Search results for: Two dimensional boundary value problems

Authors: V.Pavlika

Abstract:

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.

Keywords: Inverse problem, irrotational incompressible flow, Boundary value problem.

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Authors: Siti Khuzaimah Soid, Zanariah Mohd Yusof, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

A steady two-dimensional magnetohydrodynamics flow and heat transfer over a stretching vertical sheet influenced by radiation and porosity is studied. The governing boundary layer equations of partial differential equations are reduced to a system of ordinary differential equations using similarity transformation. The system is solved numerically by using a finite difference scheme known as the Keller-box method for some values of parameters, namely the radiation parameter N, magnetic parameter M, buoyancy parameter l , Prandtl number Pr and permeability parameter K. The effects of the parameters on the heat transfer characteristics are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M and permeability parameter K increase. Heat transfer rate at the surface decreases as the radiation parameter increases.

Keywords: Keller-box, MHD boundary layer flow, permeability stretching.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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Authors: Sylvain Amailland, Jean-Hugh Thomas, Charles Pézerat, Romuald Boucheron, Jean-Claude Pascal

Abstract:

The noise requirements for naval and research vessels have seen an increasing demand for quieter ships in order to fulfil current regulations and to reduce the effects on marine life. Hence, new methods dedicated to the characterization of propeller noise, which is the main source of noise in the far-field, are needed. The study of cavitating propellers in closed-section is interesting for analyzing hydrodynamic performance but could involve significant difficulties for hydroacoustic study, especially due to reverberation and boundary layer noise in the tunnel. The aim of this paper is to present a numerical methodology for the identification of hydroacoustic sources on marine propellers using hydrophone arrays in a large hydrodynamic tunnel. The main difficulties are linked to the reverberation of the tunnel and the boundary layer noise that strongly reduce the signal-to-noise ratio. In this paper it is proposed to estimate the reflection coefficients using an inverse method and some reference transfer functions measured in the tunnel. This approach allows to reduce the uncertainties of the propagation model used in the inverse problem. In order to reduce the boundary layer noise, a cleaning algorithm taking advantage of the low rank and sparse structure of the cross-spectrum matrices of the acoustic and the boundary layer noise is presented. This approach allows to recover the acoustic signal even well under the boundary layer noise. The improvement brought by this method is visible on acoustic maps resulting from beamforming and DAMAS algorithms.

Keywords: Acoustic imaging, boundary layer noise denoising, inverse problems, model adaptation.

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Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: Analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition.

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Authors: Antonio Breda d’Azevedo

Abstract:

Regularity has often been present in the form of regular polyhedra or tessellations; classical examples are the nine regular polyhedra consisting of the five Platonic solids (regular convex polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes can be seen as regular maps. Maps are cellular embeddings of graphs (with possibly multiple edges, loops or dangling edges) on compact connected (closed) surfaces with or without boundary. The n-dimensional abstract polytopes, particularly the regular ones, have gained popularity over recent years. The main focus of research has been their symmetries and regularity. Planification of polyhedra helps its spatial construction, yet it destroys its symmetries. To our knowledge there is no “planification” for n-dimensional polytopes. However we show that it is possible to make a “surfacification” of the n-dimensional polytope, that is, it is possible to construct a restrictedly-marked map representation of the abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. We also show that there are infinitely many ways to do this; yet there is one that is more natural that describes reflections on the sides ((n−1)-faces) of n-simplices with reflections on the sides of n-polygons. We illustrate this construction with the 4-tetrahedron (a regular 4-polytope with automorphism group of size 120) and the 4-cube (a regular 4-polytope with automorphism group of size 384).

Keywords: Maps, representation, polytopes.

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Authors: Christian H. Sanabria-Montaña, Rodrigo Huerta-Quintanilla

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A lattice network is a special type of network in which all nodes have the same number of links, and its boundary conditions are periodic. The most basic lattice network is the ring, a one-dimensional network with periodic border conditions. In contrast, the Cartesian product of d rings forms a d-dimensional lattice network. An analytical expression currently exists for the clustering coefficient in this type of network, but the theoretical value is valid only up to certain connectivity value; in other words, the analytical expression is incomplete. Here we obtain analytically the clustering coefficient expression in d-dimensional lattice networks for any link density. Our analytical results show that the clustering coefficient for a lattice network with density of links that tend to 1, leads to the value of the clustering coefficient of a fully connected network. We developed a model on criminology in which the generalized clustering coefficient expression is applied. The model states that delinquents learn the know-how of crime business by sharing knowledge, directly or indirectly, with their friends of the gang. This generalization shed light on the network properties, which is important to develop new models in different fields where network structure plays an important role in the system dynamic, such as criminology, evolutionary game theory, econophysics, among others.

