencies (estimated from the relative displacement response of the 8th-floor with respect to the basement from recorded data) were detected initially decreasing approximately 24% in the EW motion. Near the end of shaking, an increase of about 17% was detected. These analysis and results serve as baseline indicators of the occurrence of structural damage. The detected changes in wave velocities of the shear beam model are consistent with the observed damage. However, the 1-D shear beam model is not sufficient to simulate the coupling of translation and torsion responses in the NS motion. The wave method is proven for actual implementation in structural health monitoring systems based on carefully assessing the resolution and accuracy of the model for its effectiveness on post-earthquake damage detection in buildings.

Keywords: Chile earthquake, damage detection, earthquake response, impulse response function, shear beam model, shear wave velocity, structural health monitoring, torre central building, wave method

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1633 Finite Element Modeling of Ultrasonic Shot Peening Process using Multiple Pin Impacts

Authors: Chao-xun Liu, Shi-hong Lu

Abstract:

In spite of its importance to the aerospace and automobile industries, little or no attention has been devoted to the accurate modeling of the ultrasonic shot peening (USP) process. It is therefore the purpose of this study to conduct finite element analysis of the process using a realistic multiple pin impacts model with the explicit solver of ABAQUS. In this paper, we research the effect of several key parameters on the residual stress distribution within the target, including impact velocity, incident angle, friction coefficient between pins and target and impact number of times were investigated. The results reveal that the impact velocity and impact number of times have obvious effect and impacting vertically could produce the most perfect residual stress distribution. Then we compare the results with the date in USP experiment and verify the exactness of the model. The analysis of the multiple pin impacts date reveal the relationships between peening process parameters and peening quality, which are useful for identifying the parameters which need to be controlled and regulated in order to produce a more beneficial compressive residual stress distribution within the target.

Keywords: ultrasonic shot peening, finite element, multiple pins, residual stress, numerical simulation

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1632 Concentration of Droplets in a Transient Gas Flow

Authors: Timur S. Zaripov, Artur K. Gilfanov, Sergei S. Sazhin, Steven M. Begg, Morgan R. Heikal

Abstract:

The calculation of the concentration of inertial droplets in complex flows is encountered in the modelling of numerous engineering and environmental phenomena; for example, fuel droplets in internal combustion engines and airborne pollutant particles. The results of recent research, focused on the development of methods for calculating concentration and their implementation in the commercial CFD code, ANSYS Fluent, is presented here. The study is motivated by the investigation of the mixture preparation processes in internal combustion engines with direct injection of fuel sprays. Two methods are used in our analysis; the Fully Lagrangian method (also known as the Osiptsov method) and the Eulerian approach. The Osiptsov method predicts droplet concentrations along path lines by solving the equations for the components of the Jacobian of the Eulerian-Lagrangian transformation. This method significantly decreases the computational requirements as it does not require counting of large numbers of tracked droplets as in the case of the conventional Lagrangian approach. In the Eulerian approach the average droplet velocity is expressed as a function of the carrier phase velocity as an expansion over the droplet response time and transport equation can be solved in the Eulerian form. The advantage of the method is that droplet velocity can be found without solving additional partial differential equations for the droplet velocity field. The predictions from the two approaches were compared in the analysis of the problem of a dilute gas-droplet flow around an infinitely long, circular cylinder. The concentrations of inertial droplets, with Stokes numbers of 0.05, 0.1, 0.2, in steady-state and transient laminar flow conditions, were determined at various Reynolds numbers. In the steady-state case, flows with Reynolds numbers of 1, 10, and 100 were investigated. It has been shown that the results predicted using both methods are almost identical at small Reynolds and Stokes numbers. For larger values of these numbers (Stokes — 0.1, 0.2; Reynolds — 10, 100) the Eulerian approach predicted a wider spread in concentration in the perturbations caused by the cylinder that can be attributed to the averaged droplet velocity field. The transient droplet flow case was investigated for a Reynolds number of 200. Both methods predicted a high droplet concentration in the zones of high strain rate and low concentrations in zones of high vorticity. The maxima of droplet concentration predicted by the Osiptsov method was up to two orders of magnitude greater than that predicted by the Eulerian method; a significant variation for an approach widely used in engineering applications. Based on the results of these comparisons, the Osiptsov method has resulted in a more precise description of the local properties of the inertial droplet flow. The method has been applied to the analysis of the results of experimental observations of a liquid gasoline spray at representative fuel injection pressure conditions. The preliminary results show good qualitative agreement between the predictions of the model and experimental data.

Keywords: internal combustion engines, Eulerian approach, fully Lagrangian approach, gasoline fuel sprays, droplets and particle concentrations

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1631 Specific Earthquake Ground Motion Levels That Would Affect Medium-To-High Rise Buildings

Authors: Rhommel Grutas, Ishmael Narag, Harley Lacbawan

Abstract:

Construction of high-rise buildings is a means to address the increasing population in Metro Manila, Philippines. The existence of the Valley Fault System within the metropolis and other nearby active faults poses threats to a densely populated city. The distant, shallow and large magnitude earthquakes have the potential to generate slow and long-period vibrations that would affect medium-to-high rise buildings. Heavy damage and building collapse are consequences of prolonged shaking of the structure. If the ground and the building have almost the same period, there would be a resonance effect which would cause the prolonged shaking of the building. Microzoning the long-period ground response would aid in the seismic design of medium to high-rise structures. The shear-wave velocity structure of the subsurface is an important parameter in order to evaluate ground response. Borehole drilling is one of the conventional methods of determining shear-wave velocity structure however, it is an expensive approach. As an alternative geophysical exploration, microtremor array measurements can be used to infer the structure of the subsurface. Microtremor array measurement system was used to survey fifty sites around Metro Manila including some municipalities of Rizal and Cavite. Measurements were carried out during the day under good weather conditions. The team was composed of six persons for the deployment and simultaneous recording of the microtremor array sensors. The instruments were laid down on the ground away from sewage systems and leveled using the adjustment legs and bubble level. A total of four sensors were deployed for each site, three at the vertices of an equilateral triangle with one sensor at the centre. The circular arrays were set up with a maximum side length of approximately four kilometers and the shortest side length for the smallest array is approximately at 700 meters. Each recording lasted twenty to sixty minutes. From the recorded data, f-k analysis was applied to obtain phase velocity curves. Inversion technique is applied to construct the shear-wave velocity structure. This project provided a microzonation map of the metropolis and a profile showing the long-period response of the deep sedimentary basin underlying Metro Manila which would be suitable for local administrators in their land use planning and earthquake resistant design of medium to high-rise buildings.

