• 대한설비공학회지:설비저널
• /
• 제7권1호
• /
• pp.4-12
• /
• 1978

At Grashof numbers $10^{10},\;5{\times}10^{10}$, and $10^{11}$ nonlinear partial differential equations for two dimensional thermal circulation of air in a rectangular enclosure heated from below are solved numerically by finite difference explicit methood in time-dependent form. Two vertical walls and ceiling are held at low temperature and floor at high temperture. Results are compared with From's numerical solutions at $10^9{\lesssim}\;N_{Gr}\;<10^{13}$. The effective draft temperature fields are also obtained to examine cold draft problem, there included a line of constant effective draft temperature $-1.667^{\circ}C$ which is essentially Houghten's $80\%$ comfort data.

• Advances in nano research
• /
• 제8권3호
• /
• pp.245-254
• /
• 2020

This work examines the fundamental vibrational characteristics of a spinning CNT-based nano-rotor assuming a nonlocal elasticity Euler-Bernoulli beam theory. The rotary inertia, gyroscopic, and rotor mass unbalance effects are all taken into consideration in the beam model. Assuming a nonlocal theory, two coupled 6th-order partial differential equations governing the vibration of the rotating SWCNT are first derived. In order to acquire the natural frequencies and dynamic response of the nano-rotor system, the nonlinear equations of motion are numerically solved. The nano-rotor system frequency spectrum is shown to exhibit two distinct frequencies: one positive and one negative. The positive frequency is known as to represent the forward whirling mode, whereas the negative characterizes the backward mode. First, the results obtained within the framework of this numerical study are compared with few existing data (i.e., molecular dynamics) and showed an overall acceptable agreement. Then, a thorough and detailed parametric study is carried out to study the effect of several parameters on the nano-rotor frequencies such as: the nanotube radius, the input angular velocity and the small scale parameters. It is shown that the vibration characteristics of a spinning SWCNT are significantly influenced when these parameters are changed.

• Journal of Mechanical Science and Technology
• /
• 제15권9호
• /
• pp.1302-1310
• /
• 2001

This paper introduces modeling and simulation results for pipeline inspection gauge (PIG) with bypass flow control in natural gas pipeline. The dynamic behaviour of the PIG depends on the different pressure across its body and the bypass flow through it. The system dynamics includes: dynamics of driving gas flow behind the PIG, dynamics of expelled gas in front of the PIG, dynamics of bypass flow, and dynamics of the PIG. The bypass flow across the PIG is treated as incompressible flow with the assumption of its Mach number smaller than 0.45. The governing nonlinear hyperbolic partial differential equations for unsteady gas flows are solved by method of characteristics (MOC) with the regular rectangular grid under appropriate initial and boundary conditions. The Runge-Kuta method is used for solving the steady flow equations to get initial flow values and the dynamic equation of the PIG. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. The simulation is performed with a pipeline segment in the Korea Gas Corporation (KOGAS) low pressure system, Ueijungboo-Sangye line. Simulation results show us that the derived mathematical model and the proposed computational scheme are effective for estimating the position and velocity of the PIG with bypass flow under given operational conditions of pipeline.

• 한국구조물진단유지관리공학회 논문집
• /
• 제9권4호
• /
• pp.159-168
• /
• 2005

본 연구는 다양한 적층 배열을 갖는 비등방성을 보이는 첨단 복합 신소재 판구조물의 유한 차분 비선형 해석을 수행한다. 복잡한 편미분 방정식으로 표현되는 역학문제들을 수치해석 하는 경우 본 연구에서 사용한 유한차분법은 유한요소법에 비하여 체눈 생성 및 수치적분 과정을 피할 수 장점을 갖는다. 유한차분법을 이용한 많은 연구들은 단지 에너지 방법을 사용한 고정 혹은 단순 경계조건에 대하여 수행되었다. 그러나 이러한 접근방법은 자유경계에 대하여 불가피하게 발생하는 가상점 문제를 충분히 만족시킬 수 없다. 그러므로 본 연구에서는 임의의 경계조건을 갖는 비등방성 복합 적층한의 비선형 거동 문제를 보다 효과적으로 해결할 수 있는 유한차분식을 정식화 하였다. 적층 배열 변화를 비롯한 다양한 매개변수에 대하여 본 연구에서 제안한 접근방법을 사용하여 적층판의 복잡한 비선형 거동을 분석하였다.

• Advances in nano research
• /
• 제16권4호
• /
• pp.341-352
• /
• 2024

This study investigates the heat and mass transfer characteristics of a MoS₂ nanoparticle suspension in ethylene glycol over a porous stretching sheet. MoS₂ nanoparticles are known for their exceptional thermal and chemical stability which makes it convenient for enhancing the energy and mass transport properties of base fluids. Ethylene glycol, a common coolant in various industrial applications is utilized as the suspending medium due to its superior heat transfer properties. The effects of variable thermal conductivity, variable mass diffusivity, thermal radiation and thermophoresis which are crucial parameters in affecting the transport phenomena of nanofluids are taken into consideration. The governing partial differential equations representing the conservation of momentum, energy, and concentration are reduced to a set of nonlinear ordinary differential equations using appropriate similarity transformations. R software and MATLAB-bvp5c are used to compute the solutions. The impact of key parameters, including the nanoparticle volume fraction, magnetic field, Prandtl number, and thermophoresis parameter on the flow, heat and mass transfer rates is systematically examined. The study reveals that the presence of MoS₂ nanoparticles curbs the friction between the fluid and the solid boundary. Moreover, the variable thermal conductivity controls the rate of heat transfer and variable mass diffusivity regulates the rate of mass transfer. The numerical and statistical results computed are mutually justified via tables. The results obtained from this investigation provide valuable insights into the design and optimization of systems involving nanofluid-based heat and mass transfer processes, such as solar collectors, chemical reactors, and heat exchangers. Furthermore, the findings contribute to a deeper understanding of stretching sheet systems, such as in manufacturing processes involving continuous casting or polymer film production. The incorporation of MoS₂-C₂H₆O₂ nanofluids can potentially optimize temperature distribution and fluid dynamics.

