Search results for: Flux

Authors: W. R. Li, J. K. Xia, R. Q. Peng, Z. Y. Guo, L. Jiang

Abstract:

According to 3D magnetic circuit of the transverse flux PM linear machine, distribution law is presented, and analytical expression of axial end flux leakage is derived using numerical method. Maxwell stress tensor is used to solve detent force of mover. A 3D finite element model of the transverse flux PM machine is built to analyze the flux distribution and detent force. Experimental results of the prototype verified the validity of axial end flux leakage and detent force theoretical derivation, the research on axial end flux leakage and detent force provides a valuable reference to other types of linear machine.

Keywords: Transverse flux PM linear machine, flux distribution, axial end flux leakage, detent force.

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Authors: H. Fazlinejad, A. Halvaee

Abstract:

In this study, characteristics of ATIG welds using ZnO flux on aluminum was investigated and compared with TIG welds. Autogenously AC-ATIG bead on plate welding was applied on Al1050 plate with a coating of ZnO as the flux. Different levels of welding current and flux layer thickness was considered to study the effect of heat input and flux quantity on ATIG welds and was compared with those of TIG welds. Geometrical investigation of the weld cross sections revealed that penetration depth of the ATIG welds with ZnO flux, was increased up to 2 times in some samples compared to the TIG welds. Optical metallographic and Scanning Electron Microscopy (SEM) observations revealed similar microstructures in TIG and ATIG welds. Composition of the ATIG welds slag was also analyzed using X-ray diffraction. In both TIG and ATIG samples, the lowest values of microhardness were observed in the HAZ.

Keywords: ATIG, active flux, weld penetration, Al 1050, ZnO.

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Authors: Petter Eklund, Jonathan Sjölund, Sandra Eriksson, Mats Leijon

Abstract:

The spoke type rotor can be used to obtain magnetic flux concentration in permanent magnet machines. This allows the air gap magnetic flux density to exceed the remanent flux density of the permanent magnets but gives problems with leakage fluxes in the magnetic circuit. The end leakage flux of one spoke type permanent magnet rotor design is studied through measurements and finite element simulations. The measurements are performed in the end regions of a 12 kW prototype generator for a vertical axis wind turbine. The simulations are made using three dimensional finite elements to calculate the magnetic field distribution in the end regions of the machine. Also two dimensional finite element simulations are performed and the impact of the two dimensional approximation is studied. It is found that the magnetic leakage flux in the end regions of the machine is equal to about 20% of the flux in the permanent magnets. The overestimation of the performance by the two dimensional approximation is quantified and a curve-fitted expression for its behavior is suggested.

Keywords: End effects, end leakage flux, permanent magnet machine, spoke type rotor.

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

Abstract:

In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: R. G. Ramírez-Chavarría, C. Sánchez-Pérez, V. Argueta-Díaz

Abstract:

In this paper we present the design of an optical device based on a Herriott multi-pass cell fabricated on a small sized acrylic slab for heat flux measurements using the deflection of a laser beam propagating inside the cell. The beam deflection is produced by the heat flux conducted to the acrylic slab due to a gradient in the refractive index. The use of a long path cell as the sensitive element in this measurement device, gives the possibility of high sensitivity within a small size device. We present the optical design as well as some experimental results in order to validate the device’s operation principle.

Keywords: Heat flux, herriott cell, optical beam deflection, thermal conductivity.

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Authors: Yisheng Rong, Jian Sun, Weiqiang Liu, Renjun Zhan

Abstract:

A CFD study on heat flux reduction in hypersonic flow with opposing jet has been conducted. Flowfield parameters, reattachment point position, surface pressure distributions and heat flux distributions are obtained and validated with experiments. The physical mechanism of heat reduction has been analyzed. When the opposing jet blows, the freestream is blocked off, flows to the edges and not interacts with the surface to form aerodynamic heating. At the same time, the jet flows back to form cool recirculation region, which reduces the difference in temperature between the surface and the nearby gas, and then reduces the heat flux. As the pressure ratio increases, the interface between jet and freestream is gradually pushed away from the surface. Larger the total pressure ratio is, lower the heat flux is. To study the effect of the intensity of opposing jet more reasonably, a new parameter RPA has been introduced by combining the flux and the total pressure ratio. The study shows that the same shock wave position and total heat load can be obtained with the same RPA with different fluxes and the total pressures, which means the new parameter could stand for the intensity of opposing jet and could be used to analyze the influence of opposing jet on flow field and aerodynamic heating.

