Search results for: Hydrodynamic Instability

Authors: Puneet Chawla, Balwinder Singh

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Recently, increased attention has been devoted to the voltage instability phenomenon in power systems. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. In this paper P-V and Q-V curves have been generated for a 57 bus Patiala Rajpura circle of India. The power-flow program is developed in MATLAB using Newton Raphson method. Using Q-V curves the weakest bus of the power system and the maximum reactive power change permissible on that bus is calculated. STATCOMs are placed on the weakest bus to improve the voltage and hence voltage stability and also the power transmission capability of the line.

Keywords: Voltage stability, Reactive power, power flow, weakest bus, STATCOM.

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Authors: M. Yousaf, S. Usman

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The present study focused on the investigation of the effects of roughness elements on heat transfer during natural convection in a rectangular cavity using numerical technique. Roughness elements were introduced on the bottom hot wall with a normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic behaviors were studied using computational method based on Lattice Boltzmann method (LBM). Numerical studies were performed for a laminar flow in the range of Rayleigh number (Ra) from 103 to 106 for a rectangular cavity of aspect ratio (L/H) 2.0 with a fluid of Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness elements caused a minimum to maximum decrease in the heat transfer as 7% to 17% respectively compared to smooth enclosure. The results are presented for mean Nusselt number (Nu), isotherms and streamlines.

Keywords: Natural convection, Rayleigh number, surface roughness, Nusselt number, Lattice Boltzmann Method.

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Authors: Siamak Feizi, Gunvor Baardvik

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Soil erosion has special consequences for landfills that are more serious than those found at conventional construction sites. Different potential heads between two sides of a landfill and the subsequent movement of water through pores within the soil body could trigger the soil erosion and construction instability. Such condition was encountered in a landfill project in the southern part of Norway. To check the risk of internal erosion due changes in the groundwater level (because of seasonal flooding in the river), a series of numerical simulations by means of Geo-Seep software were conducted. Output of this study provides a total picture of the landfill stability, possibilities of erosions and necessary measures to prevent or reduce the risk for the landfill operator.

Keywords: Erosion, seepage, landfill, stability.

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Authors: Dmitry V. Fomichev, Vladimir I. Solonin

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This paper presents the findings from a numerical simulation of the flow in 37-rod fuel assembly models spaced by a double-wire trapezoidal wrapping as applied to the BREST-OD-300 experimental nuclear reactor. Data on a high static pressure distribution within the models, and equations for determining the fuel bundle flow friction factors have been obtained. Recommendations are provided on using the closing turbulence models available in the ANSYS Fluent. A comparative analysis has been performed against the existing empirical equations for determining the flow friction factors. The calculated and experimental data fit has been shown.

An analysis into the experimental data and results of the numerical simulation of the BREST-OD-300 fuel rod assembly hydrodynamic performance are presented.

Keywords: BREST-OD-300, ware-spaces, fuel assembly, computation fluid dynamics.

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Authors: A. Chellil, A. Nour, S. Lecheb, H. Mechakra, A. Bouderba, H. Kebir

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In this paper, a coupled damage effect in the instability of a composite rotor is presented, under dynamic loading response in the harmonic analysis condition. The analysis of the stress which operates the rotor is done. Calculations of different energies and the virtual work of the aerodynamic loads from the rotor blade are developed. The use of the composite material for the rotor offers a good stability. Numerical calculations on the model developed prove that the damage effect has a negative effect on the stability of the rotor. The study of the composite rotor in transient system allowed determining the vibratory responses due to various excitations.

Keywords: Rotor, composite, damage, finite element, numerical.

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Authors: Rusliza Ahmad, Harun Budin

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This paper studies the effect of time delay on stability of mutualism population model with limited resources for both species. First, the stability of the model without time delay is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. We analyze the effect of time delay on the stability of the stable equilibrium point. Result showed that the time delay can induce instability of the stable equilibrium point, bifurcation and stability switches.

Keywords: Bifurcation, Delay margin, Mutualism population model, Time delay

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Authors: M. Meenasaranya, S. Saravanan

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Conditions corresponding to the unconditional stability of convection in a mechanically anisotropic fluid saturated porous medium of infinite horizontal extent are determined. The medium is heated from below and its bounding surfaces are subjected to temperature modulation which consists of a steady part and a time periodic oscillating part. The Brinkman model is employed in the momentum equation with the Bousinessq approximation. The stability region is found for arbitrary values of modulational frequency and amplitude using the energy method. Higher order numerical computations are carried out to find critical boundaries and subcritical instability regions more accurately.