Keywords: earthquake, ground motion, microtremor, seismic microzonation

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1630 Ambiguity Resolution for Ground-based Pulse Doppler Radars Using Multiple Medium Pulse Repetition Frequency

Authors: Khue Nguyen Dinh, Loi Nguyen Van, Thanh Nguyen Nhu

Abstract:

In this paper, we propose an adaptive method to resolve ambiguities and a ghost target removal process to extract targets detected by a ground-based pulse-Doppler radar using medium pulse repetition frequency (PRF) waveforms. The ambiguity resolution method is an adaptive implementation of the coincidence algorithm, which is implemented on a two-dimensional (2D) range-velocity matrix to resolve range and velocity ambiguities simultaneously, with a proposed clustering filter to enhance the anti-error ability of the system. Here we consider the scenario of multiple target environments. The ghost target removal process, which is based on the power after Doppler processing, is proposed to mitigate ghosting detections to enhance the performance of ground-based radars using a short PRF schedule in multiple target environments. Simulation results on a ground-based pulsed Doppler radar model will be presented to show the effectiveness of the proposed approach.

Keywords: ambiguity resolution, coincidence algorithm, medium PRF, ghosting removal

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1629 Assessing the Geothermal Parameters by Integrating Geophysical and Geospatial Techniques at Siwa Oasis, Western Desert, Egypt

Authors: Eman Ghoneim, Amr S. Fahil

Abstract:

Many regions in Egypt are facing a reduction in crop productivity due to environmental degradation. One factor of crop deterioration includes the unsustainable drainage of surface water, leading to salinized soil conditions. Egypt has exerted time and effort to identify solutions to mitigate the surface water drawdown problem and its resulting effects by exploring renewable and sustainable sources of energy. Siwa Oasis represents one of the most favorable regions in Egypt for geothermal exploitation since it hosts an evident cluster of superficial thermal springs. Some of these hot springs are characterized by high surface temperatures and bottom hole temperatures (BHT) ranging between 20°C to 40 °C and 21 °C to 121.7°C, respectively. The depth to the Precambrian basement rock is commonly greater than 440 m, ranging from 440 m to 4724.4 m. It is this feature that makes the locality of Siwa Oasis sufficient for industrial processes and geothermal power production. In this study, BHT data from 27 deep oil wells were processed by applying the widely used Horner and Gulf of Mexico correction methods to obtain formation temperatures. BHT, commonly used in geothermal studies, remains the most abundant and readily available data source for subsurface temperature information. Outcomes of the present work indicated a geothermal gradient ranging from 18 to 42 °C/km, a heat flow ranging from 24.7 to 111.3 m.W.k⁻¹, and a thermal conductivity of 1.3–2.65 W.m⁻¹.k⁻¹. Remote sensing thermal infrared, topographic, geologic, and geothermal data were utilized to provide geothermal potential maps for the Siwa Oasis. Important physiographic variables (including surface elevation, lineament density, drainage density), geological and geophysical parameters (including land surface temperature, depth to basement, bottom hole temperature, magnetic, geothermal gradient, heat flow, thermal conductivity, and main rock units) were incorporated into GIS to produce a geothermal potential map (GTP) for the Siwa Oasis region. The model revealed that both the northeastern and southeastern sections of the study region are of high geothermal potential. The present work showed that combining bottom-hole temperature measurements and remote sensing data with the selected geospatial methodologies is a useful tool for geothermal prospecting in geologically and tectonically comparable settings in Egypt and East Africa. This work has implications for identifying sustainable resources needed to support food production and renewable energy resources.

Keywords: BHT, geothermal potential map, geothermal gradient, heat flow, thermal conductivity, satellite imagery, GIS

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1628 Acoustic Energy Harvesting Using Polyvinylidene Fluoride (PVDF) and PVDF-ZnO Piezoelectric Polymer

Authors: S. M. Giripunje, Mohit Kumar

Abstract:

Acoustic energy that exists in our everyday life and environment have been overlooked as a green energy that can be extracted, generated, and consumed without any significant negative impact to the environment. The harvested energy can be used to enable new technology like wireless sensor networks. Technological developments in the realization of truly autonomous MEMS devices and energy storage systems have made acoustic energy harvesting (AEH) an increasingly viable technology. AEH is the process of converting high and continuous acoustic waves from the environment into electrical energy by using an acoustic transducer or resonator. AEH is not popular as other types of energy harvesting methods since sound waves have lower energy density and such energy can only be harvested in very noisy environment. However, the energy requirements for certain applications are also correspondingly low and also there is a necessity to observe the noise to reduce noise pollution. So the ability to reclaim acoustic energy and store it in a usable electrical form enables a novel means of supplying power to relatively low power devices. A quarter-wavelength straight-tube acoustic resonator as an acoustic energy harvester is introduced with polyvinylidene fluoride (PVDF) and PVDF doped with ZnO nanoparticles, piezoelectric cantilever beams placed inside the resonator. When the resonator is excited by an incident acoustic wave at its first acoustic eigen frequency, an amplified acoustic resonant standing wave is developed inside the resonator. The acoustic pressure gradient of the amplified standing wave then drives the vibration motion of the PVDF piezoelectric beams, generating electricity due to the direct piezoelectric effect. In order to maximize the amount of the harvested energy, each PVDF and PVDF-ZnO piezoelectric beam has been designed to have the same structural eigen frequency as the acoustic eigen frequency of the resonator. With a single PVDF beam placed inside the resonator, the harvested voltage and power become the maximum near the resonator tube open inlet where the largest acoustic pressure gradient vibrates the PVDF beam. As the beam is moved to the resonator tube closed end, the voltage and power gradually decrease due to the decreased acoustic pressure gradient. Multiple piezoelectric beams PVDF and PVDF-ZnO have been placed inside the resonator with two different configurations: the aligned and zigzag configurations. With the zigzag configuration which has the more open path for acoustic air particle motions, the significant increases in the harvested voltage and power have been observed. Due to the interruption of acoustic air particle motion caused by the beams, it is found that placing PVDF beams near the closed tube end is not beneficial. The total output voltage of the piezoelectric beams increases linearly as the incident sound pressure increases. This study therefore reveals that the proposed technique used to harvest sound wave energy has great potential of converting free energy into useful energy.

