Search results for: Wall Shear Stress

Authors: H. Wakily, M. Mehrali, H. S. C. Metselaar

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Homogeneous composites of alumina and zirconia with a small amount of MgO (<1 wt %) were prepared by colloidal filtration. The object of using ZrO2 (15wt %) was to provide zirconia toughened alumina (ZTA). Suspensions of alumina and Zirconia with various solid loadings and various concentrations of Dolapix CE64 as surfactant were studied. The stability of these suspensions was investigated using rheological measurements. The optimum amount of using Dolapix was 0.8wt% for ZTA containing MgO suspension which gave low apparent viscosity in basic area (100 mPa s at shear rate of 50 s-1). The satisfactory mixtures were made into sample pallets using colloidal filtration. The process was completed with pressureless sintering in suitable temperature. Phase, grain size and qualitative compositional analysis were done using X-ray diffraction (XRD) and scanning electron microscopy (SEM) images. ZTA containing 0.05 wt% MgO shows the lowest grain size for alumina around 0.5 μm. Densification studies show that near full densities (>99%) were obtained for ZTA ceramic containing 0.05 wt% MgO in 1500 °C.

Keywords: Colloidal filtration, Dolapix, MgO, Zirconiatoughened alumina.

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Authors: M. Karamifard, M. Kazeminejad, A. Maghsoodloo

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Electromagnetic flow meter by measuring the varying of magnetic flux, which is related to the velocity of conductive flow, can measure the rate of fluids very carefully and precisely. Electromagnetic flow meter operation is based on famous Faraday's second Law. In these equipments, the constant magnetostatic field is produced by electromagnet (winding around the tube) outside of pipe and inducting voltage that is due to conductive liquid flow is measured by electrodes located on two end side of the pipe wall. In this research, we consider to 2-dimensional mathematical model that can be solved by numerical finite difference (FD) solution approach to calculate induction potential between electrodes. The fundamental concept to design the electromagnetic flow meter, exciting winding and simulations are come out by using MATLAB and PDE-Tool software. In the last stage, simulations results will be shown for improvement and accuracy of technical provision.

Keywords: Electromagnetic Flow Meter, Induction Voltage, Finite Difference

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Authors: Abhilash Narayan, S. Panneerselvam

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Dual bell nozzle is a promising one among the altitude adaptation nozzle concepts, which offer increased nozzle performance in rocket engines. Its advantage is the simplicity it offers due to the absence of any additional mechanical device or movable parts. Hence it offers reliability along with improved nozzle performance as demanded by future launch vehicles. Among other issues, the flow transition to the extension nozzle of a dual bell nozzle is one of the major issues being studied in the development of dual bell nozzle. A parameter named over-expansion factor, which controls the value of the wall inflection angle, has been reported to have substantial influence in this transition process. This paper studies, through CFD and cold flow experiments, the effect of overexpansion factor on flow transition in dual bell nozzles.

Keywords: Altitude adaptation, Dual bell nozzle, Nozzle pressure ratio, Over-expansion factor

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Authors: Atul K. Desai, Hemal J. Shah

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The tall windmill towers are designed as monopole tower or lattice tower. In the present research, a 125-meter high hybrid tower which is a combination of lattice and monopole type is proposed. The response of hybrid tower is compared with conventional monopole tower. The towers were analyzed in finite element method software considering nonlinear seismic time history load. The synthetic seismic time history for different soil is derived using the SeismoARTIF software. From the present research, it is concluded that, in the hybrid tower, we are not getting resonance condition. The base shear is less in hybrid tower compared to monopole tower for different soil conditions.

Keywords: Dynamic analysis, hybrid wind mill tower, resonance condition, synthetic time history.

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Exponentially shrinking sheet, magnetic field, mixed convection, suction.

