Search results for: flow line

Authors: A. Kojah, A. Nacaroğlu

Abstract:

Single phase transmission lines are used to transfer data or energy between two users. Transient conditions such as switching operations and short circuit faults cause the generation of the fluctuation on the waveform to be transmitted. Spatial voltage distribution on the single phase transmission line may change owing to the position and duration of the short circuit fault in the system. In this paper, the state space representation of the single phase transmission line for short circuit fault and for various types of terminations is given. Since the transmission line is modeled in time domain using distributed parametric elements, the mathematical representation of the event is given in state space (time domain) differential equation form. It also makes easy to solve the problem because of the time and space dependent characteristics of the voltage variations on the distributed parametrically modeled transmission line.

Keywords: Energy transmission, transient effects, transmission line, transient voltage, RLC short circuit, single phase.

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Authors: Y. Galerkin, O. Solovieva

Abstract:

Parameters of flow are calculated in vaneless diffusers with relative width 0,014–0,10. Inlet angles of flow and similarity criteria were varied. There is information on flow separation, boundary layer development, configuration of streamlines. Polytrophic efficiency, loss coefficient and recovery coefficient are used to compare effectiveness of diffusers. The sample of optimization of narrow diffuser with conical walls is presented. Three wide diffusers with narrowing walls are compared. The work is made in the R&D laboratory “Gas dynamics of turbo machines” of the TU SPb.

Keywords: Vaneless diffuser, relative width, flow angle, flow separation, loss coefficient, similarity criteria.

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Authors: T. C. Manjunath, C. Ardil

Abstract:

This paper presents an efficient method of obtaining a straight-line motion in the tool configuration space using an articulated robot between two specified points. The simulation results & the implementation results show the effectiveness of the method.

Keywords: Bounded deviation algorithm, Straight line motion, Tool configuration space, Joint space, TCV.

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Authors: László Lengyel, Tihamér Levendovszky, Hassan Charaf

Abstract:

This paper presents the visual control flow support of Visual Modeling and Transformation System (VMTS), which facilitates composing complex model transformations out of simple transformation steps and executing them. The VMTS Visual Control Flow Language (VCFL) uses stereotyped activity diagrams to specify control flow structures and OCL constraints to choose between different control flow branches. This work discusses the termination properties of VCFL and provides an algorithm to support the termination analysis of VCFL transformations.

Keywords: Control Flow, Metamodel-Based Visual Model Transformation, OCL, Termination Properties, UML.

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Authors: A. Moussouni, L. Mouzai, M. Bouhadef

Abstract:

The purpose of this investigation is to relate the rain power and the overland flow power to soil erodibility to assess the effects of both parameters on soil erosion using variable rainfall intensity on remoulded agricultural soil. Six rainfall intensities were used to simulate the natural rainfall and are as follows: 12.4mm/h, 20.3mm/h, 28.6mm/h, 52mm/h, 73.5mm/h and 103mm/h. The results have shown that the relationship between overland flow power and rain power is best represented by a linear function (R2=0.99). As regards the relationships between soil erodibility factor and rain and overland flow powers, the evolution of both parameters with the erodibility factor follow a polynomial function with high coefficient of determination. From their coefficients of determination (R2=0.95) for rain power and (R2=0.96) for overland flow power, we can conclude that the flow has more power to detach particles than rain. This could be explained by the fact that the presence of particles, already detached by rain and transported by the flow, give the flow more weight and then contribute to the detachment of particles by collision.

Keywords: Laboratory experiments, soil erosion, flow power, erodibility, rainfall intensity.

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Authors: Muhammad Marsudi, Hani Shafeek

Abstract:

The purpose of this paper is to simulate the production process of a metal stamping industry and to evaluate the utilization of the production line by using ARENA simulation software. The process time and the standard time for each process of the production line is obtained from data given by the company management. Other data are collected through direct observation of the line. There are three work stations performing ten different types of processes in order to produce a single product type. Arena simulation model is then developed based on the collected data. Verification and validation are done to the Arena model, and finally the result of Arena simulation can be analyzed. It is found that utilization at each workstation will increase if batch size is increased although throughput rate remains/is kept constant. This study is very useful for the company because the company needs to improve the efficiency and utilization of its production lines.

