Search results for: Gas-solid flows

Authors: V. Salajka, J. Kala, P. Hradil

Abstract:

The presented article deals with the description of a numerical model of a corridor at a Central Interim Spent Fuel Storage Facility (hereinafter CISFSF). The model takes into account the effect of air flows on the temperature of stored waste. The computational model was implemented in the ANSYS/CFX programming environment in the form of a CFD task solution, which was compared with an approximate analytical calculation. The article includes a categorization of the individual alternatives for the ventilation of such underground systems. The aim was to evaluate a ventilation system for a CISFSF with regard to its stability and capacity to provide sufficient ventilation for the removal of heat produced by stored casks with spent nuclear fuel.

Keywords: Temperature fields, Spent Fuel, Interim storage facility, CFD.

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Authors: Vishnu Prasad Sharma, S. Kumaraswamy, A. Mani

Abstract:

This paper reports on the results of experimental investigations on the performance of a jet pump operated under selected primary flows to optimize the related parameters. For this purpose a two-phase flow jet pump was used employing various profiles of nozzles as the primary device which was designed, fabricated and used along with the combination of mixing tube and diffuser. The profiles employed were circular, conical, and elliptical. The diameter of the nozzle used was 4 mm. The area ratio of the jet pump was 0.16. The test facility created for this purpose was an open loop continuous circulation system. Performance of the jet pump was obtained as iso-efficiency curves on characteristic curves drawn for various water flow rates. To perform the suction capability, evacuation test was conducted at best efficiency point for all the profiles.

Keywords: Evacuation test, jet pump, nozzle profile, nozzle spacing, performance test, two phase flow

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Authors: A. M. Tahsini

Abstract:

The Spalart and Allmaras turbulence model has been implemented in a numerical code to study the compressible turbulent flows, which the system of governing equations is solved with a finite volume approach using a structured grid. The AUSM+ scheme is used to calculate the inviscid fluxes. Different benchmark problems have been computed to validate the implementation and numerical results are shown. A special Attention is paid to wall jet applications. In this study, the jet is submitted to various wall boundary conditions (adiabatic or uniform heat flux) in forced convection regime and both two-dimensional and axisymmetric wall jets are considered. The comparison between the numerical results and experimental data has given the validity of this turbulence model to study the turbulent wall jets especially in engineering applications.

Keywords: Wall Jet, Heat transfer, Numerical Simulation, Spalart-Allmaras Turbulence model.

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Authors: S. Dhib, S. A. Addouche, T. Loukil, A. Elmhamedi

Abstract:

In this paper, a reverse supply chain network is investigated for a decision making. This decision is surrounded by complex flows of returned products, due to the increasing quantity, the type of returned products and the variety of recovery option products (reuse, recycling, and refurbishment). The most important problem in the reverse logistic network (RLN) is to orient returned products to the suitable type of recovery option. However, returned products orientations from collect sources to the recovery disposition have not well considered in performance model. In this study, we propose a performance model for designing a network configuration on reverse logistics. Conceptual and analytical models are developed with taking into account operational, economic and environmental factors on designing network.

Keywords: Reverse logistics, Network design, Performance model, Open loop configuration.

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Authors: Souleymane Oumtanaga, Kadjo Tanon Lambert, Koné Tiémoman, Tety Pierre, Kimou KouadioProsper

Abstract:

Multicast transmissions allow an host (the source) to send only one flow bound for a group of hosts (the receivers). Any equipment eager to belong to the group may explicitly register itself to that group via its multicast router. This router will be given the responsibility to convey all information relating to the group to all registered hosts. However in an environment in which the final receiver or the source frequently moves, the multicast flows need particular treatment. This constitutes one of the multicast transmissions problems around which several proposals were made in the Mobile IPv6 case in general. In this article, we describe the problems involved in this IPv6 multicast mobility and the existing proposals for their resolution. Then architecture will be proposed aiming to satisfy and optimize these transmissions in the specific case of a mobile multicast receiver in NC-HMIPv6 environment.

