Search results for: penetration velocity

Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: N. M. Thao, I. Dolguntseva, M. Leijon

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Flow blockages referring to the increase in flow are being considered as a vital equipment for marine current energy conversion. However, the shape of these devices will result in extracted energy under the operation. The present work investigates the effect of two configurations of a grating, convergent and divergent that located upstream, to the water flow velocity. The flow characteristics are studied by Computational Fluid Dynamic simulation by using the ANSYS Fluent solver for these specified arrangements of the grating. The results indicate that distinguished characteristics of flow velocity between “convergent” and “divergent” grating placements is up to 10% in confined conditions. Furthermore, the velocity in case of convergent grating is higher than that of divergent grating.

Keywords: Marine current energy, marine current energy converter, turbine grating, RANS simulation, water flow velocity.

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Authors: Davud Mostafa Tobnaghi

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This paper aims to investigate and emphasize the importance of the grid-connected photovoltaic (PV) systems regarding the intermittent nature of renewable generation, and the characterization of PV generation with regard to grid code compliance. The development of Photovoltaic systems and expansion plans relating to the futuristic in worldwide is elaborated. The most important impacts of grid connected photovoltaic systems on distribution networks as well as the Penetration level of PV system was investigated.

Keywords: Grid-connected photovoltaic system, distribution network, penetration levels, power quality.

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Authors: King Kuok Kuok, Po Chan Chiu

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Floods are natural phenomena, which may turn into disasters causing widespread damage, health problems and even deaths. Nowadays, floods had become more serious and more frequent due to climatic changes. During flooding, discharge measurement still can be taken by standing on the bridge across the river using portable measurement instrument. However, it is too dangerous to get near to the river especially during high flood. Therefore, this study employs Particle Image Velocimetry (PIV) as a tool to measure the surface flow velocity. PIV is a image processing technique to track the movement of water from one point to another. The PIV codes are developed using Matlab. In this study, 18 ping pong balls were scattered over the surface of the drain and images were taken with a digital SLR camera. The images obtained were analyzed using the PIV code. Results show that PIV is able to produce the flow velocity through analyzing the series of images captured.

Keywords: Particle Image Velocimetry, flow velocity, surface flow.

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Authors: M. El-Alej, D. Mba, T. Yan, M. Elforgani

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This paper presents an experimental investigation using Acoustic Emission (AE) technology to monitor sand transportation in multiphase flow. The investigations were undertaken on three-phase (air-water-sand) flow in a horizontal pipe where the superficial gas velocity (VSG) had a range of between 0.2msˉ¹ to 2.0msˉ¹ and superficial liquid velocity (VSL) had a range of between 0.2msˉ¹ to 1.0msˉ¹. The experimental findings clearly show a correlation exists between AE energy levels, sand concentration, superficial gas velocity (VSG), and superficial liquid velocity (VSL).

Keywords: Acoustic Emission (AE), multiphase flow, sand monitoring, sand minimum transport condition (MTC), condition monitoring.

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Authors: V.Pavlika

Abstract:

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.

Keywords: Inverse problem, irrotational incompressible flow, Boundary value problem.

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Authors: Kashyap L. Mokariya, Varsha A. Shah, Makarand M. Lokhande

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As the current status and growth of Indian automobile industry is remarkable, transportation sectors are the main concern in terms of energy security and climate change. Due to rising demand of fuel and its dependency on foreign countries that affects the GDP of nation, suggests that penetration of electrical vehicle will increase in near future. So in this context analysis is done if the 10 percent of conventional vehicles including cars, three wheelers and two wheelers becomes electrical vehicles in near future which is also a part of Nations Electric Mobility Mission Plan then the saving which improves the nation’s economy is analyzed in detail. Whether the Indian electricity grid is capable of taking this load with current generation and demand all over the country is also analyzed in detail. Current situation of Indian grid is analyzed and how the gap between generation and demand can be reduced is discussed in terms of increasing generation capacity and energy conservation measures. Electrical energy conservation measures in Industry and especially in rural areas have been analyzed to improve performance of Indian electricity grid in context of electrical vehicle penetration in near future. Author was a part of Vishvakarma yojna in which energy losses were measured in 255 villages of Gujarat and solutions were suggested to mitigate them and corresponding reports was submitted to the authorities of Gujarat government.