Keywords: Arena software, case study, production line, utilization.

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Authors: Tao Yin, Zeqiang Zhang, Wei Liang, Yanqing Zeng, Yu Zhang

Abstract:

To accelerate the remanufacturing process of electronic waste products, this study designs a partial disassembly line with the multi-robotic station to effectively dispose of excessive wastes. The multi-robotic partial disassembly line is a technical upgrade to the existing manual disassembly line. Balancing optimization can make the disassembly line smoother and more efficient. For partial disassembly line balancing with the multi-robotic station (PDLBMRS), a mixed-integer programming model (MIPM) considering the robotic efficiency differences is established to minimize cycle time, energy consumption and hazard index and to calculate their optimal global values. Besides, an enhanced NSGA-II algorithm (HNSGA-II) is proposed to optimize PDLBMRS efficiently. Finally, MIPM and HNSGA-II are applied to an actual mixed disassembly case of two types of computers, the comparison of the results solved by GUROBI and HNSGA-II verifies the correctness of the model and excellent performance of the algorithm, and the obtained Pareto solution set provides multiple options for decision-makers.

Keywords: Waste disposal, disassembly line balancing, multi-robot station, robotic efficiency difference, HNSGA-II.

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Authors: Yi Jianjun, Sun Yingce, Hu Diqing, Li Chenggang

Abstract:

Modularized design approach can facilitate the modeling of complex systems and support behavior analysis and simulation in an iterative and thus complex engineering process, by using encapsulated submodels of components and of their interfaces. Therefore it can improve the design efficiency and simplify the solving complicated problem. Multi-drivers off-road vehicle is comparatively complicated. Driving-line is an important core part to a vehicle; it has a significant contribution to the performance of a vehicle. Multi-driver off-road vehicles have complex driving-line, so its performance is heavily dependent on the driving-line. A typical off-road vehicle-s driving-line system consists of torque converter, transmission, transfer case and driving-axles, which transfer the power, generated by the engine and distribute it effectively to the driving wheels according to the road condition. According to its main function, this paper puts forward a modularized approach for designing and evaluation of vehicle-s driving-line. It can be used to effectively estimate the performance of driving-line during concept design stage. Through appropriate analysis and assessment method, an optimal design can be reached. This method has been applied to the practical vehicle design, it can improve the design efficiency and is convenient to assess and validate the performance of a vehicle, especially of multi-drivers off-road vehicle.

Keywords: Heavy-loaded Off-road Vehicle, Power Driving-line, Modularized Design, Performance Assessment.

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Authors: A. Esmael, A. El Shrif

Abstract:

In this study the instability problem of a modified Taylor-Couette flow between two vertical coaxial cylinders of radius R1, R2 is considered. The modification is based on the wavy shape of the inner cylinder surface, where inner cylinders with different surface amplitude and wavelength are used. The study aims to discover the effect of the inner surface geometry on the instability phenomenon that undergoes Taylor-Couette flow. The study reveals that the transition processes depends strongly on the amplitude and wavelength of the inner cylinder surface and resulting in flow instabilities that are strongly different from that encountered in the case of the classical Taylor-Couette flow.

Keywords: Hydrodynamic Instability, Modified Taylor-Couette Flow, Turbulence, Taylor vortices.

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Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang

Abstract:

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.

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Authors: Valentina Koliskina, Inta Volodko

Abstract:

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotive force per unit length of the double conductor line is calculated in the form of an improper integral.

Keywords: Transient eddy currents, Laplace transform, double conductor line.

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Authors: Rajeev Ranjan Sahay

Abstract:

Transient storage zones along the flow paths of rivers have great influence on the dispersion of pollutants that are either accidentally or otherwise led into them. The speed with which these pollution clouds get transported and dispersed downstream is, to a large extent, explained by the longitudinal dispersion coefficients in the free-flowing zones of rivers (Kf). In the present work, a new empirical expression for Kf has been derived employing genetic programming (GP) on published dispersion data. The proposed expression uses few hydraulic and geometric characteristics of a river that are readily available to field engineers. Based on various performance indices, the proposed expression is found superior to other existing expression for Kf.

