• Journal of computational fluids engineering
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• v.21 no.1
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• pp.94-102
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• 2016

The present paper deals with accuracy improvement of a bleed boundary condition model used to improve the performance of supersonic inlets. In order to accurately predict the amount of bleed mass flow rates, this study performs a scaling of sonic flow coefficient data for 90-degree bleed holes in consideration of Prandtl-Meyer expansion theory. Furthermore, it is assumed that porosity varies with stream-wise location of the porous bleed plate to accurately predict downstream boundary layer profiles. The bleed boundary condition model is demonstrated through Computational Fluid Dynamics(CFD) simulations of bleed flows on a flat plate with/without an oblique shock. As a result, the bleed model shows the improved accuracy of bleed mass rates and downstream boundary layer profiles.

• International Journal of Advanced Culture Technology
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• v.6 no.3
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• pp.173-177
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• 2018

Masks are generated by adding different fonts of learning data characters in pixel unit, and pixel values belonging to each of the masks are divided into 3 groups. Using the directional expansion operators, we expand the text area of the test data character into 4 diagonal directions in order to create the boundary areas to distinguish it from the background area. A mask with a minimum average discordance is selected as the final recognition result by calculating the degree of discordance between the expanded test data and the masks. Image comparison using directional expansion operations more accurately recognizes test data through 4 subdivided recognition processes. It is also possible to expand the ranges of 3 groups of pixel values of masks more evenly such that new fonts can easily be added to the given learning data.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• International Journal of Aeronautical and Space Sciences
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• v.6 no.1
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• pp.1-7
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• 2005

The inlet boundary condition of computations about the supersonic turbine flow is commonly applied as far-field inlet boundary condition with specified velocity. However, the inflow condition of supersonic turbine is sometimes affected by the shocks or expansion waves propagated from leading edges of blade. These shocks and expansion waves alter the inlet boundary condition. In this case, the inlet boundary condition can not be specified Therefore, in this paper, numerical analyses for three different inlet conditions - fa-field inlet boundary condition, inlet boundary condition with a linear nozzle and inlet boundary condition with a converging-diverging nozzle - have been performed and compared with experimental results to solve the problem. It is found that the inlet condition with a linear nozzle or a converging-diverging nozzle can prevent changing of inlet boundary condition, and thus predict more accurately the supersonic flow within turbine cascade than a far-field inlet boundary condition does.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.14 no.4
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• pp.293-299
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• 1985

This paper describes an economical prediction procedure for heat transfer phenomenon through a channel containing an abrupt asymmetric expansion in flow cross-seetional area. Numerical solutions for the flow field are obtained by the finite difference numerical method applied to the modified boundary layer equations. Modified boundary energy equation is used to analyze heat transfer as modified boundary momentum equation. Predictions of the method compare very favorable with exprimental data. Results of this study by modified boundary layer equation are as follows : 1. The computation time required for the scheme is at least an order of magnitude less than for the numerical solution of the full Navier-stokes and Energy eguations. 2. In laminar flow, the maximum heat transfer occurs downstream of the reattachment point.

• Journal of the Korean Ceramic Society
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• v.40 no.2
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• pp.109-112
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• 2003

The grain-boundary microcracking materials in the system $Al_2$TiO$_{5}$ -ZrTiO$_4$(ZAT) is influenced by the thermal expansion anisotropy. The range of ZAT compositions investigated had showed very low thermal expansions of 0.3~1.3$\times$10$^{-6}$ K loin compared to 8.29$\times$10$^{6}$ K of pure ZrTiO$_4$and 0.68$\times$10$^{6}$ K of polycrystalline $Al_2$TiO$_{5}$ , respectively, compared with the theoretical thermal expansion coefficient for a single crystal of $Al_2$TiO$_{5}$ , 9.70$\times$10$^{6}$ K. The low thermal expansion and microcraking temperature are apparently due to a combination of thermal contraction and expansion caused by the large thermal expansion anisotropy of the crystal a ies of the $Al_2$TiO$_{5}$ phase.

• Journal of the Korean Ceramic Society
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• v.40 no.3
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• pp.317-321
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• 2003

The grain-boundary microcracking materials in the system A1$_2$Ti $O_{5}$ -ZrTi $O_4$(ZAT) is influenced by the thermal expansion anisotropy. The range of ZAT compositions investigated had showed very low thermal expansions of 0.3~1.3$\times$10$^{-6}$K compared to 8.29$\times$10$^{-6}$K of pure ZrTi $O_4$and 0.68$\times$10$^{-6}$K of polycrystalline A1$_2$Ti $O_{5}$ , respectively, compared with the theoretical thermal expansion coefficient for a single crystal of A1$_2$Ti $O_{5}$ , 9.70$\times$10$^{-6}$K. The low thermal expansion and microcraking temperature are apparently due to a combination of thermal contraction and expansion caused by the large thermal expansion anisotropy of the crystal axes of the A1$_2$Ti $O_{5}$ phase.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of KSNVE
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• v.4 no.2
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.