Keywords: acoustic energy, acoustic resonator, energy harvester, eigenfrequency, polyvinylidene fluoride (PVDF)

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1627 A Study on Shock Formation over a Transonic Aerofoil

Authors: M. Fowsia, Dominic Xavier Fernando, Vinojitha, Rahamath Juliyana

Abstract:

Aerofoil is a primary element to be designed during the initial phase of creating any new aircraft. It is the component that forms the cross-section of the wing. The wing is used to produce lift force that balances the weight which is acting downwards. The lift force is created due to pressure difference over the top and bottom surface which is caused due to velocity variation. At sub-sonic velocities, for a real fluid, we obtain a smooth flow of air over both the surfaces. In this era of high speed travel, commercial aircraft that can travel faster than speed of sound barrier is required. However transonic velocities cause the formation of shock waves which can cause flow separation over the top and bottom surfaces. In the transonic range, shock waves move across the top and bottom surfaces of the aerofoil, until both the shock waves merge into a single shock wave that is formed near the leading edge of theaerofoil. In this paper, a transonic aerofoil is designed and its aerodynamic properties at different velocities in the Transonic range (M = 0.8; 0.9; 1; 1.1; 1.2) are studied with the help of CFD. The Pressure and Velocity distributions over the top and bottom surfaces of aerofoil are studied and the variations of shock patterns, at different velocities, are analyzed. The analysis can be used to determine the effect of drag divergence on the lift created by the aerofoil.

Keywords: transonic aerofoil, cfd, drag divergence, shock formation, viscous flow

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1626 Surface Passivation of Multicrystalline Silicon Solar Cell via Combination of LiBr/Porous Silicon and Grain Boundaies Grooving

Authors: Dimassi Wissem

Abstract:

In this work, we investigate the effect of combination between the porous silicon (PS) layer passivized with Lithium Bromide (LiBr) and grooving of grain boundaries (GB) in multi crystalline silicon. The grain boundaries were grooved in order to reduce the area of these highly recombining regions. Using optimized conditions, grooved GB's enable deep phosphorus diffusion and deep metallic contacts. We have evaluated the effects of LiBr on the surface properties of porous silicon on the performance of silicon solar cells. The results show a significant improvement of the internal quantum efficiency, which is strongly related to the photo-generated current. We have also shown a reduction of the surface recombination velocity and an improvement of the diffusion length after the LiBr process. As a result, the I–V characteristics under the dark and AM1.5 illumination were improved. It was also observed a reduction of the GB recombination velocity, which was deduced from light-beam-induced-current (LBIC) measurements. Such grooving in multi crystalline silicon enables passivization of GB-related defects. These results are discussed and compared to solar cells based on untreated multi crystalline silicon wafers.

Keywords: Multicrystalline silicon, LiBr, porous silicon, passivation

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1625 Numerical Study of the Breakdown of Surface Divergence Based Models for Interfacial Gas Transfer Velocity at Large Contamination Levels

Authors: Yasemin Akar, Jan G. Wissink, Herlina Herlina

Abstract:

The effect of various levels of contamination on the interfacial air–water gas transfer velocity is studied by Direct Numerical Simulation (DNS). The interfacial gas transfer is driven by isotropic turbulence, introduced at the bottom of the computational domain, diffusing upwards. The isotropic turbulence is generated in a separate, concurrently running the large-eddy simulation (LES). The flow fields in the main DNS and the LES are solved using fourth-order discretisations of convection and diffusion. To solve the transport of dissolved gases in water, a fifth-order-accurate WENO scheme is used for scalar convection combined with a fourth-order central discretisation for scalar diffusion. The damping effect of the surfactant contamination on the near surface (horizontal) velocities in the DNS is modelled using horizontal gradients of the surfactant concentration. An important parameter in this model, which corresponds to the level of contamination, is ReMa⁄We, where Re is the Reynolds number, Ma is the Marangoni number, and We is the Weber number. It was previously found that even small levels of contamination (ReMa⁄We small) lead to a significant drop in the interfacial gas transfer velocity KL. It is known that KL depends on both the Schmidt number Sc (ratio of the kinematic viscosity and the gas diffusivity in water) and the surface divergence β, i.e. K_L∝√(β⁄Sc). Previously it has been shown that this relation works well for surfaces with low to moderate contamination. However, it will break down for β close to zero. To study the validity of this dependence in the presence of surface contamination, simulations were carried out for ReMa⁄We=0,0.12,0.6,1.2,6,30 and Sc = 2, 4, 8, 16, 32. First, it will be shown that the scaling of KL with Sc remains valid also for larger ReMa⁄We. This is an important result that indicates that - for various levels of contamination - the numerical results obtained at low Schmidt numbers are also valid for significantly higher and more realistic Sc. Subsequently, it will be shown that - with increasing levels of ReMa⁄We - the dependency of KL on β begins to break down as the increased damping of near surface fluctuations results in an increased damping of β. Especially for large levels of contamination, this damping is so severe that KL is found to be underestimated significantly.

