Search results for: High Numerical Aperture

Authors: Thana Ananacha

Abstract:

This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered as 400 and 800 W.m-2 the corresponding initial condition temperatures were 30.5 and 38.5ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: Thermal simulation, Double Glass Wall, Velocity field.

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Authors: H. Aminfar, M. Mohammadpourfard, K. Khajeh

Abstract:

This paper has focused on the most important parameters in the LSC uptake; inlet Re number and Sc number in the presence of non-uniform magnetic field. The magnetic field is arising from the thin wire with electric current placed vertically to the arterial blood vessel. According to the results of this study, applying magnetic field can be a treatment for atherosclerosis by reducing LSC along the vessel wall. Homogeneous porous layer as a arterial wall has been regarded. Blood flow has been considered laminar and incompressible containing Ferro fluid (blood and 4 % vol. Fe₃O₄) under steady state conditions. Numerical solution of governing equations was obtained by using the single-phase model and control volume technique for flow field.

Keywords: LDL Surface Concentration (LSC), Magnetic field, Computational fluid dynamics, Porous wall.

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Authors: Chakraborty Sudipta, A. R. Kambekar, Sarma Arnab

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Sea-level rise being one of the most important impacts of anthropogenic induced climate change resulting from global warming and melting of icebergs at Arctic and Antarctic, the investigations done by various researchers both on Indian Coast and elsewhere during the last decade has been reviewed in this paper. The paper aims to ascertain the propensity of consistency of different suggested methods to predict the near-accurate future sea level rise along the coast of Mumbai. Case studies at East Coast, Southern Tip and West and South West coast of India have been reviewed. Coastal Vulnerability Index of several important international places has been compared, which matched with Intergovernmental Panel on Climate Change forecasts. The application of Geographic Information System mapping, use of remote sensing technology, both Multi Spectral Scanner and Thematic Mapping data from Landsat classified through Iterative Self-Organizing Data Analysis Technique for arriving at high, moderate and low Coastal Vulnerability Index at various important coastal cities have been observed. Instead of data driven, hindcast based forecast for Significant Wave Height, additional impact of sea level rise has been suggested. Efficacy and limitations of numerical methods vis-à-vis Artificial Neural Network has been assessed, importance of Root Mean Square error on numerical results is mentioned. Comparing between various computerized methods on forecast results obtained from MIKE 21 has been opined to be more reliable than Delft 3D model.

Keywords: Climate change, coastal vulnerability index, global warming, sea level rise.

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Authors: Md. Fazlul Karim, Esa Al-Islam

Abstract:

This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Boundary-fitted nested grid model, finite difference method, Indonesian tsunami of 2004, Southern Thailand.

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Authors: Ezzatallah Baloui Jamkhaneh, Bahram Sadeghpour-Gildeh, Gholamhossein Yari

Abstract:

This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (oc) curves of the plan is like a band having a high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the oc bands of using of binomial with the oc bands of using of Poisson distribution.

Keywords: Statistical quality control, acceptance single sampling, fuzzy number.

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Authors: M. Raciti Castelli, S. Mogno, S. Giacometti, E. Benini

Abstract:

A boundary layer wind tunnel facility has been adopted in order to conduct experimental measurements of the flow field around a model of the Panorama Giustinelli Building, Trieste (Italy). Information on the main flow structures has been obtained by means of flow visualization techniques and has been compared to the numerical predictions of the vortical structures spread on top of the roof, in order to investigate the optimal positioning for a vertical-axis wind energy conversion system, registering a good agreement between experimental measurements and numerical predictions.

Keywords: Boundary layer wind tunnel, flow around buildings, atmospheric flow field, vertical-axis wind turbine (VAWT).

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Authors: R. M. Farouk

Abstract:

In this paper, we present an analytical analysis of the representation of images as the magnitudes of their transform with the discrete wavelets. Such a representation plays as a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding, because it makes the representation insensitive to small local shifts. We found that if the signals are band limited and of zero mean, then reconstruction from the magnitudes is unique up to the sign for almost all signals. We also present an iterative reconstruction algorithm which yields very good reconstruction up to the sign minor numerical errors in the very low frequencies.