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Authors: Mirigul Altan, Huseyin Yildirim

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Plastics occupy wide place in the applications of automotive, electronics and house goods. Especially reinforced plastics become popular because of their high strength besides their advantages of low weight and easy manufacturability. In this study, mechanical and morphological properties of polypropylene (PP) and high density polyethylene (HDPE) matrix composites reinforced with surface modified nano titan dioxide (TiO2) particles were investigated. Surface modification was made by coating the nano powders with maleic anhydride grafted styrene ethylene butylene styrene (SEBS-g-MA) and silane, respectively. After surface modification, PP/TiO2 and HDPE/TiO2 composites were obtained by using twin screw extruder at titan dioxide loading of 1 wt.%, 3 wt.% and 5 wt.%. Effects of surface modification were determined by thermal and morphological analysis. SEBS-g-MA provided bridging effect between TiO2 particles and polymer matrix while silane was effective as a dispersant. Depending on that, homogenous structures without agglomeration were obtained. Mechanical tests were performed on the injection moldings of the composites for obtaining the impact strength, tensile strength, stress at break, elongation and elastic modulus. Reinforced HDPE and PP moldings gave higher tensile strength and elastic modulus due to the rigid structure of TiO2. Slight increment was seen in stress at break. Elongation and impact strength decreased due to the stiffness of the nano titan dioxide.

Keywords: High density polyethylene, mechanical properties, nano TiO2, polypropylene.

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Authors: Václav Dvořák, Petra Dančová

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The article deals with pneumatic and hot wire anemometry measurement on subsonic axi-symmetric air ejector. Performances of the ejector with and without pulsations of primary flow are compared, measuring of characteristic pressures and mass flow rates are performed and ejector efficiency is evaluated. The pulsations of primary flow are produced by a synthetic jet generator, which is placed in the supply line of the primary flow just in front of the primary nozzle. The aim of the pulsation is to intensify the mixing process. In the article we present: Pressure measuring of pulsation on the mixing chamber wall, behind the mixing chamber and behind the diffuser measured by fast pressure transducers and results of hot wire anemometry measurement. It was found out that using of primary flow pulsations yields higher back pressure behind the ejector and higher efficiency. The processes in this ejector and influences of primary flow pulsations on the mixing processes are described.

Keywords: Air ejector, pulsation flow

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Authors: Tae Yun Chung, Jungho Moon, Tae Kwon Ha

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Al/Cu clad sheet has been fabricated by using differential speed rolling (DSR) process, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100 and 150oC with speed ratios from 1.4 to 2.2, in which the total thickness reduction was in the range between 14 and 46%. Interfacial microstructure and mechanical properties of Al/Cu clad were investigated by scanning electron microscope equipped with energy dispersive X-ray detector, and tension tests. The DSR process was very effective to provide a good interface for atoms diffusion during subsequent annealing. The strength of bonding was higher with the increasing speed ratio. Post heat treatment enhanced the mechanical properties of clad sheet by forming intermetallic compounds in the interface area. 

Keywords: Aluminum/Copper clad sheet, Differential speed rolling, Interface microstructure, Annealing, Tensile test.

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Authors: M. Alwetaishi, Giulia Sonetti

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It is architecturally accepted that building form and design is considered as one of the most important aspects in affecting indoor temperature. The total area of building plan might be identical, but the design will have a major influence on the total area of external walls. This will have a clear impact on the amount of heat exchange with outdoor. Moreover, it will affect the position and area of glazing system. This has not received enough consideration in research by the specialists, since most of the publications are highlighting the impact of building envelope in terms of physical heat transfer in buildings. This research will investigate the impact of orientation of various building forms in various climatic regions. It will be concluded that orientation and glazing to wall ratio were recognized to be the most effective variables despite the shape of the building. However, linear ad radial forms were found more appropriate shapes almost across the continent.

Keywords: Architectural building design, building form, indoor air temperature, building design in different climate.

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Authors: Erdal Akyol, Mutlu Alkan, Ali Aydin

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Multi criteria decision analysis (MDCA) covers both data and experience. It is very common to solve the problems with many parameters and uncertainties. GIS supported solutions improve and speed up the decision process. Weighted grading as a MDCA method is employed for solving the geotechnical problems. In this study, geotechnical parameters namely soil type; SPT (N) blow number, shear wave velocity (Vs) and depth of underground water level (DUWL) have been engaged in MDCA and GIS. In terms of geotechnical aspects, the settlement suitability of the municipal area was analyzed by the method. MDCA results were compatible with the geotechnical observations and experience. The method can be employed in geotechnical oriented microzoning studies if the criteria are well evaluated.