Keywords: Convection, porous medium, anisotropy, temperature modulation, nonlinear stability.

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Authors: Irina Eglite, Andrei A. Kolyshkin

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The effect of small non-parallelism of the base flow on the stability of slightly curved mixing layers is analyzed in the present paper. Assuming that the instability wavelength is much smaller than the length scale of the variation of the base flow we derive an amplitude evolution equation using the method of multiple scales. The proposed asymptotic model provides connection between parallel flow approximations and takes into account slow longitudinal variation of the base flow.

Keywords: shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales

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Authors: Jun-Oh Kim, Seol-Min Yang, Seok-Heum Baek, Sangmo Kang

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In this paper, the shape design process is briefly discussed emphasizing the use of topology optimization in the conceptual design stage. The basic idea is to view feasible domains for sensitivity region concepts. In this method, the main process consists of two steps: as the design moves further inside the feasible domain using Taguchi method, and thus becoming more successful topology optimization, the sensitivity region becomes larger. In designing a double-eccentric butterfly valve, related to hydrodynamic performance and disc structure, are discussed where the use of topology optimization has proven to dramatically improve an existing design and significantly decrease the development time of a shape design. Computational Fluid Dynamics (CFD) analysis results demonstrate the validity of this approach.

Keywords: Double-eccentric butterfly valve, CFD, Topology optimization

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Authors: A. A. Purohit, A. Basu, K. A. Chavan, M. D. Kudale

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Many estuarine harbours in the world are facing the problem of siltation in docks, channel entrances, etc. The harbours in India are not an exception and require maintenance dredging to achieve navigable depths for keeping them operable. Hence, dredging is inevitable and is a costly affair. The heavy siltation in docks in well mixed tide dominated estuaries is mainly due to settlement of cohesive sediments in suspension. As such there is a need to have a permanent solution for minimising the siltation in such docks to alter the hydrodynamic flow field responsible for siltation by constructing structures outside the dock. One of such docks on the west coast of India, wherein siltation of about 2.5-3 m/annum prevails, was considered to understand the hydrodynamic flow field responsible for siltation. The dock is situated in such a region where macro type of semi-diurnal tide (range of about 5m) prevails. In order to change the flow field responsible for siltation inside the dock, suitability of Current Deflecting Wall (CDW) outside the dock was studied, which will minimise the sediment exchange rate and siltation in the dock. The well calibrated physical tidal model was used to understand the flow field during various phases of tide for the existing dock in Mumbai harbour. At the harbour entrance where the tidal flux exchanges in/out of the dock, measurements on water level and current were made to estimate the sediment transport capacity. The distorted scaled model (1:400 (H) & 1:80 (V)) of Mumbai area was used to study the tidal flow phenomenon, wherein tides are generated by automatic tide generator. Hydraulic model studies carried out under the existing condition (without CDW) reveal that, during initial hours of flood tide, flow hugs the docks breakwater and part of flow which enters the dock forms number of eddies of varying sizes inside the basin, while remaining part of flow bypasses the entrance of dock. During ebb, flow direction reverses, and part of the flow re-enters the dock from outside and creates eddies at its entrance. These eddies do not allow water/sediment-mass to come out and result in settlement of sediments in dock both due to eddies and more retention of sediment. At latter hours, current strength outside the dock entrance reduces and allows the water-mass of dock to come out. In order to improve flow field inside the dockyard, two CDWs of length 300 m and 40 m were proposed outside the dock breakwater and inline to Pier-wall at dock entrance. Model studies reveal that, during flood, major flow gets deflected away from the entrance and no eddies are formed inside the dock, while during ebb flow does not re-enter the dock, and sediment flux immediately starts emptying it during initial hours of ebb. This reduces not only the entry of sediment in dock by about 40% but also the deposition by about 42% due to less retention. Thus, CDW is a promising solution to significantly reduce siltation in dock.

Keywords: Current deflecting wall, eddies, hydraulic model, macro tide, siltation.

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Authors: Ahmad Forouzan Tabar, Mohammad Azadi, Alireza Alesaadi

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This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.