Keywords: Vehicle penetration, feasibility, Energy conservation, future grid, Energy security, Automatic pf controller.

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Authors: Mona Elsalamawy, Ashraf Ragab Mohamed, Abdellatif Elsayed Abosen

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This paper aims to evaluate the effectiveness of different crystalline coating materials concerning of chloride ions penetration. The concrete ages at the coating installation and its moisture conditions were addressed; where, these two factors may play a dominant role for the effectiveness of the used materials. Rapid chloride ions penetration test (RCPT) was conducted at different ages and moisture conditions according to the relevant standard. In addition, the contaminated area and the penetration depth of the chloride ions were investigated immediately after the RCPT test using chemical identifier, 0.1 M silver nitrate AgNO₃ solution. Results have shown that, the very low chloride ions penetrability, for the studied crystallization materials, were investigated only with the old age concrete (G1). The significant reduction in chloride ions’ penetrability was illustrated after 7 days of installing the crystalline coating layers. Using imageJ is more reliable to describe the contaminated area of chloride ions, where the distribution of aggregate and heterogeneous of cement mortar was considered in the images analysis.

Keywords: Chloride permeability, contaminated area, crystalline waterproofing materials, RCPT, XRD.

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Authors: Ashish Kumar, Sanjeev Kumar Suman

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This study investigated the influence of Cloisite-15A nanoclay on the physical, performance, and mechanical properties of bitumen binder. Cloisite-15A was blended in the bitumen in variegated percentages from 1% to 9% with increment of 2%. The blended bitumen was characterized using penetration, softening point, and dynamic viscosity using rotational viscometer, and compared with unmodified bitumen equally penetration grade 60/70. The rheological parameters were investigated using Dynamic Shear Rheometer (DSR), and mechanical properties were investigated by using Marshall Stability test. The results indicated an increase in softening point, dynamic viscosity and decrease in binder penetration. Rheological properties of bitumen increase complex modulus, decrease phase angle and improve rutting resistances as well. There was significant improvement in Marshall Stability, rather marginal improvement in flow value. The best improvement in the modified binder was obtained with 5% Cloisite-15A nanoclay.

Keywords: Cloisite-15A, complex shear modulus, phase angle, rutting resistance.

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Authors: L. Mouzai, M. Bouhadef

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Raindrops and overland flow both are erosive parameters but they do not act by the same way. The overland flow alone tends to shear the soil horizontally and concentrates into rills. In the presence of rain, the soil particles are removed from the soil surface in the form of a uniform sheet layer. In addition to this, raindrops falling on the flow roughen the water and soil surface depending on the flow depth, and retard the velocity, therefore influence shear velocity and Manning’s factor. To investigate this part, agricultural sandy soil, rainfall simulator and a laboratory soil tray of 0.2x1x3 m were the base of this work. Five overland flow depths of 0; 3.28; 4.28; 5.16; 5.60; 5.80 mm were generated under a rainfall intensity of 217.2 mm/h. Sediment concentration control is based on the proportionality of depth/microtopography. The soil loose is directly related to the presence of rain splash on thin sheet flow. The effect of shear velocity on sediment concentration is limited by the value of 5.28 cm/s. In addition to this, the rain splash reduces the soil roughness by breaking the soil crests. The rainfall intensity is the major factor influencing depth and soil erosion. In the presence of rainfall, the shear velocity of the flow is due to two simultaneous effects. The first, which is horizontal, comes from the flow and the second, vertical, is due to the raindrops.