Keywords: contamination, gas transfer, surfactants, turbulence

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1624 Evaluating the Effect of Structural Reorientation to Thermochemical and Energetic Properties of 1,4-Diamino-3,6-Dinitropyrazolo[4,3- C]Pyrazole

Authors: Lamla Thungathaa, Conrad Mahlasea, Lisa Ngcebesha

Abstract:

1,4-Diamino-3,6-dinitropyrazolo[4,3-c]pyrazole (LLM-119) and its structural isomer 3,6-dinitropyrazolo[3,4-c]pyrazole-1,4(6H)-diamine were designed by structural reorientation of the fused pyrazole rings and their respective substituents (-NO2 and -NH2). Structural reorientation involves structural rearrangement which result in different structural isomers, employing this approach, six structural isomers of LLM-119 were achieved. The effect of structural reorientation (isomerisation and derivatives) on the enthalpy of formation, detonation properties, impact sensitivity, and density of these molecules is studied Computationally. The computational method used are detailed in the document and they yielded results that are close to the literature values with a relative error of 2% for enthalpy of formation, 2% for density, 0.05% for detonation velocity, and 4% for detonation pressure. The correlation of the structural reorientation to the calculated thermochemical and detonation properties of the molecules indicated that molecules with a -NO2 group attached to a Carbon atom and -NH2 connected to a Nitrogen atom maximize the enthalpy of formation and detonation velocity. The joining of pyrazole molecules has less effect on these parameters. It was seen that density and detonation pressure improved when both –NO2 or -NH2 functional groups were on the same side of the molecular structure. The structural reorientation gave rise to 3,4-dinitropyrazolo[3,4-c]pyrazole-1,6-diamine which exhibited optimal density and detonation performance compared to other molecules.

Keywords: LLM-119, fused rings, azole, structural isomers, detonation properties

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1623 Development of Non-Point Pollutants Removal Equipments Using Media with Bacillus sp.

Authors: Han-Seul Lee, Min-Koo Kang, Sang-Ill Lee

Abstract:

This study was conducted to reduce runoff by rainwater infiltration facility using attached growth with Bacillus sp., which are reported to remove nitrogen and phosphorus, as well as organic matter effectively. This study was investigated non-point pollutants removal efficiency of organic, nitrogen, and phosphorus in column using the media attached growth with Bacillus sp. To compare attached growth with bacillus sp. and detached media, two columns filled with perlite, zeolite, vermiculite, pumice, peat-moss was installed. In A column (attached growth with bacillus sp.), in case of infiltration velocity 30 mm/hr in high concentration of influent, it showed the removal efficiency (after aging term) is SS (suspended solid) 85.8±1.2 %, T-P (total phosphorus) 67.0±8.1 %, T-N (total nitrogen) 66.0±4.9 %, COD (chemical oxygen demand) 73.6±2.9 %, NH4+-N 72.7±3.0 %. In B column (detached media), in case of infiltration velocity 30 mm/hr in high concentration of influent, it showed the removal efficiency (after aging term) is SS 86.0±2.2 %, T-P 62.5±11.3 %, T-N 53.3±3.9 %, COD 34.6±3.7 %, NH4+-N 61.5±2.8 %. Removal efficiency of A column is better than B column. As the result from this study, using media with Bacillus sp. can improve an effective removal of non-point source pollutants.

Keywords: non-point source pollutants, Bacillus sp., rainwater, infiltration facility

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1622 Meditation and Insight Interpretation Using Quantum Circle Based-on Experiment and Quantum Relativity Formalism

Authors: Somnath Bhattachryya, Montree Bunruangses, Somchat Sonasang, Preecha Yupapin

Abstract:

In this study and research on meditation and insight, the design and experiment with electronic circuits to manipulate the meditators' mental circles that call the chakras to have the same size is proposed. The shape of the circuit is 4-ports, called an add-drop multiplexer, that studies the meditation structure called the four-mindfulness foundation, then uses an AC power signal as an input instead of the meditation time function, where various behaviors with the method of re-filtering the signal (successive filtering), like eight noble paths. Start by inputting a signal at a frequency that causes the velocity of the wave on the perimeter of the circuit to cause particles to have the speed of light in a vacuum. The signal changes from electromagnetic waves and matter waves according to the velocity (frequency) until it reaches the point of the relativistic limit. The electromagnetic waves are transformed into photons with properties of wave-particle overcoming the limits of the speed of light. As for the matter wave, it will travel to the other side and cannot pass through the relativistic limit, called a shadow signal (echo) that can have power from increasing speed but cannot create speed faster than light or insight. In the experiment, the only the side where the velocity is positive, only where the speed above light or the corresponding frequency indicates intelligence. Other side(echo) can be done by changing the input signal to the other side of the circuit to get the same result. But there is no intelligence or speed beyond light. It is also used to study the stretching, contraction of time and wormholes that can be applied for teleporting, Bose-Einstein condensate and teleprinting, quantum telephone. The teleporting can happen throughout the system with wave-particle and echo, which is when the speed of the particle is faster than the stretching or contraction of time, the particle will submerge in the wormhole, when the destination and time are determined, will travel through the wormhole. In a wormhole, time can determine in the future and the past. The experimental results using the microstrip circuit have been found to be by the principle of quantum relativity, which can be further developed for both tools and meditation practitioners for quantum technology.

Keywords: quantu meditation, insight picture, quantum circuit, absolute time, teleportation

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1621 Age-Dependent Anatomical Abnormalities of the Amygdala in Autism Spectrum Disorder and their Implications for Altered Socio-Emotional Development

Authors: Gabriele Barrocas, Habon Issa

Abstract:

The amygdala is one of various brain regions that tend to be pathological in individuals with autism spectrum disorder (ASD). ASD is a prevalent and heterogeneous developmental disorder affecting all ethnic and socioeconomic groups and consists of a broad range of severity, etiology, and behavioral symptoms. Common features of ASD include but are not limited to repetitive behaviors, obsessive interests, and anxiety. Neuroscientists view the amygdala as the core of the neural system that regulates behavioral responses to anxiogenic and threatening stimuli. Despite this consensus, many previous studies and literature reviews on the amygdala’s alterations in individuals with ASD have reported inconsistent findings. In this review, we will address these conflicts by highlighting recent studies which reveal that anatomical and related socio-emotional differences detected between individuals with and without ASD are highly age-dependent. We will specifically discuss studies using functional magnetic resonance imaging (fMRI), structural MRI, and diffusion tensor imaging (DTI) to provide insights into the neuroanatomical substrates of ASD across development, with a focus on amygdala volumes, cell densities, and connectivity.