Keywords: Mobile IP, NC-HMIPv6, Multicast, MLD, PIM, SSM, Rendezvous Point.

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Authors: Amir Gholami Pastaki, Ali Reza Sahab, Seyed Mehdi Sadeghi

Abstract:

LSP routing is among the prominent issues in MPLS networks traffic engineering. The objective of this routing is to increase number of the accepted requests while guaranteeing the quality of service (QoS). Requested bandwidth is the most important QoS criterion that is considered in literatures, and a various number of heuristic algorithms have been presented with that regards. Many of these algorithms prevent flows through bottlenecks of the network in order to perform load balancing, which impedes optimum operation of the network. Here, a modern routing algorithm is proposed as MIRAD: having a little information of the network topology, links residual bandwidth, and any knowledge of the prospective requests it provides every request with a maximum bandwidth as well as minimum end-to-end delay via uniform load distribution across the network. Simulation results of the proposed algorithm show a better efficiency in comparison with similar algorithms.

Keywords: new generation networks, QoS, traffic engineering, MPLS, QoS based routing, LSP

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Authors: Nasser Ghassembaglou, Abdullah Bolek, Oktay Yilmaz, Ertan Oznergiz, Hikmet Kocabas, Safak Yilmaz

Abstract:

Nanofibers are effective materials which have frequently been investigated to produce high quality air filters. As an environmental approach our aim is to achieve nanofibers by melting. In spun-bond systems extruder, spin-pump, nozzle package and attenuator are used. Molten polymer which flows from extruder is made steady by spin-pump. Regular melt passes through nozzle holes and forms fibers under high pressure. The fibers pulled from nozzle are shrunk to micron size by an attenuator; after solidification, they are collected on a conveyor. In this research different designs of attenuator system have been studied; and also CFD analysis has been done on these different designs. Afterwards, one of these designs tested and finally some optimizations have been done to reduce pressure loss and increase air velocity.

Keywords: Attenuator, nanofiber, spun-bond.

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Authors: K. Horáková, K. Fraňa, V. Honzejk

Abstract:

This part of study deals with description of unsteady isothermal melt flow in the container with cuboid shape. This melt flow is driven by rotating magnetic field. Input data (instantaneous velocities, grid coordinates and Lorentz forces) were obtained from in-house CFD code (called NS-FEM3D) which uses DDES method of computing. Description of the flow was performed by contours of Lorentz forces and caused velocity field. Taylor magnetic numbers of the flow were used 1.10^6, 5.10^6 and 1.10^7, flow was in 3D turbulent flow regime.

Keywords: In-house computing code, Lorentz forces, magnetohydrodynamics, rotating magnetic field.

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Authors: Juraj Camaj, Martin Kendra, Jaroslav Masek

Abstract:

The paper is focused to the evaluation railway tracks in the Slovakia by using Multi-Criteria method. Evaluation of railway tracks has important impacts for the assessment of investment in technical equipment. Evaluation of railway tracks also has an important impact for the allocation of marshalling yards. Marshalling yards are in transport model as centers for the operation assigned catchment area. This model is one of the effective ways to meet the development strategy of the European Community's railways. By applying this model in practice, a transport company can guarantee a higher quality of service and then expect an increase in performance. The model is also applicable to other rail networks. This model supplements a theoretical problem of train formation problem of new ways of looking at evaluation of factors affecting the organization of wagon flows.

Keywords: Railway track, multi-criteria methods, evaluation, transportation model.

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Authors: G. Ahmadi, S.M. Shahrtash

Abstract:

A multiphase harmonic load flow algorithm is developed based on backward/forward sweep to examine the effects of various factors on the neutral to earth voltage (NEV), including unsymmetrical system configuration, load unbalance and harmonic injection. The proposed algorithm composes fundamental frequency and harmonic frequencies power flows. The algorithm and the associated models are tested on IEEE 13 bus system. The magnitude of NEV is investigated under various conditions of the number of grounding rods per feeder lengths, the grounding rods resistance and the grounding resistance of the in feeding source. Additionally, the harmonic injection of nonlinear loads has been considered and its influences on NEV under different conditions are shown.