Keywords: Clustering coefficient, criminology, generalized, regular network d-dimensional.

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Authors: A. Shahsavari, M. Nili-Ahmadabadi

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This paper presents an innovative one-dimensional optimization of a transonic compressor based on the radial equilibrium theory by means of increasing blade loading. Firstly, the rotor blade of the transonic compressor is redesigned based on the constant span-wise deHaller number and diffusion. The code is applied to extract compressor meridional plane and blade to blade geometry containing rotor and stator in order to design blade three-dimensional view. A structured grid is generated for the numerical domain of fluid. Finer grids are used for regions near walls to capture boundary layer effects and behavior. RANS equations are solved by finite volume method for rotating zones (rotor) and stationary zones (stator). The experimental data, available for the performance map of NASA Rotor67, is used to validate the results of simulations. Then, the capability of the design method is validated by CFD that is capable of predicting the performance map. The numerical results of new geometry show about 19% increase in pressure ratio and 11% improvement in overall efficiency of the transonic stage; however, the design point mass flow rate of the new compressor is 5.7% less than that of the original compressor.

Keywords: One dimensional design, deHaller number, radial equilibrium, transonic compressor.

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Authors: Mustafa Resa Becan

Abstract:

The performance of a type of fuzzy sliding mode control is researched by considering the nonlinear characteristic of a missile-target interception problem to obtain a robust interception process. The variable boundary layer by using fuzzy logic is proposed to reduce the chattering around the switching surface then is applied to the interception model which was derived. The performances of the sliding mode control with constant and fuzzy boundary layer are compared at the end of the study and the results are evaluated.

Keywords: Sliding mode control, fuzzy, boundary layer, interception problem.

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Authors: U. Yerlikaya, R. T. Balkan

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In this research, a method is developed to obtain high-dimensional configuration space for path planning problems. In typical cases, the path planning problems are solved directly in the 3-dimensional (D) workspace. However, this method is inefficient in handling the robots with various geometrical and mechanical restrictions. To overcome these difficulties, path planning may be formalized and solved in a new space which is called configuration space. The number of dimensions of the configuration space comes from the degree of freedoms of the system of interest. The method can be applied in two ways. In the first way, the point clouds of all the bodies of the system and interaction of them are used. The second way is performed via using the clearance function of simulation software where the minimum distances between surfaces of bodies are simultaneously measured. A double-turret system is held in the scope of this study. The 4-D configuration space of a double-turret system is obtained in these two ways. As a result, the difference between these two methods is around 1%, depending on the density of the point cloud. The disparity between the two forms steadily decreases as the point cloud density increases. At the end of the study, in order to verify 4-D configuration space obtained, 4-D path planning problem was realized as 2-D + 2-D and a sample path planning is carried out with using A* algorithm. Then, the accuracy of the configuration space is proved using the obtained paths on the simulation model of the double-turret system.

Keywords: A* Algorithm, autonomous turrets, high-dimensional C-Space, manifold C-Space, point clouds.

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Authors: Saeed Sarabadan, Kamal Rashedi

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This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: Rumena D. Stancheva, Ilona I. Iatcheva

Abstract:

In working mode some unexpected changes could be arise in inner structure of electromagnetic device. They influence modification in electromagnetic field propagation map. The field values at an observed boundary are also changed. The development of the process has to be watched because the arising structural changes would provoke the device to be gone out later. The probabilistic assessment of the state is possible to be made. The numerical assessment points if the resulting changes have only accidental character or they are due to the essential inner structural disturbances. The presented application example is referring to the 200MW turbine-generator. A part of the stator core end teeth zone is simulated broken. Quasi three-dimensional electromagnetic and temperature field are solved applying FEM. The stator core state diagnosis is proposed to be solved as an identification problem on the basis of a statistical criterion.

Keywords: Identification, structural disturbance, statistical criterion.