Keywords: GIS, spatial analysis, multi criteria decision analysis, geotechnics.

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Authors: A. Ghafouri, A. Falavand Jozaei, M. Salari

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In this paper, effects of using Alumina-water nanofluid on the rate of heat transfer have been investigated numerically. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the Richardson number 0.1 to 10 and the solid volume fraction 0 to 0.04. Results are presented by isotherms lines, average Nusselt number and normalized Nusselt number in different range of φ and Ri for forced, combined and natural convection dominated regime. It is found that higher heat transfer rate is predicted when the effects of nanoparticle is taken into account.

Keywords: Nanofluid, Heat Transfer Enhancement, Square Enclosure, Nusselt number.

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Authors: Yassir M. Abbas, Mohammad Iqbal Khan, Galal Fares

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In the present work, the structural responses of 12 ultra-high-performance concrete (UHPC) beams to four-point loading conditions were experimentally and analytically studied. The inclusion of a fibrous system in the UHPC material increased its compressive and flexural strengths by 31.5% and 237.8%, respectively. Based on the analysis of the load-deflection curves of UHPC beams, it was found that UHPC beams with a low reinforcement ratio are prone to sudden brittle failure. This failure behavior was changed, however, to a ductile one in beams with medium to high ratios. The implication is that improving UHPC beam tensile reinforcement could result in a higher level of safety. More reinforcement bars also enabled the load-deflection behavior to be improved, particularly after yielding.

Keywords: Ultra-high-performance concrete, moment capacity, RC beams, hybrid fiber, ductility.

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Authors: V. Azadeh Ranjbar

Abstract:

Rarefied gas flows are often occurred in micro electro mechanical systems and classical CFD could not precisely anticipate the flow and thermal behavior due to the high Knudsen number. Therefore, the heat transfer and the fluid dynamics characteristics of rarefied gas flows in both a two-dimensional simple microchannel and geometry similar to single Knudsen compressor have been investigated with a goal of increasing performance of a actual Knudsen compressor by using a particle simulation method. Thermal transpiration and thermal creep, which are rarefied gas dynamic phenomena, that cause movement of the flow from less to higher temperature is generated by using two different longitude temperature gradients (Linear, Step) along the walls of the flow microchannel. In this study the influence of amount of temperature gradient and governing pressure in various Knudsen numbers and length-to-height ratios have been examined.

Keywords: DSMC, Thermal transpiration, Thermal creep, MEMS, Knudsen Compressor.

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Authors: Volkan Isbuga, Joman M. Mahmood, Ali Firat Cabalar

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This study presents the site response analysis of mica-sand mixtures available in certain parts of the world including Izmir, a highly populated city and located in a seismically active region in western part of Turkey. We performed site response analyses by employing SHAKE, an equivalent linear approach, for the micaceous soil deposits consisting of layers with different amount of mica contents and thicknesses. Dynamic behavior of micaceous sands such as shear modulus reduction and damping ratio curves are input for the ground response analyses. Micaceous sands exhibit a unique dynamic response under a scenario earthquake with a magnitude of Mw=6. Results showed that higher amount of mica caused higher spectral accelerations.

Keywords: Micaceous sands, site response, equivalent linear approach, SHAKE.

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Authors: Yongzheng Li, Hongfang Ma, Qiwen Sun, Haitao Zhang, Weiyong Ying

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Radial profiles of particle velocities were investigated in a 6.1m high methanol-to-olefins cold model experimental device using a TSI laser Doppler velocimeter. The effect of axial height on flow development was not obvious in fully developed region under the same operating condition. Superficial gas velocity and solid circulating rate had significant influence on particle velocity in the center region of the riser. Besides, comparisons among rising, descending and average particle velocity were conducted. The particle average velocity was similar to the rising particle velocity and higher than the descending particle velocity in radial locations except the wall region of riser.