Keywords: Lyapunov stability, autonomous underwater vehicle (AUV), sliding mode controller, electronics engineering.

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Authors: Pankaj Kumar Srivastava

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Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have been included.

Keywords: Septic spline, Octic spline, Nonic spline, Tenth, Eleventh, Twelfth and Thirteenth Degree spline, parametric and non-parametric splines, thermal instability, astrophysics.

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Authors: Burak Yildirim, Muhsin Tunay Gençoğlu

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A microgrid (MG) is a small power grid composed of localized medium or low level power generation, storage systems, and loads. In this paper, the effects of a MG on power systems voltage stability are shown. The MG model, designed to demonstrate the effects of the MG, was applied to the IEEE 14 bus power system which is widely used in power system stability studies. Eigenvalue and modal analysis methods were used in simulation studies. In the study results, it is seen that MGs affect system voltage stability positively by increasing system voltage instability limit value for buses of a power system in which MG are placed.

Keywords: Eigenvalue analysis, microgrid, modal analysis, voltage stability.

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Authors: Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri

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In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited continuously.Further,biological and bionomic equilibria of the system are obtained and an optimal harvesting policy is also analysed using the Pantryagin’s Maximum Principle.Finally analytical findings are also supported by some numerical simulations.

Keywords: Phytoplankton-Zooplankton, Global stability, Bionomic Equilibrium, Pontrying-Maximum Principal.

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Authors: Donna M. G. Comissiong, Tyrone D. Dass, Harold Ramkissoon, Alana R. Sankar

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The B'enard-Marangoni thermal instability problem for a viscoelastic Jeffreys- fluid layer with internal heat generation is investigated. The fluid layer is bounded above by a realistic free deformable surface and by a plane surface below. Our analysis shows that while the internal heat generation and the relaxation time both destabilize the fluid layer, its stability may be enhanced by an increased retardation time.

Keywords: Viscoelastic fluid, Jeffreys' model, Maxwell model, internal heat generation, retardation time, relaxation time.

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Authors: Ilya Popov, Steven Hulshoff

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A numerical investigation of the effects of nanosecond barrier discharge on the stability of a two-dimensional free shear layer is performed. The computations are carried out using a compressible Navier-Stokes algorithm coupled with a thermodynamic model of the discharge. The results show that significant increases in the shear layer-s momentum thickness and Reynolds stresses occur due to actuation. Dependence on both frequency and amplitude of actuation are considered, and a comparison is made of the computed growth rates with those predicted by linear stability theory. Amplitude and frequency ranges for the efficient promotion of shear-layer instabilities are identified.

Keywords: NS-DBD, plasma, actuator, flow control, instability, shear layer

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Authors: H.A. Ashorynejad, M. Farhadi, K.Sedighi, A.Hasanpour

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We report the results of an lattice Boltzmann simulation of magnetohydrodynamic damping of sidewall convection in a rectangular enclosure filled with a porous medium. In particular we investigate the suppression of convection when a steady magnetic field is applied in the vertical direction. The left and right vertical walls of the cavity are kept at constant but different temperatures while both the top and bottom horizontal walls are insulated. The effects of the controlling parameters involved in the heat transfer and hydrodynamic characteristics are studied in detail. The heat and mass transfer mechanisms and the flow characteristics inside the enclosure depended strongly on the strength of the magnetic field and Darcy number. The average Nusselt number decreases with rising values of the Hartmann number while this increases with increasing values of the Darcy number.

Keywords: Lattice Boltzmann method , Natural convection , Magnetohydrodynamic , Porous medium

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: Pore pressure, 3D wave model, seabed liquefaction, pipeline.

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Authors: Ravindra Mallya, B. Satish Shenoy, B. Raghuvir Pai

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The study deals with the challenges in developing a test rig to test the performance of water lubricated journal bearing. The test rig is designed to simulate the working conditions of the bearing in order to understand their performance before they are put in operation. The bearing that is studied is the commercially available water lubricated bearing which has a rubber liner bonded with a rigid metal shell. The lubricant enters the bearing axially through a pressurized inlet tank and exits to an outlet tank which is at sufficiently low pressure. The load on the bearing is applied through the dead weight system which acts both in upward and downward direction so that net load acts on the bearing. The issues in feeding the lubricant into the bearing from the inlet side and preventing the leakage of the lubricant is discussed. The application of the load on the test bearing while maintaining the bearing afloat is also discussed.