Keywords: autism, amygdala, development, abnormalities

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1620 Development of Numerical Model to Compute Water Hammer Transients in Pipe Flow

Authors: Jae-Young Lee, Woo-Young Jung, Myeong-Jun Nam

Abstract:

Water hammer is a hydraulic transient problem which is commonly encountered in the penstocks of hydropower plants. The numerical model was developed to estimate the transient behavior of pressure waves in pipe systems. The computational algorithm was proposed to model the water hammer phenomenon in a pipe system with pump shutdown at midstream and sudden valve closure at downstream. To predict the pressure head and flow velocity as a function of time as a result of rapidly closing a valve and pump shutdown, two boundary conditions at the ends considering pump operation and valve control can be implemented as specified equations of the pressure head and flow velocity based on the characteristics method. It was shown that the effects of transient flow make it determine the needs for protection devices, such as surge tanks, surge relief valves, or air valves, at various points in the system against overpressure and low pressure. It produced reasonably good performance with the results of the proposed transient model for pipeline systems. The proposed numerical model can be used as an efficient tool for the safety assessment of hydropower plants due to water hammer.

Keywords: water hammer, hydraulic transient, pipe systems, characteristics method

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1619 Laser - Ultrasonic Method for the Measurement of Residual Stresses in Metals

Authors: Alexander A. Karabutov, Natalia B. Podymova, Elena B. Cherepetskaya

Abstract:

The theoretical analysis is carried out to get the relation between the ultrasonic wave velocity and the value of residual stresses. The laser-ultrasonic method is developed to evaluate the residual stresses and subsurface defects in metals. The method is based on the laser thermooptical excitation of longitudinal ultrasonic wave sand their detection by a broadband piezoelectric detector. A laser pulse with the time duration of 8 ns of the full width at half of maximum and with the energy of 300 µJ is absorbed in a thin layer of the special generator that is inclined relative to the object under study. The non-uniform heating of the generator causes the formation of a broadband powerful pulse of longitudinal ultrasonic waves. It is shown that the temporal profile of this pulse is the convolution of the temporal envelope of the laser pulse and the profile of the in-depth distribution of the heat sources. The ultrasonic waves reach the surface of the object through the prism that serves as an acoustic duct. At the interface ‚laser-ultrasonic transducer-object‘ the conversion of the most part of the longitudinal wave energy takes place into the shear, subsurface longitudinal and Rayleigh waves. They spread within the subsurface layer of the studied object and are detected by the piezoelectric detector. The electrical signal that corresponds to the detected acoustic signal is acquired by an analog-to-digital converter and when is mathematically processed and visualized with a personal computer. The distance between the generator and the piezodetector as well as the spread times of acoustic waves in the acoustic ducts are the characteristic parameters of the laser-ultrasonic transducer and are determined using the calibration samples. There lative precision of the measurement of the velocity of longitudinal ultrasonic waves is 0.05% that corresponds to approximately ±3 m/s for the steels of conventional quality. This precision allows one to determine the mechanical stress in the steel samples with the minimal detection threshold of approximately 22.7 MPa. The results are presented for the measured dependencies of the velocity of longitudinal ultrasonic waves in the samples on the values of the applied compression stress in the range of 20-100 MPa.

Keywords: laser-ultrasonic method, longitudinal ultrasonic waves, metals, residual stresses

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1618 CFD Simulation Research on a Double Diffuser for Wind Turbines

Authors: Krzysztof Skiba, Zdzislaw Kaminski

Abstract:

Wind power is based on a variety of construction solutions to convert wind energy into electrical energy. These constructions are constrained by the correlation between their energy conversion efficiency and the area they occupy. Their energy conversion efficiency can be improved by wind tunnel tests of a rotor as a diffuser to optimize shapes of aerodynamic elements, to adapt these elements to changing conditions and to increase airflow intensity. This paper discusses the results of computer simulations and aerodynamic analyzes of this innovative diffuser design. The research aims at determining the aerodynamic phenomena triggered by the airflow inside this construction, and developing a design to improve the efficiency of the wind turbine. The research results enable us to design a diffuser with a double Venturi nozzle and specially shaped blades. The design of this type uses Bernoulli’s law on the behavior of the flowing medium in the tunnel of a decreasing diameter. The air flowing along the tunnel changes its velocity so the rotor inside such a decreased tunnel diameter rotates faster in this airflow than does the wind outside this tunnel, which makes the turbine more efficient. Additionally, airflow velocity is improved by applying aerodynamic rings with extended trailing edges to achieve controlled turbulent vortices.

Keywords: wind turbine, renewable energy, cfd, numerical analysis

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1617 Case-Wise Investigation of Body-Wave Propagation in a Cross-Anisotropic Soil Exhibiting Inhomogeneity along Depth

Authors: Sumit Kumar Vishawakarma, Tapas Ranjan Panihari

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The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material, where the material properties such as Young's moduli, shear modulus, and density vary as an arbitrary continuous function of depth. In the considered model, Hook's law, strain-displacement relations along with equilibrium equations have been used to derive the governing equation. The mathematical formulation of this physical problem gives rise to an eigenvalue problem with displacement components as fundamental variables. This leads to achieving the closed-form expressions for quasi-wave velocities of SV-wave, SH-wave, and P-wave in the considered framework. These characteristics of wave propagation along with the above-stated variation have been scrutinized based on their numerical results. This parametric study reveals that wave velocity remarkably fluctuates as the magnitude of inhomogeneity parameters increases and decreases. The prominent effect has been shown depicting the dependence of wave velocity on the degree of material anisotropy. The influence of phase angle and depth of the medium has been remarkably established. The present study may facilitate the theoretical foundation and practical application in the field of earthquake source mechanisms.