Keywords: Dispersion, parameter estimation, rivers, transient pollutant.

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Authors: Liu-Chao Qiu

Abstract:

The damage caused by surge waves generated in water bodies by flow-like landslides can be very high in terms of human lives and economic losses. The complicated phenomena occurred in this highly unsteady process are difficult to model because three interacting phases: air, water and sediment are involved. The problem therefore is challenging since the effects of non-Newtonian fluid describing the rheology of the flow-like landslides, multi-phase flow and free surface have to be included in the simulation. In this work, the commercial computational fluid dynamics (CFD) package FLUENT is used to model the surge waves due to flow-like landslides. The comparison between the numerical results and experimental data reported in the literature confirms the accuracy of the method.

Keywords: Flow-like landslide, surge wave, VOF, non-Newtonian fluids, multi-phase flows, free surface flow.

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Authors: C. F. Kumru, C. Kocatepe, O. Arikan

Abstract:

In this study, electric field distribution analyses for three pylon models are carried out by a Finite Element Method (FEM) based software. Analyses are performed in both stationary and time domains to observe instantaneous values along with the effective ones. Considering the results of the study, different line geometries is considerably affecting the magnitude and distribution of electric field although the line voltages are the same. Furthermore, it is observed that maximum values of instantaneous electric field obtained in time domain analysis are quite higher than the effective ones in stationary mode. In consequence, electric field distribution analyses should be individually made for each different line model and the limit exposure values or distances to residential buildings should be defined according to the results obtained.

Keywords: Electric field, energy transmission line, finite element method, pylon.

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Authors: Suwimon Saneewong Na Ayuttaya, Chainarong Chaktranond, Phadungsak Rattanadecho

Abstract:

This study numerically investigates the effects of Electrohydrodynamic on flow patterns and heat transfer enhancement within a cavity which is on the lower wall of channel. In this simulation, effects of using ground wire and ground plate on the flow patterns are compared. Moreover, the positions of electrode wire respecting with ground are tested in the range of angles θ = 0 - 180^o. High electrical voltage exposes to air is 20 kV. Bulk mean velocity and temperature of inlet air are controlled at 0.1 m/s and 60 ^OC, respectively. The result shows when electric field is applied, swirling flow is appeared in the channel. In addition, swirling flow patterns in the main flow of using ground plate are widely spreader than that of using ground wire. Moreover, direction of swirling flow also affects the flow pattern and heat transfer in a cavity. These cause the using ground wire to give the maximum temperature and heat transfer higher than using ground plate. Furthermore, when the angle is at θ = 60^o, high shear flow effect is obtained. This results show high strength of swirling flow and effective heat transfer enhancement.

Keywords: Swirling Flow, Heat Transfer, Electrohydrodynamic, Numerical Analysis.

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Authors: S. Meikandasivam, D. Vijayakumar, Rajesh Kumar Nema, Shailendra Kumar Jain

Abstract:

This paper investigates the performance of the single TCSC and proposed split TCSC on transmission system where India’s first TCSC project is installed in Kanpur - Ballabhgarh (KB) line to ensure the fine tuning of line reactance by proposed split TCSC in place of existing KB TCSC. A three phase KB transmission system is developed in MATLAB/Simulink (SimPowerSystems) for

1. without any compensation,
2. with fixed capacitor (FC),
3. with FC + existing KB TCSC and
4. with FC + proposed split TCSC

The KB system is analyzed for a step variation of load and performance of the system is investigated with a closed loop reactance control method.

Keywords: Single TCSC, Split TCSC, TCSC Reactance characteristic curve, Power flow analysis, Sensitivity analysis.

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Authors: Deniz T. Sodiri, Venkat V S S Sastry

Abstract:

The paper presents an on-line recognition machine (RM) for continuous/isolated, dynamic and static gestures that arise in Flight Deck Officer (FDO) training. RM is based on generic pattern recognition framework. Gestures are represented as templates using summary statistics. The proposed recognition algorithm exploits temporal and spatial characteristics of gestures via dynamic programming and Markovian process. The algorithm predicts corresponding index of incremental input data in the templates in an on-line mode. Accumulated consistency in the sequence of prediction provides a similarity measurement (Score) between input data and the templates. The algorithm provides an intuitive mechanism for automatic detection of start/end frames of continuous gestures. In the present paper, we consider isolated gestures. The performance of RM is evaluated using four datasets - artificial (W TTest), hand motion (Yang) and FDO (tracker, vision-based ). RM achieves comparable results which are in agreement with other on-line and off-line algorithms such as hidden Markov model (HMM) and dynamic time warping (DTW). The proposed algorithm has the additional advantage of providing timely feedback for training purposes.

