• Title/Summary/Keyword: surface integral method

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A Numerical Solution Method of the Boundary Integral Equation -Axisymmetric Flow- (경계적분방정식의 수치해법 -축대칭 유동-)

  • Chang-Gu,Kang
    • Bulletin of the Society of Naval Architects of Korea
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    • v.27 no.3
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    • pp.38-46
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    • 1990
  • A numerical solution method of the boundary integral equation for axisymmetric potential flows is presented. Those are represented by ring source and ring vorticity distribution. Strengths of ring source and ring vorticity are approximated by linear functions of a parameter $\zeta$ on a segment. The geometry of the body is represented by a cubic B-spline. Limiting integral expressions as the field point tends to the surface having ring source and ring vorticity distribution are derived upto the order of ${\zeta}ln{\zeta}$. In numerical calculations, the principal value integrals over the adjacent segments cancel each other exactly. Thus the singular part proportional to $\(\frac{1}{\zeta}\)$ can be subtracted off in the calculation of the induced velocity by singularities. And the terms proportional to $ln{\zeta}$ and ${\zeta}ln{\zeta}$ can be integrated analytically. Thus those are subtracted off in the numerical calculations and the numerical value obtained from the analytic integrations for $ln{\zeta}$ and ${\zeta}ln{\zeta}$ are added to the induced velocity. The four point Gaussian Quadrature formula was used to evaluate the higher order terms than ${\zeta}ln{\zeta}$ in the integration over the adjacent segments to the field points and the integral over the segments off the field points. The root mean square errors, $E_2$, are examined as a function of the number of nodes to determine convergence rates. The convergence rate of this method approaches 2.

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A Study on the Design of Ship′s Bow Form using Surface Panel Method (판요소법을 이용한 선수형상 설계에 관한 연구[1])

  • Jae-Hoon Yoo;Hyo-Chul Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.3
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    • pp.35-47
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    • 1996
  • A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

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Optimized Digital Proportional Integral Derivative Controller for Heating and Cooling Injection Molding System

  • Jeong, Byeong-Ho;Kim, Nam-Hoon;Lee, Kang-Yeon
    • Journal of Electrical Engineering and Technology
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    • v.10 no.3
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    • pp.1383-1388
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    • 2015
  • Proportional integral derivative (PID) control is one of the conventional control strategies. Industrial PID control has many options, tools, and parameters for dealing with the wide spectrum of difficulties and opportunities in manufacturing plants. It has a simple control structure that is easy to understand and relatively easy to tune. Injection mold is warming up to the idea of cycling the tool surface temperature during the molding cycle rather than keeping it constant. This “heating and cooling” process has rapidly gained popularity abroad. However, it has discovered that raising the mold wall temperature above the resin’s glass-transition or crystalline melting temperature during the filling stage is followed by rapid cooling and improved product performance in applications from automotive to packaging to optics. In previous studies, optimization methods were mainly selected on the basis of the subjective experience. Appropriate techniques are necessary to optimize the cooling channels for the injection mold. In this study, a digital signal processor (DSP)-based PID control system is applied to injection molding machines. The main aim of this study is to optimize the control of the proposed structure, including a digital PID control method with a DSP chip in the injection molding machine.

Modeling, Dynamic Analysis and Control Design of Full-Bridge LLC Resonant Converters with Sliding-Mode and PI Control Scheme

  • Zheng, Kai;Zhang, Guodong;Zhou, Dongfang;Li, Jianbing;Yin, Shaofeng
    • Journal of Power Electronics
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    • v.18 no.3
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    • pp.766-777
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    • 2018
  • In this paper, a sliding mode and proportional plus integral (SM-PI) control combined with self-sustained phase shift modulation (SSPSM) for LLC resonant converters is presented. The proposed control scheme improves the transient response while preserving good steady-state performance. An averaged large signal model of an LLC converter with the ZVS modulation technique is developed for the SM control design. The sliding surface is obtained based on the input-output linearization concept. A system identification method is adopted to obtain the transform function of the LLC resonant converter, which is used to design the PI control. In order to reduce the inherent chattering problem in the steady state, the combined SM-PI control strategy is derived with fuzzy control, where the SM control is responsive during the transient state while the PI control prevails in the steady state. The combination of SSPSM and the SM-PI control provides ZVS operation, robustness and a fast transient response against step load variations. Simulation and experimental results validate the theoretical analysis and the attractive features of the proposed scheme.

A Hybrid Boundary Integral Equation Model Applied for the Calculation of Normal Incident Waves (혼합경계적분 요소법을 사용한 직교입사파랑의 반사률계산 모델)

  • 서승남;김상익
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.3 no.3
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    • pp.170-175
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    • 1991
  • In order to calculate reflection coefficients of surface waves due to underwater obstacles, the hybrid boundary integral equation method is used. Numerical results based on the linear element are verified to the exact solutions for a flat bottom. Reflection coefficient and transmission coefficients for a step are compared to Young's results and the results by EFEM (Kirby et al., 1987), in which reflection coefficients decrease to zero as the periods of incident waves decrease. Reflection coefficients for a sinusiodal hump located on a constant depth increase due to the interaction between humps.