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Authors: Naoki Yamamoto, Jun Murakami, Chiharu Okuma, Yutaro Shigeto, Satoko Saito, Takashi Izumi, Nozomi Hayashida

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Multi-dimensional principal component analysis (PCA) is the extension of the PCA, which is used widely as the dimensionality reduction technique in multivariate data analysis, to handle multi-dimensional data. To calculate the PCA the singular value decomposition (SVD) is commonly employed by the reason of its numerical stability. The multi-dimensional PCA can be calculated by using the higher-order SVD (HOSVD), which is proposed by Lathauwer et al., similarly with the case of ordinary PCA. In this paper, we apply the multi-dimensional PCA to the multi-dimensional medical data including the functional independence measure (FIM) score, and describe the results of experimental analysis.

Keywords: multi-dimensional principal component analysis, higher-order SVD (HOSVD), functional independence measure (FIM), medical data, tensor decomposition

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Authors: Arturo Ayala-Hernandez, Humberto H´ıjar

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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: M. Ashaque Meah, Md. Fazlul Karim, M. Shah Noor, Nazmun Nahar Papri, M. Khalid Hossen, M. Ismoen

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Tsunami and inundation modelling due to far field tsunami propagation in a limited area is a very challenging numerical task because it involves many aspects such as the formation of various types of waves and the irregularities of coastal boundaries. To compute the effect of far field tsunami and extent of inland inundation due to far field tsunami along the coastal belts of west coast of Malaysia and Southern Thailand, a formulated boundary condition and a moving boundary condition are simultaneously used. In this study, a boundary fitted curvilinear grid system is used in order to incorporate the coastal and island boundaries accurately as the boundaries of the model domain are curvilinear in nature and the bending is high. The tsunami response of the event 26 December 2004 along the west open boundary of the model domain is computed to simulate the effect of far field tsunami. Based on the data of the tsunami source at the west open boundary of the model domain, a boundary condition is formulated and applied to simulate the tsunami response along the coastal and island boundaries. During the simulation process, a moving boundary condition is initiated instead of fixed vertical seaside wall. The extent of inland inundation and tsunami propagation pattern are computed. Some comparisons are carried out to test the validation of the simultaneous use of the two boundary conditions. All simulations show excellent agreement with the data of observation.

Keywords: Open boundary condition, moving boundary condition, boundary-fitted curvilinear grids, far field tsunami, Shallow Water Equations, tsunami source, Indonesian tsunami of 2004.

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Authors: Nopparat Pochai, Rujira Deepana

Abstract:

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: J. Sulaiman, M. Othman, M. K. Hasan

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Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Keywords: MEG iteration, second-order finite difference, weighted parameter.

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Authors: Rachid Ahdid, Khaddouj Taifi, Said Safi, Bouzid Manaut

Abstract:

Automatic detection of facial feature points plays an important role in applications such as facial feature tracking, human-machine interaction and face recognition. The majority of facial feature points detection methods using two-dimensional or three-dimensional data are covered in existing survey papers. In this article chosen approaches to the facial features detection have been gathered and described. This overview focuses on the class of researches exploiting facial feature points detection to represent facial surface for two-dimensional or three-dimensional face. In the conclusion, we discusses advantages and disadvantages of the presented algorithms.

Keywords: Facial feature points, face recognition, facial feature tracking, two-dimensional data, three-dimensional data.

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Authors: Tomasz M. Jankowski

Abstract:

The basis of this paper is the assumption, that graviton is a measurable entity of molecular gravitational acceleration and this is not a hypothetical entity. The adoption of this assumption as an axiom is tantamount to fully opening the previously locked door to the boundary theory between laminar and turbulent flows. It leads to the theorem, that the division of flows of Newtonian (viscous) fluids into laminar and turbulent is true only, if the fluid is influenced by a powerful, external force field. The mathematical interpretation of this theorem, presented in this paper shows, that the boundary between laminar and turbulent flow can be determined theoretically. This is a novelty, because thus far the said boundary was determined empirically only and the reasons for its existence were unknown.

Keywords: Freed gravitons, free gravitons.

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: Tayeb Bensattalah, Mohamed Zidour, Mohamed Ait Amar Meziane, Tahar Hassaine Daouadji, Abdelouahed Tounsi

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In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Influence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.

Keywords: Boundary conditions, buckling, non-local, the differential transform method.

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Authors: Ali Ghobadi, Seyed Mohammad Javadi, Behnam Rahimi

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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: Gabriela R. Fernandes, Danilo H. Konda, Luiz C. F. Sanches

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In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner?s hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

Keywords: Boundary elements, Building floor structures, Platebending.