Keywords: Flow resistance, laboratory experiments, rainfall simulator, sediment concentration, shear velocity, soil erosion.

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Authors: Mohd Hafiz Musa, Zulfadhli Hasan Adli, M . N . Khairul Arifin

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In seismic survey, the information regarding the velocity of compression wave (Vp) as well as shear wave (Vs) are very useful especially during the seismic interpretation. Previous studies showed that both Vp and Vs determined by above methods are totally different with respect to each other but offered good approximation. In this study, both Vp and Vs of consolidated granite rock were studied by using ultrasonic testing method and seismic refraction method. In ultrasonic testing, two different condition of rock are used which is dry and wet. The differences between Vp and Vs getting by using ultrasonic testing and seismic refraction were investigated and studied. The effect of water content in granite rock towards the value of Vp and Vs during ultrasonic testing are also measured. Within this work, the tolerance of the differences between the velocity of seismic wave getting from ultrasonic testing and the velocity of seismic wave getting from seismic refraction are also measured and investigated.

Keywords: Compressional wave, Granite, Shear Wave, Velocity

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Authors: Lari Kela, Pekka Vähäoja

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Pressure wave velocity in a hydraulic system was determined using piezo pressure sensors without removing fluid from the system. The measurements were carried out in a low pressure range (0.2 – 6 bar) and the results were compared with the results of other studies. This method is not as accurate as measurement with separate measurement equipment, but the fluid is in the actual machine the whole time and the effect of air is taken into consideration if air is present in the system. The amount of air is estimated by calculations and comparisons between other studies. This measurement equipment can also be installed in an existing machine and it can be programmed so that it measures in real time. Thus, it could be used e.g. to control dampers.

Keywords: Bulk modulus, pressure wave, sound velocity.

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Authors: Sajith Sajeev, Brenton McLaury, Siamack Shirazi

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In the petroleum industry, solid particles are often present along with the produced fluids. It is imperative to keep particles from accumulating in flow lines. In this study, various experiments are conducted to study sand particle transport, where critical velocity is defined as the average fluid velocity to keep particles continuously moving. Many parameters related to the fluid, particles and pipe affect the transport process. Experimental results are presented varying the particle concentration. Additionally, CFD simulations using a discrete element modeling (DEM) approach are presented to compare with experimental result.

Keywords: Particle transport, critical velocity, CFD, DEM.

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Authors: Seunghee Park, Junkyeong Kim, Eun-Seok Shin, Sang-Hun Han

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In this study, two kinds of nondestructive evaluation  (NDE) techniques (rebound hardness and ultrasonic pulse velocity  methods) are investigated for the effective maintenance of underwater  concrete structures. A new methodology to estimate the underwater  concrete strengths more effectively, named “artificial neural network  (ANN) – based concrete strength estimation with the combination of  rebound hardness and ultrasonic pulse velocity methods” is proposed  and verified throughout a series of experimental works.

 

Keywords: Underwater Concrete, Rebound Hardness, Schmidt hammer, Ultrasonic Pulse Velocity, Ultrasonic Sensor, Artificial Neural Networks, ANN.

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Authors: Mahmoud Zarrini, R. N. Pralhad

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We estimate snow velocity and snow drift density on hilly terrain under the assumption that the drifting snow mass can be represented using a micro-continuum approach (i.e. using a nonclassical mechanics approach assuming a class of fluids for which basic equations of mass, momentum and energy have been derived). In our model, the theory of coupled stress fluids proposed by Stokes [1] has been employed for the computation of flow parameters. Analyses of bulk drift velocity, drift density, drift transport and mass transport of snow particles have been carried out and computations made, considering various parametric effects. Results are compared with those of classical mechanics (logarithmic wind profile). The results indicate that particle size affects the flow characteristics significantly.

Keywords: Snow velocity, snow drift density, mass transport of snow particles, snow avalanche.