Keywords: cross-anisotropic, inhomogeneity, P-wave, SH-wave, SV-wave, shear modulus, Young’s modulus

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1616 Alcohol Septal Ablation in a 19-Year-Old with Hypertrophic Obstructive Cardiomyopathy Patient: A Case Report

Authors: Christine Ysabelle G. Roman, Pauline Torres

Abstract:

Background: Hypertrophic cardiomyopathy is a disease of marked heterogeneity. It is a genetically determined heart disease characterized by significant myocardium hypertrophy that results in diastolic dysfunction, left ventricular outflow tract obstruction, and an increased risk of arrhythmias. The primary treatment in patients with such conditions is negative inotropic drugs, such as beta-blockers, calcium channel antagonists, and disopyramide. However, for those who remain symptomatic and need septal reduction therapy, surgical septal myectomy or alcohol septal ablation are options. Case Summary: A 19 – year old female presented in the authors’ institution with easy fatigability. The consult was done a year prior, and 2D echocardiography was requested which showed concentric left ventricular hypertrophy, asymmetrically hypertrophied interventricular septum (IVS) with the largest diameter of 3.3cm & subaortic dynamic obstruction with a maximum gradient of 47 mmHg. A repeat echo a year later showed asymmetric septal hypertrophy (IVS measuring at 3cm) with the systolic anterior motion of anterior mitral valve leaflet and left ventricular outflow tract obstruction (peak gradient of 50mmHg). The patient then underwent alcohol septal ablation and was discharged stable after four days of admission. Conclusion: Hypertrophic obstructive cardiomyopathy, a cardiovascular genetic disease, results in various patterns of left ventricular hypertrophy and abnormality of mitral valve apparatus. The patient is managed medically initially. However, despite optimal drug therapy and significant left ventricular outflow tract obstruction, significant heart failure symptoms or syncope require invasive treatment.

Keywords: hypertrophic obstructive cardiomyopathy, left ventricular outflow tract obstruction, alcohol septal ablation, alcohol

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1615 Gradient Length Anomaly Analysis for Landslide Vulnerability Analysis of Upper Alaknanda River Basin, Uttarakhand Himalayas, India

Authors: Hasmithaa Neha, Atul Kumar Patidar, Girish Ch Kothyari

Abstract:

The northward convergence of the Indian plate has a dominating influence over the structural and geomorphic development of the Himalayan region. The highly deformed and complex stratigraphy in the area arises from a confluence of exogenic and endogenetic geological processes. This region frequently experiences natural hazards such as debris flows, flash floods, avalanches, landslides, and earthquakes due to its harsh and steep topography and fragile rock formations. Therefore, remote sensing technique-based examination and real-time monitoring of tectonically sensitive regions may provide crucial early warnings and invaluable data for effective hazard mitigation strategies. In order to identify unusual changes in the river gradients, the current study demonstrates a spatial quantitative geomorphic analysis of the upper Alaknanda River basin, Uttarakhand Himalaya, India, using gradient length anomaly analysis (GLAA). This basin is highly vulnerable to ground creeping and landslides due to the presence of active faults/thrusts, toe-cutting of slopes for road widening, development of heavy engineering projects on the highly sheared bedrock, and periodic earthquakes. The intersecting joint sets developed in the bedrocks have formed wedges that have facilitated the recurrence of several landslides. The main objective of current research is to identify abnormal gradient lengths, indicating potential landslide-prone zones. High-resolution digital elevation data and geospatial techniques are used to perform this analysis. The results of GLAA are corroborated with the historical landslide events and ultimately used for the generation of landslide susceptibility maps of the current study area. The preliminary results indicate that approximately 3.97% of the basin is stable, while about 8.54% is classified as moderately stable and suitable for human habitation. However, roughly 19.89% fall within the zone of moderate vulnerability, 38.06% are classified as vulnerable, and 29% fall within the highly vulnerable zones, posing risks for geohazards, including landslides, glacial avalanches, and earthquakes. This research provides valuable insights into the spatial distribution of landslide-prone areas. It offers a basis for implementing proactive measures for landslide risk reduction, including land-use planning, early warning systems, and infrastructure development techniques.

Keywords: landslide vulnerability, geohazard, GLA, upper Alaknanda Basin, Uttarakhand Himalaya

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1614 Speed Control of DC Motor Using Optimization Techniques Based PID Controller

Authors: Santosh Kumar Suman, Vinod Kumar Giri

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The goal of this paper is to outline a speed controller of a DC motor by choice of a PID parameters utilizing genetic algorithms (GAs), the DC motor is extensively utilized as a part of numerous applications such as steel plants, electric trains, cranes and a great deal more. DC motor could be represented by a nonlinear model when nonlinearities such as attractive dissemination are considered. To provide effective control, nonlinearities and uncertainties in the model must be taken into account in the control design. The DC motor is considered as third order system. Objective of this paper three type of tuning techniques for PID parameter. In this paper, an independently energized DC motor utilizing MATLAB displaying, has been outlined whose velocity might be examined utilizing the Proportional, Integral, Derivative (KP, KI , KD) addition of the PID controller. Since, established controllers PID are neglecting to control the drive when weight parameters be likewise changed. The principle point of this paper is to dissect the execution of optimization techniques viz. The Genetic Algorithm (GA) for improve PID controllers parameters for velocity control of DC motor and list their points of interest over the traditional tuning strategies. The outcomes got from GA calculations were contrasted and that got from traditional technique. It was found that the optimization techniques beat customary tuning practices of ordinary PID controllers.