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Authors: Yasuo Obikane

Abstract:

The frequency dependence of the phase field model(PFM) is studied. A simple PFM is proposed, and is tested in a laminar boundary layer. The Blasius-s laminar boundary layer solution on a flat plate is used for the flow pattern, and several frequencies are imposed on the PFM, and the decay times of the interfaces are obtained. The computations were conducted for three cases: 1) no-flow, and 2) a half ball on the laminar boundary layer, 3) a line of mass sources in the laminar boundary layer. The computations show the decay time becomes shorter as the frequency goes larger, and also show that it is sensitive to both background disturbances and surface tension parameters. It is concluded that the proposed simple PFM can describe the properties of decay process, and could give the fundamentals for the decay of the interface in turbulent flows.

Keywords: Phase field model, two phase flows, Laminarboundary Layer

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Authors: G. Sarojamma, K. Vendabai

Abstract:

An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: Casson nanofluid, Boundary layer flow, Internal heat generation/absorption, Exponentially stretching cylinder, Heat transfer, Brownian motion, Thermophoresis.

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Authors: Makoto Sakamoto, Yasuo Uchida, Makoto Nagatomo, Takao Ito, Tsunehiro Yoshinaga, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani

Abstract:

In theoretical computer science, the Turing machine has played a number of important roles in understanding and exploiting basic concepts and mechanisms in computing and information processing [20]. It is a simple mathematical model of computers [9]. After that, M.Blum and C.Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern processing, and investigated their pattern recognition abilities in 1967 [7]. Since then, a lot of researchers in this field have been investigating many properties about automata on a two- or three-dimensional tape. On the other hand, the question of whether processing fourdimensional digital patterns is much more difficult than two- or threedimensional ones is of great interest from the theoretical and practical standpoints. Thus, the study of four-dimensional automata as a computasional model of four-dimensional pattern processing has been meaningful [8]-[19],[21]. This paper introduces a cooperating system of four-dimensional finite automata as one model of four-dimensional automata. A cooperating system of four-dimensional finite automata consists of a finite number of four-dimensional finite automata and a four-dimensional input tape where these finite automata work independently (in parallel). Those finite automata whose input heads scan the same cell of the input tape can communicate with each other, that is, every finite automaton is allowed to know the internal states of other finite automata on the same cell it is scanning at the moment. In this paper, we mainly investigate some accepting powers of a cooperating system of eight- or seven-way four-dimensional finite automata. The seven-way four-dimensional finite automaton is an eight-way four-dimensional finite automaton whose input head can move east, west, south, north, up, down, or in the fu-ture, but not in the past on a four-dimensional input tape.

Keywords: computational complexity, cooperating system, finite automaton, four-dimension, hierarchy, multihead.

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Authors: N. K. Singh, S. Sarkar

Abstract:

Direct numerical simulation (DNS) is used to study the evolution of a boundary layer that was laminar initially followed by separation and then reattachment owing to generation of turbulence. This creates a closed region of recirculation, known as the laminar-separation bubble. The present simulation emulates the flow environment encountered in a modern LP turbine blade, where a laminar separation bubble may occur on the suction surface. The unsteady, incompressible three-dimensional (3-D) Navier-Stokes (NS) equations have been solved over a flat plate in the Cartesian coordinates. The adverse pressure gradient, which causes the flow to separate, is created by a boundary condition. The separated shear layer undergoes transition through appearance of ╬ø vortices, stretching of these create longitudinal streaks. Breakdown of the streaks into small and irregular structures makes the flow turbulent downstream.

Keywords: Adverse pressure gradient, direct numerical simulation, laminar separation bubble.

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Authors: Arpiruk Hokpunna, Michael Manhart

Abstract:

We present a Large-Eddy simulation of a vortex cell with circular shaped. The results show that the flow field can be sub divided into four important zones, the shear layer above the cavity, the stagnation zone, the vortex core in the cavity and the boundary layer along the wall of the cavity. It is shown that the vortex core consits of solid body rotation without much turbulence activity. The vortex is mainly driven by high energy packets that are driven into the cavity from the stagnation point region and by entrainment of fluid from the cavity into the shear layer. The physics in the boundary layer along the cavity-s wall seems to be far from that of a canonical boundary layer which might be a crucial point for modelling this flow.

Keywords: Turbulent flow, Large eddy simulations, boundary layer and cavity flow, vortex cell flow.

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Authors: A. M. Tahsini

Abstract:

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

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

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Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

Abstract:

The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

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