• 제목/요약/키워드: Steady state solutions

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Head Slider Designs Using Approximation Methods

  • Yoon, Sang-Joon;Park, Dong-Hoon
    • Journal of Mechanical Science and Technology
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    • 제18권1호
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    • pp.37-44
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    • 2004
  • This paper presents an approach to optimally design the air bearing surface (ABS) of the head slider by using the approximation methods. The reduced basis concept is used to reduce the number of design variables. In the numerical calculation, the progressive quadratic response surface modeling (PQRSM) is used to handle the non-smooth and discontinuous cost function. A multi-criteria optimization problem is formulated to enhance the flying performances over the entire recording band during the steady state and track seek operations. The optimal solutions of the sliders, whose target flying heights are 12 nm and 9 nm, are automatically obtained. The flying heights during the steady state operation become closer to the target values and the flying height variations during the track seek operation are smaller than those for the initial one. The pitch and roll angles are also kept within suitable ranges over the recording band.

하향유동 영역에서 경사 등온평면에 의하여 야기된 정상상태 자연대류의 다중해 (Multiple Solutions for Steady State Natural Convection adjacent to an Inclined Isothermal Flat Plate in the Region of Largely Downflow)

  • 유갑종;이택식;조승환
    • 대한기계학회논문집
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    • 제15권3호
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    • pp.1011-1020
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    • 1991
  • 본 연구에서는 하향유동영역에서 수직면으로부터 경사각이 60˚ 이하인 경사 등온면이 저온의 물속에 잠겨 있을때 일어나는 다중정상상태 영역을 밝혀내고, 이 영 역에서 경사각이 열전달, 온도분포, 속도분포, 부력분포 및 누셀트 수에 미치는 영향 을 구명하였다. 또 해석방법은 이제까지 발표된 연구결과와 비교검토하기 위하여 기 존 논문에서와 같이 상이해석을 사용하였다.

Prediction of solute rejection and modelling of steady-state concentration polarisation effects in pressure-driven membrane filtration using computational fluid dynamics

  • Keir, Greg;Jegatheesan, Veeriah
    • Membrane and Water Treatment
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    • 제3권2호
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    • pp.77-98
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    • 2012
  • A two-dimensional (2D) steady state numerical model of concentration polarisation (CP) phenomena in a membrane channel has been developed using the commercially available computational fluid dynamics (CFD) package CFX (Ansys, Inc., USA). The model incorporates the transmembrane pressure (TMP), axially variable permeate flux, variable diffusivity and viscosity, and osmotic pressure effects. The model has been verified against several benchmark analytical and empirical solutions from the membrane literature. Additionally, the model is able to predict the rejection of an arbitrary solute by the membrane using a pore model, given some basic knowledge of the geometry of the solute molecule or particle, and the membrane pore geometry. This allows for predictive design of membrane systems without experimental determination of the membrane rejection for the specified operating conditions. A demonstration of the model is presented against experimental results for two uncharged test compounds (sucrose and PEG1000) from the literature. The model will be extended to incorporate charge effects, transient simulations, three-dimensional (3D) geometry and turbulent effects in future work.

CONVERGENCE AND DECAY ESTIMATES FOR A NON-AUTONOMOUS DISPERSIVE-DISSIPATIVE EQUATION WITH TIME-DEPENDENT COEFFICIENTS

  • Kim, Eun-Seok
    • 호남수학학술지
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    • 제44권2호
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    • pp.281-295
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    • 2022
  • This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.

회전축 정렬불량을 고려한 유연회전디스크의 진동해석 (Vibration Analysis of a Flexible Spinning Disk Considering the effect of Misalignment)

  • 정진태;허진욱;최기영
    • 대한기계학회논문집A
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    • 제26권5호
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    • pp.952-959
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    • 2002
  • The natural frequencies of a flexible spinning disk misaligned with the axis of rotation are studied in an analytic manner. The effects of misalignment on the natural frequency need to be investigated, because the misalignment between the axis of symmetry and the axis of relation cannot be avoided in the removable disks such as CD-R, CD-RW or DVD disks. Assuming that the in -plane displacements are in steady state and the out-of-plane displacement is in dynamic state, the equations of motion are derived for the misaligned spinning disk. After the exact solutions are obtained fur the steady -state in-plane displacements, they are plugged into the equation for the dynamic-state out-of-plane motion. The resultant equation is a linear equation for the out -of-plane displacement, which is discretized by the Galerkin method. Based on the discretized dquations, the effects of the misalignment are analyzed on the vibration characteristics of the spinning disk, i.e., the natural frequencies and the critical speed.

회전축 정렬불량을 가지는 유연 회전디스크의 고유치 해석 (Natural Frequencies of a Spinning Disk Misaligned with the Axis of Rotation)

  • 허진욱;정진태;김원석
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2001년도 추계학술대회논문집 II
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    • pp.817-825
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    • 2001
  • The natural frequencies of a flexible spinning disk misaligned with the axis of rotation are studied in an analytic manner. The effects of misalignment on the natural frequency need to be investigated, because the misalignment between the axis of symmetry and the axis of rotation cannot be avoided in the removable disks such as CD-R, CD-RW or DVD disks. Assuming that the in-plane displacements are in steady state and the out-of-plane displacement is in dynamic state, the equations of motion are derived for the misaligned spinning disk. After the exact solutions are obtained for the steady-state in-plane displacements, they are plugged into the equation for the dynamic-state out-of-plane motion. The resultant equation is a linear equation for the out-of-plane displacement, which is discretized by the Galerkin method. Based on the discretized equations, the effects of the misalignment are analyzed on the vibration characteristics of the spinning disk, i.e., the natural frequencies and the critical speed