Keywords: opposing jet, aerodynamic heating, total pressure ratio, thermal protection system

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Authors: O. S. Pradeep, S. Vigneshwaran, K. Praveen Kumar, K. Jeyendran, V. R. Sanal Kumar

Abstract:

The influence of injector attitude on wall heat flux plays an important role in predicting the start-up transient and also determining the combustion chamber wall durability of liquid rockets. In this paper comprehensive numerical studies have been carried out on an idealized liquid rocket combustion chamber to examine the transient wall heat flux during its start-up transient at different injector attitude. Numerical simulations have been carried out with the help of a validated 2d axisymmetric, double precision, pressure-based, transient, species transport, SST k-omega model with laminar finite rate model for governing turbulent-chemistry interaction for four cases with different jet intersection angles, viz., 0^o, 30^o, 45^o, and 60^o. We concluded that the jets intersection angle is having a bearing on the time and location of the maximum wall-heat flux zone of the liquid rocket combustion chamber during the start-up transient. We also concluded that the wall heat flux mapping in liquid rocket combustion chamber during the start-up transient is a meaningful objective for the chamber wall material selection and the lucrative design optimization of the combustion chamber for improving the payload capability of the rocket.  

Keywords: Combustion chamber, injector, liquid rocket, rocket engine wall heat flux.

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Authors: J. Soltani, H. Abootorabi Zarchi, Gh. R. Arab Markadeh

Abstract:

In this paper a sliding-mode torque and flux control is designed for encoderless synchronous reluctance motor drive. The sliding-mode plus PI controllers are designed in the stator-flux field oriented reference frame which is able to track the mentioned reference signals with a minimum pulsations in the state condition. In addition, with these controllers a fast dynamic response is also achieved for the drive system. The proposed control scheme is robust subject to parameters variation except to stator resistance. To solve this problem a simple estimator is used for on-line detecting of this parameter. Moreover, the rotor position and speed are estimated by on-line obtaining of the stator-flux-space vector. The effectiveness and capability of the proposed control approach is verified by both the simulation and experimental results.

Keywords: Synchronous Reluctance Motor, Direct Torque and Flux Control, Sliding Mode, Field-Oriented Frame, Encoderless.

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Authors: Maryam Saeidi, Ehsan Motamedian, Seyed Abbas Shojaosadati

Abstract:

Zymomonas mobilis is known as an example of the uncoupled growth phenomenon. This microorganism also has a unique metabolism that degrades glucose by the Entner–Doudoroff (ED) pathway. In this paper, a genome-scale metabolic model including 434 genes, 757 reactions and 691 metabolites was reconstructed to simulate uncoupled growth and study its effect on flux distribution in the central metabolism. The model properly predicted that ATPase was activated in experimental growth yields of Z. mobilis. Flux distribution obtained from model indicates that the major carbon flux passed through ED pathway that resulted in the production of ethanol. Small amounts of carbon source were entered into pentose phosphate pathway and TCA cycle to produce biomass precursors. Predicted flux distribution was in good agreement with experimental data. The model results also indicated that Z. mobilis metabolism is able to produce biomass with maximum growth yield of 123.7 g (mol glucose)-1 if ATP synthase is coupled with growth and produces 82 mmol ATP gDCW-1h-1. Coupling the growth and energy reduced ethanol secretion and changed the flux distribution to produce biomass precursors.