Keywords: On-line Recognition Algorithm, IsolatedDynamic/Static Gesture Recognition, On-line Markovian/DynamicProgramming, Training in Virtual Environments.

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Authors: Pyone Lai Swe, Wanna Swe, Kyaw Myo Lin

Abstract:

Voltage stability has become an important issue to many power systems around the world due to the weak systems and long line on power system networks. In this paper, MATLAB load flow program is applied to obtain the weak points in the system combined with finding the voltage stability limit. The maximum permissible loading of a system, within the voltage stability limit, is usually determined. The methods for varying tap ratio (using tap changing transformer) and applying different values of shunt capacitor injection to improve the voltage stability within the limit are also provided.

Keywords: Load flow, Voltage stability, Tap changingtransformer, Shunt capacitor injection, Voltage stability limit

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Authors: V.D. Hatamipour, M.A. Akhavan-Behabadi

Abstract:

Evaporator is an important and widely used heat exchanger in air conditioning and refrigeration industries. Different methods have been used by investigators to increase the heat transfer rates in evaporators. One of the passive techniques to enhance heat transfer coefficient is the application of microfin tubes. The mechanism of heat transfer augmentation in microfin tubes is dependent on the flow regime of two-phase flow. Therefore many investigations of the flow patterns for in-tube evaporation have been reported in literatures. The gravitational force, surface tension and the vapor-liquid interfacial shear stress are known as three dominant factors controlling the vapor and liquid distribution inside the tube. A review of the existing literature reveals that the previous investigations were concerned with the two-phase flow pattern for flow boiling in horizontal tubes [12], [9]. Therefore, the objective of the present investigation is to obtain information about the two-phase flow patterns for evaporation of R-134a inside horizontal smooth and microfin tubes. Also Investigation of heat transfer during flow boiling of R-134a inside horizontal microfin and smooth tube have been carried out experimentally The heat transfer coefficients for annular flow in the smooth tube is shown to agree well with Gungor and Winterton-s correlation [4]. All the flow patterns occurred in the test can be divided into three dominant regimes, i.e., stratified-wavy flow, wavy-annular flow and annular flow. Experimental data are plotted in two kinds of flow maps, i.e., Weber number for the vapor versus weber number for the liquid flow map and mass flux versus vapor quality flow map. The transition from wavy-annular flow to annular or stratified-wavy flow is identified in the flow maps.

Keywords: Flow boiling, Flow pattern, Heat transfer, Horizontal, Smooth tube, Microfin tube.

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Authors: Temsiri Sapsaman, Anocha Bhocarattanahkul

Abstract:

The maintenance of work rolls in hot strip processing has been lengthy and difficult tasks for hot strip manufacturer because heavy work rolls have to be taken out of the production line, which could take hours. One way to increase the time between maintenance is to improve the effectiveness of the work roll cooling system such that the wear and tear more slowly occurs, while the operation cost is kept low. Therefore, this study aims to improve the work roll cooling system by providing the manufacturer the relationship between the work-roll temperature reduced by cooling and the water flow that can help manufacturer determining the more effective water flow of the cooling system. The relationship is found using simulation with a systematic process adjustment so that the satisfying quality of product is achieved. Results suggest that the manufacturer could reduce the water flow by 9% with roughly the same performance. With the same process adjustment, the feasibility of finishing-mill-stand reduction is also investigated. Results suggest its possibility.

Keywords: Work-roll cooling system, hot strip process adjustment, feasibility study.