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Authors: Younes Matar, Fabien Candelier, Camille Solliec

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The aim of this study is to investigate the kinematics of undulatory elongated fish swimming against a velocity flow. We perform the experiments on European eel Anguilla Anguilla swimming in a hydrodynamic re-circulating tank with the velocity flow fixed at 0.2 m/s. We find that the undulating shape of overall eel body changes when it swims slantwise from the flow direction, by comparison to axial undulation shape. We examine this kinematics and we propose a general equation describing the lateral position of undulation body taking into account the direction of the eel-s swimming.

Keywords: Undulatory swimming, maneuver, eel Anguilla Anguilla, biomechanic.

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Authors: Cătălin Mărculescu, Andrei Avram, Cătălin Pârvulescu, Marioara Avram, Cătălin Mihai Bălan

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The present microfluidic study is emphasizing the flow behavior within a Y shape micro-bifurcation in two similar flow configurations. We report here a numerical and experimental investigation on the velocity profiles evolution and secondary flows, manifested at different Reynolds numbers (Re) and for two different boundary conditions. The experiments are performed using special designed setup based on optical microscopic devices. With this setup, direct visualizations and quantitative measurements of the path-lines are obtained. A Micro-PIV measurement system is used to obtain velocity profiles distributions in a spatial evolution in the main flows domains. The experimental data is compared with numerical simulations performed with commercial computational code FLUENT in a 3D geometry with the same dimensions as the experimental one. The numerical flow patterns are found to be in good agreement with the experimental manifestations.

Keywords: Micro-PIV, numerical investigations, secondary flows, velocity profiles.

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Authors: Tosapolporn Pornpibunsompop

Abstract:

The non-destructive testing of launch tube weld with radiography was investigated and evaluated with AWS D1.1 standard. The paper started with preparation of launch tube and radiographic inspection. X-Ray inspection then was done and gotten the result. The judgment of inspection results were concluded by certified person and finally, the evaluation with AWS D1.1 standard was conducted as well. The result shown that weld position P1 was not conformed to AWS D1.1 which allowed size of incomplete penetration did not exceed 4 mm. The other welds were corresponded to as mentioned standard. Additionally, the corrective actions for incomplete penetration either provided for future actions.

Keywords: Non-destructive evaluation, Weld, Launch tube, Radiography

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Authors: Abdenour Bourabaa, Mohamed Saighi, Ibrahim Belal

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A numerical study has been conducted to investigate the influence of fin pitch and relative humidity on the heat transfer performance of the fin-and-tube heat exchangers having plain fin geometry under dehumidifying conditions. The analysis is done using the ratio between the heat transfer coefficients in totally wet conditions and those in totally dry conditions using the appropriate correlations for both dry and wet conditions. For a constant relative humidity, it is found that the heat transfer coefficient increases with the increase of the air frontal velocity. By contrast, the fin efficiency decreases when the face velocity is increased. Apparently, this phenomenon is attributed to the path of condensate drainage. For the influence of relative humidity, the results showed an increase in heat transfer performance and a decrease in wet fin efficiency when relative humidity increases. This is due to the higher amount of mass transfer encountered at higher relative humidity. However, it is found that the effect of fin pitch on the heat transfer performance depends strongly on the face velocity. At lower frontal velocity the heat transfer increases with fin pitch. Conversely, an increase in fin pitch gives lower heat transfer coefficients when air velocity is increased.

Keywords: Dehumidifying conditions, Fin efficiency, Heat andmass transfer, Heat exchangers.

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Authors: Hong-fang Ma, Cong-yi He, Hai-tao Zhang, Wei-yong Ying, Ding-ye Fang

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A Ni-based catalyst supported by γ-Al₂O₃ was prepared by impregnation method, and the catalyst was used in a low CO and CO₂ concentration methanation system. The effect of temperature, pressure and space velocity on the methanation reaction was investigated in an experimental fixed-bed reactor. The methanation reaction was operated at the conditions of 190-240°C, 3000-24000ml•g^-1•h^-1 and 1.5-3.5MPa. The results show that temperature and space velocity play important role on the reaction. With the increase of reaction temperature the CO and CO₂ conversion increase and the selectivity of CH₄ increase. And with the increase of the space velocity the conversion of CO and CO₂ and the selectivity of CH₄ decrease sharply.