Keywords: NEV, Distribution System, Multi-grounded, Backward/Forward Sweep, Harmonic Analysis

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Authors: M. M. Doustdar, M. Mojtahedpoor

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The effects of flame-holder position, the ratio of flame holder diameter to combustion chamber diameter and injection angle on fuel propulsive droplets sizing and effective mass fraction have been studied by a cold flow. We named the mass of fuel vapor inside the flammability limit as the effective mass fraction. An empty cylinder as well as a flame-holder which are a simulator for duct combustion has been considered. The airflow comes into the cylinder from one side and injection operation will be done by four nozzles which are located on the entrance of cylinder. To fulfill the calculations a modified version of KIVA-3V code which is a transient, three-dimensional, multiphase, multi component code for the analysis of chemically reacting flows with sprays, is used.

Keywords: KIVA-3V, flame-holder, duct combustion, effective mass fraction, mean diameter of droplets.

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

Abstract:

This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: Axisymmetric problem, compressible Navier- Stokes equations, continuous finite elements, swirling flow.

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Authors: B. Krittacom, P. Amatachaya, W. Srimuang, K. Inla

Abstract:

The combustion of liquid fuel in the porous burner (PB) was experimented to investigate evaporation mechanism and combustion behavior. The diesel oil was used as fuel and the pebbles carefully chosen in the same size like the solid sphere homogeneously was adopted as the porous media. Two structures of the liquid porous burner, i.e. the PB without and with installation of porous emitter (PE), were performed. PE was installed by lower than PB with distance of 20 cm. The pebbles having porosity (φ) of 0.45 and 0.52 were, respectively, used in PB and PE. The fuel was supplied dropwise from the top through the PB and the combustion was occurred between PB and PE. Axial profiles of temperature along the burner length were measured to clarify the evaporation and combustion phenomena. The pollutant emission characteristics were monitored at the burner exit. From the experiment, it was found that the temperature profiles of both structures decreased with the three ways swirling air flows (QA) increasing. On the other hand, the temperature profiles increased with fuel heat input (QF). Obviously, the profile of the porous burner installed with PE was higher than that of the porous burner without PE

Keywords: Liquid fuel, Porous burner, Temperature profile.

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Authors: A. B.Bhattacharyya, B. S.K.Goswami

Abstract:

This paper presents Genetic Algorithm (GA) based approach for the allocation of FACTS (Flexible AC Transmission System) devices for the improvement of Power transfer capacity in an interconnected Power System. The GA based approach is applied on IEEE 30 BUS System. The system is reactively loaded starting from base to 200% of base load. FACTS devices are installed in the different locations of the power system and system performance is noticed with and without FACTS devices. First, the locations, where the FACTS devices to be placed is determined by calculating active and reactive power flows in the lines. Genetic Algorithm is then applied to find the amount of magnitudes of the FACTS devices. This approach of GA based placement of FACTS devices is tremendous beneficial both in terms of performance and economy is clearly observed from the result obtained.

Keywords: FACTS Devices, Line Power Flow, OptimalLocation of FACTS Devices, Genetic Algorithm.

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Authors: E. G. Bautista, J. M. Reyes, O. Bautista, J. C. Arcos

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In this work, we analyze the deformation of surface waves in shallow flows conditions, propagating in a channel of slowly varying cross-section. Based on a singular perturbation technique, the main purpose is to predict the motion of waves by using a dimensionless formulation of the governing equations, considering that the longitudinal variation of the transversal section obey a power-law distribution. We show that the spatial distribution of the waves in the varying cross-section is a function of a kinematic parameter,κ , and two geometrical parameters εh and w ε . The above spatial behavior of the surface elevation is modeled by an ordinary differential equation. The use of single formulas to model the varying cross sections or transitions considered in this work can be a useful approximation to natural or artificial geometrical configurations.