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Authors: Ali Ghobadi, Seyed Mohammad Javadi, Behnam Rahimi

Abstract:

The present study is concerned with the effect of exciting boundary layer on cooling process in a gas-turbine blades. The cooling process is numerically investigated. Observations show cooling the first row of moving or stable blades leads to increase their life-time. Results show that minimum temperature in cooling line with exciting boundary layer is lower than without exciting. Using block in cooling line of turbines' blade causes flow pattern and stability in boundary layer changed that causes increase in heat transfer coefficient. Results show at the location of block, temperature of turbines' blade is significantly decreased. The k-ε turbulence model is used.

Keywords: Cooling, Exciting Boundary Layer, Heat Transfer, Turbine Blade.

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Authors: U. P. L. Wijayarathne, K. C. Wasalathilake

Abstract:

This work presents the modelling and simulation of saponification of ethyl acetate in the presence of sodium hydroxide in a plug flow reactor using Aspen Plus simulation software. Plug flow reactors are widely used in the industry due to the non-mixing property. The use of plug flow reactors becomes significant when there is a need for continuous large scale reaction or fast reaction. Plug flow reactors have a high volumetric unit conversion as the occurrence for side reactions is minimum. In this research Aspen Plus V8.0 has been successfully used to simulate the plug flow reactor. In order to simulate the process as accurately as possible HYSYS Peng- Robinson EOS package was used as the property method. The results obtained from the simulation were verified by the experiment carried out in the EDIBON plug flow reactor module. The correlation coefficient (r2) was 0.98 and it proved that simulation results satisfactorily fit for the experimental model. The developed model can be used as a guide for understanding the reaction kinetics of a plug flow reactor.

Keywords: Aspen Plus, Modelling, Plug Flow Reactor, Simulation.

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Authors: Krasimir I. Ivanov, Elitsa N. Kolentsova, Dimitar Y. Dimitrov, Petya Ts. Petrova, Tatyana T. Tabakova

Abstract:

This work studies the effect of chemical composition on the activity and selectivity of γ–alumina supported CuO/ MnO2/Cr2O3 catalysts toward deep oxidation of CO, dimethyl ether (DME) and methanol. The catalysts were prepared by impregnation of the support with an aqueous solution of copper nitrate, manganese nitrate and CrO3 under different conditions. Thermal, XRD and TPR analysis were performed. The catalytic measurements of single compounds oxidation were carried out on continuous flow equipment with a four-channel isothermal stainless steel reactor. Flow-line equipment with an adiabatic reactor for simultaneous oxidation of all compounds under the conditions that mimic closely the industrial ones was used. The reactant and product gases were analyzed by means of on-line gas chromatographs. On the basis of XRD analysis it can be concluded that the active component of the mixed Cu-Mn-Cr/γ–alumina catalysts consists of at least six compounds – CuO, Cr2O3, MnO2, Cu1.5Mn1.5O4, Cu1.5Cr1.5O4 and CuCr2O4, depending on the Cu/Mn/Cr molar ratio. Chemical composition strongly influences catalytic properties, this influence being quite variable with regards to the different processes. The rate of CO oxidation rapidly decrease with increasing of chromium content in the active component while for the DME was observed the reverse trend. It was concluded that the best compromise are the catalysts with Cu/(Mn + Cr) molar ratio 1:5 and Mn/Cr molar ratio from 1:3 to 1:4.

Keywords: Copper-manganese-chromium oxide catalysts, CO, deep oxidation, volatile organic compounds.

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Authors: Takeshi Takeda

Abstract:

An experiment was performed for the OECD/NEA ROSA-2 Project employing the ROSA/LSTF (rig of safety assessment/large-scale test facility), which simulated a steam generator tube rupture (SGTR) accident induced by main steam line break (MSLB) with operator recovery actions in a pressurized water reactor (PWR). The primary pressure decreased to the pressure level nearly-equal to the intact steam generator (SG) secondary-side pressure even with coolant injection from the high-pressure injection (HPI) system of emergency core cooling system (ECCS) into cold legs. Multi-dimensional coolant behavior appeared such as thermal stratification in both hot and cold legs in intact loop. The RELAP5/MOD3.3 code indicated the insufficient predictions of the primary pressure, the SGTR break flow rate, and the HPI flow rate, and failed to predict the fluid temperatures in the intact loop hot and cold legs. Results obtained from the comparison among three LSTF SGTR-related tests clarified that the thermal stratification occurs in the horizontal legs by different mechanisms.