Keywords: Coke oven gas, methanation, catalyst, fixed-bed.

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Authors: Peter Antwi Buah, Yingbin Zhang, Jianxian He, Chenlin Xiang, Delali Atsu Y. Bakah

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Near-fault ground motions with velocity pulses are considered to cause significant damage to structures or slopes compared to ordinary ground motions without velocity pulses. The double pulsed pulse-like ground motion is well known to be stronger than the single pulse. This research has numerically justified this perspective by studying the dynamic response of a homogeneous rock slope subjected to four pulse-like and two non-pulse-like ground motions using the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) software. Two of the pulse-like ground motions just have a single pulse. The results show that near-fault ground motions with velocity pulses can cause a higher dynamic response than regular ground motions. The amplification of the peak ground acceleration (PGA) in horizontal direction increases with the increase of the slope elevation. The seismic response of the slope under double pulse ground motion is stronger than that of the single pulse ground motion. The PGV amplification factor under the effect of the non-pulse-like records is also smaller than those under the pulse-like records. The velocity pulse strengthens the earthquake damage to the slope, which results in producing a stronger dynamic response.

Keywords: Velocity pulses, dynamic response, PGV magnification effect, elevation effect, double pulse.

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Authors: G. M. Mir, Moinuddin, N. A. Shah

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In the age of global communications, heterogeneous networks are seen to be the best choice of strategy to ensure continuous and uninterruptible services. This will allow mobile terminal to stay in connection even they are migrating into different segment coverage through the handoff process. With the increase of teletraffic demands in mobile cellular system, hierarchical cellular systems have been adopted extensively for more efficient channel utilization and better QoS (Quality of Service). This paper presents a bidirectional call overflow scheme between two layers of microcells and macrocells, where handoffs are decided by the velocity of mobile making the call. To ensure that handoff calls are given higher priorities, it is assumed that guard channels are assigned in both macrocells and microcells. A hysteresis value introduced in mobile velocity is used to allow mobile roam in the same cell if its velocity changes back within the set threshold values. By doing this the number of handoffs is reduced thereby reducing the processing overhead and enhancing the quality of service to the end user.

Keywords: Hierarchical cellular systems, hysteresis, overflow, threshold.

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Authors: R. Pernicová

Abstract:

Chloride resistance in Ultra High Performance Concrete (UHPC) is determined in this paper. This work deals with the one dimension chloride transport, which can be potentially dangerous particularly for the durability of concrete structures. Risk of reinforcement corrosion due to exposure to the concrete surface to direct the action of chloride ions (mainly in the form de-icing salts or groundwater) is dangerously increases. The measured data are investigated depending on the depth of penetration of chloride ions into the concrete structure. Comparative measurements with normal strength concrete are done as well. The experimental results showed that UHCP have improved resistance of chlorides penetration than NSC and also chloride diffusion depth is significantly lower in UHCP.

Keywords: Chloride, One dimensional diffusion, Transport, Salinity, UHPC.

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Authors: M. H. Alhajeri, Jasem Alrajhi, Mohsen Alardhi, Saleh Alhajeri

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A numerical prediction of flow in a tube bank is reported. The flow regimes considered cover a wide range of Reynolds numbers, which range from 380 to 99000 and which are equivalent to a range of inlet velocities from very low (0.072 m/s) to very high (60 m/s). In this study, calculations were made using the standard k-e model with standard wall function. The drag coefficient, skin friction drag, pressure drag, and pressure distribution around a tube were investigated. As the velocity increased, the drag coefficient decreased until the velocity exceeded 45 m/s, after which it increased. Furthermore, the pressure drag and skin friction drag depend on the velocity.