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천이상태에 있는 커스프균열에 대한 열응력세기계수의 경계요소 해석 (Boundary Element Analysis of Thermal Stress Intensity Factors for Cusp Crack in Transient State)

  • 이강용;홍정균
    • 대한기계학회논문집
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    • 제16권9호
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    • pp.1700-1710
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    • 1992
  • 본 연구에서는 경계요소법에 의해 천이상태 열전도문제를 해석하는 프로그램 과 Sladek등이 제안한 열탄성 경계적분방정식을 기초로 하여 열탄성문제를 해석하는 프로그램을 개발하여, 유한체 내에 존재하는 Griffith 균열에 대해 정상 및 천이상태 에서 계산한 열응력세기계수와 유한체 내에 존재하는 대칭 입술형 커스프균열(symme- tric lip cusp crack)에 대해 정상상태에서 열응력세기계수를 계산한다. 그 결과를 기존의 해와 비교하여 프로그램의 타당성을 입증한다. 그후 대칭 입술형 커스프균열 에 대한 천이상태에서의 열응력세기계수를 계산하고자 한다.

시동 특성, 수소 생산 및 선택성 향상을 위한 자열개질기의 이론 및 수치해석적 연구 (Theoretical and numerical study to investigate characteristics of light-off and steady state of methane autothermal reactor for efficient light-off, high hydrogen yield and selectivity)

  • 이신구;배중면
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2007년도 춘계학술대회B
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    • pp.3353-3358
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    • 2007
  • The present paper is devoted to investigate dynamic effect and steady-state performance of methane autothermal reformer theoretically and numerically. In order to simplify the complicated phenomena in the system, axisymmetric heterogeneous reactor model is developed. As autothermal reaction takes places on catalyst surface between bulk gas and catalyst, volume averaging method is incorporated using porous medium approach. To understand the start-up process which occurs in the reactor is highly important. Therefore, in this paper we get various goverining equations to find out transient and steady solutions and time scale for start-up introducing dimensionless variables. Start-up is a significant issue in reforming reaction for automobile system and fueling of SOFC-based auxiliary power units. This paper deals with characteristics of heat and mass transfer and predicted light-off time in the reformer as oxygen to carbon ratio ($O_2$/C) and amount of feeding gas.

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Development and validation of multiphysics PWR core simulator KANT

  • Taesuk Oh;Yunseok Jeong;Husam Khalefih;Yonghee Kim
    • Nuclear Engineering and Technology
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    • 제55권6호
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    • pp.2230-2245
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    • 2023
  • KANT (KAIST Advanced Nuclear Tachygraphy) is a PWR core simulator recently developed at Korea Advance Institute of Science and Technology, which solves three-dimensional steady-state and transient multigroup neutron diffusion equations under Cartesian geometries alongside the incorporation of thermal-hydraulics feedback effect for multi-physics calculation. It utilizes the standard Nodal Expansion Method (NEM) accelerated with various Coarse Mesh Finite Difference (CMFD) methods for neutronics calculation. For thermal-hydraulics (TH) calculation, a single-phase flow model and a one-dimensional cylindrical fuel rod heat conduction model are employed. The time-dependent neutronics and TH calculations are numerically solved through an implicit Euler scheme, where a detailed coupling strategy is presented in this paper alongside a description of nodal equivalence, macroscopic depletion, and pin power reconstruction. For validation of the steady, transient, and depletion calculation with pin power reconstruction capacity of KANT, solutions for various benchmark problems are presented. The IAEA 3-D PWR and 4-group KOEBERG problems were considered for the steady-state reactor benchmark problem. For transient calculations, LMW (Lagenbuch, Maurer and Werner) LWR and NEACRP 3-D PWR benchmarks were solved, where the latter problem includes thermal-hydraulics feedback. For macroscopic depletion with pin power reconstruction, a small PWR problem modified with KAIST benchmark model was solved. For validation of the multi-physics analysis capability of KANT concerning large-sized PWRs, the BEAVRS Cycle1 benchmark has been considered. It was found that KANT solutions are accurate and consistent compared to other published works.

해안지하수개발 최적화수치모델과 해석해의 비교연구 (Comparison of a Groundwater Simulation-Optimization Numerical Model with the Analytical Solutions)

  • 시뢰;최뢰;이찬종;박남식
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 2009년도 학술발표회 초록집
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    • pp.905-908
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    • 2009
  • In the management of groundwater in coastal areas, saltwater intrusion associated with extensive groundwater pumping, is an important problem. The groundwater optimization model is an advanced method to study the aquifer and decide the optimal pumping rates or optimal well locations. Cheng and Park gave the analytical solutions to the optimization problems basing on Strack's analytical solution. However, the analytical solutions have some limitations of the property of aquifer, boundary conditions, and so on. A simulation-optimization numerical method presented in this study can deal with non-homogenous aquifers and various complex boundary conditions. This simulation-optimization model includes the sharp interface solution which solves the same governing equation with Strack's analytical solution, therefore, the freshwater head and saltwater thickness should be in the same conditions, that can lead to the comparable results in optimal pumping rates and optimal well locations for both of the solutions. It is noticed that the analytical solutions can only be applied on the infinite domain aquifer, while it is impossible to get a numerical model with infinite domain. To compare the numerical model with the analytical solutions, calculation of the equivalent boundary flux was planted into the numerical model so that the numerical model can have the same conditions in steady state with analytical solutions.

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