Keywords: Circulating fluidized bed, laser doppler velocimeter, particle velocity, radial profile.

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Authors: Sreeyuth Lal, Yohei Sato, Bojan Niceno

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With the long-term objective of Critical Heat Flux (CHF) prediction, a Direct Numerical Simulation (DNS) framework for simulation of subcooled and saturated nucleate pool boiling is developed. One case of saturated, and three cases of subcooled boiling at different subcooling levels are simulated. Grid refinement study is also reported. Both boiling and condensation phenomena can be computed simultaneously in the proposed numerical framework. Computed bubble detachment diameters of the saturated nucleate pool boiling cases agree well with the experiment. The flow structures around the growing bubble are presented and the accompanying physics is described. The relation between heat flux evolution from the heated wall and the bubble growth is studied, along with investigations of temperature distribution and flow field evolutions.

Keywords: CFD, interface tracking method, phase change model, subcooled nucleate pool boiling.

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Authors: L. Grinis, V. Haslavsky, U. Tzadka

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This paper describes an experimental, theoretical model and numerical study of concentrated vortex flow past a sphere in a hydraulic check valve. The phenomenon of the rotation of the ball around the axis of the device through which liquid flows has been found. That is, due to the rotation of the sphere in the check valve vibration is caused. We observe the rotation of the sphere around the longitudinal axis of the check valve. This rotation is induced by a vortex shedding from the sphere. We will discuss computational simulation and experimental investigations of this strong sphere rotation. The frequency of the sphere vibration and interaction with the check valve wall has been measured as a function of the wide range Reynolds Number. The validity of the computational simulation and of the assumptions on which it is based has been proved experimentally. This study demonstrates the possibility to control the vibrations in a hydraulic system and proves to be very effective suppression of the self-excited vibration.

Keywords: Check-valve, vibration, vortex shedding

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Authors: L. V. Fui, A. Ulugbek, S. S. Dol

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The in-cylinder flow and mixture formations are significant in view of today’s increasing concern on environmental issues and stringent emission regulations. In this paper, the numerical simulations of a SI engine at different engine speeds (2000-5000 rpm) at fixed intake flow pressure of 1 bar are studied using the AVL FIRE software. The simulation results show that when the engine speed at fixed intake flow pressure is increased, the volumetric efficiency of the engine decreases. This is due to a richer fuel conditions near the engine cylinder wall when engine speed is increased. Significant effects of impingement are also noted on the upper and side walls of the engine cylinder. These variations in mixture formation before ignition could affect the thermodynamics efficiency and specific fuel consumption that would lead to a reduced engine performance.

Keywords: AVL FIRE, fuel mass, IC engine, LES, RANS, turbulent intensity.

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Authors: Javed Y. Uppal

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The background of this study is the great degree of stress that the world is experiencing today, internationally among the countries, within a community among people, and even individually within one’s own self. The significance of the study is the attempt to find a solution of this stress in the philosophy of the olden times of Jalaluddin Rumi and comparatively recently of that of Allama Iqbal. The methodology adopted in this paper is firstly exploration of the perspectives of these philosophers that are being consolidated by a number of psychic and spiritual experts of today, who are being widely read but less followed. This paper further goes on presenting brief life sketches of Rumi and Iqbal. It expounds the key concepts proposed by them and the social change that was resulted in the times of the two above mentioned metaphysical philosophers. It is further amplified that with the recent advancements, in both metaphysics and the physical sciences, the gap between the two is closing down. Both Rumi and Iqbal emphasized their common essence. The old time's concepts, postulates, and philosophies are hence once again becoming valid. The findings of this paper are that the existence of human empathy, affection and mutual social attraction among humans is still valid. The positive inner belief system that dictates our thoughts and actions is vital. As a conclusion, empathy should enable us solving our problems collectively. We need to strengthen our inner communication system, to listen to the messages that come to our inner-selves. We need to get guidance and strength from them. We need to value common needs and purposes collectively to achieve results. Spiritual energy among us is to be harnessed and utilized. Connectivity is to be recognized to unify and strengthen ties among people. Mutual bonding at small and large group levels is to be employed for the survival of the disadvantaged, and sustainability of the empowering trends. With the above guidelines, hopefully, we can define a framework towards a brave and happy new humane world.