Keywords: Genome-scale metabolic model, Zymomonas mobilis, uncoupled growth, flux distribution, ATP dissipation.

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Authors: A. M. Hassanain, Nader M. A. Mohamed, M. Naguib Aly, Alya A. Badawi, M. A. Gaheen

Abstract:

The thermal, epithermal and fast fluxes were calculated for three irradiation channels at Egypt Second Research Reactor (ETRR-2) using CITVAP code. The validity of the calculations was verified by experimental measurements. There are some deviations between measurements and calculations. This is due to approximations in the calculation models used, homogenization of regions, condensation of energy groups and uncertainty in nuclear data used. Neutron flux data for the three irradiation channels are now available. This would enable predicting the irradiation conditions needed for future radioisotope production.

Keywords: ETRR-2, Neutron flux, Radioisotope production, CITVAP

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Authors: Wang Jing, Liu Shouwen, Pei Yifei

Abstract:

A satellite is being integrated and tested by BISEE (Beijing Institute of Spacecraft Environment Engineering). This paper describes the infrared lamp array simulation technology used for satellite thermal balance and thermal vacuum test. These tests were performed in KM6 space environmental simulator in Beijing, China. New software and hardware developed by BISEE, along with enhanced heat flux uniformity, provided for well accomplished thermal balance and thermal vacuum tests. The flux uniformity of lamp array was satisfied with test requirement. Monitored background radiometer offered reliable heat flux measurements with remarkable repeatability. Simulation software supplied accurate thermal flux distribution predictions.

Keywords: Satellite, Thermal test, Infrared lamp array, Heatflux

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Authors: G. R. Arab Markadeh, J. Soltani, N. R. Abjadi, M. Hajian

Abstract:

In this paper, a direct torque control - space vector modulation (DTC-SVM) scheme is presented for a six-phase speed and voltage sensorless induction motor (IM) drive. The decoupled torque and stator flux control is achieved based on IM stator flux field orientation. The rotor speed is detected by on-line estimating of the rotor angular slip speed and stator vector flux speed. In addition, a simple method is introduced to estimate the stator resistance. Moreover in this control scheme the voltage sensors are eliminated and actual motor phase voltages are approximated by using PWM inverter switching times and the dc link voltage. Finally, some simulation and experimental results are presented to verify the effectiveness and capability of the proposed control scheme.

Keywords: Stator FOC, Multiphase motors, sensorless.

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Authors: Airoldi G., Bumby J. R., Dominy C., G.L. Ingram, Lim C. H., Mahkamov K., N. L. Brown, A. Mebarki, M. Shanel

Abstract:

Axial Flux Permanent Magnet (AFPM) Machines require effective cooling due to their high power density. The detrimental effects of overheating such as degradation of the insulation materials, magnets demagnetization, and increase of Joule losses are well known. This paper describes the CFD simulations performed on a test rig model of an air cooled Axial Flux Permanent Magnet (AFPM) generator built at Durham University to identify the temperatures and heat transfer coefficient on the stator. The Reynolds Averaged Navier-Stokes and the Energy equations are solved and the flow pattern and heat transfer developing inside the machine are described. The Nusselt number on the stator surfaces has been found. The dependency of the heat transfer on the flow field is described temperature field obtained. Tests on an experimental are undergoing in order to validate the CFD results.

Keywords: Axial flux permanent magnet machines, thermal modeling, CFD.

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Authors: Qingjiang Li, Hui Xu, Haijun Liu, Xiaobo Tian

Abstract:

To judge whether the memristor can be interpreted as the fourth fundamental circuit element, we propose a variable-relation criterion of fundamental circuit elements. According to the criterion, we investigate the nature of three fundamental circuit elements and the memristor. From the perspective of variables relation, the memristor builds a direct relation between the voltage across it and the current through it, instead of a direct relation between the magnetic flux and the charge. Thus, it is better to characterize the memristor and the resistor as two special cases of the same fundamental circuit element, which is the memristive system in Chua-s new framework. Finally, the definition of memristor is refined according to the difference between the magnetic flux and the flux linkage.