Keywords: Wavelets, Image processing signal processing, Image reconstruction

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Authors: Mahmoud Roushdy, Mohamed El Naggar, Ahmed Yehia Abdelaziz

Abstract:

Anchored sheet pile has been used worldwide as front quay walls for decades. With the increase in vessel drafts and weights, those sheet pile walls need to be upgraded by increasing the depth of the dredging line in front of the wall. One of the upgrades for the sheet pile wall is to add a separated platform to the system, where the platform is structurally separated from the front wall. The platform is structurally separated from the front wall. This paper presents a numerical investigation utilizing finite element analysis on the behavior of separated relieve platforms installed within existing anchored sheet pile quay walls. The investigation was done in two steps: a verification step followed by a parametric study. In the verification step, the numerical model was verified based on field measurements performed by others. The validated model was extended within the parametric study to a series of models with different backfill soils, separation gap width, and number of pile rows supporting the platform. The results of the numerical investigation show that using stiff clay as backfill soil (neglecting consolidation) gives better performance for the front wall and the first pile row adjacent to sandy backfills. The degree of compaction of the sandy backfill slightly increases lateral deformations but reduces bending moment acting on pile rows, while the effect is minor on the front wall. In addition, the increase in the separation gap width gradually increases bending moments on the front wall regardless of the backfill soil type, while this effect is reversed on pile rows (gradually decrease). Finally, the paper studies the possibility of deepening the basin along with the separation to take advantage of the positive separation effect on piles, and front wall.

Keywords: Anchored sheet pile, relieving platform, separation gap, upgrade quay wall.

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Authors: Maxence Queyrel, Edi Prifti, Alexandre Templier, Jean-Daniel Zucker

Abstract:

Analysis of the human microbiome using metagenomic sequencing data has demonstrated high ability in discriminating various human diseases. Raw metagenomic sequencing data require multiple complex and computationally heavy bioinformatics steps prior to data analysis. Such data contain millions of short sequences read from the fragmented DNA sequences and stored as fastq files. Conventional processing pipelines consist in multiple steps including quality control, filtering, alignment of sequences against genomic catalogs (genes, species, taxonomic levels, functional pathways, etc.). These pipelines are complex to use, time consuming and rely on a large number of parameters that often provide variability and impact the estimation of the microbiome elements. Training Deep Neural Networks directly from raw sequencing data is a promising approach to bypass some of the challenges associated with mainstream bioinformatics pipelines. Most of these methods use the concept of word and sentence embeddings that create a meaningful and numerical representation of DNA sequences, while extracting features and reducing the dimensionality of the data. In this paper we present an end-to-end approach that classifies patients into disease groups directly from raw metagenomic reads: metagenome2vec. This approach is composed of four steps (i) generating a vocabulary of k-mers and learning their numerical embeddings; (ii) learning DNA sequence (read) embeddings; (iii) identifying the genome from which the sequence is most likely to come and (iv) training a multiple instance learning classifier which predicts the phenotype based on the vector representation of the raw data. An attention mechanism is applied in the network so that the model can be interpreted, assigning a weight to the influence of the prediction for each genome. Using two public real-life data-sets as well a simulated one, we demonstrated that this original approach reaches high performance, comparable with the state-of-the-art methods applied directly on processed data though mainstream bioinformatics workflows. These results are encouraging for this proof of concept work. We believe that with further dedication, the DNN models have the potential to surpass mainstream bioinformatics workflows in disease classification tasks.

Keywords: Metagenomics, phenotype prediction, deep learning, embeddings, multiple instance learning.

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Authors: Kazuhisa Koda, Tsutomu Kobayashi

Abstract:

Laura Island, which is located about 50 km away from downtown, is a source of water supply in Majuro atoll, which is the capital of the Republic of the Marshall Islands. Low and flat Majuro atoll has neither river nor lake. It is very important for Majuro atoll to ensure the conservation of its water resources. However, upconing, which is the process of partial rising of the freshwater-saltwater boundary near the water-supply well, was caused by the excess pumping from it during the severe drought in 1998. Upconing will make the water usage of the freshwater lens difficult. Thus, appropriate water usage is required to prevent up coning in the freshwater lens because there is no other water source during drought. Numerical simulation of water usage applying SEAWAT model was conducted at the central part of Laura Island, including the water supply well, which was affected by upconing. The freshwater lens was created as a result of infiltration of consistent average rainfall. The lens shape was almost the same as the one in 1985. 0 of monthly rainfall and variable daily pump discharge were used to calculate the sustainable pump discharge from the water supply well. Consequently, the total amount of pump discharge was increased as the daily pump discharge was increased, indicating that it needs more time to recover from upconing. Thus, a pump standard to reduce the pump intensity is being proposed, which is based on numerical simulation concerning the occurrence of the up-coning phenomenon in Laura Island during the drought.

Keywords: Freshwater lens, islands, numerical simulation, sustainable water use.