Keywords: Axial groove, hydrodynamic pressure, journal bearing, test rig, water lubrication.

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Authors: Benalia Nadia, Bensiali Nadia, Mekki Mounira

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In this paper, we propose an easily computable proximity index for predicting voltage collapse of a load bus using only measured values of the bus voltage and power; Using these measurements a polynomial of fourth order is obtained by using LES estimation algorithms. The sum of the absolute values of the polynomial coefficient gives an idea of the critical bus. We demonstrate the applicability of our proposed method on 6 bus test system. The results obtained verify its applicability, as well as its accuracy and the simplicity. From this indicator, it is allowed to predict the voltage instability or the proximity of a collapse. Results obtained by the PV curve are compared with corresponding values by QV curves and are observed to be in close agreement.

Keywords: least square method, Voltage Collapse, Voltage Stability, PV curve

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Authors: A. Chellil, I. Gahlouz, S. Lecheb, A. Nour, S. Chellil, H. Mechakra, H. Kebir

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In this paper, the experimental study for the instability of a separator rotor is presented, under dynamic loading response in the harmonic analysis condition. The global measurement and analysis of vibration on the cement separator RC500 is carried, the points of measurement used are radial dots, vertical, horizontal and oblique. The measures of trends and spectral analysis for reconnaissance of the main anomalies, the main defects in the separator and manifestation, the results prove that the defects effect has a negative effect on the stability of the rotor. Experimentally the study of the rotor in transient system allowed to determine the vibratory responses due to the unbalances and various excitations.

Keywords: Rotor, experimental, defect, frequency, specter.

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Authors: Alex Hou Hong Ng, Abdul Ghani Farinda, Fock Kui Kan, Ai Ling Lim, Teo Ming Ting

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Poverty is a multi-facet phenomenon in today’s globalised world. It is rooted in various causes and there are also multiple ways to do away with it. This paper begins with a review on the definitions and measurement of poverty and followed by discussing the various causes of poverty. This paper specifically identifies corruption, education, political instability, geographical characteristics, ineffective local governance and government policies as the causes of poverty. It then suggests possible solutions or recommendations to eradicate poverty based on the causes discussed earlier. Some of the suggestions include strengthening democratic transparency and government budget transparency, public awareness, creation of a framework for economic growth and transformation, and ways to increase the ability of the poor to raise their income.

Keywords: Economic Policy, Government Policy, Poverty Eradication, Sustainable Development.

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Authors: Xuan Li, Weian Huang, Jinsheng Sun, Fuhao Zhao, Zhiyuan Wang, Jintang Wang

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Natural gas hydrates (NGHs) as promising alternative energy sources have gained increasing attention. Hydrate-bearing formation in marine areas is highly unconsolidated formation and is fragile, which is composed of weakly cemented sand-clay and silty sediments. During the drilling process, the invasion of drilling fluid can easily lead to excessive water content in the formation. It will change the soil liquid plastic limit index, which significantly affects the formation quality, leading to wellbore instability due to the metastable character of hydrate-bearing sediments. Therefore, controlling the filtrate loss into the formation in the drilling process has to be highly regarded for protecting the stability of the wellbore. In this study, the temperature-sensitive nanogel of P(NIPAM-co-AMPS-co-tBA) was prepared by soap-free emulsion polymerization, and the temperature-sensitive behavior was employed to achieve self-adaptive plugging in hydrate sediments. First, the effects of additional amounts of 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS), tert-butyl acrylate (tBA), and methylene-bis-acrylamide (MBA) on the microgel synthesis process and temperature-sensitive behaviors were investigated. Results showed that, as a reactive emulsifier, AMPS can not only participate in the polymerization reaction but also act as an emulsifier to stabilize micelles and enhance the stability of nanoparticles. The volume phase transition temperature (VPTT) of nanogels gradually decreased with the increase of the contents of hydrophobic monomer tBA. An increase in the content of the cross-linking agent MBA can lead to a rise in the coagulum content and instability of the emulsion. The plugging performance of nanogel was evaluated in a core sample with a pore size distribution range of 100-1000 nm. The temperature-sensitive nanogel can effectively improve the microfiltration performance of drilling fluid. Since a combination of a series of nanogels could have a wide particle size distribution at any temperature, around 200 nm to 800 nm, the self-adaptive plugging capacity of nanogels for the hydrate sediments was revealed. Thermosensitive nanogel is a potential intelligent plugging material for drilling operations in NGH-bearing sediments.