Keywords: LSTF, SGTR, thermal stratification, RELAP5.

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Authors: S. Tupsie, A. Isaramongkolrak, P. Pao-la-or

Abstract:

This paper presents the mathematical model of electric field and magnetic field in transmission system, which performs in second-order partial differential equation. This research has conducted analyzing the electromagnetic field radiating to atmosphere around the transmission line, when there is the transmission line transposition in case of long distance distribution. The six types of 500 kV transposed HV transmission line with double circuit will be considered. The computer simulation is applied finite element method that is developed by MATLAB program. The problem is considered to two dimensions, which is time harmonic system with the graphical performance of electric field and magnetic field. The impact from simulation of six types long distance distributing transposition will not effect changing of electric field and magnetic field which surround the transmission line.

Keywords: Transposition, Electromagnetic Field, Finite Element Method (FEM), Transmission Line, Computer Simulation

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Authors: Maja Benkovic, Ingrid Bauman

Abstract:

The objective of this work was to investigate flow properties of powdered infant formula samples. Samples were purchased at a local pharmacy and differed in composition. Lactose free infant formula, gluten free infant formula and infant formulas containing dietary fibers and probiotics were tested and compared with a regular infant formula sample which did not contain any of these supplements. Particle size and bulk density were determined and their influence on flow properties was discussed. There were no significant differences in bulk densities of the samples, therefore the connection between flow properties and bulk density could not be determined. Lactose free infant formula showed flow properties different to standard supplement-free sample. Gluten free infant formula with addition of probiotic microorganisms and dietary fiber had the narrowest particle size distribution range and exhibited the best flow properties. All the other samples exhibited the same tendency of decreasing compaction coefficient with increasing flow speed, which means they all become freer flowing with higher flow speeds.

Keywords: flow properties, infant formula, powderedmaterial

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Authors: Vai Kuong Sin, Chon Kit Chio

Abstract:

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. ". In this study, we revisit the problem of reversed stagnation-point flow over a flat plate. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. This is no true in neglecting the viscous terms within the total flow field. In particular it is pointed out that for a plate impulsively accelerated from rest to a constant velocity V0 that a similarity solution to the self-similar ODE is obtained which is noteworthy completely analytical.

Keywords: reversed stagnation-point flow, similarity solutions, analytical solution, numerical solution

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Authors: M. S. Anton Merkulov

Abstract:

This article discusses the questions concerning of creating small packet networks for energy companies with application of high voltage power line carrier equipment (PLC) with functionality of IP traffic transmission. The main idea is to create converged PLC links between substations and dispatching centers where packet data and voice are transmitted in one data flow. The article contents description of basic conception of the network, evaluation of voice traffic transmission parameters, and discussion of header compression techniques in relation to PLC links. The results of exploration show us, that convergent packet PLC links can be very useful in the construction of small packet networks between substations in remote locations, such as deposits or low populated areas.

Keywords: packet PLC, VoIP, time delay, packet traffic, overhead compression

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Authors: Israt Jahan Eshita

Abstract:

Flows developed between two parallel disks have many engineering applications. Two types of non-swirling flows can be generated in such a domain. One is purely source flow in disc type domain (outward flow). Other is purely sink flow in disc type domain (inward flow). This situation often appears in some turbo machinery components such as air bearings, heat exchanger, radial diffuser, vortex gyroscope, disc valves, and viscosity meters. The main goal of this paper is to show the mesh convergence, because mesh convergence saves time, and economical to run and increase the efficiency of modeling for both sink and source flow. Then flow field is resolved using a very fine mesh near-wall, using enhanced wall treatment. After that we are going to compare this flow using standard k-epsilon, RNG k-epsilon turbulence models. Lastly compare some experimental data with numerical solution for sink flow. The good agreement of numerical solution with the experimental works validates the current modeling.

Keywords: Hydraulic diameter, k-epsilon model, meshes convergence, Reynolds number, RNG model, sink flow, source flow and wall y+.

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Authors: Yongxin Yuan

Abstract:

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

Keywords: Partially prescribed spectral information, symmetric arrow-head matrix, inverse problem, optimal approximation.

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