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Authors: F. Fekak, A. Gravouil, M. Brun, B. Depale

Abstract:

During an earthquake, a bridge crane may be subjected to multiple impacts between crane wheels and rail. In order to model such phenomena, a time-history dynamic analysis with a multi-scale approach is performed. The high frequency aspect of the impacts between wheels and rails is taken into account by a Lagrange explicit event-capturing algorithm based on a velocity-impulse formulation to resolve contacts and impacts. An implicit temporal scheme is used for the rest of the structure. The numerical coupling between the implicit and the explicit schemes is achieved with a heterogeneous asynchronous time-integrator.

Keywords: Earthquake, bridge crane, heterogeneous asynchronous time-integrator, impacts.

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Authors: Buntara Sthenly Gan

Abstract:

A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.

Keywords: Tensegrity, Form-finding, Design, Irregular, Self-stress, Force density method.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

Abstract:

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: M. Amoura, M. Alloti, A. Mouassi, N. Zeraibi

Abstract:

Heat transfer behavior of three different types of nanofluids flowing through a horizontal tube under laminar regime has been investigated numerically. The wall of tube is maintained at constant temperature. Al₂O₃-water, CuO-water and TiO₂-water are used with different Reynolds number and different volume fraction. The numerical results of heat transfer indicate that the Nusselt number of nanofluids is larger than that of the base fluid. The Pressure loss coefficient decreases by increasing Reynolds number for all types of nanofluids. Results of Nusselt number enhancement and pressure loss coefficient enhancement indicate that Al₂O₃ nanoparticules give the best results in term of thermal-hydrolic properties.

Keywords: Heat transfer, Laminar flow, Nanofluid, Numerical study.

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: S. Bennoud, M. Zergoug

Abstract:

The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models.

The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces.

The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations.

In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: Eddy current, Finite element method, Non destructive testing, Numerical simulations.

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Authors: V.Fathipour, M. A. Malakootian, S. Fathipour, M. Fathipour

Abstract:

In this paper we propose a novel RF LDMOS structure which employs a thin strained silicon layer at the top of the channel and the N-Drift region. The strain is induced by a relaxed Si0.8 Ge0.2 layer which is on top of a compositionally graded SiGe buffer. We explain the underlying physics of the device and compare the proposed device with a conventional LDMOS in terms of energy band diagram and carrier concentration. Numerical simulations of the proposed strained silicon laterally diffused MOS using a 2 dimensional device simulator indicate improvements in saturation and linear transconductance, current drivability, cut off frequency and on resistance. These improvements are however accompanied with a suppression in the break down voltage.

Keywords: High Frequency MOSFET, Design of RF LDMOS, Strained-Silicon, LDMOS.

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Authors: Arturo Ayala-Hernandez, Humberto H´ıjar

Abstract:

We propose a new alternative method for imposing fluid-solid boundary conditions in simulations of Multiparticle Collision Dynamics. Our method is based on the introduction of an explicit potential force acting between the fluid particles and a surface representing a solid boundary. We show that our method can be used in simulations of plane Poiseuille flows. Important quantities characterizing the flow and the fluid-solid interaction like the slip coefficient at the solid boundary and the effective viscosity of the fluid, are measured in terms of the set of independent parameters defining the numerical implementation. We find that our method can be used to simulate the correct hydrodynamic flow within a wide range of values of these parameters.

Keywords: Multiparticle Collision Dynamics, Fluid-Solid Boundary Conditions, Molecular Dynamics.

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Authors: Hassan A. Alshahrani, Mehdi H. Hojjati

Abstract:

In order to predict and model wrinkling which is caused by out of plane deformation due to compressive loading in the plane of the material during composite prepregs forming, it is necessary to quantitatively understand the relative magnitude of the bending stiffness. This study aims to examine the bending properties of out-of-autoclave (OOA) thermosetting prepreg under vertical cantilever test condition. A direct method for characterizing the bending behavior of composite prepregs was developed. The results from direct measurement were compared with results derived from an image-processing procedure that analyses the captured image during the vertical bending test. A numerical simulation was performed using ABAQUS to confirm the bending stiffness value.

Keywords: Bending stiffness, out of autoclave prepreg, forming process, numerical simulation.

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Authors: T. Benmiloud, A. Omari

Abstract:

This paper presents a new technique of compensation of the effect of variation parameters in the direct field oriented control of induction motor. The proposed method uses an adaptive tuning of the value of synchronous speed to obtain the robustness for the field oriented control. We show that this adaptive tuning allows having robustness for direct field oriented control to changes in rotor resistance, load torque and rotational speed. The effectiveness of the proposed control scheme is verified by numerical simulations. The numerical validation results of the proposed scheme have presented good performances compared to the usual direct-field oriented control.