Keywords: Surface waves, Asymptotic solution, Power law function, Non-dispersive waves.

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Authors: J. Vilgerts, L. Timma, D. Blumberga

Abstract:

The objective of the paper is to develop the forecast model for the HW flows. The methodology of the research included 6 modules: historical data, assumptions, choose of indicators, data processing, and data analysis with STATGRAPHICS, and forecast models. The proposed methodology was validated for the case study for Latvia. Hypothesis on the changes in HW for time period of 2010-2020 have been developed and mathematically described with confidence level of 95.0% and 50.0%. Sensitivity analysis for the analyzed scenarios was done. The results show that the growth of GDP affects the total amount of HW in the country. The total amount of the HW is projected to be within the corridor of – 27.7% in the optimistic scenario up to +87.8% in the pessimistic scenario with confidence level of 50.0% for period of 2010-2020. The optimistic scenario has shown to be the least flexible to the changes in the GDP growth.

Keywords: Forecast models, hazardous waste management, sustainable development, waste management indicators.

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Authors: Fu E. Tang, Daoyi Chen

Abstract:

Experimental investigations were carried out in the Manchester Tidal flow Facility (MTF) to study the flow patterns in the region around and adjacent to a hypothetical headland in tidal (oscillatory) ambient flow. The Planar laser-induced fluorescence (PLIF) technique was used for visualization, with fluorescent dye released at specific points around the headland perimeter and in its adjacent recirculation zone. The flow patterns can be generalized into the acceleration, stable flow and deceleration stages for each halfcycle, with small variations according to location, which are more distinct for low Keulegan-Carpenter number (KC) cases. Flow patterns in the mixing region are unstable and complex, especially in the recirculation zone. The flow patterns are in agreement with previous visualizations, and support previous results in steady ambient flow. It is suggested that the headland lee could be a viable location for siting of pollutant outfalls.

Keywords: Planar laser-induced Fluorescence, recirculation zone, tidal flow, wake flows

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Authors: C. Y. Chen

Abstract:

As the global climate changes, the threat from landslides and debris flows increases. Learning how a watershed initiates landslides under abnormal rainfall conditions and predicting landslide magnitude and frequency distribution is thus important. Landslides show a power-law distribution in the frequency-area distribution. The distribution curve shows an exponent gradient 1.0 in the Sandpile model test. Will the landslide frequency-area statistics show a distribution similar to the Sandpile model under extreme rainfall conditions? The purpose of the study is to identify the extreme rainfall-induced landslide frequency-area distribution in the Laonong River Basin in southern Taiwan. Results of the analysis show that a lower gradient of landslide frequency-area distribution could be attributed to the transportation and deposition of debris flow areas that are included in the landslide area.

Keywords: Landslide, power-law distribution, GIS.

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Authors: Norazam Arbin, Ishak Hashim

Abstract:

Double-diffusive natural convection in an open top square cavity and heated from the side is studied numerically. Constant temperatures and concentration are imposed along the right and left walls while the heat balance at the surface is assumed to obey Newton-s law of cooling. The finite difference method is used to solve the dimensionless governing equations. The numerical results are reported for the effect of Marangoni number, Biot number and Prandtl number on the contours of streamlines, temperature and concentration. The predicted results for the average Nusselt number and Sherwood number are presented for various parametric conditions. The parameters involved are as follows; the thermal Marangoni number, 0 ≤ MaT ≤1000 , the solutal Marangoni number, 0 1000 c ≤ Ma ≤ , the Biot number, 0 ≤ Bi ≤ 6 , Grashof number, 5 Gr = 10 and aspect ratio 1. The study focused on both flows; thermal dominated, N = 0.8 , and compositional dominated, N = 1.3 .

Keywords: Double-diffusive, Marangoni effects, heat and mass transfer.