Keywords: Memristor, Fundamental, Variable-Relation Criterion, Memristive system

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Authors: K. Kouzi

Abstract:

In order to have stable and high performance of direct torque and flux control (DTFC) of double star induction motor drive (DSIM), proper on-line adaptation of the stator resistance is very important. This is inevitably due to the variation of the stator resistance during operating conditions, which introduces error in estimated flux position and the magnitude of the stator flux. Error in the estimated stator flux deteriorates the performance of the DTFC drive. Also, the effect of error in estimation is very important especially at low speed. Due to this, our aim is to overcome the sensitivity of the DTFC to the stator resistance variation by proposing on-line fuzzy estimation stator resistance. The fuzzy estimation method is based on an on-line stator resistance correction through the variations of the stator current estimation error and its variations. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of the suggested algorithm control is to avoid the drive instability that may occur in certain situations and ensure the tracking of the actual stator resistance. The validity of the technique and the improvement of the whole system performance are proved by the results.

Keywords: Direct torque control, dual stator induction motor, fuzzy logic estimation, stator resistance adaptation.

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Authors: Ahmad Darabi, Hassan Moradi, Hossein Azarinfar

Abstract:

In this paper presented initial design of Low Speed Axial Flux Permanent Magnet (AFPM) Machine with Non-Slotted TORUS topology type by use of certain algorithm (Appendix). Validation of design algorithm studied by means of selected data of an initial prototype machine. Analytically design calculation carried out by means of design algorithm and obtained results compared with results of Finite Element Method (FEM).

Keywords: Axial Flux Permanent Magnet (AFPM) Machine, Design Algorithm, Finite Element Method (FEM), TORUS

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Authors: Neethu S., Shinoy K.S., A.S. Shajilal

Abstract:

This paper presents the optimal design and development of an axial flux motor for blood pump application. With the design objective of maximizing the motor efficiency and torque, different topologies of AFPM machine has been examined. Selection of optimal magnet fraction, Halbach arrangement of rotor magnets and the use of Soft Magnetic Composite (SMC) material for the stator core results in a novel motor with improved efficiency and torque profile. The results of the 3D Finite element analysis for the novel motor have been shown.

Keywords: Axial flux motor, Finite Element Methods, Halbach array, Left Ventricular Assist Device, Soft magnetic composite.

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Authors: Sheetal Kumar Parwar, J. Deb Barma, A. Majumder

Abstract:

Submerged arc welding is a very complex process. It is a very efficient and high performance welding process. In this present study an attempt have been done to reduce the welding distortion by increased amount of oxide flux through TiO2 in submerged arc welding process. Care has been taken to avoid the excessiveness of the adding agent for attainment of significant results. Data Envelopment Analysis (DEA) based BAT algorithm is used for the parametric optimization purpose in which DEA is used to convert multi response parameters into a single response parameter. The present study also helps to know the effectiveness of the addition of TiO2 in active flux during submerged arc welding process.

Keywords: BAT algorithm, design of experiment, optimization, submerged arc welding.

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Authors: V. Nikkhah Rashidabad, M. Manteghian, M. Masoumi, S. Mousavian

Abstract:

In this research, the changes in bubbles diameter and  number that may occur due to the change in heat flux of pure water  during pool boiling process. For this purpose, test equipment was  designed and developed to collect test data. The bubbles were graded  using Caliper Screen software. To calculate the growth and  nucleation rates of bubbles under different fluxes, population balance  model was employed. The results show that the increase in heat flux  from q=20 kw/m2 to q= 102 kw/m2 raised the growth and nucleation  rates of bubbles.

 

Keywords: Heat flux, bubble growth, bubble nucleation, population balance model.