Keywords: Temperature-sensitive nanogel, NIPAM, self-adaptive plugging performance, drilling operations, hydrate-bearing sediments.

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Authors: Iman Mazinani, Zubaidah Ismail, Ahmad Mustafa Hashim, Amirreza Saba

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Two tragic tsunamis that devastated the west coast of Sumatra Island, Indonesia in 2004 and North East Japan in 2011 had damaged bridges to various extents. Tsunamis have resulted in the catastrophic deterioration of infrastructures i.e. coastal structures, utilities and transportation facilities. A bridge structure performs vital roles to enable people to perform activities related to their daily needs and for development. A damaged bridge needs to be repaired expeditiously. In order to understand the effects of tsunami forces on bridges, experimental tests are carried out to measure the characteristics of hydrodynamic force at various wave heights. Coastal bridge models designed at a 1:40 scale are used in a 24.0 m long hydraulic flume with a cross section of 1.5 m by 2.0 m. The horizontal forces and uplift forces in all cases show that forces increase nonlinearly with increasing wave amplitude.

Keywords: Tsunami, bridge, horizontal force, uplift force.

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Authors: Norihan Md Arifin, Norfifah Bachok

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The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the internal heating, depth ratio and conductivity ratio. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability with internal heating are studied in detail.

Keywords: Linear stability, Marangoni convection, Internal Heatgeneration.

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Authors: S. Houssaini, L. Bahi

Abstract:

The motorway segment between Tangier and Oued R’mel has experienced, since the beginning of building works, significant instability and landslides linked to a number of geological, hydrogeological and geothermic factors affecting the different formations. The landslides observed are not fully understood, despite many studies conducted on this segment. This study aims at producing new methods to better explain the phenomena behind the landslides, taking into account the geotechnical and geothermic contexts. This analysis builds up on previous studies and geotechnical data collected in the field. The final body of data collected shall be processed through the Plaxis software for a better and customizable view of the landslide problems in the area, which will help tofind solutions and stabilize land in the area.

Keywords: Landslides, modeling, risk, stabilization.

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

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This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility.

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Authors: Sajid Iqbal, Masood Ahmed, Suhail Aftab Qureshi

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DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.

Keywords: Buck converter, boost converter, period- doubling, chaos, bifurcation, strange attractor.

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Authors: H.Y. Lai, S. C. Chang, W. L. Chen

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The hydrodynamic and thermal lattice Boltzmann methods are applied to investigate the turbulent convective heat transfer in the wavy channel flows. In this study, the turbulent phenomena are modeling by large-eddy simulations with the Smagorinsky model. As a benchmark, the laminar and turbulent backward-facing step flows are simulated first. The results give good agreement with other numerical and experimental data. For wavy channel flows, the distribution of Nusselt number and the skin-friction coefficients are calculated to evaluate the heat transfer effect and the drag force. It indicates that the vortices at the trough would affect the magnitude of drag and weaken the heat convection effects on the wavy surface. In turbulent cases, if the amplitude of the wavy boundary is large enough, the secondary vortices would be generated at troughs and contribute to the heat convection. Finally, the effects of different Re on the turbulent transport phenomena are discussed.

Keywords: Heat transfer, lattice Boltzmann method, turbulence, wavy channel.

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Authors: M. Soltan Rezaee, M. R. Ghazavi, A. Najafi, W.-H. Liao

Abstract:

Generally, different rods in shaft systems can be misaligned based on the mechanical system usages. These rods can be linked together via U-coupling easily. The system is self-stimulated and may cause instabilities due to the inherent behavior of the coupling. In this study, each rod includes an elastic shaft with an angular stiffness and structural damping. Moreover, the mass of shafts is considered via attached solid disks. The impact of the system architecture and shaft mass on the instability of such mechanism are studied. Stability charts are plotted via a method based on Floquet theory. Eventually, the unstable points have been found and analyzed in detail. The results show that stabilizing the driveline is feasible by changing the system characteristics which include shaft mass and architecture.

Keywords: Coupling, mechanical systems, oscillations, rotating shafts.

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