Keywords: Belief system, connectivity, human empathy, inner-self, mutual bonding, spiritual energy.

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Authors: S.C. Chin, N. Shafiq, M.F. Nuruddin

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To date, theoretical studies concerning the Carbon Fiber Reinforced Polymer (CFRP) strengthening of RC beams with openings have been rather limited. In addition, various numerical analyses presented so far have effectively simulated the behaviour of solid beam strengthened by FRP material. In this paper, a two dimensional nonlinear finite element analysis is presented to validate against the laboratory test results of six RC beams. All beams had the same rectangular cross-section geometry and were loaded under four point bending. The crack pattern results of the finite element model show good agreement with the crack pattern of the experimental beams. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption used between the concrete and steel reinforcement.

Keywords: CFRP, large opening, RC beam, strengthening

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Authors: Tarek Mohammad

Abstract:

The amplitude response of infrared (IR) sensors depends on the reflectance properties of the target. Therefore, in order to use IR sensor for measuring distances accurately, prior knowledge of the surface must be known. This paper describes the Phong Illumination Model for determining the properties of a surface and subsequently calculating the distance to the surface. The angular position of the IR sensor is computed as normal to the surface for simplifying the calculation. Ultrasonic (US) sensor can provide the initial information on distance to obtain the parameters for this method. In addition, the experimental results obtained by using LabView are discussed. More care should be taken when placing the objects from the sensors during acquiring data since the small change in angle could show very different distance than the actual one. Since stereo camera vision systems do not perform well under some environmental conditions such as plain wall, glass surfaces, or poor lighting conditions, the IR and US sensors can be used additionally to improve the overall vision systems of mobile robots.

Keywords: Distance Measurement, Infrared sensor, Surface properties, Ultrasonic sensor.

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Authors: Thomas Jin-Chee Liu

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In this paper, the thermo-electro-structural coupledfield in a cracked metal plate is studied using the finite element analysis. From the computational results, the compressive stresses reveal near the crack tip. This conclusion agrees with the past reference. Furthermore, the compressive condition can retard and stop the crack growth during the Joule heating process.

Keywords: Compressive stress, crack tip, Joule heating, finite element.

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Authors: Kyoungjin Kim

Abstract:

Viscous heating becomes significant in the high speed resin coating process of glass fibers for optical fiber manufacturing. This study focuses on the coating resin flows inside the capillary coating die of optical fiber coating applicator and they are numerically simulated to examine the effects of viscous heating and subsequent temperature increase in coating resin. Resin flows are driven by fast moving glass fiber and the pressurization at the coating die inlet, while the temperature dependent viscosity of liquid coating resin plays an important role in the resin flow. It is found that the severe viscous heating near the coating die wall profoundly alters the radial velocity profiles and that the increase of final coating thickness by die pressurization is amplified if viscous heating is present.

Keywords: Optical fiber manufacturing, Optical fiber coating, Capillary flow, Viscous heating, Flow simulation

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Authors: M.Hosseinjani Zamenjani, A.R.Tahmasebi Birgani, M.R.Isvandzibaei

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Vibration of thin cylindrical shells made of a functionally gradient material composed of stainless steel and nickel is presented. The effects of the FGM configuration are studied by studying the frequencies of FG cylindrical shells. In this case FG cylindrical shell has Nickel on its outer surface and stainless steel on its inner surface. The study is carried out based on third order shear deformation shell theory. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. Results are presented on the frequency characteristics, the influence of the constituent various volume fractions on the frequencies.

Keywords: Nickel, Stainless Steel, Cylindrical shell.