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Authors: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

Abstract:

The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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Authors: R. Hosseini, A. Gholaminejad, H. Jahandar

Abstract:

The present paper is an experimental investigation of roughness effects on nucleate pool boiling of refrigerant R113 on horizontal circular copper surfaces. The copper samples were treated by different sand paper grit sizes to achieve different surface roughness. The average surface roughness of the four samples was 0.901, 0.735, 0.65, and 0.09, respectively. The experiments were performed in the heat flux range of 8 to 200kW/m2. The heat transfer coefficient was calculated by measuring wall superheat of the samples and the input heat flux. The results show significant improvement of heat transfer coefficient as the surface roughness is increased. It is found that the heat transfer coefficient of the sample with Ra=0.901 is 3.4, 10.5, and 38.5% higher in comparison with surfaces with Ra of 0.735, 0.65, and 0.09 at heat flux of 170 kW/m2. Moreover, the results are compared with literature data and the well known Cooper correlation.

Keywords: Nucleate Boiling, Pool Boiling, R113, SurfaceRoughness

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Authors: A. Ourici

Abstract:

Doubly fed induction machines DFIM are used mainly for wind energy conversion in MW power plants. This paper presents a new strategy of field oriented control ,it is based on the principle of a double flux orientation of stator and rotor at the same time. Therefore, the orthogonality created between the two oriented fluxes, which must be strictly observed, leads to generate a linear and decoupled control with an optimal torque. The obtained simulation results show the feasibility and the effectiveness of the suggested method.

Keywords: Doubly fed induction machine, double fluxorientation control , vector control , PWM inverter.

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Authors: Bhausaheb L. Pangarkar, M.G. Sane, Saroj B. Parjane, Mahendra Guddad

Abstract:

The possibility of producing drinking water from brackish ground water using Vacuum membrane distillation (VMD) process was studied. It is a rising technology for seawater or brine desalination process. The process simply consists of a flat sheet hydrophobic micro porous PTFE membrane and diaphragm vacuum pump without a condenser for the water recovery or trap. In this work, VMD performance was investigated for aqueous NaCl solution and natural ground water. The influence of operational parameters such as feed flow rate (30 to 55 l/h), feed temperature (313 to 333 K), feed salt concentration (5000 to 7000 mg/l) and permeate pressure (1.5 to 6 kPa) on the membrane distillation (MD) permeation flux have been investigated. The maximum flux reached to 28.34 kg/m2 h at feed temperature, 333 K; vacuum pressure, 1.5 kPa; feed flow rate, 55 l/h and feed salt concentration, 7000 mg/l. The negligible effects in the reduction of permeate flux found over 150 h experimental run for salt water. But for the natural ground water application over 75 h, scale deposits observed on the membrane surface and 29% reduction in the permeate flux over 75 h. This reduction can be eliminated by acidification of feed water. Hence, promote the research attention in apply of VMD for the ground water purification over today-s conventional RO operation.

Keywords: VMD, hydrophobic PTFE flat membrane, desalination, ground water

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Authors: S. A. Mousavi Rad, S. A. Mirbagheri, T. Mohammadi

Abstract:

In this paper, removal of chromium(VI) from aqueous solution has been researched using reverse osmosis. The influence of transmembrane pressure and feed concentration on permeate flux, water recovery, permeate concentration, and salt rejection was studied. The results showed that according to the variation of transmembrane pressure and feed concentration, the permeate flux and salt rejection were in the range 19.17 to 58.75 l/m2.min and 99.51 to 99.8 %, respectively. The highest permeate flux, 58.75 l/m2.min, and water recovery, 42.47 %, were obtained in the highest pressure and the lowest feed concentration. On the other hand, the lowest permeate concentration, 0.01 mg/l, and the highest salt rejection, 99.8 %, were obtained in the highest pressure and the lowest feed concentration.

Keywords: solution, Chromium, Removal, Reverse osmosis.