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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: Jae Keun Park, Sung Je Hong, Kyong Hoon Kim, Tae Heum Kang, Wan Yeon Lee

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In this paper, we propose a routing scheme that guarantees the residual lifetime of wireless sensor networks where each sensor node operates with a limited budget of battery energy. The scheme maximizes the communications QoS while sustaining the residual battery lifetime of the network for a specified duration. Communication paths of wireless nodes are translated into a directed acyclic graph(DAG) and the maximum-flow algorithm is applied to the graph. The found maximum flow are assigned to sender nodes, so as to maximize their communication QoS. Based on assigned flows, the scheme determines the routing path and the transmission rate of data packet so that any sensor node on the path would not exhaust its battery energy before a specified duration.

Keywords: Sensor network, battery, residual lifetime, routingscheme, QoS

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Authors: Haksoon Kim

Abstract:

The paper investigates the relationship between the foreign direct investment (FDI) and the corporate governance or transparency by investigating the country-level FDI flows, FDI inward performance, corporate governance and transparency variables. From the regression analysis with Newey-West estimator of 28 country panel data from 1990- 2002, we find strong positive relationships between corporate governance or transparency level of hosting countries and FDI inward performance within hosting countries. A strong positive relationship is found between anti-director rights level or number of analysts of hosting countries and FDI inward performance within hosting countries. Also, we find a positive relationship between the number of analysts of hosting countries and FDI inflows. The empirical results are consistent with stock market liberalizations and corporate governance explanations of reasons for FDI.

Keywords: corporate governance, corporate transparency, FDIflows, FDI inward performance

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Authors: K. Vidya, V.Rhymend Uthariaraj

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Traffic Engineering (TE) is the process of controlling how traffic flows through a network in order to facilitate efficient and reliable network operations while simultaneously optimizing network resource utilization and traffic performance. TE improves the management of data traffic within a network and provides the better utilization of network resources. Many research works considers intra and inter Traffic Engineering separately. But in reality one influences the other. Hence the effective network performances of both inter and intra Autonomous Systems (AS) are not optimized properly. To achieve a better Joint Optimization of both Intra and Inter AS TE, we propose a joint Optimization technique by considering intra-AS features during inter – AS TE and vice versa. This work considers the important criterion say latency within an AS and between ASes. and proposes a Bi-Criteria Latency optimization model. Hence an overall network performance can be improved by considering this jointoptimization technique in terms of Latency.

Keywords: Inter-Domain Routing , Measurement, OptimizationPerformance, Traffic Engineering.

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Authors: M. Battira, R. Bessaih

Abstract:

We numerically study the three-dimensional magnetohydrodynamics (MHD) stability of oscillatory natural convection flow in a rectangular cavity, with free top surface, filled with a liquid metal, having an aspect ratio equal to A=L/H=5, and subjected to a transversal temperature gradient and a uniform magnetic field oriented in x and z directions. The finite volume method was used in order to solve the equations of continuity, momentum, energy, and potential. The stability diagram obtained in this study highlights the dependence of the critical value of the Grashof number Grcrit , with the increase of the Hartmann number Ha for two orientations of the magnetic field. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a magnetic field and shows that the flow stability is more important when the direction of magnetic field is longitudinal than when the direction is transversal.

Keywords: Natural convection, Magnetic field, Oscillatory, Cavity, Liquid metal.

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Authors: Tim Wollert, Fabian Behrendt

Abstract:

Value Stream Management (VSM) is a widely used methodology in the context of Lean Management for improving end-to-end material and information flows from a supplier to a customer from a company’s perspective. Whereas the design principles, e.g. Pull, value-adding, customer-orientation and further ones are still valid against the background of an increasing digitalized and dynamic environment, the methodology itself for mapping a value stream is characterized as time- and resource-intensive due to the high degree of manual activities. The digitalization of processes in the context of Industry 4.0 enables new opportunities to reduce these manual efforts and make the VSM approach more agile. The paper at hand aims at providing a modular data and calculation framework, utilizing the available business data, provided by information and communication technologies for automizing the value stream mapping process with focus on the manufacturing process.