Keywords: Numerical, Fluid, Flow, Turbine, Cooling, Blade.

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Authors: Václav Dvořák

Abstract:

The article deals with numerical investigation of axisymmetric subsonic air to air ejector. An analysis of flow and mixing processes in cylindrical mixing chamber are made. Several modes with different velocity and ejection ratio are presented. The mixing processes are described and differences between flow in the initial region of mixing and the main region of mixing are described. The lengths of both regions are evaluated. Transition point and point where the mixing processes are finished are identified. It was found that the length of the initial region of mixing is strongly dependent on the velocity ratio, while the length of the main region of mixing is dependent on velocity ratio only slightly.

Keywords: Air ejector, mixing chamber, CFD.

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Authors: Ali Pashaee, Parisa Shooshtari, Gholamreza Atae, Nasser Fatouraee

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Phase-Contrast MR imaging methods are widely used for measurement of blood flow velocity components. Also there are some other tools such as CT and Ultrasound for velocity map detection in intravascular studies. These data are used in deriving flow characteristics. Some clinical applications are investigated which use pressure distribution in diagnosis of intravascular disorders such as vascular stenosis. In this paper an approach to the problem of measurement of intravascular pressure field by using velocity field obtained from flow images is proposed. The method presented in this paper uses an algorithm to calculate nonlinear equations of Navier- Stokes, assuming blood as an incompressible and Newtonian fluid. Flow images usually suffer the lack of spatial resolution. Our attempt is to consider the effect of spatial resolution on the pressure distribution estimated from this method. In order to achieve this aim, velocity map of a numerical phantom is derived at six different spatial resolutions. To determine the effects of vascular stenoses on pressure distribution, a stenotic phantom geometry is considered. A comparison between the pressure distribution obtained from the phantom and the pressure resulted from the algorithm is presented. In this regard we also compared the effects of collocated and staggered computational grids on the pressure distribution resulted from this algorithm.

Keywords: Flow imaging, pressure distribution estimation, phantom, resolution.

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Authors: R. Resmi, M. R. Baiju

Abstract:

The thermal damping of a dynamic vibrating micromirror is an important factor affecting the design of MEMS based actuator systems. In the development process of new micromirror systems, assessing the extent of energy loss due to thermal damping accurately and predicting the performance of the system is very essential. In this paper, the depth of the thermal penetration layer at different eigenfrequencies and the temperature variation distributions surrounding a vibrating micromirror is analyzed. The thermal penetration depth corresponds to the thermal boundary layer in which energy is lost which is a measure of the thermal damping is found out. The energy is mainly dissipated in the thermal boundary layer and thickness of the layer is an important parameter. The detailed thermoacoustics is used to model the air domain surrounding the micromirror. The thickness of the boundary layer, temperature variations and thermal power dissipation are analyzed for a Si based torsional mode micromirror. It is found that thermal penetration depth decreases with eigenfrequency and hence operating the micromirror at higher frequencies is essential for reducing thermal damping. The temperature variations and thermal power dissipations at different eigenfrequencies are also analyzed. Both frequency-response and eigenfrequency analyses are done using COMSOL Multiphysics software.

Keywords: Eigen frequency analysis, micromirrors, thermal damping, thermoacoustic interactions.

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Authors: T. K. V. Iyengar, Punnamchandar Bitla

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The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.

Keywords: Pulsating flow, couple stress fluid, permeable beds, mass flux, shear stress.

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Authors: D. C. Lo, S. S. Leu

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In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.

Keywords: Natural convection, velocity-vorticity formulation, differential quadrature (DQ).

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Authors: Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: Boundary Layer, Exponentially Stretching/Shrinking Sheet, Generalized Slip, Heat Transfer, Numerical Solutions.

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