Keywords: DC motor, PID controller, optimization techniques, genetic algorithm (GA), objective function, IAE

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1613 Effect of Capillary Forces on Wet Granular Avalanches

Authors: Ahmed Jarray, Vanessa Magnanimo, Stefan Luding

Abstract:

Granular avalanches are ubiquitous in nature and occur in numerous industrial processes associated with particulate systems. When a small amount of liquid is added to a pile of particles, pendular bridges form and the particles are attracted by capillary forces, creating complex structure and flow behavior. We have performed an extensive series of experiments to investigate the effect of capillary force and particle size on wet granular avalanches, and we established a methodology that ensures the control of the granular flow in a rotating drum. The velocity of the free surface and the angle of repose of the particles in the rotating drum are determined using particle tracking method. The capillary force between the particles is significantly reduced by making the glass beads hydrophobic via chemical silanization. We show that the strength of the capillary forces between two adjacent particles can be deliberately manipulated through surface modification of the glass beads, thus, under the right conditions; we demonstrate that the avalanche dynamics can be controlled. The results show that the avalanche amplitude decreases when increasing the capillary force. We also find that liquid-induced cohesion increases the width of the gliding layer and the dynamic angle of repose, however, it decreases the velocity of the free surface.

Keywords: avalanche dynamics, capillary force, granular material, granular flow

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1612 Non-Pharmacological Approach to the Improvement and Maintenance of the Convergence Parameter

Authors: Andreas Aceranti, Guido Bighiani, Francesca Crotto, Marco Colorato, Stefania Zaghi, Marino Zanetti, Simonetta Vernocchi

Abstract:

The management of eye parameters such as convergence, accommodation, and miosis is very complex; in fact, both the neurovegetative system and the complex Oculocephalgiria system come into play. We have found the effectiveness of the "highvelocity low amplitude" technique directed on C7-T1 (where the cilio-spinal nucleus of the budge is located) in improving the convergence parameter through the measurement of the point of maximum convergence. With this research, we set out to investigate whether the improvement obtained through the High Velocity Low Amplitude maneuver lasts over time, carrying out a pre-manipulation measurement, one immediately after manipulation and one month after manipulation. We took a population of 30 subjects with both refractive and non-refractive problems. Of the 30 patients tested, 27 gave a positive result after the High Velocity Low Amplitude maneuver, giving an improvement in the point of maximum convergence. After a month, we retested all 27 subjects: some further improved the result, others kept, and three subjects slightly lost the gain obtained. None of the re-tested patients returned to the point of maximum convergence starting pre-manipulation. This result opens the door to a multidisciplinary approach between ophthalmologists and osteopaths with the aim of addressing oculomotricity and convergence deficits that increasingly afflict our society due to the massive use of devices and for the conduct of life in closed and restricted environments.

Keywords: point of maximum convergence, HVLA, improvement in PPC, convergence

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1611 Numerical Solution of Momentum Equations Using Finite Difference Method for Newtonian Flows in Two-Dimensional Cartesian Coordinate System

Authors: Ali Ateş, Ansar B. Mwimbo, Ali H. Abdulkarim

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General transport equation has a wide range of application in Fluid Mechanics and Heat Transfer problems. In this equation, generally when φ variable which represents a flow property is used to represent fluid velocity component, general transport equation turns into momentum equations or with its well known name Navier-Stokes equations. In these non-linear differential equations instead of seeking for analytic solutions, preferring numerical solutions is a more frequently used procedure. Finite difference method is a commonly used numerical solution method. In these equations using velocity and pressure gradients instead of stress tensors decreases the number of unknowns. Also, continuity equation, by integrating the system, number of equations is obtained as number of unknowns. In this situation, velocity and pressure components emerge as two important parameters. In the solution of differential equation system, velocities and pressures must be solved together. However, in the considered grid system, when pressure and velocity values are jointly solved for the same nodal points some problems confront us. To overcome this problem, using staggered grid system is a referred solution method. For the computerized solutions of the staggered grid system various algorithms were developed. From these, two most commonly used are SIMPLE and SIMPLER algorithms. In this study Navier-Stokes equations were numerically solved for Newtonian flow, whose mass or gravitational forces were neglected, for incompressible and laminar fluid, as a hydro dynamically fully developed region and in two dimensional cartesian coordinate system. Finite difference method was chosen as the solution method. This is a parametric study in which varying values of velocity components, pressure and Reynolds numbers were used. Differential equations were discritized using central difference and hybrid scheme. The discritized equation system was solved by Gauss-Siedel iteration method. SIMPLE and SIMPLER were used as solution algorithms. The obtained results, were compared for central difference and hybrid as discritization methods. Also, as solution algorithm, SIMPLE algorithm and SIMPLER algorithm were compared to each other. As a result, it was observed that hybrid discritization method gave better results over a larger area. Furthermore, as computer solution algorithm, besides some disadvantages, it can be said that SIMPLER algorithm is more practical and gave result in short time. For this study, a code was developed in DELPHI programming language. The values obtained in a computer program were converted into graphs and discussed. During sketching, the quality of the graph was increased by adding intermediate values to the obtained result values using Lagrange interpolation formula. For the solution of the system, number of grid and node was found as an estimated. At the same time, to indicate that the obtained results are satisfactory enough, by doing independent analysis from the grid (GCI analysis) for coarse, medium and fine grid system solution domain was obtained. It was observed that when graphs and program outputs were compared with similar studies highly satisfactory results were achieved.

Keywords: finite difference method, GCI analysis, numerical solution of the Navier-Stokes equations, SIMPLE and SIMPLER algoritms

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1610 The Numerical Model of the Onset of Acoustic Oscillation in Pulse Tube Engine

Authors: Alexander I. Dovgyallo, Evgeniy A. Zinoviev, Svetlana O. Nekrasova

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The most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, and acoustic load changes modes is in the particular interest. The aim of the present study was to develop a mathematical thermal excitation model of acoustic oscillations in pulse tube engine (PTE) as a small-scale scheme of pulse tube engine operating at atmospheric air. Unlike some previous works this standing wave configuration is a fully closed system. The improvements over previous mathematical models are the following: the model allows specifying any values of porosity for regenerator, takes into account the piston weight and the friction in the cylinder and piston unit, and determines the operating frequency. The numerical method is based on the relation equations between the pressure and volume velocity variables at the ends of each element of PTE which is recorded through the appropriate transformation matrix. A solution demonstrates that the PTE operation frequency is the complex value, and it depends on the piston mass and the dynamic friction due to its movement in the cylinder. On the basis of the determined frequency thermoacoustically induced heat transport and generation of acoustic power equations were solved for channel with temperature gradient on its ends. The results of numerical simulation demonstrate the features of the initialization process of oscillation and show that that generated acoustic power more than power on the steady mode in a factor of 3…4. But doesn`t mean the possibility of its further continuous utilizing due to its existence only in transient mode which lasts only for a 30-40 sec. The experiments were carried out on small-scale PTE. The results shows that the value of acoustic power is in the range of 0.7..1.05 W for the defined frequency range f = 13..18 Hz and pressure amplitudes 11..12 kPa. These experimental data are satisfactorily correlated with the numerical modeling results. The mathematical model can be straightforwardly applied for the thermoacoustic devices with variable temperatures of thermal reservoirs and variable transduction loads which are expected to occur in practical implementations of portable thermoacoustic engines.