Keywords: Industry 4.0, lean management 4.0, value stream management 4.0, value stream mapping.

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Authors: M. Oloomi-Buygi, M. Reza Salehizadeh

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In this paper a new approach for transmission pricing is presented. The main idea is voltage angle allocation, i.e. determining the contribution of each contract on the voltage angle of each bus. DC power flow is used to compute a primary solution for angle decomposition. To consider the impacts of system non-linearity on angle decomposition, the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow. Then, the contribution of each contract on power flow of each transmission line is computed based on angle decomposition. Contract-related flows are used as a measure for “extent of use" of transmission network capacity and consequently transmission pricing. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system.

Keywords: Deregulation, Power electric markets, Transmission pricing methodologies, decoupled Newton-Raphson power flow.

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Authors: A. Errasti, F. Doffagne, O. Foucrier, S. Kao, A. Meigne, H. Pellae, T. Rouland

Abstract:

Renewable energy recovery is an important domain of research in past few years in view of protection of our ecosystem. Several industrial companies are setting up widespread recovery systems to exploit wave energy. Most of them have a large size, are implanted near the shores and exploit current flows. However, as oceans represent 70% of Earth surface, a huge space is still unexploited to produce energy. Present analysis focuses on surface small scale wave energy recovery. The principle is exactly the opposite of wheel damper for a car on a road. Instead of maintaining the car body as non-oscillatory as possible by adapted control, a system is designed so that its oscillation amplitude under wave action will be maximized with respect to a boat carrying it in view of differential potential energy recuperation. From parametric analysis of system equations, interesting domains have been selected and expected energy output has been evaluated.

Keywords: Small scale wave, potential energy, optimized energy recovery, auto-adaptive system.

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Authors: R.Goudarzizadeh, N.Hedayat, S.H.Mousavi Jahromi

Abstract:

Channel junctions can be analyzed in two ways of division (lateral intake) and combined flows (confluence). The present paper investigates 3D flow pattern at lateral intake using Navier-Stokes equation and κ -ε (RNG) turbulent model. The equations are solved by Finite-Volume Method (FVM) and results are compared with the experimental data of (Barkdoll, B.D., 1997) to test the validity of the findings. Comparison of the results with the experimental data indicated a close proximity between the two sets of data which suggest a very close simulation. Results further indicated an inverse relation between the effects of discharge ratio ( r Q ) on the length and width of the separation zone. In other words, as the discharge ration increases, the length and width of separation zone decreases.

Keywords: 900 junction, flow division, turbulent flow, numerical modeling, flow separation zone.

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Authors: Adriana Ávila Zúñiga Nordfjeld

Abstract:

This paper provides a literature review to document the state of the art with respect to handling “human bias” in decision making within the established quality management systems (QMS) and LEAN theory, in the context of shipbuilding. Previous research shows that in shipbuilding there is a huge deviation from the planned man-hours under the project management to the actual man-hours used because of errors in planning and reworks caused by human bias in the information flows, among others. This reduces the efficiency, and increases operational costs. Thus, the research question is how QMS and LEAN handle biases. The findings show the gap in studying the integration of methods to handle human bias in decision making into QMS and lean, not only within shipbuilding, but in general. Theoretical and practical implications are discussed for researchers and practitioners in the areas of decision making, QMS and LEAN, and future research is suggested.

Keywords: Human bias, decision making, LEAN Shipbuilding, quality management systems.

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Authors: Fatma Ghangir, Andrzej F. Nowakowski, Franck C. G. A. Nicolleau, Thomas M. Michelitsch

Abstract:

The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

Keywords: Multiphase flow, gas-liquid flow, Godunov schems, Riemann solvers, HLL scheme, HLLC scheme.

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