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Nonlinear Vortical Forced Oscillation of Floating Bodies (부유체의 대진폭 운동에 기인한 동유체력)

  • 이호영;황종흘
    • Journal of the Society of Naval Architects of Korea
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    • v.30 no.2
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    • pp.86-97
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    • 1993
  • A numerical method is developed for the nonlinear motion of two-dimensional wedges and axisymmetric-forced-heaving motion using Semi-Largrangian scheme under assumption of potential flows. In two-dimensional-problem Cauchy's integral theorem is applied to calculate the complex potential and its time derivative along boundary. In three-dimensional-problem Rankine ring sources are used in a Green's theorem boundary integral formulation to salve the field equation. The solution is stepped forward numerically in time by integrating the exact kinematic and dynamic free-surface boundary condition. Numerical computations are made for the entry of a wedge with a constant velocity and for the forced harmonic heaving motion from rest. The problem of the entry of wedge compared with the calculated results of Champan[4] and Kim[11]. By Fourier transform of forces in time domain, added mass coefficient, damping coefficient, second harmonic forces are obtained and compared with Yamashita's experiment[5].

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Examination of analytical and finite element solutions regarding contact of a functionally graded layer

  • Yaylaci, Murat;Adiyaman, Gokhan;Oner, Erdal;Birinci, Ahmet
    • Structural Engineering and Mechanics
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    • v.76 no.3
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    • pp.325-336
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    • 2020
  • In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.

New Monte-Carlo based simulation program suitable for low-energy ions irradiation in pure materials

  • Ghadeer H. Al-Malkawi;Al-Montaser Bellah A. Al-Ajlony;Khaled F. Al-Shboul;Ahmed Hassanein
    • Nuclear Engineering and Technology
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    • v.55 no.4
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    • pp.1287-1299
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    • 2023
  • A new Monte-Carlo-based computer program (RDS-BASIC) is developed to simulate the transport of energetic ions in pure matter. This computer program is utilizing an algorithm that uses detailed numerical solutions for the classical scattering integral for evaluating the outcomes of the binary collision processes. This approach is adopted by several prominent similar simulation programs and is known to provide results with higher accuracy compared to other approaches that use approximations to shorten the simulation time. Furthermore, RDS-BASIC simulation program contains special methods to reduce the displacement energy threshold of surface atoms. This implementation is found essential for accurate simulation results for sputtering yield in the case of very low energy ions irradiation (near sputtering energy threshold) and also successfully solve the problem of simultaneously obtaining an acceptable number of atomic displacements per incident ions. Results of our simulation for several irradiation systems are presented and compared with their respective TRIM (SRIM-2013) and the state-of-the-art SDTrimSP simulation results. Our sputtering simulation results were also compared with available experimental data. The simulation execution time for these different simulation programs has also been compared.

Enhance photoelectric efficiency of PV by optical-thermal management of nanofilm reflector

  • Liang, Huaxu;Wang, Baisheng;Su, Ronghua;Zhang, Ao;Wang, Fuqiang;Shuai, Yong
    • Advances in nano research
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    • v.13 no.5
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    • pp.475-485
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    • 2022
  • Crystalline silicon photovoltaic cells have advantages of zero pollution, large scale and high reliability. A major challenge is that sunlight wavelength with photon energy lower than semiconductor band gap is converted into heat and increase its temperature and reduce its conversion efficiency. Traditional cooling PV method is using water flowing below the modules to cool down PV temperature. In this paper, the idea is proposed to reduce the temperature of the module and improve the energy conversion efficiency of the module through the modulation of the solar spectrum. A spectrally selective nanofilm reflector located directly on the surface of PV is designed, which can reflect sunlight wavelength with low photon energy, and even enhance absorption of sunlight wavelength with high photon energy. The results indicate that nanofilm reflector can reduce spectral reflectivity integral from 9.0% to 6.93% in 400~1100 nm wavelength range, and improve spectral reflectivity integral from 23.1% to 78.34% in long wavelength range. The nanofilm reflector can reduce temperature of PV by 4.51℃ and relatively improved energy conversion efficiency of PV by 1.25% when solar irradiance is 1000 W/m2. Furthermore, the nanofilm reflector is insensitive in sunlight's angle and polarization state, and be suitable for high irradiance environment.

Super-Cavitating Flow Problems about Two-Dimensional Symmetric Strut (2차원 대칭 스트럿 주위의 초월 공동 유동 문제의 해석)

  • Y.G.,Kim;C.S.,Lee
    • Bulletin of the Society of Naval Architects of Korea
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    • v.27 no.4
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    • pp.15-26
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    • 1990
  • This paper describes a potential-baoed panel method formulated for the analysis cf a supercavitating two-dimensional symmetri strut. The method employs normal dipoles and sources distributed on the foil and cavity surfaces to represent the potential flow around the cavitating hydrofoil. The kinematic boundary condition on the wetted portion of the foil surface is satisfied by requiring that the total potential vanish in the fictitious inner flow region of the foil, and the dynamic boundary condition on the cavity surface is satisfied by requiring that the potential vary linearly, i.e., the tangential velocity be constant. Green's theorem then results in a potential-based integral equation rather than the usual velocity-based formulation of Hess & Smith type, With the singularities distributed on the exact hydrofoil surface, the pressure distributions are predicted with improved accuracy compared to those of the linearized lifting surface theory, especially near the leading edge. The theory then predicts the cavity shape and cavitation number for an assumed cavity length. To improve the accuracy, the sources and dipoles on the cavity surface are moved to the newly computed cavity surface, where the boundary conditions are satisfied again. This iteration process is repeated until the results are converged.

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