Keywords: nonlinear processes, pulse tube engine, thermal excitation, standing wave

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1609 Energy Absorption Characteristic of a Coupler Rubber Buffer Used in Rail Vehicles

Authors: Zhixiang Li, Shuguang Yao, Wen Ma

Abstract:

Coupler rubber buffer has been widely applied on the high-speed trains and the main function of the rubber buffer is dissipating the impact energy between vehicles. The rubber buffer consists of two groups of rubbers, which are both pre-compressed and then installed into the frame body. This paper focuses on the energy absorption characteristics of the rubber buffers particularly. Firstly, the quasi-static compression tests were carried out for 1 and 3 pairs of rubber sheets and some energy absorption responses relationship, i.e. Eabn = n×Eab1, Edissn = n×Ediss1, and Ean = Ea1, were obtained. Next, a series of quasi-static tests were performed for 1 pair of rubber sheet to investigate the energy absorption performance with different compression ratio of the rubber buffers. Then the impact tests with five impact velocities were conducted and the coupler knuckle was destroyed when the impact velocity was 10.807 km/h. The impact tests results showed that with the increase of impact velocity, the Eab, Ediss and Ea of rear buffer increased a lot, but the three responses of front buffer had not much increase. Finally, the results of impact tests and quasi-static tests were contrastively analysed and the results showed that with the increase of the stroke, the values of Eab, Ediss, and Ea were all increase. However, the increasing rates of impact tests were all larger than that of quasi-static tests. The maximum value of Ea was 68.76% in impact tests, it was a relatively high value for vehicle coupler buffer. The energy capacity of the rear buffer was determined for dynamic loading, it was 22.98 kJ.

Keywords: rubber buffer, coupler, energy absorption, impact tests

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1608 Application of the Electrical Resistivity Tomography and Tunnel Seismic Prediction 303 Methods for Detection Fracture Zones Ahead of Tunnel: A Case Study

Authors: Nima Dastanboo, Xiao-Qing Li, Hamed Gharibdoost

Abstract:

The purpose of this study is to investigate about the geological properties ahead of a tunnel face with using Electrical Resistivity Tomography ERT and Tunnel Seismic Prediction TSP303 methods. In deep tunnels with hydro-geological conditions, it is important to study the geological structures of the region before excavating tunnels. Otherwise, it would lead to unexpected accidents that impose serious damage to the project. For constructing Nosoud tunnel in west of Iran, the ERT and TSP303 methods are employed to predict the geological conditions dynamically during the excavation. In this paper, based on the engineering background of Nosoud tunnel, the important results of applying these methods are discussed. This work demonstrates seismic method and electrical tomography as two geophysical techniques that are able to detect a tunnel. The results of these two methods were being in agreement with each other but the results of TSP303 are more accurate and quality. In this case, the TSP 303 method was a useful tool for predicting unstable geological structures ahead of the tunnel face during excavation. Thus, using another geophysical method together with TSP303 could be helpful as a decision support in excavating, especially in complicated geological conditions.

Keywords: tunnel seismic prediction (TSP303), electrical resistivity tomography (ERT), seismic wave, velocity analysis, low-velocity zones

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1607 Bifurcations of the Rotations in the Thermocapillary Flows

Authors: V. Batishchev, V. Getman

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We study the self-similar fluid flows in the Marangoni layers with the axial symmetry. Such flows are induced by the radial gradients of the temperatures whose distributions along the free boundary obey some power law. The self-similar solutions describe thermo-capillar flows both in the thin layers and in the case of infinite thickness. We consider both positive and negative temperature gradients. In the former case the cooling of free boundary nearby the axis of symmetry gives rise to the rotation of fluid. The rotating flow concentrates itself inside the Marangoni layer while outside of it the fluid does not revolve. In the latter case we observe no rotating flows at all. In the layers of infinite thickness the separation of the rotating flow creates two zones where the flows are directed oppositely. Both the longitudinal velocity and the temperature have exactly one critical point inside the boundary layer. It is worth to note that the profiles are monotonic in the case of non-swirling flows. We describe the flow outside the boundary layer with the use of self-similar solution of the Euler equations. This flow is slow and non-swirling. The introducing of an outer flow gives rise to the branching of swirling flows from the non-swirling ones. There is such the critical velocity of the outer flow that a non-swirling flow exists for supercritical velocities and cannot be extended to the sub-critical velocities. For the positive temperature gradients there are two non-swirling flows. For the negative temperature gradients the non-swirling flow is unique. We determine the critical velocity of the outer flow for which the branching of the swirling flows happens. In the case of a thin layer confined within free boundaries we show that the cooling of the free boundaries near the axis of symmetry leads to the separating of the layer and creates two sub-layers with opposite rotations inside. This makes sharp contrast with the case of infinite thickness. We show that such rotation arises provided the thickness of the layer exceed some critical value. In the case of a thin layer confined within free and rigid boundaries we construct the branching equation and the asymptotic approximation for the secondary swirling flows near the bifurcation point. It turns out that the bifurcation gives rise to one pair of the secondary swirling flows with different directions of swirl.

Keywords: free surface, rotation, fluid flow, bifurcation, boundary layer, Marangoni layer

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