• 한국지반공학회논문집
• /
• 제27권3호
• /
• pp.75-83
• /
• 2011

일반적인 불포화지반의 거동뿐만 아니라, 열과 관련된 분야, 지반환경 분야 등 다양한 분야에서 불포화 다공질 재료의 열적-수리적-역학적으로 결합된 문제들이 대두되면서 이러한 문제들을 해석하기 위한 수치도구 개발의 필요성이 대두되고 있다. 본 논문에서는 거시적 접근법(macroscopic approach)에 근거하여 불포화지반에 대한 열-수리-역학거동의 수식화를 하였다. 흙, 물, 공기에 대한 질량보존의 법칙, 에너지 보존법칙, 그리고 하중평형 조건식으로부터 결합된(coupled) 4개의 지배방정식을 유도하였다. Galerkin 간략화와 시간적분으로부터 주 변수인 변위(u), 가스압($P_g$), 유체압($P_1$), 온도(T)를 Newton의 반복과정을 이용하여 구하는 유한요소 프로그램(FEM)을 작성하였다. 개발된 프로그램을 이용하여 다공질재료에서 2상 흐름 문제 중 일차원 배수실험(u-$P_g-P_1$), 온도 압밀(u-$P_1$-T), 그리고 지표면 온도변화에 의한 말뚝의 주변지반에 대한 영향(u-$P_1$-T)에 대하여 수치해석을 수행하고 논의하였다.

• Smart Structures and Systems
• /
• 제19권1호
• /
• pp.21-31
• /
• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• 대한조선학회논문집
• /
• 제31권3호
• /
• pp.80-86
• /
• 1994

자유수면을 항주하는 선박에 의하여 발생되는 비선형 조파현상을 해석하기 위한 수치해석법을 개발하였다. 유동은 비점성, 비압축성으로 가정하고 선체 및 자유수면 형상과 일치하는 좌표계의 생성을 위하여 타원형 편미분방정식을 수치해석하여 물체적합 좌표계를 생성하였으며 변환된 정규격자 물체적합 좌표계에 대한 Euler방정식을 유한차분법(Finite Difference Method)을 이용하여 계산하였다. 수치해석을 위하여 시간에 대한 미분항은 전진차분, 공간에 대한 미분항은 중심차분법으로 이산화하였고 대류항에는 수치계산의 안정을 위해 인위적인 소산(dissipation)항을 첨가하였다. 자유수면의 형상은 매 시간 단계마다 자유수면 경계조건들을 만족하도록 다시 계산되었고 격자점들은 자유수면형상의 변화에 적합하게 다시 생성되도록 하였으며 압력에 대한 Poisson방정식은 반복연산법에 의하여 풀고 그 결과를 이용하여 속도를 외삽하였다. 개발된 수치해석법의 검증을 위해 수식선형인 Wigley 모형에 대한 계산을 Fn=0.250-0.408에 대하여 수행하고, 그 결과를 실험 결과와 비교하여 잘 일치함을 보였다.

• 한국자동차공학회논문집
• /
• 제2권5호
• /
• pp.58-65
• /
• 1994

In order to reduce particulate emissions from diesel vehicles, mathematical model is established and analyzed on ceramic wall-flow monolith filter. A wall-flow monolith filter placed in the exhaust stream of a diesel engine can effectively limit the emission of diesel particulates through the monolith. The accumulated particulates can then be periodically combusted inside the monolith by directing hot gas to the monolith while normal engine exhaust is routed around the monolith system. The resulting low flow rates through the monolith require consideration of gas dynamics through the channels as well as particulate combustion to analyze this regeneration process. A mathematical model of the regeneration is formulated as a system of nonlinear partial differential equations describing the conservation of mass, momentum and energy. Numerical solutions are obtained by using a finite difference techniques for the spatial discretization. So we can use filter simulation program for the purpose of filter design and actual filter regeneration

• 한국결정성장학회지
• /
• 제32권1호
• /
• pp.16-24
• /
• 2022

A computational study of combined thermal and solutal convection (double diffusive convection) in a sealed crystal growth reactor is presented, based on a two-dimensional numerical analysis of the nonlinear and strongly coupled partial differential equations and their associated boundary conditions. The average Nusselt numbers for the source regions are greater than those at the crystal regions for 9.73 × 10³ ≤ Gr_t ≤ 6.22 × 10⁵. The average Nusselt numbers for the source regions varies linearly and increases directly with the thermal Grashof number form 9.73 × 10³ ≤ Gr_t ≤ 6.22 × 10⁵ for aspect ratio, Ar (transport length-to-width) = 1 and 2. Additionally, the average Nusselt numbers for the crystal regions at Ar = 1 are much greater than those at Ar = 2. Also, the occurrence of one unicellular flow structure is caused by both the thermal and solutal convection, which is inherent during the physical vapor transport of Hg₂Br₂. When the aspect ratio of the enclosure increases, the fluid movement is hindered and results in the decrease of thermal buoyancy force.