Keywords: Induction motor, direct field-oriented control, compensation of variation parameters, fuzzy logic controller.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

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This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Ho Phu TRAN, Frédéric PLOURDE

Abstract:

The ongoing effort to develop an in-house compressible solver with multi-disciplinary physics is presented in this paper. Basic compressible solver combined with IBM technique provides us an effective numerical tool able to tackle the physics phenomena and especially physic phenomena involved in Solid Rocket Motors (SRMs). Main principles are introduced step by step describing its implementation. This paper sheds light on the whole potentiality of our proposed numerical model and we strongly believe a way to introduce multi-physics mechanisms strongly coupled is opened to ablation in nozzle, fluid/structure interaction and burning propellant surface with time.

Keywords: Compressible Flow, Immersed Boundary Method, Multi-disciplinary physics, Solid Rocket Motors.

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Authors: N. Kh. Gomidze, I. N. Jabnidze, K. A. Makharadze

Abstract:

The influence of inhomogeneities of plasma and statistical characteristics on the propagation of signal is very actual in wireless communication systems. While propagating in the media, the deformation and evaluation of the signal in time and space take place and on the receiver we get a deformed signal. The present article is dedicated to studying the space-time evolution of rectangular, sinusoidal, exponential and bi-exponential impulses via numerical experiment in the collisional, cold plasma. The presented method is not based on the Fourier-presentation of the signal. Analytically, we have received the general image depicting the space-time evolution of the radio impulse amplitude that gives an opportunity to analyze the concrete results in the case of primary impulse.

Keywords: Collisional, cold plasma, rectangular pulse signal, impulse envelope.

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Authors: Shinji Kajiwara

Abstract:

The spring-driven ball-type check valve is one of the most important components of hydraulic systems: it controls the position of the ball and prevents backward flow. To simplify the structure, the spring must be eliminated, and to accomplish this, the flow pattern and the behavior of the check ball in L-shaped pipe must be determined. In this paper, we present a full-scale model of a check ball made of acrylic resin, and we determine the relationship between the initial position of the ball, the position and diameter of the inflow port. The check flow rate increases in a standard center inflow model, and it is possible to greatly decrease the check-flow rate by shifting the inflow from the center.

Keywords: Hydraulics, Pipe Flow, Numerical Simulation, Flow Visualization, Check ball, L-shaped Pipe.

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Authors: Marco Raciti Castelli, Paolo Cioppa, Ernesto Benini

Abstract:

This paper presents a CFD analysis of the flow field around a thin flat plate of infinite span inclined at 90° to a fluid stream of infinite extent. Numerical predictions have been compared to experimental measurements, in order to assess the potential of the finite volume code of determining the aerodynamic forces acting on a bluff body invested by a fluid stream of infinite extent. Several turbulence models and spatial node distributions have been tested. Flow field characteristics in the neighborhood of the flat plate have been investigated, allowing the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and the corresponding turbulence model for the prediction of the flow field over a two-dimensional vertical flat plate.

Keywords: CFD, vertical flat plate, aerodynamic force

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Authors: Rakesh Arasu, Sasitharan Ambicapathy, Sivaraj Ponnusamy, Mohanraj Murugesan, V. R. Sanal Kumar

Abstract:

The flow field within the combustor of scramjet engine is very complex and poses a considerable challenge in the design and development of a supersonic combustor with an optimized geometry. In this paper comprehensive numerical studies on flow field characteristics of different cavity based scramjet combustors with transverse injection of hydrogen have been carried out for both non-reacting and reacting flows. The numerical studies have been carried out using a validated 2D unsteady, density based 1st-order implicit k-omega turbulence model with multi-component finite rate reacting species. The results show a wide variety of flow features resulting from the interactions between the injector flows, shock waves, boundary layers, and cavity flows. We conjectured that an optimized cavity is a good choice to stabilize the flame in the hypersonic flow, and it generates a recirculation zone in the scramjet combustor. We comprehended that the cavity based scramjet combustors having a bearing on the source of disturbance for the transverse jet oscillation, fuel/air mixing enhancement, and flameholding improvement. We concluded that cavity shape with backward facing step and 45o forward ramp is a good choice to get higher temperatures at the exit compared to other four models of scramjet combustors considered in this study.

Keywords: Flame holding, Hypersonic flow, Scramjet combustor, Supersonic combustor.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: M. Behbahani-Nejad, Y. Shekari

Abstract:

A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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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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