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Authors: Burak Yigit Katanalp, Murat Tastan, Perviz Ahmedzade, Çigdem Canbay Turkyilmaz, Emrah Turkyilmaz

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This study evaluated the mechanical and rheological performance of fly ash-based geopolymer at high temperatures. A series of laboratory tests were conducted on neat bitumen and three modified bitumen samples, which incorporated fly ash-based geopolymer at various percentages. Low-calcium fly ash was used as the alumina-silica source. The dynamic shear rheometer and rotational viscometer were employed to determine high-temperature properties, while conventional tests such as penetration and softening point were used to evaluate the physical properties of bitumen. Short-term aging resistance of the samples was assessed using the rolling thin film oven. The results show that geopolymer has a compromising effect on bitumen properties, with improved stiffness, enhanced mechanical strength, and increased thermal susceptibility of the asphalt binder.

Keywords: Bitumen, geopolymer, rutting, dynamic mechanical analysis.

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Authors: Teewin Plangsrinont, Wasawat Nakkiew

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In this study, Computational Fluid Dynamics (CFD) was utilized to simulate and predict the path of water from water soot blower through an ambient flow field in 300-megawatt tangentially burned pulverized coal boiler that utilizes a water soot blower as a cleaning device. To predict the position of the impact of water on the opposite side of the water soot blower under identical conditions, the nozzle size and water flow rate were fixed in this investigation. The simulation findings demonstrated a high degree of accuracy in predicting the direction of water flow to the boiler's water wall tube, which was validated by comparison to experimental data. Results show maximum deviation value of the water jet trajectory is 10.2%.

Keywords: Computational fluid dynamics, tangentially fired boiler, thermal power plant, water soot blower.

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Authors: Ivan Balázs, Jindřich Melcher

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Metal thin-walled members have been widely used in building industry. Usually they are utilized as purlins, girts or ceiling beams. Due to slenderness of thin-walled cross-sections these structural members are prone to stability problems (e.g. flexural buckling, lateral torsional buckling). If buckling is not constructionally prevented their resistance is limited by buckling strength. In practice planar members of roof or wall cladding can be attached to thin-walled members. These elements reduce displacement of thin-walled members and therefore increase their buckling strength. If this effect is taken into static assessment more economical sections of thin-walled members might be utilized and certain savings of material might be achieved. This paper focuses on problem of determination of critical load of steel thin-walled beams with lateral continuous restraint which is crucial for lateral torsional buckling assessment.

Keywords: Beam, buckling, numerical analysis, stability, steel.

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Authors: Raisa Kh. Bolotnova, Marat N. Galimzianov, Andrey S. Topolnikov, Uliana O. Agisheva, Valeria A. Buzina

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The paper presents the results of theoretical and numerical modeling of propagation of shock waves in bubbly liquids related to nonlinear effects (realistic equation of state, chemical reactions, two-dimensional effects). On the basis on the Rankine- Hugoniot equations the problem of determination of parameters of passing and reflected shock waves in gas-liquid medium for isothermal, adiabatic and shock compression of the gas component is solved by using the wide-range equation of state of water in the analitic form. The phenomenon of shock wave intensification is investigated in the channel of variable cross section for the propagation of a shock wave in the liquid filled with bubbles containing chemically active gases. The results of modeling of the wave impulse impact on the solid wall covered with bubble layer are presented.

Keywords: bubbly liquid, cavitation, equation of state, shock wave

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Authors: A. Nourbakhsh

Abstract:

A finite difference/front tracking method is used to study the motion of three-dimensional deformable drops suspended in plane Poiseuille flow at non-zero Reynolds numbers. A parallel version of the code was used to study the behavior of suspension on a reasonable grid resolution (grids). The viscosity and density of drops are assumed to be equal to that of the suspending medium. The effect of the Reynolds number is studied in detail. It is found that drops with small deformation behave like rigid particles and migrate to an equilibrium position about half way between the wall and the centerline (the Segre-Silberberg effect). However, for highly deformable drops there is a tendency for drops to migrate to the middle of the channel, and the maximum concentration occurs at the centerline. The effective viscosity of suspension and the fluctuation energy of the flow across the channel increases with the Reynolds number of the flow.

Keywords: Suspensions, Poiseuille flow, Effective viscosity, Reynolds number.

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Authors: Faruk Fırat Çalım, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: Circular rod, Out-of-plane free vibration analysis, Transfer Matrix Method.

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