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Authors: Ben Hamed M., Sbita L

Abstract:

This paper presents a new method for the implementation of a direct rotor flux control (DRFOC) of induction motor (IM) drives. It is based on the rotor flux components regulation. The d and q axis rotor flux components feed proportional integral (PI) controllers. The outputs of which are the target stator voltages (vdsref and vqsref). While, the synchronous speed is depicted at the output of rotor speed controller. In order to accomplish variable speed operation, conventional PI like controller is commonly used. These controllers provide limited good performances over a wide range of operations even under ideal field oriented conditions. An alternate approach is to use the so called fuzzy logic controller. The overall investigated system is implemented using dSpace system based on digital signal processor (DSP). Simulation and experimental results have been presented for a one kw IM drives to confirm the validity of the proposed algorithms.

Keywords: DRFOC, fuzzy logic, variable speed drives, control, IM and real time.

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Authors: Bhausaheb L. Pangarkar, M.G. Sane

Abstract:

Membrane distillation (MD) is a rising technology for seawater or brine desalination process. In this work, an air gap membrane distillation (AGMD) performance was investigated for aqueous NaCl solution along with natural ground water and seawater. In order to enhance the performance of the AGMD process in desalination, that is, to get more flux, it is necessary to study the effect of operating parameters on the yield of distillate water. The influence of operational parameters such as feed flow rate, feed temperature, feed salt concentration, coolant temperature and air gap thickness on the membrane distillation (MD) permeation flux have been investigated for low and high salt solution. the natural application of ground water and seawater over 90 h continuous operation, scale deposits observed on the membrane surface and reduction in flux represents 23% for ground water and 60% for seawater, in 90 h. This reduction was eliminated (less than 14 %) by acidification of feed water. Hence, promote the research attention in apply of AGMD for the ground water as well as seawater desalination over today-s conventional RO operation.

Keywords: MD, ground water, seawater, AGMD.

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Authors: P. Srinivas, P. V. N. Prasad

Abstract:

Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands.

The DTC of SRM is analyzed by two methods. In one method, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: Direct Toque Control, Simplified Torque Equation, Finite Element Analysis, Torque Ripple.

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Authors: Samira Haghshenaskashani, Hadi Pasdarshahri

Abstract:

One of the potential and effective ways of storing thermal energy in buildings is the integration of brick with phase change materials (PCMs). This paper presents a two-dimensional model for simulating and analyzing of PCM in order to minimize energy consumption in the buildings. The numerical approach has been used with the real weather data of a selected city of Iran (Tehran). Two kinds of brick integrated PCM are investigated and compared base on outdoor weather conditions and the amount of energy consumption. The results show a significant reduction in maximum entering heat flux to building about 32.8% depending on PCM quantity. The results are analyzed by various temperature contour plots. The contour plots illustrated the time dependent mechanism of entering heat flux for a brick integrated with PCM. Further analysis is developed to investigate the effect of PCM location on the inlet heat flux. The results demonstrated that to achieve maximum performance of PCM it is better to locate PCM near the outdoor.

Keywords: Building, Energy Storage, PCM, Phase Change Material

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Authors: S. Grouni, R. Ibtiouen, M. Kidouche, O. Touhami

Abstract:

Induction machine models used for steady-state and transient analysis require machine parameters that are usually considered design parameters or data. The knowledge of induction machine parameters is very important for Indirect Field Oriented Control (IFOC). A mismatched set of parameters will degrade the response of speed and torque control. This paper presents an improvement approach on rotor time constant adaptation in IFOC for Induction Machines (IM). Our approach tends to improve the estimation accuracy of the fundamental model for flux estimation. Based on the reduced order of the IM model, the rotor fluxes and rotor time constant are estimated using only the stator currents and voltages. This reduced order model offers many advantages for real time identification parameters of the IM.

Keywords: Indirect Field Oriented Control (IFOC), InductionMachine (IM), Rotor Time Constant, Parameters ApproachAdaptation. Optimum rotor flux.

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Authors: A. M. Tahsini, S. A. Hosseini

Abstract:

In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux and the one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.

Keywords: Aerodynamic heating, Heat conduction, Numerical simulation, Supersonic flight, Launch vehicle.

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